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.math3.stat.interval;
018
019import org.apache.commons.math3.distribution.NormalDistribution;
020import org.apache.commons.math3.util.FastMath;
021
022/**
023 * Implements the Wilson score method for creating a binomial proportion confidence interval.
024 *
025 * @see <a
026 *      href="http://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval#Wilson_score_interval">
027 *      Wilson score interval (Wikipedia)</a>
028 * @since 3.3
029 */
030public class WilsonScoreInterval implements BinomialConfidenceInterval {
031
032    /** {@inheritDoc} */
033    public ConfidenceInterval createInterval(int numberOfTrials, int numberOfSuccesses, double confidenceLevel) {
034        IntervalUtils.checkParameters(numberOfTrials, numberOfSuccesses, confidenceLevel);
035        final double alpha = (1.0 - confidenceLevel) / 2;
036        final NormalDistribution normalDistribution = new NormalDistribution();
037        final double z = normalDistribution.inverseCumulativeProbability(1 - alpha);
038        final double zSquared = FastMath.pow(z, 2);
039        final double mean = (double) numberOfSuccesses / (double) numberOfTrials;
040
041        final double factor = 1.0 / (1 + (1.0 / numberOfTrials) * zSquared);
042        final double modifiedSuccessRatio = mean + (1.0 / (2 * numberOfTrials)) * zSquared;
043        final double difference = z *
044                                  FastMath.sqrt(1.0 / numberOfTrials * mean * (1 - mean) +
045                                                (1.0 / (4 * FastMath.pow(numberOfTrials, 2)) * zSquared));
046
047        final double lowerBound = factor * (modifiedSuccessRatio - difference);
048        final double upperBound = factor * (modifiedSuccessRatio + difference);
049        return new ConfidenceInterval(lowerBound, upperBound, confidenceLevel);
050    }
051
052}