Package sim.util.distribution
Class Gamma
java.lang.Object
sim.util.distribution.AbstractDistribution
sim.util.distribution.AbstractContinuousDistribution
sim.util.distribution.Gamma
- All Implemented Interfaces:
Serializable
Gamma distribution; math definition,
definition of gamma function
and animated definition.
Static methods operate on a default uniform random number generator; they are synchronized.
Method: Acceptance Rejection combined with Acceptance Complement.
High performance implementation. This is a port of RandGamma used in CLHEP 1.4.0 (C++).
CLHEP's implementation, in turn, is based on gds.c from the C-RAND / WIN-RAND library.
C-RAND's implementation, in turn, is based upon
p(x) = k * x^(alpha-1) * e^(-x/beta) with k = 1/(g(alpha) * b^a)) and g(a) being the gamma function.
Valid parameter ranges: alpha > 0.
Note: For a Gamma distribution to have the mean mean and variance variance, set the parameters as follows:
alpha = mean*mean / variance; lambda = 1 / (variance / mean);
Instance methods operate on a user supplied uniform random number generator; they are unsynchronized.
Implementation:
J.H. Ahrens, U. Dieter (1974): Computer methods for sampling from gamma, beta, Poisson and binomial distributions, Computing 12, 223-246.
and
J.H. Ahrens, U. Dieter (1982): Generating gamma variates by a modified rejection technique, Communications of the ACM 25, 47-54.
- See Also:
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Field Summary
Fields inherited from class sim.util.distribution.AbstractDistribution
randomGenerator
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Constructor Summary
ConstructorDescriptionGamma
(double alpha, double lambda, MersenneTwisterFast randomGenerator) Constructs a Gamma distribution. -
Method Summary
Modifier and TypeMethodDescriptiondouble
cdf
(double x) Returns the cumulative distribution function.double
Returns a random number from the distribution.double
nextDouble
(double alpha, double lambda) Returns a random number from the distribution; bypasses the internal state.double
pdf
(double x) Returns the probability distribution function.void
setState
(double alpha, double lambda) Sets the mean and variance.toString()
Returns a String representation of the receiver.Methods inherited from class sim.util.distribution.AbstractDistribution
apply, apply, getRandomGenerator, nextInt, setRandomGenerator
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Field Details
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alpha
protected double alpha -
lambda
protected double lambda
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Constructor Details
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Gamma
Constructs a Gamma distribution. Example: alpha=1.0, lambda=1.0.- Throws:
IllegalArgumentException
- if alpha <= 0.0 || lambda <= 0.0.
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Method Details
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cdf
public double cdf(double x) Returns the cumulative distribution function. -
nextDouble
public double nextDouble()Returns a random number from the distribution.- Specified by:
nextDouble
in classAbstractDistribution
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nextDouble
public double nextDouble(double alpha, double lambda) Returns a random number from the distribution; bypasses the internal state. -
pdf
public double pdf(double x) Returns the probability distribution function. -
setState
public void setState(double alpha, double lambda) Sets the mean and variance.- Throws:
IllegalArgumentException
- if alpha <= 0.0 || lambda <= 0.0.
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toString
Returns a String representation of the receiver.
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