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diff --git a/src/main/java/org/apache/commons/math3/distribution/TDistribution.java b/src/main/java/org/apache/commons/math3/distribution/TDistribution.java
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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.util.LocalizedFormats;
+import org.apache.commons.math3.random.RandomGenerator;
+import org.apache.commons.math3.random.Well19937c;
+import org.apache.commons.math3.special.Beta;
+import org.apache.commons.math3.special.Gamma;
+import org.apache.commons.math3.util.FastMath;
+
+/**
+ * Implementation of Student's t-distribution.
+ *
+ * @see "<a href='http://en.wikipedia.org/wiki/Student&apos;s_t-distribution'>Student's
+ *     t-distribution (Wikipedia)</a>"
+ * @see "<a href='http://mathworld.wolfram.com/Studentst-Distribution.html'>Student's t-distribution
+ *     (MathWorld)</a>"
+ */
+public class TDistribution 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 = -5852615386664158222L;
+
+    /** The degrees of freedom. */
+    private final double degreesOfFreedom;
+
+    /** Inverse cumulative probability accuracy. */
+    private final double solverAbsoluteAccuracy;
+
+    /** Static computation factor based on degreesOfFreedom. */
+    private final double factor;
+
+    /**
+     * Create a t distribution using the given degrees of freedom.
+     *
+     * <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 degreesOfFreedom Degrees of freedom.
+     * @throws NotStrictlyPositiveException if {@code degreesOfFreedom <= 0}
+     */
+    public TDistribution(double degreesOfFreedom) throws NotStrictlyPositiveException {
+        this(degreesOfFreedom, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
+    }
+
+    /**
+     * Create a t distribution using the given degrees of freedom and the specified inverse
+     * cumulative probability absolute accuracy.
+     *
+     * <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 degreesOfFreedom Degrees of freedom.
+     * @param inverseCumAccuracy the maximum absolute error in inverse cumulative probability
+     *     estimates (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}).
+     * @throws NotStrictlyPositiveException if {@code degreesOfFreedom <= 0}
+     * @since 2.1
+     */
+    public TDistribution(double degreesOfFreedom, double inverseCumAccuracy)
+            throws NotStrictlyPositiveException {
+        this(new Well19937c(), degreesOfFreedom, inverseCumAccuracy);
+    }
+
+    /**
+     * Creates a t distribution.
+     *
+     * @param rng Random number generator.
+     * @param degreesOfFreedom Degrees of freedom.
+     * @throws NotStrictlyPositiveException if {@code degreesOfFreedom <= 0}
+     * @since 3.3
+     */
+    public TDistribution(RandomGenerator rng, double degreesOfFreedom)
+            throws NotStrictlyPositiveException {
+        this(rng, degreesOfFreedom, DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
+    }
+
+    /**
+     * Creates a t distribution.
+     *
+     * @param rng Random number generator.
+     * @param degreesOfFreedom Degrees of freedom.
+     * @param inverseCumAccuracy the maximum absolute error in inverse cumulative probability
+     *     estimates (defaults to {@link #DEFAULT_INVERSE_ABSOLUTE_ACCURACY}).
+     * @throws NotStrictlyPositiveException if {@code degreesOfFreedom <= 0}
+     * @since 3.1
+     */
+    public TDistribution(RandomGenerator rng, double degreesOfFreedom, double inverseCumAccuracy)
+            throws NotStrictlyPositiveException {
+        super(rng);
+
+        if (degreesOfFreedom <= 0) {
+            throw new NotStrictlyPositiveException(
+                    LocalizedFormats.DEGREES_OF_FREEDOM, degreesOfFreedom);
+        }
+        this.degreesOfFreedom = degreesOfFreedom;
+        solverAbsoluteAccuracy = inverseCumAccuracy;
+
+        final double n = degreesOfFreedom;
+        final double nPlus1Over2 = (n + 1) / 2;
+        factor =
+                Gamma.logGamma(nPlus1Over2)
+                        - 0.5 * (FastMath.log(FastMath.PI) + FastMath.log(n))
+                        - Gamma.logGamma(n / 2);
+    }
+
+    /**
+     * Access the degrees of freedom.
+     *
+     * @return the degrees of freedom.
+     */
+    public double getDegreesOfFreedom() {
+        return degreesOfFreedom;
+    }
+
+    /** {@inheritDoc} */
+    public double density(double x) {
+        return FastMath.exp(logDensity(x));
+    }
+
+    /** {@inheritDoc} */
+    @Override
+    public double logDensity(double x) {
+        final double n = degreesOfFreedom;
+        final double nPlus1Over2 = (n + 1) / 2;
+        return factor - nPlus1Over2 * FastMath.log(1 + x * x / n);
+    }
+
+    /** {@inheritDoc} */
+    public double cumulativeProbability(double x) {
+        double ret;
+        if (x == 0) {
+            ret = 0.5;
+        } else {
+            double t =
+                    Beta.regularizedBeta(
+                            degreesOfFreedom / (degreesOfFreedom + (x * x)),
+                            0.5 * degreesOfFreedom,
+                            0.5);
+            if (x < 0.0) {
+                ret = 0.5 * t;
+            } else {
+                ret = 1.0 - 0.5 * t;
+            }
+        }
+
+        return ret;
+    }
+
+    /** {@inheritDoc} */
+    @Override
+    protected double getSolverAbsoluteAccuracy() {
+        return solverAbsoluteAccuracy;
+    }
+
+    /**
+     * {@inheritDoc}
+     *
+     * <p>For degrees of freedom parameter {@code df}, the mean is
+     *
+     * <ul>
+     *   <li>if {@code df > 1} then {@code 0},
+     *   <li>else undefined ({@code Double.NaN}).
+     * </ul>
+     */
+    public double getNumericalMean() {
+        final double df = getDegreesOfFreedom();
+
+        if (df > 1) {
+            return 0;
+        }
+
+        return Double.NaN;
+    }
+
+    /**
+     * {@inheritDoc}
+     *
+     * <p>For degrees of freedom parameter {@code df}, the variance is
+     *
+     * <ul>
+     *   <li>if {@code df > 2} then {@code df / (df - 2)},
+     *   <li>if {@code 1 < df <= 2} then positive infinity ({@code Double.POSITIVE_INFINITY}),
+     *   <li>else undefined ({@code Double.NaN}).
+     * </ul>
+     */
+    public double getNumericalVariance() {
+        final double df = getDegreesOfFreedom();
+
+        if (df > 2) {
+            return df / (df - 2);
+        }
+
+        if (df > 1 && df <= 2) {
+            return Double.POSITIVE_INFINITY;
+        }
+
+        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 {@code 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 {@code 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;
+    }
+}