1 /*
2 * Licensed to the Apache Software Foundation (ASF) under one or more
3 * contributor license agreements. See the NOTICE file distributed with
4 * this work for additional information regarding copyright ownership.
5 * The ASF licenses this file to You under the Apache License, Version 2.0
6 * (the "License"); you may not use this file except in compliance with
7 * the License. You may obtain a copy of the License at
8 *
9 * https://www.apache.org/licenses/LICENSE-2.0
10 *
11 * Unless required by applicable law or agreed to in writing, software
12 * distributed under the License is distributed on an "AS IS" BASIS,
13 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14 * See the License for the specific language governing permissions and
15 * limitations under the License.
16 */
17
18 /*
19 * This is not the original file distributed by the Apache Software Foundation
20 * It has been modified by the Hipparchus project
21 */
22 package org.hipparchus.distribution.discrete;
23
24 import java.io.Serializable;
25
26 import org.hipparchus.distribution.IntegerDistribution;
27 import org.hipparchus.exception.LocalizedCoreFormats;
28 import org.hipparchus.exception.MathIllegalArgumentException;
29 import org.hipparchus.exception.MathRuntimeException;
30 import org.hipparchus.util.FastMath;
31 import org.hipparchus.util.MathUtils;
32
33 /**
34 * Base class for integer-valued discrete distributions.
35 * <p>
36 * Default implementations are provided for some of the methods that
37 * do not vary from distribution to distribution.
38 */
39 public abstract class AbstractIntegerDistribution implements IntegerDistribution, Serializable {
40
41 /** Serializable version identifier */
42 private static final long serialVersionUID = 20160320L;
43
44 /** Empty constructor.
45 * <p>
46 * This constructor is not strictly necessary, but it prevents spurious
47 * javadoc warnings with JDK 18 and later.
48 * </p>
49 * @since 3.0
50 */
51 protected AbstractIntegerDistribution() { // NOPMD - unnecessary constructor added intentionally to make javadoc happy
52 // nothing to do
53 }
54
55 /**
56 * {@inheritDoc}
57 *
58 * The default implementation uses the identity
59 * <p>
60 * {@code P(x0 < X <= x1) = P(X <= x1) - P(X <= x0)}
61 */
62 @Override
63 public double probability(int x0, int x1) throws MathIllegalArgumentException {
64 if (x1 < x0) {
65 throw new MathIllegalArgumentException(LocalizedCoreFormats.LOWER_ENDPOINT_ABOVE_UPPER_ENDPOINT,
66 x0, x1, true);
67 }
68 return cumulativeProbability(x1) - cumulativeProbability(x0);
69 }
70
71 /**
72 * {@inheritDoc}
73 *
74 * The default implementation returns
75 * <ul>
76 * <li>{@link #getSupportLowerBound()} for {@code p = 0},</li>
77 * <li>{@link #getSupportUpperBound()} for {@code p = 1}, and</li>
78 * <li>{@link #solveInverseCumulativeProbability(double, int, int)} for
79 * {@code 0 < p < 1}.</li>
80 * </ul>
81 */
82 @Override
83 public int inverseCumulativeProbability(final double p) throws MathIllegalArgumentException {
84 MathUtils.checkRangeInclusive(p, 0, 1);
85
86 int lower = getSupportLowerBound();
87 if (p == 0.0) {
88 return lower;
89 }
90 if (lower == Integer.MIN_VALUE) {
91 if (checkedCumulativeProbability(lower) >= p) {
92 return lower;
93 }
94 } else {
95 lower -= 1; // this ensures cumulativeProbability(lower) < p, which
96 // is important for the solving step
97 }
98
99 int upper = getSupportUpperBound();
100 if (p == 1.0) {
101 return upper;
102 }
103
104 // use the one-sided Chebyshev inequality to narrow the bracket
105 // cf. AbstractRealDistribution.inverseCumulativeProbability(double)
106 final double mu = getNumericalMean();
107 final double sigma = FastMath.sqrt(getNumericalVariance());
108 final boolean chebyshevApplies =
109 !(Double.isInfinite(mu) || Double.isNaN(mu) ||
110 Double.isInfinite(sigma) || Double.isNaN(sigma) ||
111 sigma == 0.0);
112 if (chebyshevApplies) {
113 double k = FastMath.sqrt((1.0 - p) / p);
114 double tmp = mu - k * sigma;
115 if (tmp > lower) {
116 lower = ((int) FastMath.ceil(tmp)) - 1;
117 }
118 k = 1.0 / k;
119 tmp = mu + k * sigma;
120 if (tmp < upper) {
121 upper = ((int) FastMath.ceil(tmp)) - 1;
122 }
123 }
124
125 return solveInverseCumulativeProbability(p, lower, upper);
126 }
127
128 /**
129 * This is a utility function used by {@link
130 * #inverseCumulativeProbability(double)}. It assumes {@code 0 < p < 1} and
131 * that the inverse cumulative probability lies in the bracket {@code
132 * (lower, upper]}. The implementation does simple bisection to find the
133 * smallest {@code p}-quantile {@code inf{x in Z | P(X<=x) >= p}}.
134 *
135 * @param p the cumulative probability
136 * @param lower a value satisfying {@code cumulativeProbability(lower) < p}
137 * @param upper a value satisfying {@code p <= cumulativeProbability(upper)}
138 * @return the smallest {@code p}-quantile of this distribution
139 */
140 protected int solveInverseCumulativeProbability(final double p, int lower, int upper) {
141 while (lower + 1 < upper) {
142 int xm = (lower + upper) / 2;
143 if (xm < lower || xm > upper) {
144 /*
145 * Overflow.
146 * There will never be an overflow in both calculation methods
147 * for xm at the same time
148 */
149 xm = lower + (upper - lower) / 2;
150 }
151
152 double pm = checkedCumulativeProbability(xm);
153 if (pm >= p) {
154 upper = xm;
155 } else {
156 lower = xm;
157 }
158 }
159 return upper;
160 }
161
162 /**
163 * Computes the cumulative probability function and checks for {@code NaN}
164 * values returned.
165 * <p>
166 * Throws {@code MathRuntimeException} if the value is {@code NaN}.
167 * Rethrows any exception encountered evaluating the cumulative
168 * probability function.
169 * Throws {@code MathRuntimeException} if the cumulative
170 * probability function returns {@code NaN}.
171 *
172 * @param argument input value
173 * @return the cumulative probability
174 * @throws MathRuntimeException if the cumulative probability is {@code NaN}
175 */
176 private double checkedCumulativeProbability(int argument)
177 throws MathRuntimeException {
178 double result = cumulativeProbability(argument);
179 if (Double.isNaN(result)) {
180 throw new MathRuntimeException(LocalizedCoreFormats.DISCRETE_CUMULATIVE_PROBABILITY_RETURNED_NAN,
181 argument);
182 }
183 return result;
184 }
185
186 /**
187 * {@inheritDoc}
188 * <p>
189 * The default implementation simply computes the logarithm of {@code probability(x)}.
190 */
191 @Override
192 public double logProbability(int x) {
193 return FastMath.log(probability(x));
194 }
195 }