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137
SimSystem/src/main/java/mathtools/distribution/ArcsineDistribution.java
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| /** | ||
| * Copyright 2024 Alexander Herzog | ||
| * | ||
| * Licensed 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 mathtools.distribution; | ||
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| import java.io.Serializable; | ||
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| import org.apache.commons.math3.distribution.AbstractRealDistribution; | ||
| import org.apache.commons.math3.exception.OutOfRangeException; | ||
| import org.apache.commons.math3.random.RandomGenerator; | ||
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| /** | ||
| * Klasse zur Abbildung der Arcus Sinus-Verteilung<br> | ||
| * Siehe auch: <a href="http://www.randomservices.org/random/special/Arcsine.html">http://www.randomservices.org/random/special/Arcsine.html</a> | ||
| * @author Alexander Herzog | ||
| */ | ||
| public class ArcsineDistribution extends AbstractRealDistribution implements Cloneable, Serializable, DistributionWithRandom { | ||
| /** | ||
| * Serialisierungs-ID der Klasse | ||
| * @see Serializable | ||
| */ | ||
| private static final long serialVersionUID=6569135516191696579L; | ||
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| /** | ||
| * Untere Grenze des Trägers | ||
| */ | ||
| public final double a; | ||
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| /** | ||
| * Obere Grenze des Trägers | ||
| */ | ||
| public final double b; | ||
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| /** | ||
| * Konstruktor | ||
| * @param a Untere Grenze des Trägers | ||
| * @param b Obere Grenze des Trägers | ||
| */ | ||
| public ArcsineDistribution(final double a, final double b) { | ||
| super(null); | ||
| this.a=a; | ||
| this.b=Math.max(a+0.0001,b); | ||
| } | ||
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| /** | ||
| * Copy-Konstruktor | ||
| * @param source Zu kopierende Ausgangsverteilung | ||
| */ | ||
| public ArcsineDistribution(final ArcsineDistribution source) { | ||
| this((source==null)?0:source.a,(source==null)?10:source.b); | ||
| } | ||
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| @Override | ||
| public double density(double x) { | ||
| if (x<=a || x>=b) return 0; | ||
| x=(x-a)/(b-a); | ||
| return 1.0/Math.PI/Math.sqrt(x*(1-x)); | ||
| } | ||
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| @Override | ||
| public double cumulativeProbability(double x) { | ||
| if (x<=a) return 0; | ||
| if (x>=b) return 1; | ||
| x=(x-a)/(b-a); | ||
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| return 2.0/Math.PI*Math.asin(Math.sqrt(x)); | ||
| } | ||
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| @Override | ||
| public ArcsineDistribution clone() { | ||
| return new ArcsineDistribution(a,b); | ||
| } | ||
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| @Override | ||
| public double getNumericalMean() { | ||
| return (a+b)/2.0; | ||
| } | ||
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| @Override | ||
| public double getNumericalVariance() { | ||
| return 1.0/8.0*(b-a)*(b-a); | ||
| } | ||
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| @Override | ||
| public double getSupportLowerBound() { | ||
| return a; | ||
| } | ||
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| @Override | ||
| public double getSupportUpperBound() { | ||
| return b; | ||
| } | ||
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| @Override | ||
| public boolean isSupportLowerBoundInclusive() { | ||
| return true; | ||
| } | ||
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| @Override | ||
| public boolean isSupportUpperBoundInclusive() { | ||
| return true; | ||
| } | ||
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| @Override | ||
| public boolean isSupportConnected() { | ||
| return true; | ||
| } | ||
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| @Override | ||
| public double inverseCumulativeProbability(final double p) throws OutOfRangeException { | ||
| if (p<0.0 || p>1.0) throw new OutOfRangeException(p,0,1); | ||
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| if (p==0.0) return getSupportLowerBound(); | ||
| if (p==1.0) return getSupportUpperBound(); | ||
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| /* p=2/pi*arcsin(sqrt(x)) <=> x=(sin(pi/2*p))^2 */ | ||
| final double z=Math.pow(Math.sin(Math.PI/2.0*p),2); | ||
| return z*(b-a)+a; | ||
| } | ||
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| @Override | ||
| public double random(final RandomGenerator generator) { | ||
| return inverseCumulativeProbability(generator.nextDouble()); | ||
| } | ||
| } |
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