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→‎{{header|Wren}}: Minor tidy
(→‎{{header|Fortran}}: Use gsl_cdf_chisq_Q, simplify code and enhance readability)
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;Task:
Write a function to verifydetermine thatwhether a given distributionset of valuesfrequency counts could plausibly have iscome from a uniform distribution by using the [[wp:Pearson's chi-square test|<math>\chi^2</math> test]] to see if the distribution haswith a likelihood of happening of at least the significance level (conventionallyof 5%).
 
The function should return a boolean that is true if and only if the distribution is one that a uniform distribution (with appropriate number of degrees of freedom) may be expected to produce.
 
Note: normally a two-tailed test would be used for this kind of problem.
 
;Reference:
:* &nbsp; an entry at the MathWorld website: &nbsp; [http://mathworld.wolfram.com/Chi-SquaredDistribution.html chi-squared distribution].
; Related task:
:* [[Statistics/Chi-squared_distribution]]
<br><br>
 
=={{header|11l}}==
{{trans|Python}}
 
<langsyntaxhighlight lang="11l">V a = 12
V k1_factrl = 1.0
[Float] c
Line 75 ⟶ 77:
V prob = chi2Probability(dof, distance)
print(‘probability: #.4’.format(prob), end' ‘ ’)
print(‘uniform? ’(I chi2IsUniform(ds, 0.05) {‘Yes’} E ‘No’))</langsyntaxhighlight>
 
{{out}}
Line 87 ⟶ 89:
=={{header|Ada}}==
First, we specify a simple package to compute the Chi-Square Distance from the uniform distribution:
<langsyntaxhighlight Adalang="ada">package Chi_Square is
type Flt is digits 18;
Line 94 ⟶ 96:
function Distance(Bins: Bins_Type) return Flt;
end Chi_Square;</langsyntaxhighlight>
 
Next, we implement that package:
 
<langsyntaxhighlight Adalang="ada">package body Chi_Square is
function Distance(Bins: Bins_Type) return Flt is
Line 124 ⟶ 126:
end Distance;
end Chi_Square;</langsyntaxhighlight>
 
Finally, we actually implement the Chi-square test. We do not actually compute the Chi-square probability; rather we hardcode a table of values for 5% significance level, which has been picked from Wikipedia [http://en.wikipedia.org/wiki/Chi-squared_distribution]:
<langsyntaxhighlight Adalang="ada">with Ada.Text_IO, Ada.Command_Line, Chi_Square; use Ada.Text_IO;
 
procedure Test_Chi_Square is
Line 154 ⟶ 156:
Put_Line("; (deviates significantly from uniform)");
end if;
end;</langsyntaxhighlight>
 
{{out}}
Line 165 ⟶ 167:
This first sections contains the functions required to compute the Chi-Squared probability.
These are not needed if a library containing the necessary function is availabile (e.g. see [[Numerical Integration]], [[Gamma function]]).
<langsyntaxhighlight lang="c">#include <stdlib.h>
#include <stdio.h>
#include <math.h>
Line 232 ⟶ 234:
 
return 1.0 - Simpson3_8( &f0, 0, y, (int)(y/h))/Gamma_Spouge(a);
}</langsyntaxhighlight>
This section contains the functions specific to the task.
<langsyntaxhighlight lang="c">double chi2UniformDistance( double *ds, int dslen)
{
double expected = 0.0;
Line 261 ⟶ 263:
double dist = chi2UniformDistance( dset, dslen);
return chi2Probability( dof, dist ) > significance;
}</langsyntaxhighlight>
Testing
<langsyntaxhighlight lang="c">int main(int argc, char **argv)
{
double dset1[] = { 199809., 200665., 199607., 200270., 199649. };
Line 287 ⟶ 289:
}
return 0;
}</langsyntaxhighlight>
 
=={{header|C#}}==
{{trans|Go}}
<syntaxhighlight lang="C#">
using System;
 
class Program
{
public delegate double Func(double x);
public static double Simpson38(Func f, double a, double b, int n)
{
double h = (b - a) / n;
double h1 = h / 3;
double sum = f(a) + f(b);
for (int j = 3 * n - 1; j > 0; j--)
{
if (j % 3 == 0)
{
sum += 2 * f(a + h1 * j);
}
else
{
sum += 3 * f(a + h1 * j);
}
}
 
return h * sum / 8;
}
 
// Lanczos Approximation for Gamma Function
private static double SpecialFunctionGamma(double z)
{
double[] p =
{
676.5203681218851,
-1259.1392167224028,
771.32342877765313,
-176.61502916214059,
12.507343278686905,
-0.13857109526572012,
9.9843695780195716e-6,
1.5056327351493116e-7
};
if (z < 0.5)
return Math.PI / (Math.Sin(Math.PI * z) * SpecialFunctionGamma(1 - z));
z -= 1;
double x = 0.99999999999980993;
for (int i = 0; i < p.Length; i++)
{
x += p[i] / (z + i + 1);
}
 
double t = z + p.Length - 0.5;
return Math.Sqrt(2 * Math.PI) * Math.Pow(t, z + 0.5) * Math.Exp(-t) * x;
}
 
public static double GammaIncQ(double a, double x)
{
double aa1 = a - 1;
Func f = t => Math.Pow(t, aa1) * Math.Exp(-t);
double y = aa1;
double h = 1.5e-2;
while (f(y) * (x - y) > 2e-8 && y < x)
{
y += .4;
}
 
if (y > x)
{
y = x;
}
 
return 1 - Simpson38(f, 0, y, (int)(y / h / SpecialFunctionGamma(a)));
}
 
public static double Chi2Ud(int[] ds)
{
double sum = 0, expected = 0;
foreach (var d in ds)
{
expected += d;
}
 
expected /= ds.Length;
foreach (var d in ds)
{
double x = d - expected;
sum += x * x;
}
 
return sum / expected;
}
 
public static double Chi2P(int dof, double distance)
{
return GammaIncQ(.5 * dof, .5 * distance);
}
 
const double SigLevel = .05;
static void Main(string[] args)
{
int[][] datasets = new int[][]
{
new int[]
{
199809,
200665,
199607,
200270,
199649
},
new int[]
{
522573,
244456,
139979,
71531,
21461
},
};
foreach (var dset in datasets)
{
UTest(dset);
}
}
 
static void UTest(int[] dset)
{
Console.WriteLine("Uniform distribution test");
int sum = 0;
foreach (var c in dset)
{
sum += c;
}
 
Console.WriteLine($" dataset: {string.Join(", ", dset)}");
Console.WriteLine($" samples: {sum}");
Console.WriteLine($" categories: {dset.Length}");
int dof = dset.Length - 1;
Console.WriteLine($" degrees of freedom: {dof}");
double dist = Chi2Ud(dset);
Console.WriteLine($" chi square test statistic: {dist}");
double p = Chi2P(dof, dist);
Console.WriteLine($" p-value of test statistic: {p}");
bool sig = p < SigLevel;
Console.WriteLine($" significant at {SigLevel * 100}% level? {sig}");
Console.WriteLine($" uniform? {!sig}\n");
}
}
</syntaxhighlight>
{{out}}
<pre>
Uniform distribution test
dataset: 199809, 200665, 199607, 200270, 199649
samples: 1000000
categories: 5
degrees of freedom: 4
chi square test statistic: 4.14628
p-value of test statistic: 0.386570833082767
significant at 5% level? False
uniform? True
 
Uniform distribution test
dataset: 522573, 244456, 139979, 71531, 21461
samples: 1000000
categories: 5
degrees of freedom: 4
chi square test statistic: 790063.27594
p-value of test statistic: 2.35282904270662E-11
significant at 5% level? True
uniform? False
 
 
</pre>
 
=={{header|C++}}==
<syntaxhighlight lang="c++">
 
#include <iostream>
#include <vector>
#include <cmath>
#include <iomanip>
 
void print_vector(const std::vector<int32_t>& list) {
std::cout << "[";
for ( uint64_t i = 0; i < list.size() - 1; ++i ) {
std::cout << list[i] << ", ";
}
std::cout << list.back() << "]" << std::endl;
}
 
bool is_significant(const double p_value, const double significance_level) {
return p_value > significance_level;
}
 
// The normalised lower incomplete gamma function.
double gamma_cdf(const double aX, const double aK) {
double result = 0.0;
for ( uint32_t m = 0; m <= 99; ++m ) {
result += pow(aX, m) / tgamma(aK + m + 1);
}
result *= pow(aX, aK) * exp(-aX);
return std::isnan(result) ? 1.0 : result;
}
 
// The cumulative probability function of the Chi-squared distribution.
double cdf(const double aX, const double aK) {
if ( aX > 1'000 && aK < 100 ) {
return 1.0;
}
return ( aX > 0.0 && aK > 0.0 ) ? gamma_cdf(aX / 2, aK / 2) : 0.0;
}
 
void chi_squared_test(const std::vector<int32_t>& observed) {
double sum = 0.0;
for ( uint64_t i = 0; i < observed.size(); ++i ) {
sum += observed[i];
}
const double expected = sum / observed.size();
 
const int32_t degree_freedom = observed.size() - 1;
 
double test_statistic = 0.0;
for ( uint64_t i = 0; i < observed.size(); ++i ) {
test_statistic += pow(observed[i] - expected, 2) / expected;
}
 
const double p_value = 1.0 - cdf(test_statistic, degree_freedom);
 
std::cout << "\nUniform distribution test" << std::setprecision(6) << std::endl;
std::cout << " observed values : "; print_vector(observed);
std::cout << " expected value : " << expected << std::endl;
std::cout << " degrees of freedom: " << degree_freedom << std::endl;
std::cout << " test statistic : " << test_statistic << std::endl;
std::cout.setf(std::ios::fixed);
std::cout << " p-value : " << p_value << std::endl;
std::cout.unsetf(std::ios::fixed);
std::cout << " is 5% significant?: " << std::boolalpha << is_significant(p_value, 0.05) << std::endl;
}
 
int main() {
const std::vector<std::vector<int32_t>> datasets = { { 199809, 200665, 199607, 200270, 199649 },
{ 522573, 244456, 139979, 71531, 21461 } };
for ( std::vector<int32_t> dataset : datasets ) {
chi_squared_test(dataset);
}
}
</syntaxhighlight>
{{ out }}
<pre>
 
Uniform distribution test
observed values : [199809, 200665, 199607, 200270, 199649]
expected value : 200000
degrees of freedom: 4
test statistic : 4.14628
p-value : 0.386571
is 5% significant?: true
 
Uniform distribution test
observed values : [522573, 244456, 139979, 71531, 21461]
expected value : 200000
degrees of freedom: 4
test statistic : 790063
p-value : 0.000000
is 5% significant?: false
</pre>
 
=={{header|D}}==
<langsyntaxhighlight lang="d">import std.stdio, std.algorithm, std.mathspecial;
 
real x2Dist(T)(in T[] data) pure nothrow @safe @nogc {
Line 319 ⟶ 588:
dof, dist, prob, ds.x2IsUniform ? "YES" : "NO", ds);
}
}</langsyntaxhighlight>
{{out}}
<pre> dof distance probability Uniform? dataset
Line 327 ⟶ 596:
=={{header|Elixir}}==
{{trans|Ruby}}
<langsyntaxhighlight lang="elixir">defmodule Verify do
defp gammaInc_Q(a, x) do
a1 = a-1
Line 389 ⟶ 658:
:io.fwrite " probability: ~.4f~n", [Verify.chi2Probability(dof, distance)]
:io.fwrite " uniform? ~s~n", [(if Verify.chi2IsUniform(ds), do: "Yes", else: "No")]
end)</langsyntaxhighlight>
 
{{out}}
Line 412 ⟶ 681:
Instead of implementing the chi-squared distribution by ourselves, we bind to GNU Scientific Library; so we need a module to interface to the function we need (<tt>gsl_cdf_chisq_Q</tt>)
 
<langsyntaxhighlight lang="fortran">module gsl_mini_bind_m
 
use iso_c_binding
Line 440 ⟶ 709:
end function p_value
 
end module gsl_mini_bind_m</langsyntaxhighlight>
 
Now we're ready to complete the task.
 
<langsyntaxhighlight lang="fortran">program chi2test
 
use gsl_mini_bind_m, only: p_value
Line 490 ⟶ 759:
end function chisq
 
end program chi2test</langsyntaxhighlight>
 
Output:
<syntaxhighlight lang="txt">Dataset 1: 199809.0000 200665.0000 199607.0000 200270.0000 199649.0000
dof: 4 chisq: 4.1463
probability: 0.3866
uniform? T
 
Dataset 2: 522573.0000 244456.0000 139979.0000 71531.0000 21461.0000
dof: 4 chisq: 790063.2500
probability: 0.0000
uniform? F</syntaxhighlight>
 
=={{header|Go}}==
{{trans|C}}
Go has a nice gamma function in the library. Otherwise, it's mostly a port from C. Note, this implementation of the incomplete gamma function works for these two test cases, but, I believe, has serious limitations. See talk page.
<langsyntaxhighlight lang="go">package main
 
import (
Line 584 ⟶ 864:
fmt.Printf(" significant at %2.0f%% level? %t\n", sigLevel*100, sig)
fmt.Println(" uniform? ", !sig, "\n")
}</langsyntaxhighlight>
Output:
<pre>
Line 609 ⟶ 889:
 
=={{header|Hy}}==
<langsyntaxhighlight lang="lisp">(import
[scipy.stats [chisquare]]
[collections [Counter]])
Line 619 ⟶ 899:
size 'alpha'."
(<= alpha (second (chisquare
(.values (Counter (take repeats (repeatedly f))))))))</langsyntaxhighlight>
 
Examples of use:
 
<langsyntaxhighlight lang="lisp">(import [random [randint]])
 
(for [f [
(fn [] (randint 1 10))
(fn [] (if (randint 0 1) (randint 1 9) (randint 1 10)))]]
(print (uniform? f 5000)))</langsyntaxhighlight>
 
=={{header|J}}==
'''Solution (Tacit):'''
<langsyntaxhighlight lang="j">require 'stats/base'
 
countCats=: #@~. NB. counts the number of unique items
Line 644 ⟶ 924:
NB. y is: distribution to test
NB. x is: optionally specify number of categories possible
isUniform=: (countCats $: ]) : (0.95 > calcDf chisqcdf :: 1: calcX2)</langsyntaxhighlight>
 
'''Solution (Explicit):'''
<langsyntaxhighlight lang="j">require 'stats/base'
 
NB.*isUniformX v Tests (5%) whether y is uniformly distributed
Line 662 ⟶ 942:
degfreedom=. <: x NB. degrees of freedom
signif > degfreedom chisqcdf :: 1: X2
)</langsyntaxhighlight>
 
'''Example Usage:'''
<langsyntaxhighlight lang="j"> FairDistrib=: 1e6 ?@$ 5
UnfairDistrib=: (9.5e5 ?@$ 5) , (5e4 ?@$ 4)
isUniformX FairDistrib
Line 674 ⟶ 954:
1
4 isUniform 4 4 4 5 5 5 5 5 5 5 NB. not uniform if 4 categories possible
0</langsyntaxhighlight>
 
=={{header|Java}}==
{{trans|D}}
{{works with|Java|8}}
<langsyntaxhighlight lang="java">import static java.lang.Math.pow;
import java.util.Arrays;
import static java.util.Arrays.stream;
Line 716 ⟶ 996:
}
}
}</langsyntaxhighlight>
<pre> dof distance probability Uniform? dataset
4 4,146 0,38657083 YES [199809.0, 200665.0, 199607.0, 200270.0, 199649.0]
4 790063,276 0,00000000 NO [522573.0, 244456.0, 139979.0, 71531.0, 21461.0]</pre>
 
=={{header|jq}}==
{{works with|jq}}
'''Also works with gojq, the Go implementation of jq.'''
 
This entry uses a two-tailed test, as is appropriate for this type of problem as illustrated
by the last example. The test is based on the assumption that the sample size is large
enough for the χ2 distribution to be used.
 
The implementation of `Chi2_cdf` here uses the recursion relation for
the gamma function and should be both fast, accurate and quite robust.
For an industrial-strength algorithm, see
e.g. https://people.sc.fsu.edu/~jburkardt/c_src/asa239/asa239.c
 
'''Generic Functions'''
<syntaxhighlight lang=jq>
def round($dec):
if type == "string" then .
else pow(10;$dec) as $m
| . * $m | floor / $m
end;
 
# sum of squares
def ss(s): reduce s as $x (0; . + ($x * $x));
 
# Cumulative density function of the chi-squared distribution with $k
# degrees of freedom
# The recursion formula for gamma is used for efficiency and robustness.
def Chi2_cdf($x; $k):
if $x == 0 then 0
elif $x > (1e3 * $k) then 1
else 1e-15 as $tol # for example
| { s: 0, m: 0, term: (1 / ((($k/2)+1)|gamma)) }
| until (.term|length < $tol; # length here is abs
.s += .term
| .m += 1
| .term *= (($x/2) / (($k/2) + .m )) )
| .s * ( ((-$x/2) + ($k/2)*(($x/2)|log)) | exp)
end ;
</syntaxhighlight>
'''Tasks'''
<syntaxhighlight lang=jq>
# Input: array of frequencies
def chi2UniformDistance:
(add / length) as $expected
| ss(.[] - $expected) / $expected;
 
# Input: a number
# Output: an indication of the probability of observing this value or higher
# assuming the value is drawn from a chi-squared distribution with $dof degrees
# of freedom
def chi2Probability($dof):
(1 - Chi2_cdf(.; $dof))
| if . < 1e-10 then "< 1e-10"
else .
end;
 
# Input: array of frequencies
# Output: result of a two-tailed test based on the chi-squared statistic
# assuming the sample size is large enough
def chiIsUniform($significance):
(length - 1) as $dof
| chi2UniformDistance
| Chi2_cdf(.; $dof) as $cdf
| if $cdf
then ($significance/2) as $s
| $cdf > $s and $cdf < (1-$s)
else false
end;
def dsets: [
[199809, 200665, 199607, 200270, 199649],
[522573, 244456, 139979, 71531, 21461],
[19,14,6,18,7,5,1], # low entropy
[9,11,9,10,15,11,5], # high entropy
[20,20,20] # made-up
];
 
def task:
dsets[]
| "Dataset: \(.)",
( chi2UniformDistance as $dist
| (length - 1) as $dof
| "DOF: \($dof) D (Distance): \($dist)",
" Estimated probability of observing a value >= D: \($dist|chi2Probability($dof)|round(2))",
" Uniform? \( (select(chiIsUniform(0.05)) | "Yes") // "No" )\n" ) ;
 
task
</syntaxhighlight>
<pre>
Dataset: [199809,200665,199607,200270,199649]
DOF: 4 D (Distance): 4.14628
Estimated probability of observing a value >= D: 0.38
Uniform? Yes
 
Dataset: [522573,244456,139979,71531,21461]
DOF: 4 D (Distance): 790063.27594
Estimated probability of observing a value >= D: < 1e-10
Uniform? No
 
Dataset: [19,14,6,18,7,5,1]
DOF: 6 D (Distance): 29.2
Estimated probability of observing a value >= D: 0
Uniform? No
 
Dataset: [9,11,9,10,15,11,5]
DOF: 6 D (Distance): 5.4
Estimated probability of observing a value >= D: 0.49
Uniform? Yes
 
Dataset: [20,20,20]
DOF: 2 D (Distance): 0
Estimated probability of observing a value >= D: 1
Uniform? No
</pre>
 
=={{header|Julia}}==
<langsyntaxhighlight lang="julia"># v0.6
 
using Distributions
Line 740 ⟶ 1,135:
println("Data:\n$data")
println("Hypothesis test: the original population is ", (eqdist(data) ? "" : "not "), "uniform.\n")
end</langsyntaxhighlight>
 
{{out}}
Line 754 ⟶ 1,149:
=={{header|Kotlin}}==
This program reuses Kotlin code from the [[Gamma function]] and [[Numerical Integration]] tasks but otherwise is a translation of the C entry for this task.
<langsyntaxhighlight lang="scala">// version 1.1.51
 
typealias Func = (Double) -> Double
Line 830 ⟶ 1,225:
println(" Uniform? $uniform\n")
}
}</langsyntaxhighlight>
 
{{out}}
Line 843 ⟶ 1,238:
=={{header|Mathematica}}/{{header|Wolfram Language}}==
This code explicity assumes a discrete uniform distribution since the chi square test is a poor test choice for continuous distributions and requires Mathematica version 2 or later
<langsyntaxhighlight Mathematicalang="mathematica">discreteUniformDistributionQ[data_, {min_Integer, max_Integer}, confLevel_: .05] :=
If[$VersionNumber >= 8,
confLevel <= PearsonChiSquareTest[data, DiscreteUniformDistribution[{min, max}]],
Line 850 ⟶ 1,245:
GammaRegularized[k/2, 0, v/2] <= 1 - confLevel]]
 
discreteUniformDistributionQ[data_] :=discreteUniformDistributionQ[data, data[[Ordering[data][[{1, -1}]]]]]</langsyntaxhighlight>
code used to create test data requires Mathematica version 6 or later
<langsyntaxhighlight Mathematicalang="mathematica">uniformData = RandomInteger[10, 100];
nonUniformData = Total@RandomInteger[10, {5, 100}];</langsyntaxhighlight>
<syntaxhighlight lang Mathematica="mathematica">{discreteUniformDistributionQ[uniformData],discreteUniformDistributionQ[nonUniformData]}</langsyntaxhighlight>
{{out}}<pre>{True,False}</pre>
 
Line 861 ⟶ 1,256:
We use the gamma function from the “math” module. To simplify the code, we use also the “lenientops” module which provides mixed operations between floats ane integers.
 
<langsyntaxhighlight Nimlang="nim">import lenientops, math, stats, strformat, sugar
 
func simpson38(f: (float) -> float; a, b: float; n: int): float =
Line 921 ⟶ 1,316:
for dset in [[199809, 200665, 199607, 200270, 199649],
[522573, 244456, 139979, 71531, 21461]]:
utest(dset)</langsyntaxhighlight>
 
{{out}}
Line 947 ⟶ 1,342:
This code needs to be compiled with library [http://oandrieu.nerim.net/ocaml/gsl/ gsl.cma].
 
<langsyntaxhighlight lang="ocaml">let sqr x = x *. x
 
let chi2UniformDistance distrib =
Line 980 ⟶ 1,375:
[| 199809; 200665; 199607; 200270; 199649 |];
[| 522573; 244456; 139979; 71531; 21461 |]
]</langsyntaxhighlight>
 
Output
Line 992 ⟶ 1,387:
 
The sample data for the test was taken from [[#Go|Go]].
<langsyntaxhighlight lang="parigp">cumChi2(chi2,dof)={
my(g=gamma(dof/2));
incgam(dof/2,chi2/2,g)/g
Line 1,008 ⟶ 1,403:
 
test([199809, 200665, 199607, 200270, 199649])
test([522573, 244456, 139979, 71531, 21461])</langsyntaxhighlight>
 
=={{header|Perl}}==
{{trans|Raku}}
<langsyntaxhighlight lang="perl">use List::Util qw(sum reduce);
use constant pi => 3.14159265;
 
Line 1,054 ⟶ 1,449:
for $dataset ([199809, 200665, 199607, 200270, 199649], [522573, 244456, 139979, 71531, 21461]) {
printf "C2 = %10.3f, p-value = %.3f, uniform = %s\n", chi_squared_test(@$dataset);
}</langsyntaxhighlight>
{{out}}
<pre>C2 = 4.146, p-value = 0.387, uniform = True
Line 1,061 ⟶ 1,456:
=={{header|Phix}}==
{{trans|Go}}
<!--<langsyntaxhighlight Phixlang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">aa1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">)</span>
Line 1,141 ⟶ 1,536:
<span style="color: #000000;">utest</span><span style="color: #0000FF;">({</span><span style="color: #000000;">199809</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">200665</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">199607</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">200270</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">199649</span><span style="color: #0000FF;">})</span>
<span style="color: #000000;">utest</span><span style="color: #0000FF;">({</span><span style="color: #000000;">522573</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">244456</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">139979</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">71531</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">21461</span><span style="color: #0000FF;">})</span>
<!--</langsyntaxhighlight>-->
{{out}}
<pre>
Line 1,169 ⟶ 1,564:
Implements the Chi Square Probability function with an integration. I'm
sure there are better ways to do this. Compare to OCaml implementation.
<langsyntaxhighlight lang="python">import math
import random
 
Line 1,235 ⟶ 1,630:
prob = chi2Probability( dof, distance)
print "probability: %.4f"%prob,
print "uniform? ", "Yes"if chi2IsUniform(ds,0.05) else "No"</langsyntaxhighlight>
Output:
<pre>Data set: [199809, 200665, 199607, 200270, 199649]
Line 1,245 ⟶ 1,640:
This uses the library routine [https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.chisquare.html scipy.stats.chisquare].
 
<langsyntaxhighlight lang="python">from scipy.stats import chisquare
 
 
Line 1,255 ⟶ 1,650:
dist, pvalue = chisquare(ds)
uni = 'YES' if pvalue > 0.05 else 'NO'
print(f"{dist:12.3f} {pvalue:12.8f} {uni:^8} {ds}")</langsyntaxhighlight>
 
{{out}}
Line 1,264 ⟶ 1,659:
=={{header|R}}==
R being a statistical computating language, the chi-squared test is built in with the function "chisq.test"
<langsyntaxhighlight lang="tcl">
dset1=c(199809,200665,199607,200270,199649)
dset2=c(522573,244456,139979,71531,21461)
Line 1,277 ⟶ 1,672:
print(paste("uniform?",chi2IsUniform(ds)))
}
</syntaxhighlight>
</lang>
 
Output:
Line 1,300 ⟶ 1,695:
 
=={{header|Racket}}==
<langsyntaxhighlight lang="racket">
#lang racket
(require
Line 1,341 ⟶ 1,736:
; Test whether the constant generator fails:
(is-uniform? (λ(_) 5) 1000 0.05)
</syntaxhighlight>
</lang>
Output:
<langsyntaxhighlight lang="racket">
#t
#f
</syntaxhighlight>
</lang>
 
=={{header|Raku}}==
Line 1,355 ⟶ 1,750:
in closed form, as we only need its value at integers and half integers.
 
<syntaxhighlight lang="raku" perl6line>sub incomplete-γ-series($s, $z) {
my \numers = $z X** 1..*;
my \denoms = [\*] $s X+ 1..*;
Line 1,395 ⟶ 1,790:
say 'data: ', $dataset;
say "χ² = {%t<chi-squared>}, p-value = {%t<p-value>.fmt('%.4f')}, uniform = {%t<uniform>}";
}</langsyntaxhighlight>
{{out}}
<pre>data: 199809 200665 199607 200270 199649
Line 1,414 ⟶ 1,809:
either an integer, &nbsp; or a number which is a multiple of &nbsp; <big>'''<sup>1</sup>/<sub>2</sub>'''</big>, &nbsp; both of these cases can be calculated with
<br>a straight─forward calculation.
<langsyntaxhighlight lang="rexx">/*REXX program performs a chi─squared test to verify a given distribution is uniform. */
numeric digits length( pi() ) - length(.) /*enough decimal digs for calculations.*/
@.=; @.1= 199809 200665 199607 200270 199649
Line 1,484 ⟶ 1,879:
say pad "significant at " sigPC'% level? ' word('no yes', sig + 1)
say pad " is the dataset uniform? " word('no yes', (\(sig))+ 1)
return</langsyntaxhighlight>
{{out|output|text=&nbsp; when using the default inputs:}}
<pre>
Line 1,506 ⟶ 1,901:
=={{header|Ruby}}==
{{trans|Python}}
<langsyntaxhighlight lang="ruby">def gammaInc_Q(a, x)
a1, a2 = a-1, a-2
f0 = lambda {|t| t**a1 * Math.exp(-t)}
Line 1,566 ⟶ 1,961:
puts " probability: %.4f" % chi2Probability(dof, distance)
puts " uniform? %s" % (chi2IsUniform(ds) ? "Yes" : "No")
end</langsyntaxhighlight>
 
{{out}}
Line 1,583 ⟶ 1,978:
 
=={{header|Rust}}==
<langsyntaxhighlight lang="rust">
use statrs::function::gamma::gamma_li;
 
Line 1,621 ⟶ 2,016:
}
 
</syntaxhighlight>
</lang>
{{out}}
<pre>
Line 1,635 ⟶ 2,030:
{{libheader|Scastie qualified}}
{{works with|Scala|2.13}}
<langsyntaxhighlight Scalalang="scala">import org.apache.commons.math3.special.Gamma.regularizedGammaQ
 
object ChiSquare extends App {
Line 1,664 ⟶ 2,059:
dof, dist, χ2Prob(dof.toDouble, dist), if (χ2IsUniform(ds, 0.05)) "YES" else "NO", ds.mkString(", "))
}
}</langsyntaxhighlight>
 
=={{header|Sidef}}==
<langsyntaxhighlight lang="ruby"># Confluent hypergeometric function of the first kind F_1(a;b;z)
func F1(a, b, z, limit=100) {
sum(0..limit, {|k|
Line 1,708 ⟶ 2,103:
say "data: #{dataset}"
say "χ² = #{r[0]}, p-value = #{r[1].round(-4)}, uniform = #{r[2]}\n"
}</langsyntaxhighlight>
{{out}}
<pre>
Line 1,721 ⟶ 2,116:
{{works with|Tcl|8.5}}
{{tcllib|math::statistics}}
<langsyntaxhighlight lang="tcl">package require Tcl 8.5
package require math::statistics
 
Line 1,735 ⟶ 2,130:
[expr {$degreesOfFreedom / 2.0}] [expr {$X2 / 2.0}]]
expr {$likelihoodOfRandom > $significance}
}</langsyntaxhighlight>
Testing:
<langsyntaxhighlight lang="tcl">proc makeDistribution {operation {count 1000000}} {
for {set i 0} {$i<$count} {incr i} {incr distribution([uplevel 1 $operation])}
return [array get distribution]
Line 1,745 ⟶ 2,140:
puts "distribution \"$distFair\" assessed as [expr [isUniform $distFair]?{fair}:{unfair}]"
set distUnfair [makeDistribution {expr int(rand()*rand()*5)}]
puts "distribution \"$distUnfair\" assessed as [expr [isUniform $distUnfair]?{fair}:{unfair}]"</langsyntaxhighlight>
Output:
<pre>distribution "0 199809 4 199649 1 200665 2 199607 3 200270" assessed as fair
Line 1,752 ⟶ 2,147:
=={{header|VBA}}==
The built in worksheetfunction ChiSq_Dist of Excel VBA is used. Output formatted like R.
<langsyntaxhighlight lang="vb">Private Function Test4DiscreteUniformDistribution(ObservationFrequencies() As Variant, Significance As Single) As Boolean
'Returns true if the observed frequencies pass the Pearson Chi-squared test at the required significance level.
Dim Total As Long, Ei As Long, i As Integer
Line 1,781 ⟶ 2,176:
O = [{522573,244456,139979,71531,21461}]
Debug.Print "[1] ""Uniform? "; Test4DiscreteUniformDistribution(O, 0.05); """"
End Sub</langsyntaxhighlight>
{{out}<pre>[1] "Data set:" 199809 200665 199607 200270 199649
Chi-squared test for given frequencies
Line 1,790 ⟶ 2,185:
X-squared = 790063.27594 , df = 4 , p-value = 0.0000
[1] "Uniform? False"</pre>
 
=={{header|V (Vlang)}}==
{{trans|Go}}
<syntaxhighlight lang="v (vlang)">import math
 
type Ifctn = fn(f64) f64
fn simpson38(f Ifctn, a f64, b f64, n int) f64 {
h := (b - a) / f64(n)
h1 := h / 3
mut sum := f(a) + f(b)
for j := 3*n - 1; j > 0; j-- {
if j%3 == 0 {
sum += 2 * f(a+h1*f64(j))
} else {
sum += 3 * f(a+h1*f64(j))
}
}
return h * sum / 8
}
fn gamma_inc_q(a f64, x f64) f64 {
aa1 := a - 1
f := Ifctn(fn[aa1](t f64) f64 {
return math.pow(t, aa1) * math.exp(-t)
})
mut y := aa1
h := 1.5e-2
for f(y)*(x-y) > 2e-8 && y < x {
y += .4
}
if y > x {
y = x
}
return 1 - simpson38(f, 0, y, int(y/h/math.gamma(a)))
}
fn chi2ud(ds []int) f64 {
mut sum, mut expected := 0.0,0.0
for d in ds {
expected += f64(d)
}
expected /= f64(ds.len)
for d in ds {
x := f64(d) - expected
sum += x * x
}
return sum / expected
}
fn chi2p(dof int, distance f64) f64 {
return gamma_inc_q(.5*f64(dof), .5*distance)
}
const sig_level = .05
fn main() {
for dset in [
[199809, 200665, 199607, 200270, 199649],
[522573, 244456, 139979, 71531, 21461],
] {
utest(dset)
}
}
fn utest(dset []int) {
println("Uniform distribution test")
mut sum := 0
for c in dset {
sum += c
}
println(" dataset: $dset")
println(" samples: $sum")
println(" categories: $dset.len")
dof := dset.len - 1
println(" degrees of freedom: $dof")
dist := chi2ud(dset)
println(" chi square test statistic: $dist")
p := chi2p(dof, dist)
println(" p-value of test statistic: $p")
sig := p < sig_level
println(" significant at ${sig_level*100:2.0f}% level? $sig")
println(" uniform? ${!sig}\n")
}</syntaxhighlight>
{{out}}
<pre>
Uniform distribution test
dataset: [199809 200665 199607 200270 199649]
samples: 1000000
categories: 5
degrees of freedom: 4
chi square test statistic: 4.14628
p-value of test statistic: 0.3865708330827673
significant at 5% level? false
uniform? true
 
Uniform distribution test
dataset: [522573 244456 139979 71531 21461]
samples: 1000000
categories: 5
degrees of freedom: 4
chi square test statistic: 790063.27594
p-value of test statistic: 2.3528290427066167e-11
significant at 5% level? true
uniform? false
</pre>
 
=={{header|Wren}}==
Line 1,795 ⟶ 2,300:
{{libheader|Wren-math}}
{{libheader|Wren-fmt}}
<langsyntaxhighlight ecmascriptlang="wren">import "./math" for Math, Nums
import "./fmt" for Fmt
 
var integrate = Fn.new { |a, b, n, f|
Line 1,845 ⟶ 2,350:
var uniform = chiIsUniform.call(ds, 0.05) ? "Yes" : "No"
System.print(" Uniform? %(uniform)\n")
}</langsyntaxhighlight>
 
{{out}}
Line 1,859 ⟶ 2,364:
{{trans|C}}
{{trans|D}}
<langsyntaxhighlight lang="zkl">/* Numerical integration method */
fcn Simpson3_8(f,a,b,N){ // fcn,double,double,Int --> double
h,h1:=(b - a)/N, h/3.0;
Line 1,895 ⟶ 2,400:
if(y>x) y=x;
1.0 - Simpson3_8(f,0.0,y,(y/h).toInt())/Gamma_Spouge(a);
}</langsyntaxhighlight>
<langsyntaxhighlight lang="zkl">fcn chi2UniformDistance(ds){ // --> double
dslen :=ds.len();
expected:=dslen.reduce('wrap(sum,k){ sum + ds[k] },0.0)/dslen;
Line 1,907 ⟶ 2,412:
fcn chiIsUniform(dset,significance=0.05){
significance < chi2Probability(-1.0 + dset.len(),chi2UniformDistance(dset))
}</langsyntaxhighlight>
<langsyntaxhighlight lang="zkl">datasets:=T( T(199809.0, 200665.0, 199607.0, 200270.0, 199649.0),
T(522573.0, 244456.0, 139979.0, 71531.0, 21461.0) );
println(" %4s %12s %12s %8s %s".fmt(
Line 1,919 ⟶ 2,424:
dof, dist, prob, chiIsUniform(ds) and "YES" or "NO",
ds.concat(",")));
}</langsyntaxhighlight>
{{out}}
<pre>
PureFox
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