de.lmu.ifi.dbs.elki.math.statistics.distribution

Class SkewGeneralizedNormalDistribution

java.lang.Object

de.lmu.ifi.dbs.elki.math.statistics.distribution.AbstractDistribution

de.lmu.ifi.dbs.elki.math.statistics.distribution.SkewGeneralizedNormalDistribution

All Implemented Interfaces:

Distribution

@Reference(authors="J. R. M. Hosking, J. R. Wallis",
           title="Regional frequency analysis: an approach based on L-moments",
           booktitle="Regional frequency analysis: an approach based on L-moments",
           url="https://doi.org/10.1017/CBO9780511529443",
           bibkey="doi:10.1017/CBO9780511529443")
public class SkewGeneralizedNormalDistribution
extends AbstractDistribution

Generalized normal distribution by adding a skew term, similar to lognormal distributions.

This is one kind of generalized normal distributions. Note that there are multiple that go by the name of a "Generalized Normal Distribution"; this is what is currently called "version 2" in English Wikipedia.

Reference:

J. R. M. Hosking, J. R. Wallis
Regional frequency analysis: an approach based on L-moments

Since:

0.6.0

Author:

Erich Schubert

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	SkewGeneralizedNormalDistribution.Parameterizer Parameterization class

Field Summary

Fields

Modifier and Type	Field and Description
private double	loc Location.
private double	scale Scale.
private double	skew Skew.

Fields inherited from class de.lmu.ifi.dbs.elki.math.statistics.distribution.AbstractDistribution

random

Constructor Summary

Constructors

Constructor and Description
SkewGeneralizedNormalDistribution(double loc, double scale, double skew) Constructor for Gaussian distribution
SkewGeneralizedNormalDistribution(double loc, double scale, double skew, java.util.Random random) Constructor for Gaussian distribution
SkewGeneralizedNormalDistribution(double loc, double scale, double skew, RandomFactory random) Constructor for Gaussian distribution

Method Summary

Modifier and Type	Method and Description
double	cdf(double val) Return the cumulative density function at the given value.
static double	cdf(double x, double mu, double sigma, double skew) Cumulative probability density function (CDF) of a normal distribution.
double	getLocation() Get the location parameter
double	getScale() Get the scale parameter
double	getSkew() Get the skew parameter.
double	logpdf(double val) Return the log density of an existing value
static double	logpdf(double x, double mu, double sigma, double skew) Probability density function of the skewed normal distribution.
double	nextRandom() Generate a new random value
double	pdf(double val) Return the density of an existing value
static double	pdf(double x, double mu, double sigma, double skew) Probability density function of the skewed normal distribution.
double	quantile(double q) Quantile aka probit (for normal) aka inverse CDF (invcdf, cdf^-1) function.
static double	quantile(double x, double mu, double sigma, double skew) Inverse cumulative probability density function (probit) of a normal distribution.
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

loc

private double loc

Location.

scale

private double scale

Scale.

skew

private double skew

Skew.

Constructor Detail

SkewGeneralizedNormalDistribution

public SkewGeneralizedNormalDistribution(double loc,
                                         double scale,
                                         double skew,
                                         java.util.Random random)

Constructor for Gaussian distribution

Parameters:

loc - Location

scale - Scale

skew - Skew

random - Random generator

SkewGeneralizedNormalDistribution

public SkewGeneralizedNormalDistribution(double loc,
                                         double scale,
                                         double skew,
                                         RandomFactory random)

Constructor for Gaussian distribution

Parameters:

loc - Location

scale - Scale

skew - Skew

random - Random generator

SkewGeneralizedNormalDistribution

public SkewGeneralizedNormalDistribution(double loc,
                                         double scale,
                                         double skew)

Constructor for Gaussian distribution

Parameters:

loc - Location

scale - Scale

skew - Skew

Method Detail

getLocation

public double getLocation()

Get the location parameter

Returns:

Location

getScale

public double getScale()

Get the scale parameter

Returns:

Scale

getSkew

public double getSkew()

Get the skew parameter.

Returns:

Skew parameter

pdf

public double pdf(double val)

Description copied from interface: Distribution

Return the density of an existing value

Parameters:

val - existing value

Returns:

distribution density

logpdf

public double logpdf(double val)

Description copied from interface: Distribution

Return the log density of an existing value

Parameters:

val - existing value

Returns:

log distribution density

cdf

public double cdf(double val)

Description copied from interface: Distribution

Return the cumulative density function at the given value.

Parameters:

val - existing value

Returns:

cumulative density

quantile

public double quantile(double q)

Description copied from interface: Distribution

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

Parameters:

q - Quantile to find

Returns:

Quantile position

nextRandom

public double nextRandom()

Description copied from interface: Distribution

Generate a new random value

Specified by:

nextRandom in interface Distribution

Overrides:

nextRandom in class AbstractDistribution

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

pdf

public static double pdf(double x,
                         double mu,
                         double sigma,
                         double skew)

Probability density function of the skewed normal distribution.

Parameters:

x - The value.

mu - The mean.

sigma - The standard deviation.

Returns:

PDF of the given normal distribution at x.

logpdf

public static double logpdf(double x,
                            double mu,
                            double sigma,
                            double skew)

Probability density function of the skewed normal distribution.

Parameters:

x - The value.

mu - The mean.

sigma - The standard deviation.

Returns:

log PDF of the given normal distribution at x.

cdf

public static double cdf(double x,
                         double mu,
                         double sigma,
                         double skew)

Cumulative probability density function (CDF) of a normal distribution.

Parameters:

x - value to evaluate CDF at

mu - Mean value

sigma - Standard deviation.

Returns:

The CDF of the given normal distribution at x.

quantile

public static double quantile(double x,
                              double mu,
                              double sigma,
                              double skew)

Inverse cumulative probability density function (probit) of a normal distribution.

Parameters:

x - value to evaluate probit function at

mu - Mean value

sigma - Standard deviation.

Returns:

The probit of the given normal distribution at x.