/*
* 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.math4.distribution;
import org.apache.commons.math4.distribution.NormalDistribution;
import org.apache.commons.math4.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);
double tol = 1e-5;
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);
}
}