org.apache.commons.math3.stat.inference

## Class BinomialConfidenceInterval

• java.lang.Object
• org.apache.commons.math3.stat.inference.BinomialConfidenceInterval

• public class BinomialConfidenceInterval
extends Object
Factory methods to generate confidence intervals for a binomial proportion. The supported methods are:
• Clopper-Pearson method (exact method)
• Normal approximation (based on central limit theorem)
• Agresti-Coull interval
• Wilson score interval
Since:
3.3
Version:
$Id: BinomialConfidenceInterval.html 885258 2013-11-03 02:46:49Z tn$
Binomial proportion confidence interval (Wikipedia)
• ### Constructor Summary

Constructors
Constructor and Description
BinomialConfidenceInterval()
• ### Method Summary

Methods
Modifier and Type Method and Description
ConfidenceInterval getAgrestiCoullInterval(int numberOfTrials, int numberOfSuccesses, double confidenceLevel)
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.
ConfidenceInterval getClopperPearsonInterval(int numberOfTrials, int numberOfSuccesses, double 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.
ConfidenceInterval getNormalApproximationInterval(int numberOfTrials, int numberOfSuccesses, double 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.
ConfidenceInterval getWilsonScoreInterval(int numberOfTrials, int numberOfSuccesses, double 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.
• ### Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
• ### Constructor Detail

• #### BinomialConfidenceInterval

public BinomialConfidenceInterval()
• ### Method Detail

• #### getClopperPearsonInterval

public ConfidenceInterval getClopperPearsonInterval(int numberOfTrials,
int numberOfSuccesses,
double 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.

Preconditions:

• numberOfTrials must be positive
• numberOfSuccesses may not exceed numberOfTrials
• confidenceLevel must be strictly between 0 and 1 (exclusive)

Parameters:
numberOfTrials - number of trials
numberOfSuccesses - number of successes
confidenceLevel - desired probability that the true probability of success falls within the returned interval
Returns:
Confidence interval containing the probability of success with probability confidenceLevel
Throws:
NotStrictlyPositiveException - if numberOfTrials <= 0.
NotPositiveException - if numberOfSuccesses < 0.
NumberIsTooLargeException - if numberOfSuccesses > numberOfTrials.
OutOfRangeException - if confidenceLevel is not in the interval (0, 1).
• #### getNormalApproximationInterval

public ConfidenceInterval getNormalApproximationInterval(int numberOfTrials,
int numberOfSuccesses,
double 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.
Parameters:
numberOfTrials - number of trials
numberOfSuccesses - number of successes
confidenceLevel - desired probability that the true probability of success falls within the interval
Returns:
Confidence interval containing the probability of success with probability confidenceLevel
• #### getAgrestiCoullInterval

public ConfidenceInterval getAgrestiCoullInterval(int numberOfTrials,
int numberOfSuccesses,
double confidenceLevel)
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.
Parameters:
numberOfTrials - number of trials
numberOfSuccesses - number of successes
confidenceLevel - desired probability that the true probability of success falls within the returned interval
Returns:
Confidence interval containing the probability of success with probability confidenceLevel
Throws:
NotStrictlyPositiveException - if numberOfTrials <= 0.
NotPositiveException - if numberOfSuccesses < 0.
NumberIsTooLargeException - if numberOfSuccesses > numberOfTrials.
OutOfRangeException - if confidenceLevel is not in the interval (0, 1).
• #### getWilsonScoreInterval

public ConfidenceInterval getWilsonScoreInterval(int numberOfTrials,
int numberOfSuccesses,
double 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.
Parameters:
numberOfTrials - number of trials
numberOfSuccesses - number of successes
confidenceLevel - desired probability that the true probability of success falls within the returned interval
Returns:
Confidence interval containing the probability of success with probability confidenceLevel
Throws:
NotStrictlyPositiveException - if numberOfTrials <= 0.
NotPositiveException - if numberOfSuccesses < 0.
NumberIsTooLargeException - if numberOfSuccesses > numberOfTrials.
OutOfRangeException - if confidenceLevel is not in the interval (0, 1).