## Class IncompleteBeta

• public final class IncompleteBeta
extends Object
Incomplete Beta function.

$B_x(a,b) = \int_0^x t^{a-1}\,(1-t)^{b-1}\,dt$

This code has been adapted from the Boost c++ implementation <boost/math/special_functions/beta.hpp>.

Since:
1.1
See Also:
Boost C++ Incomplete Beta functions
• ### Method Summary

All Methods
Modifier and Type Method Description
static double complement​(double x, double a, double b)
Computes the complement of the incomplete beta function B(x, a, b).
static double complement​(double x, double a, double b, double epsilon, int maxIterations)
Computes the complement of the incomplete beta function B(x, a, b).
static double value​(double x, double a, double b)
Computes the value of the incomplete beta function B(x, a, b).
static double value​(double x, double a, double b, double epsilon, int maxIterations)
Computes the value of the incomplete beta function B(x, a, b).
• ### Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
• ### Method Detail

• #### value

public static double value​(double x,
double a,
double b)
Computes the value of the incomplete beta function B(x, a, b).

$B_x(a,b) = \int_0^x t^{a-1}\,(1-t)^{b-1}\,dt$

Parameters:
x - Value.
a - Parameter a.
b - Parameter b.
Returns:
the incomplete beta function $$B_x(a, b)$$.
Throws:
ArithmeticException - if the series evaluation fails to converge.
• #### value

public static double value​(double x,
double a,
double b,
double epsilon,
int maxIterations)
Computes the value of the incomplete beta function B(x, a, b).

$B_x(a,b) = \int_0^x t^{a-1}\,(1-t)^{b-1}\,dt$

Parameters:
x - the value.
a - Parameter a.
b - Parameter b.
epsilon - Tolerance in series evaluation.
maxIterations - Maximum number of iterations in series evaluation.
Returns:
the incomplete beta function $$B_x(a, b)$$.
Throws:
ArithmeticException - if the series evaluation fails to converge.
• #### complement

public static double complement​(double x,
double a,
double b)
Computes the complement of the incomplete beta function B(x, a, b).

$B(a, b) - B_x(a,b) = B_{1-x}(b, a)$

where $$B(a, b)$$ is the beta function.

Parameters:
x - Value.
a - Parameter a.
b - Parameter b.
Returns:
the complement of the incomplete beta function $$B(a, b) - B_x(a, b)$$.
Throws:
ArithmeticException - if the series evaluation fails to converge.
• #### complement

public static double complement​(double x,
double a,
double b,
double epsilon,
int maxIterations)
Computes the complement of the incomplete beta function B(x, a, b).

$B(a, b) - B_x(a,b) = B_{1-x}(b, a)$

where $$B(a, b)$$ is the beta function.

Parameters:
x - the value.
a - Parameter a.
b - Parameter b.
epsilon - Tolerance in series evaluation.
maxIterations - Maximum number of iterations in series evaluation.
Returns:
the complement of the incomplete beta function $$B(a, b) - B_x(a, b)$$.
Throws:
ArithmeticException - if the series evaluation fails to converge.