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SimSystem/src/main/java/mathtools/distribution/KumaraswamyDistribution.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; | ||
| import org.apache.commons.math3.special.Gamma; | ||
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| /** | ||
| * Klasse zur Abbildung der Kumaraswamy-Verteilung | ||
| * @author Alexander Herzog | ||
| */ | ||
| public class KumaraswamyDistribution extends AbstractRealDistribution implements Cloneable, Serializable, DistributionWithRandom { | ||
| /** | ||
| * Serialisierungs-ID der Klasse | ||
| * @see Serializable | ||
| */ | ||
| private static final long serialVersionUID=-5073494121705653463L; | ||
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| /** | ||
| * Parameter 1 | ||
| */ | ||
| public final double a; | ||
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| /** | ||
| * Parameter 2 | ||
| */ | ||
| public final double b; | ||
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| /** | ||
| * Untere Grenze des Trägers | ||
| */ | ||
| public final double c; | ||
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| /** | ||
| * Obere Grenze des Trägers | ||
| */ | ||
| public final double d; | ||
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| /** | ||
| * Vorab berechneter Erwartungswert | ||
| * @see #getNumericalMean() | ||
| */ | ||
| private final double mean; | ||
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| /** | ||
| * Vorab berechnete Varianz | ||
| * @see #getNumericalVariance() | ||
| */ | ||
| private final double variance; | ||
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| /** | ||
| * Konstruktor | ||
| * @param a Erster Parameter | ||
| * @param b Zweiter Parameter | ||
| * @param c Untere Grenze des Trägers | ||
| * @param d Obere Grenze des Trägers | ||
| */ | ||
| public KumaraswamyDistribution(final double a, final double b, final double c, final double d) { | ||
| super(null); | ||
| this.a=Math.max(0.0001,a); | ||
| this.b=Math.max(0.0001,b); | ||
| this.c=c; | ||
| this.d=Math.max(this.c+0.0001,d); | ||
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| final double m1=this.b*Gamma.gamma(1+1/this.a)*Gamma.gamma(this.b)/Gamma.gamma(1+1/this.a+this.b); | ||
| mean=m1*(this.d-this.c)+this.c; | ||
| final double m2=this.b*Gamma.gamma(1+2/this.a)*Gamma.gamma(this.b)/Gamma.gamma(1+2/this.a+this.b); | ||
| variance=(m2-m1*m1)*(this.d-this.c)*(this.d-this.c); | ||
| } | ||
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| /** | ||
| * Copy-Konstruktor | ||
| * @param source Zu kopierende Ausgangsverteilung | ||
| */ | ||
| public KumaraswamyDistribution(final KumaraswamyDistribution source) { | ||
| this((source==null)?0:source.a,(source==null)?10:source.b,(source==null)?0:source.c,(source==null)?10:source.d); | ||
| } | ||
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| @Override | ||
| public double density(double x) { | ||
| if (x<c || x>d) return 0; | ||
| x=(x-c)/(d-c); | ||
| return a*b*Math.pow(x,a-1)*Math.pow(1-Math.pow(x,a),b-1); | ||
| } | ||
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| @Override | ||
| public double cumulativeProbability(double x) { | ||
| if (x<=c) return 0; | ||
| if (x>=d) return 1; | ||
| x=(x-c)/(d-c); | ||
| return 1-Math.pow(1-Math.pow(x,a),b); | ||
| } | ||
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| @Override | ||
| public KumaraswamyDistribution clone() { | ||
| return new KumaraswamyDistribution(a,b,c,d); | ||
| } | ||
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| @Override | ||
| public double getNumericalMean() { | ||
| return mean; | ||
| } | ||
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| @Override | ||
| public double getNumericalVariance() { | ||
| return variance; | ||
| } | ||
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| @Override | ||
| public double getSupportLowerBound() { | ||
| return c; | ||
| } | ||
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| @Override | ||
| public double getSupportUpperBound() { | ||
| return d; | ||
| } | ||
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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=1-(1-x^a)^b | ||
| 1-x^a= | ||
| (1-(1-p)^(1/b))^(1/a)=x | ||
| */ | ||
| return Math.pow(1-Math.pow(1-p,1/b),1/a)*(d-c)+c; | ||
| } | ||
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| @Override | ||
| public double random(final RandomGenerator generator) { | ||
| return inverseCumulativeProbability(generator.nextDouble()); | ||
| } | ||
| } |
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