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

Class ExponentiallyModifiedGaussianDistribution

java.lang.Object

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

All Implemented Interfaces:

Distribution, DistributionWithRandom

@Alias(value="exgaussian")
public class ExponentiallyModifiedGaussianDistribution
extends Object
implements DistributionWithRandom

Exponentially modified Gaussian (EMG) distribution (ExGaussian distribution) is a combination of a normal distribution and an exponential distribution.

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	ExponentiallyModifiedGaussianDistribution.OlivierNorbergEstimator Naive distribution estimation using mean and sample variance.

Field Summary

Fields

Modifier and Type	Field and Description
private double	lambda Exponential rate.
private double	mean Mean value for the generator
static ExponentiallyModifiedGaussianDistribution.OlivierNorbergEstimator	OLIVIER_NORBERG_ESTIMATOR Static estimator class.
private Random	rnd Random generator.
private double	stddev Standard deviation

Constructor Summary

Constructors

Constructor and Description
ExponentiallyModifiedGaussianDistribution(double mean, double stddev, double lambda) Constructor for ExGaussian distribution
ExponentiallyModifiedGaussianDistribution(double mean, double stddev, double lambda, Random rnd) Constructor for ExGaussian distribution

Method Summary

Methods

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	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!
String	toString() Describe the distribution

Methods inherited from class java.lang.Object

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

Field Detail

OLIVIER_NORBERG_ESTIMATOR

public static ExponentiallyModifiedGaussianDistribution.OlivierNorbergEstimator OLIVIER_NORBERG_ESTIMATOR

Static estimator class.

mean

private double mean

Mean value for the generator

stddev

private double stddev

Standard deviation

lambda

private double lambda

Exponential rate.

rnd

private Random rnd

Random generator.

Constructor Detail

ExponentiallyModifiedGaussianDistribution

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

Constructor for ExGaussian distribution

Parameters:

mean - Mean

stddev - Standard Deviation

lambda - Rate

rnd - 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

Specified by:

pdf in interface Distribution

Parameters:

val - existing value

Returns:

distribution density

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

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.

Specified by:

quantile in interface Distribution

Parameters:

q - Quantile to find

Returns:

Quantile position

nextRandom

public double nextRandom()

Description copied from interface: DistributionWithRandom

Generate a new random value

Specified by:

nextRandom in interface DistributionWithRandom

Returns:

new random value

toString

public String toString()

Description copied from interface: Distribution

Describe the distribution

Specified by:

toString in interface Distribution

Overrides:

toString in class 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.

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.