/*
    * 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.rng.UniformRandomProvider;
  
  /**
   * Implementation of the chi-squared distribution.
   *
   * <p>The probability density function of \( X \) is:
   *
   * <p>\[ f(x; k) = \frac{1}{2^{k/2} \Gamma(k/2)} x^{k/2 -1} e^{-x/2} \]
   *
   * <p>for \( k &gt; 0 \) the degrees of freedom,
   * \( \Gamma(k/2) \) is the gamma function, and
   * \( x \in [0, \infty) \).
   *
   * @see <a href="https://en.wikipedia.org/wiki/Chi-squared_distribution">Chi-squared distribution (Wikipedia)</a>
   * @see <a href="https://mathworld.wolfram.com/Chi-SquaredDistribution.html">Chi-squared distribution (MathWorld)</a>
   */
  public final class ChiSquaredDistribution extends AbstractContinuousDistribution {
      /** Internal Gamma distribution. */
      private final GammaDistribution gamma;
  
      /**
       * @param degreesOfFreedom Degrees of freedom.
       */
      private ChiSquaredDistribution(double degreesOfFreedom) {
          gamma = GammaDistribution.of(degreesOfFreedom / 2, 2);
      }
  
      /**
       * Creates a chi-squared distribution.
       *
       * @param degreesOfFreedom Degrees of freedom.
       * @return the distribution
       * @throws IllegalArgumentException if {@code degreesOfFreedom <= 0}.
       */
      public static ChiSquaredDistribution of(double degreesOfFreedom) {
          return new ChiSquaredDistribution(degreesOfFreedom);
      }
  
      /**
       * Gets the degrees of freedom parameter of this distribution.
       *
       * @return the degrees of freedom.
       */
      public double getDegreesOfFreedom() {
          return gamma.getShape() * 2;
      }
  
      /** {@inheritDoc}
       *
       * <p>Returns the limit when {@code x = 0}:
       * <ul>
       * <li>{@code df < 2}: Infinity
       * <li>{@code df == 2}: 1 / 2
       * <li>{@code df > 2}: 0
       * </ul>
       */
      @Override
      public double density(double x) {
          return gamma.density(x);
      }
  
      /** {@inheritDoc}
       *
       * <p>Returns the limit when {@code x = 0}:
       * <ul>
       * <li>{@code df < 2}: Infinity
       * <li>{@code df == 2}: log(1 / 2)
       * <li>{@code df > 2}: -Infinity
       * </ul>
       */
      @Override
      public double logDensity(double x) {
          return gamma.logDensity(x);
      }
  
      /** {@inheritDoc} */
      @Override
      public double cumulativeProbability(double x)  {
          return gamma.cumulativeProbability(x);
      }
  
     /** {@inheritDoc} */
     @Override
     public double survivalProbability(double x) {
         return gamma.survivalProbability(x);
     }
 
     /** {@inheritDoc} */
     @Override
     public double inverseCumulativeProbability(double p) {
         return gamma.inverseCumulativeProbability(p);
     }
 
     /** {@inheritDoc} */
     @Override
     public double inverseSurvivalProbability(double p) {
         return gamma.inverseSurvivalProbability(p);
     }
 
     /**
      * {@inheritDoc}
      *
      * <p>For \( k \) degrees of freedom, the mean is \( k \).
      */
     @Override
     public double getMean() {
         return getDegreesOfFreedom();
     }
 
     /**
      * {@inheritDoc}
      *
      * <p>For \( k \) degrees of freedom, the variance is \( 2k \).
      */
     @Override
     public double getVariance() {
         return 2 * getDegreesOfFreedom();
     }
 
     /**
      * {@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 positive infinity.
      *
      * @return {@linkplain Double#POSITIVE_INFINITY positive infinity}.
      */
     @Override
     public double getSupportUpperBound() {
         return Double.POSITIVE_INFINITY;
     }
 
     /** {@inheritDoc} */
     @Override
     public ContinuousDistribution.Sampler createSampler(final UniformRandomProvider rng) {
         return gamma.createSampler(rng);
     }
 }