Apache Commons Math 3.6.1 · org.apache.commons.math3.special.Beta

Modifier and Type	Field and Description
private static final double	DEFAULT_EPSILON Maximum allowed numerical error.
private static final double[]	DELTA The coefficients of the series expansion of the Δ function.</center>
private static final double	HALF_LOG_TWO_PI The constant value of ½log 2π.

Access	Constructor and Description
private	Beta() Default constructor.

Method Summary

Modifier and Type	Method and Description
private static double	Returns: the value of `Delta(b) - Delta(a + b)` deltaMinusDeltaSum(final double First argument. a, final double Second argument. b) Returns the value of Δ(b) - Δ(a + b), with 0 ≤ a ≤ b and b ≥ 10.
public static double	Returns: log(B(a, b)). logBeta(double Parameter `a`. a, double Parameter `b`. b, double This parameter is ignored. epsilon, int This parameter is ignored. maxIterations) Deprecated as of version 3.1, this method is deprecated as the computation of the beta function is no longer iterative; it will be removed in version 4.0. Returns the natural logarithm of the beta function B(a, b).
public static double	Returns: the value of `log(Beta(p, q))`, `NaN` if `p <= 0` or `q <= 0`. logBeta(final double First argument. p, final double Second argument. q) Returns the value of log B(p, q) for 0 ≤ x ≤ 1 and p, q > 0.
private static double	Returns: the value of `log(Gamma(b) / Gamma(a + b))`. logGammaMinusLogGammaSum(final double First argument. a, final double Second argument. b) Returns the value of log[Γ(b) / Γ(a + b)] for a ≥ 0 and b ≥ 10.
private static double	Returns: the value of `log(Gamma(a + b))`. logGammaSum(final double First argument. a, final double Second argument. b) Returns the value of log Γ(a + b) for 1 ≤ a, b ≤ 2.
public static double	Returns: the regularized beta function I(x, a, b). regularizedBeta(double Value. x, double Parameter `a`. a, double Parameter `b`. b) Returns the regularized beta function I(x, a, b).
public static double	Returns: the regularized beta function I(x, a, b) regularizedBeta(double Value. x, double Parameter `a`. a, double Parameter `b`. b, double When the absolute value of the nth item in the series is less than epsilon the approximation ceases to calculate further elements in the series. epsilon) Returns the regularized beta function I(x, a, b).
public static double	Returns: the regularized beta function I(x, a, b) regularizedBeta(double the value. x, double Parameter `a`. a, double Parameter `b`. b, int Maximum number of "iterations" to complete. maxIterations) Returns the regularized beta function I(x, a, b).
public static double	Returns: the regularized beta function I(x, a, b) regularizedBeta(double the value. x, final double Parameter `a`. a, final double Parameter `b`. b, double When the absolute value of the nth item in the series is less than epsilon the approximation ceases to calculate further elements in the series. epsilon, int Maximum number of "iterations" to complete. maxIterations) Returns the regularized beta function I(x, a, b).
private static double	Returns: the value of `Delta(p) + Delta(q) - Delta(p + q)`. sumDeltaMinusDeltaSum(final double First argument. p, final double Second argument. q) Returns the value of Δ(p) + Δ(q) - Δ(p + q), with p, q ≥ 10.

Inherited from java.lang.Object:: clone equals finalize getClass hashCode notify notifyAll toString wait wait wait

DEFAULT_EPSILON	back to summary
private static final double DEFAULT_EPSILON Maximum allowed numerical error.

DELTA	back to summary
private static final double[] DELTA The coefficients of the series expansion of the Δ function. This function is defined as follows Δ(x) = log Γ(x) - (x - 0.5) log a + a - 0.5 log 2π, see equation (23) in Didonato and Morris (1992). The series expansion, which applies for x ≥ 10, reads 14 ==== 1 \ 2 n Δ(x) = --- > d (10 / x) x / n ==== n = 0

HALF_LOG_TWO_PI	back to summary
private static final double HALF_LOG_TWO_PI The constant value of ½log 2π.

Beta	back to summary
private Beta() Default constructor. Prohibit instantiation.

Method Detail

deltaMinusDeltaSum back to summary

deltaMinusDeltaSum	back to summary
private static double deltaMinusDeltaSum(final double a, final double b) throws OutOfRangeException, NumberIsTooSmallException Returns the value of Δ(b) - Δ(a + b), with 0 ≤ a ≤ b and b ≥ 10. Based on equations (26), (27) and (28) in Didonato and Morris (1992). Parameters a:double First argument. b:double Second argument. Returns:double the value of `Delta(b) - Delta(a + b)` Exceptions OutOfRangeException: if `a < 0` or `a > b` NumberIsTooSmallException: if `b < 10`

private static double deltaMinusDeltaSum(final double a, final double b) throws OutOfRangeException, NumberIsTooSmallException

Returns the value of Δ(b) - Δ(a + b), with 0 ≤ a ≤ b and b ≥ 10. Based on equations (26), (27) and (28) in Didonato and Morris (1992).

Parameters

a:double: First argument.
b:double: Second argument.

Returns:double

the value of Delta(b) - Delta(a + b)

Exceptions

OutOfRangeException:: if a < 0 or a > b
NumberIsTooSmallException:: if b < 10

logBeta back to summary

logBeta	back to summary
public static double logBeta(double a, double b, double epsilon, int maxIterations) Deprecated as of version 3.1, this method is deprecated as the computation of the beta function is no longer iterative; it will be removed in version 4.0. Current implementation of this method internally calls `logBeta(double, double)`. Returns the natural logarithm of the beta function B(a, b). The implementation of this method is based on: Beta Function, equation (1). Parameters a:double Parameter `a`. b:double Parameter `b`. epsilon:double This parameter is ignored. maxIterations:int This parameter is ignored. Returns:double log(B(a, b)). Annotations @Deprecated

public static double logBeta(double a, double b, double epsilon, int maxIterations)

Deprecated

as of version 3.1, this method is deprecated as the computation of the beta function is no longer iterative; it will be removed in version 4.0. Current implementation of this method internally calls logBeta(double, double).

Returns the natural logarithm of the beta function B(a, b). The implementation of this method is based on:

Beta Function, equation (1).

Parameters

a:double: Parameter a.
b:double: Parameter b.
epsilon:double: This parameter is ignored.
maxIterations:int: This parameter is ignored.

Returns:double

log(B(a, b)).

Annotations

@Deprecated

logBeta back to summary

logBeta	back to summary
public static double logBeta(final double p, final double q) Returns the value of log B(p, q) for 0 ≤ x ≤ 1 and p, q > 0. Based on the NSWC Library of Mathematics Subroutines implementation, `DBETLN`. Parameters p:double First argument. q:double Second argument. Returns:double the value of `log(Beta(p, q))`, `NaN` if `p <= 0` or `q <= 0`.

public static double logBeta(final double p, final double q)

Returns the value of log B(p, q) for 0 ≤ x ≤ 1 and p, q > 0. Based on the NSWC Library of Mathematics Subroutines implementation, DBETLN.

Parameters

p:double: First argument.
q:double: Second argument.

Returns:double

the value of log(Beta(p, q)), NaN if p <= 0 or q <= 0.

logGammaMinusLogGammaSum back to summary

logGammaMinusLogGammaSum	back to summary
private static double logGammaMinusLogGammaSum(final double a, final double b) throws NumberIsTooSmallException Returns the value of log[Γ(b) / Γ(a + b)] for a ≥ 0 and b ≥ 10. Based on the NSWC Library of Mathematics Subroutines double precision implementation, `DLGDIV`. In `BetaTest.testLogGammaMinusLogGammaSum()`, this private method is accessed through reflection. Parameters a:double First argument. b:double Second argument. Returns:double the value of `log(Gamma(b) / Gamma(a + b))`. Exceptions NumberIsTooSmallException: if `a < 0.0` or `b < 10.0`.

private static double logGammaMinusLogGammaSum(final double a, final double b) throws NumberIsTooSmallException

Returns the value of log[Γ(b) / Γ(a + b)] for a ≥ 0 and b ≥ 10. Based on the NSWC Library of Mathematics Subroutines double precision implementation, DLGDIV. In BetaTest.testLogGammaMinusLogGammaSum(), this private method is accessed through reflection.

Parameters

a:double: First argument.
b:double: Second argument.

Returns:double

the value of log(Gamma(b) / Gamma(a + b)).

Exceptions

NumberIsTooSmallException:: if a < 0.0 or b < 10.0.

logGammaSum back to summary

logGammaSum	back to summary
private static double logGammaSum(final double a, final double b) throws OutOfRangeException Returns the value of log Γ(a + b) for 1 ≤ a, b ≤ 2. Based on the NSWC Library of Mathematics Subroutines double precision implementation, `DGSMLN`. In `BetaTest.testLogGammaSum()`, this private method is accessed through reflection. Parameters a:double First argument. b:double Second argument. Returns:double the value of `log(Gamma(a + b))`. Exceptions OutOfRangeException: if `a` or `b` is lower than `1.0` or greater than `2.0`.

private static double logGammaSum(final double a, final double b) throws OutOfRangeException

Returns the value of log Γ(a + b) for 1 ≤ a, b ≤ 2. Based on the NSWC Library of Mathematics Subroutines double precision implementation, DGSMLN. In BetaTest.testLogGammaSum(), this private method is accessed through reflection.

Parameters

a:double: First argument.
b:double: Second argument.

Returns:double

the value of log(Gamma(a + b)).

Exceptions

OutOfRangeException:: if a or b is lower than 1.0 or greater than 2.0.

regularizedBeta back to summary

regularizedBeta	back to summary
public static double regularizedBeta(double x, double a, double b) Returns the regularized beta function I(x, a, b). Parameters x:double Value. a:double Parameter `a`. b:double Parameter `b`. Returns:double the regularized beta function I(x, a, b). Exceptions MaxCountExceededException: if the algorithm fails to converge.

public static double regularizedBeta(double x, double a, double b)

Returns the regularized beta function I(x, a, b).

Parameters

x:double: Value.
a:double: Parameter a.
b:double: Parameter b.

Returns:double

the regularized beta function I(x, a, b).

Exceptions

MaxCountExceededException:: if the algorithm fails to converge.

regularizedBeta back to summary

regularizedBeta	back to summary
public static double regularizedBeta(double x, double a, double b, double epsilon) Returns the regularized beta function I(x, a, b). Parameters x:double Value. a:double Parameter `a`. b:double Parameter `b`. epsilon:double When the absolute value of the nth item in the series is less than epsilon the approximation ceases to calculate further elements in the series. Returns:double the regularized beta function I(x, a, b) Exceptions MaxCountExceededException: if the algorithm fails to converge.

public static double regularizedBeta(double x, double a, double b, double epsilon)

Returns the regularized beta function I(x, a, b).

Parameters

x:double: Value.
a:double: Parameter a.
b:double: Parameter b.
epsilon:double: When the absolute value of the nth item in the series is less than epsilon the approximation ceases to calculate further elements in the series.

Returns:double

the regularized beta function I(x, a, b)

Exceptions

MaxCountExceededException:: if the algorithm fails to converge.

regularizedBeta back to summary

regularizedBeta	back to summary
public static double regularizedBeta(double x, double a, double b, int maxIterations) Returns the regularized beta function I(x, a, b). Parameters x:double the value. a:double Parameter `a`. b:double Parameter `b`. maxIterations:int Maximum number of "iterations" to complete. Returns:double the regularized beta function I(x, a, b) Exceptions MaxCountExceededException: if the algorithm fails to converge.

public static double regularizedBeta(double x, double a, double b, int maxIterations)

Returns the regularized beta function I(x, a, b).

Parameters

x:double: the value.
a:double: Parameter a.
b:double: Parameter b.
maxIterations:int: Maximum number of "iterations" to complete.

Returns:double

the regularized beta function I(x, a, b)

Exceptions

MaxCountExceededException:: if the algorithm fails to converge.

regularizedBeta back to summary

regularizedBeta	back to summary
public static double regularizedBeta(double x, final double a, final double b, double epsilon, int maxIterations) Returns the regularized beta function I(x, a, b). The implementation of this method is based on: Regularized Beta Function. Regularized Beta Function. Parameters x:double the value. a:double Parameter `a`. b:double Parameter `b`. epsilon:double When the absolute value of the nth item in the series is less than epsilon the approximation ceases to calculate further elements in the series. maxIterations:int Maximum number of "iterations" to complete. Returns:double the regularized beta function I(x, a, b) Exceptions MaxCountExceededException: if the algorithm fails to converge.

public static double regularizedBeta(double x, final double a, final double b, double epsilon, int maxIterations)

Returns the regularized beta function I(x, a, b). The implementation of this method is based on:

Parameters

x:double: the value.
a:double: Parameter a.
b:double: Parameter b.
epsilon:double: When the absolute value of the nth item in the series is less than epsilon the approximation ceases to calculate further elements in the series.
maxIterations:int: Maximum number of "iterations" to complete.

Returns:double

the regularized beta function I(x, a, b)

Exceptions

MaxCountExceededException:: if the algorithm fails to converge.

sumDeltaMinusDeltaSum back to summary

sumDeltaMinusDeltaSum	back to summary
private static double sumDeltaMinusDeltaSum(final double p, final double q) Returns the value of Δ(p) + Δ(q) - Δ(p + q), with p, q ≥ 10. Based on the NSWC Library of Mathematics Subroutines double precision implementation, `DBCORR`. In `BetaTest.testSumDeltaMinusDeltaSum()`, this private method is accessed through reflection. Parameters p:double First argument. q:double Second argument. Returns:double the value of `Delta(p) + Delta(q) - Delta(p + q)`. Exceptions NumberIsTooSmallException: if `p < 10.0` or `q < 10.0`.

private static double sumDeltaMinusDeltaSum(final double p, final double q)

Returns the value of Δ(p) + Δ(q) - Δ(p + q), with p, q ≥ 10. Based on the NSWC Library of Mathematics Subroutines double precision implementation, DBCORR. In BetaTest.testSumDeltaMinusDeltaSum(), this private method is accessed through reflection.

Parameters

p:double: First argument.
q:double: Second argument.

Returns:double

the value of Delta(p) + Delta(q) - Delta(p + q).

Exceptions

NumberIsTooSmallException:: if p < 10.0 or q < 10.0.

public Class Beta

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