/*
* 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.FunctionEvaluationException;
import org.apache.commons.math.MathException;
import org.apache.commons.math.MathRuntimeException;
/**
* Base class for integer-valued discrete distributions. Default
* implementations are provided for some of the methods that do not vary
* from distribution to distribution.
*
* @version $Revision: 920558 $ $Date: 2010-03-08 17:57:32 -0500 (Mon, 08 Mar 2010) $
*/
public abstract class AbstractIntegerDistribution extends AbstractDistribution
implements IntegerDistribution, Serializable {
/**
* Message for endpoints in wrong order.
*/
private static final String WRONG_ORDER_ENDPOINTS_MESSAGE =
"lower endpoint ({0}) must be less than or equal to upper endpoint ({1})";
/**
* Message for out of range point.
*/
private static final String OUT_OF_RANGE_POINT =
"{0} out of [{1}, {2}] range";
/**
* Serializable version identifier
*/
private static final long serialVersionUID = -1146319659338487221L;
/**
* Default constructor.
*/
protected AbstractIntegerDistribution() {
super();
}
/**
* 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, or
* CDF, for this distribution.
* <p/>
* If <code>x</code> does not represent an integer value, the CDF is
* evaluated at the greatest integer less than x.
*
* @param x the value at which the distribution function is evaluated.
* @return cumulative probability that a random variable with this
* distribution takes a value less than or equal to <code>x</code>
* @throws MathException if the cumulative probability can not be
* computed due to convergence or other numerical errors.
*/
@Override
public double cumulativeProbability(double x) throws MathException {
return cumulativeProbability((int) Math.floor(x));
}
/**
* For a random variable X whose values are distributed according
* to this distribution, this method returns P(x0 ≤ X ≤ x1).
*
* @param x0 the (inclusive) lower bound
* @param x1 the (inclusive) upper bound
* @return the probability that a random variable with this distribution
* will take a value between <code>x0</code> and <code>x1</code>,
* including the endpoints.
* @throws MathException if the cumulative probability can not be
* computed due to convergence or other numerical errors.
* @throws IllegalArgumentException if <code>x0 > x1</code>
*/
@Override
public double cumulativeProbability(double x0, double x1)
throws MathException {
if (x0 > x1) {
throw MathRuntimeException.createIllegalArgumentException(
WRONG_ORDER_ENDPOINTS_MESSAGE, x0, x1);
}
if (Math.floor(x0) < x0) {
return cumulativeProbability(((int) Math.floor(x0)) + 1,
(int) Math.floor(x1)); // don't want to count mass below x0
} else { // x0 is mathematical integer, so use as is
return cumulativeProbability((int) Math.floor(x0),
(int) Math.floor(x1));
}
}
/**
* 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 distribution function, or PDF,
* for this distribution.
*
* @param x the value at which the PDF is evaluated.
* @return PDF for this distribution.
* @throws MathException if the cumulative probability can not be
* computed due to convergence or other numerical errors.
*/
@Override
public abstract double cumulativeProbability(int x) throws MathException;
/**
* 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, or PMF, for the distribution.
* <p/>
* If <code>x</code> does not represent an integer value, 0 is returned.
*
* @param x the value at which the probability density function is evaluated
* @return the value of the probability density function at x
*/
@Override
public double probability(double x) {
double fl = Math.floor(x);
if (fl == x) {
return this.probability((int) x);
} else {
return 0;
}
}
/**
* For a random variable X whose values are distributed according
* to this distribution, this method returns P(x0 ≤ X ≤ x1).
*
* @param x0 the inclusive, lower bound
* @param x1 the inclusive, upper bound
* @return the cumulative probability.
* @throws MathException if the cumulative probability can not be
* computed due to convergence or other numerical errors.
* @throws IllegalArgumentException if x0 > x1
*/
@Override
public double cumulativeProbability(int x0, int x1) throws MathException {
if (x0 > x1) {
throw MathRuntimeException.createIllegalArgumentException(
WRONG_ORDER_ENDPOINTS_MESSAGE, x0, x1);
}
return cumulativeProbability(x1) - cumulativeProbability(x0 - 1);
}
/**
* For a random variable X whose values are distributed according
* to this distribution, this method returns the largest x, such
* that P(X ≤ x) ≤ <code>p</code>.
*
* @param p the desired probability
* @return the largest x such that P(X ≤ x) <= p
* @throws MathException if the inverse cumulative probability can not be
* computed due to convergence or other numerical errors.
* @throws IllegalArgumentException if p < 0 or p > 1
*/
@Override
public int inverseCumulativeProbability(final double p) throws MathException {
if (p < 0.0 || p > 1.0) {
throw MathRuntimeException.createIllegalArgumentException(
OUT_OF_RANGE_POINT, p, 0.0, 1.0);
}
// by default, do simple bisection.
// subclasses can override if there is a better method.
int x0 = getDomainLowerBound(p);
int x1 = getDomainUpperBound(p);
double pm;
while (x0 < x1) {
int xm = x0 + (x1 - x0) / 2;
pm = checkedCumulativeProbability(xm);
if (pm > p) {
// update x1
if (xm == x1) {
// this can happen with integer division
// simply decrement x1
--x1;
} else {
// update x1 normally
x1 = xm;
}
} else {
// update x0
if (xm == x0) {
// this can happen with integer division
// simply increment x0
++x0;
} else {
// update x0 normally
x0 = xm;
}
}
}
// insure x0 is the correct critical point
pm = checkedCumulativeProbability(x0);
while (pm > p) {
--x0;
pm = checkedCumulativeProbability(x0);
}
// ensure x0 lies within domain bounds
x0 = x0>=getDomainLowerBound(p) ? x0 : getDomainLowerBound(p);
x0 = x0<=getDomainUpperBound(p) ? x0 : getDomainUpperBound(p);
return x0;
}
/**
* Computes the cumulative probablity function and checks for NaN values returned.
* Throws MathException if the value is NaN. Wraps and rethrows any MathException encountered
* evaluating the cumulative probability function in a FunctionEvaluationException. Throws
* FunctionEvaluationException of the cumulative probability function returns NaN.
*
* @param argument input value
* @return cumulative probability
* @throws FunctionEvaluationException if a MathException occurs computing the cumulative probability
*/
private double checkedCumulativeProbability(int argument) throws FunctionEvaluationException {
double result = Double.NaN;
try {
result = cumulativeProbability(argument);
} catch (MathException ex) {
throw new FunctionEvaluationException(ex, argument, ex.getPattern(), ex.getArguments());
}
if (Double.isNaN(result)) {
throw new FunctionEvaluationException(argument,
"Discrete cumulative probability function returned NaN for argument {0}", argument);
}
return result;
}
/**
* Access the domain value lower bound, based on <code>p</code>, used to
* bracket a PDF root. This method is used by
* {@link #inverseCumulativeProbability(double)} to find critical values.
*
* @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>
*/
protected abstract int getDomainLowerBound(double p);
/**
* Access the domain value upper bound, based on <code>p</code>, used to
* bracket a PDF root. This method is used by
* {@link #inverseCumulativeProbability(double)} to find critical values.
*
* @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>
*/
protected abstract int getDomainUpperBound(double p);
}