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jBasics is a collection of useful utility classes for Java. This includes helper for XML, mathematic functions, restful web services helper, pattern oriented programming interfaces and more. Currently Java7 and up is supported. Version 1.0 will required at leaset Java8.
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/*
 * Copyright (c) 2009-2015
 * 	IT-Consulting Stephan Schloepke (http://www.schloepke.de/)
 * 	klemm software consulting Mirko Klemm (http://www.klemm-scs.com/)
 *
 * Permission is hereby granted, free of charge, to any person obtaining a copy
 * of this software and associated documentation files (the "Software"), to deal
 * in the Software without restriction, including without limitation the rights
 * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 * copies of the Software, and to permit persons to whom the Software is
 * furnished to do so, subject to the following conditions:
 *
 * The above copyright notice and this permission notice shall be included in
 * all copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
 * THE SOFTWARE.
 */
package org.jbasics.math.distribution;

import org.jbasics.checker.ContractCheck;
import org.jbasics.math.AlgorithmStrategy;
import org.jbasics.math.BigDecimalMathLibrary;
import org.jbasics.math.BoundedMathFunction;
import org.jbasics.math.IrationalNumber;
import org.jbasics.math.MathFunction;
import org.jbasics.math.NumberConverter;
import org.jbasics.math.approximation.Approximation;
import org.jbasics.math.approximation.BiSectionApproximation;
import org.jbasics.math.approximation.ChainedApproximation;
import org.jbasics.math.approximation.NewtonRhapsonApproximation;
import org.jbasics.math.strategies.GammaIncompleteAlgorithmStrategy;

import java.math.BigDecimal;
import java.math.MathContext;

public class GammaDistribution implements Distribution {
	protected static final BigDecimal LOW_BOUND_ALL_FUNC = BigDecimal.ZERO;
	protected static final BigDecimal UPPER_BOUND_ALL_FUNC = null; // BigDecimal.ONE.scaleByPowerOfTen(6);

	protected final AlgorithmStrategy P_STRATEGY = new GammaIncompleteAlgorithmStrategy();

	protected final BigDecimal alpha;
	protected final BigDecimal beta;
	protected final IrationalNumber lnGammaAlpha;

	private MathFunction probabilityDensityFunction;
	private MathFunction inverseProbabilityDensityFunction;
	private MathFunction cumulativeDensityFunction;
	private MathFunction inverseCumulativeDensityFunction;

	public GammaDistribution(final BigDecimal alpha, final BigDecimal beta) {
		this.alpha = alpha;
		this.beta = beta;
		this.lnGammaAlpha = BigDecimalMathLibrary.lnGamma(GammaDistribution.this.alpha);
	}

	@Override
	public MathFunction probabilityDensityFunction() {
		if (this.probabilityDensityFunction == null) {
			this.probabilityDensityFunction = new MathFunction.AbstractMathFunction() {
				@Override
				public BigDecimal calculate(final MathContext mc, final Number xNum) {
					final BigDecimal x = NumberConverter.toBigDecimal(xNum);
					if (ContractCheck.mustNotBeNull(x, "x").signum() <= 0) { //$NON-NLS-1$
						return BigDecimal.ZERO;
					}
					final BigDecimal xDivBeta = x.divide(GammaDistribution.this.beta, mc);
					return BigDecimalMathLibrary.exp(GammaDistribution.this.alpha.multiply(BigDecimalMathLibrary.ln(xDivBeta).valueToPrecision(mc))
							.subtract(GammaDistribution.this.lnGammaAlpha.valueToPrecision(mc)).subtract(xDivBeta)).valueToPrecision(mc)
							.divide(x, mc);
				}
			};
		}
		return this.probabilityDensityFunction;
	}

	@Override
	public MathFunction inverseProbabilityDensityFunction() {
		if (this.inverseProbabilityDensityFunction == null) {
			this.inverseProbabilityDensityFunction = new BoundedMathFunction.AbstractBoundedMathFunction() {
				@Override
				public BigDecimal calculate(final MathContext mc, final Number xNum) {
					final BigDecimal x = NumberConverter.toBigDecimal(xNum);
					if (ContractCheck.mustNotBeNull(x, "x").signum() <= 0) { //$NON-NLS-1$
						return BigDecimal.ZERO;
					}
					return BigDecimalMathLibrary
							.pow(GammaDistribution.this.beta, GammaDistribution.this.alpha)
							.valueToPrecision(mc)
							.divide(BigDecimalMathLibrary.gamma(GammaDistribution.this.alpha).valueToPrecision(mc), mc)
							.multiply(
									BigDecimalMathLibrary.pow(x, GammaDistribution.this.alpha.negate().subtract(BigDecimal.ONE)).valueToPrecision(mc),
									mc)
							.multiply(BigDecimalMathLibrary.exp(GammaDistribution.this.beta.negate().divide(x, mc)).valueToPrecision(mc), mc);
				}

				@Override
				public BigDecimal lowerBoundery() {
					return GammaDistribution.LOW_BOUND_ALL_FUNC;
				}

				@Override
				public BigDecimal upperBoundery() {
					return GammaDistribution.UPPER_BOUND_ALL_FUNC;
				}
			};
		}
		return this.inverseProbabilityDensityFunction;
	}

	@Override
	public MathFunction cumulativeDensityFunction() {
		if (this.cumulativeDensityFunction == null) {
			this.cumulativeDensityFunction = new BoundedMathFunction.AbstractBoundedMathFunction() {
				@Override
				public BigDecimal calculate(final MathContext mc, final Number xNum) {
					final BigDecimal x = NumberConverter.toBigDecimal(xNum);
					return GammaDistribution.this.P_STRATEGY.calculate(mc, null, x.divide(GammaDistribution.this.beta, mc),
							GammaDistribution.this.alpha);
				}

				@Override
				public BigDecimal lowerBoundery() {
					return GammaDistribution.LOW_BOUND_ALL_FUNC;
				}

				@Override
				public BigDecimal upperBoundery() {
					return GammaDistribution.UPPER_BOUND_ALL_FUNC;
				}
			};
		}
		return this.cumulativeDensityFunction;
	}

	@Override
	public MathFunction inverseCumulativeDensityFunction() {
		if (this.inverseCumulativeDensityFunction == null) {
			this.inverseCumulativeDensityFunction = new BoundedMathFunction.AbstractBoundedMathFunction() {
				private final Approximation approximator = new ChainedApproximation(new BiSectionApproximation(cumulativeDensityFunction(), 1500,
						300, true), new NewtonRhapsonApproximation(cumulativeDensityFunction(), probabilityDensityFunction()));

				@Override
				public BigDecimal calculate(final MathContext mc, final Number xNum) {
					return this.approximator.approximate(mc, NumberConverter.toBigDecimal(xNum), null).getApproximatedValue();
				}

				@Override
				public BigDecimal lowerBoundery() {
					return GammaDistribution.LOW_BOUND_ALL_FUNC;
				}

				@Override
				public BigDecimal upperBoundery() {
					return GammaDistribution.UPPER_BOUND_ALL_FUNC;
				}
			};
		}
		return this.inverseCumulativeDensityFunction;
	}

	@Override
	public BigDecimal mean(final MathContext mc) {
		return this.alpha.multiply(this.beta, mc);
	}

	@Override
	public BigDecimal variance(final MathContext mc) {
		return this.alpha.multiply(this.beta.pow(2, mc), mc);
	}

	@Override
	public BigDecimal quantile(final MathContext mc, final Number x) {
		return inverseCumulativeDensityFunction().calculate(mc, x);
	}

	@Override
	public BigDecimal pdf(final MathContext mc, final Number x) {
		return probabilityDensityFunction().calculate(mc, x);
	}

	@Override
	public BigDecimal cdf(final MathContext mc, final Number x) {
		return cumulativeDensityFunction().calculate(mc, x);
	}
}