edu.uah.math.distributions
Class LogisticDistribution

java.lang.Object
  edu.uah.math.distributions.Distribution
      edu.uah.math.distributions.LogisticDistribution

All Implemented Interfaces:

java.io.Serializable

public class LogisticDistribution
extends Distribution
implements java.io.Serializable

This class models the logistic distribution.

Version:

August, 2003

Author:

Kyle Siegrist, Dawn Duehring

See Also:

Serialized Form

Field Summary

Fields inherited from class edu.uah.math.distributions.Distribution

CONTINUOUS, DISCRETE, MIXED

Constructor Summary

LogisticDistribution()
This default constructor creates a new logsitic distribution and sets up the default computational domain (−7, 7).

Method Summary

double	getCDF(double x) This method computes the cumulative distribution function, which is F(x) = ex / (1 + ex)
double	getDensity(double x) This method computes the probability density function,which is f(x) = ex / (1 + ex)2
double	getMaxDensity() This method computes the maximum value of the density function, which is 1/4, the value of the density at x = 0.
double	getMean() This method returns the mean of the distribution, which is 0.
double	getMGF(double t) This method computes the moment generating function, which is Γ(1 + t) / Γ(1 − t).
double	getQuantile(double p) This method comptues the quantile function.
double	getVariance() This method computes the variance of the distribution, which is π2 / 3.
java.lang.String	toString() This method returns a string that gives the name of the distribution and the values of the parameters.

Methods inherited from class edu.uah.math.distributions.Distribution

getDomain, getFailureRate, getMedian, getMoment, getMoment, getPGF, getSD, getType, setDomain, setDomain, simulate

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Constructor Detail

LogisticDistribution

public LogisticDistribution()

This default constructor creates a new logsitic distribution and sets up the default computational domain (−7, 7).

Method Detail

getDensity

public double getDensity(double x)

This method computes the probability density function,which is f(x) = e^x / (1 + e^x)²

Specified by:

getDensity in class Distribution

Parameters:

x - a real number

Returns:

the probability density at x

getMaxDensity

public double getMaxDensity()

This method computes the maximum value of the density function, which is 1/4, the value of the density at x = 0.

Overrides:

getMaxDensity in class Distribution

Returns:

the maximum value of the density function

getCDF

public double getCDF(double x)

This method computes the cumulative distribution function, which is F(x) = e^x / (1 + e^x)

Overrides:

getCDF in class Distribution

Parameters:

x - a real number

Returns:

the cumulative probability at x

getQuantile

public double getQuantile(double p)

This method comptues the quantile function.

Overrides:

getQuantile in class Distribution

Parameters:

p - a probability in (0, 1)

Returns:

the quantile of order p

getMean

public double getMean()

This method returns the mean of the distribution, which is 0.

Overrides:

getMean in class Distribution

Returns:

the mean

getVariance

public double getVariance()

This method computes the variance of the distribution, which is π² / 3.

Overrides:

getVariance in class Distribution

Returns:

the variance method in Distribution.

getMGF

public double getMGF(double t)

This method computes the moment generating function, which is Γ(1 + t) / Γ(1 − t).

Overrides:

getMGF in class Distribution

Parameters:

t - a number < 1

Returns:

the moment generating function at t

toString

public java.lang.String toString()

This method returns a string that gives the name of the distribution and the values of the parameters.

Overrides:

toString in class Distribution

Returns:

a string giving the name of the distribution and the values of the parameters