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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.distribution;
+
+import org.apache.commons.math3.exception.NotStrictlyPositiveException;
+import org.apache.commons.math3.exception.NumberIsTooSmallException;
+import org.apache.commons.math3.exception.util.LocalizedFormats;
+import org.apache.commons.math3.random.RandomGenerator;
+import org.apache.commons.math3.random.Well19937c;
+import org.apache.commons.math3.special.Gamma;
+import org.apache.commons.math3.util.FastMath;
+
+/**
+ * This class implements the Nakagami distribution.
+ *
+ * @see <a href="http://en.wikipedia.org/wiki/Nakagami_distribution">Nakagami Distribution
+ *     (Wikipedia)</a>
+ * @since 3.4
+ */
+public class NakagamiDistribution extends AbstractRealDistribution {
+
+    /** Default inverse cumulative probability accuracy. */
+    public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY = 1e-9;
+
+    /** Serializable version identifier. */
+    private static final long serialVersionUID = 20141003;
+
+    /** The shape parameter. */
+    private final double mu;
+
+    /** The scale parameter. */
+    private final double omega;
+
+    /** Inverse cumulative probability accuracy. */
+    private final double inverseAbsoluteAccuracy;
+
+    /**
+     * Build a new instance.
+     *
+     * <p><b>Note:</b> this constructor will implicitly create an instance of {@link Well19937c} as
+     * random generator to be used for sampling only (see {@link #sample()} and {@link
+     * #sample(int)}). In case no sampling is needed for the created distribution, it is advised to
+     * pass {@code null} as random generator via the appropriate constructors to avoid the
+     * additional initialisation overhead.
+     *
+     * @param mu shape parameter
+     * @param omega scale parameter (must be positive)
+     * @throws NumberIsTooSmallException if {@code mu < 0.5}
+     * @throws NotStrictlyPositiveException if {@code omega <= 0}
+     */
+    public NakagamiDistribution(double mu, double omega) {
+        this(mu, omega, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
+    }
+
+    /**
+     * Build a new instance.
+     *
+     * <p><b>Note:</b> this constructor will implicitly create an instance of {@link Well19937c} as
+     * random generator to be used for sampling only (see {@link #sample()} and {@link
+     * #sample(int)}). In case no sampling is needed for the created distribution, it is advised to
+     * pass {@code null} as random generator via the appropriate constructors to avoid the
+     * additional initialisation overhead.
+     *
+     * @param mu shape parameter
+     * @param omega scale parameter (must be positive)
+     * @param inverseAbsoluteAccuracy the maximum absolute error in inverse cumulative probability
+     *     estimates (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}).
+     * @throws NumberIsTooSmallException if {@code mu < 0.5}
+     * @throws NotStrictlyPositiveException if {@code omega <= 0}
+     */
+    public NakagamiDistribution(double mu, double omega, double inverseAbsoluteAccuracy) {
+        this(new Well19937c(), mu, omega, inverseAbsoluteAccuracy);
+    }
+
+    /**
+     * Build a new instance.
+     *
+     * @param rng Random number generator
+     * @param mu shape parameter
+     * @param omega scale parameter (must be positive)
+     * @param inverseAbsoluteAccuracy the maximum absolute error in inverse cumulative probability
+     *     estimates (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}).
+     * @throws NumberIsTooSmallException if {@code mu < 0.5}
+     * @throws NotStrictlyPositiveException if {@code omega <= 0}
+     */
+    public NakagamiDistribution(
+            RandomGenerator rng, double mu, double omega, double inverseAbsoluteAccuracy) {
+        super(rng);
+
+        if (mu < 0.5) {
+            throw new NumberIsTooSmallException(mu, 0.5, true);
+        }
+        if (omega <= 0) {
+            throw new NotStrictlyPositiveException(LocalizedFormats.NOT_POSITIVE_SCALE, omega);
+        }
+
+        this.mu = mu;
+        this.omega = omega;
+        this.inverseAbsoluteAccuracy = inverseAbsoluteAccuracy;
+    }
+
+    /**
+     * Access the shape parameter, {@code mu}.
+     *
+     * @return the shape parameter.
+     */
+    public double getShape() {
+        return mu;
+    }
+
+    /**
+     * Access the scale parameter, {@code omega}.
+     *
+     * @return the scale parameter.
+     */
+    public double getScale() {
+        return omega;
+    }
+
+    /** {@inheritDoc} */
+    @Override
+    protected double getSolverAbsoluteAccuracy() {
+        return inverseAbsoluteAccuracy;
+    }
+
+    /** {@inheritDoc} */
+    public double density(double x) {
+        if (x <= 0) {
+            return 0.0;
+        }
+        return 2.0
+                * FastMath.pow(mu, mu)
+                / (Gamma.gamma(mu) * FastMath.pow(omega, mu))
+                * FastMath.pow(x, 2 * mu - 1)
+                * FastMath.exp(-mu * x * x / omega);
+    }
+
+    /** {@inheritDoc} */
+    public double cumulativeProbability(double x) {
+        return Gamma.regularizedGammaP(mu, mu * x * x / omega);
+    }
+
+    /** {@inheritDoc} */
+    public double getNumericalMean() {
+        return Gamma.gamma(mu + 0.5) / Gamma.gamma(mu) * FastMath.sqrt(omega / mu);
+    }
+
+    /** {@inheritDoc} */
+    public double getNumericalVariance() {
+        double v = Gamma.gamma(mu + 0.5) / Gamma.gamma(mu);
+        return omega * (1 - 1 / mu * v * v);
+    }
+
+    /** {@inheritDoc} */
+    public double getSupportLowerBound() {
+        return 0;
+    }
+
+    /** {@inheritDoc} */
+    public double getSupportUpperBound() {
+        return Double.POSITIVE_INFINITY;
+    }
+
+    /** {@inheritDoc} */
+    public boolean isSupportLowerBoundInclusive() {
+        return true;
+    }
+
+    /** {@inheritDoc} */
+    public boolean isSupportUpperBoundInclusive() {
+        return false;
+    }
+
+    /** {@inheritDoc} */
+    public boolean isSupportConnected() {
+        return true;
+    }
+}