Beta Class

Beta functions.

Inheritance Hierarchy

SystemObject
Accord.MathBeta

Namespace: Accord.Math
Assembly: Accord.Math (in Accord.Math.dll) Version: 3.8.0

Syntax

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public static class Beta

Public NotInheritable Class Beta

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The Beta type exposes the following members.

Methods

	Name	Description
	Function	Beta function as gamma(a) * gamma(b) / gamma(a+b).
	Incbcf	Continued fraction expansion #1 for incomplete beta integral.
	Incbd	Continued fraction expansion #2 for incomplete beta integral.
	Incomplete	Incomplete (regularized) Beta function Ix(a, b).
	IncompleteInverse	Inverse of incomplete beta integral.
	Log	Natural logarithm of the Beta function.
	Multinomial	Multinomial Beta function.
	PowerSeries	Power series for incomplete beta integral. Use when b*x is small and x not too close to 1.

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Remarks

This class offers implementations for the many Beta functions, such as the Beta function itself, its logarithm, the Incomplete(Double, Double, Double) incomplete regularized functions and others

The beta function was studied by Euler and Legendre and was given its name by Jacques Binet; its symbol Β is a Greek capital β rather than the similar Latin capital B.

References:

Cephes Math Library, http://www.netlib.org/cephes/
Wikipedia contributors, "Beta function,". Wikipedia, The Free Encyclopedia. Available at: http://en.wikipedia.org/wiki/Beta_function

Examples

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Beta.Function(4, 0.42);       // 1.2155480852832423
Beta.Log(4, 15.2);            // -9.46087817876467
Beta.Incbcf(4, 2, 4.2);       // -0.23046874999999992
Beta.Incbd(4, 2, 4.2);        // 0.7375
Beta.PowerSeries(4, 2, 4.2);  // -3671.801280000001

Beta.Incomplete(a: 5, b: 4, x: 0.5);   // 0.36328125
Beta.IncompleteInverse(0.5, 0.6, 0.1); // 0.019145979066925722
Beta.Multinomial(0.42, 0.5, 5.2 );     // 0.82641912952987062

Reference

Accord.Math Namespace