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 log-normal (gaussian) distribution.
030 *
031 * <p>
032 * <strong>Parameters:</strong>
033 * {@code X} is log-normally distributed if its natural logarithm {@code log(X)}
034 * is normally distributed. The probability distribution function of {@code X}
035 * is given by (for {@code x > 0})
036 * </p>
037 * <p>
038 * {@code exp(-0.5 * ((ln(x) - m) / s)^2) / (s * sqrt(2 * pi) * x)}
039 * </p>
040 * <ul>
041 * <li>{@code m} is the <em>scale</em> parameter: this is the mean of the
042 * normally distributed natural logarithm of this distribution,</li>
043 * <li>{@code s} is the <em>shape</em> parameter: this is the standard
044 * deviation of the normally distributed natural logarithm of this
045 * distribution.
046 * </ul>
047 *
048 * @see <a href="http://en.wikipedia.org/wiki/Log-normal_distribution">
049 * Log-normal distribution (Wikipedia)</a>
050 * @see <a href="http://mathworld.wolfram.com/LogNormalDistribution.html">
051 * Log Normal distribution (MathWorld)</a>
052 *
053 * @version $Id: LogNormalDistribution.java 1422195 2012-12-15 06:45:18Z psteitz $
054 * @since 3.0
055 */
056 public class LogNormalDistribution extends AbstractRealDistribution {
057 /** Default inverse cumulative probability accuracy. */
058 public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY = 1e-9;
059
060 /** Serializable version identifier. */
061 private static final long serialVersionUID = 20120112;
062
063 /** √(2 π) */
064 private static final double SQRT2PI = FastMath.sqrt(2 * FastMath.PI);
065
066 /** √(2) */
067 private static final double SQRT2 = FastMath.sqrt(2.0);
068
069 /** The scale parameter of this distribution. */
070 private final double scale;
071
072 /** The shape parameter of this distribution. */
073 private final double shape;
074
075 /** Inverse cumulative probability accuracy. */
076 private final double solverAbsoluteAccuracy;
077
078 /**
079 * Create a log-normal distribution, where the mean and standard deviation
080 * of the {@link NormalDistribution normally distributed} natural
081 * logarithm of the log-normal distribution are equal to zero and one
082 * respectively. In other words, the scale of the returned distribution is
083 * {@code 0}, while its shape is {@code 1}.
084 */
085 public LogNormalDistribution() {
086 this(0, 1);
087 }
088
089 /**
090 * Create a log-normal distribution using the specified scale and shape.
091 *
092 * @param scale the scale parameter of this distribution
093 * @param shape the shape parameter of this distribution
094 * @throws NotStrictlyPositiveException if {@code shape <= 0}.
095 */
096 public LogNormalDistribution(double scale, double shape)
097 throws NotStrictlyPositiveException {
098 this(scale, shape, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
099 }
100
101 /**
102 * Create a log-normal distribution using the specified scale, shape and
103 * inverse cumulative distribution accuracy.
104 *
105 * @param scale the scale parameter of this distribution
106 * @param shape the shape parameter of this distribution
107 * @param inverseCumAccuracy Inverse cumulative probability accuracy.
108 * @throws NotStrictlyPositiveException if {@code shape <= 0}.
109 */
110 public LogNormalDistribution(double scale, double shape, double inverseCumAccuracy)
111 throws NotStrictlyPositiveException {
112 this(new Well19937c(), scale, shape, inverseCumAccuracy);
113 }
114
115 /**
116 * Creates a log-normal distribution.
117 *
118 * @param rng Random number generator.
119 * @param scale Scale parameter of this distribution.
120 * @param shape Shape parameter of this distribution.
121 * @param inverseCumAccuracy Inverse cumulative probability accuracy.
122 * @throws NotStrictlyPositiveException if {@code shape <= 0}.
123 * @since 3.1
124 */
125 public LogNormalDistribution(RandomGenerator rng,
126 double scale,
127 double shape,
128 double inverseCumAccuracy)
129 throws NotStrictlyPositiveException {
130 super(rng);
131
132 if (shape <= 0) {
133 throw new NotStrictlyPositiveException(LocalizedFormats.SHAPE, shape);
134 }
135
136 this.scale = scale;
137 this.shape = shape;
138 this.solverAbsoluteAccuracy = inverseCumAccuracy;
139 }
140
141 /**
142 * Returns the scale parameter of this distribution.
143 *
144 * @return the scale parameter
145 */
146 public double getScale() {
147 return scale;
148 }
149
150 /**
151 * Returns the shape parameter of this distribution.
152 *
153 * @return the shape parameter
154 */
155 public double getShape() {
156 return shape;
157 }
158
159 /**
160 * {@inheritDoc}
161 *
162 * For scale {@code m}, and shape {@code s} of this distribution, the PDF
163 * is given by
164 * <ul>
165 * <li>{@code 0} if {@code x <= 0},</li>
166 * <li>{@code exp(-0.5 * ((ln(x) - m) / s)^2) / (s * sqrt(2 * pi) * x)}
167 * otherwise.</li>
168 * </ul>
169 */
170 public double density(double x) {
171 if (x <= 0) {
172 return 0;
173 }
174 final double x0 = FastMath.log(x) - scale;
175 final double x1 = x0 / shape;
176 return FastMath.exp(-0.5 * x1 * x1) / (shape * SQRT2PI * x);
177 }
178
179 /**
180 * {@inheritDoc}
181 *
182 * For scale {@code m}, and shape {@code s} of this distribution, the CDF
183 * is given by
184 * <ul>
185 * <li>{@code 0} if {@code x <= 0},</li>
186 * <li>{@code 0} if {@code ln(x) - m < 0} and {@code m - ln(x) > 40 * s}, as
187 * in these cases the actual value is within {@code Double.MIN_VALUE} of 0,
188 * <li>{@code 1} if {@code ln(x) - m >= 0} and {@code ln(x) - m > 40 * s},
189 * as in these cases the actual value is within {@code Double.MIN_VALUE} of
190 * 1,</li>
191 * <li>{@code 0.5 + 0.5 * erf((ln(x) - m) / (s * sqrt(2))} otherwise.</li>
192 * </ul>
193 */
194 public double cumulativeProbability(double x) {
195 if (x <= 0) {
196 return 0;
197 }
198 final double dev = FastMath.log(x) - scale;
199 if (FastMath.abs(dev) > 40 * shape) {
200 return dev < 0 ? 0.0d : 1.0d;
201 }
202 return 0.5 + 0.5 * Erf.erf(dev / (shape * SQRT2));
203 }
204
205 /**
206 * {@inheritDoc}
207 *
208 * @deprecated See {@link RealDistribution#cumulativeProbability(double,double)}
209 */
210 @Override@Deprecated
211 public double cumulativeProbability(double x0, double x1)
212 throws NumberIsTooLargeException {
213 return probability(x0, x1);
214 }
215
216 /** {@inheritDoc} */
217 @Override
218 public double probability(double x0,
219 double x1)
220 throws NumberIsTooLargeException {
221 if (x0 > x1) {
222 throw new NumberIsTooLargeException(LocalizedFormats.LOWER_ENDPOINT_ABOVE_UPPER_ENDPOINT,
223 x0, x1, true);
224 }
225 if (x0 <= 0 || x1 <= 0) {
226 return super.probability(x0, x1);
227 }
228 final double denom = shape * SQRT2;
229 final double v0 = (FastMath.log(x0) - scale) / denom;
230 final double v1 = (FastMath.log(x1) - scale) / denom;
231 return 0.5 * Erf.erf(v0, v1);
232 }
233
234 /** {@inheritDoc} */
235 @Override
236 protected double getSolverAbsoluteAccuracy() {
237 return solverAbsoluteAccuracy;
238 }
239
240 /**
241 * {@inheritDoc}
242 *
243 * For scale {@code m} and shape {@code s}, the mean is
244 * {@code exp(m + s^2 / 2)}.
245 */
246 public double getNumericalMean() {
247 double s = shape;
248 return FastMath.exp(scale + (s * s / 2));
249 }
250
251 /**
252 * {@inheritDoc}
253 *
254 * For scale {@code m} and shape {@code s}, the variance is
255 * {@code (exp(s^2) - 1) * exp(2 * m + s^2)}.
256 */
257 public double getNumericalVariance() {
258 final double s = shape;
259 final double ss = s * s;
260 return (FastMath.exp(ss) - 1) * FastMath.exp(2 * scale + ss);
261 }
262
263 /**
264 * {@inheritDoc}
265 *
266 * The lower bound of the support is always 0 no matter the parameters.
267 *
268 * @return lower bound of the support (always 0)
269 */
270 public double getSupportLowerBound() {
271 return 0;
272 }
273
274 /**
275 * {@inheritDoc}
276 *
277 * The upper bound of the support is always positive infinity
278 * no matter the parameters.
279 *
280 * @return upper bound of the support (always
281 * {@code Double.POSITIVE_INFINITY})
282 */
283 public double getSupportUpperBound() {
284 return Double.POSITIVE_INFINITY;
285 }
286
287 /** {@inheritDoc} */
288 public boolean isSupportLowerBoundInclusive() {
289 return true;
290 }
291
292 /** {@inheritDoc} */
293 public boolean isSupportUpperBoundInclusive() {
294 return false;
295 }
296
297 /**
298 * {@inheritDoc}
299 *
300 * The support of this distribution is connected.
301 *
302 * @return {@code true}
303 */
304 public boolean isSupportConnected() {
305 return true;
306 }
307
308 /** {@inheritDoc} */
309 @Override
310 public double sample() {
311 final double n = random.nextGaussian();
312 return FastMath.exp(scale + shape * n);
313 }
314 }