001    /*
002     * Licensed to the Apache Software Foundation (ASF) under one or more
003     * contributor license agreements.  See the NOTICE file distributed with
004     * this work for additional information regarding copyright ownership.
005     * The ASF licenses this file to You under the Apache License, Version 2.0
006     * (the "License"); you may not use this file except in compliance with
007     * the License.  You may obtain a copy of the License at
008     *
009     *      http://www.apache.org/licenses/LICENSE-2.0
010     *
011     * Unless required by applicable law or agreed to in writing, software
012     * distributed under the License is distributed on an "AS IS" BASIS,
013     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014     * See the License for the specific language governing permissions and
015     * limitations under the License.
016     */
017    package org.apache.commons.math3.distribution;
018    
019    import org.apache.commons.math3.exception.NumberIsTooLargeException;
020    import org.apache.commons.math3.exception.OutOfRangeException;
021    
022    /**
023     * Base interface for distributions on the reals.
024     *
025     * @version $Id: RealDistribution.java 1416643 2012-12-03 19:37:14Z tn $
026     * @since 3.0
027     */
028    public interface RealDistribution {
029        /**
030         * For a random variable {@code X} whose values are distributed according
031         * to this distribution, this method returns {@code P(X = x)}. In other
032         * words, this method represents the probability mass function (PMF)
033         * for the distribution.
034         *
035         * @param x the point at which the PMF is evaluated
036         * @return the value of the probability mass function at point {@code x}
037         */
038        double probability(double x);
039    
040        /**
041         * Returns the probability density function (PDF) of this distribution
042         * evaluated at the specified point {@code x}. In general, the PDF is
043         * the derivative of the {@link #cumulativeProbability(double) CDF}.
044         * If the derivative does not exist at {@code x}, then an appropriate
045         * replacement should be returned, e.g. {@code Double.POSITIVE_INFINITY},
046         * {@code Double.NaN}, or  the limit inferior or limit superior of the
047         * difference quotient.
048         *
049         * @param x the point at which the PDF is evaluated
050         * @return the value of the probability density function at point {@code x}
051         */
052        double density(double x);
053    
054        /**
055         * For a random variable {@code X} whose values are distributed according
056         * to this distribution, this method returns {@code P(X <= x)}. In other
057         * words, this method represents the (cumulative) distribution function
058         * (CDF) for this distribution.
059         *
060         * @param x the point at which the CDF is evaluated
061         * @return the probability that a random variable with this
062         * distribution takes a value less than or equal to {@code x}
063         */
064        double cumulativeProbability(double x);
065    
066        /**
067         * For a random variable {@code X} whose values are distributed according
068         * to this distribution, this method returns {@code P(x0 < X <= x1)}.
069         *
070         * @param x0 the exclusive lower bound
071         * @param x1 the inclusive upper bound
072         * @return the probability that a random variable with this distribution
073         * takes a value between {@code x0} and {@code x1},
074         * excluding the lower and including the upper endpoint
075         * @throws NumberIsTooLargeException if {@code x0 > x1}
076         *
077         * @deprecated As of 3.1. In 4.0, this method will be renamed
078         * {@code probability(double x0, double x1)}.
079         */
080        @Deprecated
081        double cumulativeProbability(double x0, double x1) throws NumberIsTooLargeException;
082    
083        /**
084         * Computes the quantile function of this distribution. For a random
085         * variable {@code X} distributed according to this distribution, the
086         * returned value is
087         * <ul>
088         * <li><code>inf{x in R | P(X<=x) >= p}</code> for {@code 0 < p <= 1},</li>
089         * <li><code>inf{x in R | P(X<=x) > 0}</code> for {@code p = 0}.</li>
090         * </ul>
091         *
092         * @param p the cumulative probability
093         * @return the smallest {@code p}-quantile of this distribution
094         * (largest 0-quantile for {@code p = 0})
095         * @throws OutOfRangeException if {@code p < 0} or {@code p > 1}
096         */
097        double inverseCumulativeProbability(double p) throws OutOfRangeException;
098    
099        /**
100         * Use this method to get the numerical value of the mean of this
101         * distribution.
102         *
103         * @return the mean or {@code Double.NaN} if it is not defined
104         */
105        double getNumericalMean();
106    
107        /**
108         * Use this method to get the numerical value of the variance of this
109         * distribution.
110         *
111         * @return the variance (possibly {@code Double.POSITIVE_INFINITY} as
112         * for certain cases in {@link TDistribution}) or {@code Double.NaN} if it
113         * is not defined
114         */
115        double getNumericalVariance();
116    
117        /**
118         * Access the lower bound of the support. This method must return the same
119         * value as {@code inverseCumulativeProbability(0)}. In other words, this
120         * method must return
121         * <p><code>inf {x in R | P(X <= x) > 0}</code>.</p>
122         *
123         * @return lower bound of the support (might be
124         * {@code Double.NEGATIVE_INFINITY})
125         */
126        double getSupportLowerBound();
127    
128        /**
129         * Access the upper bound of the support. This method must return the same
130         * value as {@code inverseCumulativeProbability(1)}. In other words, this
131         * method must return
132         * <p><code>inf {x in R | P(X <= x) = 1}</code>.</p>
133         *
134         * @return upper bound of the support (might be
135         * {@code Double.POSITIVE_INFINITY})
136         */
137        double getSupportUpperBound();
138    
139        /**
140         * Whether or not the lower bound of support is in the domain of the density
141         * function.  Returns true iff {@code getSupporLowerBound()} is finite and
142         * {@code density(getSupportLowerBound())} returns a non-NaN, non-infinite
143         * value.
144         *
145         * @return true if the lower bound of support is finite and the density
146         * function returns a non-NaN, non-infinite value there
147         * @deprecated to be removed in 4.0
148         */
149        boolean isSupportLowerBoundInclusive();
150    
151        /**
152         * Whether or not the upper bound of support is in the domain of the density
153         * function.  Returns true iff {@code getSupportUpperBound()} is finite and
154         * {@code density(getSupportUpperBound())} returns a non-NaN, non-infinite
155         * value.
156         *
157         * @return true if the upper bound of support is finite and the density
158         * function returns a non-NaN, non-infinite value there
159         * @deprecated to be removed in 4.0
160         */
161        boolean isSupportUpperBoundInclusive();
162    
163        /**
164         * Use this method to get information about whether the support is connected,
165         * i.e. whether all values between the lower and upper bound of the support
166         * are included in the support.
167         *
168         * @return whether the support is connected or not
169         */
170        boolean isSupportConnected();
171    
172        /**
173         * Reseed the random generator used to generate samples.
174         *
175         * @param seed the new seed
176         */
177        void reseedRandomGenerator(long seed);
178    
179        /**
180         * Generate a random value sampled from this distribution.
181         *
182         * @return a random value.
183         */
184        double sample();
185    
186        /**
187         * Generate a random sample from the distribution.
188         *
189         * @param sampleSize the number of random values to generate
190         * @return an array representing the random sample
191         * @throws org.apache.commons.math3.exception.NotStrictlyPositiveException
192         * if {@code sampleSize} is not positive
193         */
194        double[] sample(int sampleSize);
195    }