ArcsineDistribution Class

public class ArcsineDistribution : ContinuousDistribution

Public Class ArcsineDistribution
	Inherits ContinuousDistribution

public ref class ArcsineDistribution : public ContinuousDistribution

type ArcsineDistribution = 
    class
        inherit ContinuousDistribution
    end

Inheritance

Object  →  Distribution  →  ContinuousDistribution  →  ArcsineDistribution

The arcsine distribution is a probability distribution for a random variable whose probability density function is proportional to the reciprocal of the square root of the product of the variable and one minus the variable.

This distribution is a special case of the beta distribution with parameters (1/2, 1/2). It is used in various fields such as physics, finance, and engineering to model phenomena with bounded support.

In particular, the arcsine distribution is related to the beta distribution and can be used to model the distribution of the fraction of time a Brownian motion spends above zero.

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

// Distribution parameters
var dist = new ArcsineDistribution(0.0, 1.0);
Console.WriteLine($"Lower Bound: {dist.LowerBound}");
Console.WriteLine($"Upper Bound: {dist.UpperBound}");

// Functions
double pdf = dist.ProbabilityDensityFunction(0.5);
double cdf = dist.DistributionFunction(0.5);
double invCdf = dist.InverseDistributionFunction(0.5);
Console.WriteLine($"PDF at 0.5: {pdf}");
Console.WriteLine($"CDF at 0.5: {cdf}");
Console.WriteLine($"Inverse CDF at 0.5: {invCdf}");

// Moments
Console.WriteLine($"Mean: {dist.Mean}");
Console.WriteLine($"Variance: {dist.Variance}");
Console.WriteLine($"Skewness: {dist.Skewness}");
Console.WriteLine($"Kurtosis: {dist.Kurtosis}");

// Other properties
Console.WriteLine($"Is Symmetrical: {dist.IsSymmetrical}");
Console.WriteLine($"Entropy: {dist.Entropy}");
Console.WriteLine($"Mode: {dist.Mode}");
Console.WriteLine($"Number of Modes: {dist.NumberOfModes}");
Console.WriteLine($"Support: {dist.Support}");

This example demonstrates how to create an instance of the ArcsineDistribution class, access its parameters, and use its methods to compute the probability density function, cumulative distribution function, and inverse cumulative distribution function. It also shows how to retrieve various statistical moments and properties of the distribution.

Reference