| /* |
| * Licensed to the Apache Software Foundation (ASF) under one or more |
| * contributor license agreements. See the NOTICE file distributed with |
| * this work for additional information regarding copyright ownership. |
| * The ASF licenses this file to You under the Apache License, Version 2.0 |
| * (the "License"); you may not use this file except in compliance with |
| * the License. You may obtain a copy of the License at |
| * |
| * http://www.apache.org/licenses/LICENSE-2.0 |
| * |
| * Unless required by applicable law or agreed to in writing, software |
| * distributed under the License is distributed on an "AS IS" BASIS, |
| * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| * See the License for the specific language governing permissions and |
| * limitations under the License. |
| */ |
| package org.apache.commons.math4.legacy.stat.interval; |
| |
| import org.apache.commons.statistics.distribution.NormalDistribution; |
| import org.apache.commons.math4.legacy.core.jdkmath.AccurateMath; |
| |
| /** |
| * Implements the <a href="http://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval#Wilson_score_interval"> |
| * Wilson score method</a> for creating a binomial proportion confidence interval. |
| * |
| * @since 3.3 |
| */ |
| public class WilsonScoreInterval implements BinomialConfidenceInterval { |
| |
| /** {@inheritDoc} */ |
| @Override |
| public ConfidenceInterval createInterval(int numberOfTrials, int numberOfSuccesses, double confidenceLevel) { |
| IntervalUtils.checkParameters(numberOfTrials, numberOfSuccesses, confidenceLevel); |
| final double alpha = (1 - confidenceLevel) / 2; |
| final NormalDistribution normalDistribution = NormalDistribution.of(0, 1); |
| final double z = normalDistribution.inverseCumulativeProbability(1 - alpha); |
| final double zSquared = z * z; |
| final double oneOverNumTrials = 1d / numberOfTrials; |
| final double zSquaredOverNumTrials = zSquared * oneOverNumTrials; |
| final double mean = oneOverNumTrials * numberOfSuccesses; |
| |
| final double factor = 1 / (1 + zSquaredOverNumTrials); |
| final double modifiedSuccessRatio = mean + zSquaredOverNumTrials / 2; |
| final double difference = z * AccurateMath.sqrt(oneOverNumTrials * mean * (1 - mean) + |
| (oneOverNumTrials * zSquaredOverNumTrials / 4)); |
| |
| final double lowerBound = factor * (modifiedSuccessRatio - difference); |
| final double upperBound = factor * (modifiedSuccessRatio + difference); |
| return new ConfidenceInterval(lowerBound, upperBound, confidenceLevel); |
| } |
| } |