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Java example source code file (NormalDistributionTest.java)

This example Java source code file (NormalDistributionTest.java) is included in the alvinalexander.com "Java Source Code Warehouse" project. The intent of this project is to help you "Learn Java by Example" TM.

Learn more about this Java project at its project page.

Java - Java tags/keywords

normaldistribution, normaldistributiontest, override, realdistribution, realdistributionabstracttest, test

The NormalDistributionTest.java Java example source code

/*
 * 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.junit.Assert;
import org.junit.Test;

/**
 * Test cases for {@link NormalDistribution}. Extends
 * {@link RealDistributionAbstractTest}. See class javadoc of that class
 * for details.
 *
 */
public class NormalDistributionTest extends RealDistributionAbstractTest {

    //-------------- Implementations for abstract methods -----------------------

    /** Creates the default real distribution instance to use in tests. */
    @Override
    public NormalDistribution makeDistribution() {
        return new NormalDistribution(2.1, 1.4);
    }

    /** Creates the default cumulative probability distribution test input values */
    @Override
    public double[] makeCumulativeTestPoints() {
        // quantiles computed using R
        return new double[] {-2.226325228634938d, -1.156887023657177d, -0.643949578356075d, -0.2027950777320613d, 0.305827808237559d,
                6.42632522863494d, 5.35688702365718d, 4.843949578356074d, 4.40279507773206d, 3.89417219176244d};
    }

    /** Creates the default cumulative probability density test expected values */
    @Override
    public double[] makeCumulativeTestValues() {
        return new double[] {0.001d, 0.01d, 0.025d, 0.05d, 0.1d, 0.999d,
                0.990d, 0.975d, 0.950d, 0.900d};
    }

    /** Creates the default probability density test expected values */
    @Override
    public double[] makeDensityTestValues() {
        return new double[] {0.00240506434076, 0.0190372444310, 0.0417464784322, 0.0736683145538, 0.125355951380,
                0.00240506434076, 0.0190372444310, 0.0417464784322, 0.0736683145538, 0.125355951380};
    }

    // --------------------- Override tolerance  --------------
    protected double defaultTolerance = NormalDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY;
    @Override
    public void setUp() {
        super.setUp();
        setTolerance(defaultTolerance);
    }

    //---------------------------- Additional test cases -------------------------

    private void verifyQuantiles() {
        NormalDistribution distribution = (NormalDistribution) getDistribution();
        double mu = distribution.getMean();
        double sigma = distribution.getStandardDeviation();
        setCumulativeTestPoints( new double[] {mu - 2 *sigma, mu - sigma,
                mu, mu + sigma, mu + 2 * sigma,  mu + 3 * sigma, mu + 4 * sigma,
                mu + 5 * sigma});
        // Quantiles computed using R (same as Mathematica)
        setCumulativeTestValues(new double[] {0.02275013194817921, 0.158655253931457, 0.5, 0.841344746068543,
                0.977249868051821, 0.99865010196837, 0.999968328758167,  0.999999713348428});
        verifyCumulativeProbabilities();
    }

    @Test
    public void testQuantiles() {
        setDensityTestValues(new double[] {0.0385649760808, 0.172836231799, 0.284958771715, 0.172836231799, 0.0385649760808,
                0.00316560600853, 9.55930184035e-05, 1.06194251052e-06});
        verifyQuantiles();
        verifyDensities();

        setDistribution(new NormalDistribution(0, 1));
        setDensityTestValues(new double[] {0.0539909665132, 0.241970724519, 0.398942280401, 0.241970724519, 0.0539909665132,
                0.00443184841194, 0.000133830225765, 1.48671951473e-06});
        verifyQuantiles();
        verifyDensities();

        setDistribution(new NormalDistribution(0, 0.1));
        setDensityTestValues(new double[] {0.539909665132, 2.41970724519, 3.98942280401, 2.41970724519,
                0.539909665132, 0.0443184841194, 0.00133830225765, 1.48671951473e-05});
        verifyQuantiles();
        verifyDensities();
    }

    @Test
    public void testInverseCumulativeProbabilityExtremes() {
        setInverseCumulativeTestPoints(new double[] {0, 1});
        setInverseCumulativeTestValues(
                new double[] {Double.NEGATIVE_INFINITY, Double.POSITIVE_INFINITY});
        verifyInverseCumulativeProbabilities();
    }

    // MATH-1257
    @Test
    public void testCumulativeProbability() {
        final RealDistribution dist = new NormalDistribution(0, 1);
        double x = -10;
        double expected = 7.61985e-24;
        double v = dist.cumulativeProbability(x);
        Assert.assertEquals(1, v / expected, 1e-5);
    }

    @Test
    public void testGetMean() {
        NormalDistribution distribution = (NormalDistribution) getDistribution();
        Assert.assertEquals(2.1, distribution.getMean(), 0);
    }

    @Test
    public void testGetStandardDeviation() {
        NormalDistribution distribution = (NormalDistribution) getDistribution();
        Assert.assertEquals(1.4, distribution.getStandardDeviation(), 0);
    }

    @Test(expected=NotStrictlyPositiveException.class)
    public void testPreconditions() {
        new NormalDistribution(1, 0);
    }

    @Test
    public void testDensity() {
        double [] x = new double[]{-2, -1, 0, 1, 2};
        // R 2.5: print(dnorm(c(-2,-1,0,1,2)), digits=10)
        checkDensity(0, 1, x, new double[]{0.05399096651, 0.24197072452, 0.39894228040, 0.24197072452, 0.05399096651});
        // R 2.5: print(dnorm(c(-2,-1,0,1,2), mean=1.1), digits=10)
        checkDensity(1.1, 1, x, new double[]{0.003266819056,0.043983595980,0.217852177033,0.396952547477,0.266085249899});
    }

    private void checkDensity(double mean, double sd, double[] x, double[] expected) {
        NormalDistribution d = new NormalDistribution(mean, sd);
        for (int i = 0; i < x.length; i++) {
            Assert.assertEquals(expected[i], d.density(x[i]), 1e-9);
        }
    }

    /**
     * Check to make sure top-coding of extreme values works correctly.
     * Verifies fixes for JIRA MATH-167, MATH-414
     */
    @Test
    public void testExtremeValues() {
        NormalDistribution distribution = new NormalDistribution(0, 1);
        for (int i = 0; i < 100; i++) { // make sure no convergence exception
            double lowerTail = distribution.cumulativeProbability(-i);
            double upperTail = distribution.cumulativeProbability(i);
            if (i < 9) { // make sure not top-coded
                // For i = 10, due to bad tail precision in erf (MATH-364), 1 is returned
                // TODO: once MATH-364 is resolved, replace 9 with 30
                Assert.assertTrue(lowerTail > 0.0d);
                Assert.assertTrue(upperTail < 1.0d);
            }
            else { // make sure top coding not reversed
                Assert.assertTrue(lowerTail < 0.00001);
                Assert.assertTrue(upperTail > 0.99999);
            }
        }

        Assert.assertEquals(distribution.cumulativeProbability(Double.MAX_VALUE), 1, 0);
        Assert.assertEquals(distribution.cumulativeProbability(-Double.MAX_VALUE), 0, 0);
        Assert.assertEquals(distribution.cumulativeProbability(Double.POSITIVE_INFINITY), 1, 0);
        Assert.assertEquals(distribution.cumulativeProbability(Double.NEGATIVE_INFINITY), 0, 0);
    }

    @Test
    public void testMath280() {
        NormalDistribution normal = new NormalDistribution(0,1);
        double result = normal.inverseCumulativeProbability(0.9986501019683698);
        Assert.assertEquals(3.0, result, defaultTolerance);
        result = normal.inverseCumulativeProbability(0.841344746068543);
        Assert.assertEquals(1.0, result, defaultTolerance);
        result = normal.inverseCumulativeProbability(0.9999683287581673);
        Assert.assertEquals(4.0, result, defaultTolerance);
        result = normal.inverseCumulativeProbability(0.9772498680518209);
        Assert.assertEquals(2.0, result, defaultTolerance);
    }

    @Test
    public void testMoments() {
        final double tol = 1e-9;
        NormalDistribution dist;

        dist = new NormalDistribution(0, 1);
        Assert.assertEquals(dist.getNumericalMean(), 0, tol);
        Assert.assertEquals(dist.getNumericalVariance(), 1, tol);

        dist = new NormalDistribution(2.2, 1.4);
        Assert.assertEquals(dist.getNumericalMean(), 2.2, tol);
        Assert.assertEquals(dist.getNumericalVariance(), 1.4 * 1.4, tol);

        dist = new NormalDistribution(-2000.9, 10.4);
        Assert.assertEquals(dist.getNumericalMean(), -2000.9, tol);
        Assert.assertEquals(dist.getNumericalVariance(), 10.4 * 10.4, tol);
    }
}

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