/*
    * 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;
  
  import org.apache.commons.numbers.gamma.LogBeta;
  import org.apache.commons.numbers.gamma.RegularizedBeta;
  import org.apache.commons.rng.UniformRandomProvider;
  import org.apache.commons.rng.sampling.distribution.ChengBetaSampler;
  
  /**
   * Implementation of the beta distribution.
   *
   * <p>The probability density function of \( X \) is:
   *
   * <p>\[ f(x; \alpha, \beta) = \frac{1}{ B(\alpha, \beta)} x^{\alpha-1} (1-x)^{\beta-1} \]
   *
   * <p>for \( \alpha &gt; 0 \),
   * \( \beta &gt; 0 \), \( x \in [0, 1] \), and
   * the beta function, \( B \), is a normalization constant:
   *
   * <p>\[ B(\alpha, \beta) = \frac{\Gamma(\alpha+\beta)}{\Gamma(\alpha) \Gamma(\beta)} \]
   *
   * <p>where \( \Gamma \) is the gamma function.
   *
   * <p>\( \alpha \) and \( \beta \) are <em>shape</em> parameters.
   *
   * @see <a href="https://en.wikipedia.org/wiki/Beta_distribution">Beta distribution (Wikipedia)</a>
   * @see <a href="https://mathworld.wolfram.com/BetaDistribution.html">Beta distribution (MathWorld)</a>
   */
  public final class BetaDistribution extends AbstractContinuousDistribution {
      /** First shape parameter. */
      private final double alpha;
      /** Second shape parameter. */
      private final double beta;
      /** Normalizing factor used in log density computations. log(beta(a, b)). */
      private final double logBeta;
      /** Cached value for inverse probability function. */
      private final double mean;
      /** Cached value for inverse probability function. */
      private final double variance;
  
      /**
       * @param alpha First shape parameter (must be positive).
       * @param beta Second shape parameter (must be positive).
       */
      private BetaDistribution(double alpha,
                               double beta) {
          this.alpha = alpha;
          this.beta = beta;
          logBeta = LogBeta.value(alpha, beta);
          final double alphabetasum = alpha + beta;
          mean = alpha / alphabetasum;
          variance = (alpha * beta) / ((alphabetasum * alphabetasum) * (alphabetasum + 1));
      }
  
      /**
       * Creates a beta distribution.
       *
       * @param alpha First shape parameter (must be positive).
       * @param beta Second shape parameter (must be positive).
       * @return the distribution
       * @throws IllegalArgumentException if {@code alpha <= 0} or {@code beta <= 0}.
       */
      public static BetaDistribution of(double alpha,
                                        double beta) {
          if (alpha <= 0) {
              throw new DistributionException(DistributionException.NOT_STRICTLY_POSITIVE, alpha);
          }
          if (beta <= 0) {
              throw new DistributionException(DistributionException.NOT_STRICTLY_POSITIVE, beta);
          }
          return new BetaDistribution(alpha, beta);
      }
  
      /**
       * Gets the first shape parameter of this distribution.
       *
       * @return the first shape parameter.
       */
      public double getAlpha() {
          return alpha;
      }
  
      /**
       * Gets the second shape parameter of this distribution.
      *
      * @return the second shape parameter.
      */
     public double getBeta() {
         return beta;
     }
 
     /** {@inheritDoc}
      *
      * <p>The density is not defined when {@code x = 0, alpha < 1}, or {@code x = 1, beta < 1}.
      * In this case the limit of infinity is returned.
      */
     @Override
     public double density(double x) {
         if (x < 0 || x > 1) {
             return 0;
         }
         return RegularizedBeta.derivative(x, alpha, beta);
     }
 
     /** {@inheritDoc}
      *
      * <p>The density is not defined when {@code x = 0, alpha < 1}, or {@code x = 1, beta < 1}.
      * In this case the limit of infinity is returned.
      */
     @Override
     public double logDensity(double x) {
         if (x < 0 || x > 1) {
             return Double.NEGATIVE_INFINITY;
         } else if (x == 0) {
             if (alpha < 1) {
                 // Distribution is not valid when x=0, alpha<1
                 // due to a divide by zero error.
                 // Do not raise an exception and return the limit.
                 return Double.POSITIVE_INFINITY;
             }
             // Special case of cancellation: x^(a-1) (1-x)^(b-1) / B(a, b) = 1 / B(a, b)
             if (alpha == 1) {
                 return -logBeta;
             }
             return Double.NEGATIVE_INFINITY;
         } else if (x == 1) {
             if (beta < 1) {
                 // Distribution is not valid when x=1, beta<1
                 // due to a divide by zero error.
                 // Do not raise an exception and return the limit.
                 return Double.POSITIVE_INFINITY;
             }
             // Special case of cancellation: x^(a-1) (1-x)^(b-1) / B(a, b) = 1 / B(a, b)
             if (beta == 1) {
                 return -logBeta;
             }
             return Double.NEGATIVE_INFINITY;
         }
 
         // Log computation
         final double logX = Math.log(x);
         final double log1mX = Math.log1p(-x);
         return (alpha - 1) * logX + (beta - 1) * log1mX - logBeta;
     }
 
     /** {@inheritDoc} */
     @Override
     public double cumulativeProbability(double x)  {
         if (x <= 0) {
             return 0;
         } else if (x >= 1) {
             return 1;
         } else {
             return RegularizedBeta.value(x, alpha, beta);
         }
     }
 
     /** {@inheritDoc} */
     @Override
     public double survivalProbability(double x) {
         if (x <= 0) {
             return 1;
         } else if (x >= 1) {
             return 0;
         } else {
             return RegularizedBeta.complement(x, alpha, beta);
         }
     }
 
     /**
      * {@inheritDoc}
      *
      * <p>For first shape parameter \( \alpha \) and second shape parameter
      * \( \beta \), the mean is:
      *
      * <p>\[ \frac{\alpha}{\alpha + \beta} \]
      */
     @Override
     public double getMean() {
         return mean;
     }
 
     /**
      * {@inheritDoc}
      *
      * <p>For first shape parameter \( \alpha \) and second shape parameter
      * \( \beta \), the variance is:
      *
      * <p>\[ \frac{\alpha \beta}{(\alpha + \beta)^2 (\alpha + \beta + 1)} \]
      */
     @Override
     public double getVariance() {
         return variance;
     }
 
     /**
      * {@inheritDoc}
      *
      * <p>The lower bound of the support is always 0.
      *
      * @return 0.
      */
     @Override
     public double getSupportLowerBound() {
         return 0;
     }
 
     /**
      * {@inheritDoc}
      *
      * <p>The upper bound of the support is always 1.
      *
      * @return 1.
      */
     @Override
     public double getSupportUpperBound() {
         return 1;
     }
 
     /** {@inheritDoc} */
     @Override
     public ContinuousDistribution.Sampler createSampler(final UniformRandomProvider rng) {
         // Beta distribution sampler.
         return ChengBetaSampler.of(rng, alpha, beta)::sample;
     }
 }