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+/*
+ * 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.math3.stat.descriptive.moment;
+
+import java.io.Serializable;
+
+import org.apache.commons.math3.exception.MathIllegalArgumentException;
+import org.apache.commons.math3.exception.NullArgumentException;
+import org.apache.commons.math3.stat.descriptive.AbstractStorelessUnivariateStatistic;
+import org.apache.commons.math3.util.FastMath;
+import org.apache.commons.math3.util.MathUtils;
+
+
+/**
+ * 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.
+ *  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  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
+     * @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}
+     */
+    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 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 (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 = FastMath.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 += FastMath.pow(values[i] - mean, 4.0);
+            }
+            accum3 /= FastMath.pow(stdDev, 4.0d);
+
+            // Get N
+            double n0 = length;
+
+            double coefficientOne =
+                (n0 * (n0 + 1)) / ((n0 - 1) * (n0 - 2) * (n0 - 3));
+            double termTwo =
+                (3 * FastMath.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 {
+        MathUtils.checkNotNull(source);
+        MathUtils.checkNotNull(dest);
+        dest.setData(source.getDataRef());
+        dest.moment = source.moment.copy();
+        dest.incMoment = source.incMoment;
+    }
+
+}