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java.lang.Objectcern.colt.PersistentObject
cern.jet.random.AbstractDistribution
cern.jet.random.AbstractContinousDistribution
cern.jet.random.Gamma
Gamma distribution; math definition, definition of gamma function and animated definition.
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.
| Field Summary | 
| Fields inherited from class cern.colt.PersistentObject | 
| serialVersionUID | 
| Constructor Summary | |
| Gamma(double alpha,
      double lambda,
      RandomEngine randomGenerator)Constructs a Gamma distribution. | |
| Method Summary | |
|  double | cdf(double x)Returns the cumulative distribution function. | 
|  double | nextDouble()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. | 
| static double | staticNextDouble(double alpha,
                 double lambda)Returns a random number from the distribution. | 
|  String | toString()Returns a String representation of the receiver. | 
| Methods inherited from class cern.jet.random.AbstractDistribution | 
| apply, apply, clone, makeDefaultGenerator, nextInt | 
| Methods inherited from class java.lang.Object | 
| equals, getClass, hashCode, notify, notifyAll, wait, wait, wait | 
| Constructor Detail | 
public Gamma(double alpha,
             double lambda,
             RandomEngine randomGenerator)
IllegalArgumentException - if alpha <= 0.0 || lambda <= 0.0.| Method Detail | 
public double cdf(double x)
public double nextDouble()
nextDouble in class AbstractDistribution
public double nextDouble(double alpha,
                         double lambda)
public double pdf(double x)
public void setState(double alpha,
                     double lambda)
IllegalArgumentException - if alpha <= 0.0 || lambda <= 0.0.
public static double staticNextDouble(double alpha,
                                      double lambda)
IllegalArgumentException - if alpha <= 0.0 || lambda <= 0.0.public String toString()
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