/*
    * 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 logistic distribution.
   *
   * <p>The probability density function of \( X \) is:
   *
   * <p>\[ f(x; \mu, s) = \frac{e^{-(x-\mu)/s}} {s\left(1+e^{-(x-\mu)/s}\right)^2} \]
   *
   * <p>for \( \mu \) the location,
   * \( s &gt; 0 \) the scale, and
   * \( x \in (-\infty, \infty) \).
   *
   * @see <a href="https://en.wikipedia.org/wiki/Logistic_distribution">Logistic distribution (Wikipedia)</a>
   * @see <a href="https://mathworld.wolfram.com/LogisticDistribution.html">Logistic distribution (MathWorld)</a>
   */
  public final class LogisticDistribution 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>/3. https://oeis.org/A195055. */
      private static final double PI_SQUARED_OVER_THREE = 3.289868133696452872944830;
      /** Location parameter. */
      private final double mu;
      /** Scale parameter. */
      private final double scale;
      /** Logarithm of "scale". */
      private final double logScale;
  
      /**
       * @param mu Location parameter.
       * @param scale Scale parameter (must be positive).
       */
      private LogisticDistribution(double mu,
                                   double scale) {
          this.mu = mu;
          this.scale = scale;
          this.logScale = Math.log(scale);
      }
  
      /**
       * Creates a logistic distribution.
       *
       * @param mu Location parameter.
       * @param scale Scale parameter (must be positive).
       * @return the distribution
       * @throws IllegalArgumentException if {@code scale <= 0}.
       */
      public static LogisticDistribution of(double mu,
                                            double scale) {
          if (scale <= 0) {
              throw new DistributionException(DistributionException.NOT_STRICTLY_POSITIVE,
                                              scale);
          }
          return new LogisticDistribution(mu, scale);
      }
  
      /**
       * 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 scale;
      }
  
      /** {@inheritDoc} */
      @Override
      public double density(double x) {
          if (x <= SUPPORT_LO ||
              x >= SUPPORT_HI) {
              return 0;
          }
 
         // Ensure symmetry around location by using the absolute.
         // This also ensures exp(z) is between 1 and 0 and avoids
         // overflow for large negative values of (x - mu).
         // Exploits the reciprocal relation: exp(-x) == 1 / exp(x)
         //     exp(-z)                   1                exp(z)     exp(z)
         // --------------- = -------------------------- * ------ = --------------
         // (1 + exp(-z))^2    exp(z) (1 + 1 / exp(z))^2   exp(z)   (1 + exp(z))^2
         final double z = -Math.abs(x - mu) / scale;
         final double v = Math.exp(z);
         return v / ((1 + v) * (1 + v)) / scale;
     }
 
     /** {@inheritDoc} */
     @Override
     public double logDensity(double x) {
         if (x <= SUPPORT_LO ||
             x >= SUPPORT_HI) {
             return Double.NEGATIVE_INFINITY;
         }
 
         // Ensure symmetry around location by using the absolute
         final double z = -Math.abs(x - mu) / scale;
         final double v = Math.exp(z);
         return z - 2 * Math.log1p(v) - logScale;
     }
 
     /** {@inheritDoc} */
     @Override
     public double cumulativeProbability(double x) {
         final double z = (x - mu) / scale;
         return 1 / (1 + Math.exp(-z));
     }
 
     /** {@inheritDoc} */
     @Override
     public double survivalProbability(double x) {
         final double z = (x - mu) / scale;
         return 1 / (1 + Math.exp(z));
     }
 
     /** {@inheritDoc} */
     @Override
     public double inverseCumulativeProbability(double p) {
         ArgumentUtils.checkProbability(p);
         if (p == 0) {
             return SUPPORT_LO;
         } else if (p == 1) {
             return SUPPORT_HI;
         } else {
             return scale * Math.log(p / (1 - p)) + mu;
         }
     }
 
     /** {@inheritDoc} */
     @Override
     public double inverseSurvivalProbability(double p) {
         ArgumentUtils.checkProbability(p);
         if (p == 1) {
             return SUPPORT_LO;
         } else if (p == 0) {
             return SUPPORT_HI;
         } else {
             return scale * -Math.log(p / (1 - p)) + mu;
         }
     }
 
     /**
      * {@inheritDoc}
      *
      * <p>The mean is equal to the {@linkplain #getLocation() location}.
      */
     @Override
     public double getMean() {
         return getLocation();
     }
 
     /**
      * {@inheritDoc}
      *
      * <p>For scale parameter \( s \), the variance is:
      *
      * <p>\[ \frac{s^2 \pi^2}{3} \]
      */
     @Override
     public double getVariance() {
         return scale * scale * PI_SQUARED_OVER_THREE;
     }
 
     /**
      * {@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.
         return mu;
     }
 }