/*
* 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.LogNormalDistribution;
import org.apache.commons.math4.exception.NotStrictlyPositiveException;
import org.junit.Assert;
import org.junit.Test;
/**
* Test cases for {@link LogNormalDistribution}. Extends
* {@link RealDistributionAbstractTest}. See class javadoc of that class
* for details.
*
* @since 3.0
*/
public class LogNormalDistributionTest extends RealDistributionAbstractTest {
//-------------- Implementations for abstract methods -----------------------
/** Creates the default real distribution instance to use in tests. */
@Override
public LogNormalDistribution makeDistribution() {
return new LogNormalDistribution(2.1, 1.4);
}
/** Creates the default cumulative probability distribution test input values */
@Override
public double[] makeCumulativeTestPoints() {
// quantiles computed using R
return new double[] { -2.226325228634938, -1.156887023657177,
-0.643949578356075, -0.2027950777320613,
0.305827808237559, 6.42632522863494,
5.35688702365718, 4.843949578356074,
4.40279507773206, 3.89417219176244 };
}
/** Creates the default cumulative probability density test expected values */
@Override
public double[] makeCumulativeTestValues() {
return new double[] { 0, 0, 0, 0, 0.00948199951485, 0.432056525076,
0.381648158697, 0.354555726206, 0.329513316888,
0.298422824228 };
}
/** Creates the default probability density test expected values */
@Override
public double[] makeDensityTestValues() {
return new double[] { 0, 0, 0, 0, 0.0594218160072, 0.0436977691036,
0.0508364857798, 0.054873528325, 0.0587182664085,
0.0636229042785 };
}
/**
* Creates the default inverse cumulative probability distribution test
* input values.
*/
@Override
public double[] makeInverseCumulativeTestPoints() {
// Exclude the test points less than zero, as they have cumulative
// probability of zero, meaning the inverse returns zero, and not the
// points less than zero.
double[] points = makeCumulativeTestValues();
double[] points2 = new double[points.length - 4];
System.arraycopy(points, 4, points2, 0, points2.length - 4);
return points2;
//return Arrays.copyOfRange(points, 4, points.length - 4);
}
/**
* Creates the default inverse cumulative probability test expected
* values.
*/
@Override
public double[] makeInverseCumulativeTestValues() {
// Exclude the test points less than zero, as they have cumulative
// probability of zero, meaning the inverse returns zero, and not the
// points less than zero.
double[] points = makeCumulativeTestPoints();
double[] points2 = new double[points.length - 4];
System.arraycopy(points, 4, points2, 0, points2.length - 4);
return points2;
//return Arrays.copyOfRange(points, 1, points.length - 4);
}
// --------------------- Override tolerance --------------
@Override
public void setUp() {
super.setUp();
setTolerance(LogNormalDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY);
}
//---------------------------- Additional test cases -------------------------
private void verifyQuantiles() {
LogNormalDistribution distribution = (LogNormalDistribution)getDistribution();
double mu = distribution.getScale();
double sigma = distribution.getShape();
setCumulativeTestPoints( new double[] { mu - 2 *sigma, mu - sigma,
mu, mu + sigma, mu + 2 * sigma,
mu + 3 * sigma,mu + 4 * sigma,
mu + 5 * sigma });
verifyCumulativeProbabilities();
}
@Test
public void testQuantiles() {
setCumulativeTestValues(new double[] {0, 0.0396495152787,
0.16601209243, 0.272533253269,
0.357618409638, 0.426488363093,
0.483255136841, 0.530823013877});
setDensityTestValues(new double[] {0, 0.0873055825147, 0.0847676303432,
0.0677935186237, 0.0544105523058,
0.0444614628804, 0.0369750288945,
0.0312206409653});
verifyQuantiles();
verifyDensities();
setDistribution(new LogNormalDistribution(0, 1));
setCumulativeTestValues(new double[] {0, 0, 0, 0.5, 0.755891404214,
0.864031392359, 0.917171480998,
0.946239689548});
setDensityTestValues(new double[] {0, 0, 0, 0.398942280401,
0.156874019279, 0.07272825614,
0.0381534565119, 0.0218507148303});
verifyQuantiles();
verifyDensities();
setDistribution(new LogNormalDistribution(0, 0.1));
setCumulativeTestValues(new double[] {0, 0, 0, 1.28417563064e-117,
1.39679883412e-58,
1.09839325447e-33,
2.52587961726e-20,
2.0824223487e-12});
setDensityTestValues(new double[] {0, 0, 0, 2.96247992535e-114,
1.1283370232e-55, 4.43812313223e-31,
5.85346445002e-18,
2.9446618076e-10});
verifyQuantiles();
verifyDensities();
}
@Test
public void testInverseCumulativeProbabilityExtremes() {
setInverseCumulativeTestPoints(new double[] {0, 1});
setInverseCumulativeTestValues(
new double[] {0, Double.POSITIVE_INFINITY});
verifyInverseCumulativeProbabilities();
}
@Test
public void testGetScale() {
LogNormalDistribution distribution = (LogNormalDistribution)getDistribution();
Assert.assertEquals(2.1, distribution.getScale(), 0);
}
@Test
public void testGetShape() {
LogNormalDistribution distribution = (LogNormalDistribution)getDistribution();
Assert.assertEquals(1.4, distribution.getShape(), 0);
}
@Test(expected=NotStrictlyPositiveException.class)
public void testPreconditions() {
new LogNormalDistribution(1, 0);
}
@Test
public void testDensity() {
double [] x = new double[]{-2, -1, 0, 1, 2};
// R 2.13: print(dlnorm(c(-2,-1,0,1,2)), digits=10)
checkDensity(0, 1, x, new double[] { 0.0000000000, 0.0000000000,
0.0000000000, 0.3989422804,
0.1568740193 });
// R 2.13: print(dlnorm(c(-2,-1,0,1,2), mean=1.1), digits=10)
checkDensity(1.1, 1, x, new double[] { 0.0000000000, 0.0000000000,
0.0000000000, 0.2178521770,
0.1836267118});
}
private void checkDensity(double scale, double shape, double[] x,
double[] expected) {
LogNormalDistribution d = new LogNormalDistribution(scale, shape);
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() {
LogNormalDistribution d = new LogNormalDistribution(0, 1);
for (int i = 0; i < 1e5; i++) { // make sure no convergence exception
double upperTail = d.cumulativeProbability(i);
if (i <= 72) { // make sure not top-coded
Assert.assertTrue(upperTail < 1.0d);
}
else { // make sure top coding not reversed
Assert.assertTrue(upperTail > 0.99999);
}
}
Assert.assertEquals(d.cumulativeProbability(Double.MAX_VALUE), 1, 0);
Assert.assertEquals(d.cumulativeProbability(-Double.MAX_VALUE), 0, 0);
Assert.assertEquals(d.cumulativeProbability(Double.POSITIVE_INFINITY), 1, 0);
Assert.assertEquals(d.cumulativeProbability(Double.NEGATIVE_INFINITY), 0, 0);
}
@Test
public void testMeanVariance() {
final double tol = 1e-9;
LogNormalDistribution dist;
dist = new LogNormalDistribution(0, 1);
Assert.assertEquals(dist.getNumericalMean(), 1.6487212707001282, tol);
Assert.assertEquals(dist.getNumericalVariance(),
4.670774270471604, tol);
dist = new LogNormalDistribution(2.2, 1.4);
Assert.assertEquals(dist.getNumericalMean(), 24.046753552064498, tol);
Assert.assertEquals(dist.getNumericalVariance(),
3526.913651880464, tol);
dist = new LogNormalDistribution(-2000.9, 10.4);
Assert.assertEquals(dist.getNumericalMean(), 0.0, tol);
Assert.assertEquals(dist.getNumericalVariance(), 0.0, tol);
}
@Test
public void testTinyVariance() {
LogNormalDistribution dist = new LogNormalDistribution(0, 1e-9);
double t = dist.getNumericalVariance();
Assert.assertEquals(1e-18, t, 1e-20);
}
}