/*
    * 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
    *
    *      https://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.
   */
  
  /*
   * This is not the original file distributed by the Apache Software Foundation
   * It has been modified by the Hipparchus project
   */
  package org.hipparchus.distribution.continuous;
  
  import org.hipparchus.exception.LocalizedCoreFormats;
  import org.hipparchus.exception.MathIllegalArgumentException;
  import org.hipparchus.special.Beta;
  import org.hipparchus.special.Gamma;
  import org.hipparchus.util.FastMath;
  
  /**
   * Implementation of Student's t-distribution.
   */
  public class TDistribution extends AbstractRealDistribution {
      /** Serializable version identifier */
      private static final long serialVersionUID = 20160320L;
      /** The degrees of freedom. */
      private final double degreesOfFreedom;
      /** Static computation factor based on degreesOfFreedom. */
      private final double factor;
  
      /**
       * Create a t distribution using the given degrees of freedom.
       *
       * @param degreesOfFreedom Degrees of freedom.
       * @throws MathIllegalArgumentException if {@code degreesOfFreedom <= 0}
       */
      public TDistribution(double degreesOfFreedom)
          throws MathIllegalArgumentException {
          this(degreesOfFreedom, DEFAULT_SOLVER_ABSOLUTE_ACCURACY);
      }
  
      /**
       * Create a t distribution using the given degrees of freedom and the
       * specified inverse cumulative probability absolute accuracy.
       *
       * @param degreesOfFreedom Degrees of freedom.
       * @param inverseCumAccuracy the maximum absolute error in inverse
       * cumulative probability estimates
       * (defaults to {@link #DEFAULT_SOLVER_ABSOLUTE_ACCURACY}).
       * @throws MathIllegalArgumentException if {@code degreesOfFreedom <= 0}
       */
      public TDistribution(double degreesOfFreedom, double inverseCumAccuracy)
          throws MathIllegalArgumentException {
          super(inverseCumAccuracy);
  
          if (degreesOfFreedom <= 0) {
              throw new MathIllegalArgumentException(LocalizedCoreFormats.DEGREES_OF_FREEDOM,
                                                     degreesOfFreedom);
          }
          this.degreesOfFreedom = degreesOfFreedom;
  
          final double n = degreesOfFreedom;
          final double nPlus1Over2 = (n + 1) / 2;
          factor = Gamma.logGamma(nPlus1Over2) -
                   0.5 * (FastMath.log(FastMath.PI) + FastMath.log(n)) -
                   Gamma.logGamma(n / 2);
      }
  
      /**
       * Access the degrees of freedom.
       *
       * @return the degrees of freedom.
       */
      public double getDegreesOfFreedom() {
          return degreesOfFreedom;
      }
  
      /** {@inheritDoc} */
      @Override
      public double density(double x) {
          return FastMath.exp(logDensity(x));
      }
  
      /** {@inheritDoc} */
      @Override
      public double logDensity(double x) {
          final double n = degreesOfFreedom;
          final double nPlus1Over2 = (n + 1) / 2;
          return factor - nPlus1Over2 * FastMath.log(1 + x * x / n);
     }
 
     /** {@inheritDoc} */
     @Override
     public double cumulativeProbability(double x) {
         double ret;
         if (x == 0) {
             ret = 0.5;
         } else {
             double t =
                 Beta.regularizedBeta(
                     degreesOfFreedom / (degreesOfFreedom + (x * x)),
                     0.5 * degreesOfFreedom,
                     0.5);
             if (x < 0.0) {
                 ret = 0.5 * t;
             } else {
                 ret = 1.0 - 0.5 * t;
             }
         }
 
         return ret;
     }
 
     /**
      * {@inheritDoc}
      *
      * For degrees of freedom parameter {@code df}, the mean is
      * <ul>
      *  <li>if {@code df > 1} then {@code 0},</li>
      * <li>else undefined ({@code Double.NaN}).</li>
      * </ul>
      */
     @Override
     public double getNumericalMean() {
         final double df = getDegreesOfFreedom();
 
         if (df > 1) {
             return 0;
         }
 
         return Double.NaN;
     }
 
     /**
      * {@inheritDoc}
      *
      * For degrees of freedom parameter {@code df}, the variance is
      * <ul>
      *  <li>if {@code df > 2} then {@code df / (df - 2)},</li>
      *  <li>if {@code 1 < df <= 2} then positive infinity
      *  ({@code Double.POSITIVE_INFINITY}),</li>
      *  <li>else undefined ({@code Double.NaN}).</li>
      * </ul>
      */
     @Override
     public double getNumericalVariance() {
         final double df = getDegreesOfFreedom();
 
         if (df > 2) {
             return df / (df - 2);
         }
 
         if (df > 1 && df <= 2) {
             return Double.POSITIVE_INFINITY;
         }
 
         return Double.NaN;
     }
 
     /**
      * {@inheritDoc}
      *
      * The lower bound of the support is always negative infinity no matter the
      * parameters.
      *
      * @return lower bound of the support (always
      * {@code Double.NEGATIVE_INFINITY})
      */
     @Override
     public double getSupportLowerBound() {
         return Double.NEGATIVE_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})
      */
     @Override
     public double getSupportUpperBound() {
         return Double.POSITIVE_INFINITY;
     }
 
     /**
      * {@inheritDoc}
      *
      * The support of this distribution is connected.
      *
      * @return {@code true}
      */
     @Override
     public boolean isSupportConnected() {
         return true;
     }
 }