This UDF provides functionality for statistical hypothesis testing, descriptive sample statistics, propability distributions and numerical mathematics:

• probability distributions (probality density, cumulative density and quantile function) for:
  • continuous uniform distribution
  • gaussian normal distribution (also standard normal distribution) + random number generation
  • F-distribution
  • Student-t-distribution
  • Beta-distribution
  • Chi²-distribution
  • Kolmogorov-Smirnov distribution
• statistical hypothesis tests:
  • one sample Kolmogorov-Smirnov-test
  • Lilliefors-Test
  • unpaired two sample student's t-test
  • unpaired two sample Welch-test
  • F-test for variance equality
  • Wilcoxon-Mann-Whitney-Test
  • combined test with condition check for these tests
• descriptive statistics:
  • arithmetic mean, modal value, median
  • standard deviation, average deviation, standard error of mean, variance, skewness, curtosis
  • minima, maxima, range, sum, length
  • quantiles
  • ranks
  • histogram
• numerical mathematics:
  • single parameter function solver and root finding
  • single parameter integration
• basic funtions:
  • Gamma-function (gamma, log-gamma, inverse gamma, incomplete gamma)
  • Gauss error function, complementary Gauss error function, inverse complementary Gauss error function
  • Beta-function (beta, incomplete beta, regularized incomplete beta, inversed regularized incomplete beta
  • inverse of x * log(x)

What can you do with it?
Well, you could for example check if the AutoIt-Random function really returns evenly distributed values:

statistical test if AutoIt-Random produces uniformly distributed values

#include "Stat.au3"

; create AutoIt sample data
    Local Const $N = 1e3
    Local $a_Sample[1e3]
    Local $lower = 0, $upper = 100
    For $i = 0 To $N -1
        $a_Sample[$i] = Random($lower, $upper)
    Next

; Test for uniform distribution:
    Local $a_Params = ["CallArgArray", 0, $lower, $upper]
    $a_Ret = _stat_test_KS($a_Sample, 0.05, _stat_uniform_cdf, $a_Params)
    _ArrayDisplay($a_Ret, "Is Random() uniformly distributed?")
    MsgBox(0, "Is Random() uniformly distributed?", ($a_Ret[5][1] ? "Random is uniformly distributed" : "Random is NOT uniformly distributed"))

Or you can check whether two samples have the same mean value (with normal distribution) or the same central tendency.
The function automatically checks the respective prerequisites for the internal tests:

test if two samples have equal values on average

#include "Stat.au3"

; Test whether two samples have the same mean values (with normal distribution) or central tendencies.
    Local $a_Sample1[1000], $a_Sample2[1000]
    For $i = 0 To 999
    ; generates normally distributed samples (for t- and Welch-test)
        $a_Sample1[$i] = _stat_norm_ran(100, 5)
        $a_Sample2[$i] = _stat_norm_ran(99.0, 4.5)
    ; generates non-normally distributed samples (for Wilcoxon blablabla test)
        ;  $a_Sample1[$i] = Random(0,100)
        ;  $a_Sample2[$i] = Random(10,90)
    Next

    $a_Results = _stat_test_SampleEquality($a_Sample1, $a_Sample2)
    _ArrayDisplay($a_Results, "test results")
    MsgBox(0, "", $a_Results[4][1] ? "Samples have equal values on average" : "Samples have different values on average")

; ========== Test pattern of _stat_test_SampleEquality =============
;   If both samples are normally distributed (Lilliefors test):
;       If variances are equal (F-test):
;            t-test
;       else:
;            Welch-Test
;   else:
;       Wilcoxon-Mann-Whitney-Test