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Diffstat (limited to 'src/main/java/org/apache/commons/math3/stat/interval')
8 files changed, 569 insertions, 0 deletions
diff --git a/src/main/java/org/apache/commons/math3/stat/interval/AgrestiCoullInterval.java b/src/main/java/org/apache/commons/math3/stat/interval/AgrestiCoullInterval.java new file mode 100644 index 0000000..b71c718 --- /dev/null +++ b/src/main/java/org/apache/commons/math3/stat/interval/AgrestiCoullInterval.java @@ -0,0 +1,48 @@ +/* + * 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.math3.stat.interval; + +import org.apache.commons.math3.distribution.NormalDistribution; +import org.apache.commons.math3.util.FastMath; + +/** + * Implements the Agresti-Coull method for creating a binomial proportion confidence interval. + * + * @see <a + * href="http://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval#Agresti-Coull_Interval"> + * Agresti-Coull interval (Wikipedia)</a> + * @since 3.3 + */ +public class AgrestiCoullInterval implements BinomialConfidenceInterval { + + /** {@inheritDoc} */ + public ConfidenceInterval createInterval(int numberOfTrials, int numberOfSuccesses, double confidenceLevel) { + IntervalUtils.checkParameters(numberOfTrials, numberOfSuccesses, confidenceLevel); + final double alpha = (1.0 - confidenceLevel) / 2; + final NormalDistribution normalDistribution = new NormalDistribution(); + final double z = normalDistribution.inverseCumulativeProbability(1 - alpha); + final double zSquared = FastMath.pow(z, 2); + final double modifiedNumberOfTrials = numberOfTrials + zSquared; + final double modifiedSuccessesRatio = (1.0 / modifiedNumberOfTrials) * (numberOfSuccesses + 0.5 * zSquared); + final double difference = z * + FastMath.sqrt(1.0 / modifiedNumberOfTrials * modifiedSuccessesRatio * + (1 - modifiedSuccessesRatio)); + return new ConfidenceInterval(modifiedSuccessesRatio - difference, modifiedSuccessesRatio + difference, + confidenceLevel); + } + +} diff --git a/src/main/java/org/apache/commons/math3/stat/interval/BinomialConfidenceInterval.java b/src/main/java/org/apache/commons/math3/stat/interval/BinomialConfidenceInterval.java new file mode 100644 index 0000000..532679a --- /dev/null +++ b/src/main/java/org/apache/commons/math3/stat/interval/BinomialConfidenceInterval.java @@ -0,0 +1,62 @@ +/* + * 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.math3.stat.interval; + +import org.apache.commons.math3.exception.NumberIsTooLargeException; +import org.apache.commons.math3.exception.OutOfRangeException; +import org.apache.commons.math3.exception.NotPositiveException; +import org.apache.commons.math3.exception.NotStrictlyPositiveException; + +/** + * Interface to generate confidence intervals for a binomial proportion. + * + * @see <a + * href="http://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval">Binomial + * proportion confidence interval (Wikipedia)</a> + * @since 3.3 + */ +public interface BinomialConfidenceInterval { + + /** + * Create a confidence interval for the true probability of success + * of an unknown binomial distribution with the given observed number + * of trials, successes and confidence level. + * <p> + * Preconditions: + * <ul> + * <li>{@code numberOfTrials} must be positive</li> + * <li>{@code numberOfSuccesses} may not exceed {@code numberOfTrials}</li> + * <li>{@code confidenceLevel} must be strictly between 0 and 1 (exclusive)</li> + * </ul> + * </p> + * + * @param numberOfTrials number of trials + * @param numberOfSuccesses number of successes + * @param confidenceLevel desired probability that the true probability of + * success falls within the returned interval + * @return Confidence interval containing the probability of success with + * probability {@code confidenceLevel} + * @throws NotStrictlyPositiveException if {@code numberOfTrials <= 0}. + * @throws NotPositiveException if {@code numberOfSuccesses < 0}. + * @throws NumberIsTooLargeException if {@code numberOfSuccesses > numberOfTrials}. + * @throws OutOfRangeException if {@code confidenceLevel} is not in the interval {@code (0, 1)}. + */ + ConfidenceInterval createInterval(int numberOfTrials, int numberOfSuccesses, double confidenceLevel) + throws NotStrictlyPositiveException, NotPositiveException, + NumberIsTooLargeException, OutOfRangeException; + +} diff --git a/src/main/java/org/apache/commons/math3/stat/interval/ClopperPearsonInterval.java b/src/main/java/org/apache/commons/math3/stat/interval/ClopperPearsonInterval.java new file mode 100644 index 0000000..34a0d57 --- /dev/null +++ b/src/main/java/org/apache/commons/math3/stat/interval/ClopperPearsonInterval.java @@ -0,0 +1,58 @@ +/* + * 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.math3.stat.interval; + +import org.apache.commons.math3.distribution.FDistribution; + +/** + * Implements the Clopper-Pearson method for creating a binomial proportion confidence interval. + * + * @see <a + * href="http://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval#Clopper-Pearson_interval"> + * Clopper-Pearson interval (Wikipedia)</a> + * @since 3.3 + */ +public class ClopperPearsonInterval implements BinomialConfidenceInterval { + + /** {@inheritDoc} */ + public ConfidenceInterval createInterval(int numberOfTrials, int numberOfSuccesses, + double confidenceLevel) { + IntervalUtils.checkParameters(numberOfTrials, numberOfSuccesses, confidenceLevel); + double lowerBound = 0; + double upperBound = 0; + final double alpha = (1.0 - confidenceLevel) / 2.0; + + final FDistribution distributionLowerBound = new FDistribution(2 * (numberOfTrials - numberOfSuccesses + 1), + 2 * numberOfSuccesses); + final double fValueLowerBound = distributionLowerBound.inverseCumulativeProbability(1 - alpha); + if (numberOfSuccesses > 0) { + lowerBound = numberOfSuccesses / + (numberOfSuccesses + (numberOfTrials - numberOfSuccesses + 1) * fValueLowerBound); + } + + final FDistribution distributionUpperBound = new FDistribution(2 * (numberOfSuccesses + 1), + 2 * (numberOfTrials - numberOfSuccesses)); + final double fValueUpperBound = distributionUpperBound.inverseCumulativeProbability(1 - alpha); + if (numberOfSuccesses > 0) { + upperBound = (numberOfSuccesses + 1) * fValueUpperBound / + (numberOfTrials - numberOfSuccesses + (numberOfSuccesses + 1) * fValueUpperBound); + } + + return new ConfidenceInterval(lowerBound, upperBound, confidenceLevel); + } + +} diff --git a/src/main/java/org/apache/commons/math3/stat/interval/ConfidenceInterval.java b/src/main/java/org/apache/commons/math3/stat/interval/ConfidenceInterval.java new file mode 100644 index 0000000..0147c8c --- /dev/null +++ b/src/main/java/org/apache/commons/math3/stat/interval/ConfidenceInterval.java @@ -0,0 +1,109 @@ +/* + * 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.math3.stat.interval; + +import org.apache.commons.math3.exception.MathIllegalArgumentException; +import org.apache.commons.math3.exception.util.LocalizedFormats; + +/** + * Represents an interval estimate of a population parameter. + * + * @since 3.3 + */ +public class ConfidenceInterval { + + /** Lower endpoint of the interval */ + private double lowerBound; + + /** Upper endpoint of the interval */ + private double upperBound; + + /** + * The asserted probability that the interval contains the population + * parameter + */ + private double confidenceLevel; + + /** + * Create a confidence interval with the given bounds and confidence level. + * <p> + * Preconditions: + * <ul> + * <li>{@code lower} must be strictly less than {@code upper}</li> + * <li>{@code confidenceLevel} must be strictly between 0 and 1 (exclusive)</li> + * </ul> + * </p> + * + * @param lowerBound lower endpoint of the interval + * @param upperBound upper endpoint of the interval + * @param confidenceLevel coverage probability + * @throws MathIllegalArgumentException if the preconditions are not met + */ + public ConfidenceInterval(double lowerBound, double upperBound, double confidenceLevel) { + checkParameters(lowerBound, upperBound, confidenceLevel); + this.lowerBound = lowerBound; + this.upperBound = upperBound; + this.confidenceLevel = confidenceLevel; + } + + /** + * @return the lower endpoint of the interval + */ + public double getLowerBound() { + return lowerBound; + } + + /** + * @return the upper endpoint of the interval + */ + public double getUpperBound() { + return upperBound; + } + + /** + * @return the asserted probability that the interval contains the + * population parameter + */ + public double getConfidenceLevel() { + return confidenceLevel; + } + + /** + * @return String representation of the confidence interval + */ + @Override + public String toString() { + return "[" + lowerBound + ";" + upperBound + "] (confidence level:" + confidenceLevel + ")"; + } + + /** + * Verifies that (lower, upper) is a valid non-empty interval and confidence + * is strictly between 0 and 1. + * + * @param lower lower endpoint + * @param upper upper endpoint + * @param confidence confidence level + */ + private void checkParameters(double lower, double upper, double confidence) { + if (lower >= upper) { + throw new MathIllegalArgumentException(LocalizedFormats.LOWER_BOUND_NOT_BELOW_UPPER_BOUND, lower, upper); + } + if (confidence <= 0 || confidence >= 1) { + throw new MathIllegalArgumentException(LocalizedFormats.OUT_OF_BOUNDS_CONFIDENCE_LEVEL, confidence, 0, 1); + } + } +} diff --git a/src/main/java/org/apache/commons/math3/stat/interval/IntervalUtils.java b/src/main/java/org/apache/commons/math3/stat/interval/IntervalUtils.java new file mode 100644 index 0000000..0613c99 --- /dev/null +++ b/src/main/java/org/apache/commons/math3/stat/interval/IntervalUtils.java @@ -0,0 +1,174 @@ +/* + * 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.math3.stat.interval; + +import org.apache.commons.math3.exception.NotPositiveException; +import org.apache.commons.math3.exception.NotStrictlyPositiveException; +import org.apache.commons.math3.exception.NumberIsTooLargeException; +import org.apache.commons.math3.exception.OutOfRangeException; +import org.apache.commons.math3.exception.util.LocalizedFormats; + +/** + * Factory methods to generate confidence intervals for a binomial proportion. + * The supported methods are: + * <ul> + * <li>Agresti-Coull interval</li> + * <li>Clopper-Pearson method (exact method)</li> + * <li>Normal approximation (based on central limit theorem)</li> + * <li>Wilson score interval</li> + * </ul> + * + * @since 3.3 + */ +public final class IntervalUtils { + + /** Singleton Agresti-Coull instance. */ + private static final BinomialConfidenceInterval AGRESTI_COULL = new AgrestiCoullInterval(); + + /** Singleton Clopper-Pearson instance. */ + private static final BinomialConfidenceInterval CLOPPER_PEARSON = new ClopperPearsonInterval(); + + /** Singleton NormalApproximation instance. */ + private static final BinomialConfidenceInterval NORMAL_APPROXIMATION = new NormalApproximationInterval(); + + /** Singleton Wilson score instance. */ + private static final BinomialConfidenceInterval WILSON_SCORE = new WilsonScoreInterval(); + + /** + * Prevent instantiation. + */ + private IntervalUtils() { + } + + /** + * Create an Agresti-Coull binomial confidence interval for the true + * probability of success of an unknown binomial distribution with the given + * observed number of trials, successes and confidence level. + * + * @param numberOfTrials number of trials + * @param numberOfSuccesses number of successes + * @param confidenceLevel desired probability that the true probability of + * success falls within the returned interval + * @return Confidence interval containing the probability of success with + * probability {@code confidenceLevel} + * @throws NotStrictlyPositiveException if {@code numberOfTrials <= 0}. + * @throws NotPositiveException if {@code numberOfSuccesses < 0}. + * @throws NumberIsTooLargeException if {@code numberOfSuccesses > numberOfTrials}. + * @throws OutOfRangeException if {@code confidenceLevel} is not in the interval {@code (0, 1)}. + */ + public static ConfidenceInterval getAgrestiCoullInterval(int numberOfTrials, int numberOfSuccesses, + double confidenceLevel) { + return AGRESTI_COULL.createInterval(numberOfTrials, numberOfSuccesses, confidenceLevel); + } + + /** + * Create a Clopper-Pearson binomial confidence interval for the true + * probability of success of an unknown binomial distribution with the given + * observed number of trials, successes and confidence level. + * <p> + * Preconditions: + * <ul> + * <li>{@code numberOfTrials} must be positive</li> + * <li>{@code numberOfSuccesses} may not exceed {@code numberOfTrials}</li> + * <li>{@code confidenceLevel} must be strictly between 0 and 1 (exclusive)</li> + * </ul> + * </p> + * + * @param numberOfTrials number of trials + * @param numberOfSuccesses number of successes + * @param confidenceLevel desired probability that the true probability of + * success falls within the returned interval + * @return Confidence interval containing the probability of success with + * probability {@code confidenceLevel} + * @throws NotStrictlyPositiveException if {@code numberOfTrials <= 0}. + * @throws NotPositiveException if {@code numberOfSuccesses < 0}. + * @throws NumberIsTooLargeException if {@code numberOfSuccesses > numberOfTrials}. + * @throws OutOfRangeException if {@code confidenceLevel} is not in the interval {@code (0, 1)}. + */ + public static ConfidenceInterval getClopperPearsonInterval(int numberOfTrials, int numberOfSuccesses, + double confidenceLevel) { + return CLOPPER_PEARSON.createInterval(numberOfTrials, numberOfSuccesses, confidenceLevel); + } + + /** + * Create a binomial confidence interval for the true probability of success + * of an unknown binomial distribution with the given observed number of + * trials, successes and confidence level using the Normal approximation to + * the binomial distribution. + * + * @param numberOfTrials number of trials + * @param numberOfSuccesses number of successes + * @param confidenceLevel desired probability that the true probability of + * success falls within the interval + * @return Confidence interval containing the probability of success with + * probability {@code confidenceLevel} + */ + public static ConfidenceInterval getNormalApproximationInterval(int numberOfTrials, int numberOfSuccesses, + double confidenceLevel) { + return NORMAL_APPROXIMATION.createInterval(numberOfTrials, numberOfSuccesses, confidenceLevel); + } + + /** + * Create a Wilson score binomial confidence interval for the true + * probability of success of an unknown binomial distribution with the given + * observed number of trials, successes and confidence level. + * + * @param numberOfTrials number of trials + * @param numberOfSuccesses number of successes + * @param confidenceLevel desired probability that the true probability of + * success falls within the returned interval + * @return Confidence interval containing the probability of success with + * probability {@code confidenceLevel} + * @throws NotStrictlyPositiveException if {@code numberOfTrials <= 0}. + * @throws NotPositiveException if {@code numberOfSuccesses < 0}. + * @throws NumberIsTooLargeException if {@code numberOfSuccesses > numberOfTrials}. + * @throws OutOfRangeException if {@code confidenceLevel} is not in the interval {@code (0, 1)}. + */ + public static ConfidenceInterval getWilsonScoreInterval(int numberOfTrials, int numberOfSuccesses, + double confidenceLevel) { + return WILSON_SCORE.createInterval(numberOfTrials, numberOfSuccesses, confidenceLevel); + } + + /** + * Verifies that parameters satisfy preconditions. + * + * @param numberOfTrials number of trials (must be positive) + * @param numberOfSuccesses number of successes (must not exceed numberOfTrials) + * @param confidenceLevel confidence level (must be strictly between 0 and 1) + * @throws NotStrictlyPositiveException if {@code numberOfTrials <= 0}. + * @throws NotPositiveException if {@code numberOfSuccesses < 0}. + * @throws NumberIsTooLargeException if {@code numberOfSuccesses > numberOfTrials}. + * @throws OutOfRangeException if {@code confidenceLevel} is not in the interval {@code (0, 1)}. + */ + static void checkParameters(int numberOfTrials, int numberOfSuccesses, double confidenceLevel) { + if (numberOfTrials <= 0) { + throw new NotStrictlyPositiveException(LocalizedFormats.NUMBER_OF_TRIALS, numberOfTrials); + } + if (numberOfSuccesses < 0) { + throw new NotPositiveException(LocalizedFormats.NEGATIVE_NUMBER_OF_SUCCESSES, numberOfSuccesses); + } + if (numberOfSuccesses > numberOfTrials) { + throw new NumberIsTooLargeException(LocalizedFormats.NUMBER_OF_SUCCESS_LARGER_THAN_POPULATION_SIZE, + numberOfSuccesses, numberOfTrials, true); + } + if (confidenceLevel <= 0 || confidenceLevel >= 1) { + throw new OutOfRangeException(LocalizedFormats.OUT_OF_BOUNDS_CONFIDENCE_LEVEL, + confidenceLevel, 0, 1); + } + } + +} diff --git a/src/main/java/org/apache/commons/math3/stat/interval/NormalApproximationInterval.java b/src/main/java/org/apache/commons/math3/stat/interval/NormalApproximationInterval.java new file mode 100644 index 0000000..25a213a --- /dev/null +++ b/src/main/java/org/apache/commons/math3/stat/interval/NormalApproximationInterval.java @@ -0,0 +1,44 @@ +/* + * 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.math3.stat.interval; + +import org.apache.commons.math3.distribution.NormalDistribution; +import org.apache.commons.math3.util.FastMath; + +/** + * Implements the normal approximation method for creating a binomial proportion confidence interval. + * + * @see <a + * href="http://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval#Normal_approximation_interval"> + * Normal approximation interval (Wikipedia)</a> + * @since 3.3 + */ +public class NormalApproximationInterval implements BinomialConfidenceInterval { + + /** {@inheritDoc} */ + public ConfidenceInterval createInterval(int numberOfTrials, int numberOfSuccesses, + double confidenceLevel) { + IntervalUtils.checkParameters(numberOfTrials, numberOfSuccesses, confidenceLevel); + final double mean = (double) numberOfSuccesses / (double) numberOfTrials; + final double alpha = (1.0 - confidenceLevel) / 2; + final NormalDistribution normalDistribution = new NormalDistribution(); + final double difference = normalDistribution.inverseCumulativeProbability(1 - alpha) * + FastMath.sqrt(1.0 / numberOfTrials * mean * (1 - mean)); + return new ConfidenceInterval(mean - difference, mean + difference, confidenceLevel); + } + +} diff --git a/src/main/java/org/apache/commons/math3/stat/interval/WilsonScoreInterval.java b/src/main/java/org/apache/commons/math3/stat/interval/WilsonScoreInterval.java new file mode 100644 index 0000000..9932835 --- /dev/null +++ b/src/main/java/org/apache/commons/math3/stat/interval/WilsonScoreInterval.java @@ -0,0 +1,52 @@ +/* + * 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.math3.stat.interval; + +import org.apache.commons.math3.distribution.NormalDistribution; +import org.apache.commons.math3.util.FastMath; + +/** + * Implements the Wilson score method for creating a binomial proportion confidence interval. + * + * @see <a + * href="http://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval#Wilson_score_interval"> + * Wilson score interval (Wikipedia)</a> + * @since 3.3 + */ +public class WilsonScoreInterval implements BinomialConfidenceInterval { + + /** {@inheritDoc} */ + public ConfidenceInterval createInterval(int numberOfTrials, int numberOfSuccesses, double confidenceLevel) { + IntervalUtils.checkParameters(numberOfTrials, numberOfSuccesses, confidenceLevel); + final double alpha = (1.0 - confidenceLevel) / 2; + final NormalDistribution normalDistribution = new NormalDistribution(); + final double z = normalDistribution.inverseCumulativeProbability(1 - alpha); + final double zSquared = FastMath.pow(z, 2); + final double mean = (double) numberOfSuccesses / (double) numberOfTrials; + + final double factor = 1.0 / (1 + (1.0 / numberOfTrials) * zSquared); + final double modifiedSuccessRatio = mean + (1.0 / (2 * numberOfTrials)) * zSquared; + final double difference = z * + FastMath.sqrt(1.0 / numberOfTrials * mean * (1 - mean) + + (1.0 / (4 * FastMath.pow(numberOfTrials, 2)) * zSquared)); + + final double lowerBound = factor * (modifiedSuccessRatio - difference); + final double upperBound = factor * (modifiedSuccessRatio + difference); + return new ConfidenceInterval(lowerBound, upperBound, confidenceLevel); + } + +} diff --git a/src/main/java/org/apache/commons/math3/stat/interval/package-info.java b/src/main/java/org/apache/commons/math3/stat/interval/package-info.java new file mode 100644 index 0000000..34f43d9 --- /dev/null +++ b/src/main/java/org/apache/commons/math3/stat/interval/package-info.java @@ -0,0 +1,22 @@ +/* + * 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. + */ +/** + * + * Classes providing binomial proportion confidence interval construction. + * + */ +package org.apache.commons.math3.stat.interval; |