SSJ
V. labo.

umontreal.iro.lecuyer.probdist
Class LoglogisticDist

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

public class LoglogisticDist
extends ContinuousDistribution

LoglogisticDist

Extends the class ContinuousDistribution for the Log-Logistic distribution with shape parameter α > 0 and scale parameter β > 0. Its density is

f (x) = (α(x/β)α-1)/(β[1 + (x/β)α]2)                for x > 0

and its distribution function is

F(x) = 1/(1 + (x/β)-α)                for x > 0.

The complementary distribution is

$\displaystyle \bar{F}$(x) = 1/(1 + (x/β)α)                for x > 0.


Field Summary
 
Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
decPrec
 
Constructor Summary
LoglogisticDist(double alpha, double beta)
          .
 
Method Summary
 double barF(double x)
          Returns the complementary distribution function.
static double barF(double alpha, double beta, double x)
          .
 double cdf(double x)
          .
static double cdf(double alpha, double beta, double x)
          .
 double density(double x)
          [hide24]
static double density(double alpha, double beta, double x)
          .
 double getAlpha()
          .
 double getBeta()
          .
static LoglogisticDist getInstanceFromMLE(double[] x, int n)
          .
 double getMean()
          Returns the mean.
static double getMean(double alpha, double beta)
          .
static double[] getMLE(double[] x, int n)
          .
 double[] getParams()
          .
 double getStandardDeviation()
          Returns the standard deviation.
static double getStandardDeviation(double alpha, double beta)
          .
 double getVariance()
          Returns the variance.
static double getVariance(double alpha, double beta)
          .
 double inverseF(double u)
          Returns the inverse distribution function x = F-1(u).
static double inverseF(double alpha, double beta, double u)
          .
 void setParams(double alpha, 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

LoglogisticDist

public LoglogisticDist(double alpha,
                       double beta)
. \begin{tabb}
 Constructs a log-logistic distribution with parameters
 $\alpha$\ and $\beta$.
 \end{tabb}

Method Detail

density

public double density(double x)
[hide24]

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 alpha,
                             double beta,
                             double x)
. \begin{tabb}Computes the density function
 for a log-logisitic distribution with parameters $\alpha$
 and $\beta$.
 \end{tabb}


cdf

public static double cdf(double alpha,
                         double beta,
                         double x)
. \begin{tabb}
 Computes the distribution function of the
 log-logistic distribution with parameters $\alpha$\ and $\beta$.
 \end{tabb}


barF

public static double barF(double alpha,
                          double beta,
                          double x)
. \begin{tabb}
 Computes the complementary distribution function
 of the log-logistic distribution with parameters $\alpha$\ and $\beta$.
 \end{tabb}


inverseF

public static double inverseF(double alpha,
                              double beta,
                              double u)
. \begin{tabb}
 Computes the inverse of the log-logistic distribution
 with parameters $\alpha$\ and $\beta$.
 \end{tabb}


getMLE

public static double[] getMLE(double[] x,
                              int n)
. \begin{tabb}
 Estimates the parameters $(\alpha,\beta)$\ of the log-logistic dis...
 ... 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}}$, $ \hat{{\beta}}$]


getInstanceFromMLE

public static LoglogisticDist getInstanceFromMLE(double[] x,
                                                 int n)
. \begin{tabb}
 Creates a new instance of a log-logistic distribution with paramet...
 ...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 alpha,
                             double beta)
. \begin{tabb}Computes and returns the mean
 of the log-logistic distribution with parameters $\alpha$\ and $\beta$.
 \end{tabb}
the mean of the log-logistic distribution E[X] = βθ cosec(θ), where θ = π/α


getVariance

public static double getVariance(double alpha,
                                 double beta)
. \begin{tabb}Computes and returns the variance
 of the log-logistic distribution with parameters $\alpha$\ and $\beta$.
 \end{tabb}
the variance of the log-logistic distribution Var[X] = β2θ(2cosec(2θ) - θ[cosec(θ)]2), where θ = π/α


getStandardDeviation

public static double getStandardDeviation(double alpha,
                                          double beta)
. \begin{tabb}Computes and returns the standard deviation of the log-logistic
 distribution with parameters $\alpha$\ and $\beta$.
 \end{tabb}
the standard deviation of the log-logistic distribution


getAlpha

public double getAlpha()
. \begin{tabb}Return the parameter $\alpha$\ of this object.
 \end{tabb}


getBeta

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


setParams

public void setParams(double alpha,
                      double beta)
. \begin{tabb}Sets the parameters $\alpha$\ and $\beta$\ of this object.
 \end{tabb}


getParams

public double[] getParams()
. \begin{tabb}
 Return a table containing the parameters of the current distribution.
 This table is put in regular order: [$\alpha$, $\beta$].
 \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.