Catalano.Statistics.Distributions

Class ParetoDistribution

java.lang.Object

Catalano.Statistics.Distributions.ParetoDistribution

All Implemented Interfaces:

IDistribution

public class ParetoDistribution
extends java.lang.Object
implements IDistribution

Pareto's Distribution. The Pareto distribution, named after the Italian economist Vilfredo Pareto, is a power law probability distribution that coincides with social, scientific, geophysical, actuarial, and many other types of observable phenomena. Outside the field of economics it is sometimes referred to as the Bradford distribution.

Constructor Summary

Constructors

Constructor and Description
ParetoDistribution(double scale, double shape) Creates new Pareto 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	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	Median() Gets the median for this distribution.
double	Mode() Gets the mode 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

ParetoDistribution

public ParetoDistribution(double scale,
                          double shape)

Creates new Pareto distribution.

Parameters:

scale - The scale parameter x.

shape - The shape parameter alpha.

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.

Mode

public double Mode()

Gets the mode for this distribution.

Returns:

The distribution's mode value.

Median

public double Median()

Gets the median for this distribution.

Returns:

The distribution's median value.

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.