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The Apache Commons RNG Sampling module provides samplers for various distributions.
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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.rng.sampling.distribution;

import org.apache.commons.rng.UniformRandomProvider;

/**
 * Sampling from the Gamma distribution.
 * 
 *  
 *   For {@code 0 < theta < 1}:
 *   
 *    Ahrens, J. H. and Dieter, U.,
 *    Computer methods for sampling from gamma, beta, Poisson and binomial distributions,
 *    Computing, 12, 223-246, 1974.
 *   
 *  
 *  
 *  For {@code theta >= 1}:
 *   
 *   Marsaglia and Tsang, A Simple Method for Generating
 *   Gamma Variables. ACM Transactions on Mathematical Software,
 *   Volume 26 Issue 3, September, 2000.
 *   
 *  
 * 
 *
 * @since 1.0
 */
public class AhrensDieterMarsagliaTsangGammaSampler
    extends SamplerBase
    implements ContinuousSampler {
    /** 1/3 */
    private static final double ONE_THIRD = 1d / 3;
    /** The shape parameter. */
    private final double theta;
    /** The alpha parameter. */
    private final double alpha;
    /** Inverse of "theta". */
    private final double oneOverTheta;
    /** Optimization (see code). */
    private final double bGSOptim;
    /** Optimization (see code). */
    private final double dOptim;
    /** Optimization (see code). */
    private final double cOptim;
    /** Gaussian sampling. */
    private final NormalizedGaussianSampler gaussian;
    /** Underlying source of randomness. */
    private final UniformRandomProvider rng;

    /**
     * @param rng Generator of uniformly distributed random numbers.
     * @param alpha Alpha parameter of the distribution.
     * @param theta Theta parameter of the distribution.
     */
    public AhrensDieterMarsagliaTsangGammaSampler(UniformRandomProvider rng,
                                                  double alpha,
                                                  double theta) {
        super(null);
        this.rng = rng;
        this.alpha = alpha;
        this.theta = theta;
        gaussian = new ZigguratNormalizedGaussianSampler(rng);
        oneOverTheta = 1 / theta;
        bGSOptim = 1 + theta / Math.E;
        dOptim = theta - ONE_THIRD;
        cOptim = ONE_THIRD / Math.sqrt(dOptim);
    }

    /** {@inheritDoc} */
    @Override
    public double sample() {
        if (theta < 1) {
            // [1]: p. 228, Algorithm GS.

            while (true) {
                // Step 1:
                final double u = rng.nextDouble();
                final double p = bGSOptim * u;

                if (p <= 1) {
                    // Step 2:

                    final double x = Math.pow(p, oneOverTheta);
                    final double u2 = rng.nextDouble();

                    if (u2 > Math.exp(-x)) {
                        // Reject.
                        continue;
                    } else {
                        return alpha * x;
                    }
                } else {
                    // Step 3:

                    final double x = -Math.log((bGSOptim - p) * oneOverTheta);
                    final double u2 = rng.nextDouble();

                    if (u2 > Math.pow(x, theta - 1)) {
                        // Reject.
                        continue;
                    } else {
                        return alpha * x;
                    }
                }
            }
        } else {
            while (true) {
                final double x = gaussian.sample();
                final double oPcTx = 1 + cOptim * x;
                final double v = oPcTx * oPcTx * oPcTx;

                if (v <= 0) {
                    continue;
                }

                final double x2 = x * x;
                final double u = rng.nextDouble();

                // Squeeze.
                if (u < 1 - 0.0331 * x2 * x2) {
                    return alpha * dOptim * v;
                }

                if (Math.log(u) < 0.5 * x2 + dOptim * (1 - v + Math.log(v))) {
                    return alpha * dOptim * v;
                }
            }
        }
    }

    /** {@inheritDoc} */
    @Override
    public String toString() {
        return "Ahrens-Dieter-Marsaglia-Tsang Gamma deviate [" + rng.toString() + "]";
    }
}