/*
* 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.stat.descriptive.rank;
import java.util.Arrays;
import org.apache.commons.math3.distribution.NormalDistribution;
import org.apache.commons.math3.exception.MathIllegalArgumentException;
import org.apache.commons.math3.exception.NotANumberException;
import org.apache.commons.math3.exception.NullArgumentException;
import org.apache.commons.math3.exception.OutOfRangeException;
import org.apache.commons.math3.random.JDKRandomGenerator;
import org.apache.commons.math3.random.RandomGenerator;
import org.apache.commons.math3.random.Well1024a;
import org.apache.commons.math3.stat.descriptive.UnivariateStatistic;
import org.apache.commons.math3.stat.descriptive.UnivariateStatisticAbstractTest;
import org.apache.commons.math3.stat.descriptive.rank.Percentile.EstimationType;
import org.apache.commons.math3.stat.ranking.NaNStrategy;
import org.apache.commons.math3.util.CentralPivotingStrategy;
import org.apache.commons.math3.util.KthSelector;
import org.apache.commons.math3.util.MathArrays;
import org.apache.commons.math3.util.MedianOf3PivotingStrategy;
import org.apache.commons.math3.util.PivotingStrategyInterface;
import org.apache.commons.math3.util.RandomPivotingStrategy;
import org.junit.Assert;
import org.junit.Before;
import org.junit.Test;
/**
* Test cases for the {@link UnivariateStatistic} class.
*/
public class PercentileTest extends UnivariateStatisticAbstractTest{
protected Percentile stat;
private double quantile;
/**
* {@link org.apache.commons.math3.stat.descriptive.rank.Percentile.EstimationType type}
* of estimation to be used while calling {@link #getUnivariateStatistic()}
*/
private Percentile.EstimationType type;
/**
* {@link NaNStrategy}
* of estimation to be used while calling {@link #getUnivariateStatistic()}
*/
private NaNStrategy nanStrategy;
/**
* kth selector
*/
private KthSelector kthSelector;
/**
* A default percentile to be used for {@link #getUnivariateStatistic()}
*/
protected final double DEFAULT_PERCENTILE = 95d;
/**
* Before method to ensure defaults retained
*/
@Before
public void before() {
quantile = 95.0;
type = Percentile.EstimationType.LEGACY;
nanStrategy = NaNStrategy.REMOVED;
kthSelector = new KthSelector(new MedianOf3PivotingStrategy());
}
private void reset(final double p, final Percentile.EstimationType type) {
this.quantile = p;
this.type = type;
nanStrategy = (type == Percentile.EstimationType.LEGACY) ? NaNStrategy.FIXED : NaNStrategy.REMOVED;
}
/**
* {@inheritDoc}
*/
@Override
public Percentile getUnivariateStatistic() {
return new Percentile(quantile).
withEstimationType(type).
withNaNStrategy(nanStrategy).
withKthSelector(kthSelector);
}
/**
* {@inheritDoc}
*/
@Override
public double expectedValue() {
return this.percentile95;
}
@Test
public void testHighPercentile(){
final double[] d = new double[]{1, 2, 3};
final Percentile p = new Percentile(75);
Assert.assertEquals(3.0, p.evaluate(d), 1.0e-5);
}
@Test
public void testLowPercentile() {
final double[] d = new double[] {0, 1};
final Percentile p = new Percentile(25);
Assert.assertEquals(0d, p.evaluate(d), Double.MIN_VALUE);
}
@Test
public void testPercentile() {
final double[] d = new double[] {1, 3, 2, 4};
final Percentile p = new Percentile(30);
Assert.assertEquals(1.5, p.evaluate(d), 1.0e-5);
p.setQuantile(25);
Assert.assertEquals(1.25, p.evaluate(d), 1.0e-5);
p.setQuantile(75);
Assert.assertEquals(3.75, p.evaluate(d), 1.0e-5);
p.setQuantile(50);
Assert.assertEquals(2.5, p.evaluate(d), 1.0e-5);
// invalid percentiles
try {
p.evaluate(d, 0, d.length, -1.0);
Assert.fail();
} catch (final MathIllegalArgumentException ex) {
// success
}
try {
p.evaluate(d, 0, d.length, 101.0);
Assert.fail();
} catch (final MathIllegalArgumentException ex) {
// success
}
}
@Test
public void testNISTExample() {
final double[] d = new double[] {95.1772, 95.1567, 95.1937, 95.1959,
95.1442, 95.0610, 95.1591, 95.1195, 95.1772, 95.0925, 95.1990, 95.1682
};
final Percentile p = new Percentile(90);
Assert.assertEquals(95.1981, p.evaluate(d), 1.0e-4);
Assert.assertEquals(95.1990, p.evaluate(d,0,d.length, 100d), 0);
}
@Test
public void test5() {
final Percentile percentile = new Percentile(5);
Assert.assertEquals(this.percentile5, percentile.evaluate(testArray), getTolerance());
}
@Test
public void testNullEmpty() {
final Percentile percentile = new Percentile(50);
final double[] nullArray = null;
final double[] emptyArray = new double[] {};
try {
percentile.evaluate(nullArray);
Assert.fail("Expecting MathIllegalArgumentException for null array");
} catch (final MathIllegalArgumentException ex) {
// expected
}
Assert.assertTrue(Double.isNaN(percentile.evaluate(emptyArray)));
}
@Test
public void testSingleton() {
final Percentile percentile = new Percentile(50);
final double[] singletonArray = new double[] {1d};
Assert.assertEquals(1d, percentile.evaluate(singletonArray), 0);
Assert.assertEquals(1d, percentile.evaluate(singletonArray, 0, 1), 0);
Assert.assertEquals(1d, percentile.evaluate(singletonArray, 0, 1, 5), 0);
Assert.assertEquals(1d, percentile.evaluate(singletonArray, 0, 1, 100), 0);
Assert.assertTrue(Double.isNaN(percentile.evaluate(singletonArray, 0, 0)));
}
@Test
public void testSpecialValues() {
final Percentile percentile = new Percentile(50);
double[] specialValues = new double[] {0d, 1d, 2d, 3d, 4d, Double.NaN};
Assert.assertEquals(/*2.5d*/2d, percentile.evaluate(specialValues), 0);
specialValues = new double[] {Double.NEGATIVE_INFINITY, 1d, 2d, 3d,
Double.NaN, Double.POSITIVE_INFINITY};
Assert.assertEquals(/*2.5d*/2d, percentile.evaluate(specialValues), 0);
specialValues = new double[] {1d, 1d, Double.POSITIVE_INFINITY,
Double.POSITIVE_INFINITY};
Assert.assertTrue(Double.isInfinite(percentile.evaluate(specialValues)));
specialValues = new double[] {1d, 1d, Double.NaN,
Double.NaN};
Assert.assertTrue(!Double.isNaN(percentile.evaluate(specialValues)));
Assert.assertTrue(1d==percentile.evaluate(specialValues));
specialValues = new double[] {1d, 1d, Double.NEGATIVE_INFINITY,
Double.NEGATIVE_INFINITY};
// Interpolation results in NEGATIVE_INFINITY + POSITIVE_INFINITY
Assert.assertTrue(Double.isNaN(percentile.evaluate(specialValues)));
}
@Test
public void testSetQuantile() {
final Percentile percentile = new Percentile(10);
percentile.setQuantile(100); // OK
Assert.assertEquals(100, percentile.getQuantile(), 0);
try {
percentile.setQuantile(0);
Assert.fail("Expecting MathIllegalArgumentException");
} catch (final MathIllegalArgumentException ex) {
// expected
}
try {
new Percentile(0);
Assert.fail("Expecting MathIllegalArgumentException");
} catch (final MathIllegalArgumentException ex) {
// expected
}
}
//Below tests are basically to run for all estimation types.
/**
* While {@link #testHighPercentile()} checks only for the existing
* implementation; this method verifies for all the types including Percentile.Type.CM Percentile.Type.
*/
@Test
public void testAllTechniquesHighPercentile() {
final double[] d = new double[] { 1, 2, 3 };
testAssertMappedValues(d, new Object[][] { { Percentile.EstimationType.LEGACY, 3d }, { Percentile.EstimationType.R_1, 3d },
{ Percentile.EstimationType.R_2, 3d }, { Percentile.EstimationType.R_3, 2d }, { Percentile.EstimationType.R_4, 2.25 }, { Percentile.EstimationType.R_5, 2.75 },
{ Percentile.EstimationType.R_6, 3d }, { Percentile.EstimationType.R_7, 2.5 },{ Percentile.EstimationType.R_8, 2.83333 }, {Percentile.EstimationType.R_9,2.81250} },
75d, 1.0e-5);
}
@Test
public void testAllTechniquesLowPercentile() {
final double[] d = new double[] { 0, 1 };
testAssertMappedValues(d, new Object[][] { { Percentile.EstimationType.LEGACY, 0d }, { Percentile.EstimationType.R_1, 0d },
{ Percentile.EstimationType.R_2, 0d }, { Percentile.EstimationType.R_3, 0d }, { Percentile.EstimationType.R_4, 0d }, {Percentile.EstimationType.R_5, 0d}, {Percentile.EstimationType.R_6, 0d},
{ Percentile.EstimationType.R_7, 0.25 }, { Percentile.EstimationType.R_8, 0d }, {Percentile.EstimationType.R_9, 0d} },
25d, Double.MIN_VALUE);
}
public void checkAllTechniquesPercentile() {
final double[] d = new double[] { 1, 3, 2, 4 };
testAssertMappedValues(d, new Object[][] { { Percentile.EstimationType.LEGACY, 1.5d },
{ Percentile.EstimationType.R_1, 2d }, { Percentile.EstimationType.R_2, 2d }, { Percentile.EstimationType.R_3, 1d }, { Percentile.EstimationType.R_4, 1.2 }, {Percentile.EstimationType.R_5, 1.7},
{ Percentile.EstimationType.R_6, 1.5 },{ Percentile.EstimationType.R_7, 1.9 }, { Percentile.EstimationType.R_8, 1.63333 },{ Percentile.EstimationType.R_9, 1.65 } },
30d, 1.0e-05);
testAssertMappedValues(d, new Object[][] { { Percentile.EstimationType.LEGACY, 1.25d },
{ Percentile.EstimationType.R_1, 1d }, { Percentile.EstimationType.R_2, 1.5d }, { Percentile.EstimationType.R_3, 1d }, { Percentile.EstimationType.R_4, 1d }, {Percentile.EstimationType.R_5, 1.5},
{ Percentile.EstimationType.R_6, 1.25 },{ Percentile.EstimationType.R_7, 1.75 },
{ Percentile.EstimationType.R_8, 1.41667 }, { Percentile.EstimationType.R_9, 1.43750 } }, 25d, 1.0e-05);
testAssertMappedValues(d, new Object[][] { { Percentile.EstimationType.LEGACY, 3.75d },
{ Percentile.EstimationType.R_1, 3d }, { Percentile.EstimationType.R_2, 3.5d }, { Percentile.EstimationType.R_3, 3d }, { Percentile.EstimationType.R_4, 3d },
{ Percentile.EstimationType.R_5, 3.5d },{ Percentile.EstimationType.R_6, 3.75d }, { Percentile.EstimationType.R_7, 3.25 },
{ Percentile.EstimationType.R_8, 3.58333 },{ Percentile.EstimationType.R_9, 3.56250} }, 75d, 1.0e-05);
testAssertMappedValues(d, new Object[][] { { Percentile.EstimationType.LEGACY, 2.5d },
{ Percentile.EstimationType.R_1, 2d }, { Percentile.EstimationType.R_2, 2.5d }, { Percentile.EstimationType.R_3, 2d }, { Percentile.EstimationType.R_4, 2d },
{ Percentile.EstimationType.R_5, 2.5 },{ Percentile.EstimationType.R_6, 2.5 },{ Percentile.EstimationType.R_7, 2.5 },
{ Percentile.EstimationType.R_8, 2.5 },{ Percentile.EstimationType.R_9, 2.5 } }, 50d, 1.0e-05);
// invalid percentiles
for (final Percentile.EstimationType e : Percentile.EstimationType.values()) {
try {
reset(-1.0, e);
getUnivariateStatistic().evaluate(d, 0, d.length);
Assert.fail();
} catch (final MathIllegalArgumentException ex) {
// success
}
}
for (final Percentile.EstimationType e : Percentile.EstimationType.values()) {
try {
reset(101.0, e);
getUnivariateStatistic().evaluate(d, 0, d.length);
Assert.fail();
} catch (final MathIllegalArgumentException ex) {
// success
}
}
}
@Test
public void testAllTechniquesPercentileUsingMedianOf3Pivoting() {
kthSelector = new KthSelector(new MedianOf3PivotingStrategy());
Assert.assertEquals(MedianOf3PivotingStrategy.class,
getUnivariateStatistic().getPivotingStrategy().getClass());
checkAllTechniquesPercentile();
}
@Test
public void testAllTechniquesPercentileUsingCentralPivoting() {
kthSelector = new KthSelector(new CentralPivotingStrategy());
Assert.assertEquals(CentralPivotingStrategy.class,
getUnivariateStatistic().getPivotingStrategy().getClass());
checkAllTechniquesPercentile();
}
@Test
public void testAllTechniquesPercentileUsingRandomPivoting() {
kthSelector = new KthSelector(new RandomPivotingStrategy(new Well1024a(0x268a7fb4194240f6l)));
Assert.assertEquals(RandomPivotingStrategy.class,
getUnivariateStatistic().getPivotingStrategy().getClass());
checkAllTechniquesPercentile();
}
@Test
public void testAllTechniquesNISTExample() {
final double[] d =
new double[] { 95.1772, 95.1567, 95.1937, 95.1959, 95.1442,
95.0610, 95.1591, 95.1195, 95.1772, 95.0925, 95.1990,
95.1682 };
testAssertMappedValues(d, new Object[][] { { Percentile.EstimationType.LEGACY, 95.1981 },
{ Percentile.EstimationType.R_1, 95.19590 }, { Percentile.EstimationType.R_2, 95.19590 }, { Percentile.EstimationType.R_3, 95.19590 },
{ Percentile.EstimationType.R_4, 95.19546 }, { Percentile.EstimationType.R_5, 95.19683 }, { Percentile.EstimationType.R_6, 95.19807 },
{ Percentile.EstimationType.R_7, 95.19568 }, { Percentile.EstimationType.R_8, 95.19724 }, { Percentile.EstimationType.R_9, 95.19714 } }, 90d,
1.0e-04);
for (final Percentile.EstimationType e : Percentile.EstimationType.values()) {
reset(100.0, e);
Assert.assertEquals(95.1990, getUnivariateStatistic().evaluate(d), 1.0e-4);
}
}
@Test
public void testAllTechniques5() {
reset(5, Percentile.EstimationType.LEGACY);
final UnivariateStatistic percentile = getUnivariateStatistic();
Assert.assertEquals(this.percentile5, percentile.evaluate(testArray),
getTolerance());
testAssertMappedValues(testArray,
new Object[][] { { Percentile.EstimationType.LEGACY, percentile5 }, { Percentile.EstimationType.R_1, 8.8000 },
{ Percentile.EstimationType.R_2, 8.8000 }, { Percentile.EstimationType.R_3, 8.2000 }, { Percentile.EstimationType.R_4, 8.2600 },
{ Percentile.EstimationType.R_5, 8.5600 }, { Percentile.EstimationType.R_6, 8.2900 },
{ Percentile.EstimationType.R_7, 8.8100 }, { Percentile.EstimationType.R_8, 8.4700 },
{ Percentile.EstimationType.R_9, 8.4925 }}, 5d, getTolerance());
}
@Test
public void testAllTechniquesNullEmpty() {
final double[] nullArray = null;
final double[] emptyArray = new double[] {};
for (final Percentile.EstimationType e : Percentile.EstimationType.values()) {
reset (50, e);
final UnivariateStatistic percentile = getUnivariateStatistic();
try {
percentile.evaluate(nullArray);
Assert.fail("Expecting MathIllegalArgumentException "
+ "for null array");
} catch (final MathIllegalArgumentException ex) {
// expected
}
Assert.assertTrue(Double.isNaN(percentile.evaluate(emptyArray)));
}
}
@Test
public void testAllTechniquesSingleton() {
final double[] singletonArray = new double[] { 1d };
for (final Percentile.EstimationType e : Percentile.EstimationType.values()) {
reset (50, e);
final UnivariateStatistic percentile = getUnivariateStatistic();
Assert.assertEquals(1d, percentile.evaluate(singletonArray), 0);
Assert.assertEquals(1d, percentile.evaluate(singletonArray, 0, 1),
0);
Assert.assertEquals(1d,
new Percentile().evaluate(singletonArray, 0, 1, 5), 0);
Assert.assertEquals(1d,
new Percentile().evaluate(singletonArray, 0, 1, 100), 0);
Assert.assertTrue(Double.isNaN(percentile.evaluate(singletonArray,
0, 0)));
}
}
@Test
public void testAllTechniquesEmpty() {
final double[] singletonArray = new double[] { };
for (final Percentile.EstimationType e : Percentile.EstimationType.values()) {
reset (50, e);
final UnivariateStatistic percentile = getUnivariateStatistic();
Assert.assertEquals(Double.NaN, percentile.evaluate(singletonArray),
0);
Assert.assertEquals(Double.NaN, percentile.evaluate(singletonArray,
0, 0),
0);
Assert.assertEquals(Double.NaN,
new Percentile().evaluate(singletonArray, 0, 0, 5), 0);
Assert.assertEquals(Double.NaN,
new Percentile().evaluate(singletonArray, 0, 0, 100), 0);
Assert.assertTrue(Double.isNaN(percentile.evaluate(singletonArray,
0, 0)));
}
}
@Test
public void testReplaceNanInRange() {
final double[] specialValues =
new double[] { 0d, 1d, 2d, 3d, 4d, Double.NaN, Double.NaN, 5d,
7d, Double.NaN, 8d};
Assert.assertEquals(/*Double.NaN*/3.5,new Percentile(50d).evaluate(specialValues),0d);
reset (50, Percentile.EstimationType.R_1);
Assert.assertEquals(3d, getUnivariateStatistic().evaluate(specialValues),0d);
reset (50, Percentile.EstimationType.R_2);
Assert.assertEquals(3.5d, getUnivariateStatistic().evaluate(specialValues),0d);
Assert.assertEquals(Double.POSITIVE_INFINITY,new Percentile(70)
.withNaNStrategy(NaNStrategy.MAXIMAL)
.evaluate(specialValues),0d);
}
@Test
public void testRemoveNan() {
final double[] specialValues =
new double[] { 0d, 1d, 2d, 3d, 4d, Double.NaN };
final double[] expectedValues =
new double[] { 0d, 1d, 2d, 3d, 4d };
reset (50, Percentile.EstimationType.R_1);
Assert.assertEquals(2.0, getUnivariateStatistic().evaluate(specialValues), 0d);
Assert.assertEquals(2.0, getUnivariateStatistic().evaluate(expectedValues),0d);
Assert.assertTrue(Double.isNaN(getUnivariateStatistic().evaluate(specialValues,5,1)));
Assert.assertEquals(4d, getUnivariateStatistic().evaluate(specialValues, 4, 2), 0d);
Assert.assertEquals(3d, getUnivariateStatistic().evaluate(specialValues,3,3),0d);
reset(50, Percentile.EstimationType.R_2);
Assert.assertEquals(3.5d, getUnivariateStatistic().evaluate(specialValues,3,3),0d);
}
@Test
public void testPercentileCopy() {
reset(50d, Percentile.EstimationType.LEGACY);
final Percentile original = getUnivariateStatistic();
final Percentile copy = new Percentile(original);
Assert.assertEquals(original.getNaNStrategy(),copy.getNaNStrategy());
Assert.assertEquals(original.getQuantile(), copy.getQuantile(),0d);
Assert.assertEquals(original.getEstimationType(),copy.getEstimationType());
Assert.assertEquals(NaNStrategy.FIXED, original.getNaNStrategy());
}
@Test
public void testAllTechniquesSpecialValues() {
reset(50d, Percentile.EstimationType.LEGACY);
final UnivariateStatistic percentile = getUnivariateStatistic();
double[] specialValues =
new double[] { 0d, 1d, 2d, 3d, 4d, Double.NaN };
Assert.assertEquals(2.5d, percentile.evaluate(specialValues), 0);
testAssertMappedValues(specialValues, new Object[][] {
{ Percentile.EstimationType.LEGACY, 2.5d }, { Percentile.EstimationType.R_1, 2.0 }, { Percentile.EstimationType.R_2, 2.0 }, { Percentile.EstimationType.R_3, 1.0 },
{ Percentile.EstimationType.R_4, 1.5 }, { Percentile.EstimationType.R_5, 2.0 }, { Percentile.EstimationType.R_6, 2.0 },
{ Percentile.EstimationType.R_7, 2.0 }, { Percentile.EstimationType.R_8, 2.0 }, { Percentile.EstimationType.R_9, 2.0 }}, 50d, 0d);
specialValues =
new double[] { Double.NEGATIVE_INFINITY, 1d, 2d, 3d,
Double.NaN, Double.POSITIVE_INFINITY };
Assert.assertEquals(2.5d, percentile.evaluate(specialValues), 0);
testAssertMappedValues(specialValues, new Object[][] {
{ Percentile.EstimationType.LEGACY, 2.5d }, { Percentile.EstimationType.R_1, 2.0 }, { Percentile.EstimationType.R_2, 2.0 }, { Percentile.EstimationType.R_3, 1.0 },
{ Percentile.EstimationType.R_4, 1.5 }, { Percentile.EstimationType.R_5, 2.0 }, { Percentile.EstimationType.R_7, 2.0 }, { Percentile.EstimationType.R_7, 2.0 },
{ Percentile.EstimationType.R_8, 2.0 }, { Percentile.EstimationType.R_9, 2.0 } }, 50d, 0d);
specialValues =
new double[] { 1d, 1d, Double.POSITIVE_INFINITY,
Double.POSITIVE_INFINITY };
Assert.assertTrue(Double.isInfinite(percentile.evaluate(specialValues)));
testAssertMappedValues(specialValues, new Object[][] {
// This is one test not matching with R results.
{ Percentile.EstimationType.LEGACY, Double.POSITIVE_INFINITY },
{ Percentile.EstimationType.R_1,/* 1.0 */Double.NaN },
{ Percentile.EstimationType.R_2, /* Double.POSITIVE_INFINITY */Double.NaN },
{ Percentile.EstimationType.R_3, /* 1.0 */Double.NaN }, { Percentile.EstimationType.R_4, /* 1.0 */Double.NaN },
{ Percentile.EstimationType.R_5, Double.POSITIVE_INFINITY },
{ Percentile.EstimationType.R_6, Double.POSITIVE_INFINITY },
{ Percentile.EstimationType.R_7, Double.POSITIVE_INFINITY },
{ Percentile.EstimationType.R_8, Double.POSITIVE_INFINITY },
{ Percentile.EstimationType.R_9, Double.POSITIVE_INFINITY }, }, 50d, 0d);
specialValues = new double[] { 1d, 1d, Double.NaN, Double.NaN };
Assert.assertTrue(Double.isNaN(percentile.evaluate(specialValues)));
testAssertMappedValues(specialValues, new Object[][] {
{ Percentile.EstimationType.LEGACY, Double.NaN }, { Percentile.EstimationType.R_1, 1.0 }, { Percentile.EstimationType.R_2, 1.0 }, { Percentile.EstimationType.R_3, 1.0 },
{ Percentile.EstimationType.R_4, 1.0 }, { Percentile.EstimationType.R_5, 1.0 },{ Percentile.EstimationType.R_6, 1.0 },{ Percentile.EstimationType.R_7, 1.0 },
{ Percentile.EstimationType.R_8, 1.0 }, { Percentile.EstimationType.R_9, 1.0 },}, 50d, 0d);
specialValues =
new double[] { 1d, 1d, Double.NEGATIVE_INFINITY,
Double.NEGATIVE_INFINITY };
testAssertMappedValues(specialValues, new Object[][] {
{ Percentile.EstimationType.LEGACY, Double.NaN }, { Percentile.EstimationType.R_1, Double.NaN },
{ Percentile.EstimationType.R_2, Double.NaN }, { Percentile.EstimationType.R_3, Double.NaN }, { Percentile.EstimationType.R_4, Double.NaN },
{ Percentile.EstimationType.R_5, Double.NaN }, { Percentile.EstimationType.R_6, Double.NaN },
{ Percentile.EstimationType.R_7, Double.NaN }, { Percentile.EstimationType.R_8, Double.NaN }, { Percentile.EstimationType.R_9, Double.NaN }
}, 50d, 0d);
}
@Test
public void testAllTechniquesSetQuantile() {
for (final Percentile.EstimationType e : Percentile.EstimationType.values()) {
reset(10, e);
final Percentile percentile = getUnivariateStatistic();
percentile.setQuantile(100); // OK
Assert.assertEquals(100, percentile.getQuantile(), 0);
try {
percentile.setQuantile(0);
Assert.fail("Expecting MathIllegalArgumentException");
} catch (final MathIllegalArgumentException ex) {
// expected
}
try {
new Percentile(0);
Assert.fail("Expecting MathIllegalArgumentException");
} catch (final MathIllegalArgumentException ex) {
// expected
}
}
}
@Test
public void testAllTechniquesEvaluateArraySegmentWeighted() {
for (final Percentile.EstimationType e : Percentile.EstimationType.values()) {
reset(quantile, e);
testEvaluateArraySegmentWeighted();
}
}
@Test
public void testAllTechniquesEvaluateArraySegment() {
for (final Percentile.EstimationType e : Percentile.EstimationType.values()) {
reset(quantile, e);
testEvaluateArraySegment();
}
}
@Test
public void testAllTechniquesWeightedConsistency() {
for (final Percentile.EstimationType e : Percentile.EstimationType.values()) {
reset(quantile, e);
testWeightedConsistency();
}
}
@Test
public void testAllTechniquesEvaluation() {
testAssertMappedValues(testArray, new Object[][] { { Percentile.EstimationType.LEGACY, 20.820 },
{ Percentile.EstimationType.R_1, 19.800 }, { Percentile.EstimationType.R_2, 19.800 }, { Percentile.EstimationType.R_3, 19.800 },
{ Percentile.EstimationType.R_4, 19.310 }, { Percentile.EstimationType.R_5, 20.280 }, { Percentile.EstimationType.R_6, 20.820 },
{ Percentile.EstimationType.R_7, 19.555 }, { Percentile.EstimationType.R_8, 20.460 },{ Percentile.EstimationType.R_9, 20.415} },
DEFAULT_PERCENTILE, tolerance);
}
@Test
public void testPercentileWithTechnique() {
reset (50, Percentile.EstimationType.LEGACY);;
final Percentile p = getUnivariateStatistic();
Assert.assertTrue(Percentile.EstimationType.LEGACY.equals(p.getEstimationType()));
Assert.assertFalse(Percentile.EstimationType.R_1.equals(p.getEstimationType()));
}
static final int TINY = 10, SMALL = 50, NOMINAL = 100, MEDIUM = 500,
STANDARD = 1000, BIG = 10000, VERY_BIG = 50000, LARGE = 1000000,
VERY_LARGE = 10000000;
static final int[] sampleSizes= {TINY , SMALL , NOMINAL , MEDIUM ,
STANDARD, BIG };
@Test
public void testStoredVsDirect() {
final RandomGenerator rand= new JDKRandomGenerator();
rand.setSeed(Long.MAX_VALUE);
for (final int sampleSize:sampleSizes) {
final double[] data = new NormalDistribution(rand,4000, 50)
.sample(sampleSize);
for (final double p:new double[] {50d,95d}) {
for (final Percentile.EstimationType e : Percentile.EstimationType.values()) {
reset(p, e);
final Percentile pStoredData = getUnivariateStatistic();
pStoredData.setData(data);
final double storedDataResult=pStoredData.evaluate();
pStoredData.setData(null);
final Percentile pDirect = getUnivariateStatistic();
Assert.assertEquals("Sample="+sampleSize+",P="+p+" e="+e,
storedDataResult,
pDirect.evaluate(data),0d);
}
}
}
}
@Test
public void testPercentileWithDataRef() {
reset(50.0, Percentile.EstimationType.R_7);
final Percentile p = getUnivariateStatistic();
p.setData(testArray);
Assert.assertTrue(Percentile.EstimationType.R_7.equals(p.getEstimationType()));
Assert.assertFalse(Percentile.EstimationType.R_1.equals(p.getEstimationType()));
Assert.assertEquals(12d, p.evaluate(), 0d);
Assert.assertEquals(12.16d, p.evaluate(60d), 0d);
}
@SuppressWarnings("deprecation")
@Test
public void testMedianOf3() {
reset(50.0, Percentile.EstimationType.R_7);
final Percentile p = getUnivariateStatistic();
Assert.assertEquals(0, p.medianOf3(testArray, 0, testArray.length));
Assert.assertEquals(10, p.medianOf3(testWeightsArray, 0, testWeightsArray.length));
}
@Test(expected=NullArgumentException.class)
public void testNullEstimation() {
type = null;
getUnivariateStatistic();
}
@Test
public void testAllEstimationTechniquesOnlyLimits() {
final int N=testArray.length;
final double[] input=MathArrays.copyOf(testArray);
Arrays.sort(input);
final double min = input[0];
final double max=input[input.length-1];
//limits may be ducked by 0.01 to induce the condition of p<pMin
final Object[][] map =
new Object[][] { { Percentile.EstimationType.LEGACY, 0d, 1d }, { Percentile.EstimationType.R_1, 0d, 1d },
{ Percentile.EstimationType.R_2, 0d,1d }, { Percentile.EstimationType.R_3, 0.5/N,1d },
{ Percentile.EstimationType.R_4, 1d/N-0.001,1d },
{ Percentile.EstimationType.R_5, 0.5/N-0.001,(N-0.5)/N}, { Percentile.EstimationType.R_6, 0.99d/(N+1),
1.01d*N/(N+1)},
{ Percentile.EstimationType.R_7, 0d,1d}, { Percentile.EstimationType.R_8, 1.99d/3/(N+1d/3),
(N-1d/3)/(N+1d/3)},
{ Percentile.EstimationType.R_9, 4.99d/8/(N+0.25), (N-3d/8)/(N+0.25)} };
for(final Object[] arr:map) {
final Percentile.EstimationType t= (Percentile.EstimationType) arr[0];
double pMin=(Double)arr[1];
final double pMax=(Double)arr[2];
Assert.assertEquals("Type:"+t,0d, t.index(pMin, N),0d);
Assert.assertEquals("Type:"+t,N, t.index(pMax, N),0.5d);
pMin=pMin==0d?pMin+0.01:pMin;
testAssertMappedValues(testArray, new Object[][] { { t, min }}, pMin, 0.01);
testAssertMappedValues(testArray, new Object[][] { { t, max }}, pMax * 100, tolerance);
}
}
@Test
public void testAllEstimationTechniquesOnly() {
Assert.assertEquals("Legacy Apache Commons Math",Percentile.EstimationType.LEGACY.getName());
final Object[][] map =
new Object[][] { { Percentile.EstimationType.LEGACY, 20.82 }, { Percentile.EstimationType.R_1, 19.8 },
{ Percentile.EstimationType.R_2, 19.8 }, { Percentile.EstimationType.R_3, 19.8 }, { Percentile.EstimationType.R_4, 19.310 },
{ Percentile.EstimationType.R_5, 20.280}, { Percentile.EstimationType.R_6, 20.820},
{ Percentile.EstimationType.R_7, 19.555 }, { Percentile.EstimationType.R_8, 20.460 },{Percentile.EstimationType.R_9,20.415} };
try {
Percentile.EstimationType.LEGACY.evaluate(testArray, -1d, new KthSelector(new MedianOf3PivotingStrategy()));
} catch (final OutOfRangeException oore) {
}
try {
Percentile.EstimationType.LEGACY.evaluate(testArray, 101d, new KthSelector());
} catch (final OutOfRangeException oore) {
}
try {
Percentile.EstimationType.LEGACY.evaluate(testArray, 50d, new KthSelector());
} catch(final OutOfRangeException oore) {
}
for (final Object[] o : map) {
final Percentile.EstimationType e = (Percentile.EstimationType) o[0];
final double expected = (Double) o[1];
final double result = e.evaluate(testArray, DEFAULT_PERCENTILE, new KthSelector());
Assert.assertEquals("expected[" + e + "] = " + expected +
" but was = " + result, expected, result, tolerance);
}
}
@Test
public void testAllEstimationTechniquesOnlyForAllPivotingStrategies() {
Assert.assertEquals("Legacy Apache Commons Math",Percentile.EstimationType.LEGACY.getName());
for (final PivotingStrategyInterface strategy : new PivotingStrategyInterface[] {
new MedianOf3PivotingStrategy(),
new CentralPivotingStrategy(),
new RandomPivotingStrategy(new Well1024a(0xf097c734e4740053l))
}) {
kthSelector = new KthSelector(strategy);
testAllEstimationTechniquesOnly();
}
}
@Test
public void testAllEstimationTechniquesOnlyForExtremeIndexes() {
final double MAX=100;
final Object[][] map =
new Object[][] { { Percentile.EstimationType.LEGACY, 0d, MAX}, { Percentile.EstimationType.R_1, 0d,MAX+0.5 },
{ Percentile.EstimationType.R_2, 0d,MAX}, { Percentile.EstimationType.R_3, 0d,MAX }, { Percentile.EstimationType.R_4, 0d,MAX },
{ Percentile.EstimationType.R_5, 0d,MAX }, { Percentile.EstimationType.R_6, 0d,MAX },
{ Percentile.EstimationType.R_7, 0d,MAX }, { Percentile.EstimationType.R_8, 0d,MAX }, { Percentile.EstimationType.R_9, 0d,MAX } };
for (final Object[] o : map) {
final Percentile.EstimationType e = (Percentile.EstimationType) o[0];
Assert.assertEquals(((Double)o[1]).doubleValue(),
e.index(0d, (int)MAX),0d);
Assert.assertEquals("Enum:"+e,((Double)o[2]).doubleValue(),
e.index(1.0, (int)MAX),0d);
}
}
@Test
public void testAllEstimationTechniquesOnlyForNullsAndOOR() {
final Object[][] map =
new Object[][] { { Percentile.EstimationType.LEGACY, 20.82 }, { Percentile.EstimationType.R_1, 19.8 },
{ Percentile.EstimationType.R_2, 19.8 }, { Percentile.EstimationType.R_3, 19.8 }, { Percentile.EstimationType.R_4, 19.310 },
{ Percentile.EstimationType.R_5, 20.280}, { Percentile.EstimationType.R_6, 20.820},
{ Percentile.EstimationType.R_7, 19.555 }, { Percentile.EstimationType.R_8, 20.460 },{ Percentile.EstimationType.R_9, 20.415 } };
for (final Object[] o : map) {
final Percentile.EstimationType e = (Percentile.EstimationType) o[0];
try {
e.evaluate(null, DEFAULT_PERCENTILE, new KthSelector());
Assert.fail("Expecting NullArgumentException");
} catch (final NullArgumentException nae) {
// expected
}
try {
e.evaluate(testArray, 120, new KthSelector());
Assert.fail("Expecting OutOfRangeException");
} catch (final OutOfRangeException oore) {
// expected
}
}
}
/**
* Simple test assertion utility method assuming {@link NaNStrategy default}
* nan handling strategy specific to each {@link EstimationType type}
*
* @param data input data
* @param map of expected result against a {@link EstimationType}
* @param p the quantile to compute for
* @param tolerance the tolerance of difference allowed
*/
protected void testAssertMappedValues(final double[] data, final Object[][] map,
final Double p, final Double tolerance) {
for (final Object[] o : map) {
final Percentile.EstimationType e = (Percentile.EstimationType) o[0];
final double expected = (Double) o[1];
try {
reset(p, e);
final double result = getUnivariateStatistic().evaluate(data);
Assert.assertEquals("expected[" + e + "] = " + expected +
" but was = " + result, expected, result, tolerance);
} catch(final Exception ex) {
Assert.fail("Exception occured for estimation type "+e+":"+
ex.getLocalizedMessage());
}
}
}
// Some NaNStrategy specific testing
@Test
public void testNanStrategySpecific() {
double[] specialValues = new double[] { 0d, 1d, 2d, 3d, 4d, Double.NaN };
Assert.assertTrue(Double.isNaN(new Percentile(50d).withEstimationType(Percentile.EstimationType.LEGACY).withNaNStrategy(NaNStrategy.MAXIMAL).evaluate(specialValues, 3, 3)));
Assert.assertEquals(2d,new Percentile(50d).withEstimationType(Percentile.EstimationType.R_1).withNaNStrategy(NaNStrategy.REMOVED).evaluate(specialValues),0d);
Assert.assertEquals(Double.NaN,new Percentile(50d).withEstimationType(Percentile.EstimationType.R_5).withNaNStrategy(NaNStrategy.REMOVED).evaluate(new double[] {Double.NaN,Double.NaN,Double.NaN}),0d);
Assert.assertEquals(50d,new Percentile(50d).withEstimationType(Percentile.EstimationType.R_7).withNaNStrategy(NaNStrategy.MINIMAL).evaluate(new double[] {50d,50d,50d},1,2),0d);
specialValues = new double[] { 0d, 1d, 2d, 3d, 4d, Double.NaN, Double.NaN };
Assert.assertEquals(3.5,new Percentile().evaluate(specialValues, 3, 4),0d);
Assert.assertEquals(4d,new Percentile().evaluate(specialValues, 4, 3),0d);
Assert.assertTrue(Double.isNaN(new Percentile().evaluate(specialValues, 5, 2)));
specialValues = new double[] { 0d, 1d, 2d, 3d, 4d, Double.NaN, Double.NaN, 5d, 6d };
Assert.assertEquals(4.5,new Percentile().evaluate(specialValues, 3, 6),0d);
Assert.assertEquals(5d,new Percentile().evaluate(specialValues, 4, 5),0d);
Assert.assertTrue(Double.isNaN(new Percentile().evaluate(specialValues, 5, 2)));
Assert.assertTrue(Double.isNaN(new Percentile().evaluate(specialValues, 5, 1)));
Assert.assertEquals(5.5,new Percentile().evaluate(specialValues, 5, 4),0d);
}
// Some NaNStrategy specific testing
@Test(expected=NotANumberException.class)
public void testNanStrategyFailed() {
double[] specialValues =
new double[] { 0d, 1d, 2d, 3d, 4d, Double.NaN };
new Percentile(50d).
withEstimationType(Percentile.EstimationType.R_9).
withNaNStrategy(NaNStrategy.FAILED).
evaluate(specialValues);
}
@Test
public void testAllTechniquesSpecialValuesWithNaNStrategy() {
double[] specialValues =
new double[] { 0d, 1d, 2d, 3d, 4d, Double.NaN };
try {
new Percentile(50d).withEstimationType(Percentile.EstimationType.LEGACY).withNaNStrategy(null);
Assert.fail("Expecting NullArgumentArgumentException "
+ "for null Nan Strategy");
} catch (NullArgumentException ex) {
// expected
}
//This is as per each type's default NaNStrategy
testAssertMappedValues(specialValues, new Object[][] {
{ Percentile.EstimationType.LEGACY, 2.5d }, { Percentile.EstimationType.R_1, 2.0 }, { Percentile.EstimationType.R_2, 2.0 }, { Percentile.EstimationType.R_3, 1.0 },
{ Percentile.EstimationType.R_4, 1.5 }, { Percentile.EstimationType.R_5, 2.0 }, { Percentile.EstimationType.R_6, 2.0 },
{ Percentile.EstimationType.R_7, 2.0 }, { Percentile.EstimationType.R_8, 2.0 }, { Percentile.EstimationType.R_9, 2.0 }}, 50d, 0d);
//This is as per MAXIMAL and hence the values tend a +0.5 upward
testAssertMappedValues(specialValues, new Object[][] {
{ Percentile.EstimationType.LEGACY, 2.5d }, { Percentile.EstimationType.R_1, 2.0 }, { Percentile.EstimationType.R_2, 2.5 }, { Percentile.EstimationType.R_3, 2.0 },
{ Percentile.EstimationType.R_4, 2.0 }, { Percentile.EstimationType.R_5, 2.5 }, { Percentile.EstimationType.R_6, 2.5 },
{ Percentile.EstimationType.R_7, 2.5 }, { Percentile.EstimationType.R_8, 2.5 }, { Percentile.EstimationType.R_9, 2.5 }}, 50d, 0d,
NaNStrategy.MAXIMAL);
//This is as per MINIMAL and hence the values tend a -0.5 downward
testAssertMappedValues(specialValues, new Object[][] {
{ Percentile.EstimationType.LEGACY, 1.5d }, { Percentile.EstimationType.R_1, 1.0 }, { Percentile.EstimationType.R_2, 1.5 }, { Percentile.EstimationType.R_3, 1.0 },
{ Percentile.EstimationType.R_4, 1.0 }, { Percentile.EstimationType.R_5, 1.5 }, { Percentile.EstimationType.R_6, 1.5 },
{ Percentile.EstimationType.R_7, 1.5 }, { Percentile.EstimationType.R_8, 1.5 }, { Percentile.EstimationType.R_9, 1.5 }}, 50d, 0d,
NaNStrategy.MINIMAL);
//This is as per REMOVED as here Percentile.Type.CM changed its value from default
//while rest of Estimation types were anyways defaulted to REMOVED
testAssertMappedValues(specialValues, new Object[][] {
{ Percentile.EstimationType.LEGACY, 2.0 }, { Percentile.EstimationType.R_1, 2.0 }, { Percentile.EstimationType.R_2, 2.0 }, { Percentile.EstimationType.R_3, 1.0 },
{ Percentile.EstimationType.R_4, 1.5 }, { Percentile.EstimationType.R_5, 2.0 }, { Percentile.EstimationType.R_6, 2.0 },
{ Percentile.EstimationType.R_7, 2.0 }, { Percentile.EstimationType.R_8, 2.0 }, { Percentile.EstimationType.R_9, 2.0 }}, 50d, 0d,
NaNStrategy.REMOVED);
}
/**
* Simple test assertion utility method
*
* @param data input data
* @param map of expected result against a {@link EstimationType}
* @param p the quantile to compute for
* @param tolerance the tolerance of difference allowed
* @param nanStrategy NaNStrategy to be passed
*/
protected void testAssertMappedValues(double[] data, Object[][] map,
Double p, Double tolerance, NaNStrategy nanStrategy) {
for (Object[] o : map) {
Percentile.EstimationType e = (Percentile.EstimationType) o[0];
double expected = (Double) o[1];
try {
double result = new Percentile(p).withEstimationType(e).withNaNStrategy(nanStrategy).evaluate(data);
Assert.assertEquals("expected[" + e + "] = " + expected + " but was = " + result,
expected, result, tolerance);
} catch(Exception ex) {
Assert.fail("Exception occured for estimation type " + e + ":" + ex.getLocalizedMessage());
}
}
}
}