ChiSquareDistribution Class

[SerializableAttribute]
public class ChiSquareDistribution : ContinuousDistribution

<SerializableAttribute>
Public Class ChiSquareDistribution
	Inherits ContinuousDistribution

[SerializableAttribute]
public ref class ChiSquareDistribution : public ContinuousDistribution

[<SerializableAttribute>]
type ChiSquareDistribution = 
    class
        inherit ContinuousDistribution
    end

Inheritance

Object  →  Distribution  →  ContinuousDistribution  →  ChiSquareDistribution

The chi-squared distribution is a continuous probability distribution that is widely used in statistical significance testing. It is defined by the degrees of freedom parameter, which is typically a positive integer.

The sum of the squares of n independent normal variables with zero mean and unit variance has a chi-squared distribution with n degrees of freedom. This means it also describes the Variance of samples taken from a normal distribution.

From this last property, we can see the usefulness of the chi-squared distribution as a test of statistical significance. We can determine the likelihood of obtaining a sample that deviates from the expected value by a specified amount.

The sum of two or more variables that have a chi-squared distribution also has a chi-squared distribution. The number of degrees of freedom of the new distribution equals the sum of the degrees of freedom of the original distributions.

Applications of the chi-squared distribution include hypothesis testing, particularly the chi-squared test for independence and the chi-squared test for goodness of fit.

This example demonstrates creating a chi-squared distribution with 3 degrees of freedom, and then using its properties and methods to compute and display various values.

// Example of using the ChiSquareDistribution class
using System;
using Numerics.NET.Statistics.Distributions;

// Create a chi-squared distribution with 3 degrees of freedom
var chiSquare = new ChiSquareDistribution(3);

// Distribution parameters
Console.WriteLine($"Degrees of Freedom: {chiSquare.DegreesOfFreedom}");

// Distribution functions
double x = 2.0;
Console.WriteLine($"CDF at x={x}: {chiSquare.DistributionFunction(x)}");
Console.WriteLine($"PDF at x={x}: {chiSquare.ProbabilityDensityFunction(x)}");

// Moments
Console.WriteLine($"Mean: {chiSquare.Mean}");
Console.WriteLine($"Variance: {chiSquare.Variance}");

// Other properties
Console.WriteLine($"Mode: {chiSquare.Mode}");
Console.WriteLine($"Support: {chiSquare.Support}");

Reference