| /* |
| * Licensed to the Apache Software Foundation (ASF) under one or more |
| * contributor license agreements. See the NOTICE file distributed with |
| * this work for additional information regarding copyright ownership. |
| * The ASF licenses this file to You under the Apache License, Version 2.0 |
| * (the "License"); you may not use this file except in compliance with |
| * the License. You may obtain a copy of the License at |
| * |
| * http://www.apache.org/licenses/LICENSE-2.0 |
| * |
| * Unless required by applicable law or agreed to in writing, software |
| * distributed under the License is distributed on an "AS IS" BASIS, |
| * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| * See the License for the specific language governing permissions and |
| * limitations under the License. |
| */ |
| package org.apache.commons.math4.legacy.distribution; |
| |
| import org.apache.commons.statistics.distribution.ContinuousDistribution; |
| import org.apache.commons.math4.legacy.analysis.UnivariateFunction; |
| import org.apache.commons.math4.legacy.analysis.solvers.UnivariateSolverUtils; |
| import org.apache.commons.math4.legacy.exception.NumberIsTooLargeException; |
| import org.apache.commons.math4.legacy.exception.OutOfRangeException; |
| import org.apache.commons.math4.legacy.exception.util.LocalizedFormats; |
| import org.apache.commons.rng.UniformRandomProvider; |
| import org.apache.commons.rng.sampling.distribution.InverseTransformContinuousSampler; |
| import org.apache.commons.rng.sampling.distribution.ContinuousInverseCumulativeProbabilityFunction; |
| import org.apache.commons.rng.sampling.distribution.ContinuousSampler; |
| import org.apache.commons.math4.legacy.core.jdkmath.AccurateMath; |
| |
| /** |
| * Base class for probability distributions on the reals. |
| * Default implementations are provided for some of the methods |
| * that do not vary from distribution to distribution. |
| * |
| * <p> |
| * This base class provides a default factory method for creating |
| * a {@link org.apache.commons.statistics.distribution.ContinuousDistribution.Sampler |
| * sampler instance} that uses the |
| * <a href="http://en.wikipedia.org/wiki/Inverse_transform_sampling"> |
| * inversion method</a> for generating random samples that follow the |
| * distribution. |
| * </p> |
| * |
| * @since 3.0 |
| */ |
| public abstract class AbstractRealDistribution |
| implements ContinuousDistribution { |
| /** Default absolute accuracy for inverse cumulative computation. */ |
| public static final double SOLVER_DEFAULT_ABSOLUTE_ACCURACY = 1e-6; |
| |
| /** |
| * For a random variable {@code X} whose values are distributed according |
| * to this distribution, this method returns {@code P(x0 < X <= x1)}. |
| * |
| * @param x0 Lower bound (excluded). |
| * @param x1 Upper bound (included). |
| * @return the probability that a random variable with this distribution |
| * takes a value between {@code x0} and {@code x1}, excluding the lower |
| * and including the upper endpoint. |
| * @throws NumberIsTooLargeException if {@code x0 > x1}. |
| * |
| * The default implementation uses the identity |
| * {@code P(x0 < X <= x1) = P(X <= x1) - P(X <= x0)} |
| * |
| * @since 3.1 |
| */ |
| @Override |
| public double probability(double x0, |
| double x1) { |
| if (x0 > x1) { |
| throw new NumberIsTooLargeException(LocalizedFormats.LOWER_ENDPOINT_ABOVE_UPPER_ENDPOINT, |
| x0, x1, true); |
| } |
| return cumulativeProbability(x1) - cumulativeProbability(x0); |
| } |
| |
| /** |
| * {@inheritDoc} |
| * |
| * The default implementation returns |
| * <ul> |
| * <li>{@link #getSupportLowerBound()} for {@code p = 0},</li> |
| * <li>{@link #getSupportUpperBound()} for {@code p = 1}.</li> |
| * </ul> |
| */ |
| @Override |
| public double inverseCumulativeProbability(final double p) throws OutOfRangeException { |
| /* |
| * IMPLEMENTATION NOTES |
| * -------------------- |
| * Where applicable, use is made of the one-sided Chebyshev inequality |
| * to bracket the root. This inequality states that |
| * P(X - mu >= k * sig) <= 1 / (1 + k^2), |
| * mu: mean, sig: standard deviation. Equivalently |
| * 1 - P(X < mu + k * sig) <= 1 / (1 + k^2), |
| * F(mu + k * sig) >= k^2 / (1 + k^2). |
| * |
| * For k = sqrt(p / (1 - p)), we find |
| * F(mu + k * sig) >= p, |
| * and (mu + k * sig) is an upper-bound for the root. |
| * |
| * Then, introducing Y = -X, mean(Y) = -mu, sd(Y) = sig, and |
| * P(Y >= -mu + k * sig) <= 1 / (1 + k^2), |
| * P(-X >= -mu + k * sig) <= 1 / (1 + k^2), |
| * P(X <= mu - k * sig) <= 1 / (1 + k^2), |
| * F(mu - k * sig) <= 1 / (1 + k^2). |
| * |
| * For k = sqrt((1 - p) / p), we find |
| * F(mu - k * sig) <= p, |
| * and (mu - k * sig) is a lower-bound for the root. |
| * |
| * In cases where the Chebyshev inequality does not apply, geometric |
| * progressions 1, 2, 4, ... and -1, -2, -4, ... are used to bracket |
| * the root. |
| */ |
| if (p < 0.0 || p > 1.0) { |
| throw new OutOfRangeException(p, 0, 1); |
| } |
| |
| double lowerBound = getSupportLowerBound(); |
| if (p == 0.0) { |
| return lowerBound; |
| } |
| |
| double upperBound = getSupportUpperBound(); |
| if (p == 1.0) { |
| return upperBound; |
| } |
| |
| final double mu = getMean(); |
| final double sig = AccurateMath.sqrt(getVariance()); |
| final boolean chebyshevApplies; |
| chebyshevApplies = !(Double.isInfinite(mu) || Double.isNaN(mu) || |
| Double.isInfinite(sig) || Double.isNaN(sig)); |
| |
| if (lowerBound == Double.NEGATIVE_INFINITY) { |
| if (chebyshevApplies) { |
| lowerBound = mu - sig * AccurateMath.sqrt((1. - p) / p); |
| } else { |
| lowerBound = -1.0; |
| while (cumulativeProbability(lowerBound) >= p) { |
| lowerBound *= 2.0; |
| } |
| } |
| } |
| |
| if (upperBound == Double.POSITIVE_INFINITY) { |
| if (chebyshevApplies) { |
| upperBound = mu + sig * AccurateMath.sqrt(p / (1. - p)); |
| } else { |
| upperBound = 1.0; |
| while (cumulativeProbability(upperBound) < p) { |
| upperBound *= 2.0; |
| } |
| } |
| } |
| |
| final UnivariateFunction toSolve = new UnivariateFunction() { |
| /** {@inheritDoc} */ |
| @Override |
| public double value(final double x) { |
| return cumulativeProbability(x) - p; |
| } |
| }; |
| |
| double x = UnivariateSolverUtils.solve(toSolve, |
| lowerBound, |
| upperBound, |
| getSolverAbsoluteAccuracy()); |
| |
| if (!isSupportConnected()) { |
| /* Test for plateau. */ |
| final double dx = getSolverAbsoluteAccuracy(); |
| if (x - dx >= getSupportLowerBound()) { |
| double px = cumulativeProbability(x); |
| if (cumulativeProbability(x - dx) == px) { |
| upperBound = x; |
| while (upperBound - lowerBound > dx) { |
| final double midPoint = 0.5 * (lowerBound + upperBound); |
| if (cumulativeProbability(midPoint) < px) { |
| lowerBound = midPoint; |
| } else { |
| upperBound = midPoint; |
| } |
| } |
| return upperBound; |
| } |
| } |
| } |
| return x; |
| } |
| |
| /** |
| * Returns the solver absolute accuracy for inverse cumulative computation. |
| * You can override this method in order to use a Brent solver with an |
| * absolute accuracy different from the default. |
| * |
| * @return the maximum absolute error in inverse cumulative probability estimates |
| */ |
| protected double getSolverAbsoluteAccuracy() { |
| return SOLVER_DEFAULT_ABSOLUTE_ACCURACY; |
| } |
| |
| /** |
| * {@inheritDoc} |
| * <p> |
| * The default implementation simply computes the logarithm of {@code density(x)}. |
| */ |
| @Override |
| public double logDensity(double x) { |
| return AccurateMath.log(density(x)); |
| } |
| |
| /** |
| * Utility function for allocating an array and filling it with {@code n} |
| * samples generated by the given {@code sampler}. |
| * |
| * @param n Number of samples. |
| * @param sampler Sampler. |
| * @return an array of size {@code n}. |
| */ |
| public static double[] sample(int n, |
| ContinuousDistribution.Sampler sampler) { |
| final double[] samples = new double[n]; |
| for (int i = 0; i < n; i++) { |
| samples[i] = sampler.sample(); |
| } |
| return samples; |
| } |
| |
| /**{@inheritDoc} */ |
| @Override |
| public ContinuousDistribution.Sampler createSampler(final UniformRandomProvider rng) { |
| return new ContinuousDistribution.Sampler() { |
| /** |
| * Inversion method distribution sampler. |
| */ |
| private final ContinuousSampler sampler = |
| new InverseTransformContinuousSampler(rng, createICPF()); |
| |
| /** {@inheritDoc} */ |
| @Override |
| public double sample() { |
| return sampler.sample(); |
| } |
| }; |
| } |
| |
| /** |
| * @return an instance for use by {@link #createSampler(UniformRandomProvider)} |
| */ |
| private ContinuousInverseCumulativeProbabilityFunction createICPF() { |
| return new ContinuousInverseCumulativeProbabilityFunction() { |
| /** {@inheritDoc} */ |
| @Override |
| public double inverseCumulativeProbability(double p) { |
| return AbstractRealDistribution.this.inverseCumulativeProbability(p); |
| } |
| }; |
| } |
| } |
