/*
* 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.math.distribution;
import java.io.Serializable;
import org.apache.commons.math.MathRuntimeException;
import org.apache.commons.math.exception.util.LocalizedFormats;
import org.apache.commons.math.util.FastMath;
/**
* Implementation for the {@link ZipfDistribution}.
*
* @version $Revision: 1054524 $ $Date: 2011-01-03 05:59:18 +0100 (lun. 03 janv. 2011) $
*/
public class ZipfDistributionImpl extends AbstractIntegerDistribution
implements ZipfDistribution, Serializable {
/** Serializable version identifier. */
private static final long serialVersionUID = -140627372283420404L;
/** Number of elements. */
private int numberOfElements;
/** Exponent parameter of the distribution. */
private double exponent;
/**
* Create a new Zipf distribution with the given number of elements and
* exponent. Both values must be positive; otherwise an
* <code>IllegalArgumentException</code> is thrown.
*
* @param numberOfElements the number of elements
* @param exponent the exponent
* @exception IllegalArgumentException if n ≤ 0 or s ≤ 0.0
*/
public ZipfDistributionImpl(final int numberOfElements, final double exponent)
throws IllegalArgumentException {
setNumberOfElementsInternal(numberOfElements);
setExponentInternal(exponent);
}
/**
* Get the number of elements (e.g. corpus size) for the distribution.
*
* @return the number of elements
*/
public int getNumberOfElements() {
return numberOfElements;
}
/**
* Set the number of elements (e.g. corpus size) for the distribution.
* The parameter value must be positive; otherwise an
* <code>IllegalArgumentException</code> is thrown.
*
* @param n the number of elements
* @exception IllegalArgumentException if n ≤ 0
* @deprecated as of 2.1 (class will become immutable in 3.0)
*/
@Deprecated
public void setNumberOfElements(final int n) {
setNumberOfElementsInternal(n);
}
/**
* Set the number of elements (e.g. corpus size) for the distribution.
* The parameter value must be positive; otherwise an
* <code>IllegalArgumentException</code> is thrown.
*
* @param n the number of elements
* @exception IllegalArgumentException if n ≤ 0
*/
private void setNumberOfElementsInternal(final int n)
throws IllegalArgumentException {
if (n <= 0) {
throw MathRuntimeException.createIllegalArgumentException(
LocalizedFormats.INSUFFICIENT_DIMENSION, n, 0);
}
this.numberOfElements = n;
}
/**
* Get the exponent characterising the distribution.
*
* @return the exponent
*/
public double getExponent() {
return exponent;
}
/**
* Set the exponent characterising the distribution.
* The parameter value must be positive; otherwise an
* <code>IllegalArgumentException</code> is thrown.
*
* @param s the exponent
* @exception IllegalArgumentException if s ≤ 0.0
* @deprecated as of 2.1 (class will become immutable in 3.0)
*/
@Deprecated
public void setExponent(final double s) {
setExponentInternal(s);
}
/**
* Set the exponent characterising the distribution.
* The parameter value must be positive; otherwise an
* <code>IllegalArgumentException</code> is thrown.
*
* @param s the exponent
* @exception IllegalArgumentException if s ≤ 0.0
*/
private void setExponentInternal(final double s)
throws IllegalArgumentException {
if (s <= 0.0) {
throw MathRuntimeException.createIllegalArgumentException(
LocalizedFormats.NOT_POSITIVE_EXPONENT,
s);
}
this.exponent = s;
}
/**
* The probability mass function P(X = x) for a Zipf distribution.
*
* @param x the value at which the probability density function is evaluated.
* @return the value of the probability mass function at x
*/
public double probability(final int x) {
if (x <= 0 || x > numberOfElements) {
return 0.0;
}
return (1.0 / FastMath.pow(x, exponent)) / generalizedHarmonic(numberOfElements, exponent);
}
/**
* The probability distribution function P(X <= x) for a Zipf distribution.
*
* @param x the value at which the PDF is evaluated.
* @return Zipf distribution function evaluated at x
*/
@Override
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);
}
/**
* Access the domain value lower bound, based on <code>p</code>, used to
* bracket a PDF root.
*
* @param p the desired probability for the critical value
* @return domain value lower bound, i.e.
* P(X < <i>lower bound</i>) < <code>p</code>
*/
@Override
protected int getDomainLowerBound(final double p) {
return 0;
}
/**
* Access the domain value upper bound, based on <code>p</code>, used to
* bracket a PDF root.
*
* @param p the desired probability for the critical value
* @return domain value upper bound, i.e.
* P(X < <i>upper bound</i>) > <code>p</code>
*/
@Override
protected int getDomainUpperBound(final double p) {
return numberOfElements;
}
/**
* Calculates the Nth generalized harmonic number. See
* <a href="http://mathworld.wolfram.com/HarmonicSeries.html">Harmonic
* Series</a>.
*
* @param n the term in the series to calculate (must be ≥ 1)
* @param m the exponent; special case m == 1.0 is the harmonic series
* @return the nth 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;
}
/**
* Returns the lower bound of the support for the distribution.
*
* The lower bound of the support is always 1 no matter the parameters.
*
* @return lower bound of the support (always 1)
* @since 2.2
*/
public int getSupportLowerBound() {
return 1;
}
/**
* Returns the upper bound of the support for the distribution.
*
* The upper bound of the support is the number of elements
*
* @return upper bound of the support
* @since 2.2
*/
public int getSupportUpperBound() {
return getNumberOfElements();
}
/**
* Returns the mean.
*
* For number of elements N and exponent s, the mean is
* <code>Hs1 / Hs</code> where
* <ul>
* <li><code>Hs1 = generalizedHarmonic(N, s - 1)</code></li>
* <li><code>Hs = generalizedHarmonic(N, s)</code></li>
* </ul>
*
* @return the mean
* @since 2.2
*/
protected double getNumericalMean() {
final int N = getNumberOfElements();
final double s = getExponent();
final double Hs1 = generalizedHarmonic(N, s - 1);
final double Hs = generalizedHarmonic(N, s);
return Hs1 / Hs;
}
/**
* Returns the variance.
*
* For number of elements N and exponent s, the mean is
* <code>(Hs2 / Hs) - (Hs1^2 / Hs^2)</code> where
* <ul>
* <li><code>Hs2 = generalizedHarmonic(N, s - 2)</code></li>
* <li><code>Hs1 = generalizedHarmonic(N, s - 1)</code></li>
* <li><code>Hs = generalizedHarmonic(N, s)</code></li>
* </ul>
*
* @return the variance
* @since 2.2
*/
protected double getNumericalVariance() {
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));
}
}