/*
    * 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.math4.legacy.stat.descriptive.moment;
  
  import org.apache.commons.math4.legacy.exception.MathIllegalArgumentException;
  import org.apache.commons.math4.legacy.exception.NullArgumentException;
  import org.apache.commons.math4.legacy.stat.descriptive.AbstractStorelessUnivariateStatistic;
  import org.apache.commons.math4.core.jdkmath.JdkMath;
  import org.apache.commons.math4.legacy.core.MathArrays;
  
  
  /**
   * Computes the Kurtosis of the available values.
   * <p>
   * We use the following (unbiased) formula to define kurtosis:</p>
   * <p>
   * kurtosis = { [n(n+1) / (n -1)(n - 2)(n-3)] sum[(x_i - mean)^4] / std^4 } - [3(n-1)^2 / (n-2)(n-3)]
   * </p><p>
   * where n is the number of values, mean is the {@link Mean} and std is the
   * {@link StandardDeviation}</p>
   * <p>
   * Note that this statistic is undefined for {@code n < 4}.  <code>Double.Nan</code>
   * is returned when there is not sufficient data to compute the statistic.
   * Note that Double.NaN may also be returned if the input includes NaN
   * and / or infinite values.</p>
   * <p>
   * <strong>Note that this implementation is not synchronized.</strong> If
   * multiple threads access an instance of this class concurrently, and at least
   * one of the threads invokes the <code>increment()</code> or
   * <code>clear()</code> method, it must be synchronized externally.</p>
   */
  public class Kurtosis extends AbstractStorelessUnivariateStatistic {
      /**Fourth Moment on which this statistic is based. */
      protected FourthMoment moment;
  
      /**
       * Determines whether or not this statistic can be incremented or cleared.
       * <p>
       * Statistics based on (constructed from) external moments cannot
       * be incremented or cleared.</p>
       */
      protected boolean incMoment;
  
      /**
       * Construct a Kurtosis.
       */
      public Kurtosis() {
          incMoment = true;
          moment = new FourthMoment();
      }
  
      /**
       * Construct a Kurtosis from an external moment.
       *
       * @param m4 external Moment
       */
      public Kurtosis(final FourthMoment m4) {
          incMoment = false;
          this.moment = m4;
      }
  
      /**
       * Copy constructor, creates a new {@code Kurtosis} identical
       * to the {@code original}.
       *
       * @param original the {@code Kurtosis} instance to copy
       * @throws NullArgumentException if original is null
       */
      public Kurtosis(Kurtosis original) throws NullArgumentException {
          copy(original, this);
      }
  
      /**
       * {@inheritDoc}
       * <p>Note that when {@link #Kurtosis(FourthMoment)} is used to
       * create a Variance, this method does nothing. In that case, the
       * FourthMoment should be incremented directly.</p>
       */
      @Override
      public void increment(final double d) {
          if (incMoment) {
              moment.increment(d);
          }
      }
  
     /**
      * {@inheritDoc}
      */
     @Override
     public double getResult() {
         double kurtosis = Double.NaN;
         if (moment.getN() > 3) {
             double variance = moment.m2 / (moment.n - 1);
                 if (moment.n <= 3 || variance < 10E-20) {
                     kurtosis = 0.0;
                 } else {
                     double n = moment.n;
                     kurtosis =
                         (n * (n + 1) * moment.getResult() -
                                 3 * moment.m2 * moment.m2 * (n - 1)) /
                                 ((n - 1) * (n -2) * (n -3) * variance * variance);
                 }
         }
         return kurtosis;
     }
 
     /**
      * {@inheritDoc}
      */
     @Override
     public void clear() {
         if (incMoment) {
             moment.clear();
         }
     }
 
     /**
      * {@inheritDoc}
      */
     @Override
     public long getN() {
         return moment.getN();
     }
 
     /* UnivariateStatistic Approach  */
 
     /**
      * Returns the kurtosis of the entries in the specified portion of the
      * input array.
      * <p>
      * See {@link Kurtosis} for details on the computing algorithm.</p>
      * <p>
      * Throws <code>IllegalArgumentException</code> if the array is null.</p>
      *
      * @param values the input array
      * @param begin index of the first array element to include
      * @param length the number of elements to include
      * @return the kurtosis of the values or Double.NaN if length is less than 4
      * @throws MathIllegalArgumentException if the input array is null or the array
      * index parameters are not valid
      */
     @Override
     public double evaluate(final double[] values, final int begin, final int length)
         throws MathIllegalArgumentException {
 
         // Initialize the kurtosis
         double kurt = Double.NaN;
 
         if (MathArrays.verifyValues(values, begin, length) && length > 3) {
             // Compute the mean and standard deviation
             Variance variance = new Variance();
             variance.incrementAll(values, begin, length);
             double mean = variance.moment.m1;
             double stdDev = JdkMath.sqrt(variance.getResult());
 
             // Sum the ^4 of the distance from the mean divided by the
             // standard deviation
             double accum3 = 0.0;
             for (int i = begin; i < begin + length; i++) {
                 accum3 += JdkMath.pow(values[i] - mean, 4.0);
             }
             accum3 /= JdkMath.pow(stdDev, 4.0d);
 
             // Get N
             double n0 = length;
 
             double coefficientOne =
                 (n0 * (n0 + 1)) / ((n0 - 1) * (n0 - 2) * (n0 - 3));
             double termTwo =
                 (3 * JdkMath.pow(n0 - 1, 2.0)) / ((n0 - 2) * (n0 - 3));
 
             // Calculate kurtosis
             kurt = (coefficientOne * accum3) - termTwo;
         }
         return kurt;
     }
 
     /**
      * {@inheritDoc}
      */
     @Override
     public Kurtosis copy() {
         Kurtosis result = new Kurtosis();
         // No try-catch because args are guaranteed non-null
         copy(this, result);
         return result;
     }
 
     /**
      * Copies source to dest.
      * <p>Neither source nor dest can be null.</p>
      *
      * @param source Kurtosis to copy
      * @param dest Kurtosis to copy to
      * @throws NullArgumentException if either source or dest is null
      */
     public static void copy(Kurtosis source, Kurtosis dest)
         throws NullArgumentException {
         NullArgumentException.check(source);
         NullArgumentException.check(dest);
         dest.moment = source.moment.copy();
         dest.incMoment = source.incMoment;
     }
 }