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

Class ExpGammaDistribution

java.lang.Object

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

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

All Implemented Interfaces:

Distribution

public class ExpGammaDistribution
extends AbstractDistribution

Exp-Gamma Distribution, with random generation and density functions. This distribution can be outlined as Y ~ log[Gamma] distributed, or equivalently exp(Y) ~ Gamma. Note: this matches the loggamma of SciPy, whereas Wolfram calls this the Exponential Gamma Distribution "at times confused with the LogGammaDistribution".

Since:

0.6.0

Author:

Erich Schubert

Nested Class Summary

Nested Classes

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

Field Summary

Fields

Modifier and Type	Field and Description
private double	k Alpha == k.
private double	shift Translation offset.
private double	theta Theta == 1 / Beta.

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

random

Constructor Summary

Constructors

Constructor and Description
ExpGammaDistribution(double k, double theta, double shift) Constructor for Gamma distribution.
ExpGammaDistribution(double k, double theta, double shift, java.util.Random random) Constructor for Gamma distribution.
ExpGammaDistribution(double k, double theta, double shift, RandomFactory random) Constructor for Gamma 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 k, double theta, double shift) The CDF, static version.
double	getK()
double	getTheta()
static double	logcdf(double x, double k, double theta, double shift) The log CDF, static version.
double	logpdf(double val) Return the log density of an existing value
static double	logpdf(double x, double k, double theta, double shift) ExpGamma distribution logPDF
double	nextRandom() Generate a new random value
double	pdf(double val) Return the density of an existing value
static double	pdf(double x, double k, double theta, double shift) ExpGamma distribution PDF (with 0.0 for x < 0)
double	quantile(double val) Quantile aka probit (for normal) aka inverse CDF (invcdf, cdf^-1) function.
static double	quantile(double p, double k, double theta, double shift) Compute probit (inverse cdf) for ExpGamma distributions.
java.lang.String	toString() Simple toString explaining the distribution parameters.

Methods inherited from class java.lang.Object

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

Field Detail

k

private final double k

Alpha == k.

theta

private final double theta

Theta == 1 / Beta.

shift

private final double shift

Translation offset.

Constructor Detail

ExpGammaDistribution

public ExpGammaDistribution(double k,
                            double theta,
                            double shift,
                            java.util.Random random)

Constructor for Gamma distribution.

Parameters:

k - k, alpha aka. "shape" parameter

theta - Theta = 1.0/Beta aka. "scaling" parameter

shift - Location offset

random - Random generator

ExpGammaDistribution

public ExpGammaDistribution(double k,
                            double theta,
                            double shift,
                            RandomFactory random)

Constructor for Gamma distribution.

Parameters:

k - k, alpha aka. "shape" parameter

theta - Theta = 1.0/Beta aka. "scaling" parameter

shift - Location offset

random - Random generator

ExpGammaDistribution

public ExpGammaDistribution(double k,
                            double theta,
                            double shift)

Constructor for Gamma distribution.

Parameters:

k - k, alpha aka. "shape" parameter

theta - Theta = 1.0/Beta aka. "scaling" parameter

shift - Location offset

Method Detail

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 val)

Description copied from interface: Distribution

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

Parameters:

val - 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()

Simple toString explaining the distribution parameters. Used in producing a model description.

Specified by:

toString in interface Distribution

Overrides:

toString in class java.lang.Object

Returns:

description

getK

public double getK()

Returns:

the value of k

getTheta

public double getTheta()

Returns:

the standard deviation

cdf

public static double cdf(double x,
                         double k,
                         double theta,
                         double shift)

The CDF, static version.

Parameters:

x - Value

k - Shape k

theta - Theta = 1.0/Beta aka. "scaling" parameter

Returns:

cdf value

logcdf

public static double logcdf(double x,
                            double k,
                            double theta,
                            double shift)

The log CDF, static version.

Parameters:

x - Value

k - Shape k

theta - Theta = 1.0/Beta aka. "scaling" parameter

Returns:

cdf value

pdf

public static double pdf(double x,
                         double k,
                         double theta,
                         double shift)

ExpGamma distribution PDF (with 0.0 for x < 0)

Parameters:

x - query value

k - Alpha

theta - Theta = 1 / Beta

Returns:

probability density

logpdf

public static double logpdf(double x,
                            double k,
                            double theta,
                            double shift)

ExpGamma distribution logPDF

Parameters:

x - query value

k - Alpha

theta - Theta = 1 / Beta

Returns:

log probability density

quantile

public static double quantile(double p,
                              double k,
                              double theta,
                              double shift)

Compute probit (inverse cdf) for ExpGamma distributions.

Parameters:

p - Probability

k - k, alpha aka. "shape" parameter

theta - Theta = 1.0/Beta aka. "scaling" parameter

shift - Shift parameter

Returns:

Probit for ExpGamma distribution