Difference between revisions of "Mid"

Latest revision as of 18:08, 18 July 2017

Mid(x)

Evaluates «x» in Mid-Mode, i.e. deterministically.

Whenever an expression or subexpression is evaluated, it is evaluated either in Mid-mode or Sample-mode, in which sample-mode carries through information about uncertainty whereas mid-mode does not. The article on Evaluation Modes explains this in detail. Mid(x) forces the evaluation of «x» to occur in Mid-mode even when the current evaluation mode is sample-mode.

The Sample function does the opposite -- forcing «x» to be evaluated in sample mode.

Distribution functions return their median value in Mid-mode, or a Monte Carlo when evaluated in Sample-mode.

Mid is also used as an meta-expression in a MultiTable to show the computed value of «x».

Examples

Suppose x := Uniform(-1, 1)^2

Mid(x) → 0

Median(x) → 0.25

Mean(x) → 0.3333

When Mid is evaluated, the median value of Uniform(-1, 1) is used, which is 0 and is then squared to get the mid-value of x. As seen, this is not equivalent to the median of x when uncertainty is properly accounted for.

@@ Line 1: / Line 1: @@
 [[category:Evaluation Functions]]
 [[category:Statistical Functions]]
-[[Category:Doc Status C]] <!-- For Lumina use, do not change -->
-==Mid(X)==
+==Mid(x)==
-Evaluates «X» in [[Evaluation Modes|Mid-Mode]].
+Evaluates «x» in [[Evaluation Modes|Mid-Mode]], i.e. deterministically.
+Whenever an expression or subexpression is evaluated, it is evaluated either in ''Mid-mode'' or ''Sample-mode'', in which sample-mode carries through information about uncertainty whereas mid-mode does not. The article on [[Evaluation Modes]] explains this in detail. [[Mid]](x) forces the evaluation of «x» to occur in Mid-mode even when the current evaluation mode is sample-mode.
+The [[Sample]] function does the opposite -- forcing «x» to be evaluated in sample mode.
+Distribution functions return their [[median]] value in Mid-mode, or a Monte Carlo when evaluated in Sample-mode.
+[[Mid]] is also used as an ''meta-expression'' in a [[MultiTable]] to show the computed value of «x».
+== Examples ==
+Suppose <code>x := Uniform(-1, 1)^2</code>
+:<code>Mid(x) &rarr; 0</code>
+:<code>Median(x) &rarr; 0.25</code>
+:<code>Mean(x) &rarr; 0.3333</code>
+When [[Mid]] is evaluated, the median value of <code>Uniform(-1, 1)</code> is used, which is 0 and is then squared to get the mid-value of <code>x</code>. As seen, this is not equivalent to the median of <code>x</code> when uncertainty is properly accounted for.
 == See Also ==
 * [[Evaluation Modes]]
+* [[Median]]
+* [[Mean]]
 * [[Sample]]
 * [[Random]]
+* [[Uniform]]
 * [[Function Parameter Qualifiers]]