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

Class InverseGaussianDistribution

java.lang.Object

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

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

All Implemented Interfaces:

Distribution

@Alias(value={"invgauss","wald","de.lmu.ifi.dbs.elki.math.statistics.distribution.WaldDistribution"})
public class InverseGaussianDistribution
extends AbstractDistribution

Inverse Gaussian distribution aka Wald distribution. Beware that SciPy uses a different location parameter. InverseGaussian(a, x) ~ scipy.stats.invgauss(a/x, x) Our parameter scheme is in line with common literature. SciPy naming scheme has comparable notion of location and scale across distributions. So both have their benefits.

Since:

0.6.0

Author:

Erich Schubert

Nested Class Summary

Nested Classes

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

Field Summary

Fields

Modifier and Type	Field and Description
private double	mean Location value
private double	shape Shape parameter

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

random

Constructor Summary

Constructors

Constructor and Description
InverseGaussianDistribution(double mean, double shape) Constructor for Gaussian distribution
InverseGaussianDistribution(double mean, double shape, java.util.Random random) Constructor for wald distribution
InverseGaussianDistribution(double mean, double shape, RandomFactory random) Constructor for wald 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 shape) Cumulative probability density function (CDF) of a Wald distribution.
double	getMean() Mean parameter.
double	getShape() Shape parameter.
double	logpdf(double val) Return the log density of an existing value
static double	logpdf(double x, double mu, double shape) Probability density function of the Wald 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 shape) Probability density function of the Wald distribution.
double	quantile(double q) Deprecated. NOT YET IMPLEMENTED.
static double	quantile(double x, double mu, double shape) 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

Location value

shape

private double shape

Shape parameter

Constructor Detail

InverseGaussianDistribution

public InverseGaussianDistribution(double mean,
                                   double shape,
                                   java.util.Random random)

Constructor for wald distribution

Parameters:

mean - Mean

shape - Shape parameter

random - Random generator

InverseGaussianDistribution

public InverseGaussianDistribution(double mean,
                                   double shape,
                                   RandomFactory random)

Constructor for wald distribution

Parameters:

mean - Mean

shape - Shape parameter

random - Random generator

InverseGaussianDistribution

public InverseGaussianDistribution(double mean,
                                   double shape)

Constructor for Gaussian distribution

Parameters:

mean - Mean

shape - Shape parameter

Method Detail

getMean

public double getMean()

Mean parameter.

Returns:

Mean

getShape

public double getShape()

Shape parameter.

Returns:

Shape

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

pdf

public static double pdf(double x,
                         double mu,
                         double shape)

Probability density function of the Wald distribution.

Parameters:

x - The value.

mu - The mean.

shape - Shape parameter

Returns:

PDF of the given Wald distribution at x.

logpdf

public static double logpdf(double x,
                            double mu,
                            double shape)

Probability density function of the Wald distribution.

Parameters:

x - The value.

mu - The mean.

shape - Shape parameter

Returns:

log PDF of the given Wald distribution at x.

cdf

public static double cdf(double x,
                         double mu,
                         double shape)

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

Parameters:

x - value to evaluate CDF at

mu - Mean value

shape - Shape parameter

Returns:

The CDF of the given Wald distribution at x.

quantile

@Deprecated
public static double quantile(double x,
                                          double mu,
                                          double shape)

Deprecated. NOT YET IMPLEMENTED.

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

Parameters:

x - value to evaluate probit function at

mu - Mean value

shape - Shape parameter

Returns:

The probit of the given Wald distribution at x.