Catalano.Statistics.Distributions

Class InverseGammaDistribution

java.lang.Object

Catalano.Statistics.Distributions.InverseGammaDistribution

All Implemented Interfaces:

IDistribution

public class InverseGammaDistribution
extends java.lang.Object
implements IDistribution

The Inverse Gaussian distribution. The Inverse Gaussian distribution is a two-parameter family of continuous probability distributions with support on (0,∞). As λ tends to infinity, the inverse Gaussian distribution becomes more like a normal (Gaussian) distribution. The inverse Gaussian distribution has several properties analogous to a Gaussian distribution. The name can be misleading: it is an "inverse" only in that, while the Gaussian describes a Brownian Motion's level at a fixed time, the inverse Gaussian describes the distribution of the time a Brownian Motion with positive drift takes to reach a fixed positive level.

Constructor Summary

Constructors

Constructor and Description
InverseGammaDistribution(double mean, double shape) Constructs a new Inverse Gaussian distribution.

Method Summary

Modifier and Type	Method and Description
double	DistributionFunction(double x) Gets the cumulative distribution function (cdf) for this distribution evaluated at point x.
double	Entropy() Gets the entropy for this distribution.
double	getShape()
double	LogProbabilityDensityFunction(double x) Gets the log-probability density function (pdf) for this distribution evaluated at point x.
double	Mean() Gets the mean for this distribution.
double	ProbabilityDensityFunction(double x) Gets the probability density function (pdf) for this distribution evaluated at point x.
double	Variance() Gets the variance for this distribution.

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

InverseGammaDistribution

public InverseGammaDistribution(double mean,
                                double shape)

Constructs a new Inverse Gaussian distribution.

Parameters:

mean - The mean parameter mu.

shape - The shape parameter lambda.

Method Detail

getShape

public double getShape()

Variance

public double Variance()

Description copied from interface: IDistribution

Gets the variance for this distribution.

Specified by:

Variance in interface IDistribution

Returns:

The distribution's variance.

DistributionFunction

public double DistributionFunction(double x)

Description copied from interface: IDistribution

Gets the cumulative distribution function (cdf) for this distribution evaluated at point x.
The Cumulative Distribution Function (CDF) describes the cumulative probability that a given value or any value smaller than it will occur.

Specified by:

DistributionFunction in interface IDistribution

Parameters:

x - A single point in the distribution range.

Returns:

The probability of x occurring in the current distribution.

ProbabilityDensityFunction

public double ProbabilityDensityFunction(double x)

Description copied from interface: IDistribution

Gets the probability density function (pdf) for this distribution evaluated at point x.
The Probability Density Function (PDF) describes the probability that a given value x will occur.

Specified by:

ProbabilityDensityFunction in interface IDistribution

Parameters:

x - A single point in the distribution range.

Returns:

The probability of x occurring in the current distribution.

LogProbabilityDensityFunction

public double LogProbabilityDensityFunction(double x)

Description copied from interface: IDistribution

Gets the log-probability density function (pdf) for this distribution evaluated at point x.
The Probability Density Function (PDF) describes the probability that a given value x will occur.

Specified by:

LogProbabilityDensityFunction in interface IDistribution

Parameters:

x - A single point in the distribution range.

Returns:

The probability of x occurring in the current distribution.

Mean

public double Mean()

Description copied from interface: IDistribution

Gets the mean for this distribution.

Specified by:

Mean in interface IDistribution

Returns:

The distribution's mean value.

Entropy

public double Entropy()

Description copied from interface: IDistribution

Gets the entropy for this distribution.

Specified by:

Entropy in interface IDistribution

Returns:

The distribution's entropy.