Catalano.Statistics.Distributions

Class RayleighDistribution

java.lang.Object

Catalano.Statistics.Distributions.RayleighDistribution

All Implemented Interfaces:

IDistribution

public class RayleighDistribution
extends java.lang.Object
implements IDistribution

Rayleigh distribution. In probability theory and statistics, the Rayleigh distribution is a continuous probability distribution. A Rayleigh distribution is often observed when the overall magnitude of a vector is related to its directional components. One example where the Rayleigh distribution naturally arises is when wind speed is analyzed into its orthogonal 2-dimensional vector components. Assuming that the magnitude of each component is uncorrelated and normally distributed with equal variance, then the overall wind speed (vector magnitude) will be characterized by a Rayleigh distribution.

Constructor Summary

Constructors

Constructor and Description
RayleighDistribution(double sigma) Initializes a new instance of the RayleighDistribution class.

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

RayleighDistribution

public RayleighDistribution(double sigma)

Initializes a new instance of the RayleighDistribution class.

Parameters:

sigma - The Rayleight distribution's sigma.

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.