cern.jet.random
Class Pareto

java.lang.Object
  cern.colt.PersistentObject
      cern.jet.random.AbstractDistribution
          cern.jet.random.AbstractContinousDistribution
              cern.jet.random.Pareto

All Implemented Interfaces:

DoubleFunction, IntFunction, java.io.Serializable, java.lang.Cloneable

Direct Known Subclasses:

TruncatedPareto

public class Pareto
extends AbstractContinousDistribution

Pareto Distribution. See the math definition animated definition.

p(x) = shape*scale^shape*x^{-(1+shape)} for x >= scale, shape > 0.

The mean is infinite if shape <= 1 and variance is infinite if shape <= 2.

Instance methods operate on a user supplied uniform random number generator; they are unsynchronized.

Static methods operate on a default uniform random number generator; they are synchronized.

Version:

0.1, 26-Nov-99

Author:

Andy Ogielski ato@renesys.com

See Also:

Serialized Form

Constructor Summary

Pareto(double k, double alpha, RandomElement randomGenerator)
Constructs a Pareto distribution.

Method Summary

double	cdf(double x) Returns the cumulative distribution function.
double	nextDouble() Returns a random number from the distribution.
double	nextDouble(double k, double alpha) Returns a random number from the distribution; bypasses the internal state.
double	pdf(double x) Returns the probability distribution function.
void	setState(double k, double alpha) Sets the parameters.
static double	staticNextDouble(double k, double alpha) Returns a random number from the distribution with the given scale = k, and shape = alpha.
java.lang.String	toString() Returns a String representation of the receiver.

Methods inherited from class cern.jet.random.AbstractDistribution

apply, apply, clone, makeDefaultGenerator, nextInt

Methods inherited from class java.lang.Object

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

Constructor Detail

Pareto

public Pareto(double k,
              double alpha,
              RandomElement randomGenerator)

Constructs a Pareto distribution.

Method Detail

cdf

public double cdf(double x)

Returns the cumulative distribution function.

nextDouble

public double nextDouble()

Returns a random number from the distribution.

Specified by:

nextDouble in class AbstractDistribution

nextDouble

public double nextDouble(double k,
                         double alpha)

Returns a random number from the distribution; bypasses the internal state.

pdf

public double pdf(double x)

Returns the probability distribution function.

setState

public void setState(double k,
                     double alpha)

Sets the parameters.

toString

public java.lang.String toString()

Returns a String representation of the receiver.

Overrides:

toString in class java.lang.Object

staticNextDouble

public static double staticNextDouble(double k,
                                      double alpha)

Returns a random number from the distribution with the given scale = k, and shape = alpha.