org.hipparchus.distribution.discrete

Class ZipfDistribution

java.lang.Object

org.hipparchus.distribution.discrete.AbstractIntegerDistribution

org.hipparchus.distribution.discrete.ZipfDistribution

All Implemented Interfaces:

Serializable, IntegerDistribution

public class ZipfDistribution
extends AbstractIntegerDistribution

Implementation of the Zipf distribution.

Parameters: For a random variable X whose values are distributed according to this distribution, the probability mass function is given by

   P(X = k) = H(N,s) * 1 / k^s    for  k = 1,2,...,N.
 

H(N,s) is the normalizing constant which corresponds to the generalized harmonic number of order N of s.

• N is the number of elements
• s is the exponent

See Also:

Zipf's law (Wikipedia), Generalized harmonic numbers, Serialized Form

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method and Description
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).
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	logProbability(int x) For a random variable X whose values are distributed according to this distribution, this method returns log(P(X = x)), where log is the natural logarithm.
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.hipparchus.distribution.discrete.AbstractIntegerDistribution

inverseCumulativeProbability, probability, solveInverseCumulativeProbability

Methods inherited from class java.lang.Object

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

Constructor Detail

ZipfDistribution

public ZipfDistribution(int numberOfElements,
                        double exponent)
                 throws MathIllegalArgumentException

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

Parameters:

numberOfElements - Number of elements.

exponent - Exponent.

Throws:

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

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

logProbability

public double logProbability(int x)

For a random variable X whose values are distributed according to this distribution, this method returns log(P(X = x)), where log is the natural logarithm. In other words, this method represents the logarithm of the probability mass function (PMF) for the distribution. Note that due to the floating point precision and under/overflow issues, this method will for some distributions be more precise and faster than computing the logarithm of IntegerDistribution.probability(int).

The default implementation simply computes the logarithm of probability(x).

Specified by:

logProbability in interface IntegerDistribution

Overrides:

logProbability in class AbstractIntegerDistribution

Parameters:

x - the point at which the PMF is evaluated

Returns:

the logarithm of 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

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