ChiDistribution Class

[SerializableAttribute]
public class ChiDistribution : ContinuousDistribution

<SerializableAttribute>
Public Class ChiDistribution
	Inherits ContinuousDistribution

[SerializableAttribute]
public ref class ChiDistribution : public ContinuousDistribution

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

Inheritance

Object  →  Distribution  →  ContinuousDistribution  →  ChiDistribution

The chi distribution is a continuous probability distribution. It describes the distribution of the square root of the sum of the squares of n independent normal variables with zero mean and unit variance. The parameter n is known as the degrees of freedom.

The chi distribution is used in various statistical applications, including hypothesis testing and confidence interval estimation. It is particularly useful in the context of the chi-square test, where the chi distribution describes the distribution of the standard deviation of samples taken from a normal distribution.

The chi distribution is closely related to the chi-square distribution. If X has a chi distribution, then X² has a chi-square distribution with the same degrees of freedom.

Two special cases of the chi distribution are worth noting. The Rayleigh distribution is a chi distribution with two degrees of freedom. The Maxwell distribution is a chi distribution with three degrees of freedom.

Example

using System;
using Numerics.NET.Statistics.Distributions;

// Create a chi distribution with 3 degrees of freedom
var chiDist = new ChiDistribution(3);

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

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

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

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

Reference