diff --git a/commons-statistics-distribution/src/main/java/org/apache/commons/statistics/distribution/DistributionException.java b/commons-statistics-distribution/src/main/java/org/apache/commons/statistics/distribution/DistributionException.java
index 447fee2..8aa7d82 100644
--- a/commons-statistics-distribution/src/main/java/org/apache/commons/statistics/distribution/DistributionException.java
+++ b/commons-statistics-distribution/src/main/java/org/apache/commons/statistics/distribution/DistributionException.java
@@ -28,10 +28,14 @@
     static final String TOO_SMALL = "%s < %s";
     /** Error message for "out of range" condition. */
     static final String OUT_OF_RANGE = "Number %s is out of range [%s, %s]";
+    /** Error message for "invalid range" condition. */
+    static final String INVALID_RANGE = "Lower bound %s is not below the upper bound %s";
     /** Error message for "invalid probability" condition. */
     static final String INVALID_PROBABILITY = "Not a probability: %s is out of range [0, 1]";
     /** Error message for "out of range" condition. */
     static final String NEGATIVE = "Number %s is negative";
+    /** Error message for "not strictly positive" condition. */
+    static final String NOT_STRICTLY_POSITIVE = "Number %s is not greater than 0";
     /** Error message for "mismatch" condition. */
     static final String MISMATCH = "Expected %s but was %s";
 
diff --git a/commons-statistics-distribution/src/main/java/org/apache/commons/statistics/distribution/TruncatedNormalDistribution.java b/commons-statistics-distribution/src/main/java/org/apache/commons/statistics/distribution/TruncatedNormalDistribution.java
new file mode 100644
index 0000000..935b63a
--- /dev/null
+++ b/commons-statistics-distribution/src/main/java/org/apache/commons/statistics/distribution/TruncatedNormalDistribution.java
@@ -0,0 +1,182 @@
+/*
+ * 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.statistics.distribution;
+
+/**
+ * Implementation of the truncated normal distribution.
+ *
+ * @see <a href="http://en.wikipedia.org/wiki/Truncated_normal_distribution">
+ * Truncated normal distribution (Wikipedia)</a>
+ */
+public class TruncatedNormalDistribution extends AbstractContinuousDistribution {
+    /** Mean of parent normal distribution. */
+    private final double parentMean;
+    /** Standard deviation of parent normal distribution. */
+    private final double parentSd;
+    /** Mean of this distribution. */
+    private final double mean;
+    /** Variance of this distribution. */
+    private final double variance;
+    /** Lower bound of this distribution. */
+    private final double lower;
+    /** Upper bound of this distribution. */
+    private final double upper;
+
+    /** A standard normal distribution used for calculations. */
+    private final NormalDistribution standardNormal;
+    /** Stored value of @{code standardNormal.cumulativeProbability((lower - mean) / sd)} for faster computations. */
+    private final double cdfAlpha;
+    /**
+     * Stored value of @{code standardNormal.cumulativeProbability((upper - mean) / sd) - cdfAlpha}
+     * for faster computations.
+     */
+    private final double cdfDelta;
+
+    /**
+     * Creates a truncated normal distribution.
+     * Note that the {@code mean} and {@code sd} is of the parent normal distribution,
+     * and not the true mean and standard deviation of the truncated normal distribution.
+     *
+     * @param mean mean for this distribution.
+     * @param sd standard deviation for this distribution.
+     * @param lower lower bound (inclusive) of the distribution, can be {@link Double#NEGATIVE_INFINITY}.
+     * @param upper upper bound (inclusive) of the distribution, can be {@link Double#POSITIVE_INFINITY}.
+     * @throws IllegalArgumentException if {@code sd <= 0} or if {@code upper <= lower}.
+     */
+    public TruncatedNormalDistribution(double mean, double sd, double lower, double upper) {
+        if (sd <= 0) {
+            throw new DistributionException(DistributionException.NOT_STRICTLY_POSITIVE, sd);
+        }
+        if (upper <= lower) {
+            throw new DistributionException(DistributionException.INVALID_RANGE, lower, upper);
+        }
+
+        this.lower = lower;
+        this.upper = upper;
+
+        parentMean = mean;
+        parentSd = sd;
+        standardNormal = new NormalDistribution(0, 1);
+
+        final double alpha = (lower - mean) / sd;
+        final double beta = (upper - mean) / sd;
+
+        final double cdfBeta = standardNormal.cumulativeProbability(beta);
+        cdfAlpha = standardNormal.cumulativeProbability(alpha);
+        cdfDelta = cdfBeta - cdfAlpha;
+
+        // Calculation of variance and mean.
+        final double pdfAlpha = standardNormal.density(alpha);
+        final double pdfBeta = standardNormal.density(beta);
+        final double pdfCdfDelta = (pdfAlpha - pdfBeta) / cdfDelta;
+        final double alphaBetaDelta = (alpha * pdfAlpha - beta * pdfBeta) / cdfDelta;
+
+        if (lower == Double.NEGATIVE_INFINITY) {
+            if (upper == Double.POSITIVE_INFINITY) {
+                // No truncation
+                this.mean = mean;
+                variance = sd * sd;
+            } else {
+                // One-sided lower tail truncation
+                final double betaRatio = pdfBeta / cdfBeta;
+                this.mean = mean - sd * betaRatio;
+                variance = sd * sd * (1 - beta * betaRatio - betaRatio * betaRatio);
+            }
+        } else {
+            if (upper == Double.POSITIVE_INFINITY) {
+                // One-sided upper tail truncation
+                final double alphaRatio = pdfAlpha / cdfDelta;
+                this.mean = mean + sd * alphaRatio;
+                variance = sd * sd * (1 + alpha * alphaRatio - alphaRatio * alphaRatio);
+            } else {
+                // Two-sided truncation
+                this.mean = mean + pdfCdfDelta * parentSd;
+                variance = sd * sd * (1 + alphaBetaDelta - pdfCdfDelta * pdfCdfDelta);
+            }
+        }
+    }
+
+    /** {@inheritDoc} */
+    @Override
+    public double density(double x) {
+        if (x < lower || x > upper) {
+            return 0;
+        }
+        return standardNormal.density((x - parentMean) / parentSd) / (parentSd * cdfDelta);
+    }
+
+    /** {@inheritDoc} */
+    @Override
+    public double cumulativeProbability(double x) {
+        if (x <= lower) {
+            return 0;
+        } else if (x >= upper) {
+            return 1;
+        }
+        return (standardNormal.cumulativeProbability((x - parentMean) / parentSd) - cdfAlpha) / cdfDelta;
+    }
+
+    /** {@inheritDoc} */
+    @Override
+    public double inverseCumulativeProbability(double p) {
+        if (p < 0 || p > 1) {
+            throw new DistributionException(DistributionException.INVALID_PROBABILITY, p);
+        }
+        return standardNormal.inverseCumulativeProbability(cdfAlpha + p * cdfDelta) * parentSd + parentMean;
+    }
+
+    /**
+     * {@inheritDoc}
+     *
+     * Represents the true mean of the truncated normal distribution rather
+     * than the parent normal distribution mean.
+     */
+    @Override
+    public double getMean() {
+        return mean;
+    }
+
+    /**
+     * {@inheritDoc}
+     *
+     * Represents the true variance of the truncated normal distribution rather
+     * than the parent normal distribution variance.
+     */
+    @Override
+    public double getVariance() {
+        return variance;
+    }
+
+    /** {@inheritDoc} */
+    @Override
+    public double getSupportLowerBound() {
+        return lower;
+    }
+
+    /** {@inheritDoc} */
+    @Override
+    public double getSupportUpperBound() {
+        return upper;
+    }
+
+    /** {@inheritDoc} */
+    @Override
+    public boolean isSupportConnected() {
+        return true;
+    }
+}
diff --git a/commons-statistics-distribution/src/test/java/org/apache/commons/statistics/distribution/TruncatedNormalDistributionTest.java b/commons-statistics-distribution/src/test/java/org/apache/commons/statistics/distribution/TruncatedNormalDistributionTest.java
new file mode 100644
index 0000000..ce49e46
--- /dev/null
+++ b/commons-statistics-distribution/src/test/java/org/apache/commons/statistics/distribution/TruncatedNormalDistributionTest.java
@@ -0,0 +1,232 @@
+/*
+ * 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.statistics.distribution;
+
+import org.junit.jupiter.api.Assertions;
+import org.junit.jupiter.api.BeforeEach;
+import org.junit.jupiter.api.Test;
+
+/**
+ * Test class for {@link TruncatedNormalDistribution}.
+ * All test values were computed using Python with SciPy v1.6.0.
+ */
+class TruncatedNormalDistributionTest extends ContinuousDistributionAbstractTest {
+    /** Distribution to test with. */
+    private TruncatedNormalDistribution distribution = new TruncatedNormalDistribution(1.9, 1.3, -1.1, 3.4);
+    /** Percentiles to test with. */
+    private double[] ppfValues = new double[]{0, 0.0001, 0.001, 0.01, 0.025, 0.05, 0.1, 0.25, 0.5, 0.75, 0.9, 0.95,
+                                              0.975, 0.99, 0.999, 0.9999, 1};
+    /** Expected cumulative values for percentiles. */
+    private double[] cdfValues = new double[]{-1.1, -1.09597275767544, -1.0609616183922, -0.79283350106842,
+                                              -0.505331829887808, -0.192170173599874, 0.21173317261645,
+                                              0.925791281910463, 1.71399518338879, 2.43413009451536, 2.94473113856785,
+                                              3.15310057075828, 3.27036798398733, 3.34641874981679, 3.39452729074341,
+                                              3.39945153287941, 3.4};
+    /** Expected density values for percentiles. */
+    private double[] pdfValues = new double[]{0.0247422752302618, 0.0249196707321102, 0.0265057408263321,
+                                              0.0415071096500185, 0.0640403254340905, 0.0971457789636,
+                                              0.152622492901864, 0.267853863255995, 0.35107475879338, 0.325977522502844,
+                                              0.25680502248913, 0.222886115806507, 0.203494915087054, 0.190997946666992,
+                                              0.183167918885238, 0.182370706542209, 0.182281965373914};
+    /** Expected distribution mean. */
+    private double mean = 1.63375792365723;
+    /** Expected distribution variance. */
+    private double variance = 1.03158703914439;
+
+    /** Overrides tolerance and sets up distribution. */
+    @BeforeEach
+    void setUp() {
+        setTolerance(1e-7);
+        super.setUp();
+    }
+
+    /** {@inheritDoc} */
+    @Override
+    public ContinuousDistribution makeDistribution() {
+        return distribution;
+    }
+
+    /** {@inheritDoc} */
+    @Override
+    public double[] makeCumulativeTestPoints() {
+        return cdfValues;
+    }
+
+    /** {@inheritDoc} */
+    @Override
+    public double[] makeCumulativeTestValues() {
+        return ppfValues;
+    }
+
+    /** {@inheritDoc} */
+    @Override
+    public double[] makeDensityTestValues() {
+        return pdfValues;
+    }
+
+    /**
+     * Configures new test values and runs relevant tests in this class and {@link ContinuousDistributionAbstractTest}.
+     *
+     * @param testDistribution distribution to test with.
+     * @param expectedPpfValues expected percentiles to test with.
+     * @param expectedCdfValues expected cumulative values for percentiles.
+     * @param expectedPdfValues expected density values for percentiles.
+     * @param expectedMean expected mean.
+     * @param expectedVariance expected variance.
+     */
+    private void testAdditionalDistribution(
+            TruncatedNormalDistribution testDistribution,
+            double[] expectedPpfValues,
+            double[] expectedCdfValues,
+            double[] expectedPdfValues,
+            double expectedMean,
+            double expectedVariance) {
+        this.distribution = testDistribution;
+        this.ppfValues = expectedPpfValues;
+        this.cdfValues = expectedCdfValues;
+        this.pdfValues = expectedPdfValues;
+        this.mean = expectedMean;
+        this.variance = expectedVariance;
+
+        setUp();
+
+        testMoments();
+
+        testConsistency();
+        testSampler();
+        testOutsideSupport();
+        testDensities();
+        testLogDensities();
+        testOutsideSupport();
+        testInverseCumulativeProbabilities();
+        testDensityIntegrals();
+        testCumulativeProbabilities();
+        testIsSupportConnected();
+        testPrecondition1();
+        testPrecondition2();
+        testPrecondition3();
+    }
+
+    /** Test a one-sided truncation with a lower tail. */
+    @Test
+    void testOneSidedLowerTail() {
+        testAdditionalDistribution(
+                new TruncatedNormalDistribution(12, 2.4, Double.NEGATIVE_INFINITY, 7.1),
+                new double[]{0, 0.00108276414971883, 0.00433032247708514, 0.0155754809421998, 0.0504271331622245,
+                             0.147106879016387, 0.387159643321778, 0.920668099879139, 1},
+                new double[]{Double.NEGATIVE_INFINITY, 2.20249292901062, 3.00511196424565, 3.80773099948069,
+                             4.61035003471573, 5.41296906995077, 6.21558810518581, 7.01820714042084, 7.1},
+                new double[]{0, 0.00194181137319567, 0.00719165311538403, 0.0238165586714952, 0.0705273999981105,
+                             0.186752027463317, 0.442182309739316, 0.936194292830215, 1.00423817618302},
+                6.21558810518581,
+                0.644197315721623);
+    }
+
+    /** Test a one-sided truncation with an upper tail. */
+    @Test
+    void testOneSidedUpperTail() {
+        testAdditionalDistribution(
+                new TruncatedNormalDistribution(-9.6, 17, -15, Double.POSITIVE_INFINITY),
+                new double[]{0, 0.164539974698729, 0.564800349576255, 0.836443289017693, 0.957226746540945,
+                             0.992394081771774, 0.999093968560336, 0.999928403010774, 1},
+                new double[]{-15, -10.5314720401464, 0.723583450712814, 11.978638941572, 23.2336944324312,
+                             34.4887499232902, 45.7438054141485, 56.9988609050074, Double.POSITIVE_INFINITY},
+                new double[]{0.035721742043989, 0.0375137766818179, 0.0312438063187719, 0.0167870518464031,
+                             0.00581865051705663, 0.00130109036611494, 0.000187685186297558, 1.74658560715427e-05, 0},
+                0.723583450712812,
+                126.676274102319);
+    }
+
+    /** Test no truncation. */
+    @Test
+    void testNoTruncation() {
+        testAdditionalDistribution(
+                new TruncatedNormalDistribution(3, 1.1, Double.NEGATIVE_INFINITY, Double.POSITIVE_INFINITY),
+                new double[]{0, 2.86651571879193e-07, 3.16712418331199e-05, 0.00134989803163009, 0.0227501319481792,
+                             0.158655253931457, 0.5, 0.841344746068543, 0.977249868051821, 0.99865010196837,
+                             0.999968328758167, 0.999999713348428, 1},
+                new double[]{Double.NEGATIVE_INFINITY, -2.5, -1.4, -0.300000000000001, 0.799999999999999, 1.9, 3,
+                             4.1, 5.2, 6.3, 7.4, 8.49999999996719, Double.POSITIVE_INFINITY},
+                new double[]{0, 1.35156319521299e-06, 0.000121663841604441, 0.00402895310176182, 0.0490826968301709,
+                             0.219973385926494, 0.362674800364939, 0.219973385926494, 0.0490826968301709,
+                             0.00402895310176184, 0.000121663841604441, 1.35156319541454e-06, 0},
+                3,
+                1.21);
+    }
+
+    /** Test a truncation range that is completely below the mean. */
+    @Test
+    void testLowerTailOnly() {
+        testAdditionalDistribution(
+                new TruncatedNormalDistribution(0, 1, Double.NEGATIVE_INFINITY, -5),
+                new double[]{0, 0.00196196451357246, 0.00597491488512203, 0.0176247203066899, 0.0503595643590926,
+                             0.139390045971621, 0.373761183487683, 0.970943041215359, 1},
+                new double[]{Double.NEGATIVE_INFINITY, -6.09061174025149, -5.90979018562636, -5.72896863100123,
+                             -5.54814707637611, -5.36732552175098, -5.18650396712585, -5.00568241250073, -5},
+                new double[]{0, 0.0122562922051934, 0.0362705138555484, 0.103883943928261, 0.287967362544455,
+                             0.772570689127439, 2.00601097433085, 5.04113700754108, 5.18650396712585},
+                -5.18650396712585,
+                0.0326964346170475);
+    }
+
+    /** Test a truncation range that is completely above the mean. */
+    @Test
+    void testUpperTailOnly() {
+        testAdditionalDistribution(
+                new TruncatedNormalDistribution(0, 1, 5, Double.POSITIVE_INFINITY),
+                new double[]{0, 0.0290569590230917, 0.626238816822898, 0.860609954247549, 0.949640435971243,
+                             0.982375279755296, 0.994025085266282, 0.998038035551444, 1},
+                new double[]{5, 5.00568241254803, 5.18650396728068, 5.36732552203467, 5.54814707752324,
+                             5.72896863159791, 5.90979018980065, 6.09061174555624, Double.POSITIVE_INFINITY},
+                new double[]{5.18650396712585, 5.04113700634745, 2.00601097272001, 0.772570687951075,
+                             0.287967360711704, 0.103883943573147, 0.0362705129607846, 0.0122562918092027, 0},
+                5.18650396712585,
+                0.0326964346170475);
+    }
+
+    /** Test a narrow truncation range. */
+    @Test
+    void testNarrowTruncatedRange() {
+        testAdditionalDistribution(
+                new TruncatedNormalDistribution(7.1, 9.9, 7.0999999, 7.1000001),
+                new double[]{0, 0.5, 1},
+                new double[]{7.0999999, 7.1, 7.1000001},
+                new double[]{5000000.00238838, 5000000.00238838, 5000000.00238838},
+                7.1,
+                1.13584123966337e-07);
+    }
+
+    /** Test mean and variance moments. */
+    @Test
+    void testMoments() {
+        Assertions.assertEquals(mean, distribution.getMean(), getTolerance());
+        Assertions.assertEquals(variance, distribution.getVariance(), getTolerance());
+    }
+
+    /** Test constructor precondition when the standard deviation is less than or equal to 0. */
+    @Test
+    void testConstructorSdPrecondition() {
+        Assertions.assertThrows(DistributionException.class, () -> new TruncatedNormalDistribution(1, 0, -1, 1));
+    }
+
+    /** Test constructor precondition when the lower bound is greater than the upper bound. */
+    @Test
+    void testConstructorBoundsPrecondition() {
+        Assertions.assertThrows(DistributionException.class, () -> new TruncatedNormalDistribution(1, 1, 1, -1));
+    }
+}