```001/*
002 * Licensed to the Apache Software Foundation (ASF) under one or more
003 * contributor license agreements.  See the NOTICE file distributed with
005 * The ASF licenses this file to You under the Apache License, Version 2.0
006 * (the "License"); you may not use this file except in compliance with
007 * the License.  You may obtain a copy of the License at
008 *
010 *
011 * Unless required by applicable law or agreed to in writing, software
013 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
014 * See the License for the specific language governing permissions and
015 * limitations under the License.
016 */
017package org.apache.commons.math4.stat.interval;
018
019import org.apache.commons.statistics.distribution.NormalDistribution;
020import org.apache.commons.math4.util.FastMath;
021
022/**
023 * Implements the Agresti-Coull method for creating a binomial proportion confidence interval.
024 *
025 * @see <a
026 *      href="http://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval#Agresti-Coull_Interval">
027 *      Agresti-Coull interval (Wikipedia)</a>
028 * @since 3.3
029 */
030public class AgrestiCoullInterval implements BinomialConfidenceInterval {
031
032    /** {@inheritDoc} */
033    @Override
034    public ConfidenceInterval createInterval(int numberOfTrials, int numberOfSuccesses, double confidenceLevel) {
035        IntervalUtils.checkParameters(numberOfTrials, numberOfSuccesses, confidenceLevel);
036        final double alpha = (1.0 - confidenceLevel) / 2;
037        final NormalDistribution normalDistribution = new NormalDistribution(0, 1);
038        final double z = normalDistribution.inverseCumulativeProbability(1 - alpha);
039        final double zSquared = FastMath.pow(z, 2);
040        final double modifiedNumberOfTrials = numberOfTrials + zSquared;
041        final double modifiedSuccessesRatio = (1.0 / modifiedNumberOfTrials) * (numberOfSuccesses + 0.5 * zSquared);
042        final double difference = z *
043                                  FastMath.sqrt(1.0 / modifiedNumberOfTrials * modifiedSuccessesRatio *
044                                                (1 - modifiedSuccessesRatio));
045        return new ConfidenceInterval(modifiedSuccessesRatio - difference, modifiedSuccessesRatio + difference,
046                                      confidenceLevel);
047    }
048
049}

```