org.apache.commons.math3.distribution
Class ZipfDistribution

java.lang.Object
  org.apache.commons.math3.distribution.AbstractIntegerDistribution
      org.apache.commons.math3.distribution.ZipfDistribution

All Implemented Interfaces:

Serializable, IntegerDistribution

public class ZipfDistribution
extends AbstractIntegerDistribution

Implementation of the Zipf distribution.

Version:

$Id: ZipfDistribution.java 1416643 2012-12-03 19:37:14Z tn $

See Also:

Zipf distribution (MathWorld), Serialized Form

Field Summary

private double	exponent Exponent parameter of the distribution.
private int	numberOfElements Number of elements.
private double	numericalMean Cached numerical mean
private boolean	numericalMeanIsCalculated Whether or not the numerical mean has been calculated
private double	numericalVariance Cached numerical variance
private boolean	numericalVarianceIsCalculated Whether or not the numerical variance has been calculated
private static long	serialVersionUID Serializable version identifier.

Fields inherited from class org.apache.commons.math3.distribution.AbstractIntegerDistribution

random, randomData

Constructor Summary

ZipfDistribution(int numberOfElements, double exponent)
Create a new Zipf distribution with the given number of elements and exponent.

ZipfDistribution(RandomGenerator rng, int numberOfElements, double exponent)
Creates a Zipf distribution.

Method Summary

protected double	calculateNumericalMean() Used by getNumericalMean().
protected double	calculateNumericalVariance() Used by getNumericalVariance().
double	cumulativeProbability(int x) For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x).
private double	generalizedHarmonic(int n, double m) Calculates the Nth generalized harmonic number.
double	getExponent() Get the exponent characterizing the distribution.
int	getNumberOfElements() Get the number of elements (e.g.
double	getNumericalMean() Use this method to get the numerical value of the mean of this distribution.
double	getNumericalVariance() Use this method to get the numerical value of the variance of this distribution.
int	getSupportLowerBound() Access the lower bound of the support.
int	getSupportUpperBound() Access the upper bound of the support.
boolean	isSupportConnected() Use this method to get information about whether the support is connected, i.e.
double	probability(int x) For a random variable X whose values are distributed according to this distribution, this method returns P(X = x).

Methods inherited from class org.apache.commons.math3.distribution.AbstractIntegerDistribution

cumulativeProbability, inverseCumulativeProbability, reseedRandomGenerator, sample, sample, solveInverseCumulativeProbability

Methods inherited from class java.lang.Object

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

Field Detail

serialVersionUID

private static final long serialVersionUID

Serializable version identifier.

See Also:

Constant Field Values

numberOfElements

private final int numberOfElements

Number of elements.

exponent

private final double exponent

Exponent parameter of the distribution.

numericalMean

private double numericalMean

Cached numerical mean

numericalMeanIsCalculated

private boolean numericalMeanIsCalculated

Whether or not the numerical mean has been calculated

numericalVariance

private double numericalVariance

Cached numerical variance

numericalVarianceIsCalculated

private boolean numericalVarianceIsCalculated

Whether or not the numerical variance has been calculated

Constructor Detail

ZipfDistribution

public ZipfDistribution(int numberOfElements,
                        double exponent)

Create a new Zipf distribution with the given number of elements and exponent.

Parameters:

numberOfElements - Number of elements.

exponent - Exponent.

Throws:

NotStrictlyPositiveException - if numberOfElements <= 0 or exponent <= 0.

ZipfDistribution

public ZipfDistribution(RandomGenerator rng,
                        int numberOfElements,
                        double exponent)
                 throws NotStrictlyPositiveException

Creates a Zipf distribution.

Parameters:

rng - Random number generator.

numberOfElements - Number of elements.

exponent - Exponent.

Throws:

NotStrictlyPositiveException - if numberOfElements <= 0 or exponent <= 0.

Since:

3.1

Method Detail

getNumberOfElements

public int getNumberOfElements()

Get the number of elements (e.g. corpus size) for the distribution.

Returns:

the number of elements

getExponent

public double getExponent()

Get the exponent characterizing the distribution.

Returns:

the exponent

probability

public double probability(int x)

For a random variable X whose values are distributed according to this distribution, this method returns P(X = x). In other words, this method represents the probability mass function (PMF) for the distribution.

Parameters:

x - the point at which the PMF is evaluated

Returns:

the value of the probability mass function at x

cumulativeProbability

public double cumulativeProbability(int x)

For a random variable X whose values are distributed according to this distribution, this method returns P(X <= x). In other words, this method represents the (cumulative) distribution function (CDF) for this distribution.

Parameters:

x - the point at which the CDF is evaluated

Returns:

the probability that a random variable with this distribution takes a value less than or equal to x

getNumericalMean

public double getNumericalMean()

Use this method to get the numerical value of the mean of this distribution. For number of elements N and exponent s, the mean is Hs1 / Hs, where

• Hs1 = generalizedHarmonic(N, s - 1),
• Hs = generalizedHarmonic(N, s).

Returns:

the mean or Double.NaN if it is not defined

calculateNumericalMean

protected double calculateNumericalMean()

Used by getNumericalMean().

Returns:

the mean of this distribution

getNumericalVariance

public double getNumericalVariance()

Use this method to get the numerical value of the variance of this distribution. For number of elements N and exponent s, the mean is (Hs2 / Hs) - (Hs1^2 / Hs^2), where

• Hs2 = generalizedHarmonic(N, s - 2),
• Hs1 = generalizedHarmonic(N, s - 1),
• Hs = generalizedHarmonic(N, s).

Returns:

the variance (possibly Double.POSITIVE_INFINITY or Double.NaN if it is not defined)

calculateNumericalVariance

protected double calculateNumericalVariance()

Used by getNumericalVariance().

Returns:

the variance of this distribution

generalizedHarmonic

private double generalizedHarmonic(int n,
                                   double m)

Calculates the Nth generalized harmonic number. See Harmonic Series.

Parameters:

n - Term in the series to calculate (must be larger than 1)

m - Exponent (special case m = 1 is the harmonic series).

Returns:

the n^th generalized harmonic number.

getSupportLowerBound

public int getSupportLowerBound()

Access the lower bound of the support. This method must return the same value as inverseCumulativeProbability(0). In other words, this method must return

inf {x in Z | P(X <= x) > 0}.

The lower bound of the support is always 1 no matter the parameters.

Returns:

lower bound of the support (always 1)

getSupportUpperBound

public int getSupportUpperBound()

Access the upper bound of the support. This method must return the same value as inverseCumulativeProbability(1). In other words, this method must return

inf {x in R | P(X <= x) = 1}.

The upper bound of the support is the number of elements.

Returns:

upper bound of the support

isSupportConnected

public boolean isSupportConnected()

Use this method to get information about whether the support is connected, i.e. whether all integers between the lower and upper bound of the support are included in the support. The support of this distribution is connected.

Returns:

true