SSJ
V. 2.0.

umontreal.iro.lecuyer.probdist
Class LogisticDist

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

public class LogisticDist
extends ContinuousDistribution

Extends the class ContinuousDistribution for the logistic distribution. It has location parameter α and scale parameter λ > 0. The density is

f (x) = (λe-λ(x-α))/((1 + e-λ(x-α))2)                for - ∞ < x < ∞.

and the distribution function is

F(x) = 1/[1 + e-λ(x-α)]                for - ∞ < x < ∞.

For λ = 1 and α = 0, one can write

F(x) = $\displaystyle {\frac{{1 + \tanh({x/2})}}{{2}}}$.

The inverse distribution function is given by

F-1(u) = ln(u/(1 - u))/λ + α        for 0 <= u < 1.


Field Summary
 
Fields inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
decPrec
 
Constructor Summary
LogisticDist()
          Constructs a LogisticDist object with default parameters α = 0 and λ = 1.
LogisticDist(double alpha, double lambda)
          Constructs a LogisticDist object with parameters α = alpha and λ = lambda.
 
Method Summary
 double barF(double x)
          Returns bar(F)(x) = 1 - F(x).
static double barF(double alpha, double lambda, double x)
          Computes the complementary distribution function 1 - F(x).
 double cdf(double x)
          Computes and returns the distribution function F(x).
static double cdf(double alpha, double lambda, double x)
          Computes the distribution function F(x).
 double density(double x)
          Returns f (x), the density evaluated at x.
static double density(double alpha, double lambda, double x)
          Computes the density function f (x).
 double getAlpha()
          Return the parameter α of this object.
static LogisticDist getInstanceFromMLE(double[] x, int n)
          Creates a new instance of a logistic distribution with parameters α and λ estimated using the maximum likelihood method based on the n observations x[i], i = 0, 1,…, n - 1.
 double getLambda()
          Returns the parameter λ of this object.
static double[] getMaximumLikelihoodEstimate(double[] x, int n)
          Deprecated.
 double getMean()
          Returns the mean of the distribution function.
static double getMean(double alpha, double lambda)
          Computes and returns the mean E[X] = α of the logistic distribution with parameters α and λ.
static double[] getMLE(double[] x, int n)
          Estimates the parameters (α, λ) of the 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 lambda)
          Computes and returns the standard deviation of the logistic distribution with parameters α and λ.
 double getVariance()
          Returns the variance of the distribution function.
static double getVariance(double alpha, double lambda)
          Computes and returns the variance Var[X] = π2/(3λ2) of the logistic distribution with parameters α and λ.
 double inverseF(double u)
          Computes and returns the inverse distribution function F-1(u), defined in.
static double inverseF(double alpha, double lambda, double u)
          Computes the inverse distribution function F-1(u).
 void setParams(double alpha, double lambda)
          Sets the parameters α and λ 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

LogisticDist

public LogisticDist()
Constructs a LogisticDist object with default parameters α = 0 and λ = 1.


LogisticDist

public LogisticDist(double alpha,
                    double lambda)
Constructs a LogisticDist object with parameters α = alpha and λ = lambda.

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 lambda,
                             double x)
Computes the density function f (x).


cdf

public static double cdf(double alpha,
                         double lambda,
                         double x)
Computes the distribution function F(x).


barF

public static double barF(double alpha,
                          double lambda,
                          double x)
Computes the complementary distribution function 1 - F(x).


inverseF

public static double inverseF(double alpha,
                              double lambda,
                              double u)
Computes the inverse distribution function F-1(u).


getMLE

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

Parameters:
x - the list of observations used to evaluate parameters
n - the number of observations used to evaluate parameters
Returns:
returns the parameter [ hat(α), hat(λ)]

getMaximumLikelihoodEstimate

public static double[] getMaximumLikelihoodEstimate(double[] x,
                                                    int n)
Deprecated. Same as getMLE.


getInstanceFromMLE

public static LogisticDist getInstanceFromMLE(double[] x,
                                              int n)
Creates a new instance of a logistic distribution with parameters α and λ 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 lambda)
Computes and returns the mean E[X] = α of the logistic distribution with parameters α and λ.

Returns:
the mean of the logistic distribution E[X] = α

getVariance

public static double getVariance(double alpha,
                                 double lambda)
Computes and returns the variance Var[X] = π2/(3λ2) of the logistic distribution with parameters α and λ.

Returns:
the variance of the logistic distribution Var[X] = 1/3π2*(1/λ2)

getStandardDeviation

public static double getStandardDeviation(double alpha,
                                          double lambda)
Computes and returns the standard deviation of the logistic distribution with parameters α and λ.

Returns:
the standard deviation of the logistic distribution

getAlpha

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


getLambda

public double getLambda()
Returns the parameter λ of this object.


setParams

public void setParams(double alpha,
                      double lambda)
Sets the parameters α and λ 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, λ].


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.