Package cern.jet.stat
Class Gamma
java.lang.Object
cern.jet.math.Constants
cern.jet.stat.Gamma
Gamma and Beta functions.
Some code taken and adapted from the Java 2D Graph Package 2.4,
which in turn is a port from the Cephes 2.2 Math Library (C).
Most Cephes code (missing from the 2D Graph Package) directly ported.
Implementation:
- Version:
- 0.9, 22-Jun-99
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Field Summary
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Constructor Summary
ConstructorsModifierConstructorDescriptionprotected
Gamma()
Makes this class non instantiable, but still let's others inherit from it. -
Method Summary
Modifier and TypeMethodDescriptionstatic double
beta
(double a, double b) Returns the beta function of the arguments.static double
gamma
(double x) Returns the Gamma function of the argument.static double
incompleteBeta
(double aa, double bb, double xx) Returns the Incomplete Beta Function evaluated from zero to xx; formerly named ibeta.(package private) static double
incompleteBetaFraction1
(double a, double b, double x) Continued fraction expansion #1 for incomplete beta integral; formerly named incbcf.(package private) static double
incompleteBetaFraction2
(double a, double b, double x) Continued fraction expansion #2 for incomplete beta integral; formerly named incbd.static double
incompleteGamma
(double a, double x) Returns the Incomplete Gamma function; formerly named igamma.static double
incompleteGammaComplement
(double a, double x) Returns the Complemented Incomplete Gamma function; formerly named igamc.static double
logGamma
(double x) Returns the natural logarithm of the gamma function; formerly named lgamma.(package private) static double
powerSeries
(double a, double b, double x) Power series for incomplete beta integral; formerly named pseries.(package private) static double
stirlingFormula
(double x) Returns the Gamma function computed by Stirling's formula; formerly named stirf.
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Constructor Details
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Gamma
protected Gamma()Makes this class non instantiable, but still let's others inherit from it.
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Method Details
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beta
Returns the beta function of the arguments.- - | (a) | (b) beta( a, b ) = -----------. - | (a+b)
- Throws:
ArithmeticException
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gamma
Returns the Gamma function of the argument.- Throws:
ArithmeticException
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incompleteBeta
Returns the Incomplete Beta Function evaluated from zero to xx; formerly named ibeta.- Parameters:
aa
- the alpha parameter of the beta distribution.bb
- the beta parameter of the beta distribution.xx
- the integration end point.- Throws:
ArithmeticException
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incompleteBetaFraction1
Continued fraction expansion #1 for incomplete beta integral; formerly named incbcf.- Throws:
ArithmeticException
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incompleteBetaFraction2
Continued fraction expansion #2 for incomplete beta integral; formerly named incbd.- Throws:
ArithmeticException
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incompleteGamma
Returns the Incomplete Gamma function; formerly named igamma.- Parameters:
a
- the parameter of the gamma distribution.x
- the integration end point.- Throws:
ArithmeticException
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incompleteGammaComplement
Returns the Complemented Incomplete Gamma function; formerly named igamc.- Parameters:
a
- the parameter of the gamma distribution.x
- the integration start point.- Throws:
ArithmeticException
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logGamma
Returns the natural logarithm of the gamma function; formerly named lgamma.- Throws:
ArithmeticException
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powerSeries
Power series for incomplete beta integral; formerly named pseries. Use when b*x is small and x not too close to 1.- Throws:
ArithmeticException
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stirlingFormula
Returns the Gamma function computed by Stirling's formula; formerly named stirf. The polynomial STIR is valid for 33 invalid input: '<'= x invalid input: '<'= 172.- Throws:
ArithmeticException
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