SSJ
V. 2.2.

umontreal.iro.lecuyer.probdist
Class Pearson5Dist

java.lang.Object
  extended by umontreal.iro.lecuyer.probdist.ContinuousDistribution
      extended by umontreal.iro.lecuyer.probdist.Pearson5Dist
All Implemented Interfaces:
Distribution

public class Pearson5Dist
extends ContinuousDistribution

Extends the class ContinuousDistribution for the Pearson type V distribution with shape parameter α > 0 and scale parameter β > 0. The density function is given by

f (x) = (x-(α+1)exp-β/x)/(β-αΓ(α))        for x > 0,

and f (x) = 0 otherwise, where Γ is the gamma function. The distribution function is given by

F(x) = 1 - FG(1/x),    for x > 0,

and F(x) = 0 otherwise, where FG(x) is the distribution function of a gamma distribution with shape parameter α and scale parameter β.


Field Summary
 
Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
decPrec
 
Constructor Summary
Pearson5Dist(double alpha, double beta)
          Constructs a Pearson5Dist object with parameters α = alpha and β = beta.
 
Method Summary
 double barF(double x)
          Returns the complementary distribution function.
static double barF(double alpha, double beta, double x)
          Computes the complementary distribution function of a Pearson V distribution with shape parameter α and scale parameter β.
 double cdf(double x)
          Returns the distribution function F(x).
static double cdf(double alpha, double beta, double x)
          Computes the density function of a Pearson V distribution with shape parameter α and scale parameter β.
 double density(double x)
          Returns f (x), the density evaluated at x.
static double density(double alpha, double beta, double x)
          Computes the density function of a Pearson V distribution with shape parameter α and scale parameter β.
 double getAlpha()
          Returns the α parameter of this object.
 double getBeta()
          Returns the β parameter of this object.
static Pearson5Dist getInstanceFromMLE(double[] x, int n)
          Creates a new instance of a Pearson V distribution with parameters α and β estimated using the maximum likelihood method based on the n observations x[i], i = 0, 1,…, n - 1.
static double[] getMaximumLikelihoodEstimate(double[] x, int n)
          Deprecated. 
 double getMean()
          Returns the mean.
static double getMean(double alpha, double beta)
          Computes and returns the mean E[X] = β/(α - 1) of a Pearson V distribution with shape parameter α and scale parameter β.
static double[] getMLE(double[] x, int n)
          Estimates the parameters (α, β) of the Pearson V 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 beta)
          Computes and returns the standard deviation of a Pearson V distribution with shape parameter α and scale parameter β.
 double getVariance()
          Returns the variance.
static double getVariance(double alpha, double beta)
          Computes and returns the variance Var[X] = β2/((α -1)2(α - 2) of a Pearson V distribution with shape parameter α and scale parameter β.
 double inverseF(double u)
          Returns the inverse distribution function x = F-1(u).
static double inverseF(double alpha, double beta, double u)
          Computes the inverse distribution function of a Pearson V distribution with shape parameter α and scale parameter β.
 void setParam(double alpha, double beta)
          Sets the parameters α and β of this object.
 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

Pearson5Dist

public Pearson5Dist(double alpha,
                    double beta)
Constructs a Pearson5Dist object with parameters α = alpha and β = beta.

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 beta,
                             double x)
Computes the density function of a Pearson V distribution with shape parameter α and scale parameter β.


cdf

public static double cdf(double alpha,
                         double beta,
                         double x)
Computes the density function of a Pearson V distribution with shape parameter α and scale parameter β.


barF

public static double barF(double alpha,
                          double beta,
                          double x)
Computes the complementary distribution function of a Pearson V distribution with shape parameter α and scale parameter β.


inverseF

public static double inverseF(double alpha,
                              double beta,
                              double u)
Computes the inverse distribution function of a Pearson V distribution with shape parameter α and scale parameter β.


getMLE

public static double[] getMLE(double[] x,
                              int n)
Estimates the parameters (α, β) of the Pearson V 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, β].

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(β)]

getMaximumLikelihoodEstimate

@Deprecated
public static double[] getMaximumLikelihoodEstimate(double[] x,
                                                               int n)
Deprecated. 

Same as getMLE.


getInstanceFromMLE

public static Pearson5Dist getInstanceFromMLE(double[] x,
                                              int n)
Creates a new instance of a Pearson V distribution with parameters α and β 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 beta)
Computes and returns the mean E[X] = β/(α - 1) of a Pearson V distribution with shape parameter α and scale parameter β.


getVariance

public static double getVariance(double alpha,
                                 double beta)
Computes and returns the variance Var[X] = β2/((α -1)2(α - 2) of a Pearson V distribution with shape parameter α and scale parameter β.


getStandardDeviation

public static double getStandardDeviation(double alpha,
                                          double beta)
Computes and returns the standard deviation of a Pearson V distribution with shape parameter α and scale parameter β.


getAlpha

public double getAlpha()
Returns the α parameter of this object.


getBeta

public double getBeta()
Returns the β parameter of this object.


setParam

public void setParam(double alpha,
                     double beta)
Sets the parameters α and β of this object.


getParams

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


toString

public String toString()
Overrides:
toString in class Object

SSJ
V. 2.2.

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