/*
* 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.interval;
import org.apache.commons.math3.distribution.FDistribution;
/**
* Implements the Clopper-Pearson method for creating a binomial proportion confidence interval.
*
* @see <a
* href="http://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval#Clopper-Pearson_interval">
* Clopper-Pearson interval (Wikipedia)</a>
* @since 3.3
*/
public class ClopperPearsonInterval implements BinomialConfidenceInterval {
/** {@inheritDoc} */
public ConfidenceInterval createInterval(int numberOfTrials, int numberOfSuccesses,
double confidenceLevel) {
IntervalUtils.checkParameters(numberOfTrials, numberOfSuccesses, confidenceLevel);
double lowerBound = 0;
double upperBound = 0;
final double alpha = (1.0 - confidenceLevel) / 2.0;
final FDistribution distributionLowerBound = new FDistribution(2 * (numberOfTrials - numberOfSuccesses + 1),
2 * numberOfSuccesses);
final double fValueLowerBound = distributionLowerBound.inverseCumulativeProbability(1 - alpha);
if (numberOfSuccesses > 0) {
lowerBound = numberOfSuccesses /
(numberOfSuccesses + (numberOfTrials - numberOfSuccesses + 1) * fValueLowerBound);
}
final FDistribution distributionUpperBound = new FDistribution(2 * (numberOfSuccesses + 1),
2 * (numberOfTrials - numberOfSuccesses));
final double fValueUpperBound = distributionUpperBound.inverseCumulativeProbability(1 - alpha);
if (numberOfSuccesses > 0) {
upperBound = (numberOfSuccesses + 1) * fValueUpperBound /
(numberOfTrials - numberOfSuccesses + (numberOfSuccesses + 1) * fValueUpperBound);
}
return new ConfidenceInterval(lowerBound, upperBound, confidenceLevel);
}
}