Package org.apache.commons.numbers.gamma
Class IncompleteBeta
java.lang.Object
org.apache.commons.numbers.gamma.IncompleteBeta
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:
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Constructor Summary
Constructors -
Method Summary
Modifier and TypeMethodDescriptionstatic 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).
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Constructor Details
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IncompleteBeta
private IncompleteBeta()Private constructor.
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Method Details
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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
- Parametera
.b
- Parameterb
.- Returns:
- the incomplete beta function \( B_x(a, b) \).
- Throws:
ArithmeticException
- if the series evaluation fails to converge.
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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
- Parametera
.b
- Parameterb
.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.
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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
- Parametera
.b
- Parameterb
.- Returns:
- the complement of the incomplete beta function \( B(a, b) - B_x(a, b) \).
- Throws:
ArithmeticException
- if the series evaluation fails to converge.
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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
- Parametera
.b
- Parameterb
.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.
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