Package org.apache.commons.statistics.interval

Enum BinomialConfidenceInterval

java.lang.Object

java.lang.Enum<BinomialConfidenceInterval>

org.apache.commons.statistics.interval.BinomialConfidenceInterval

All Implemented Interfaces:

Serializable, Comparable<BinomialConfidenceInterval>

public enum BinomialConfidenceInterval
extends Enum<BinomialConfidenceInterval>

Generate confidence intervals for a binomial proportion.

Note: To avoid overshoot, the confidence intervals are clipped to be in the [0, 1] interval in the case of the normal approximation and Agresti-Coull methods.

Since:

1.2

See Also:

Binomial proportion confidence interval (Wikipedia)

Enum Constant Summary

Enum Constants

Enum Constant	Description
AGRESTI_COULL	Implements the Agresti-Coull method for creating a binomial proportion confidence interval.
CLOPPER_PEARSON	Implements the Clopper-Pearson method for creating a binomial proportion confidence interval.
JEFFREYS	Implements the Jeffreys method for creating a binomial proportion confidence interval.
NORMAL_APPROXIMATION	Implements the normal approximation method for creating a binomial proportion confidence interval.
WILSON_SCORE	Implements the Wilson score method for creating a binomial proportion confidence interval.

Method Summary

Modifier and Type	Method	Description
Interval	fromErrorRate(int numberOfTrials, int numberOfSuccesses, double alpha)	Create a confidence interval for the true probability of success of an unknown binomial distribution with the given observed number of trials, successes and error rate.
static BinomialConfidenceInterval	valueOf(String name)	Returns the enum constant of this type with the specified name.
static BinomialConfidenceInterval[]	values()	Returns an array containing the constants of this enum type, in the order they are declared.

Methods inherited from class java.lang.Enum

clone, compareTo, equals, finalize, getDeclaringClass, hashCode, name, ordinal, toString, valueOf

Methods inherited from class java.lang.Object

getClass, notify, notifyAll, wait, wait, wait

Enum Constant Detail

NORMAL_APPROXIMATION

public static final BinomialConfidenceInterval NORMAL_APPROXIMATION

Implements the normal approximation method for creating a binomial proportion confidence interval.

This method clips the confidence interval to be in [0, 1].

See Also:

Normal approximation interval (Wikipedia)

WILSON_SCORE

public static final BinomialConfidenceInterval WILSON_SCORE

Implements the Wilson score method for creating a binomial proportion confidence interval.

See Also:

Normal approximation interval (Wikipedia)

JEFFREYS

public static final BinomialConfidenceInterval JEFFREYS

Implements the Jeffreys method for creating a binomial proportion confidence interval.

In order to avoid the coverage probability tending to zero when p tends towards 0 or 1, when x = 0 the lower limit is set to 0, and when x = n the upper limit is set to 1.

See Also:

Jeffreys interval (Wikipedia)

CLOPPER_PEARSON

public static final BinomialConfidenceInterval CLOPPER_PEARSON

Implements the Clopper-Pearson method for creating a binomial proportion confidence interval.

See Also:

Clopper-Pearson interval (Wikipedia)

AGRESTI_COULL

public static final BinomialConfidenceInterval AGRESTI_COULL

Implements the Agresti-Coull method for creating a binomial proportion confidence interval.

This method clips the confidence interval to be in [0, 1].

See Also:

Agresti-Coull interval (Wikipedia)

Method Detail

values

public static BinomialConfidenceInterval[] values()

Returns an array containing the constants of this enum type, in the order they are declared. This method may be used to iterate over the constants as follows:

for (BinomialConfidenceInterval c : BinomialConfidenceInterval.values())
    System.out.println(c);

Returns:

an array containing the constants of this enum type, in the order they are declared

valueOf

public static BinomialConfidenceInterval valueOf(String name)

Returns the enum constant of this type with the specified name. The string must match exactly an identifier used to declare an enum constant in this type. (Extraneous whitespace characters are not permitted.)

Parameters:

name - the name of the enum constant to be returned.

Returns:

the enum constant with the specified name

Throws:

IllegalArgumentException - if this enum type has no constant with the specified name

NullPointerException - if the argument is null

fromErrorRate

public Interval fromErrorRate(int numberOfTrials,
                              int numberOfSuccesses,
                              double alpha)

Create a confidence interval for the true probability of success of an unknown binomial distribution with the given observed number of trials, successes and error rate.

The error rate alpha is related to the confidence level that the interval contains the true probability of success as alpha = 1 - confidence, where confidence is the confidence level in [0, 1]. For example a 95% confidence level is an alpha of 0.05.

Parameters:

numberOfTrials - Number of trials.

numberOfSuccesses - Number of successes.

alpha - Desired error rate that the true probability of success falls outside the returned interval.

Returns:

Confidence interval containing the probability of success with error rate alpha

Throws:

IllegalArgumentException - if numberOfTrials <= 0, if numberOfSuccesses < 0, if numberOfSuccesses > numberOfTrials, or if alpha is not in the open interval (0, 1).