SSJ
V. 1.2.5.

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 of X 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 in table x[i], i = 0, 1,…, n - 1.
 double getLambda()
          Returns the parameter λ of this object.
static double[] getMaximumLikelihoodEstimate(double[] x, int n)
          Estimates and returns the parameters [ hat(α), hat(λ)] of the log-normal distribution using the maximum likelihood method based on the n observations in table x[i], i = 0, 1,…, n - 1.
 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.
 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.
 
Methods inherited from class umontreal.iro.lecuyer.probdist.ContinuousDistribution
inverseBisection, inverseBrent
 
Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, toString, 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 of X 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).


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 in table 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

getMaximumLikelihoodEstimate

public static double[] getMaximumLikelihoodEstimate(double[] x,
                                                    int n)
Estimates and returns the parameters [ hat(α), hat(λ)] of the log-normal distribution using the maximum likelihood method based on the n observations in table x[i], i = 0, 1,…, n - 1.

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)]

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.


SSJ
V. 1.2.5.

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