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}