View source for ProbDist - Custom continuous distribution using density points

[[category:Continuous distributions]]
[[category:Bounded distributions]]
[[category:Univariate distributions]]
[[category:Custom distributions]]
[[Category:Doc Status D]] <!-- For Lumina use, do not change -->

Use these functions to specify a custom continuous probability distribution by specifying probability density points at selected values.

To use, you need to specify (p_i, r_i) points, where «p_i» is an array of relative non-negative densities indexed by «<code>I</code>» and «r_i» is an increasing array of values, also indexed by «<code>I</code>». The values in «p_i» are relative -- the function normalizes them so that the area under the distribution adds to 1. 

It produces a density function using linear interpolation between the specified points on the density function.

Usually the first and last values in «p_i» are zero.  If not, it extrapolates out for a distance equal to the spacing between the first two points (or last two points) before reaching zero.

The index parameter «<code>I</code>» can be omitted if either «p_i» or «r_i» is itself an index (in which case the other is an array indexed by that).

== Functions ==
=== ProbDist(p_i, r_i'', I, over'') ===
The distribution function. Use this to specify a quantity that has your custom distribution. 

If you want to define independent and identically distributed quantities along one or more indexes, list those indexes in the optional «over» parameter.

=== <div id="DensProbDist">DensProbDist( x, p_i, r_i'', I, over'')</div> ===
''New to [[Analytica 5.2]]''

The analytic density function. Computes the probability density at «x» according to your custom distribution, after any normalization has been applied.

=== <div id="CumProbDist">CumProbDist( x, p_i, r_i'', I, over'')</div> ===
''New to [[Analytica 5.2]]''
The analytic cumulative density function. Computes the probability that a random outcome is less than or equal to «x».

=== <div id="CumProbDistInv">CumProbDistInv( p, p_i, r_i'', I, over'')</div> ===
''New to [[Analytica 5.2]]''
The analytic inverse cumulative density function (aka ''quantile function''). Computes the «p»<sup>th</sup> fractile/quartile/percentile.

== See Also ==
* [[CumDist]]
* [[ProbTable]]
* [[ChanceDist]] -- the discrete distribution analog.
* [[Keelin distribution]] 
* [[Custom continuous distributions]]
* [[Distribution Densities Library]]