gov.sandia.cognition.statistics.distribution
Class GammaDistribution

java.lang.Object
  extended by gov.sandia.cognition.util.AbstractCloneableSerializable
      extended by gov.sandia.cognition.statistics.AbstractDistribution<NumberType>
          extended by gov.sandia.cognition.statistics.AbstractClosedFormUnivariateDistribution<Double>
              extended by gov.sandia.cognition.statistics.AbstractClosedFormSmoothUnivariateDistribution
                  extended by gov.sandia.cognition.statistics.distribution.GammaDistribution
All Implemented Interfaces:
Vectorizable, ClosedFormComputableDistribution<Double>, ClosedFormDistribution<Double>, ClosedFormUnivariateDistribution<Double>, ComputableDistribution<Double>, Distribution<Double>, DistributionWithMean<Double>, EstimableDistribution<Double,GammaDistribution>, SmoothUnivariateDistribution, UnivariateDistribution<Double>, CloneableSerializable, Serializable, Cloneable
Direct Known Subclasses:
GammaDistribution.CDF, GammaDistribution.PDF

@PublicationReference(author="Wikipedia",
                      title="Gamma distribution",
                      type=WebPage,
                      year=2009,
                      url="http://en.wikipedia.org/wiki/Gamma_distribution")
public class GammaDistribution
extends AbstractClosedFormSmoothUnivariateDistribution
implements EstimableDistribution<Double,GammaDistribution>

Class representing the Gamma distribution. This is a two-parameter family of continuous distributions. The well-known exponential and chi-square distributions are special cases of the Gamma distribution. Please note that we use the "shape" and "scale" parameters to describe the PDF/CDF, whereas octave/MATLAB use "shape" and "1.0/scale" to parameterize a Gamma distribution, so please beware when comparing results to octave/MATLAB.

Since:
2.0
Author:
Kevin R. Dixon
See Also:
Serialized Form

Nested Class Summary
static class GammaDistribution.CDF
          CDF of the Gamma distribution
static class GammaDistribution.MomentMatchingEstimator
          Computes the parameters of a Gamma distribution by the Method of Moments
static class GammaDistribution.PDF
          Closed-form PDF of the Gamma distribution
static class GammaDistribution.WeightedMomentMatchingEstimator
          Estimates the parameters of a Gamma distribution using the matching of moments, not maximum likelihood.
 
Field Summary
static double DEFAULT_SCALE
          Default scale, 1.0.
static double DEFAULT_SHAPE
          Default shape, 1.0.
 
Constructor Summary
GammaDistribution()
          Default constructor.
GammaDistribution(double shape, double scale)
          Creates a new instance of GammaDistribution
GammaDistribution(GammaDistribution other)
          Copy constructor
 
Method Summary
 GammaDistribution clone()
          This makes public the clone method on the Object class and removes the exception that it throws.
 void convertFromVector(Vector parameters)
          Sets the parameters of the distribution
 Vector convertToVector()
          Gets the parameters of the distribution
 GammaDistribution.CDF getCDF()
          Gets the CDF of a scalar distribution.
 GammaDistribution.MomentMatchingEstimator getEstimator()
          Gets an estimator associated with this distribution.
 Double getMaxSupport()
          Gets the minimum support (domain or input) of the distribution.
 Double getMean()
          Gets the arithmetic mean, or "first central moment" or "expectation", of the distribution.
 Double getMinSupport()
          Gets the minimum support (domain or input) of the distribution.
 GammaDistribution.PDF getProbabilityFunction()
          Gets the distribution function associated with this Distribution, either the PDF or PMF.
 double getScale()
          Getter for scale
 double getShape()
          Getter for shape
 double getVariance()
          Gets the variance of the distribution.
static ArrayList<Double> sample(double shape, double scale, Random random, int numSamples)
          Efficiently samples from a Gamma distribution given by the shape and scale parameters.
 ArrayList<Double> sample(Random random, int numSamples)
          Draws multiple random samples from the distribution.
 void setScale(double scale)
          Setter for scale
 void setShape(double shape)
          Setter for shape
 String toString()
           
 
Methods inherited from class gov.sandia.cognition.statistics.AbstractDistribution
sample
 
Methods inherited from class java.lang.Object
equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait
 
Methods inherited from interface gov.sandia.cognition.statistics.Distribution
sample
 

Field Detail

DEFAULT_SHAPE

public static final double DEFAULT_SHAPE
Default shape, 1.0.

See Also:
Constant Field Values

DEFAULT_SCALE

public static final double DEFAULT_SCALE
Default scale, 1.0.

See Also:
Constant Field Values
Constructor Detail

GammaDistribution

public GammaDistribution()
Default constructor.


GammaDistribution

public GammaDistribution(double shape,
                         double scale)
Creates a new instance of GammaDistribution

Parameters:
shape - Shape parameter of the Gamma distribution, often written as "k", must be greater than zero
scale - Scale parameters of the Gamma distribution, often written as "theta", must be greater than zero. Note that this is the INVERSE of what octave uses!!

GammaDistribution

public GammaDistribution(GammaDistribution other)
Copy constructor

Parameters:
other - GammaDistribution to copy
Method Detail

clone

public GammaDistribution clone()
Description copied from class: AbstractCloneableSerializable
This makes public the clone method on the Object class and removes the exception that it throws. Its default behavior is to automatically create a clone of the exact type of object that the clone is called on and to copy all primitives but to keep all references, which means it is a shallow copy. Extensions of this class may want to override this method (but call super.clone() to implement a "smart copy". That is, to target the most common use case for creating a copy of the object. Because of the default behavior being a shallow copy, extending classes only need to handle fields that need to have a deeper copy (or those that need to be reset). Some of the methods in ObjectUtil may be helpful in implementing a custom clone method. Note: The contract of this method is that you must use super.clone() as the basis for your implementation.

Specified by:
clone in interface Vectorizable
Specified by:
clone in interface CloneableSerializable
Overrides:
clone in class AbstractClosedFormUnivariateDistribution<Double>
Returns:
A clone of this object.

getShape

public double getShape()
Getter for shape

Returns:
Shape parameter of the Gamma distribution, often written as "k", must be greater than zero

setShape

public void setShape(double shape)
Setter for shape

Parameters:
shape - Shape parameter of the Gamma distribution, often written as "k", must be greater than zero

getScale

public double getScale()
Getter for scale

Returns:
Scale parameters of the Gamma distribution, often written as "theta", must be greater than zero. Note that this is the INVERSE of what octave uses!!

setScale

public void setScale(double scale)
Setter for scale

Parameters:
scale - Scale parameters of the Gamma distribution, often written as "theta", must be greater than zero. Note that this is the INVERSE of what octave uses!!

getMean

public Double getMean()
Description copied from interface: DistributionWithMean
Gets the arithmetic mean, or "first central moment" or "expectation", of the distribution.

Specified by:
getMean in interface DistributionWithMean<Double>
Specified by:
getMean in interface SmoothUnivariateDistribution
Returns:
Mean of the distribution.

getVariance

public double getVariance()
Description copied from interface: UnivariateDistribution
Gets the variance of the distribution. This is sometimes called the second central moment by more pedantic people, which is equivalent to the square of the standard deviation.

Specified by:
getVariance in interface UnivariateDistribution<Double>
Returns:
Variance of the distribution.

convertToVector

public Vector convertToVector()
Gets the parameters of the distribution

Specified by:
convertToVector in interface Vectorizable
Returns:
2-dimensional Vector with (shape scale)

convertFromVector

public void convertFromVector(Vector parameters)
Sets the parameters of the distribution

Specified by:
convertFromVector in interface Vectorizable
Parameters:
parameters - 2-dimensional Vector with (shape scale)

sample

public static ArrayList<Double> sample(double shape,
                                       double scale,
                                       Random random,
                                       int numSamples)
Efficiently samples from a Gamma distribution given by the shape and scale parameters.

Parameters:
shape - Shape parameter of the Gamma distribution, often written as "k", must be greater than zero
scale - Scale parameters of the Gamma distribution, often written as "theta", must be greater than zero. Note that this is the INVERSE of what octave uses!!
random - Random number generator
numSamples - Number of samples to generate
Returns:
Samples simulated from the Gamma distribution.

sample

public ArrayList<Double> sample(Random random,
                                int numSamples)
Description copied from interface: Distribution
Draws multiple random samples from the distribution. It is generally more efficient to use this multiple-sample method than multiple calls of the single-sample method. (But not always.)

Specified by:
sample in interface Distribution<Double>
Parameters:
random - Random-number generator to use in order to generate random numbers.
numSamples - Number of samples to draw from the distribution.
Returns:
Samples drawn according to this distribution.

getCDF

public GammaDistribution.CDF getCDF()
Description copied from interface: UnivariateDistribution
Gets the CDF of a scalar distribution.

Specified by:
getCDF in interface ClosedFormUnivariateDistribution<Double>
Specified by:
getCDF in interface SmoothUnivariateDistribution
Specified by:
getCDF in interface UnivariateDistribution<Double>
Returns:
CDF of the scalar distribution.

getProbabilityFunction

public GammaDistribution.PDF getProbabilityFunction()
Description copied from interface: ComputableDistribution
Gets the distribution function associated with this Distribution, either the PDF or PMF.

Specified by:
getProbabilityFunction in interface ComputableDistribution<Double>
Specified by:
getProbabilityFunction in interface SmoothUnivariateDistribution
Returns:
Distribution function associated with this Distribution.

toString

public String toString()
Overrides:
toString in class Object

getMinSupport

public Double getMinSupport()
Description copied from interface: UnivariateDistribution
Gets the minimum support (domain or input) of the distribution.

Specified by:
getMinSupport in interface UnivariateDistribution<Double>
Returns:
Minimum support.

getMaxSupport

public Double getMaxSupport()
Description copied from interface: UnivariateDistribution
Gets the minimum support (domain or input) of the distribution.

Specified by:
getMaxSupport in interface UnivariateDistribution<Double>
Returns:
Minimum support.

getEstimator

public GammaDistribution.MomentMatchingEstimator getEstimator()
Description copied from interface: EstimableDistribution
Gets an estimator associated with this distribution.

Specified by:
getEstimator in interface EstimableDistribution<Double,GammaDistribution>
Returns:
A distribution estimator associated for this distribution.