/*
 * 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.math.stat.descriptive.moment;

import java.io.Serializable;

import org.apache.commons.math.MathRuntimeException;
import org.apache.commons.math.stat.descriptive.AbstractStorelessUnivariateStatistic;

/**
 * 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 n < 4. <code>Double.Nan</code> is
 * returned when there is not sufficient data to compute the statistic.
 * </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>
 * 
 * @version $Revision$ $Date$
 */
public class Kurtosis extends AbstractStorelessUnivariateStatistic implements Serializable {

	/** Serializable version identifier */
	private static final long serialVersionUID = 2784465764798260919L;

	/** 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
	 */
	public Kurtosis(Kurtosis original) {
		copy(original, this);
	}

	/**
	 * {@inheritDoc}
	 */
	@Override
	public void increment(final double d) {
		if (incMoment) {
			moment.increment(d);
		} else {
			throw MathRuntimeException
					.createIllegalStateException("statistics constructed from external moments cannot be incremented");
		}
	}

	/**
	 * {@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.m4 - 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();
		} else {
			throw MathRuntimeException
					.createIllegalStateException("statistics constructed from external moments cannot be cleared");
		}
	}

	/**
	 * {@inheritDoc}
	 */
	public long getN() {
		return moment.getN();
	}

	/* UnvariateStatistic 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 IllegalArgumentException
	 *             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) {
		// Initialize the kurtosis
		double kurt = Double.NaN;

		if (test(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 = Math.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 += Math.pow((values[i] - mean), 4.0);
			}
			accum3 /= Math.pow(stdDev, 4.0d);

			// Get N
			double n0 = length;

			double coefficientOne = (n0 * (n0 + 1)) / ((n0 - 1) * (n0 - 2) * (n0 - 3));
			double termTwo = ((3 * Math.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();
		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 NullPointerException
	 *             if either source or dest is null
	 */
	public static void copy(Kurtosis source, Kurtosis dest) {
		dest.moment = source.moment.copy();
		dest.incMoment = source.incMoment;
	}

}
