001/*
002 * Licensed to the Apache Software Foundation (ASF) under one or more
003 * contributor license agreements.  See the NOTICE file distributed with
004 * this work for additional information regarding copyright ownership.
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 *
009 *      http://www.apache.org/licenses/LICENSE-2.0
010 *
011 * Unless required by applicable law or agreed to in writing, software
012 * distributed under the License is distributed on an "AS IS" BASIS,
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 <a href="http://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval#Wilson_score_interval">
024 * Wilson score method</a> for creating a binomial proportion confidence interval.
025 *
026 * @since 3.3
027 */
028public class WilsonScoreInterval implements BinomialConfidenceInterval {
029
030    /** {@inheritDoc} */
031    @Override
032    public ConfidenceInterval createInterval(int numberOfTrials, int numberOfSuccesses, double confidenceLevel) {
033        IntervalUtils.checkParameters(numberOfTrials, numberOfSuccesses, confidenceLevel);
034        final double alpha = (1 - confidenceLevel) / 2;
035        final NormalDistribution normalDistribution = new NormalDistribution(0, 1);
036        final double z = normalDistribution.inverseCumulativeProbability(1 - alpha);
037        final double zSquared = z * z;
038        final double oneOverNumTrials = 1d / numberOfTrials;
039        final double zSquaredOverNumTrials = zSquared * oneOverNumTrials;
040        final double mean = oneOverNumTrials * numberOfSuccesses;
041
042        final double factor = 1 / (1 + zSquaredOverNumTrials);
043        final double modifiedSuccessRatio = mean + zSquaredOverNumTrials / 2;
044        final double difference = z * FastMath.sqrt(oneOverNumTrials * mean * (1 - mean) +
045                                                    (oneOverNumTrials * zSquaredOverNumTrials / 4));
046
047        final double lowerBound = factor * (modifiedSuccessRatio - difference);
048        final double upperBound = factor * (modifiedSuccessRatio + difference);
049        return new ConfidenceInterval(lowerBound, upperBound, confidenceLevel);
050    }
051}