Analytica Docs - User contributions [en]

ConcatRows

2023-08-29T15:11:33Z

Drice: typo, «i» should have been «k»

[[category:Array Flattening Functions]]
[[Category:Doc Status C]] 

=== ConcatRows(a, i, j'', k'') ===
Flattens array «a» by replacing the two indexes «i» and «j» by a single new index «k» that includes all combinations of values from «i» and «j». If you don't specify «i», it generates a local index with the name <code>.ConcatIndex</code>, containing all those combinations. If you do specify «k», it must have length equal to <code>[[IndexLength]](i)*[[IndexLength]](j)</code>.

=== Examples ===
Let
:<code>Variable A:=</code>
:{|class="wikitable"
! !! colspan="4" | J ▶
|-
! I ▼ !!1 !! 2 !! 3 !! 4
|-
! 1 || 'a' || 'b' || 'c' || 'd'
|-
! 2 || 'e' || 'f' || 'g' || 'h'
|}

Then
:<code>ConcatRows(A, I, J) →</code>
:{| class="wikitable"
! colspan=8| .ConcatIndex ▶
|-
!1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 !! 8
|-
| 'a' || 'b' || 'c' || 'd' || 'e' || 'f' || 'g' || 'h'
|}

:<code>ConcatRows(A, J, I) →</code>
:{| class="wikitable"
! colspan=8| .ConcatIndex ▶
|-
! 1 !! 2 !! 3 !! 4 !! 5 !! 6 !! 7 !! 8
|-
| 'a' || 'e' || 'b' || 'f' || 'c' || 'g' || 'd' || 'h'
|}

To flatten three dimensions,<code> I1</code>,<code> I2</code> and <code>I3</code>, use:
:<code>Var tmp := ConcatRows(A, I1, I2) Do ConcatRows(tmp, tmp. ConcatIndex, I3)</code>

=== Inverse of ConcatRows ===
It is often useful to do the inverse of [[ConcatRows]] -- that is, unflatten a 1D array indexed by <code>K</code> to produce a 2D array indexed by <code>I</code> and <code>J</code>. As with [[ConcatRows]], <code>K</code> must have <code>Size(I)*Size(J)</code> elements. You can do this by defining this function:

:<code>Function UnconcatRows(X: Array[K]; I, J, K: Index)</code>
:<code>Definition: X[K = (@I - 1)*Size(J) + @J]</code>

You can use this function to extend a variety of 1D transformation functions to their 2D equivalents. For example, <code>Rank(X, I)</code> returns the sort rank of each element in <code>X</code>. Given a 2D array, apply [[ConcatRows]] to flatten it, then apply the 1D transformation [[Rank]]() to the 1D result, and finally use <code>UnConcatRows()</code> to get back the 2D array of ranks:

:<code>Var B := ConcatRows(A, I, J);</code>
:<code>LocalAlias K := Handle(B.ConcatIndex);</code>
:<code>UnconcatRows(Rank(B, K), I, J, K)</code>

Some other 1D transformation functions that can be usefully extended to 2D equivalents in this fashion are: [[Sort]], [[Cumulate]], [[Uncumulate]], [[CumProduct]], [[Dispatch]], [[GetFract]], [[Frequency]]. The technique could be applied to [[Integrate]], [[Cdf]], [[Pdf]], [[LinearInterp]] and [[CubicInterp]] functions, but the results might not be quite the same as what you would normally think of as the 2D generalization of the functions, so use with care in those cases.

=== See Also ===
* [[Concat]]
* [[ConcatN]]
* [[Text Concatenation Operator: &]]
* [[MdArrayToTable]]
* [[Flatten]]
* [[media:Flattening_and_Unflatting_Arrays.ana | Flattening_and_Unflatting_Arrays.ana]] -- a downloadable model
* [http://WebinarArchive.analytica.com/2008-01-31-Array-Flattening.wmv Array-Flattening.wmv] -- a webinar recording
* [[Array-reducing functions]]

Attribute panel

2023-04-04T18:33:49Z

Drice: Description of the More... option, a release 6.3 addition.

[[Category: Analytica User Guide]]
[[Category: Windows and dialogs]]
[[Category: Attributes]]
<breadcrumbs>Analytica User Guide > Examining a Model > {{PAGENAME}}</breadcrumbs>
{{ReleaseBar}}

The '''''Attribute panel '''''offers a handy way to rapidly explore the [[definition]]s, descriptions, or other [[attributes]] of the variables and other nodes in a [[Diagram window]]. You can open the panel below the diagram, and use it to view or edit any attribute of the node you select. It shows the same attributes that you can see in the [[Object window]], and often several other attributes.

{{Release||4.6|
:[[File:Chapter1_43.png]]
}}{{Release|5.0||
{{CalloutAnnotationBlock|[[image:Rent vs Buy Model Diagram.png]]|
{{CalloutAnnotation|Select node to see its attribute below|pt=32,92|v=70|style=border-style:none;padding:0px;text-align:right}}
{{CalloutAnnotation|Panel opener is open|pt=11,358|v=350|style=border-style:none;padding:0px;text-align:right}}
{{CalloutAnnotation|Drag partition to change panel height|pt=452,360|path=l|v=340|style=border-style:none;padding:0px;left:690px}}
{{CalloutAnnotation|Title of the selected object|pt=13,377|v=380|style=border-style:none;padding:0px;text-align:right}}
{{CalloutAnnotation|Value of the attribute|pt=27,403|v=480|path=t|style=border-style:none;padding:0px;text-align:center;left:135px}}
{{CalloutAnnotation|Attribute menu from which you select the attribute to show|pt=259,380|path=t|v=480|style=border-style:none;padding:0px;text-align:center;left:380px}}
{{CalloutAnnotation|Drag box to change panel height and diagram width|pt=451,446|path=t|v=480|style=border-style:none;padding:0px;left:580px}}
}}}}

Click the {{Release||4.6|key icon [[File:Chapter1_44.png]]}}{{Release|5.0||panel opener icon [[image:Attribute panel opener button.png]]}} to open the '''Attribute '''panel. Here are things you can do in this panel:

* Select another node in the diagram to see the selected attribute of a different object.
* Click the background of the diagram to see the [[attributes]] of the parent module.
* Select another option from the '''Attribute '''menu to see a different attribute.
* To enter or edit the attribute value, make sure you are in edit mode, and click in the '''Attribute''' panel, and start typing. (Not all attributes are user-editable.)

Different classes of objects have different sets of attributes.

{{Release|5.0||
{{CalloutAnnotationBlock|[[Image:AttributePanel.png|center]]
{{CalloutAnnotation|[[image:AttributeMenuVariableOptions{{Release|6.3||6_3}}.png]]
'''Variable'''|v=150|pt=239,33|path=t|style=border-style:none;padding:0px;text-align:center}}
{{CalloutAnnotation|[[image:AttributeMenuModuleOptions{{Release|6.3||6_3}}.png]]
'''Module'''|v=150|pt=239,33|path=t|style=border-style:none;padding:0px;left:230px;text-align:center}}
{{CalloutAnnotation|[[image:AttributeMenuFunctionOptions{{Release|6.3||6_3}}.png]]
'''Function'''|v=150|pt=239,33|path=t|style=border-style:none;padding:0px;left:460px;text-align:center}}
|styleRhs=left:0px;height:650px;width:680px;text-align:center
}}
}}{{Release||4.6|:[[File:Chapter1_45.png]]}}

If you try to see an attribute not defined for an object, it shows its description.

See the [[Glossary]] for descriptions of these attributes.

For simplicity, less common attributes are not usually on the dropdown. {{Release|6.3||The '''More...''' option displays a submenu where you can add or remove an attribute from the menu for the current object only. This adds (or removes) the attribute to the menu and selects it for editing.}} To display other attributes or to add new attributes to the dropdown{{Release|6.3|| for all objects, so it is always or never there}}, see [[Managing attributes]].

To close the '''Attribute '''panel, click the {{Release||4.6|key icon [[File:Chapter1_44.png]]}}{{Release|5.0||panel opener button [[image:Attribute panel closer button.png]]}} again.

==See Also==
* [[Attributes]]
* [[Manage attributes]]
* [[Objects_and_Their_Attributes_-_Part_1_of_3|Objects and Their Attributes]]
* [[To edit an attribute]]
* [[Entering Attributes using the Attribute panel]]
* [[Tutorial: Reviewing a model#Using_the_Attribute_panel|Tutorial: Using the Attribute panel]]
* [[Tutorial: Create a model#Entering_attributes_using_the_Attribute_panel|Tutorial: Creating and entering attributes using the Attribute panel]]
* [[Tutorial: Reviewing a model#Inspecting_definitions_in_the_Attribute_panel|Tutorial: Inspecting definitions in the Attribute panel]]
* [[Tutorial: Reviewing a model#Inspecting_values_in_the_Attribute_panel|Tutorial: Inspecting values in the Attribute panel]]

<footer>Object window / {{PAGENAME}} / Values in Object Window </footer>

File:AttributeMenuModuleOptions6 3.png

2023-04-04T18:26:48Z

Drice: Drice uploaded a new version of File:AttributeMenuModuleOptions6 3.png

File:AttributeMenuFunctionOptions6 3.png

2023-04-04T18:24:30Z

Drice:

File:AttributeMenuModuleOptions6 3.png

2023-04-04T18:23:48Z

Drice:

Attribute panel

2023-04-04T18:22:23Z

Drice: Images of attribute menus with More>> from release 6.3

[[Category: Analytica User Guide]]
[[Category: Windows and dialogs]]
[[Category: Attributes]]
<breadcrumbs>Analytica User Guide > Examining a Model > {{PAGENAME}}</breadcrumbs>
{{ReleaseBar}}

The '''''Attribute panel '''''offers a handy way to rapidly explore the [[definition]]s, descriptions, or other [[attributes]] of the variables and other nodes in a [[Diagram window]]. You can open the panel below the diagram, and use it to view or edit any attribute of the node you select. It shows the same attributes that you can see in the [[Object window]], and often several other attributes.

{{Release||4.6|
:[[File:Chapter1_43.png]]
}}{{Release|5.0||
{{CalloutAnnotationBlock|[[image:Rent vs Buy Model Diagram.png]]|
{{CalloutAnnotation|Select node to see its attribute below|pt=32,92|v=70|style=border-style:none;padding:0px;text-align:right}}
{{CalloutAnnotation|Panel opener is open|pt=11,358|v=350|style=border-style:none;padding:0px;text-align:right}}
{{CalloutAnnotation|Drag partition to change panel height|pt=452,360|path=l|v=340|style=border-style:none;padding:0px;left:690px}}
{{CalloutAnnotation|Title of the selected object|pt=13,377|v=380|style=border-style:none;padding:0px;text-align:right}}
{{CalloutAnnotation|Value of the attribute|pt=27,403|v=480|path=t|style=border-style:none;padding:0px;text-align:center;left:135px}}
{{CalloutAnnotation|Attribute menu from which you select the attribute to show|pt=259,380|path=t|v=480|style=border-style:none;padding:0px;text-align:center;left:380px}}
{{CalloutAnnotation|Drag box to change panel height and diagram width|pt=451,446|path=t|v=480|style=border-style:none;padding:0px;left:580px}}
}}}}

Click the {{Release||4.6|key icon [[File:Chapter1_44.png]]}}{{Release|5.0||panel opener icon [[image:Attribute panel opener button.png]]}} to open the '''Attribute '''panel. Here are things you can do in this panel:

* Select another node in the diagram to see the selected attribute of a different object.
* Click the background of the diagram to see the [[attributes]] of the parent module.
* Select another option from the '''Attribute '''menu to see a different attribute.
* To enter or edit the attribute value, make sure you are in edit mode, and click in the '''Attribute''' panel, and start typing. (Not all attributes are user-editable.)

Different classes of objects have different sets of attributes.

{{Release|5.0||
{{CalloutAnnotationBlock|[[Image:AttributePanel.png|center]]
{{CalloutAnnotation|[[image:AttributeMenuVariableOptions{{Release|6.3||6_3}}.png]]
'''Variable'''|v=150|pt=239,33|path=t|style=border-style:none;padding:0px;text-align:center}}
{{CalloutAnnotation|[[image:AttributeMenuModuleOptions{{Release|6.3||6_3}}.png]]
'''Module'''|v=150|pt=239,33|path=t|style=border-style:none;padding:0px;left:230px;text-align:center}}
{{CalloutAnnotation|[[image:AttributeMenuFunctionOptions{{Release|6.3||6_3}}.png]]
'''Function'''|v=150|pt=239,33|path=t|style=border-style:none;padding:0px;left:460px;text-align:center}}
|styleRhs=left:0px;height:650px;width:680px;text-align:center
}}
}}{{Release||4.6|:[[File:Chapter1_45.png]]}}

If you try to see an attribute not defined for an object, it shows its description.

See the [[Glossary]] for descriptions of these attributes. To display other attributes or to add new attributes, see [[Managing attributes]].

To close the '''Attribute '''panel, click the {{Release||4.6|key icon [[File:Chapter1_44.png]]}}{{Release|5.0||panel opener button [[image:Attribute panel closer button.png]]}} again.

==See Also==
* [[Attributes]]
* [[Manage attributes]]
* [[Objects_and_Their_Attributes_-_Part_1_of_3|Objects and Their Attributes]]
* [[To edit an attribute]]
* [[Entering Attributes using the Attribute panel]]
* [[Tutorial: Reviewing a model#Using_the_Attribute_panel|Tutorial: Using the Attribute panel]]
* [[Tutorial: Create a model#Entering_attributes_using_the_Attribute_panel|Tutorial: Creating and entering attributes using the Attribute panel]]
* [[Tutorial: Reviewing a model#Inspecting_definitions_in_the_Attribute_panel|Tutorial: Inspecting definitions in the Attribute panel]]
* [[Tutorial: Reviewing a model#Inspecting_values_in_the_Attribute_panel|Tutorial: Inspecting values in the Attribute panel]]

<footer>Object window / {{PAGENAME}} / Values in Object Window </footer>

File:AttributeMenuVariableOptions6 3.png

2023-04-04T18:21:37Z

Drice:

File:Anderson-Darling test example.ana

2023-03-27T22:53:40Z

Drice:

Anderson-Darling test

2023-03-27T22:53:23Z

Drice:

The Anderson-Darling test is used to detect whether a set of univariate continuous samples comes from a known distribution. The [[Kolmogorov-Smirnov Tests]] are used for the same thing, but differ in the choice of metric used to measure the distance between distributions. The Anderson-Darling test is more powerful (i.e., more likely to detect a difference in distribution when one exists) in many cases.

However, the Anderson-Darling test does not have a closed-form for the distribution function. Even though the test is distribution-free in theory, in practice, many different critical value tables are compiled for different forms for the null hypothesis distribution. These are usually estimated tables obtained after simulating many examples and then fitting a parametric model to approximate the true values.

Here, instead of assuming any particular distribution, I show how to compute the p-value for ''any'' distribution null hypothesis in Analytica. The trade-off is that this is indeed distribution-free, but requires a Monte Carlo simulation to compute every p-value.

== The test ==
Given a sample of data, <code>X</code>, indexed by <code>I</code>, where each cell is a scalar, we ask the question: Was this data sampled from the distribution <code>F</code>? To answer this, we compute the p-value, which is the probability of observing an Anderson-Darling distance greater than the measured distance under the assumption that the data was indeed generated by <code>F</code>. This assumption is called the ''null hypothesis''. If the computed p-value < 0.05, then we will conclude that there is evidence (i.e., statistically significant evidence) that the data's distribution is not the same as <code>F</code>.

To perform the test, in addition to the data, you need to be able to compute two things:
* The CDF of the hypothesized distribution at any value <code>x</code>, written <code>F(x)</code>.
* A random sample from the hypothesized distribution.

If you want to test whether the data comes from a <code>[[Normal]](10,2)</code> distribution, then you'll need these:
* <code>Function F(x) := CumNormal( x, 10, 2 )</code> { To compute the CDF }
* <code>[[Normal]](10,2)</code> { To generate the sample }

== The Anderson-Darling distance ==
The Anderson-Darling distance is a metric that compares the distance (in distribution) of a sample of points to a known distribution. It is implemented in Analytica as follows:

Function AD_dist( x : [I] ; I : Index ; F : Function(x) atom )
'''Definition''':
[[Local]] xs := [[Sort]](x,I);
[[Local]] n := [[Sum]](x<>Null, I);
[[Local]] S := [[Sum]]( (2*@I-1)/n * ([[Ln]](F(xs)) + [[Ln]](1-F([[Reverse]](xs,I)))), I );
-n - S

The distance from your data to the hypothesized distribution is given by:
:Variable A2 := <code>AD_dist( X, I, F )</code>

== Computing the p-value ==
To compute the p-value by Monte Carlo simulation, create a chance variable that samples from the hypothesized distribution. For example, if the null hypothesis is that the data comes from a <code>[[Normal]](10,2)</code> distribution, then your chance variable will be defined as:

:Chance Xr := <code>[[Normal]]( 10, 2 )</code>

Use two more variables as follows:
:Variable Sim_AD_dist_given_H0 := <code>AD_dist( Xr, I, F )</code>
:Variable p_value := <code>Probability( Sim_AD_dist_given_H0 > A2 )</code>

== Notes ==
This approach generalizes to any hypothesis test.

The computed p-value has some sampling error due to the fact that it is approximated using Monte Carlo sampling. You can reduce this error by increasing the [[Uncertainty Setup dialog|Sample Size]]. A larger sample size takes longer and requires more memory, but is more accurate. However, a default sample size of 1000 is sufficient in almost all cases, especially if you aren't right on the 0.05 threshold.

== A working example ==
'''Download:''' [[media:Anderson-Darling test example.ana]]

This model implements the test. Data points are generated by sampling from a <code>[[Logistic]]( 10, 2)</code> distribution (see variable <code>X</code>). This is our data set.

You can select from two null hypotheses:
* <code>[[Normal]](10,2)</code> { A different distribution }
* <code>[[Logistic]](10,2)</code> { The same distribution }

A successful result is a p-Value < 0.05 in the first case, and a p-Value > 0.05 in the second case.

== See Also ==
* [[Kolmogorov-Smirnov Tests]]
* [[Tutorial_videos#Session_8:_Hypothesis_Testing|Webinar on Hypothesis Testing]]

Kolmogorov-Smirnov Tests

2023-03-27T22:42:03Z

Drice: fixed a hyperlink

Are the data points in a sample drawn from a specific known distribution? For example, are they drawn from a <code>[[Gamma]](3,2)</code> distribution? Are the data points in one sample drawn from the same distribution as the data points in a second sample?

The Kolmogorov-Smirnov test(s) can be used to answer either of these questions.
* The data must be univariate and continuous (i.e., each sample point is a single real number).
* It works for any continuous distribution -- there is no assumption that the distribution is [[Normal]] or anything else.

The tests return a p-value, which is the probability of seeing as much distance between the two distributions (in the one-sample case, between the sample and the reference) if there is no difference in distribution. A small p-value, say p-value < 0.05, means a difference was detected, with a false-positive rate equal to 0.05. If the p-value > 0.05, you can't conclude that they are the same distribution -- only that the test and amount of data did not provide enough power to detect any difference if one exists.

== Kolmogorov-Smirnov Tests Library ==

'''Download:''' [[media:Kolmogorov-Smirnov Tests Library.ana]]

To use this library, use '''File / Add Library...''' from the File menu after downloading.

This library provides two functions:
; <code>KS_test_one_dist( x, I, refCdf )</code>
: Tests whether the empirical distribution of data «x», which is indexed by «<code>I</code>», matches a hypothesized distribution whose cumulative probability function is passed as the 3rd parameter.
; <code>KS_test_two_dist( xi, xj, I, J )</code>
:Tests whether the data in «xi» and data in «xj» appear to be from the same distribution. «xi» is indexed by «<code>I</code>» and «xj» is indexed by «<code>J</code>».

Both functions return the p-value.
;If p-value < 0.05
:Conclude (with statistical significance 0.05) that the distributions differ.
;If p-value > 0.05
:You can't conclude that they have the same or different distributions. Just that there is not enough statistical power in the test, or enough data. to detect a difference in distribution if one exists.

== Using KS_test_one_dist ==

To do a one-sample test, you need to provide a cdf function for your hypothesized distribution. You can do this either by creating a new global [[UDF]], or by using a [[Local functions and local value captures|Local function]].

To test whether the data in <code>X</code> is distributed as <code>Gamma( 5.9, 1.65 )</code>, you can first create a [[UDF]]:
:<code>Function MyHypothCDF(x) ::= CumGamma( x, 5.9, 1.65)</code>
And then pass this to the function using:
:<code>KS_test_one_dist( x, I, MyHypothCDF )</code>

Alternately, you can use a local function like this:
:<code>[[Local functions and local value captures|Function]] hypCdf(x) : CumGamma( x, 5.9, 1.65 );</code>
:<code>KS_test_one_dist( x, I, hypCdf )</code>

It is important to notice that a sole colon is used between the function declaration and its defining expression in the local declaration (i.e., not an assignment operator, <code>:=</code>).

== Using KS_test_two_dist ==
When comparing two data sets, each may have its own index, and each can be a different length. The usage is easy -- just pass each, then pass the index of each:
:<code>KS_test_two_dist( xi, xj, I, J )</code>

== Limitations ==
* The p-value from <code>KS_test_one_dist</code> is overly weak when you use the data to estimate parameters of your hypothesized distribution. If you do this and still get a p-value < 0.05, you are safe to conclude that the distributions differ, but in general, the p-value will be more conservative than necessary. In that case, other statistical tests will be more powerful.
* Stronger statistical tests exist for specific distributions. KS is weaker since it makes no distributional assumption.

There are some things that should be cleaned up in this model.
* The identifiers that appear in the '''Examples''' module don't have a namespace prefix. Hence, they are at risk for name collisions. (If name collisions occur, you'll see a dialog when you Add the library to your model).
* You'll get a warning if you open this in a release prior to [[Analytica 6.3]]. You can ignore the warning as long as your release is fairly recent (like 6.x).

== See Also ==
* [[Tutorial_videos#Session_8:_Hypothesis_Testing|Hypothesis Testing]] (A webinar)
* [[Anderson-Darling test]]

Kolmogorov-Smirnov Tests

2023-03-27T22:41:37Z

Drice: link to Anderson-Darling test

Are the data points in a sample drawn from a specific known distribution? For example, are they drawn from a <code>[[Gamma]](3,2)</code> distribution? Are the data points in one sample drawn from the same distribution as the data points in a second sample?

The Kolmogorov-Smirnov test(s) can be used to answer either of these questions.
* The data must be univariate and continuous (i.e., each sample point is a single real number).
* It works for any continuous distribution -- there is no assumption that the distribution is [[Normal]] or anything else.

The tests return a p-value, which is the probability of seeing as much distance between the two distributions (in the one-sample case, between the sample and the reference) if there is no difference in distribution. A small p-value, say p-value < 0.05, means a difference was detected, with a false-positive rate equal to 0.05. If the p-value > 0.05, you can't conclude that they are the same distribution -- only that the test and amount of data did not provide enough power to detect any difference if one exists.

== Kolmogorov-Smirnov Tests Library ==

'''Download:''' [[media:Kolmogorov-Smirnov Tests Library.ana]]

To use this library, use '''File / Add Library...''' from the File menu after downloading.

This library provides two functions:
; <code>KS_test_one_dist( x, I, refCdf )</code>
: Tests whether the empirical distribution of data «x», which is indexed by «<code>I</code>», matches a hypothesized distribution whose cumulative probability function is passed as the 3rd parameter.
; <code>KS_test_two_dist( xi, xj, I, J )</code>
:Tests whether the data in «xi» and data in «xj» appear to be from the same distribution. «xi» is indexed by «<code>I</code>» and «xj» is indexed by «<code>J</code>».

Both functions return the p-value.
;If p-value < 0.05
:Conclude (with statistical significance 0.05) that the distributions differ.
;If p-value > 0.05
:You can't conclude that they have the same or different distributions. Just that there is not enough statistical power in the test, or enough data. to detect a difference in distribution if one exists.

== Using KS_test_one_dist ==

To do a one-sample test, you need to provide a cdf function for your hypothesized distribution. You can do this either by creating a new global [[UDF]], or by using a [[Local functions and local value captures|Local function]].

To test whether the data in <code>X</code> is distributed as <code>Gamma( 5.9, 1.65 )</code>, you can first create a [[UDF]]:
:<code>Function MyHypothCDF(x) ::= CumGamma( x, 5.9, 1.65)</code>
And then pass this to the function using:
:<code>KS_test_one_dist( x, I, MyHypothCDF )</code>

Alternately, you can use a local function like this:
:<code>[[Local functions and local value captures|Function]] hypCdf(x) : CumGamma( x, 5.9, 1.65 );</code>
:<code>KS_test_one_dist( x, I, hypCdf )</code>

It is important to notice that a sole colon is used between the function declaration and its defining expression in the local declaration (i.e., not an assignment operator, <code>:=</code>).

== Using KS_test_two_dist ==
When comparing two data sets, each may have its own index, and each can be a different length. The usage is easy -- just pass each, then pass the index of each:
:<code>KS_test_two_dist( xi, xj, I, J )</code>

== Limitations ==
* The p-value from <code>KS_test_one_dist</code> is overly weak when you use the data to estimate parameters of your hypothesized distribution. If you do this and still get a p-value < 0.05, you are safe to conclude that the distributions differ, but in general, the p-value will be more conservative than necessary. In that case, other statistical tests will be more powerful.
* Stronger statistical tests exist for specific distributions. KS is weaker since it makes no distributional assumption.

There are some things that should be cleaned up in this model.
* The identifiers that appear in the '''Examples''' module don't have a namespace prefix. Hence, they are at risk for name collisions. (If name collisions occur, you'll see a dialog when you Add the library to your model).
* You'll get a warning if you open this in a release prior to [[Analytica 6.3]]. You can ignore the warning as long as your release is fairly recent (like 6.x).

== See Also ==
* [[https://docs.analytica.com/index.php/Tutorial_videos#Session_8:_Hypothesis_Testing|Hypothesis Testing]] (A webinar)
* [[Anderson-Darling test]]

Anderson-Darling test

2023-03-27T22:41:22Z

Drice: sample size

The Anderson-Darling test is used to detect whether a set of univariate continuous samples comes from a known distribution. The [[Kolmogorov-Smirnov Tests]] are used for the same thing, but differ in the choice of metric used to measure the distance between distributions. The Anderson-Darling test is more powerful (i.e., more likely to detect a difference in distribution when one exists) in many cases.

However, the Anderson-Darling test does not have a closed-form for the distribution function. Even though the test is distribution-free in theory, in practice, many different critical value tables are compiled for different forms for the null hypothesis distribution. These are usually estimated tables obtained after simulating many examples and then fitting a parametric model to approximate the true values.

Here, instead of assuming any particular distribution, I show how to compute the p-value for ''any'' distribution null hypothesis in Analytica. The trade-off is that this is indeed distribution-free, but requires a Monte Carlo simulation to compute every p-value.

== The test ==
Given a sample of data, <code>X</code>, indexed by <code>I</code>, where each cell is a scalar, we ask the question: Was this data sampled from the distribution <code>F</code>? To answer this, we compute the p-value, which is the probability of observing an Anderson-Darling distance greater than the measured distance under the assumption that the data was indeed generated by <code>F</code>. This assumption is called the ''null hypothesis''. If the computed p-value < 0.05, then we will conclude that there is evidence (i.e., statistically significant evidence) that the data's distribution is not the same as <code>F</code>.

To perform the test, in addition to the data, you need to be able to compute two things:
* The CDF of the hypothesized distribution at any value <code>x</code>, written <code>F(x)</code>.
* A random sample from the hypothesized distribution.

If you want to test whether the data comes from a <code>[[Normal]](10,2)</code> distribution, then you'll need these:
* <code>Function F(x) := CumNormal( x, 10, 2 )</code> { To compute the CDF }
* <code>[[Normal]](10,2)</code> { To generate the sample }

== The Anderson-Darling distance ==
The Anderson-Darling distance is a metric that compares the distance (in distribution) of a sample of points to a known distribution. It is implemented in Analytica as follows:

Function AD_dist( x : [I] ; I : Index ; F : Function(x) atom )
'''Definition''':
[[Local]] xs := [[Sort]](x,I);
[[Local]] n := [[Sum]](x<>Null, I);
[[Local]] S := [[Sum]]( (2*@I-1)/n * ([[Ln]](F(xs)) + [[Ln]](1-F([[Reverse]](xs,I)))), I );
-n - S

The distance from your data to the hypothesized distribution is given by:
:Variable A2 := <code>AD_dist( X, I, F )</code>

== Computing the p-value ==
To compute the p-value by Monte Carlo simulation, create a chance variable that samples from the hypothesized distribution. For example, if the null hypothesis is that the data comes from a <code>[[Normal]](10,2)</code> distribution, then your chance variable will be defined as:

:Chance Xr := <code>[[Normal]]( 10, 2 )</code>

Use two more variables as follows:
:Variable Sim_AD_dist_given_H0 := <code>AD_dist( Xr, I, F )</code>
:Variable p_value := <code>Probability( Sim_AD_dist_given_H0 > A2 )</code>

== Notes ==
This approach generalizes to any hypothesis test.

The computed p-value has some sampling error due to the fact that it is approximated using Monte Carlo sampling. You can reduce this error by increasing the [[Uncertainty Setup dialog|Sample Size]]. A larger sample size takes longer and requires more memory, but is more accurate. However, a default sample size of 1000 is sufficient in almost all cases, especially if you aren't right on the 0.05 threshold.

== See Also ==
* [[Kolmogorov-Smirnov Tests]]
* [[Tutorial_videos#Session_8:_Hypothesis_Testing|Webinar on Hypothesis Testing]]

Anderson-Darling test

2023-03-27T22:37:11Z

Drice: Created page with "The Anderson-Darling test is used to detect whether a set of univariate continuous samples comes from a known distribution. The Kolmogorov-Smirnov Tests are used for the s..."

The Anderson-Darling test is used to detect whether a set of univariate continuous samples comes from a known distribution. The [[Kolmogorov-Smirnov Tests]] are used for the same thing, but differ in the choice of metric used to measure the distance between distributions. The Anderson-Darling test is more powerful (i.e., more likely to detect a difference in distribution when one exists) in many cases.

However, the Anderson-Darling test does not have a closed-form for the distribution function. Even though the test is distribution-free in theory, in practice, many different critical value tables are compiled for different forms for the null hypothesis distribution. These are usually estimated tables obtained after simulating many examples and then fitting a parametric model to approximate the true values.

Here, instead of assuming any particular distribution, I show how to compute the p-value for ''any'' distribution null hypothesis in Analytica. The trade-off is that this is indeed distribution-free, but requires a Monte Carlo simulation to compute every p-value.

== The test ==
Given a sample of data, <code>X</code>, indexed by <code>I</code>, where each cell is a scalar, we ask the question: Was this data sampled from the distribution <code>F</code>? To answer this, we compute the p-value, which is the probability of observing an Anderson-Darling distance greater than the measured distance under the assumption that the data was indeed generated by <code>F</code>. This assumption is called the ''null hypothesis''. If the computed p-value < 0.05, then we will conclude that there is evidence (i.e., statistically significant evidence) that the data's distribution is not the same as <code>F</code>.

To perform the test, in addition to the data, you need to be able to compute two things:
* The CDF of the hypothesized distribution at any value <code>x</code>, written <code>F(x)</code>.
* A random sample from the hypothesized distribution.

If you want to test whether the data comes from a <code>[[Normal]](10,2)</code> distribution, then you'll need these:
* <code>Function F(x) := CumNormal( x, 10, 2 )</code> { To compute the CDF }
* <code>[[Normal]](10,2)</code> { To generate the sample }

== The Anderson-Darling distance ==
The Anderson-Darling distance is a metric that compares the distance (in distribution) of a sample of points to a known distribution. It is implemented in Analytica as follows:

Function AD_dist( x : [I] ; I : Index ; F : Function(x) atom )
'''Definition''':
[[Local]] xs := [[Sort]](x,I);
[[Local]] n := [[Sum]](x<>Null, I);
[[Local]] S := [[Sum]]( (2*@I-1)/n * ([[Ln]](F(xs)) + [[Ln]](1-F([[Reverse]](xs,I)))), I );
-n - S

The distance from your data to the hypothesized distribution is given by:
:Variable A2 := <code>AD_dist( X, I, F )</code>

== Computing the p-value ==
To compute the p-value by Monte Carlo simulation, create a chance variable that samples from the hypothesized distribution. For example, if the null hypothesis is that the data comes from a <code>[[Normal]](10,2)</code> distribution, then your chance variable will be defined as:

:Chance Xr := <code>[[Normal]]( 10, 2 )</code>

Use two more variables as follows:
:Variable Sim_AD_dist_given_H0 := <code>AD_dist( Xr, I, F )</code>
:Variable p_value := <code>Probability( Sim_AD_dist_given_H0 > A2 )</code>

== Notes ==
This approach generalizes to any hypothesis test.

== See Also ==
* [[Kolmogorov-Smirnov Tests]]
* [[Tutorial_videos#Session_8:_Hypothesis_Testing|Webinar on Hypothesis Testing]]

Kolmogorov-Smirnov Tests

2023-03-27T21:40:54Z

Drice: /* Limitations */

Kolmogorov-Smirnov Tests

2023-03-27T21:33:03Z

Drice:

Are the data points in a sample drawn from a specific known distribution? For example, are they drawn from a <code>[[Gamma]](3,2)</code> distribution? Are the data points in one sample drawn from the same distribution as the data points in a second sample?

The Kolmogorov-Smirnov test(s) can be used to answer either of these questions.
* The data must be univariate and continuous (i.e., each sample point is a single real number).
* It works for any continuous distribution -- there is no assumption that the distribution is [[Normal]] or anything else.

The tests return a p-value, which is the probability of seeing as much distance between the two distributions (in the one-sample case, between the sample and the reference) if there is no difference in distribution. A small p-value, say p-value < 0.05, means a difference was detected, with a false-positive rate equal to 0.05. If the p-value > 0.05, you can't conclude that they are the same distribution -- only that the test and amount of data did not provide enough power to detect any difference if one exists.

== Kolmogorov-Smirnov Tests Library ==

'''Download:''' [[media:Kolmogorov-Smirnov Tests Library.ana]]

To use this library, use '''File / Add Library...''' from the File menu after downloading.

This library provides two functions:
; <code>KS_test_one_dist( x, I, refCdf )</code>
: Tests whether the empirical distribution of data «x», which is indexed by «<code>I</code>», matches a hypothesized distribution whose cumulative probability function is passed as the 3rd parameter.
; <code>KS_test_two_dist( xi, xj, I, J )</code>
:Tests whether the data in «xi» and data in «xj» appear to be from the same distribution. «xi» is indexed by «<code>I</code>» and «xj» is indexed by «<code>J</code>».

Both functions return the p-value.
;If p-value < 0.05
:Conclude (with statistical significance 0.05) that the distributions differ.
;If p-value > 0.05
:You can't conclude that they have the same or different distributions. Just that there is not enough statistical power in the test, or enough data. to detect a difference in distribution if one exists.

== Using KS_test_one_dist ==

To do a one-sample test, you need to provide a cdf function for your hypothesized distribution. You can do this either by creating a new global [[UDF]], or by using a [[Local functions and local value captures|Local function]].

To test whether the data in <code>X</code> is distributed as <code>Gamma( 5.9, 1.65 )</code>, you can first create a [[UDF]]:
:<code>Function MyHypothCDF(x) ::= CumGamma( x, 5.9, 1.65)</code>
And then pass this to the function using:
:<code>KS_test_one_dist( x, I, MyHypothCDF )</code>

Alternately, you can use a local function like this:
:<code>[[Local functions and local value captures|Function]] hypCdf(x) : CumGamma( x, 5.9, 1.65 );</code>
:<code>KS_test_one_dist( x, I, hypCdf )</code>

It is important to notice that a sole colon is used between the function declaration and its defining expression in the local declaration (i.e., not an assignment operator, <code>:=</code>).

== Using KS_test_two_dist ==
When comparing two data sets, each may have its own index, and each can be a different length. The usage is easy -- just pass each, then pass the index of each:
:<code>KS_test_two_dist( xi, xj, I, J )</code>

== Limitations ==
There are some things that should be cleaned up in this model.
* The identifiers that appear in the '''Examples''' module don't have a namespace prefix. Hence, they are at risk for name collisions. (If name collisions occur, you'll see a dialog when you Add the library to your model).
* You'll get a warning if you open this in a release prior to [[Analytica 6.3]]. You can ignore the warning as long as your release is fairly recent (like 6.x).

Kolmogorov-Smirnov Tests

2023-03-27T21:20:11Z

Drice: Created

Are the data points in a sample drawn from a specific known distribution? For example, are they drawn from a <code>[[Gamma]](3,2)</code> distribution? Are the data points in one sample drawn from the same distribution as the data points in a second sample?

The Kolmogorov-Smirnov test(s) can be used to answer either of these questions.
* The data must be univariate and continuous (i.e., each sample point is a single real number).
* It works for any continuous distribution -- there is no assumption that the distribution is [[Normal]] or anything else.

The tests return a p-value, which is the probability of seeing as much distance between the two distributions (in the one-sample case, between the sample and the reference) if there is no difference in distribution. A small p-value, say p-value < 0.05, means a difference was detected, with a false-positive rate equal to 0.05. If the p-value > 0.05, you can't conclude that they are the same distribution -- only that the test and amount of data did not provide enough power to detect any difference if one exists.

== Kolmogorov-Smirnov Tests Library ==

'''Download:''' [[media:Kolmogorov-Smirnov Tests Library.ana]]

This library provides two functions:
; <code>KS_test_one_dist( x, I, refCdf )</code>
: Tests whether the empirical distribution of data «x», which is indexed by «<code>I</code>», matches a hypothesized distribution whose cumulative probability function is passed as the 3rd parameter.
; <code>KS_test_two_dist( xi, xj, I, J )</code>
:Tests whether the data in «xi» and data in «xj» appear to be from the same distribution. «xi» is indexed by «<code>I</code>» and «xj» is indexed by «<code>J</code>».

Both functions return the p-value.
;If p-value < 0.05
:Conclude (with statistical significance 0.05) that the distributions differ.
;If p-value > 0.05
:You can't conclude that they have the same or different distributions. Just that there is not enough statistical power in the test, or enough data. to detect a difference in distribution if one exists.

== Using KS_test_one_dist ==

To do a one-sample test, you need to provide a cdf function for your hypothesized distribution. You can do this either by creating a new global [[UDF]], or by using a [[Local functions and local value captures|Local function]].

To test whether the data in <code>X</code> is distributed as <code>Gamma( 5.9, 1.65 )</code>, you can first create a [[UDF]]:
:<code>Function MyHypothCDF(x) ::= CumGamma( x, 5.9, 1.65)</code>
And then pass this to the function using:
:<code>KS_test_one_dist( x, I, MyHypothCDF )</code>

Alternately, you can use a local function like this:
:<code>[[Local functions and local value captures|Function]] hypCdf(x) : CumGamma( x, 5.9, 1.65 );</code>
:<code>KS_test_one_dist( x, I, hypCdf )</code>

It is important to notice that a sole colon is used between the function declaration and its defining expression in the local declaration (i.e., not an assignment operator, <code>:=</code>).

== Using KS_test_two_dist ==
When comparing two data sets, each may have its own index, and each can be a different length. The usage is easy -- just pass each, then pass the index of each:
:<code>KS_test_two_dist( xi, xj, I, J )</code>

File:Kolmogorov-Smirnov Tests Library.ana

2023-03-27T21:07:36Z

Drice:

File:Cash flow question.ana

2022-03-02T19:36:27Z

Drice:

Configuring an RLM Server

2021-12-01T17:45:59Z

Drice: Changed to activation.analytica.com and refreshed a screenshot

[[Category: Analytica installation and licenses]]

__TOC__

The [http://www.reprisesoftware.com Reprise License Manager] (RLM) makes it easier to manage and track multiple Analytica and ADE licenses within an organization than having each user manage their own license. If you use Floating licenses (a license shared among multiple users), you require RLM.

This page explains how to install and configure RLM for an IT manager who manages software licenses. Analytica end-users that wish to install the software should see [[How to Install Analytica -- Individual License]] and [[How to Install Analytica -- Centrally Managed License]].

[http://WebinarArchive.Analytica.com/2009-06-04-RLM_Install.wmv This video] shows how to install the RLM server, use the RLM administration console, and activate [http://lumina.com Lumina] codes.

== What you need ==
;Selecting a computer to run the License Server
:You'll need to select a server computer that will host the [http://www.reprisesoftware.com Reprise License Manager] (RLM) server. This server must be on your internal company network, accessible by all the computers in your organization that may need to check out licenses.
:'''Note''': RLM must be hosted on a '''physical (non-virtual) server''', and the server must be running a Windows operating system. Licenses will not activate if RLM is hosted on a virtual machine, and Lumina licenses are not honored on Linux (or other non-Windows) installations of RLM.
:It should also be a server with high availability -- i.e., never turned off.
:RLM can serve licenses for software from other vendors that use RLM.
:Running RLM for Analytica imposes a minimal load on the server, so it certainly need not be dedicated . You can easily use a computer whose primary purpose is for something else.
:The Server can be nearly any platform supported by Reprise, including Windows or Unix.
:RLM does support redundant failover servers, but this is seldom required and isn't covered here.

;Generic RLM Server Software
:If you already run RLM for other applications using RLM 7 or later, you already have what you need. Otherwise, download the end-user bundle from [http://www.reprisesoftware.com/admin/software-licensing.php reprisesoftware.com]. For a windows platform, this is downloaded as a file <code>x86_w1.enduser.zip</code>.
:You'll also need the Lumina-specific settings file (right click, select '''Save Target As...''') [[media:lumina.set|lumina.set]], and save it in your RLM directory.

;Analytica or ADE license(s).
:These are provided to you by [http://lumina.com Lumina] when you purchase [[ADE]] or Analytica.
:They should contain 16 numeric digits, such as: <code>1234-5678-9012-3456</code>
:If you have a multi-seat license, then each activation key also has a ''count'' (i.e.''number of seats'') associated with it. Most commonly, licenses are 1-seat licenses, so if you were not given a count with your activation key, you can assume it is a 1-seat license.

== To Install RLM ==
These steps are to install RLM on a Windows server -- but it's almost the same on a Unix machine. For Windows computers, especially Vista, you'll probably need an administrator account.

1. Download the [https://www.reprisesoftware.com/admin/software-licensing-downloads.php RLM License Administration bundle] for Windows.

2. Double click the file and extract it to a directory of your choice, such as:

:<code>C:\Program Files (x86)\Reprise\RlmServer</code>

:[[File:Extract_screenshot.png]]

3. Copy the [[media:lumina.set|lumina.set]] file to the same directory.

4. (This step is only required starting with RLM v13. Without this step, the '''Activate license''' button won't appear).
* Run NotePad (or your favorite text editor) as administrator. You can do this by clicking the Windows start button and typing NotePad. When it appears, right click on it and select ''Run as administrator''
* Enter the line: <code>admin::all</code>
* Save the file as <code>rlm.pw</code> in the RLM install folder.

5. Start a command-line window.
:On Windows Vista and Windows 7, start the command-line window as Administrator:
# Click on the Start menu on the bottom left.
# Type in <code>cmd</code> in the Search box.
# Press ''Ctrl + Shift + Enter''

6. Navigate to the chosen directory by typing <code>cd</code> and then the address of the chosen directory.
: For example: <code>cd C:\Program Files\Reprise\RlmServer</code>

7. Type <code>rlm -dlog "address" -install_service</code> where address is the path to the log file. For example:
:<code>rlm -dlog "c:\Program Files (x86)\Reprise\RlmServer\rlm.log" -install_service</code>
:If you are running RLM v14BL5 or later, use
:<code>rlm -dlog "c:\Program Files (x86)\Reprise\RlmServer\rlm.log" -z -install_service</code>
:if you want to allow a blank password in Step 4. Without the -z, you'll have 10 minutes after it starts running to set a password from the console.

* You must include the full path to the log file, without using relative paths.
* There are additional configuration options, for a listing help type: <code>rlm -?</code>
* The local system account (which the RLM service will run under) must have write permissions to the <code>RlmServer</code> directory, so that it can write activated license files and the log file.

8. Type: <code>net start rlm</code>
:The RLM service should now be running.

:[[File:RlmServer_install.png]]

9. Enter the administration panel:
* Point a browser to [http://localhost:5054 http://localhost:5054].
* ''Do not use the (now obsolete) Internet Explorer browser.'' The RLM console is not compatible with IE.

10. If you did Step 4 above, a Login will appear at the top left. Enter <code>admin</code> as the user and leave the password blank.
* Press [Change Password] and set a password. Without the -z in Step 7, you need to do this within the first 10 minutes.

11. Install any Analytica or ADE licenses.
:Lumina should have provided you with Activation keys for your Analytica or [[ADE]]; the keys contain 16 numeric digits, such as <code>1234-5678-9012-3456</code>
* Click the '''Activate License''' button
* Click '''BEGIN License Activation''', then enter these fields:
** Check ''Other (URL)'' and enter <code>Activation.Analytica.com</code> into the text-box.
**:[[Image:ActivationServerUrl.jpg]]
** ''ISV'': <code>lumina</code>.
** ''License activation key'': <code>1234-5678-9012-3456</code> { Your activation code here }
**:[[File:ISV_lumina.png]]
** ''License Server hostid'': { Use the value filled in for you }
** ''License count'': { The number of seats. Normally 1. }
** ''License File to create'': { A <code>*.lic</code> file in the licenses directory from step 2}
** Press '''REQUEST LICENSE'''.
*::If an error occurs, see [[/Solving problems during managed license activation|Solving problems during managed license activation]].
** When prompted, restart RLM server to reread licenses.

12. Click on '''Status'''
* Verify that the <code>Lumina ISV</code> is listed.

13. If you have more than one activation key, repeat steps 9-10 for each.

== Additional Configuration ==
You, as an IT manager, may want to configure RLM permissions to control who can use the Analytica licenses and who can manage the RLM server. On the bottom left of the RLM Administration Console, there is a link to the '''RLM Manual...'''

To control access to the RLM server, and administration of its capabilities, see the section on '''RLM Options File'''. Among the access control settings you can configure are these (copied from that manual):

:{| class="wikitable"
!Privilege
!Name to use in RLM options file
!Meaning
|-
|edit_options||edit_options||Allows editing options files for ISV servers
|-
|edit_rlm_options||edit_rlm_options||Allows editing options files for the rlm server
|-
|edit_transfer||edit_transfer||Allows editing server-server license transfer settings for ISV servers
|-
|reread||reread||Allows access to the functions which do reread commands on license servers
|-
|shutdown||shutdown||Allows access to the functions which shut down license servers
|-
|status||status||Allows display of status and debug log information from the license servers
|}

You may also want to restrict which users can checkout licenses, for example, restricting usage to specific users in your department. For that, see the section '''The ISV Options File''' in the '''RLM Manual'''. Also consult that section for information on assigning named-user licenses to specific users.

== See Also ==
* [[Installation and licenses]]
* [[What License do I Purchase?]]
* [[How to Install Analytica -- Individual License]]
* [[How to Install Analytica -- Centrally Managed License]]
* [[License Roaming]]
* [http://www.reprisesoftware.com Reprise License Manager]
* [http://WebinarArchive.Analytica.com//2009-06-04-RLM_Install.wmv RLM_Install.wmv]: Video - installing RLM and Activating centrally managed Analytica licenses (22 minutes)
* [[Configuring an RLM Server/Solving problems during managed license activation|Solving problems during managed license activation]]
* [[Configuring an RLM Server/Debugging problems with RLM]]
* [http://www.reprisesoftware.com/admin/software-licensing.php RLM for License Administrators and Users] -- info, downloads, FAQs and troubleshooting tips from Reprise
* [http://lumina.com/ana/manualActivation.htm Manual Activation]

Configuring an RLM Server

2021-12-01T17:44:37Z

Drice:

[[Category: Analytica installation and licenses]]

__TOC__

The [http://www.reprisesoftware.com Reprise License Manager] (RLM) makes it easier to manage and track multiple Analytica and ADE licenses within an organization than having each user manage their own license. If you use Floating licenses (a license shared among multiple users), you require RLM.

This page explains how to install and configure RLM for an IT manager who manages software licenses. Analytica end-users that wish to install the software should see [[How to Install Analytica -- Individual License]] and [[How to Install Analytica -- Centrally Managed License]].

[http://WebinarArchive.Analytica.com/2009-06-04-RLM_Install.wmv This video] shows how to install the RLM server, use the RLM administration console, and activate [http://lumina.com Lumina] codes.

== What you need ==
;Selecting a computer to run the License Server
:You'll need to select a server computer that will host the [http://www.reprisesoftware.com Reprise License Manager] (RLM) server. This server must be on your internal company network, accessible by all the computers in your organization that may need to check out licenses.
:'''Note''': RLM must be hosted on a '''physical (non-virtual) server''', and the server must be running a Windows operating system. Licenses will not activate if RLM is hosted on a virtual machine, and Lumina licenses are not honored on Linux (or other non-Windows) installations of RLM.
:It should also be a server with high availability -- i.e., never turned off.
:RLM can serve licenses for software from other vendors that use RLM.
:Running RLM for Analytica imposes a minimal load on the server, so it certainly need not be dedicated . You can easily use a computer whose primary purpose is for something else.
:The Server can be nearly any platform supported by Reprise, including Windows or Unix.
:RLM does support redundant failover servers, but this is seldom required and isn't covered here.

;Generic RLM Server Software
:If you already run RLM for other applications using RLM 7 or later, you already have what you need. Otherwise, download the end-user bundle from [http://www.reprisesoftware.com/admin/software-licensing.php reprisesoftware.com]. For a windows platform, this is downloaded as a file <code>x86_w1.enduser.zip</code>.
:You'll also need the Lumina-specific settings file (right click, select '''Save Target As...''') [[media:lumina.set|lumina.set]], and save it in your RLM directory.

;Analytica or ADE license(s).
:These are provided to you by [http://lumina.com Lumina] when you purchase [[ADE]] or Analytica.
:They should contain 16 numeric digits, such as: <code>1234-5678-9012-3456</code>
:If you have a multi-seat license, then each activation key also has a ''count'' (i.e.''number of seats'') associated with it. Most commonly, licenses are 1-seat licenses, so if you were not given a count with your activation key, you can assume it is a 1-seat license.

== To Install RLM ==
These steps are to install RLM on a Windows server -- but it's almost the same on a Unix machine. For Windows computers, especially Vista, you'll probably need an administrator account.

1. Download the [https://www.reprisesoftware.com/admin/software-licensing-downloads.php RLM License Administration bundle] for Windows.

2. Double click the file and extract it to a directory of your choice, such as:

:<code>C:\Program Files (x86)\Reprise\RlmServer</code>

:[[File:Extract_screenshot.png]]

3. Copy the [[media:lumina.set|lumina.set]] file to the same directory.

4. (This step is only required starting with RLM v13. Without this step, the '''Activate license''' button won't appear).
* Run NotePad (or your favorite text editor) as administrator. You can do this by clicking the Windows start button and typing NotePad. When it appears, right click on it and select ''Run as administrator''
* Enter the line: <code>admin::all</code>
* Save the file as <code>rlm.pw</code> in the RLM install folder.

5. Start a command-line window.
:On Windows Vista and Windows 7, start the command-line window as Administrator:
# Click on the Start menu on the bottom left.
# Type in <code>cmd</code> in the Search box.
# Press ''Ctrl + Shift + Enter''

6. Navigate to the chosen directory by typing <code>cd</code> and then the address of the chosen directory.
: For example: <code>cd C:\Program Files\Reprise\RlmServer</code>

7. Type <code>rlm -dlog "address" -install_service</code> where address is the path to the log file. For example:
:<code>rlm -dlog "c:\Program Files (x86)\Reprise\RlmServer\rlm.log" -install_service</code>
:If you are running RLM v14BL5 or later, use
:<code>rlm -dlog "c:\Program Files (x86)\Reprise\RlmServer\rlm.log" -z -install_service</code>
:if you want to allow a blank password in Step 4. Without the -z, you'll have 10 minutes after it starts running to set a password from the console.

* You must include the full path to the log file, without using relative paths.
* There are additional configuration options, for a listing help type: <code>rlm -?</code>
* The local system account (which the RLM service will run under) must have write permissions to the <code>RlmServer</code> directory, so that it can write activated license files and the log file.

8. Type: <code>net start rlm</code>
:The RLM service should now be running.

:[[File:RlmServer_install.png]]

9. Enter the administration panel:
* Point a browser to [http://localhost:5054 http://localhost:5054].
* ''Do not use the (now obsolete) Internet Explorer browser.'' The RLM console is not compatible with IE.

10. If you did Step 4 above, a Login will appear at the top left. Enter <code>admin</code> as the user and leave the password blank.
* Press [Change Password] and set a password. Without the -z in Step 7, you need to do this within the first 10 minutes.

11. Install any Analytica or ADE licenses.
:Lumina should have provided you with Activation keys for your Analytica or [[ADE]]; the keys contain 16 numeric digits, such as <code>1234-5678-9012-3456</code>
* Click the '''Activate License''' button
* Click '''BEGIN License Activation''', then enter these fields:
** Check ''Other (URL)'' and enter <code>AnalyticaOnline.com</code> into the text-box.
**:[[Image:ActivationServerUrl.jpg]]
** ''ISV'': <code>lumina</code>.
** ''License activation key'': <code>1234-5678-9012-3456</code> { Your activation code here }
**:[[File:ISV_lumina.png]]
** ''License Server hostid'': { Use the value filled in for you }
** ''License count'': { The number of seats. Normally 1. }
** ''License File to create'': { A <code>*.lic</code> file in the licenses directory from step 2}
** Press '''REQUEST LICENSE'''.
*::If an error occurs, see [[/Solving problems during managed license activation|Solving problems during managed license activation]].
** When prompted, restart RLM server to reread licenses.

12. Click on '''Status'''
* Verify that the <code>Lumina ISV</code> is listed.

13. If you have more than one activation key, repeat steps 9-10 for each.

== Additional Configuration ==
You, as an IT manager, may want to configure RLM permissions to control who can use the Analytica licenses and who can manage the RLM server. On the bottom left of the RLM Administration Console, there is a link to the '''RLM Manual...'''

To control access to the RLM server, and administration of its capabilities, see the section on '''RLM Options File'''. Among the access control settings you can configure are these (copied from that manual):

:{| class="wikitable"
!Privilege
!Name to use in RLM options file
!Meaning
|-
|edit_options||edit_options||Allows editing options files for ISV servers
|-
|edit_rlm_options||edit_rlm_options||Allows editing options files for the rlm server
|-
|edit_transfer||edit_transfer||Allows editing server-server license transfer settings for ISV servers
|-
|reread||reread||Allows access to the functions which do reread commands on license servers
|-
|shutdown||shutdown||Allows access to the functions which shut down license servers
|-
|status||status||Allows display of status and debug log information from the license servers
|}

You may also want to restrict which users can checkout licenses, for example, restricting usage to specific users in your department. For that, see the section '''The ISV Options File''' in the '''RLM Manual'''. Also consult that section for information on assigning named-user licenses to specific users.

== See Also ==
* [[Installation and licenses]]
* [[What License do I Purchase?]]
* [[How to Install Analytica -- Individual License]]
* [[How to Install Analytica -- Centrally Managed License]]
* [[License Roaming]]
* [http://www.reprisesoftware.com Reprise License Manager]
* [http://WebinarArchive.Analytica.com//2009-06-04-RLM_Install.wmv RLM_Install.wmv]: Video - installing RLM and Activating centrally managed Analytica licenses (22 minutes)
* [[Configuring an RLM Server/Solving problems during managed license activation|Solving problems during managed license activation]]
* [[Configuring an RLM Server/Debugging problems with RLM]]
* [http://www.reprisesoftware.com/admin/software-licensing.php RLM for License Administrators and Users] -- info, downloads, FAQs and troubleshooting tips from Reprise
* [http://lumina.com/ana/manualActivation.htm Manual Activation]

File:ActivationServerUrl.jpg

2021-12-01T17:42:35Z

Drice: Drice uploaded a new version of File:ActivationServerUrl.jpg

What's new in Analytica 6.0?

2021-10-12T18:36:29Z

Drice: /* Number format and Cell-level formats */ link to post on User Forum

This page list the enhancements that are new to Analytica 6.0 since [[Analytica 5.4]]. Analytica 6.0 is currently in beta, so that [[Analytica 5.4]] is still the current official release. If you have an Analytica subscription, you can use or test drive Analytica 6.0 beta. For information on how, visit the [[Beta Tester Page]].

<center>[[image:System dynamics diagram with curved arrows.png|600px]]</center>

= Diagrams =
== Arrows ==
You can now modify arrows to have multiple line segments or curves, very handy when you want to avoid arrows crossing other arrows or nodes. You can also set arrows' thickness, linestyle and colors.

=== Bends and Curves ===
Here's how to add segments or spline curves to an arrow:
* Click a straight arrow to select it (in Edit mode). It will show a square and round handles in the middle of the arrow.
* For two straight line segments, drag the square handle.
* For a curved arrow, drag the round handle.

To modify a segmented or curved arrow, click to select it and then:
* To move the waypoints (dark circles or squares), just drag them.
* To add more lines or curves, drag a new midpoints handle (open circle or square).

=== Arrow menu styles ===
For more options, right-click on a multi-segment arrow to see the arrow menu:

<center>[[image:Arrow menu.png|500px]]</center>
* Select '''Curved''' on the context menu to toggle between curved and straight segments.
* Select '''Remove way point''' to remove a segment.
* Select '''Remove all way points''' to restore a simple straight arrow.
* Select '''Dash style''' to change line style t o solid, dashes, dots, dash-dot, or Dash-dot-dot.
* Select '''Thickness''' to make the arrow thicker or thinner.
* Select '''double line''


=== Colors and line formats ===
* To change the arrow color, click the arrow to select it, and click a color from the [[Color palette]].

=== Showing and hiding arrows ===
As before, you can use the [[Diagram Style dialog]] to control whether to show arrows to and from indexes and functions (off by default) or modules (on by default) or use the [[Node Style dialog]] to control whether to show inputs and outputs to a node. Now, you can now show or hide individual arrows using the Arrow menu:
* Select "'Hide arrow''' to hide an arrow entirely that would otherwise show.
* Or '''Show arrow''' to show a hidden arrow (but first you'll have to click around to find the arrow and right-click menu:-).


== Rounded corners ==
The borders of Text nodes, Frame nodes, Pictures, and User Inputs and Outputs (when shown) , were formerly rectangles with sharp corners. They are now have rounded corners for a more modern, less formal, look.
* There isn't a user interfacee to change the rounding radius for these node types. But you can do it in the [[Typescript]]. For example, if you prefer the old-fashioned rectangle view for all Text nodes, set the 18th field of <code>[[NodeInfo]] of Text</code> to 0 (instead of the default 12). The last 0 is the corner radius:
:<code>NodeInfo of Text:1,0,0,,0,0,,,,,,,0,,,,,0</code>

== Proactive calculation of outputs ==

Normally, Analytica computes variables only when you ask to view a result value. And when you change an input, any user output influenced by the input reverts to the '''[calc]''' button. So you need to click any results that depend on the input again to recompute them. In some cases, especially with ACP, it's more user-friendly to have result tables and graphs compute and appear automatically when you view a Diagram (or ACP Tab). A new library <code>"Configure Proactive User Outputs"</code> lets you easily configure your UI's proactive evaluation behavior.
*:[[image:Configure proactive configuration.png]]

See [[Proactive Evaluation]] for details.

== Larger default node size ==
* The default node size for new models has been increased from 96x48 to 128x48 pixels.
:Note: You can still modify the default node size from the [[Diagram Style dialog]].

= Graphs =

== Custom graph titles==
*You can now include the title of the graph on the graph image itself, above the grid. To include the title, check the '''Graph title''' check box in Graph setup / Text.
* From there you can select the font, size and color for the title.
* You can customize the title, making it different from the variable's own title.
** To do this, right-click on the title on the graph and select '''Change graph title'''. This takes you to the [[Graph title expression attribute]], where you can enter a custom title.
** The [[Graph title expression attribute]] is an expression, so that you can compute your own title (for example, changing the title based on the uncertainty view or current slicer selections). The locals <code>info</code> and <code>roles</code> that are provided to [[OnGraphDraw]] are also provided to your expression here.
** If you want a simple (non-computed) title, just make sure your text has quotes around it.

== Dash style role ==
* Using the new dash style (aka stipple) role and key you can depict some information using line color and different information using the line dash style.
* To enable this option, enable the checkbox for '''''Separate dash style key''''' in the [[Graph_setup_dialog#Chart_Type_tab|Graph setup dialog]] / Chart type / Line style settings.
* When enabled, a new '''''Dash style''''' pivot control appears in the result window.
* This works best for depicting short indexes with no more than 5 items.

== Hiding labels for one axis ==
* People often find the numeric values for the probability density of a continuous variable to be confusing. So you may prefer to hide the labels for the density axis.
* You can hide labels for any axis from Graph Setup / Axis Ranges, by checking the ''Hide labels'' checkbox.
* This setting is associated with the specific graph dimension on the axis at the time you select it, So if you pivot or change view mode, other axes aren't hidden.

== OnGraphClick ==
A new expression attribute, [[OnGraphClick]] has been added, which is evaluated when you mouse-click on a graph.
Your code can access information about what was clicked on, and set variables in your model based on what was clicked.

== New Grid options ==
* There are now 3 new grid options: Solid line mesh (in addition to the former & current default, dotted line mesh), x-axis-only and y-axis-only.
* The default grid has been changed to solid line mesh.
* The default grid color has been lightened a little, from 0x9c9c9c to 0xe0e0e0.

== New hover icons ==
* There are new hover icons to switch an axis to log-scale or back to linear-scale in a single click.

== Computed Axis Title ==
* It is now possible to compute an axis or key title dynamically when the graph is drawn. An example would be to base the title on which item is selected in one of the slicers for the result.
* This is enabled by the addition of "Title" to the [[GraphFillerInfo]] index.
* See [[Using a computed axis title in a graph]] for details and an example.

= Copy/Paste =
* When you copy/paste from an expression attribute (like a Definition) into another application such as a gmail message, it now preserves the fixed-width font, the indentation of each line, and the syntax colors.

= Filed Modules and Libraries =
<center>[[image:Missing module and library.png]]</center>
It now treats the situation differently when you open a model that uses a filed module or filed library that cannot be found.
* It keeps a placeholder "Missing module" or "Missing library" object in your model.
* The Missing module/library looks like a module or library with a big crack through it.
* You don't experience two extra error messages during the file load when you tell it to skip a filed module, because the node location and size attributes that cause these still apply to the missing module object.
* If you save your model after not loading a filed module or library, the new scheme doesn't forget that it uses the filed module/library.
* A hover icon on the missing module placeholder allows you to find and load the file to correct the missing module after the model is loaded.

= Expressions =
* Added [[Formatted Text Literals]] (a.k.a. F-strings). For example:
*:<code>F"Golden ratio={(1+sqrt(5))/2}"</code> → "Golden ratio=1.618"
* You can now nest comments in curly braces " {} ". For example, if you have <code>{ start of comment { interior comment } more comment }</code>, the comment doesn't end until it gets to the second " } ". This makes it easier to temporarily comment out blocks of code that contain comments. Previously, the first } ended the comment. When loading a legacy model with an unbalanced comments, it automatically adds a balancing " } " so that the comment still ends it the same place it doesn't break the model.
* You can now omit a capture destination in a multiple-return-value assignment operator. This makes a common pattern more convenient and terse. For example, previously a pattern such as this was common:<code>
:[[Local]] txt;
:(txt, Filename) := [[ReadTextFile]]("");
:txt
</code>
where <code>Filename</code> is defined as a [[ComputedBy]]. The third line (txt) was already unnecessary, since the result of the assignment is the first parameter value. Now even the [[Local]] declaration is unnecessary, so that the above becomes just
:<code>( , Filename) := [[ReadTextFile]]("")</code>
The result of the full expression is the first return value, with the second return value assigned to <code>Filename</code>.
* You have long been able to select an item in a [[Choice]] control using the assignment operator. For example,
::<code>Select_fruit := "apple"</code>
:But, there was not an easy way to select the All option. Now you can select it by assigning the full index value, assigning an ordered list of all the options, or assigning the text "All" or "«All»" (as long as "All" (or "«All»" respectively) is not one of the choice items. ([[MultiChoice]] does the same, but that's not new to 6.0).

= Built-in functions =
* There is now a sliding window option for [[CumMin]] and [[CumMax]], which uses an O(n) algorithm, and which also handles the «passNull» and «reset» options.
* You can list multiple arguments when calling [[ConsolePrint]]. They are printed on the same line, with no separation, and without combining the indexes of the parameters.
* Added an optional «rollover» index to the [[Dispatch]] function, which you can use to rollover unmet demand or unused capacity to the next time period.
* Added these new items to [[DatePart]]. <code>DatePart( d, 'Date')</code> returns the date part of a date time (dropping the time part), and <code>DatePart(d, 'Time')</code> returns the time part (dropping the date part). Also, <code>[[Mod]](d,1)</code> now returns a date-time number when d is a date-time number, and is equivalent to <code>DatePart(d,'Time')</code> (formerly it returned a float).
* Null values in «x» or «y» to [[CanvasDrawPolygon]] now cause it to start a new, distinct polygon.
* Added the ''[[:Category:Cell format functions|Cell formatting functions]]'' system library to the definition menu.
* A collection of [[:category|File system functions]] were added to the [[Analytica Enterprise|Enterprise edition]] (and higher). These functions are: [[FileFullPath]], [[FilePathPart]], [[FileSystemCopy]], [[FileSystemDelete]], [[FileSystemListing]], [[FileSystemMove]], and [[FileSystemNewFolder]].
** These functions are ''enabled'' in the [[Analytica Cloud Platform]], and provide secure ways of viewing and manipulating files within your own ACP project.
** Similar functionality is also possible using previously functions like [[RunConsoleProcess]] or [[COM Integration]]. But for security reasons, these other methods may be disabled when your model runs on our public [https://acp.analytica.com ACP server].
** [[FileFullPath]] and [[FilePathPart]] are available in all editions.
* You can test whether an array has a specific index using the new built-in functions [[HasImplicitDimension]] or [[HasIndex]].
* There are a few new advanced math functions, including the [[Airy functions]] and [[Bessel Functions|Bessel zero functions]].
* A bug fix to [[DbQuery]]() and [[DbWrite]]() -- affects mostly [[DbWrite]]. These have a feature that splits queries on double semi-colons, and sends each part as separate queries. For example
*:<code>INSERT INTO Tab(X) Value(3);;</code>
*:<code>INSERT INTO Tab(Y) Value(2)</code>
:Gets sent as two separate queries. Some databases won't process sequential statements in the same query, so this feature provides a way around that. All queries are done in the same context, which is also sometimes relevant. A bug was causing it to split on a single semi-colon, which was a problem, especially in complex queries with SQL variables. With this fix, single semi-colons are part of the same query and don't split them into separate queries. Unfortunately, this could break some SQL queries that used a single semi-colon and depended on them being split. SQL statements in this category would almost always be to [[DbWrite]](), and very unlikely to impact queries that read data.

= Batch processing =
You can now [[Running a model in a command line workflow|run a model in a batch process]] from a Windows command line or script. So, you can run Analytica as part of an automated workflow. You were always about to do this using the [[ADE User Guide|Analytica Decision Engine (ADE)]] product. Now you can do it with Analytica alone. See [[Running a model in a command line workflow]].

The key additions that enable this capability include:
* The parameter <code>/eval</code> to the [[Analytica Command Line]].
* The [[Bye]] command, lets you automate the exit of an Analytica process.
* An option to the [[Bye]] command let's you exit without saving (or asking to save) changes to the model if the model has been modified.
* The command line option <code>/NoSplash</code> suppresses the splash screen when starting Analytica, which removes some startup delay.

= Example Models & Libraries =
== Supply Chain ==
<center>[[image:brewery_supply_chain.png|600px]]</center>
The <code>"Beer Distribution Supply Chain.ana"</code> model in the Business Examples folder applies probabilistic supply and production disruptions to evaluate which operational decisions can mitigate order fulfillment disruptions.

== Boolean circuits ==
<center>[[image:Boolean circuits.png]]</center>
This new example model was developed partially by a 7 year-old who was learning about boolean circuits, and enjoyed drawing and simulating his own circuits in Analytica. You can draw your own boolean circuit using AND gates, OR gates and NOT inverter gates, and toggle input bits to see how the 0s and 1s flow through the circuit. A nice model to teach young kids about boolean circuits and allow them to build their own simple feed-forward circuits.
== Power law distribution library ==
The [[Power law distribution]] is implemented in a library that is now included with Analytica. The [[Power law distribution]] is useful in a number of applications, but perhaps even more important is that this library provides an example template that you can follow for adding other distributions to Analytica when you need one that isn't already built-in.

== New ACP Styles Library ==
The [[ACP Style Library]] has been completely rewritten, and is tailored to the newest [[Analytica Cloud Platform]] release.

== Other distributions ==
* Added the function [[Normal_p1_p2]] to the [[:category:Distribution Variations library functions|Distribution Variations Library]]. This function defines a [[Normal distribution]] given any two percentiles.

=Optimizer=
* When you have an array constraint has both intrinsic and extrinsic indexes, the positions of Null constraints can now appear at different (intrinsic) coordinates in each extrinsic slice. Formerly, it assumed that Null constraints appear at the same coordinates in every extrinsic slice. For example, in <code>If b Then x<y</code>, where b is an array of booleans, <code>b</code> b can now vary along both intrinsic AND extrinsic indexes. Scalar constraints are not sent to the solver engine for positions where <code>b=0</code> (hence are not counted in your total number of constraints).

= Attributes and Object window =
* The attribute that used to be titled "Cloud Player Styles" or "AWP Styles" is now "[[AcpStyles Attribute Values|AcpStyles]]".
** In the Object window, it has syntax coloring and expression assist.
* In the [[Object Window]], you can right-click in the row-header column to select which [[Object Window#Selecting Attributes to Display|attributes to display]] or hide for this object. Applies to this object only, and saves you from having to do it globally in the [[Attributes dialog]].
* The default text for the [[author]] attribute is improved, using your first and last name and organization if possible (as opposed to your window login name). It is able to find this information if you had entered that information in the installer while installing Analytica. You can also customize your default author signature, which will then be used as your default text when you create new models. To do this, edit the author attribute (in the [[Object Window]] or [[Attribute pane]]) to be as you wish, then right-click on it to bring up the context menu. Select the new option '''Save author signature'''. Subsequently, the same context menu will also have a '''Use saved author signature''' option.
* A right-mouse context menu option makes is easier to set (or unset) the "[[Computed_cell_formats#Edit_Tables|apply computed cell formats to edit table]]" flag.
* When typing an expression, [[Expression Assist]] can now suggest the names of indexes for a local identifier in appropriate contexts when the dimensionality of the local has been declared.

= Number format and Cell-level formats =
* In a date template, it now accepts capital letters for D, DD, YY and YYYY, so MM/DD/YYYY can be used as well as MM/dd/yyyy. Formerly it recognized only lower case dd and yyyy.
* On the [[Cell format dialog]], the text entry options has been moved from the ''Alignment'' tab to its own ''Entry'' tab.
** The options for Entry are now split into checkboxes for each data type
** Added data type options for '''Null''' and '''Identifiers''' (handles)
* The suffix number format displays (and has always done displayed) a G suffix for Giga (<math>10^9</math>) and a u suffix for micro (<math>10^{-6}</math>). We added a «GigaOrMuSuffixChars» field to the [[NumberFormat]] attribute (item 18) that gives you a way to use a B suffix for Giga (B=billion in English) and µ for micro (greek letter mu). If you want to change this, at present you'll have to change the [[Sys_DefaultNumberFmt]] system variable from the [[Typescript window]]. To see the exact syntax, and for Library with a UI for configuring this, see [https://lumina.com/community/models-and-application-examples/displaying-b-for-billion-%c2%b5-for-micro/ Displaying B for billion, µ for micro] on the User Forum.

= Misc =
* When a window loses focus, its non-active scrollbars now have a more modern appearance.
* You can now evaluate an expression when [[Links_or_URL_in_model_attributes|a hyperlink]] is clicked. This might be a call to [[ShowWindow]](), for example, to jump to a particular result or diagram, or a button identifier to "press" an existing button.
* When it generates an identifier from a title, it uses only a single underscore where multiple successive characters in the title are not valid in the identifier. For example, from the title "Taxes & Depreciation", the automatically generated identifier will now be <code>Taxes_Depreciation</code> rather than <code>Taxes___Depreciation</code>.
* The option '''Run at load time''' has been added to the right-mouse edit-mode context menu for a button. Sets the 32-bit of [[ProactivelyEvaluate]] for the button, causing it to be run when the model is loaded.
* Faster saving of model file when you save to a remote drive over a VPN connection.
* Added the system variable [[Sys_WarningsToIgnore]].
* Jump to the [https://lumina/community Analytica User Forum] easily from Analytica using the new '''Analytica Q&A forum''' option on the [[Help menu|'''Help''' menu]]. Have questions about Analytica or suggestions? Ask them there, and answer questions other people ask.
* Added ''Copy identifier'' to the right-mouse context menu for a node (in the diagram window).
* Added a '''Server''' combo box to the [[Publish To Cloud dialog]]. Although rare, if you have access to an ACP server other than [https://Acp.analytica.com|Lumina's public ACP server], you can enter your server domain into the combo and then have an easy way to select which server you are publishing to.

== No more 32-bit application and no "64" bit labels ==
Long ago, most software including Analytica were 32-bit applications. When we produced a 64-bit version, we used the '64-bit' label win many places. Today, we only produce a 64-bit, the 32-bit version is obsolete. So we've eliminated the "64-bit" from application file names, including:
* The installer filename is now <code>AnaSetup«ver».exe</code>, not <code>Ana64Setup«ver».exe</code>.
* The executables are now <code>Analytica.exe</code> and <code>Ade.exe</code>, not <code>Analytica64.exe</code> and <code>Ade64.exe</code>. Similarly, <code>ADEW.DLL</code> replaces <code>ADEW64.DLL</code> and <code>AnalyticaUpdateCheck.exe</code> replaces <code>Analytica64UpdateCheck.exe</code>.
* Edition names omit "64-bit". So it now says "Analytica Enterprise" and not "Analytica Enterprise 64-bit".
* The user's registry hive is now <code>HKCU/Software/Lumina Decision Systems/Analytica/6.0</code>, not <code>.../6.0x64</code>
* License names omit the 64, e.g., analytica_enterprise_6_2 instead of analytica64_enterprise_6_2

Smooth Fractile

2021-06-10T00:32:20Z

Drice: /* Example */

[[Category:Distribution Functions]]
[[Category: Distribution Variations library functions]]
[[Category:Doc Status C]] 

== Smooth_Fractile(fract, F) ==
Given a set of fractiles, this function returns a smooth distribution with tails having the indicated fractiles. The fractiles to use must be specified in «F», each value being between 0 and 1, and the fractile values must be in «fract».

Declaration:
:[[Smooth_Fractile]](fract: Ascending[F]; F: positive ascending Index)

== Library ==
Distribution Variations library ([[media:Distribution Variations.ana|Distribution Variations.ana]])
:Use [[File menu|File]] → '''Add Library...''' to add this library

== Example ==
To specify a distribution having a ''P10'', ''P50'' and ''P90'' of 7, 13, and 15, set:
:<code>F := [0.1, 0.5, 0.9]</code>
:<code>fract := [[Table]](F) (7, 13, 15)</code>

and call
:<code>Smooth_Fractile(fract, F)</code>
:[[image:Smooth_fractile_CDF.png]][[image:Smooth_fractile_PDF.png]]

==See Also==
* [[media:Distribution Variations.ana | Distribution Variations.ana]]
* [[Fractiles]]
* [[Table]]
* [[Kernel Density Smoothing]]
* [[Distribution Densities Library]]
* [[Keelin (MetaLog) distribution]]

Smooth Fractile

2021-06-10T00:31:17Z

Drice: /* See Also */ -- Keelin distribution

[[Category:Distribution Functions]]
[[Category: Distribution Variations library functions]]
[[Category:Doc Status C]] 

== Smooth_Fractile(fract, F) ==
Given a set of fractiles, this function returns a smooth distribution with tails having the indicated fractiles. The fractiles to use must be specified in «F», each value being between 0 and 1, and the fractile values must be in «fract».

Declaration:
:[[Smooth_Fractile]](fract: Ascending[F]; F: positive ascending Index)

== Library ==
Distribution Variations library ([[media:Distribution Variations.ana|Distribution Variations.ana]])
:Use [[File menu|File]] → '''Add Library...''' to add this library

== Example ==
To specify a distribution having a ''P10'', ''P50'' and ''P90'' of 7, 13, and 15, set:
:<code>F := [0.1, 0.5, 0.9]</code>
:<code>fract := Tabl(F) (7, 13, 15)</code>

and call
:<code>Smooth_Fractile(fract, F)</code>
:[[image:Smooth_fractile_CDF.png]][[image:Smooth_fractile_PDF.png]]

==See Also==
* [[media:Distribution Variations.ana | Distribution Variations.ana]]
* [[Fractiles]]
* [[Table]]
* [[Kernel Density Smoothing]]
* [[Distribution Densities Library]]
* [[Keelin (MetaLog) distribution]]

Normal p1 p2

2021-06-10T00:28:34Z

Drice: /* See Also */ UncertainLMH

[[category:Distribution Variations library functions]]

''New in [[Analytica 6.0]]''

== Normal_p1_p2( q1, q2, p1, p2 ) ==

This distribution function found in the [[:category:Distribution Variations library functions|Distribution Variations library]] defines a [[Normal distribution]] given any two percentile estimates. «q1» and «q2» are the percentile estimates, and «p1» and «p2» specify which percentiles these are. It must be that <math>q1<q2</math> and <math>p1<p2</math>.

For example, given that the 5% percentile is 5 and the 25% percentile is 8, the distribution is
:[[Normal_p1_p2]]( 5, 8, 5%, 25% ) → [[image:Normal_p1_p2_ex1.png]]

As with other distribution functions, you can also use this distribution in the function [[Random]].

== Library==

To use this function, you must first use '''[[Filed modules and libraries|Add Library]]''' to add the [[:category:Distribution Variations library functions|Distribution Variations Library]] to your model.

== See Also ==
* [[Normal distribution]]
* [[UncertainLMH]]

Normal p1 p2

2021-06-10T00:27:38Z

Drice: Library

Log-normal distribution

2021-06-10T00:25:57Z

Drice: Balanced parens

[[category:Continuous distributions]]
[[category:Semi-bounded distributions]]
[[category:Unimodal distributions]]
[[Category:Doc Status C]] 
[[Category:Ana: Status R]] 
{{ReleaseBar}}

A [[Log-normal distribution]] is a [[:category:Continuous distributions|continuous distribution]] whose [[Ln|logarithm]] is [[Normal distribution|normally distributed]]. In other words, <code>[[Ln]](x)</code> has a [[Normal distribution]] when <code>x</code> has a log-normal distribution.

<center><code>LogNormal(median:3,stddev:2)</code> → [[image:LogNormal(median=3,stddev=2).png]]</center>

[[Log-normal distribution]]s are useful for many quantities that are always positive and have long upper tails, such as concentration of a pollutant, or amount of rainfall. The distribution is [[:category:Semi-bounded distributions|semi-bounded]] (positive-only) and [[:category:Unimodal distributions|unimodal]], and often has a long right tail.

The central limit theorem says that the product of a long series of independent and identically distributed positive random variables converges to a log-normal distribution for any positive, finite-variance distribution.

== Functions ==

The log-normal is specified by specifying any two of the following four parameters.
; median
The [[Median]], must be >0.
; gsdev
The geometric standard deviation>=1.
; mean
The arithmetic [[Mean]], >0
; stddev
The arithmetic [[SDeviation|standard deviation]], >=0.

A named-parameter convention is recommended, such as:
:<code>LogNormal( gsdev:1.5, mean: 4 )</code>

=== LogNormal(''median, gsdev, mean, stddev, over'') ===
The distribution function. Use this to specify that a chance variable or uncertain quantity is log-normally distributed. You must specify exactly two of the core parameters.

To create independent and identically distributed log-normal distributions along one or more indexes, specify those indexes using the optional «over» parameter.

Generates a sample with a lognormal distribution given «median» and «gsdev» (geometric standard deviation), or «mean» and «stddev» (standard deviation).

=== <div id="DensLogNormal">Dens{{Release||4.6|_}}LogNormal( x'', median, gsdev, mean, stddev'' )</div> ===
{{Release||4.6|To use this, you need to add the [[Distribution Densities Library]] to your model. }}

The analytic probability density function. Returns the probability density at «x». Exactly two of the parameters «median», «gsdev», «mean», or «stddev» must be provided.

=== <div id="CumLogNormal">CumLogNormal( x'', median, gsdev, mean, stddev'' )</div> ===
{{Release||4.6|To use this, you need to add the [[Distribution Densities Library]] to your model. }}

The analytic cumulative density function. Returns the probability that the outcome is less than or equal to «x».

Exactly two of the parameters «median», «gsdev», «mean», or «stddev» must be provided.

=== <div id="CumLogNormalInv">CumLogNormalInv( p'', median, gsdev, mean, stddev'' )</div> ===
{{Release||4.6|To use this, you need to add the [[Distribution Densities Library]] to your model. }}

The inverse cumulative density function (aka quantile function). Returns the «p»<sup>th</sup> fractile/quantile/percentile.

Exactly two of the parameters «median», «gsdev», «mean», or «stddev» must be provided.

== Statistics ==

== Examples ==
A [[Normal]] distribution is symmetric around its [[mean]]:
:If <code>x := Normal(mean, sdev)</code>, then <code>P(x <= mean - sdev) = P(x >= mean + sdev) = .15</code>.

Analogously, a lognormal distribution is ratio-symmetric around its median:
:If <code>y := LogNormal(median, gsdev)</code>, then <code>P(y <= median/gsdev) = P(y >= median*gsdev) = .15</code>.

If you specify no parameters, it defaults to standard lognormal -- i.e. whose natural logarithm is a unit normal, mean 0 and standard deviation 1.

You can actually specify any two of the four parameters, from which it can compute the other two:
:<code>LogNormal(median: med, gsdev: gs)</code> or just <code>LogNormal(med, gs)</code>
:<code>LogNormal(median: med, stddev: sd)</code>
:<code>LogNormal(median: med, mean: mu)</code>
:<code>LogNormal(mean: mu, stddev: s)</code>
:<code>LogNormal(mean: mu, gsdev: gs)</code>
:<code>LogNormal(gsdev: gs, stddev: sd)</code>
If you specify more than two parameters, it will give an error.

Like other distributions, you can also give one or more «Over» indexes. These cause it to generate an array of independent lognormal distributions over the specified index(es). For example,
:<code>LogNormal(m, gsd, Over: i)</code>

[[Syntax]]:
:[[LogNormal]](median, gsdev, mean, stddev: Optional Positive; over: ... Optional Atom)

== Parameter Estimation ==
Suppose <code>X</code> contains sampled historical data indexed by <code>I</code>, and consisting solely of positive values. To estimate the parameters of the best-fit [[LogNormal]] distribution, the following parameter estimation formulae can be used:

:<code>«median» := Median(X, I)</code> or <code>Exp(Mean(Ln(X), I))</code>
:<code>«gsdev» := Exp(SDeviation(Ln(X), I))</code>

A more general form, with one extra degree-of-freedom, is the [[LogNormal]] with an offset, i.e.,:
:<code>LogNormal(median, gsdev) - offset</code>

The more general form can be adapted to data sets containing negative numbers. The offset is constrained so that
:<code>offset > -Min(X, I)</code>

To my knowledge, a closed form formula for offset does not exist, so that finding the optimal value of offset requires a 1-D search or optimization. However, I have found that the following heuristic estimation formulae comes extremely close to the best-fit parameters with offset:
:<code>offset := -Min(X, I) + 2*(Median(X, I) - Min(X, I))/Sum(1, I)</code>
:<code>median := Median(X + offset, I)</code>
:<code>gsdev := Exp(SDeviation(Ln(X + offset), I))</code>

=== From Median and Percentile ===
Suppose you have a median (m) and 95th percentile estimate (p95). This is enough to uniquely determine the log normal distribution. In this case the «gsdev» is given by
:<math>\left( {p95 \over m} \right)^{\left({1 \over {\Phi^{-1}(0.95)}}\right)} = \left( {p95 \over m} \right)^{0.6079568319149189}</math>
where <math>\Phi^{-1}(p)</math> is the [[CumNormalInv]] function. Hence the distribution expression is
:<code>[[LogNormal]](m, (p95/m)^0.6079568319149189 )</code>

The general form for the <math>p^{th}</math> percentile, when <math>p>0.5</math>, where <math>q</math> is the percentile estimate, is
:<code>[[LogNormal]]( m, (q/m)^(1/[[CumNormalInv]](p)) )</code>
For <math>p<0.5</math>, the expression is
:<code>[[LogNormal]]( m, (m/q)^(1/[[CumNormalInv]](1-p)) )</code>

== See Also ==
* [[Normal distribution]]
* [[Gamma distribution]] -- similar shaped distribution
* [[Parametric continuous distributions]]
* [[Distribution Functions]]
* [[Distribution Densities Library]]
* [[Ln]] -- the natural logarithm
* [[LogTen]]
* [[Normal_p1_p2]]

Log-normal distribution

2021-06-10T00:24:30Z

Drice: /* See Also */

[[category:Continuous distributions]]
[[category:Semi-bounded distributions]]
[[category:Unimodal distributions]]
[[Category:Doc Status C]] 
[[Category:Ana: Status R]] 
{{ReleaseBar}}

A [[Log-normal distribution]] is a [[:category:Continuous distributions|continuous distribution]] whose [[Ln|logarithm]] is [[Normal distribution|normally distributed]]. In other words, <code>[[Ln]](x)</code> has a [[Normal distribution]] when <code>x</code> has a log-normal distribution.

<center><code>LogNormal(median:3,stddev:2)</code> → [[image:LogNormal(median=3,stddev=2).png]]</center>

[[Log-normal distribution]]s are useful for many quantities that are always positive and have long upper tails, such as concentration of a pollutant, or amount of rainfall. The distribution is [[:category:Semi-bounded distributions|semi-bounded]] (positive-only) and [[:category:Unimodal distributions|unimodal]], and often has a long right tail.

The central limit theorem says that the product of a long series of independent and identically distributed positive random variables converges to a log-normal distribution for any positive, finite-variance distribution.

== Functions ==

The log-normal is specified by specifying any two of the following four parameters.
; median
The [[Median]], must be >0.
; gsdev
The geometric standard deviation>=1.
; mean
The arithmetic [[Mean]], >0
; stddev
The arithmetic [[SDeviation|standard deviation]], >=0.

A named-parameter convention is recommended, such as:
:<code>LogNormal( gsdev:1.5, mean: 4 )</code>

=== LogNormal(''median, gsdev, mean, stddev, over'') ===
The distribution function. Use this to specify that a chance variable or uncertain quantity is log-normally distributed. You must specify exactly two of the core parameters.

To create independent and identically distributed log-normal distributions along one or more indexes, specify those indexes using the optional «over» parameter.

Generates a sample with a lognormal distribution given «median» and «gsdev» (geometric standard deviation), or «mean» and «stddev» (standard deviation).

=== <div id="DensLogNormal">Dens{{Release||4.6|_}}LogNormal( x'', median, gsdev, mean, stddev'' )</div> ===
{{Release||4.6|To use this, you need to add the [[Distribution Densities Library]] to your model. }}

The analytic probability density function. Returns the probability density at «x». Exactly two of the parameters «median», «gsdev», «mean», or «stddev» must be provided.

=== <div id="CumLogNormal">CumLogNormal( x'', median, gsdev, mean, stddev'' )</div> ===
{{Release||4.6|To use this, you need to add the [[Distribution Densities Library]] to your model. }}

The analytic cumulative density function. Returns the probability that the outcome is less than or equal to «x».

Exactly two of the parameters «median», «gsdev», «mean», or «stddev» must be provided.

=== <div id="CumLogNormalInv">CumLogNormalInv( p'', median, gsdev, mean, stddev'' )</div> ===
{{Release||4.6|To use this, you need to add the [[Distribution Densities Library]] to your model. }}

The inverse cumulative density function (aka quantile function). Returns the «p»<sup>th</sup> fractile/quantile/percentile.

Exactly two of the parameters «median», «gsdev», «mean», or «stddev» must be provided.

== Statistics ==

== Examples ==
A [[Normal]] distribution is symmetric around its [[mean]]:
:If <code>x := Normal(mean, sdev)</code>, then <code>P(x <= mean - sdev) = P(x >= mean + sdev) = .15</code>.

Analogously, a lognormal distribution is ratio-symmetric around its median:
:If <code>y := LogNormal(median, gsdev)</code>, then <code>P(y <= median/gsdev) = P(y >= median*gsdev) = .15</code>.

If you specify no parameters, it defaults to standard lognormal -- i.e. whose natural logarithm is a unit normal, mean 0 and standard deviation 1.

You can actually specify any two of the four parameters, from which it can compute the other two:
:<code>LogNormal(median: med, gsdev: gs)</code> or just <code>LogNormal(med, gs)</code>
:<code>LogNormal(median: med, stddev: sd)</code>
:<code>LogNormal(median: med, mean: mu)</code>
:<code>LogNormal(mean: mu, stddev: s)</code>
:<code>LogNormal(mean: mu, gsdev: gs)</code>
:<code>LogNormal(gsdev: gs, stddev: sd)</code>
If you specify more than two parameters, it will give an error.

Like other distributions, you can also give one or more «Over» indexes. These cause it to generate an array of independent lognormal distributions over the specified index(es). For example,
:<code>LogNormal(m, gsd, Over: i)</code>

[[Syntax]]:
:[[LogNormal]](median, gsdev, mean, stddev: Optional Positive; over: ... Optional Atom)

== Parameter Estimation ==
Suppose <code>X</code> contains sampled historical data indexed by <code>I</code>, and consisting solely of positive values. To estimate the parameters of the best-fit [[LogNormal]] distribution, the following parameter estimation formulae can be used:

:<code>«median» := Median(X, I)</code> or <code>Exp(Mean(Ln(X), I))</code>
:<code>«gsdev» := Exp(SDeviation(Ln(X), I))</code>

A more general form, with one extra degree-of-freedom, is the [[LogNormal]] with an offset, i.e.,:
:<code>LogNormal(median, gsdev) - offset</code>

The more general form can be adapted to data sets containing negative numbers. The offset is constrained so that
:<code>offset > -Min(X, I)</code>

To my knowledge, a closed form formula for offset does not exist, so that finding the optimal value of offset requires a 1-D search or optimization. However, I have found that the following heuristic estimation formulae comes extremely close to the best-fit parameters with offset:
:<code>offset := -Min(X, I) + 2*(Median(X, I) - Min(X, I))/Sum(1, I)</code>
:<code>median := Median(X + offset, I)</code>
:<code>gsdev := Exp(SDeviation(Ln(X + offset), I))</code>

=== From Median and Percentile ===
Suppose you have a median (m) and 95th percentile estimate (p95). This is enough to uniquely determine the log normal distribution. In this case the «gsdev» is given by
:<math>\left( {p95 \over m} \right)^{\left({1 \over {\Phi^{-1}(0.95)}}\right)} = \left( {p95 \over m} \right)^{0.6079568319149189}</math>
where <math>\Phi^{-1}(p)</math> is the [[CumNormalInv]] function. Hence the distribution expression is
:<code>[[LogNormal]](m, (p95/m)^0.6079568319149189 )</code>

The general form for the <math>p^{th}</math> percentile, when <math>p>0.5</math>, where <math>q</math> is the percentile estimate, is
:<code>[[LogNormal]]( m, (q/m)^(1/[[CumNormalInv]](p) )</code>
For <math>p<0.5</math>, the expression is
:<code>[[LogNormal]]( m, (m/q)^(1/[[CumNormalInv]](1-p) )</code>

== See Also ==
* [[Normal distribution]]
* [[Gamma distribution]] -- similar shaped distribution
* [[Parametric continuous distributions]]
* [[Distribution Functions]]
* [[Distribution Densities Library]]
* [[Ln]] -- the natural logarithm
* [[LogTen]]
* [[Normal_p1_p2]]

Alphabetical Function List

2021-06-10T00:22:26Z

Drice: Airy functions, Bessel zeros, Normal_p1_p2, PowerMod, FileSystem*, DownloadFileToClient, HasImplicitDimension, HasIndex

[[Category:Functions]]
(Back to [[Analytica Reference]])

See also [[:Category: Functions]] and [[Functions by category]].

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* [[CumGeometricInv]] ([[Distribution Densities Library]])
* [[CumIPmt]]
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* [[CumKeelinInv]]
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* [[CumLogisticInv]] ([[Distribution Densities Library]])
* [[CumLogNormal]] ([[Distribution Densities Library]])
* [[CumLogNormalInv]] ([[Distribution Densities Library]])
* [[CumMax]]
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* [[CumNegativeBinomInv]] ([[Distribution Densities Library]])
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* [[CumPoissonInv]]
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* [[Dereference Operator::#|Dereference Operator: #R]] : Return the value pointed to by a reference R.
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* [[Invert]]
* [[InvertedWishart]] (Distribution Variations.ana)
* [[InvLogit]] (Generalized Regression.ana)
* [[IPmt]]
* [[Irr]]
* [[IsDateTime]]
* [[IsHandle]]
* [[Data_Type_Functions#Function_IsNaN| IsNaN]]
* [[Data_Type_Functions#Function_IsNotSpecified| IsNotSpecified]]
* [[IsNull]]
* [[Data_Type_Functions#Function_IsNumber| IsNumber]]
* [[IsRealNumber]]
* [[Data_Type_Functions#Function_IsReference| IsReference]]
* [[IsResultComputed]]
* [[Data_Type_Functions#Function_IsText| IsText]]
* [[Data_Type_Functions#Function_IsUndef| IsUndef]]
* [[Iterate]]
* [[Join]]
* [[JoinText]]
* [[Keelin]]
* [[KeelinCoefficients]]
* [[Kurtosis]]
* [[LDens_InvertedWishart]] (Distribution Densities.ana)
* [[LDens_Wishart]] (Distribution Densities.ana)
* [[Legendre_kth_root]] ([[Legendre Library]])
* [[LegendreP]] ([[Legendre Library]])
* [[LegendreP_coefs]] ([[Legendre Library]])
* [[LegendreP_deriv]] ([[Legendre Library]])
* [[LGamma]]
* [[LinearInterp]]
* [[ListOfHandles]]
* [[LL_First]] (Linked List Library.ana)
* [[LL_Length]] (Linked List Library.ana)
* [[LL_Nth]] (Linked List Library.ana)
* [[LL_Push]] (Linked List Library.ana)
* [[LL_Remove_First]] (Linked List Library.ana)
* [[LL_To_Array]] (Linked List Library.ana)
* [[LL_to_RArray]] (Linked List Library.ana)
* [[Ln]]
* [[Local Index Operator::A.I]] : Get an index (usually a local index) of an array
* [[Logistic]]
* [[Logistic_Regression]] (Generalized Regression.ana)
* [[Logit]] (Generalized Regression.ana)
* [[LogNormal]]
* [[Lognormal_m_sd]] (Distribution variations.ana) - obsolete, use [[LogNormal]] (mean:m,stddev:sd)
* [[LogTen]]
* [[Lorenzian]] (Distribution variations.ana)
* [[LpDefine]]
* [[LpFindIIS]]
* [[LpObjSa]]
* [[LpOpt]]
* [[LpRead]]
* [[LpReducedCost]]
* [[LpRhsSa]]
* [[LpShadow]]
* [[LpSlack]]
* [[LpSolution]]
* [[LpStatusNum]]
* [[LpStatusText]]
* [[LpWrite]]
* [[LpWriteIIS]]
* [[MakeCSV]]
* [[Date_Functions#MakeDate.28year.2C_month.2C_day.29| MakeDate]]
* [[MakeJSON]]
* [[MantissaAndExponent]]
* [[MatrixMultiply]]
* [[Functions_Min_and_Max| Max]]
* [[MdArrayToTable]]
* [[MdTable]]
* [[MdxQuery]]
* [[Mean]]
* [[Median]]
* [[MemoryInUseBy]]
* [[Mid]]
* [[Functions_Min_and_Max| Min]]
* [[Mod]]
* [[MonoCubicInterp]]
* [[Move]]
* [[MsgBox]]
* [[MultiChoice]]
* [[Multinomial]] (Multivariate Distributions.ana)
* [[MultiNormal]] (Multivariate Distributions.ana)
* [[MultiTable]]
* [[MultiUniform]] (Multivariate Distributions.ana)
* [[NegBinomial]] (Distribution Variations.ana)
* [[NegativeBinomial]]
* [[NlpDefine]]
* [[Normal]]
* [[Normal_additive_gro]] (Multivariate Distributions.ana)
* [[Normal_compound_gro]] (Multivariate Distributions.ana)
* [[Normal_correl]] (Multivariate Distributions.ana)
* [[Normal_p1_p2]] ([[:category:Distribution Variations library functions|Distribution Variations.ana]])
* [[Normal_serial_correl]] (Multivariate Distributions.ana)
* [[Normalize]]
* [[Not]]
* [[NPer]]
* [[Npv]]
* [[NumberToText]]
* [[OnDraw_Google_map]] ( [[:Category:Google Maps from OnGraphDraw library functions|Google Maps from OnGraphDraw library]] )
* [[OpenExcelFile]] -- deprecated: use [[SpreadsheetOpen]]
* [[OpenModelFile]]
* [[OpenURL]]
* [[OptEngineInfo]]
* [[OptFindIIS]]
* [[OptGuess]]
* [[OptInfo]]
* [[OptObjective]]
* [[OptObjectiveSa]]
* [[OptRead]]
* [[OptReducedCost]]
* [[OptRhsSa]]
* [[OptScalarToConstraint]]
* [[OptScalarToDecision]]
* [[OptShadow]]
* [[OptSlack]]
* [[OptSolution]]
* [[OptStatusNum]]
* [[OptStatusText]]
* [[OptWrite]]
* [[OptWriteIIS]]
* [[Or]]
* [[Pareto]] (Distribution Variations.ana)
* [[ParseCSV]]
* [[ParseDate]]
* [[ParseExpression]]
* [[ParsedExprFunction]]
* [[ParsedExprParameters]]
* [[ParseJSON]]
* [[ParseNum]] (Flat file library.ana - for Analytica 4.1)
* [[ParseNumber]]
* [[Partitions]]
* [[Pdf]]
* [[Permutations]]
* [[Pert]] (Distribution Variations.ana)
* [[Plot_error_bars]] ([[:Category:OnGraphDraw annotations library functions|OnGraphDraw annotations library]])
* [[Plot_point_labels]] ([[:Category:OnGraphDraw annotations library functions|OnGraphDraw annotations library]])
* [[Plot_solid_band]] ([[:Category:OnGraphDraw annotations library functions|OnGraphDraw annotations library]])
* [[Plot_solid_prob_bands]] ([[:Category:OnGraphDraw annotations library functions|OnGraphDraw annotations library]])
* [[Plot_Tukey_bars]] ([[:Category:OnGraphDraw annotations library functions|OnGraphDraw annotations library]])
* [[Pmt]]
* [[Poisson]]
* [[PolarToC]] (Complex Library.ana)
* [[Index Position Operator::@|Position Operator: @I, @[I=x] ]] : Get the numeric position of index elements
* [[PositionInIndex]]
* [[PowerMod]]
* [[PPmt]]
* [[Probability]]
* [[ProbBands]]
* [[ProbDist]]
* [[Probit_Regression]] (Generalized Regression.ana)
* [[ProbTable]]
* [[Prob_Bernoulli]] ([[Distribution Densities Library]])
* [[Prob_Binomial]] ([[Distribution Densities Library]])
* [[Prob_ChanceDist]] ([[Distribution Densities Library]])
* [[Prob_Geometric]] ([[Distribution Densities Library]])
* [[Prob_HyperGeometric]] ([[Distribution Densities Library]])
* [[Prob_NegativeBinomia]] ([[Distribution Densities Library]])
* [[Prob_Poisson]] ([[Distribution Densities Library]])
* [[ProbWilcoxon]]
* [[Product]]
* [[ProductLog]]
* [[Putoption]] (Financial Library.ana)
* [[Pv]]
* [[Pvgperp]] (Financial Library.ana)
* [[Pvperp]] (Financial Library.ana)
* [[QpDefine]]
* [[Q_infromrec]]
* [[Q_makerect]]
* [[Q_squareinterp]]
* [[Radians]]
* [[Random]]
* [[Rank]]
* [[RankCorrel]]
* [[Rate]]
* [[Rayleigh]] (Distribution variations.ana)
* [[Re]] (Complex Library.ana)
* [[ReadBinaryFile]]
* [[ReadCsvFile]]
* [[ReadExportFile]]
* [[ReadFromUrl]]
* [[ReadImageFile]]
* [[ReadTextFile]]
* [[RealPart]]
* [[Reference Operator::\|Reference Operator: \X]] : Return a reference to X
* [[Reform]]
* [[Regression]]
* [[RegressionDist]] (Multivariate Distributions.ana)
* [[RegressionFitProb]] (Multivariate Distributions.ana)
* [[RegressionNoise]] (Multivariate Distributions.ana)
* [[ReThrow]]
* [[Reverse]]
* [[Round]]
* [[RunConsoleProcess]]
* [[Sample]]
* [[SampleCorrelation]] (Multivariate Distributions.ana)
* [[SampleCovariance]] (Multivariate Distributions.ana)
* [[SaveExcelWorkbook]] -- deprecated: use [[SpreadsheetSave]]
* [[ScanAttFromModelFile]]
* [[SchedulePublish]]
* [[SDeviation]]
* [[SelectText]]
* [[Sequence]]
* [[Sequence Operator|Sequence Operator: first..last]]
* [[SetContains]]
* [[SetDifference]]
* [[SetEvaluationFlag]]
* [[SetIntersection]]
* [[SetUnion]]
* [[ShowAskAttribute]]
* [[ShowPdfFile]]
* [[ShowProgressBar]]
* [[ShowWindow]]
* [[Shuffle]]
* [[Sign]]
* [[Trig Functions| Sin]]
* [[SingularValueDecomp]]
* [[Trig Functions| Sinh]]
* [[SipDecode]]
* [[SipEncode]]
* [[Size]]
* [[Skewness]]
* [[Sleep]]
* [[Slice]]
* [[Subscript/Slice Operator| Slice Operator: [@I=n] ]]
* [[Smooth_Fractile]] (Distribution variations.ana)
* [[SobolSequence]]
* [[Solve]] (Optimization Functions.ana)
* [[SolverInfo]]
* [[Sort]]
* [[SortIndex]]
* [[Split]]
* [[SplitText]]
* [[SpreadsheetCell]]
* [[SpreadsheetInfo]]
* [[SpreadsheetOpen]]
* [[SpreadsheetRange]]
* [[SpreadsheetSave]]
* [[SpreadsheetSetCell]]
* [[SpreadsheetSetInfo]]
* [[SpreadsheetSetRange]]
* [[SqlDriverInfo]]
* [[Sqr]]
* [[Sqrt]]
* [[Statistics]]
* [[StepInterp]]
* [[StringLength]]
* [[StringLowercase]]
* [[StringMixedCase]]
* [[StringReplace]]
* [[StringUpperCase]]
* [[StudentT]]
* [[SubFindString]]
* [[SubIndex]]
* [[Subscript]]
* [[Subscript/Slice Operator| Subscript Operator: [I=x] ]]
* [[Subset]]
* [[SubString]]
* [[SubTable]]
* [[Sum]]
* [[Sys_coordindex]]
* [[Sys_localindex]]
* [[Table]]
* [[TableJoin]]
* [[Trig Functions| Tan]]
* [[Trig Functions| Tanh]]
* [[Test_map_pivot_slice]] ( [[:Category:Google Maps from OnGraphDraw library functions|Google Maps from OnGraphDraw library]] )
* [[Test_map_pivot_vars]] ( [[:Category:Google Maps from OnGraphDraw library functions|Google Maps from OnGraphDraw library]] )
* [[TestHeapConsistency]]
* [[TextCharacterEncode]]
* [[Text Concatenation Operator: &|Text Concatenation Operator: A&B]] : Concatenate two text strings
* [[TextDistance]]
* [[TextLength]]
* [[TextLowerCase]]
* [[TextReplace]]
* [[TextSentenceCase]]
* [[TextTrim]]
* [[TextUpperCase]]
* [[Today]]
* [[Transpose]]
* [[Triangular]]
* [[Triangular_10_50_90]] (Distribution Variations.ana)
* [[Triangular_10_mode_90]] (Distribution Variations.ana)
* [[Truncate]]
* [[Try]]
* [[Data_Type_Functions#Function_TypeOf| TypeOf]]
* [[UncertainLMH]]
* [[Uncumulate]]
* [[Unflatten]]
* [[Uniform]]
* [[UniformSpherical]] (Multivariate distributions.ana)
* [[Unique]]
* [[Using..Do]]
* [[Var..Do]]
* [[Variance]]
* [[VarTerm]]
* [[VectorCrossProduct]]
* [[Wacc]] (Financial Library.ana)
* [[Wald]] (Distribution Variations.ana)
* [[Warp_Dist]] (Distribution variations.ana)
* [[Weibull]]
* [[WhatIf]]
* [[WhatIfAll]]
* [[While..Do]]
* [[Wilcoxon]]
* [[Wishart]] (Distribution variations.ana)
* [[WorksheetCell]] -- deprecated: use [[SpreadsheetCell]]
* [[WorksheetRange]] -- deprecated: use [[SpreadsheetRange]]
* [[WriteBinaryFile]]
* [[WriteCsvFile]]
* [[WriteImageFile]]
* [[WriteTableSql]] (ODBC Library.ana)
* [[WriteTextFile]]
* [[WriteWorksheetCell]] -- deprecated: use [[SpreadsheetSetCell]]
* [[WriteWorksheetRange]] -- deprecated: use [[SpreadsheetSetRange]]
* [[XIrr]]
* [[XNpv]]
* [[YearFrac]]

BesselYzero

2021-06-10T00:15:13Z

Drice: Redirected page to Bessel Functions

#REDIRECT [[Bessel Functions]]

BesselJzero

2021-06-10T00:15:04Z

Drice: Redirected page to Bessel Functions

#REDIRECT [[Bessel Functions]]

Airy Bi zero

2021-06-10T00:14:32Z