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/*
* Copyright 2013 Stefan Zobel
*
* 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 math.distribution;
/**
* The Χ2(k) distribution for x >= 0 with PDF:
*
* f(x; k) = (1 / (2k/2 * Γ(k/2))) * x(k/2) - 1 * e-x/2
* where Γ() is the Gamma function.
*
* Valid parameter ranges: k > 0; x > 0 (if
* k = 1, otherwise x >= 0).
*
* See
* Wikipedia
* Chi-square distribution.
*/
public class ChiSquare implements ContinuousDistribution {
private static final double BIG = 100.0;
private final double degreesOfFreedom;
private final Gamma gamma;
public ChiSquare(double degreesOfFreedom) {
if (degreesOfFreedom <= 0.0) {
throw new IllegalArgumentException("degreesOfFreedom <= 0.0 : " + degreesOfFreedom);
}
this.degreesOfFreedom = degreesOfFreedom;
this.gamma = new Gamma(this.degreesOfFreedom / 2.0, 2.0);
}
@Override
public double pdf(double x) {
if (x <= 0.0) {
return 0.0;
}
return gamma.pdf(x);
}
@Override
public double cdf(double x) {
if (x <= 0.0) {
return 0.0;
}
if (x >= BIG * degreesOfFreedom) {
return 1.0;
}
return gamma.cdf(x);
}
/**
* Inverse of the Chi-squared cumulative distribution function.
*
* @param probability
* a given probability
* @return the value X for which P(x<=X).
*/
public double inverseCdf(double probability) {
if (probability <= 0.0) {
return 0.0;
}
if (probability >= 1.0) {
return Double.MAX_VALUE;
}
return gamma.inverseCdf(probability);
}
@Override
public double mean() {
return degreesOfFreedom;
}
@Override
public double variance() {
return 2.0 * degreesOfFreedom;
}
/**
* @return the degreesOfFreedom
*/
public double getDegreesOfFreedom() {
return degreesOfFreedom;
}
}