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 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 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 modifiedNumberOfTrials = numberOfTrials + zSquared; 040 final double modifiedSuccessesRatio = (1.0 / modifiedNumberOfTrials) * (numberOfSuccesses + 0.5 * zSquared); 041 final double difference = z * 042 FastMath.sqrt(1.0 / modifiedNumberOfTrials * modifiedSuccessesRatio * 043 (1 - modifiedSuccessesRatio)); 044 return new ConfidenceInterval(modifiedSuccessesRatio - difference, modifiedSuccessesRatio + difference, 045 confidenceLevel); 046 } 047 048}