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

Class ExponentiallyModifiedGaussianDistribution

java.lang.Object

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

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

All Implemented Interfaces:

Distribution

@Alias(value="exgaussian")
public class ExponentiallyModifiedGaussianDistribution
extends AbstractDistribution

Exponentially modified Gaussian (EMG) distribution (ExGaussian distribution) is a combination of a normal distribution and an exponential distribution. Note that scipy uses a subtly different parameterization. TODO: implement quantile function!

Since:

0.6.0

Author:

Erich Schubert

Nested Class Summary

Nested Classes

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

Field Summary

Fields

Modifier and Type	Field and Description
private double	lambda Exponential rate.
private double	mean Mean value for the generator
private double	stddev Standard deviation

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

random

Constructor Summary

Constructors

Constructor and Description
ExponentiallyModifiedGaussianDistribution(double mean, double stddev, double lambda) Constructor for ExGaussian distribution
ExponentiallyModifiedGaussianDistribution(double mean, double stddev, double lambda, java.util.Random random) Constructor for ExGaussian distribution
ExponentiallyModifiedGaussianDistribution(double mean, double stddev, double lambda, RandomFactory random) Constructor for ExGaussian 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 lambda) Cumulative probability density function (CDF) of an exgauss distribution.
double	getLambda()
double	getMean()
double	getStddev()
double	logpdf(double val) Return the log density of an existing value
static double	logpdf(double x, double mu, double sigma, double lambda) Probability density function of the ExGaussian 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 lambda) Probability density function of the ExGaussian distribution.
double	quantile(double q) Deprecated. Not yet implemented!
static double	quantile(double x, double mu, double sigma, double lambda) Deprecated. Not yet implemented!
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

mean

private double mean

Mean value for the generator

stddev

private double stddev

Standard deviation

lambda

private double lambda

Exponential rate.

Constructor Detail

ExponentiallyModifiedGaussianDistribution

public ExponentiallyModifiedGaussianDistribution(double mean,
                                                 double stddev,
                                                 double lambda,
                                                 java.util.Random random)

Constructor for ExGaussian distribution

Parameters:

mean - Mean

stddev - Standard Deviation

lambda - Rate

random - Random

ExponentiallyModifiedGaussianDistribution

public ExponentiallyModifiedGaussianDistribution(double mean,
                                                 double stddev,
                                                 double lambda,
                                                 RandomFactory random)

Constructor for ExGaussian distribution

Parameters:

mean - Mean

stddev - Standard Deviation

lambda - Rate

random - Random

ExponentiallyModifiedGaussianDistribution

public ExponentiallyModifiedGaussianDistribution(double mean,
                                                 double stddev,
                                                 double lambda)

Constructor for ExGaussian distribution

Parameters:

mean - Mean

stddev - Standard Deviation

lambda - Rate

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

@Deprecated
public double quantile(double q)

Deprecated. Not yet implemented!

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

getMean

public double getMean()

Returns:

the mean

getStddev

public double getStddev()

Returns:

the standard deviation

getLambda

public double getLambda()

Returns:

the lambda value.

pdf

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

Probability density function of the ExGaussian distribution.

Parameters:

x - The value.

mu - The mean.

sigma - The standard deviation.

lambda - Rate parameter.

Returns:

PDF of the given exgauss distribution at x.

logpdf

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

Probability density function of the ExGaussian distribution.

Parameters:

x - The value.

mu - The mean.

sigma - The standard deviation.

lambda - Rate parameter.

Returns:

PDF of the given exgauss distribution at x.

cdf

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

Cumulative probability density function (CDF) of an exgauss distribution.

Parameters:

x - value to evaluate CDF at.

mu - Mean value.

sigma - Standard deviation.

lambda - Rate parameter.

Returns:

The CDF of the given exgauss distribution at x.

quantile

@Deprecated
public static double quantile(double x,
                                          double mu,
                                          double sigma,
                                          double lambda)

Deprecated. Not yet implemented!

Inverse cumulative probability density function (probit) of an exgauss distribution.

Parameters:

x - value to evaluate probit function at.

mu - Mean value.

sigma - Standard deviation.

lambda - Rate parameter.

Returns:

The probit of the given exgauss distribution at x.