/*
 * 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

Weibull Distribution, equations (1) and (2).
See Also:
Weibull distribution (Wikipedia)
Weibull distribution (MathWorld)
Since:
1.1 (changed to concrete class in 3.0)/**
 * 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/**
     * Default inverse cumulative probability accuracy.
     * @since 2.1
     */
    public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY = 1e-9;
    
Serializable version identifier. /** Serializable version identifier. */
    private static final long serialVersionUID = 8589540077390120676L;
    
The shape parameter. /** The shape parameter. */
    private final double shape;
    
The scale parameter. /** The scale parameter. */
    private final double scale;
    
Inverse cumulative probability accuracy. /** Inverse cumulative probability accuracy. */
    private final double solverAbsoluteAccuracy;
    
Cached numerical mean /** Cached numerical mean */
    private double numericalMean = Double.NaN;
    
Whether or not the numerical mean has been calculated /** Whether or not the numerical mean has been calculated */
    private boolean numericalMeanIsCalculated = false;
    
Cached numerical variance /** Cached numerical variance */
    private double numericalVariance = Double.NaN;
    
Whether or not the numerical variance has been calculated /** 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.

Note: this constructor will implicitly create an instance of Well19937c as random generator to be used for sampling only (see AbstractRealDistribution.sample() and AbstractRealDistribution.sample(int)). In case no sampling is needed for the created distribution, it is advised to pass null as random generator via the appropriate constructors to avoid the additional initialisation overhead. 
Params:
alpha – Shape parameter.
beta – Scale parameter.
Throws:
NotStrictlyPositiveException – if alpha <= 0 or beta <= 0./**
     * 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.

Note: this constructor will implicitly create an instance of Well19937c as random generator to be used for sampling only (see AbstractRealDistribution.sample() and AbstractRealDistribution.sample(int)). In case no sampling is needed for the created distribution, it is advised to pass null as random generator via the appropriate constructors to avoid the additional initialisation overhead. 
Params:
alpha – Shape parameter.
beta – Scale parameter.
inverseCumAccuracy – Maximum absolute error in inverse cumulative probability estimates (defaults to DEFAULT_INVERSE_ABSOLUTE_ACCURACY).
Throws:
NotStrictlyPositiveException – if alpha <= 0 or beta <= 0.
Since:
2.1/**
     * 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.
Params:
rng – Random number generator.
alpha – Shape parameter.
beta – Scale parameter.
Throws:
NotStrictlyPositiveException – if alpha <= 0 or beta <= 0.
Since:
3.3/**
     * 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.
Params:
rng – Random number generator.
alpha – Shape parameter.
beta – Scale parameter.
inverseCumAccuracy – Maximum absolute error in inverse cumulative probability estimates (defaults to DEFAULT_INVERSE_ABSOLUTE_ACCURACY).
Throws:
NotStrictlyPositiveException – if alpha <= 0 or beta <= 0.
Since:
3.1/**
     * 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, alpha. 
Returns:
the shape parameter, alpha./**
     * Access the shape parameter, {@code alpha}.
     *
     * @return the shape parameter, {@code alpha}.
     */
    public double getShape() {
        return shape;
    }

    
Access the scale parameter, beta. 
Returns:
the scale parameter, beta./**
     * Access the scale parameter, {@code beta}.
     *
     * @return the scale parameter, {@code beta}.
     */
    public double getScale() {
        return scale;
    }

    
{@inheritDoc} /** {@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} /** {@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} /** {@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} Returns 0 when p == 0 and Double.POSITIVE_INFINITY when p == 1. /**
     * {@inheritDoc}
     *
     * 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.
Returns:
the solver absolute accuracy.
Since:
2.1/**
     * 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} The mean is scale * Gamma(1 + (1 / shape)), where Gamma() is the Gamma-function. /**
     * {@inheritDoc}
     *
     * 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 getNumericalMean() 
Returns:
the mean of this distribution/**
     * 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} The variance is scale^2 * Gamma(1 + (2 / shape)) - mean^2 where Gamma() is the Gamma-function. /**
     * {@inheritDoc}
     *
     * 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 getNumericalVariance() 
Returns:
the variance of this distribution/**
     * 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}
The lower bound of the support is always 0 no matter the parameters.
Returns:
lower bound of the support (always 0)/**
     * {@inheritDoc}
     *
     * 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}
The upper bound of the support is always positive infinity
no matter the parameters.
Returns:
upper bound of the support (always Double.POSITIVE_INFINITY)/**
     * {@inheritDoc}
     *
     * 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} /** {@inheritDoc} */
    public boolean isSupportLowerBoundInclusive() {
        return true;
    }

    
{@inheritDoc} /** {@inheritDoc} */
    public boolean isSupportUpperBoundInclusive() {
        return false;
    }

    
{@inheritDoc}
The support of this distribution is connected.
Returns:
true/**
     * {@inheritDoc}
     *
     * The support of this distribution is connected.
     *
     * @return {@code true}
     */
    public boolean isSupportConnected() {
        return true;
    }
}