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.legacy.stat.interval; 018 019import org.apache.commons.statistics.distribution.NormalDistribution; 020import org.apache.commons.math4.core.jdkmath.JdkMath; 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 = NormalDistribution.of(0, 1); 036 final double z = normalDistribution.inverseSurvivalProbability(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 * JdkMath.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}