Package elki.math.statistics.distribution

Class GeneralizedLogisticDistribution

java.lang.Object

elki.math.statistics.distribution.GeneralizedLogisticDistribution

All Implemented Interfaces:

Distribution

public class GeneralizedLogisticDistribution
extends java.lang.Object
implements Distribution

Generalized logistic distribution. (Type I, Skew-logistic distribution)

One of multiple ways of generalizing the logistic distribution.
pdf(x) = shape * exp(-x) / (1 + exp(-x))**(shape+1)
cdf(x) = pow(1+exp(-x), -shape)
Where shape=1 yields the regular logistic distribution.

Since:

0.6.0

Author:

Erich Schubert

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static class	GeneralizedLogisticDistribution.Par	Parameterization class

Nested classes/interfaces inherited from interface elki.math.statistics.distribution.Distribution

Distribution.Parameterizer

Field Summary

Fields

Modifier and Type	Field	Description
(package private) double	location	Parameters: location and scale
(package private) double	scale	Parameters: location and scale
(package private) double	shape	Shape parameter, for generalized logistic distribution.

Constructor Summary

Constructors

Constructor	Description
GeneralizedLogisticDistribution(double location, double scale, double shape)	Constructor.

Method Summary

Modifier and Type	Method	Description
double	cdf(double val)	Return the cumulative density function at the given value.
static double	cdf(double val, double loc, double scale, double shape)	Cumulative density function.
static double	logcdf(double val, double loc, double scale, double shape)	log Cumulative density function.
double	logpdf(double val)	Return the log density of an existing value
static double	logpdf(double val, double loc, double scale, double shape)	log Probability density function.
double	nextRandom(java.util.Random random)	Generate a new random value
double	pdf(double val)	Return the density of an existing value
static double	pdf(double val, double loc, double scale, double shape)	Probability density function.
double	quantile(double val)	Quantile aka probit (for normal) aka inverse CDF (invcdf, cdf^-1) function.
static double	quantile(double val, double loc, double scale, double shape)	Quantile function.
java.lang.String	toString()	Describe the distribution

Methods inherited from class java.lang.Object

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

Field Detail

location

double location

Parameters: location and scale

scale

double scale

Parameters: location and scale

shape

double shape

Shape parameter, for generalized logistic distribution.

Constructor Detail

GeneralizedLogisticDistribution

public GeneralizedLogisticDistribution(double location,
                                       double scale,
                                       double shape)

Constructor.

Parameters:

location - Location

scale - Scale

shape - Shape parameter

Method Detail

pdf

public double pdf(double val)

Description copied from interface: Distribution

Return the density of an existing value

Specified by:

pdf in interface Distribution

Parameters:

val - existing value

Returns:

distribution density

pdf

public static double pdf(double val,
                         double loc,
                         double scale,
                         double shape)

Probability density function.

Parameters:

val - Value

loc - Location

scale - Scale

shape - Shape

Returns:

PDF

logpdf

public double logpdf(double val)

Description copied from interface: Distribution

Return the log density of an existing value

Specified by:

logpdf in interface Distribution

Parameters:

val - existing value

Returns:

log distribution density

logpdf

public static double logpdf(double val,
                            double loc,
                            double scale,
                            double shape)

log Probability density function.

Parameters:

val - Value

loc - Location

scale - Scale

shape - Shape

Returns:

log PDF

cdf

public double cdf(double val)

Description copied from interface: Distribution

Return the cumulative density function at the given value.

Specified by:

cdf in interface Distribution

Parameters:

val - existing value

Returns:

cumulative density

cdf

public static double cdf(double val,
                         double loc,
                         double scale,
                         double shape)

Cumulative density function.

Parameters:

val - Value

loc - Location

scale - Scale

shape - Shape

Returns:

CDF

logcdf

public static double logcdf(double val,
                            double loc,
                            double scale,
                            double shape)

log Cumulative density function. TODO: untested.

Parameters:

val - Value

loc - Location

scale - Scale

shape - Shape

Returns:

log PDF

quantile

public static double quantile(double val,
                              double loc,
                              double scale,
                              double shape)

Quantile function.

Parameters:

val - Value

loc - Location

scale - Scale

shape - Shape

Returns:

Quantile

quantile

public double quantile(double val)

Description copied from interface: Distribution

Quantile aka probit (for normal) aka inverse CDF (invcdf, cdf^-1) function.

Specified by:

quantile in interface Distribution

Parameters:

val - Quantile to find

Returns:

Quantile position

nextRandom

public double nextRandom(java.util.Random random)

Description copied from interface: Distribution

Generate a new random value

Specified by:

nextRandom in interface Distribution

Parameters:

random - Random number generator

Returns:

new random value

toString

public java.lang.String toString()

Description copied from interface: Distribution

Describe the distribution

Specified by:

toString in interface Distribution

Overrides:

toString in class java.lang.Object

Returns:

description