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.math4.stat.interval;
018
019import org.apache.commons.statistics.distribution.NormalDistribution;
020import org.apache.commons.math4.util.FastMath;
021
022/**
023 * Implements the normal approximation method for creating a binomial proportion confidence interval.
024 *
025 * @see <a
026 *      href="http://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval#Normal_approximation_interval">
027 *      Normal approximation interval (Wikipedia)</a>
028 * @since 3.3
029 */
030public class NormalApproximationInterval implements BinomialConfidenceInterval {
031
032    /** {@inheritDoc} */
033    @Override
034    public ConfidenceInterval createInterval(int numberOfTrials, int numberOfSuccesses,
035                                             double confidenceLevel) {
036        IntervalUtils.checkParameters(numberOfTrials, numberOfSuccesses, confidenceLevel);
037        final double mean = (double) numberOfSuccesses / (double) numberOfTrials;
038        final double alpha = (1.0 - confidenceLevel) / 2;
039        final NormalDistribution normalDistribution = new NormalDistribution(0, 1);
040        final double difference = normalDistribution.inverseCumulativeProbability(1 - alpha) *
041                                  FastMath.sqrt(1.0 / numberOfTrials * mean * (1 - mean));
042        return new ConfidenceInterval(mean - difference, mean + difference, confidenceLevel);
043    }
044
045}