Package org.apache.commons.numbers.gamma
Class RegularizedGamma.Q
java.lang.Object
org.apache.commons.numbers.gamma.RegularizedGamma.Q
- Enclosing class:
RegularizedGamma
Upper regularized Gamma function \( Q(a, x) \).
\[ Q(a,x) = 1 - P(a,x) = \frac{\Gamma(a,x)}{\Gamma(a)} = \frac{1}{\Gamma(a)} \int_x^{\infty} t^{a-1}\,e^{-t}\,dt \]
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Constructor Summary
Constructors -
Method Summary
Modifier and TypeMethodDescriptionstatic double
derivative
(double a, double x) Computes the derivative of the upper regularized gamma function \( Q(a, x) \).static double
value
(double a, double x) Computes the upper regularized gamma function \( Q(a, x) \).static double
value
(double a, double x, double epsilon, int maxIterations) Computes the upper regularized gamma function \( Q(a, x) \).
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Constructor Details
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Q
private Q()Prevent instantiation.
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Method Details
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value
public static double value(double a, double x) Computes the upper regularized gamma function \( Q(a, x) \).- Parameters:
a
- Argument.x
- Argument.- Returns:
- \( Q(a, x) \).
- Throws:
ArithmeticException
- if the series evaluation fails to converge.
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value
public static double value(double a, double x, double epsilon, int maxIterations) Computes the upper regularized gamma function \( Q(a, x) \).- Parameters:
a
- Argument.x
- Argument.epsilon
- Tolerance in series evaluation.maxIterations
- Maximum number of iterations in series evaluation.- Returns:
- \( Q(a, x) \).
- Throws:
ArithmeticException
- if the series evaluation fails to converge.
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derivative
public static double derivative(double a, double x) Computes the derivative of the upper regularized gamma function \( Q(a, x) \).\[ \frac{\delta}{\delta x} Q(a,x) = -\frac{e^{-x} x^{a-1}}{\Gamma(a)} \]
This function has uses in some statistical distributions.
- Parameters:
a
- Argument.x
- Argument.- Returns:
- derivative of \( Q(a,x) \) with respect to x.
- Since:
- 1.1
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