Catalano.Statistics.Distributions

Class LaplaceDistribution

java.lang.Object

Catalano.Statistics.Distributions.LaplaceDistribution

All Implemented Interfaces:

IDistribution

public class LaplaceDistribution
extends java.lang.Object
implements IDistribution

Laplace's Distribution. In probability theory and statistics, the Laplace distribution is a continuous probability distribution named after Pierre-Simon Laplace. It is also sometimes called the double exponential distribution. The difference between two independent identically distributed exponential random variables is governed by a Laplace distribution, as is a Brownian motion evaluated at an exponentially distributed random time. Increments of Laplace motion or a variance gamma process evaluated over the time scale also have a Laplace distribution. The probability density function of the Laplace distribution is also reminiscent of the normal distribution; however, whereas the normal distribution is expressed in terms of the squared difference from the mean μ, the Laplace density is expressed in terms of the absolute difference from the mean. Consequently the Laplace distribution has fatter tails than the normal distribution.

Constructor Summary

Constructors

Constructor and Description
LaplaceDistribution(double location, double scale)

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	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

LaplaceDistribution

public LaplaceDistribution(double location,
                           double scale)

Method Detail

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.

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.

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.

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.