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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.math.distribution;
+
+import org.apache.commons.math.MathException;
+import org.apache.commons.math.MathRuntimeException;
+import org.apache.commons.math.exception.util.LocalizedFormats;
+import org.apache.commons.math.special.Gamma;
+import org.apache.commons.math.special.Beta;
+import org.apache.commons.math.util.FastMath;
+
+/**
+ * Implements the Beta distribution.
+ * <p>
+ * References:
+ * <ul>
+ * <li><a href="http://en.wikipedia.org/wiki/Beta_distribution">
+ * Beta distribution</a></li>
+ * </ul>
+ * </p>
+ * @version $Revision: 1054524 $ $Date: 2011-01-03 05:59:18 +0100 (lun. 03 janv. 2011) $
+ * @since 2.0
+ */
+public class BetaDistributionImpl
+    extends AbstractContinuousDistribution implements BetaDistribution {
+
+    /**
+     * Default inverse cumulative probability accuracy
+     * @since 2.1
+     */
+    public static final double DEFAULT_INVERSE_ABSOLUTE_ACCURACY = 1e-9;
+
+    /** Serializable version identifier. */
+    private static final long serialVersionUID = -1221965979403477668L;
+
+    /** First shape parameter. */
+    private double alpha;
+
+    /** Second shape parameter. */
+    private double beta;
+
+    /** Normalizing factor used in density computations.
+     * updated whenever alpha or beta are changed.
+     */
+    private double z;
+
+    /** Inverse cumulative probability accuracy */
+    private final double solverAbsoluteAccuracy;
+
+    /**
+     * Build a new instance.
+     * @param alpha first shape parameter (must be positive)
+     * @param beta second shape parameter (must be positive)
+     * @param inverseCumAccuracy the maximum absolute error in inverse cumulative probability estimates
+     * (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY})
+     * @since 2.1
+     */
+    public BetaDistributionImpl(double alpha, double beta, double inverseCumAccuracy) {
+        this.alpha = alpha;
+        this.beta = beta;
+        z = Double.NaN;
+        solverAbsoluteAccuracy = inverseCumAccuracy;
+    }
+
+    /**
+     * Build a new instance.
+     * @param alpha first shape parameter (must be positive)
+     * @param beta second shape parameter (must be positive)
+     */
+    public BetaDistributionImpl(double alpha, double beta) {
+        this(alpha, beta, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
+    }
+
+    /** {@inheritDoc}
+     * @deprecated as of 2.1 (class will become immutable in 3.0)
+     */
+    @Deprecated
+    public void setAlpha(double alpha) {
+        this.alpha = alpha;
+        z = Double.NaN;
+    }
+
+    /** {@inheritDoc} */
+    public double getAlpha() {
+        return alpha;
+    }
+
+    /** {@inheritDoc}
+     * @deprecated as of 2.1 (class will become immutable in 3.0)
+     */
+    @Deprecated
+    public void setBeta(double beta) {
+        this.beta = beta;
+        z = Double.NaN;
+    }
+
+    /** {@inheritDoc} */
+    public double getBeta() {
+        return beta;
+    }
+
+    /**
+     * Recompute the normalization factor.
+     */
+    private void recomputeZ() {
+        if (Double.isNaN(z)) {
+            z = Gamma.logGamma(alpha) + Gamma.logGamma(beta) - Gamma.logGamma(alpha + beta);
+        }
+    }
+
+    /**
+     * Return the probability density for a particular point.
+     *
+     * @param x The point at which the density should be computed.
+     * @return The pdf at point x.
+     * @deprecated
+     */
+    @Deprecated
+    public double density(Double x) {
+        return density(x.doubleValue());
+    }
+
+    /**
+     * Return the probability density for a particular point.
+     *
+     * @param x The point at which the density should be computed.
+     * @return The pdf at point x.
+     * @since 2.1
+     */
+    @Override
+    public double density(double x) {
+        recomputeZ();
+        if (x < 0 || x > 1) {
+            return 0;
+        } else if (x == 0) {
+            if (alpha < 1) {
+                throw MathRuntimeException.createIllegalArgumentException(
+                        LocalizedFormats.CANNOT_COMPUTE_BETA_DENSITY_AT_0_FOR_SOME_ALPHA, alpha);
+            }
+            return 0;
+        } else if (x == 1) {
+            if (beta < 1) {
+                throw MathRuntimeException.createIllegalArgumentException(
+                        LocalizedFormats.CANNOT_COMPUTE_BETA_DENSITY_AT_1_FOR_SOME_BETA, beta);
+            }
+            return 0;
+        } else {
+            double logX = FastMath.log(x);
+            double log1mX = FastMath.log1p(-x);
+            return FastMath.exp((alpha - 1) * logX + (beta - 1) * log1mX - z);
+        }
+    }
+
+    /** {@inheritDoc} */
+    @Override
+    public double inverseCumulativeProbability(double p) throws MathException {
+        if (p == 0) {
+            return 0;
+        } else if (p == 1) {
+            return 1;
+        } else {
+            return super.inverseCumulativeProbability(p);
+        }
+    }
+
+    /** {@inheritDoc} */
+    @Override
+    protected double getInitialDomain(double p) {
+        return p;
+    }
+
+    /** {@inheritDoc} */
+    @Override
+    protected double getDomainLowerBound(double p) {
+        return 0;
+    }
+
+    /** {@inheritDoc} */
+    @Override
+    protected double getDomainUpperBound(double p) {
+        return 1;
+    }
+
+    /** {@inheritDoc} */
+    public double cumulativeProbability(double x) throws MathException {
+        if (x <= 0) {
+            return 0;
+        } else if (x >= 1) {
+            return 1;
+        } else {
+            return Beta.regularizedBeta(x, alpha, beta);
+        }
+    }
+
+    /** {@inheritDoc} */
+    @Override
+    public double cumulativeProbability(double x0, double x1) throws MathException {
+        return cumulativeProbability(x1) - cumulativeProbability(x0);
+    }
+
+    /**
+     * Return the absolute accuracy setting of the solver used to estimate
+     * inverse cumulative probabilities.
+     *
+     * @return the solver absolute accuracy
+     * @since 2.1
+     */
+    @Override
+    protected double getSolverAbsoluteAccuracy() {
+        return solverAbsoluteAccuracy;
+    }
+
+    /**
+     * Returns the lower bound of the support for this distribution.
+     * The support of the Beta distribution is always [0, 1], regardless
+     * of the parameters, so this method always returns 0.
+     *
+     * @return lower bound of the support (always 0)
+     * @since 2.2
+     */
+    public double getSupportLowerBound() {
+        return 0;
+    }
+
+    /**
+     * Returns the upper bound of the support for this distribution.
+     * The support of the Beta distribution is always [0, 1], regardless
+     * of the parameters, so this method always returns 1.
+     *
+     * @return lower bound of the support (always 1)
+     * @since 2.2
+     */
+    public double getSupportUpperBound() {
+        return 1;
+    }
+
+    /**
+     * Returns the mean.
+     *
+     * For first shape parameter <code>s1</code> and
+     * second shape parameter <code>s2</code>, the mean is
+     * <code>s1 / (s1 + s2)</code>
+     *
+     * @return the mean
+     * @since 2.2
+     */
+    public double getNumericalMean() {
+        final double a = getAlpha();
+        return a / (a + getBeta());
+    }
+
+    /**
+     * Returns the variance.
+     *
+     * For first shape parameter <code>s1</code> and
+     * second shape parameter <code>s2</code>,
+     * the variance is
+     * <code>[ s1 * s2 ] / [ (s1 + s2)^2 * (s1 + s2 + 1) ]</code>
+     *
+     * @return the variance
+     * @since 2.2
+     */
+    public double getNumericalVariance() {
+        final double a = getAlpha();
+        final double b = getBeta();
+        final double alphabetasum = a + b;
+        return (a * b) / ((alphabetasum * alphabetasum) * (alphabetasum + 1));
+    }
+
+}