org.apache.commons.math3.distribution
Class GammaDistribution

java.lang.Object
  extended by org.apache.commons.math3.distribution.AbstractRealDistribution
      extended by org.apache.commons.math3.distribution.GammaDistribution
All Implemented Interfaces:
Serializable, RealDistribution

public class GammaDistribution
extends AbstractRealDistribution

Implementation of the Gamma distribution.

Version:
$Id: GammaDistribution.java 1244107 2012-02-14 16:17:55Z erans $
See Also:
Gamma distribution (Wikipedia), Gamma distribution (MathWorld), Serialized Form

Field Summary
private  double alpha
          The shape parameter.
private  double beta
          The scale parameter.
static double DEFAULT_INVERSE_ABSOLUTE_ACCURACY
          Default inverse cumulative probability accuracy.
private static long serialVersionUID
          Serializable version identifier.
private  double solverAbsoluteAccuracy
          Inverse cumulative probability accuracy.
 
Fields inherited from class org.apache.commons.math3.distribution.AbstractRealDistribution
randomData, SOLVER_DEFAULT_ABSOLUTE_ACCURACY
 
Constructor Summary
GammaDistribution(double alpha, double beta)
          Create a new gamma distribution with the given alpha and beta values.
GammaDistribution(double alpha, double beta, double inverseCumAccuracy)
          Create a new gamma distribution with the given alpha and beta values.
 
Method Summary
 double cumulativeProbability(double x)
          For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x).
 double density(double x)
          Returns the probability density function (PDF) of this distribution evaluated at the specified point x.
 double getAlpha()
          Access the alpha shape parameter.
 double getBeta()
          Access the beta scale parameter.
 double getNumericalMean()
          Use this method to get the numerical value of the mean of this distribution.
 double getNumericalVariance()
          Use this method to get the numerical value of the variance of this distribution.
protected  double getSolverAbsoluteAccuracy()
          Returns the solver absolute accuracy for inverse cumulative computation.
 double getSupportLowerBound()
          Access the lower bound of the support.
 double getSupportUpperBound()
          Access the upper bound of the support.
 boolean isSupportConnected()
          Use this method to get information about whether the support is connected, i.e.
 boolean isSupportLowerBoundInclusive()
          Use this method to get information about whether the lower bound of the support is inclusive or not.
 boolean isSupportUpperBoundInclusive()
          Use this method to get information about whether the upper bound of the support is inclusive or not.
 double probability(double x)
          For a random variable X whose values are distributed according to this distribution, this method returns P(X = x).
 
Methods inherited from class org.apache.commons.math3.distribution.AbstractRealDistribution
cumulativeProbability, inverseCumulativeProbability, reseedRandomGenerator, sample, sample
 
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Field Detail

DEFAULT_INVERSE_ABSOLUTE_ACCURACY

public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY
Default inverse cumulative probability accuracy.

Since:
2.1
See Also:
Constant Field Values

serialVersionUID

private static final long serialVersionUID
Serializable version identifier.

See Also:
Constant Field Values

alpha

private final double alpha
The shape parameter.


beta

private final double beta
The scale parameter.


solverAbsoluteAccuracy

private final double solverAbsoluteAccuracy
Inverse cumulative probability accuracy.

Constructor Detail

GammaDistribution

public GammaDistribution(double alpha,
                         double beta)
Create a new gamma distribution with the given alpha and beta values.

Parameters:
alpha - the shape parameter.
beta - the scale parameter.

GammaDistribution

public GammaDistribution(double alpha,
                         double beta,
                         double inverseCumAccuracy)
                  throws NotStrictlyPositiveException
Create a new gamma distribution with the given alpha and beta values.

Parameters:
alpha - Shape parameter.
beta - Scale parameter.
inverseCumAccuracy - Maximum absolute error in inverse cumulative probability estimates (defaults to DEFAULT_INVERSE_ABSOLUTE_ACCURACY).
Throws:
NotStrictlyPositiveException - if alpha <= 0 or beta <= 0.
Since:
2.1
Method Detail

getAlpha

public double getAlpha()
Access the alpha shape parameter.

Returns:
alpha.

getBeta

public double getBeta()
Access the beta scale parameter.

Returns:
beta.

probability

public double probability(double x)
For a random variable X whose values are distributed according to this distribution, this method returns P(X = x). In other words, this method represents the probability mass function (PMF) for the distribution. For this distribution P(X = x) always evaluates to 0.

Parameters:
x - the point at which the PMF is evaluated
Returns:
0

density

public double density(double x)
Returns the probability density function (PDF) of this distribution evaluated at the specified point x. In general, the PDF is the derivative of the CDF. If the derivative does not exist at x, then an appropriate replacement should be returned, e.g. Double.POSITIVE_INFINITY, Double.NaN, or the limit inferior or limit superior of the difference quotient.

Parameters:
x - the point at which the PDF is evaluated
Returns:
the value of the probability density function at point x

cumulativeProbability

public double cumulativeProbability(double x)
For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x). In other words, this method represents the (cumulative) distribution function (CDF) for this distribution. The implementation of this method is based on:

Parameters:
x - the point at which the CDF is evaluated
Returns:
the probability that a random variable with this distribution takes a value less than or equal to x

getSolverAbsoluteAccuracy

protected double getSolverAbsoluteAccuracy()
Returns the solver absolute accuracy for inverse cumulative computation. You can override this method in order to use a Brent solver with an absolute accuracy different from the default.

Overrides:
getSolverAbsoluteAccuracy in class AbstractRealDistribution
Returns:
the maximum absolute error in inverse cumulative probability estimates

getNumericalMean

public double getNumericalMean()
Use this method to get the numerical value of the mean of this distribution. For shape parameter alpha and scale parameter beta, the mean is alpha * beta.

Returns:
the mean or Double.NaN if it is not defined

getNumericalVariance

public double getNumericalVariance()
Use this method to get the numerical value of the variance of this distribution. For shape parameter alpha and scale parameter beta, the variance is alpha * beta^2.

Returns:
the variance (possibly Double.POSITIVE_INFINITY as for certain cases in TDistribution) or Double.NaN if it is not defined

getSupportLowerBound

public double getSupportLowerBound()
Access the lower bound of the support. This method must return the same value as inverseCumulativeProbability(0). In other words, this method must return

inf {x in R | P(X <= x) > 0}.

The lower bound of the support is always 0 no matter the parameters.

Returns:
lower bound of the support (always 0)

getSupportUpperBound

public double getSupportUpperBound()
Access the upper bound of the support. This method must return the same value as inverseCumulativeProbability(1). In other words, this method must return

inf {x in R | P(X <= x) = 1}.

The upper bound of the support is always positive infinity no matter the parameters.

Returns:
upper bound of the support (always Double.POSITIVE_INFINITY)

isSupportLowerBoundInclusive

public boolean isSupportLowerBoundInclusive()
Use this method to get information about whether the lower bound of the support is inclusive or not.

Returns:
whether the lower bound of the support is inclusive or not

isSupportUpperBoundInclusive

public boolean isSupportUpperBoundInclusive()
Use this method to get information about whether the upper bound of the support is inclusive or not.

Returns:
whether the upper bound of the support is inclusive or not

isSupportConnected

public boolean isSupportConnected()
Use this method to get information about whether the support is connected, i.e. whether all values between the lower and upper bound of the support are included in the support. The support of this distribution is connected.

Returns:
true


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