SSJ
V. 2.0.

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 bar(F)(x) = 1 - F(x).
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)
          Computes and 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 of the distribution function.
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 of the distribution function.
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 of the distribution function.
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)
          Computes and returns the inverse distribution function F-1(u), defined in.
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
inverseBisection, inverseBrent
 
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
Computes and 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 interface: Distribution
Returns 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 interface: Distribution
Computes and returns the inverse distribution function F-1(u), defined in.

Specified by:
inverseF in interface Distribution
Overrides:
inverseF in class ContinuousDistribution
Parameters:
u - value in the interval (0, 1) for which the inverse distribution function is evaluated
Returns:
the inverse distribution function evaluated at u

getMean

public double getMean()
Description copied from interface: Distribution
Returns the mean of the distribution function.


getVariance

public double getVariance()
Description copied from interface: Distribution
Returns the variance of the distribution function.


getStandardDeviation

public double getStandardDeviation()
Description copied from interface: Distribution
Returns the standard deviation of the distribution function.


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

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. 2.0.

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