SSJ
V. 2.6.

umontreal.iro.lecuyer.probdist
Class GammaDist

java.lang.Object
  extended by umontreal.iro.lecuyer.probdist.ContinuousDistribution
      extended by umontreal.iro.lecuyer.probdist.GammaDist
All Implemented Interfaces:
Distribution
Direct Known Subclasses:
ErlangDist, GammaDistFromMoments

public class GammaDist
extends ContinuousDistribution

Extends the class ContinuousDistribution for the gamma distribution with shape parameter α > 0 and scale parameter λ > 0. The density is

f (x) = λαxα-1e-λx/Γ(α),        for x > 0,

where Γ is the gamma function, defined by

Γ(α) = ∫0xα-1e-xdx.

In particular, Γ(n) = (n - 1)! when n is a positive integer.


Field Summary
 
Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
decPrec
 
Constructor Summary
GammaDist(double alpha)
          Constructs a GammaDist object with parameters α = alpha and λ = 1.
GammaDist(double alpha, double lambda)
          Constructs a GammaDist object with parameters α = alpha and λ = lambda.
GammaDist(double alpha, double lambda, int d)
          Constructs a GammaDist object with parameters α = alpha and λ = lambda, and approximations of roughly d decimal digits of precision when computing functions.
 
Method Summary
 double barF(double x)
          Returns the complementary distribution function.
static double barF(double alpha, double lambda, int d, double x)
          Computes the complementary distribution function.
static double barF(double alpha, int d, double x)
          Same as barF (alpha, 1.0, d, x).
 double cdf(double x)
          Returns the distribution function F(x).
static double cdf(double alpha, double lambda, int d, double x)
          Returns an approximation of the gamma distribution function with parameters α = alpha and λ = lambda.
static double cdf(double alpha, int d, double x)
          Equivalent to cdf (alpha, 1.0, d, x).
 double density(double x)
          Returns f (x), the density evaluated at x.
static double density(double alpha, double lambda, double x)
          Computes the density function at x.
 double getAlpha()
          Return the parameter α for this object.
static GammaDist getInstanceFromMLE(double[] x, int n)
          Creates a new instance of a gamma distribution with parameters α and λ estimated using the maximum likelihood method based on the n observations x[i], i = 0, 1,…, n - 1.
 double getLambda()
          Return the parameter λ for this object.
 double getMean()
          Returns the mean.
static double getMean(double alpha, double lambda)
          Computes and returns the mean E[X] = α/λ of the gamma distribution with parameters α and λ.
static double[] getMLE(double[] x, int n)
          Estimates the parameters (α, λ) of the gamma distribution using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1.
 double[] getParams()
          Return a table containing the parameters of the current distribution.
 double getStandardDeviation()
          Returns the standard deviation.
static double getStandardDeviation(double alpha, double lambda)
          Computes and returns the standard deviation of the gamma distribution with parameters α and λ.
 double getVariance()
          Returns the variance.
static double getVariance(double alpha, double lambda)
          Computes and returns the variance Var[X] = α/λ2 of the gamma distribution with parameters α and λ.
 double inverseF(double u)
          Returns the inverse distribution function x = F-1(u).
static double inverseF(double alpha, double lambda, int d, double u)
          Computes the inverse distribution function.
static double inverseF(double alpha, int d, double u)
          Same as inverseF (alpha, 1, d, u).
 void setParams(double alpha, double lambda, int d)
           
 String toString()
           
 
Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
getXinf, getXsup, inverseBisection, inverseBrent, setXinf, setXsup
 
Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, wait, wait, wait
 

Constructor Detail

GammaDist

public GammaDist(double alpha)
Constructs a GammaDist object with parameters α = alpha and λ = 1.


GammaDist

public GammaDist(double alpha,
                 double lambda)
Constructs a GammaDist object with parameters α = alpha and λ = lambda.


GammaDist

public GammaDist(double alpha,
                 double lambda,
                 int d)
Constructs a GammaDist object with parameters α = alpha and λ = lambda, and approximations of roughly d decimal digits of precision when computing functions.

Method Detail

density

public double density(double x)
Description copied from class: ContinuousDistribution
Returns f (x), the density evaluated at x.

Specified by:
density in class ContinuousDistribution
Parameters:
x - value at which the density is evaluated
Returns:
density function evaluated at x

cdf

public double cdf(double x)
Description copied from interface: Distribution
Returns the distribution function F(x).

Parameters:
x - value at which the distribution function is evaluated
Returns:
distribution function evaluated at x

barF

public double barF(double x)
Description copied from class: ContinuousDistribution
Returns the complementary distribution function. The default implementation computes bar(F)(x) = 1 - F(x).

Specified by:
barF in interface Distribution
Overrides:
barF in class ContinuousDistribution
Parameters:
x - value at which the complementary distribution function is evaluated
Returns:
complementary distribution function evaluated at x

inverseF

public double inverseF(double u)
Description copied from class: ContinuousDistribution
Returns the inverse distribution function x = F-1(u). Restrictions: u∈[0, 1].

Specified by:
inverseF in interface Distribution
Overrides:
inverseF in class ContinuousDistribution
Parameters:
u - value at which the inverse distribution function is evaluated
Returns:
the inverse distribution function evaluated at u

getMean

public double getMean()
Description copied from class: ContinuousDistribution
Returns the mean.

Specified by:
getMean in interface Distribution
Overrides:
getMean in class ContinuousDistribution
Returns:
the mean

getVariance

public double getVariance()
Description copied from class: ContinuousDistribution
Returns the variance.

Specified by:
getVariance in interface Distribution
Overrides:
getVariance in class ContinuousDistribution
Returns:
the variance

getStandardDeviation

public double getStandardDeviation()
Description copied from class: ContinuousDistribution
Returns the standard deviation.

Specified by:
getStandardDeviation in interface Distribution
Overrides:
getStandardDeviation in class ContinuousDistribution
Returns:
the standard deviation

density

public static double density(double alpha,
                             double lambda,
                             double x)
Computes the density function at x.


cdf

public static double cdf(double alpha,
                         double lambda,
                         int d,
                         double x)
Returns an approximation of the gamma distribution function with parameters α = alpha and λ = lambda. The function tries to return d decimals digits of precision. For α not too large (e.g., α <= 1000), d gives a good idea of the precision attained.


cdf

public static double cdf(double alpha,
                         int d,
                         double x)
Equivalent to cdf (alpha, 1.0, d, x).


barF

public static double barF(double alpha,
                          double lambda,
                          int d,
                          double x)
Computes the complementary distribution function.


barF

public static double barF(double alpha,
                          int d,
                          double x)
Same as barF (alpha, 1.0, d, x).


inverseF

public static double inverseF(double alpha,
                              double lambda,
                              int d,
                              double u)
Computes the inverse distribution function.


inverseF

public static double inverseF(double alpha,
                              int d,
                              double u)
Same as inverseF (alpha, 1, d, u).


getMLE

public static double[] getMLE(double[] x,
                              int n)
Estimates the parameters (α, λ) of the gamma distribution using the maximum likelihood method, from the n observations x[i], i = 0, 1,…, n - 1. The estimates are returned in a two-element array, in regular order: [α, λ].

Parameters:
x - the list of observations to use to evaluate parameters
n - the number of observations to use to evaluate parameters
Returns:
returns the parameters [ hat(α), hat(λ)]

getInstanceFromMLE

public static GammaDist getInstanceFromMLE(double[] x,
                                           int n)
Creates a new instance of a gamma distribution with parameters α and λ estimated using the maximum likelihood method based on the n observations x[i], i = 0, 1,…, n - 1.

Parameters:
x - the list of observations to use to evaluate parameters
n - the number of observations to use to evaluate parameters

getMean

public static double getMean(double alpha,
                             double lambda)
Computes and returns the mean E[X] = α/λ of the gamma distribution with parameters α and λ.

Returns:
the mean of the gamma distribution E[X] = α/λ

getVariance

public static double getVariance(double alpha,
                                 double lambda)
Computes and returns the variance Var[X] = α/λ2 of the gamma distribution with parameters α and λ.

Returns:
the variance of the gamma distribution Var[X] = α/λ2

getStandardDeviation

public static double getStandardDeviation(double alpha,
                                          double lambda)
Computes and returns the standard deviation of the gamma distribution with parameters α and λ.

Returns:
the standard deviation of the gamma distribution

getAlpha

public double getAlpha()
Return the parameter α for this object.


getLambda

public double getLambda()
Return the parameter λ for this object.


setParams

public void setParams(double alpha,
                      double lambda,
                      int d)

getParams

public double[] getParams()
Return a table containing the parameters of the current distribution. This table is put in regular order: [α, λ].


toString

public String toString()
Overrides:
toString in class Object

SSJ
V. 2.6.

To submit a bug or ask questions, send an e-mail to Pierre L'Ecuyer.