Verify distribution uniformity/Chi-squared test: Difference between revisions
Verify distribution uniformity/Chi-squared test (view source)
Revision as of 10:29, 16 February 2024
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return 0;
}</syntaxhighlight>
=={{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++}}==
Line 2,126 ⟶ 2,300:
{{libheader|Wren-math}}
{{libheader|Wren-fmt}}
<syntaxhighlight lang="
import "./fmt" for Fmt
var integrate = Fn.new { |a, b, n, f|
| |||