IntervalUtils (Apache Commons Math 3.3 API)

org.apache.commons.math3.stat.interval

## Class IntervalUtils

- java.lang.Object
- - org.apache.commons.math3.stat.interval.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
  Version:
    $Id: IntervalUtils.java 1560551 2014-01-22 22:35:21Z tn $

- - ### Method Summary

    Methods
    Modifier and Type | Method and 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)`.

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