ChiSquareGoodnessOfFitTest Class

public sealed class ChiSquareGoodnessOfFitTest : OneSampleTest<double>

Public NotInheritable Class ChiSquareGoodnessOfFitTest
	Inherits OneSampleTest(Of Double)

public ref class ChiSquareGoodnessOfFitTest sealed : public OneSampleTest<double>

[<SealedAttribute>]
type ChiSquareGoodnessOfFitTest = 
    class
        inherit OneSampleTest<float>
    end

Inheritance

Object  →  HypothesisTest  →  OneSampleTest<Double>  →  ChiSquareGoodnessOfFitTest

Use the ChiSquareGoodnessOfFitTest class to test whether a sample comes from a specific distribution. The null hypothesis is that the sample comes from the specified distribution. The test statistic follows a chi-square distribution.

The sample can be supplied as either a vector or a categorical vector.

The distribution can be specified as a probability distribution (a class that inherits from Distribution) or a vector. The distribution can be discrete or continuous.

If the sample and distribution are both supplied as a vector, the boundaries must be identical.

A chi-square test uses binned data. A drawback is that the results of the test depend on how the data is binned. The test also needs a sufficient sample size for the chi-square approximation to be valid.

The AndersonDarlingTest and OneSampleKolmogorovSmirnovTest tests are alternatives to the chi-square goodness-of-fit test, but they are valid only for continuous distributions.

The following example demonstrates how to use the ChiSquareGoodnessOfFitTest class to perform a chi-square goodness-of-fit test.

using Numerics.NET;
using Numerics.NET.Statistics;
using Numerics.NET.Statistics.Distributions;
using Numerics.NET.Statistics.Tests;

// Example 1: Using a sample vector and a distribution
Vector<double> sample = [1.0, 2.0, 3.0, 4.0, 5.0];
Distribution distribution = new NormalDistribution(3.0, 1.0);
ChiSquareGoodnessOfFitTest test1 = new ChiSquareGoodnessOfFitTest(sample, distribution);
double statistic1 = test1.CalculateStatistic();
Console.WriteLine($"Test Statistic: {statistic1}");
Console.WriteLine($"Degrees of Freedom: {test1.DegreesOfFreedom}");
Console.WriteLine($"P-Value: {test1.GetPValue(HypothesisType.OneTailedUpper)}");

// Example 2: Using a categorical vector and an expected vector
Vector<int> sample = [1, 2, 3, 1, 2, 1, 1, 1, 1, 3, 3, 1, 2, 3, 3, 2];
var categoricalSample = sample.AsCategorical();
Vector<double> expected = [4.0, 4.0, 8.0];
ChiSquareGoodnessOfFitTest test2 = new ChiSquareGoodnessOfFitTest(categoricalSample, expected);
double statistic2 = test2.CalculateStatistic();
Console.WriteLine($"Test Statistic: {statistic2}");
Console.WriteLine($"Degrees of Freedom: {test2.DegreesOfFreedom}");
Console.WriteLine($"P-Value: {test2.GetPValue(HypothesisType.OneTailedUpper)}");

Reference