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
018 package org.apache.commons.math3.distribution;
019
020 import org.apache.commons.math3.exception.NotStrictlyPositiveException;
021 import org.apache.commons.math3.exception.NumberIsTooLargeException;
022 import org.apache.commons.math3.exception.util.LocalizedFormats;
023 import org.apache.commons.math3.special.Erf;
024 import org.apache.commons.math3.util.FastMath;
025 import org.apache.commons.math3.random.RandomGenerator;
026 import org.apache.commons.math3.random.Well19937c;
027
028 /**
029 * Implementation of the normal (gaussian) distribution.
030 *
031 * @see <a href="http://en.wikipedia.org/wiki/Normal_distribution">Normal distribution (Wikipedia)</a>
032 * @see <a href="http://mathworld.wolfram.com/NormalDistribution.html">Normal distribution (MathWorld)</a>
033 * @version $Id: NormalDistribution.java 1416643 2012-12-03 19:37:14Z tn $
034 */
035 public class NormalDistribution extends AbstractRealDistribution {
036 /**
037 * Default inverse cumulative probability accuracy.
038 * @since 2.1
039 */
040 public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY = 1e-9;
041 /** Serializable version identifier. */
042 private static final long serialVersionUID = 8589540077390120676L;
043 /** √(2 π) */
044 private static final double SQRT2PI = FastMath.sqrt(2 * FastMath.PI);
045 /** √(2) */
046 private static final double SQRT2 = FastMath.sqrt(2.0);
047 /** Mean of this distribution. */
048 private final double mean;
049 /** Standard deviation of this distribution. */
050 private final double standardDeviation;
051 /** Inverse cumulative probability accuracy. */
052 private final double solverAbsoluteAccuracy;
053
054 /**
055 * Create a normal distribution with mean equal to zero and standard
056 * deviation equal to one.
057 */
058 public NormalDistribution() {
059 this(0, 1);
060 }
061
062 /**
063 * Create a normal distribution using the given mean and standard deviation.
064 *
065 * @param mean Mean for this distribution.
066 * @param sd Standard deviation for this distribution.
067 * @throws NotStrictlyPositiveException if {@code sd <= 0}.
068 */
069 public NormalDistribution(double mean, double sd)
070 throws NotStrictlyPositiveException {
071 this(mean, sd, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
072 }
073
074 /**
075 * Create a normal distribution using the given mean, standard deviation and
076 * inverse cumulative distribution accuracy.
077 *
078 * @param mean Mean for this distribution.
079 * @param sd Standard deviation for this distribution.
080 * @param inverseCumAccuracy Inverse cumulative probability accuracy.
081 * @throws NotStrictlyPositiveException if {@code sd <= 0}.
082 * @since 2.1
083 */
084 public NormalDistribution(double mean, double sd, double inverseCumAccuracy)
085 throws NotStrictlyPositiveException {
086 this(new Well19937c(), mean, sd, inverseCumAccuracy);
087 }
088
089 /**
090 * Creates a normal distribution.
091 *
092 * @param rng Random number generator.
093 * @param mean Mean for this distribution.
094 * @param sd Standard deviation for this distribution.
095 * @param inverseCumAccuracy Inverse cumulative probability accuracy.
096 * @throws NotStrictlyPositiveException if {@code sd <= 0}.
097 * @since 3.1
098 */
099 public NormalDistribution(RandomGenerator rng,
100 double mean,
101 double sd,
102 double inverseCumAccuracy)
103 throws NotStrictlyPositiveException {
104 super(rng);
105
106 if (sd <= 0) {
107 throw new NotStrictlyPositiveException(LocalizedFormats.STANDARD_DEVIATION, sd);
108 }
109
110 this.mean = mean;
111 standardDeviation = sd;
112 solverAbsoluteAccuracy = inverseCumAccuracy;
113 }
114
115 /**
116 * Access the mean.
117 *
118 * @return the mean for this distribution.
119 */
120 public double getMean() {
121 return mean;
122 }
123
124 /**
125 * Access the standard deviation.
126 *
127 * @return the standard deviation for this distribution.
128 */
129 public double getStandardDeviation() {
130 return standardDeviation;
131 }
132
133 /** {@inheritDoc} */
134 public double density(double x) {
135 final double x0 = x - mean;
136 final double x1 = x0 / standardDeviation;
137 return FastMath.exp(-0.5 * x1 * x1) / (standardDeviation * SQRT2PI);
138 }
139
140 /**
141 * {@inheritDoc}
142 *
143 * If {@code x} is more than 40 standard deviations from the mean, 0 or 1
144 * is returned, as in these cases the actual value is within
145 * {@code Double.MIN_VALUE} of 0 or 1.
146 */
147 public double cumulativeProbability(double x) {
148 final double dev = x - mean;
149 if (FastMath.abs(dev) > 40 * standardDeviation) {
150 return dev < 0 ? 0.0d : 1.0d;
151 }
152 return 0.5 * (1 + Erf.erf(dev / (standardDeviation * SQRT2)));
153 }
154
155 /**
156 * {@inheritDoc}
157 *
158 * @deprecated See {@link RealDistribution#cumulativeProbability(double,double)}
159 */
160 @Override@Deprecated
161 public double cumulativeProbability(double x0, double x1)
162 throws NumberIsTooLargeException {
163 return probability(x0, x1);
164 }
165
166 /** {@inheritDoc} */
167 @Override
168 public double probability(double x0,
169 double x1)
170 throws NumberIsTooLargeException {
171 if (x0 > x1) {
172 throw new NumberIsTooLargeException(LocalizedFormats.LOWER_ENDPOINT_ABOVE_UPPER_ENDPOINT,
173 x0, x1, true);
174 }
175 final double denom = standardDeviation * SQRT2;
176 final double v0 = (x0 - mean) / denom;
177 final double v1 = (x1 - mean) / denom;
178 return 0.5 * Erf.erf(v0, v1);
179 }
180
181 /** {@inheritDoc} */
182 @Override
183 protected double getSolverAbsoluteAccuracy() {
184 return solverAbsoluteAccuracy;
185 }
186
187 /**
188 * {@inheritDoc}
189 *
190 * For mean parameter {@code mu}, the mean is {@code mu}.
191 */
192 public double getNumericalMean() {
193 return getMean();
194 }
195
196 /**
197 * {@inheritDoc}
198 *
199 * For standard deviation parameter {@code s}, the variance is {@code s^2}.
200 */
201 public double getNumericalVariance() {
202 final double s = getStandardDeviation();
203 return s * s;
204 }
205
206 /**
207 * {@inheritDoc}
208 *
209 * The lower bound of the support is always negative infinity
210 * no matter the parameters.
211 *
212 * @return lower bound of the support (always
213 * {@code Double.NEGATIVE_INFINITY})
214 */
215 public double getSupportLowerBound() {
216 return Double.NEGATIVE_INFINITY;
217 }
218
219 /**
220 * {@inheritDoc}
221 *
222 * The upper bound of the support is always positive infinity
223 * no matter the parameters.
224 *
225 * @return upper bound of the support (always
226 * {@code Double.POSITIVE_INFINITY})
227 */
228 public double getSupportUpperBound() {
229 return Double.POSITIVE_INFINITY;
230 }
231
232 /** {@inheritDoc} */
233 public boolean isSupportLowerBoundInclusive() {
234 return false;
235 }
236
237 /** {@inheritDoc} */
238 public boolean isSupportUpperBoundInclusive() {
239 return false;
240 }
241
242 /**
243 * {@inheritDoc}
244 *
245 * The support of this distribution is connected.
246 *
247 * @return {@code true}
248 */
249 public boolean isSupportConnected() {
250 return true;
251 }
252
253 /** {@inheritDoc} */
254 @Override
255 public double sample() {
256 return standardDeviation * random.nextGaussian() + mean;
257 }
258 }