/*
* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.commons.math3.distribution;
import org.apache.commons.math3.exception.NotStrictlyPositiveException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
import org.apache.commons.math3.random.RandomGenerator;
import org.apache.commons.math3.random.Well19937c;
import org.apache.commons.math3.util.FastMath;
/**
* Implementation of the Zipf distribution.
*
* @see <a href="http://mathworld.wolfram.com/ZipfDistribution.html">Zipf distribution (MathWorld)</a>
*/
public class ZipfDistribution extends AbstractIntegerDistribution {
/** Serializable version identifier. */
private static final long serialVersionUID = -140627372283420404L;
/** Number of elements. */
private final int numberOfElements;
/** Exponent parameter of the distribution. */
private final double exponent;
/** Cached numerical mean */
private double numericalMean = Double.NaN;
/** Whether or not the numerical mean has been calculated */
private boolean numericalMeanIsCalculated = false;
/** Cached numerical variance */
private double numericalVariance = Double.NaN;
/** Whether or not the numerical variance has been calculated */
private boolean numericalVarianceIsCalculated = false;
/**
* Create a new Zipf distribution with the given number of elements and
* exponent.
* <p>
* <b>Note:</b> this constructor will implicitly create an instance of
* {@link Well19937c} as random generator to be used for sampling only (see
* {@link #sample()} and {@link #sample(int)}). In case no sampling is
* needed for the created distribution, it is advised to pass {@code null}
* as random generator via the appropriate constructors to avoid the
* additional initialisation overhead.
*
* @param numberOfElements Number of elements.
* @param exponent Exponent.
* @exception NotStrictlyPositiveException if {@code numberOfElements <= 0}
* or {@code exponent <= 0}.
*/
public ZipfDistribution(final int numberOfElements, final double exponent) {
this(new Well19937c(), numberOfElements, exponent);
}
/**
* Creates a Zipf distribution.
*
* @param rng Random number generator.
* @param numberOfElements Number of elements.
* @param exponent Exponent.
* @exception NotStrictlyPositiveException if {@code numberOfElements <= 0}
* or {@code exponent <= 0}.
* @since 3.1
*/
public ZipfDistribution(RandomGenerator rng,
int numberOfElements,
double exponent)
throws NotStrictlyPositiveException {
super(rng);
if (numberOfElements <= 0) {
throw new NotStrictlyPositiveException(LocalizedFormats.DIMENSION,
numberOfElements);
}
if (exponent <= 0) {
throw new NotStrictlyPositiveException(LocalizedFormats.EXPONENT,
exponent);
}
this.numberOfElements = numberOfElements;
this.exponent = exponent;
}
/**
* Get the number of elements (e.g. corpus size) for the distribution.
*
* @return the number of elements
*/
public int getNumberOfElements() {
return numberOfElements;
}
/**
* Get the exponent characterizing the distribution.
*
* @return the exponent
*/
public double getExponent() {
return exponent;
}
/** {@inheritDoc} */
public double probability(final int x) {
if (x <= 0 || x > numberOfElements) {
return 0.0;
}
return (1.0 / FastMath.pow(x, exponent)) / generalizedHarmonic(numberOfElements, exponent);
}
/** {@inheritDoc} */
@Override
public double logProbability(int x) {
if (x <= 0 || x > numberOfElements) {
return Double.NEGATIVE_INFINITY;
}
return -FastMath.log(x) * exponent - FastMath.log(generalizedHarmonic(numberOfElements, exponent));
}
/** {@inheritDoc} */
public double cumulativeProbability(final int x) {
if (x <= 0) {
return 0.0;
} else if (x >= numberOfElements) {
return 1.0;
}
return generalizedHarmonic(x, exponent) / generalizedHarmonic(numberOfElements, exponent);
}
/**
* {@inheritDoc}
*
* For number of elements {@code N} and exponent {@code s}, the mean is
* {@code Hs1 / Hs}, where
* <ul>
* <li>{@code Hs1 = generalizedHarmonic(N, s - 1)},</li>
* <li>{@code Hs = generalizedHarmonic(N, s)}.</li>
* </ul>
*/
public double getNumericalMean() {
if (!numericalMeanIsCalculated) {
numericalMean = calculateNumericalMean();
numericalMeanIsCalculated = true;
}
return numericalMean;
}
/**
* Used by {@link #getNumericalMean()}.
*
* @return the mean of this distribution
*/
protected double calculateNumericalMean() {
final int N = getNumberOfElements();
final double s = getExponent();
final double Hs1 = generalizedHarmonic(N, s - 1);
final double Hs = generalizedHarmonic(N, s);
return Hs1 / Hs;
}
/**
* {@inheritDoc}
*
* For number of elements {@code N} and exponent {@code s}, the mean is
* {@code (Hs2 / Hs) - (Hs1^2 / Hs^2)}, where
* <ul>
* <li>{@code Hs2 = generalizedHarmonic(N, s - 2)},</li>
* <li>{@code Hs1 = generalizedHarmonic(N, s - 1)},</li>
* <li>{@code Hs = generalizedHarmonic(N, s)}.</li>
* </ul>
*/
public double getNumericalVariance() {
if (!numericalVarianceIsCalculated) {
numericalVariance = calculateNumericalVariance();
numericalVarianceIsCalculated = true;
}
return numericalVariance;
}
/**
* Used by {@link #getNumericalVariance()}.
*
* @return the variance of this distribution
*/
protected double calculateNumericalVariance() {
final int N = getNumberOfElements();
final double s = getExponent();
final double Hs2 = generalizedHarmonic(N, s - 2);
final double Hs1 = generalizedHarmonic(N, s - 1);
final double Hs = generalizedHarmonic(N, s);
return (Hs2 / Hs) - ((Hs1 * Hs1) / (Hs * Hs));
}
/**
* Calculates the Nth generalized harmonic number. See
* <a href="http://mathworld.wolfram.com/HarmonicSeries.html">Harmonic
* Series</a>.
*
* @param n Term in the series to calculate (must be larger than 1)
* @param m Exponent (special case {@code m = 1} is the harmonic series).
* @return the n<sup>th</sup> generalized harmonic number.
*/
private double generalizedHarmonic(final int n, final double m) {
double value = 0;
for (int k = n; k > 0; --k) {
value += 1.0 / FastMath.pow(k, m);
}
return value;
}
/**
* {@inheritDoc}
*
* The lower bound of the support is always 1 no matter the parameters.
*
* @return lower bound of the support (always 1)
*/
public int getSupportLowerBound() {
return 1;
}
/**
* {@inheritDoc}
*
* The upper bound of the support is the number of elements.
*
* @return upper bound of the support
*/
public int getSupportUpperBound() {
return getNumberOfElements();
}
/**
* {@inheritDoc}
*
* The support of this distribution is connected.
*
* @return {@code true}
*/
public boolean isSupportConnected() {
return true;
}
}