Add function to Math UDF

[tim292stro]

I'd like to get a function added to the Math UDF, Standard Deviation. This function is usefull in determining in a set of values are well distributed within a bathtub plot. I've already written it and an example:

The Function:

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; #FUNCTION# ====================================================================================================================
; Name...........: _StandardDeviation()
; Description ...: Returns the standard deviation for all entries in an array
; Syntax.........: _StandardDeviation( $ArrayVariable )
; Parameters ....: $ArrayVariable = The array variable to calculate Standard Deviation for
; Return values .: On Success: = Sets @Error and Returns the Standard Deviation for the array variable's entries
;                  On Failure: = Sets @Error and Returns -1
;                  @ERROR:     = 0 = No error.
;                                -1 = The variable passed was not an array
; Author ........: "tim292stro" Tim Strommen <tim292stro at yahoo.com dot com>
; Remarks .......: Array must be 1 based, entry 0 in the array should be the count of the array elements
; Example .......: MsgBox ( 0, "Standard Deviation of $SomeArrayVariable:", _StandardDeviation ( $SomeArrayVariable ) )
; ===============================================================================================================================
Func _StandardDeviation ( $StandardDevArray = "" )
    Local $SDAveLoop = 0
    Local $SDAveVal = 0
    Local $SDDeviationArray[1] = [0]
    Local $DevArrayPopLoop = 0
    Local $SDCalc = 0
    If IsArray ( $StandardDevArray ) Then
        For $SDAveLoop = 1 To $StandardDevArray[0]
            $SDAveVal = $SDAveVal + $StandardDevArray[$SDAveLoop]
        Next
        $SDAveVal = $SDAveVal / $StandardDevArray[0]
        For $DevArrayPopLoop = 1 To $StandardDevArray[0]
            _ArrayAdd ( $SDDeviationArray, ( $StandardDevArray[$DevArrayPopLoop] - $SDAveVal )^2 )
            $SDDeviationArray[0] = $SDDeviationArray[0] + 1
        Next
        $SDAveVal = 0
        For $SDCalc = 1 To $SDDeviationArray[0]
            $SDAveVal = $SDAveVal + $SDDeviationArray[$SDCalc]
        Next
        @error = 0
        Return ( $SDAveVal / ( $SDDeviationArray[0] - 1 ) )
    Else
        @error = -1
        Return -1
    EndIf
EndFunc

And an example:

#include-once
#include <array.au3>
Global $SomeArrayVariable[25] = [24,34,35,35,34,33,33,33,34,34,33,35,34,34,35,34,33,33,32,33,31,32,33,33,32]

MsgBox ( 0, "Standard Deviation of $SomeArrayVariable:", _StandardDeviation ( $SomeArrayVariable ) )

For those who haven't used a standard deviation before, it is more or less a way of evaluating how good a data set is. There are plenty of websites describing the use of this function - just google "Standard Deviation".

Best,

-Tim

Edited March 2, 2010 by tim292stro

[jchd]

That's nice to have but I believe it belongs to a Statistics UDF rather than the (basic) Maths UDF.

There might be a need for classical functions of statistical analysis (mean, median, variance, quantile, multivariate stuf, usual distributions and their related functions, non-linear fit, data smoothing, inter- & extrapolation, ...) but I find they should be set apart. Not because they stink, simply because then there would be no good reason not to include as well matrix & tensor calculus, number theoretic stuff, and endless [interesting] functions as well. Mere users needing only Floor or Sqrt would see useless bloat in their scripts just by including <Maths.au3>.

[andybiochem]

You should specify that your function assumes a population sample in the array and applies Bessel's Correction as a default. Otherwise, your function will return the incorrect standard deviation if the array contains the entire population, especially at low degrees of freedom.