org.apache.commons.math3.distribution

## Class EnumeratedIntegerDistribution

- java.lang.Object
- - org.apache.commons.math3.distribution.AbstractIntegerDistribution
  - - org.apache.commons.math3.distribution.EnumeratedIntegerDistribution

- All Implemented Interfaces:
    Serializable, IntegerDistribution

      public class EnumeratedIntegerDistribution
      extends AbstractIntegerDistribution

  Implementation of an integer-valued `EnumeratedDistribution`.

  Values with zero-probability are allowed but they do not extend the support.
  Duplicate values are allowed. Probabilities of duplicate values are combined when computing cumulative probabilities and statistics.

  Since:
    3.2
  Version:
    $Id: EnumeratedIntegerDistribution.java 1456769 2013-03-15 04:51:34Z psteitz $
  See Also:
    Serialized Form

- - ### Field Summary

    Fields
    Modifier and Type | Field and Description
    --- | ---
    `protected EnumeratedDistribution<Integer>` | `innerDistribution` `EnumeratedDistribution` instance (using the `Integer` wrapper) used to generate the pmf.

    - ### Fields inherited from class org.apache.commons.math3.distribution.AbstractIntegerDistribution

      `random, randomData`

  - ### Constructor Summary

    Constructors
    Constructor and Description
    `EnumeratedIntegerDistribution(int[] singletons, double[] probabilities)` Create a discrete distribution using the given probability mass function definition.
    `EnumeratedIntegerDistribution(RandomGenerator rng, int[] singletons, double[] probabilities)` Create a discrete distribution using the given random number generator and probability mass function definition.

  - ### Method Summary

    Methods
    Modifier and Type | Method and Description
    --- | ---
    `double` | `cumulativeProbability(int x)` For a random variable `X` whose values are distributed according to this distribution, this method returns `P(X <= x)`.
    `double` | `getNumericalMean()` Use this method to get the numerical value of the mean of this distribution.
    `double` | `getNumericalVariance()` Use this method to get the numerical value of the variance of this distribution.
    `int` | `getSupportLowerBound()` Access the lower bound of the support.
    `int` | `getSupportUpperBound()` Access the upper bound of the support.
    `boolean` | `isSupportConnected()` Use this method to get information about whether the support is connected, i.e.
    `double` | `probability(int x)` For a random variable `X` whose values are distributed according to this distribution, this method returns `P(X = x)`.
    `int` | `sample()` Generate a random value sampled from this distribution.

    - ### Methods inherited from class org.apache.commons.math3.distribution.AbstractIntegerDistribution

      `cumulativeProbability, inverseCumulativeProbability, logProbability, reseedRandomGenerator, sample, solveInverseCumulativeProbability`

    - ### Methods inherited from class java.lang.Object

      `clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`

- - ### Field Detail

    - #### innerDistribution

          protected final EnumeratedDistribution<Integer> innerDistribution

      `EnumeratedDistribution` instance (using the `Integer` wrapper) used to generate the pmf.

  - ### Constructor Detail

    - #### EnumeratedIntegerDistribution

          public EnumeratedIntegerDistribution(int[] singletons,
                                       double[] probabilities)
                                        throws DimensionMismatchException,
                                               NotPositiveException,
                                               MathArithmeticException,
                                               NotFiniteNumberException,
                                               NotANumberException

      Create a discrete distribution using the given probability mass function definition.
      Parameters:
        `singletons` - array of random variable values.
        `probabilities` - array of probabilities.
      Throws:
        `DimensionMismatchException` - if `singletons.length != probabilities.length`
        `NotPositiveException` - if any of the probabilities are negative.
        `NotFiniteNumberException` - if any of the probabilities are infinite.
        `NotANumberException` - if any of the probabilities are NaN.
        `MathArithmeticException` - all of the probabilities are 0.

    - #### EnumeratedIntegerDistribution

          public EnumeratedIntegerDistribution(RandomGenerator rng,
                                       int[] singletons,
                                       double[] probabilities)
                                        throws DimensionMismatchException,
                                               NotPositiveException,
                                               MathArithmeticException,
                                               NotFiniteNumberException,
                                               NotANumberException

      Create a discrete distribution using the given random number generator and probability mass function definition.
      Parameters:
        `rng` - random number generator.
        `singletons` - array of random variable values.
        `probabilities` - array of probabilities.
      Throws:
        `DimensionMismatchException` - if `singletons.length != probabilities.length`
        `NotPositiveException` - if any of the probabilities are negative.
        `NotFiniteNumberException` - if any of the probabilities are infinite.
        `NotANumberException` - if any of the probabilities are NaN.
        `MathArithmeticException` - all of the probabilities are 0.

  - ### Method Detail

    - #### probability

          public double probability(int x)

      For a random variable `X` whose values are distributed according to this distribution, this method returns `P(X = x)`. In other words, this method represents the probability mass function (PMF) for the distribution.
      Parameters:
        `x` - the point at which the PMF is evaluated
      Returns:
        the value of the probability mass function at `x`

    - #### cumulativeProbability

          public double cumulativeProbability(int x)

      For a random variable `X` whose values are distributed according to this distribution, this method returns `P(X <= x)`. In other words, this method represents the (cumulative) distribution function (CDF) for this distribution.
      Parameters:
        `x` - the point at which the CDF is evaluated
      Returns:
        the probability that a random variable with this distribution takes a value less than or equal to `x`

    - #### getNumericalMean

          public double getNumericalMean()

      Use this method to get the numerical value of the mean of this distribution.
      Returns:
        `sum(singletons[i] * probabilities[i])`

    - #### getNumericalVariance

          public double getNumericalVariance()

      Use this method to get the numerical value of the variance of this distribution.
      Returns:
        `sum((singletons[i] - mean) ^ 2 * probabilities[i])`

    - #### getSupportLowerBound

          public int getSupportLowerBound()

      Access the lower bound of the support. This method must return the same value as `inverseCumulativeProbability(0)`. In other words, this method must return

      `inf {x in Z | P(X <= x) > 0}`.

      Returns the lowest value with non-zero probability.
      Returns:
        the lowest value with non-zero probability.

    - #### getSupportUpperBound

          public int getSupportUpperBound()

      Access the upper bound of the support. This method must return the same value as `inverseCumulativeProbability(1)`. In other words, this method must return

      `inf {x in R | P(X <= x) = 1}`.

      Returns the highest value with non-zero probability.
      Returns:
        the highest value with non-zero probability.

    - #### isSupportConnected

          public boolean isSupportConnected()

      Use this method to get information about whether the support is connected, i.e. whether all integers between the lower and upper bound of the support are included in the support. The support of this distribution is connected.
      Returns:
        `true`

    - #### sample

          public int sample()

      Generate a random value sampled from this distribution. The default implementation uses the inversion method.
      Specified by:
        `sample` in interface `IntegerDistribution`
      Overrides:
        `sample` in class `AbstractIntegerDistribution`
      Returns:
        a random value

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