1 /*
2 * Licensed to the Apache Software Foundation (ASF) under one or more
3 * contributor license agreements. See the NOTICE file distributed with
4 * this work for additional information regarding copyright ownership.
5 * The ASF licenses this file to You under the Apache License, Version 2.0
6 * (the "License"); you may not use this file except in compliance with
7 * the License. You may obtain a copy of the License at
8 *
9 * http://www.apache.org/licenses/LICENSE-2.0
10 *
11 * Unless required by applicable law or agreed to in writing, software
12 * distributed under the License is distributed on an "AS IS" BASIS,
13 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14 * See the License for the specific language governing permissions and
15 * limitations under the License.
16 */
17 package org.apache.commons.math4.legacy.stat.interval;
18
19 import org.apache.commons.statistics.distribution.NormalDistribution;
20 import org.apache.commons.math4.core.jdkmath.JdkMath;
21
22 /**
23 * Implements the Agresti-Coull method for creating a binomial proportion confidence interval.
24 *
25 * @see <a
26 * href="http://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval#Agresti-Coull_Interval">
27 * Agresti-Coull interval (Wikipedia)</a>
28 * @since 3.3
29 */
30 public class AgrestiCoullInterval implements BinomialConfidenceInterval {
31
32 /** {@inheritDoc} */
33 @Override
34 public ConfidenceInterval createInterval(int numberOfTrials, int numberOfSuccesses, double confidenceLevel) {
35 IntervalUtils.checkParameters(numberOfTrials, numberOfSuccesses, confidenceLevel);
36 final double alpha = (1.0 - confidenceLevel) / 2;
37 final NormalDistribution normalDistribution = NormalDistribution.of(0, 1);
38 final double z = normalDistribution.inverseSurvivalProbability(alpha);
39 final double zSquared = JdkMath.pow(z, 2);
40 final double modifiedNumberOfTrials = numberOfTrials + zSquared;
41 final double modifiedSuccessesRatio = (1.0 / modifiedNumberOfTrials) * (numberOfSuccesses + 0.5 * zSquared);
42 final double difference = z *
43 JdkMath.sqrt(1.0 / modifiedNumberOfTrials * modifiedSuccessesRatio *
44 (1 - modifiedSuccessesRatio));
45 return new ConfidenceInterval(modifiedSuccessesRatio - difference, modifiedSuccessesRatio + difference,
46 confidenceLevel);
47 }
48 }