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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.OutOfRangeException;
+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.util.FastMath;
+
+/**
+ * Implementation of the Cauchy distribution.
+ *
+ * @see <a href="http://en.wikipedia.org/wiki/Cauchy_distribution">Cauchy distribution
+ *     (Wikipedia)</a>
+ * @see <a href="http://mathworld.wolfram.com/CauchyDistribution.html">Cauchy Distribution
+ *     (MathWorld)</a>
+ * @since 1.1 (changed to concrete class in 3.0)
+ */
+public class CauchyDistribution extends AbstractRealDistribution {
+    /**
+     * 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 = 8589540077390120676L;
+
+    /** The median of this distribution. */
+    private final double median;
+
+    /** The scale of this distribution. */
+    private final double scale;
+
+    /** Inverse cumulative probability accuracy */
+    private final double solverAbsoluteAccuracy;
+
+    /** Creates a Cauchy distribution with the median equal to zero and scale equal to one. */
+    public CauchyDistribution() {
+        this(0, 1);
+    }
+
+    /**
+     * Creates a Cauchy distribution using the given median and scale.
+     *
+     * <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 median Median for this distribution.
+     * @param scale Scale parameter for this distribution.
+     */
+    public CauchyDistribution(double median, double scale) {
+        this(median, scale, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
+    }
+
+    /**
+     * Creates a Cauchy distribution using the given median and scale.
+     *
+     * <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 median Median for this distribution.
+     * @param scale Scale parameter for this distribution.
+     * @param inverseCumAccuracy Maximum absolute error in inverse cumulative probability estimates
+     *     (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}).
+     * @throws NotStrictlyPositiveException if {@code scale <= 0}.
+     * @since 2.1
+     */
+    public CauchyDistribution(double median, double scale, double inverseCumAccuracy) {
+        this(new Well19937c(), median, scale, inverseCumAccuracy);
+    }
+
+    /**
+     * Creates a Cauchy distribution.
+     *
+     * @param rng Random number generator.
+     * @param median Median for this distribution.
+     * @param scale Scale parameter for this distribution.
+     * @throws NotStrictlyPositiveException if {@code scale <= 0}.
+     * @since 3.3
+     */
+    public CauchyDistribution(RandomGenerator rng, double median, double scale) {
+        this(rng, median, scale, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
+    }
+
+    /**
+     * Creates a Cauchy distribution.
+     *
+     * @param rng Random number generator.
+     * @param median Median for this distribution.
+     * @param scale Scale parameter for this distribution.
+     * @param inverseCumAccuracy Maximum absolute error in inverse cumulative probability estimates
+     *     (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}).
+     * @throws NotStrictlyPositiveException if {@code scale <= 0}.
+     * @since 3.1
+     */
+    public CauchyDistribution(
+            RandomGenerator rng, double median, double scale, double inverseCumAccuracy) {
+        super(rng);
+        if (scale <= 0) {
+            throw new NotStrictlyPositiveException(LocalizedFormats.SCALE, scale);
+        }
+        this.scale = scale;
+        this.median = median;
+        solverAbsoluteAccuracy = inverseCumAccuracy;
+    }
+
+    /** {@inheritDoc} */
+    public double cumulativeProbability(double x) {
+        return 0.5 + (FastMath.atan((x - median) / scale) / FastMath.PI);
+    }
+
+    /**
+     * Access the median.
+     *
+     * @return the median for this distribution.
+     */
+    public double getMedian() {
+        return median;
+    }
+
+    /**
+     * Access the scale parameter.
+     *
+     * @return the scale parameter for this distribution.
+     */
+    public double getScale() {
+        return scale;
+    }
+
+    /** {@inheritDoc} */
+    public double density(double x) {
+        final double dev = x - median;
+        return (1 / FastMath.PI) * (scale / (dev * dev + scale * scale));
+    }
+
+    /**
+     * {@inheritDoc}
+     *
+     * <p>Returns {@code Double.NEGATIVE_INFINITY} when {@code p == 0} and {@code
+     * Double.POSITIVE_INFINITY} when {@code p == 1}.
+     */
+    @Override
+    public double inverseCumulativeProbability(double p) throws OutOfRangeException {
+        double ret;
+        if (p < 0 || p > 1) {
+            throw new OutOfRangeException(p, 0, 1);
+        } else if (p == 0) {
+            ret = Double.NEGATIVE_INFINITY;
+        } else if (p == 1) {
+            ret = Double.POSITIVE_INFINITY;
+        } else {
+            ret = median + scale * FastMath.tan(FastMath.PI * (p - .5));
+        }
+        return ret;
+    }
+
+    /** {@inheritDoc} */
+    @Override
+    protected double getSolverAbsoluteAccuracy() {
+        return solverAbsoluteAccuracy;
+    }
+
+    /**
+     * {@inheritDoc}
+     *
+     * <p>The mean is always undefined no matter the parameters.
+     *
+     * @return mean (always Double.NaN)
+     */
+    public double getNumericalMean() {
+        return Double.NaN;
+    }
+
+    /**
+     * {@inheritDoc}
+     *
+     * <p>The variance is always undefined no matter the parameters.
+     *
+     * @return variance (always Double.NaN)
+     */
+    public double getNumericalVariance() {
+        return Double.NaN;
+    }
+
+    /**
+     * {@inheritDoc}
+     *
+     * <p>The lower bound of the support is always negative infinity no matter the parameters.
+     *
+     * @return lower bound of the support (always Double.NEGATIVE_INFINITY)
+     */
+    public double getSupportLowerBound() {
+        return Double.NEGATIVE_INFINITY;
+    }
+
+    /**
+     * {@inheritDoc}
+     *
+     * <p>The upper bound of the support is always positive infinity no matter the parameters.
+     *
+     * @return upper bound of the support (always Double.POSITIVE_INFINITY)
+     */
+    public double getSupportUpperBound() {
+        return Double.POSITIVE_INFINITY;
+    }
+
+    /** {@inheritDoc} */
+    public boolean isSupportLowerBoundInclusive() {
+        return false;
+    }
+
+    /** {@inheritDoc} */
+    public boolean isSupportUpperBoundInclusive() {
+        return false;
+    }
+
+    /**
+     * {@inheritDoc}
+     *
+     * <p>The support of this distribution is connected.
+     *
+     * @return {@code true}
+     */
+    public boolean isSupportConnected() {
+        return true;
+    }
+}