/*
    * 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.statistics.distribution;
  
  /**
   * Implementation of the Gumbel distribution.
   *
   * <p>The probability density function of \( X \) is:
   *
   * <p>\[ f(x; \mu, \beta) =  \frac{1}{\beta} e^{-(z+e^{-z})} \]
   *
   * <p>where \[ z = \frac{x - \mu}{\beta} \]
   *
   * <p>for \( \mu \) the location,
   * \( \beta &gt; 0 \) the scale, and
   * \( x \in (-\infty, \infty) \).
   *
   * @see <a href="https://en.wikipedia.org/wiki/Gumbel_distribution">Gumbel distribution (Wikipedia)</a>
   * @see <a href="https://mathworld.wolfram.com/GumbelDistribution.html">Gumbel distribution (MathWorld)</a>
   */
  public final class GumbelDistribution extends AbstractContinuousDistribution {
      /** Support lower bound. */
      private static final double SUPPORT_LO = Double.NEGATIVE_INFINITY;
      /** Support upper bound. */
      private static final double SUPPORT_HI = Double.POSITIVE_INFINITY;
      /** &pi;<sup>2</sup>/6. https://oeis.org/A013661. */
      private static final double PI_SQUARED_OVER_SIX = 1.644934066848226436472415166646;
      /**
       * <a href="https://en.wikipedia.org/wiki/Euler%27s_constant">
       * Approximation of Euler's constant</a>.
       * https://oeis.org/A001620.
       */
      private static final double EULER = 0.5772156649015328606065;
      /** ln(ln(2)). https://oeis.org/A074785. */
      private static final double LN_LN_2 = -0.3665129205816643270124;
      /** Location parameter. */
      private final double mu;
      /** Scale parameter. */
      private final double beta;
  
      /**
       * @param mu Location parameter.
       * @param beta Scale parameter (must be positive).
       */
      private GumbelDistribution(double mu,
                                 double beta) {
          this.beta = beta;
          this.mu = mu;
      }
  
      /**
       * Creates a Gumbel distribution.
       *
       * @param mu Location parameter.
       * @param beta Scale parameter (must be positive).
       * @return the distribution
       * @throws IllegalArgumentException if {@code beta <= 0}
       */
      public static GumbelDistribution of(double mu,
                                          double beta) {
          if (beta <= 0) {
              throw new DistributionException(DistributionException.NOT_STRICTLY_POSITIVE, beta);
          }
          return new GumbelDistribution(mu, beta);
      }
  
      /**
       * Gets the location parameter of this distribution.
       *
       * @return the location parameter.
       */
      public double getLocation() {
          return mu;
      }
  
      /**
       * Gets the scale parameter of this distribution.
       *
       * @return the scale parameter.
       */
      public double getScale() {
          return beta;
      }
  
      /** {@inheritDoc} */
     @Override
     public double density(double x) {
         if (x <= SUPPORT_LO) {
             return 0;
         }
 
         final double z = (x - mu) / beta;
         final double t = Math.exp(-z);
         return Math.exp(-z - t) / beta;
     }
 
     /** {@inheritDoc} */
     @Override
     public double logDensity(double x) {
         if (x <= SUPPORT_LO) {
             return Double.NEGATIVE_INFINITY;
         }
 
         final double z = (x - mu) / beta;
         final double t = Math.exp(-z);
         return -z - t - Math.log(beta);
     }
 
     /** {@inheritDoc} */
     @Override
     public double cumulativeProbability(double x) {
         final double z = (x - mu) / beta;
         return Math.exp(-Math.exp(-z));
     }
 
     /** {@inheritDoc} */
     @Override
     public double survivalProbability(double x) {
         final double z = (x - mu) / beta;
         return -Math.expm1(-Math.exp(-z));
     }
 
     /** {@inheritDoc} */
     @Override
     public double inverseCumulativeProbability(double p) {
         ArgumentUtils.checkProbability(p);
         if (p == 0) {
             return Double.NEGATIVE_INFINITY;
         } else if (p == 1) {
             return Double.POSITIVE_INFINITY;
         }
         return mu - Math.log(-Math.log(p)) * beta;
     }
 
     /** {@inheritDoc} */
     @Override
     public double inverseSurvivalProbability(double p) {
         ArgumentUtils.checkProbability(p);
         if (p == 1) {
             return Double.NEGATIVE_INFINITY;
         } else if (p == 0) {
             return Double.POSITIVE_INFINITY;
         }
         return mu - Math.log(-Math.log1p(-p)) * beta;
     }
 
     /**
      * {@inheritDoc}
      *
      * <p>For location parameter \( \mu \) and scale parameter \( \beta \), the mean is:
      *
      * <p>\[ \mu + \beta \gamma \]
      *
      * <p>where \( \gamma \) is the
      * <a href="https://mathworld.wolfram.com/Euler-MascheroniConstantApproximations.html">
      * Euler-Mascheroni constant</a>.
      */
     @Override
     public double getMean() {
         return mu + EULER * beta;
     }
 
     /**
      * {@inheritDoc}
      *
      * <p>For scale parameter \( \beta \), the variance is:
      *
      * <p>\[ \frac{\pi^2}{6} \beta^2 \]
      */
     @Override
     public double getVariance() {
         return PI_SQUARED_OVER_SIX * beta * beta;
     }
 
     /**
      * {@inheritDoc}
      *
      * <p>The lower bound of the support is always negative infinity.
      *
      * @return {@linkplain Double#NEGATIVE_INFINITY negative infinity}.
      */
     @Override
     public double getSupportLowerBound() {
         return SUPPORT_LO;
     }
 
     /**
      * {@inheritDoc}
      *
      * <p>The upper bound of the support is always positive infinity.
      *
      * @return {@linkplain Double#POSITIVE_INFINITY positive infinity}.
      */
     @Override
     public double getSupportUpperBound() {
         return SUPPORT_HI;
     }
 
     /** {@inheritDoc} */
     @Override
     double getMedian() {
         // Overridden for the probability(double, double) method.
         // This is intentionally not a public method.
         // u - beta * ln(ln(2))
         return mu - beta * LN_LN_2;
     }
 }