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+/*
+ * 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.math3.distribution;
+
+import org.apache.commons.math3.exception.NotStrictlyPositiveException;
+import org.apache.commons.math3.exception.OutOfRangeException;
+import org.apache.commons.math3.exception.util.LocalizedFormats;
+import org.apache.commons.math3.random.RandomGenerator;
+import org.apache.commons.math3.random.Well19937c;
+import org.apache.commons.math3.special.Gamma;
+import org.apache.commons.math3.util.FastMath;
+
+/**
+ * Implementation of the Weibull distribution. This implementation uses the two parameter form of
+ * the distribution defined by <a href="http://mathworld.wolfram.com/WeibullDistribution.html">
+ * Weibull Distribution</a>, equations (1) and (2).
+ *
+ * @see <a href="http://en.wikipedia.org/wiki/Weibull_distribution">Weibull distribution
+ *     (Wikipedia)</a>
+ * @see <a href="http://mathworld.wolfram.com/WeibullDistribution.html">Weibull distribution
+ *     (MathWorld)</a>
+ * @since 1.1 (changed to concrete class in 3.0)
+ */
+public class WeibullDistribution extends AbstractRealDistribution {
+    /**
+     * Default inverse cumulative probability accuracy.
+     *
+     * @since 2.1
+     */
+    public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY = 1e-9;
+
+    /** Serializable version identifier. */
+    private static final long serialVersionUID = 8589540077390120676L;
+
+    /** The shape parameter. */
+    private final double shape;
+
+    /** The scale parameter. */
+    private final double scale;
+
+    /** Inverse cumulative probability accuracy. */
+    private final double solverAbsoluteAccuracy;
+
+    /** Cached numerical mean */
+    private double numericalMean = Double.NaN;
+
+    /** Whether or not the numerical mean has been calculated */
+    private boolean numericalMeanIsCalculated = false;
+
+    /** Cached numerical variance */
+    private double numericalVariance = Double.NaN;
+
+    /** Whether or not the numerical variance has been calculated */
+    private boolean numericalVarianceIsCalculated = false;
+
+    /**
+     * Create a Weibull distribution with the given shape and scale and a location equal to zero.
+     *
+     * <p><b>Note:</b> this constructor will implicitly create an instance of {@link Well19937c} as
+     * random generator to be used for sampling only (see {@link #sample()} and {@link
+     * #sample(int)}). In case no sampling is needed for the created distribution, it is advised to
+     * pass {@code null} as random generator via the appropriate constructors to avoid the
+     * additional initialisation overhead.
+     *
+     * @param alpha Shape parameter.
+     * @param beta Scale parameter.
+     * @throws NotStrictlyPositiveException if {@code alpha <= 0} or {@code beta <= 0}.
+     */
+    public WeibullDistribution(double alpha, double beta) throws NotStrictlyPositiveException {
+        this(alpha, beta, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
+    }
+
+    /**
+     * Create a Weibull distribution with the given shape, scale and inverse cumulative probability
+     * accuracy and a location equal to zero.
+     *
+     * <p><b>Note:</b> this constructor will implicitly create an instance of {@link Well19937c} as
+     * random generator to be used for sampling only (see {@link #sample()} and {@link
+     * #sample(int)}). In case no sampling is needed for the created distribution, it is advised to
+     * pass {@code null} as random generator via the appropriate constructors to avoid the
+     * additional initialisation overhead.
+     *
+     * @param alpha Shape parameter.
+     * @param beta Scale parameter.
+     * @param inverseCumAccuracy Maximum absolute error in inverse cumulative probability estimates
+     *     (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}).
+     * @throws NotStrictlyPositiveException if {@code alpha <= 0} or {@code beta <= 0}.
+     * @since 2.1
+     */
+    public WeibullDistribution(double alpha, double beta, double inverseCumAccuracy) {
+        this(new Well19937c(), alpha, beta, inverseCumAccuracy);
+    }
+
+    /**
+     * Creates a Weibull distribution.
+     *
+     * @param rng Random number generator.
+     * @param alpha Shape parameter.
+     * @param beta Scale parameter.
+     * @throws NotStrictlyPositiveException if {@code alpha <= 0} or {@code beta <= 0}.
+     * @since 3.3
+     */
+    public WeibullDistribution(RandomGenerator rng, double alpha, double beta)
+            throws NotStrictlyPositiveException {
+        this(rng, alpha, beta, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
+    }
+
+    /**
+     * Creates a Weibull distribution.
+     *
+     * @param rng Random number generator.
+     * @param alpha Shape parameter.
+     * @param beta Scale parameter.
+     * @param inverseCumAccuracy Maximum absolute error in inverse cumulative probability estimates
+     *     (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}).
+     * @throws NotStrictlyPositiveException if {@code alpha <= 0} or {@code beta <= 0}.
+     * @since 3.1
+     */
+    public WeibullDistribution(
+            RandomGenerator rng, double alpha, double beta, double inverseCumAccuracy)
+            throws NotStrictlyPositiveException {
+        super(rng);
+
+        if (alpha <= 0) {
+            throw new NotStrictlyPositiveException(LocalizedFormats.SHAPE, alpha);
+        }
+        if (beta <= 0) {
+            throw new NotStrictlyPositiveException(LocalizedFormats.SCALE, beta);
+        }
+        scale = beta;
+        shape = alpha;
+        solverAbsoluteAccuracy = inverseCumAccuracy;
+    }
+
+    /**
+     * Access the shape parameter, {@code alpha}.
+     *
+     * @return the shape parameter, {@code alpha}.
+     */
+    public double getShape() {
+        return shape;
+    }
+
+    /**
+     * Access the scale parameter, {@code beta}.
+     *
+     * @return the scale parameter, {@code beta}.
+     */
+    public double getScale() {
+        return scale;
+    }
+
+    /** {@inheritDoc} */
+    public double density(double x) {
+        if (x < 0) {
+            return 0;
+        }
+
+        final double xscale = x / scale;
+        final double xscalepow = FastMath.pow(xscale, shape - 1);
+
+        /*
+         * FastMath.pow(x / scale, shape) =
+         * FastMath.pow(xscale, shape) =
+         * FastMath.pow(xscale, shape - 1) * xscale
+         */
+        final double xscalepowshape = xscalepow * xscale;
+
+        return (shape / scale) * xscalepow * FastMath.exp(-xscalepowshape);
+    }
+
+    /** {@inheritDoc} */
+    @Override
+    public double logDensity(double x) {
+        if (x < 0) {
+            return Double.NEGATIVE_INFINITY;
+        }
+
+        final double xscale = x / scale;
+        final double logxscalepow = FastMath.log(xscale) * (shape - 1);
+
+        /*
+         * FastMath.pow(x / scale, shape) =
+         * FastMath.pow(xscale, shape) =
+         * FastMath.pow(xscale, shape - 1) * xscale
+         */
+        final double xscalepowshape = FastMath.exp(logxscalepow) * xscale;
+
+        return FastMath.log(shape / scale) + logxscalepow - xscalepowshape;
+    }
+
+    /** {@inheritDoc} */
+    public double cumulativeProbability(double x) {
+        double ret;
+        if (x <= 0.0) {
+            ret = 0.0;
+        } else {
+            ret = 1.0 - FastMath.exp(-FastMath.pow(x / scale, shape));
+        }
+        return ret;
+    }
+
+    /**
+     * {@inheritDoc}
+     *
+     * <p>Returns {@code 0} when {@code p == 0} and {@code Double.POSITIVE_INFINITY} when {@code p
+     * == 1}.
+     */
+    @Override
+    public double inverseCumulativeProbability(double p) {
+        double ret;
+        if (p < 0.0 || p > 1.0) {
+            throw new OutOfRangeException(p, 0.0, 1.0);
+        } else if (p == 0) {
+            ret = 0.0;
+        } else if (p == 1) {
+            ret = Double.POSITIVE_INFINITY;
+        } else {
+            ret = scale * FastMath.pow(-FastMath.log1p(-p), 1.0 / shape);
+        }
+        return ret;
+    }
+
+    /**
+     * Return the absolute accuracy setting of the solver used to estimate inverse cumulative
+     * probabilities.
+     *
+     * @return the solver absolute accuracy.
+     * @since 2.1
+     */
+    @Override
+    protected double getSolverAbsoluteAccuracy() {
+        return solverAbsoluteAccuracy;
+    }
+
+    /**
+     * {@inheritDoc}
+     *
+     * <p>The mean is {@code scale * Gamma(1 + (1 / shape))}, where {@code Gamma()} is the
+     * Gamma-function.
+     */
+    public double getNumericalMean() {
+        if (!numericalMeanIsCalculated) {
+            numericalMean = calculateNumericalMean();
+            numericalMeanIsCalculated = true;
+        }
+        return numericalMean;
+    }
+
+    /**
+     * used by {@link #getNumericalMean()}
+     *
+     * @return the mean of this distribution
+     */
+    protected double calculateNumericalMean() {
+        final double sh = getShape();
+        final double sc = getScale();
+
+        return sc * FastMath.exp(Gamma.logGamma(1 + (1 / sh)));
+    }
+
+    /**
+     * {@inheritDoc}
+     *
+     * <p>The variance is {@code scale^2 * Gamma(1 + (2 / shape)) - mean^2} where {@code Gamma()} is
+     * the Gamma-function.
+     */
+    public double getNumericalVariance() {
+        if (!numericalVarianceIsCalculated) {
+            numericalVariance = calculateNumericalVariance();
+            numericalVarianceIsCalculated = true;
+        }
+        return numericalVariance;
+    }
+
+    /**
+     * used by {@link #getNumericalVariance()}
+     *
+     * @return the variance of this distribution
+     */
+    protected double calculateNumericalVariance() {
+        final double sh = getShape();
+        final double sc = getScale();
+        final double mn = getNumericalMean();
+
+        return (sc * sc) * FastMath.exp(Gamma.logGamma(1 + (2 / sh))) - (mn * mn);
+    }
+
+    /**
+     * {@inheritDoc}
+     *
+     * <p>The lower bound of the support is always 0 no matter the parameters.
+     *
+     * @return lower bound of the support (always 0)
+     */
+    public double getSupportLowerBound() {
+        return 0;
+    }
+
+    /**
+     * {@inheritDoc}
+     *
+     * <p>The upper bound of the support is always positive infinity no matter the parameters.
+     *
+     * @return upper bound of the support (always {@code Double.POSITIVE_INFINITY})
+     */
+    public double getSupportUpperBound() {
+        return Double.POSITIVE_INFINITY;
+    }
+
+    /** {@inheritDoc} */
+    public boolean isSupportLowerBoundInclusive() {
+        return true;
+    }
+
+    /** {@inheritDoc} */
+    public boolean isSupportUpperBoundInclusive() {
+        return false;
+    }
+
+    /**
+     * {@inheritDoc}
+     *
+     * <p>The support of this distribution is connected.
+     *
+     * @return {@code true}
+     */
+    public boolean isSupportConnected() {
+        return true;
+    }
+}