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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 <a href="http://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval#Wilson_score_interval">
24   * Wilson score method</a> for creating a binomial proportion confidence interval.
25   *
26   * @since 3.3
27   */
28  public class WilsonScoreInterval implements BinomialConfidenceInterval {
29  
30      /** {@inheritDoc} */
31      @Override
32      public ConfidenceInterval createInterval(int numberOfTrials, int numberOfSuccesses, double confidenceLevel) {
33          IntervalUtils.checkParameters(numberOfTrials, numberOfSuccesses, confidenceLevel);
34          final double alpha = (1 - confidenceLevel) / 2;
35          final NormalDistribution normalDistribution = NormalDistribution.of(0, 1);
36          final double z = normalDistribution.inverseSurvivalProbability(alpha);
37          final double zSquared = z * z;
38          final double oneOverNumTrials = 1d / numberOfTrials;
39          final double zSquaredOverNumTrials = zSquared * oneOverNumTrials;
40          final double mean = oneOverNumTrials * numberOfSuccesses;
41  
42          final double factor = 1 / (1 + zSquaredOverNumTrials);
43          final double modifiedSuccessRatio = mean + zSquaredOverNumTrials / 2;
44          final double difference = z * JdkMath.sqrt(oneOverNumTrials * mean * (1 - mean) +
45                                                      (oneOverNumTrials * zSquaredOverNumTrials / 4));
46  
47          final double lowerBound = factor * (modifiedSuccessRatio - difference);
48          final double upperBound = factor * (modifiedSuccessRatio + difference);
49          return new ConfidenceInterval(lowerBound, upperBound, confidenceLevel);
50      }
51  }