SSJ
V. labo.

umontreal.iro.lecuyer.probdist
Class Pearson6Dist

java.lang.Object
  extended by umontreal.iro.lecuyer.probdist.ContinuousDistribution
      extended by umontreal.iro.lecuyer.probdist.Pearson6Dist
All Implemented Interfaces:
Distribution

public class Pearson6Dist
extends ContinuousDistribution

Pearson6Dist

Extends the class ContinuousDistribution for the Pearson type VI distribution with shape parameters α1 > 0 and α2 > 0, and scale parameter β > 0. The density function is given by

f (x) = (x/β)α1-1/(βB(α1, α2)[1 + x/β]α1+α2)        for x > 0,

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

F(x) = FB(x/(x + β))        for x > 0,

and F(x) = 0 otherwise, where FB(x) is the distribution function of a beta distribution with shape parameters α1 and α2.


Field Summary
 
Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
decPrec
 
Constructor Summary
Pearson6Dist(double alpha1, double alpha2, double beta)
          .
 
Method Summary
 double barF(double x)
          Returns the complementary distribution function.
static double barF(double alpha1, double alpha2, double beta, double x)
          .
 double cdf(double x)
          .
static double cdf(double alpha1, double alpha2, double beta, double x)
          .
 double density(double x)
          Returns f (x), the density evaluated at x.
static double density(double alpha1, double alpha2, double beta, double x)
          .
 double getAlpha1()
          .
 double getAlpha2()
          .
 double getBeta()
          .
static Pearson6Dist getInstanceFromMLE(double[] x, int n)
          .
 double getMean()
          Returns the mean.
static double getMean(double alpha1, double alpha2, double beta)
          .
static double[] getMLE(double[] x, int n)
          .
 double[] getParams()
          .
 double getStandardDeviation()
          Returns the standard deviation.
static double getStandardDeviation(double alpha1, double alpha2, double beta)
          .
 double getVariance()
          Returns the variance.
static double getVariance(double alpha1, double alpha2, double beta)
          .
 double inverseF(double u)
          Returns the inverse distribution function x = F-1(u).
static double inverseF(double alpha1, double alpha2, double beta, double u)
          .
 void setParam(double alpha1, double alpha2, double beta)
          .
 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

Pearson6Dist

public Pearson6Dist(double alpha1,
                    double alpha2,
                    double beta)
. \begin{tabb}
 Constructs a \texttt{Pearson6Dist} object with parameters $\alpha_...
 ...{alpha1}, $\alpha_2$\ = \texttt{alpha2} and $\beta$\ = \texttt{beta}.
 \end{tabb}

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
. \begin{tabb}Returns the distribution function $F(x)$.
 \end{tabb}
xvalue at which the distribution function is evaluated 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 alpha1,
                             double alpha2,
                             double beta,
                             double x)
. \begin{tabb}
 Computes the density function of a Pearson VI distribution with shape
 parameters $\alpha_1$
 and $\alpha_2$, and scale parameter $\beta$.
 \end{tabb}


cdf

public static double cdf(double alpha1,
                         double alpha2,
                         double beta,
                         double x)
. \begin{tabb}
 Computes the distribution function of a Pearson VI distribution wi...
 ...e parameters $\alpha_1$
 and $\alpha_2$, and scale parameter $\beta$.
 \end{tabb}


barF

public static double barF(double alpha1,
                          double alpha2,
                          double beta,
                          double x)
. \begin{tabb}
 Computes the complementary distribution function of a Pearson VI d...
 ...e parameters $\alpha_1$\ and $\alpha_2$, and scale parameter $\beta$.
 \end{tabb}


inverseF

public static double inverseF(double alpha1,
                              double alpha2,
                              double beta,
                              double u)
. \begin{tabb}
 Computes the inverse distribution function of a Pearson VI distrib...
 ...e parameters $\alpha_1$\ and $\alpha_2$, and scale parameter $\beta$.
 \end{tabb}


getMLE

public static double[] getMLE(double[] x,
                              int n)
. \begin{tabb}
 Estimates the parameters $(\alpha_1,\alpha_2,\beta)$\ of the Pears...
 ... function, using the Uncmin package\cite{iSCHa,iVERa}.
 \end{detailed}\end{tabb}
xthe list of observations to use to evaluate parameters nthe number of observations to use to evaluate parameters returns the parameters [ $ \hat{{\alpha_1}}$,$ \hat{{\alpha_2}}$,$ \hat{{\beta}}$]


getInstanceFromMLE

public static Pearson6Dist getInstanceFromMLE(double[] x,
                                              int n)
. \begin{tabb}
 Creates a new instance of a Pearson VI distribution with parameter...
 ...thod based on
 the $n$\ observations $x[i]$, $i = 0, 1, \ldots, n-1$.
 \end{tabb}
xthe list of observations to use to evaluate parameters nthe number of observations to use to evaluate parameters


getMean

public static double getMean(double alpha1,
                             double alpha2,
                             double beta)
. \begin{tabb}
 Computes and returns the mean $E[X] = (\beta \alpha_1) / (\alpha_2...
 ... parameters $\alpha_1$\ and $\alpha_2$, and
 scale parameter $\beta$.
 \end{tabb}


getVariance

public static double getVariance(double alpha1,
                                 double alpha2,
                                 double beta)
. \begin{tabb}
 Computes and returns the variance
 $\mbox{Var}[X] = [\beta^2 \alph...
 ...
 parameters $\alpha_1$\ and $\alpha_2$, and scale parameter $\beta$.
 \end{tabb}


getStandardDeviation

public static double getStandardDeviation(double alpha1,
                                          double alpha2,
                                          double beta)
. \begin{tabb}
 Computes and returns the standard deviation of a Pearson VI
 distri...
 ...
 parameters $\alpha_1$\ and $\alpha_2$, and scale parameter $\beta$.
 \end{tabb}


getAlpha1

public double getAlpha1()
. \begin{tabb}
 Returns the $\alpha_1$\ parameter of this object.
 \end{tabb}


getAlpha2

public double getAlpha2()
. \begin{tabb}
 Returns the $\alpha_2$\ parameter of this object.
 \end{tabb}


getBeta

public double getBeta()
. \begin{tabb}
 Returns the $\beta$\ parameter of this object.
 \end{tabb}


setParam

public void setParam(double alpha1,
                     double alpha2,
                     double beta)
. \begin{tabb}
 Sets the parameters $\alpha_1$, $\alpha_2$\ and $\beta$\ of this object.
 \end{tabb}


getParams

public double[] getParams()
. \begin{tabb}
 Return a table containing the parameters of the current distributi...
 ...his table is put in regular order: [$\alpha_1$, $\alpha_2$, $\beta$].
 \end{tabb}

 


toString

public String toString()
. \begin{hide}
 \par
 \begin{tabb}
 Returns a \texttt{String} containing information about the current distribution.
 \end{tabb}\end{hide}

Overrides:
toString in class Object

SSJ
V. labo.

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