## Class IntervalUtils

• public final class IntervalUtils
extends Object
Factory methods to generate confidence intervals for a binomial proportion. The supported methods are:
• Agresti-Coull interval
• Clopper-Pearson method (exact method)
• Normal approximation (based on central limit theorem)
• Wilson score interval
Since:
3.3
• ### Method Summary

All Methods
Modifier and Type Method Description
static 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.
static 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.
static 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.
static 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
• ### Method Detail

• #### getAgrestiCoullInterval

public static 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).
• #### getClopperPearsonInterval

public static 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 static 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
• #### getWilsonScoreInterval

public static 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).