/*
* 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.NormalDistribution;
import org.apache.commons.math3.util.FastMath;
/**
* Implements the Agresti-Coull method for creating a binomial proportion confidence interval.
*
* @see <a
* href="http://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval#Agresti-Coull_Interval">
* Agresti-Coull interval (Wikipedia)</a>
* @since 3.3
*/
public class AgrestiCoullInterval implements BinomialConfidenceInterval {
/** {@inheritDoc} */
public ConfidenceInterval createInterval(int numberOfTrials, int numberOfSuccesses, double confidenceLevel) {
IntervalUtils.checkParameters(numberOfTrials, numberOfSuccesses, confidenceLevel);
final double alpha = (1.0 - confidenceLevel) / 2;
final NormalDistribution normalDistribution = new NormalDistribution();
final double z = normalDistribution.inverseCumulativeProbability(1 - alpha);
final double zSquared = FastMath.pow(z, 2);
final double modifiedNumberOfTrials = numberOfTrials + zSquared;
final double modifiedSuccessesRatio = (1.0 / modifiedNumberOfTrials) * (numberOfSuccesses + 0.5 * zSquared);
final double difference = z *
FastMath.sqrt(1.0 / modifiedNumberOfTrials * modifiedSuccessesRatio *
(1 - modifiedSuccessesRatio));
return new ConfidenceInterval(modifiedSuccessesRatio - difference, modifiedSuccessesRatio + difference,
confidenceLevel);
}
}