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 }