SSJ
V. 2.0.

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

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

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)
          Constructs a log-logistic distribution with parameters α and β.
 
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 the log-logistic distribution with parameters α and β.
 double cdf(double x)
          Computes and returns the distribution function F(x).
static double cdf(double alpha, double beta, double x)
          Computes the distribution function of the log-logistic distribution with parameters α and 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 for a log-logisitic distribution with parameters α and β.
 double getAlpha()
          Return the parameter α of this object.
 double getBeta()
          Returns the parameter β of this object.
static LoglogisticDist getInstanceFromMLE(double[] x, int n)
          Creates a new instance of a log-logistic 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 of the log-logistic distribution with parameters α and β.
static double[] getMLE(double[] x, int n)
          Estimates the parameters (α, β) of the log-logistic 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 the log-logistic distribution with parameters α and β.
 double getVariance()
          Returns the variance of the distribution function.
static double getVariance(double alpha, double beta)
          Computes and returns the variance of the log-logistic distribution with parameters α and 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 of the log-logistic distribution with parameters α and β.
 void setParams(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

LoglogisticDist

public LoglogisticDist(double alpha,
                       double beta)
Constructs a log-logistic distribution with parameters α and β.

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 for a log-logisitic distribution with parameters α and β.


cdf

public static double cdf(double alpha,
                         double beta,
                         double x)
Computes the distribution function of the log-logistic distribution with parameters α and β.


barF

public static double barF(double alpha,
                          double beta,
                          double x)
Computes the complementary distribution function of the log-logistic distribution with parameters α and β.


inverseF

public static double inverseF(double alpha,
                              double beta,
                              double u)
Computes the inverse of the log-logistic distribution with parameters α and β.


getMLE

public static double[] getMLE(double[] x,
                              int n)
Estimates the parameters (α, β) of the log-logistic 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 LoglogisticDist getInstanceFromMLE(double[] x,
                                                 int n)
Creates a new instance of a log-logistic 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 of the log-logistic distribution with parameters α and β.

Returns:
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)
Computes and returns the variance of the log-logistic distribution with parameters α and β.

Returns:
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)
Computes and returns the standard deviation of the log-logistic distribution with parameters α and β.

Returns:
the standard deviation of the log-logistic distribution

getAlpha

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


getBeta

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


setParams

public void setParams(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.