org.apache.commons.math.distribution
Class ZipfDistributionImpl

java.lang.Object
  org.apache.commons.math.distribution.AbstractDistribution
      org.apache.commons.math.distribution.AbstractIntegerDistribution
          org.apache.commons.math.distribution.ZipfDistributionImpl

All Implemented Interfaces:

java.io.Serializable, DiscreteDistribution, Distribution, IntegerDistribution, ZipfDistribution

public class ZipfDistributionImpl
extends AbstractIntegerDistribution
implements ZipfDistribution, java.io.Serializable

Implementation for the ZipfDistribution.

Version:

$Id: ZipfDistributionImpl.java 1131229 2011-06-03 20:49:25Z luc $

See Also:

Serialized Form

Field Summary

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

randomData

Constructor Summary

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

Method Summary

protected double	calculateNumericalMean() Use this method to actually calculate the mean for the specific distribution.
protected double	calculateNumericalVariance() Use this method to actually calculate the variance for the specific distribution.
double	cumulativeProbability(int x) The probability distribution function P(X <= x) for a Zipf distribution.
protected int	getDomainLowerBound(double p) Access the domain value lower bound, based on p, used to bracket a PDF root.
protected int	getDomainUpperBound(double p) Access the domain value upper bound, based on p, used to bracket a PDF root.
double	getExponent() Get the exponent characterising the distribution.
int	getNumberOfElements() Get the number of elements (e.g. corpus size) for the distribution.
int	getSupportLowerBound() Access the lower bound of the support.
int	getSupportUpperBound() Access the upper bound of the support.
double	probability(int x) The probability mass function P(X = x) for a Zipf distribution.

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

cumulativeProbability, cumulativeProbability, cumulativeProbability, inverseCumulativeProbability, isSupportLowerBoundInclusive, isSupportUpperBoundInclusive, probability, reseedRandomGenerator, sample, sample

Methods inherited from class org.apache.commons.math.distribution.AbstractDistribution

getNumericalMean, getNumericalVariance, isSupportConnected

Methods inherited from class java.lang.Object

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

Methods inherited from interface org.apache.commons.math.distribution.IntegerDistribution

cumulativeProbability, inverseCumulativeProbability, reseedRandomGenerator, sample, sample

Methods inherited from interface org.apache.commons.math.distribution.DiscreteDistribution

probability

Methods inherited from interface org.apache.commons.math.distribution.Distribution

cumulativeProbability, cumulativeProbability, getNumericalMean, getNumericalVariance, isSupportConnected, isSupportLowerBoundInclusive, isSupportUpperBoundInclusive

Constructor Detail

ZipfDistributionImpl

public ZipfDistributionImpl(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.

Method Detail

getNumberOfElements

public int getNumberOfElements()

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

Specified by:

getNumberOfElements in interface ZipfDistribution

Returns:

the number of elements

getExponent

public double getExponent()

Get the exponent characterising the distribution.

Specified by:

getExponent in interface ZipfDistribution

Returns:

the exponent

probability

public double probability(int x)

The probability mass function P(X = x) for a Zipf distribution.

Specified by:

probability in interface IntegerDistribution

Parameters:

x - Value at which the probability density function is evaluated.

Returns:

the value of the probability mass function at x.

cumulativeProbability

public double cumulativeProbability(int x)

The probability distribution function P(X <= x) for a Zipf distribution.

Specified by:

cumulativeProbability in interface IntegerDistribution

Specified by:

cumulativeProbability in class AbstractIntegerDistribution

Parameters:

x - Value at which the PDF is evaluated.

Returns:

Zipf distribution function evaluated at x.

getDomainLowerBound

protected int getDomainLowerBound(double p)

Access the domain value lower bound, based on p, used to bracket a PDF root.

Specified by:

getDomainLowerBound in class AbstractIntegerDistribution

Parameters:

p - Desired probability for the critical value.

Returns:

the domain value lower bound, i.e. P(X < 'lower bound') < p.

getDomainUpperBound

protected int getDomainUpperBound(double p)

Access the domain value upper bound, based on p, used to bracket a PDF root.

Specified by:

getDomainUpperBound in class AbstractIntegerDistribution

Parameters:

p - Desired probability for the critical value

Returns:

the domain value upper bound, i.e. P(X < 'upper bound') > p.

getSupportLowerBound

public int getSupportLowerBound()

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

Specified by:

getSupportLowerBound in class AbstractIntegerDistribution

Returns:

lower bound of the support (always 1)

getSupportUpperBound

public int getSupportUpperBound()

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

Specified by:

getSupportUpperBound in class AbstractIntegerDistribution

Returns:

upper bound of the support

calculateNumericalMean

protected double calculateNumericalMean()

Use this method to actually calculate the mean for the specific distribution. Use AbstractDistribution.getNumericalMean() (which implements caching) to actually get the mean. For number of elements N and exponent s, the mean is Hs1 / Hs where

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

Specified by:

calculateNumericalMean in class AbstractDistribution

Returns:

the mean or Double.NaN if it's not defined

calculateNumericalVariance

protected double calculateNumericalVariance()

Use this method to actually calculate the variance for the specific distribution. Use AbstractDistribution.getNumericalVariance() (which implements caching) to actually get the variance. 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)

Specified by:

calculateNumericalVariance in class AbstractDistribution

Returns:

the variance or Double.NaN if it's not defined