org.apache.commons.math3.distribution

## Class EnumeratedRealDistribution

- java.lang.Object
- - org.apache.commons.math3.distribution.AbstractRealDistribution
  - - org.apache.commons.math3.distribution.EnumeratedRealDistribution

- All Implemented Interfaces:
    Serializable, RealDistribution

      public class EnumeratedRealDistribution
      extends AbstractRealDistribution

  Implementation of a real-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
  See Also:
    Serialized Form

- - ### Field Summary

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

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

      `random, randomData, SOLVER_DEFAULT_ABSOLUTE_ACCURACY`

  - ### Constructor Summary

    Constructors
    Constructor and Description
    `EnumeratedRealDistribution(double[] data)` Create a discrete real-valued distribution from the input data.
    `EnumeratedRealDistribution(double[] singletons, double[] probabilities)` Create a discrete real-valued distribution using the given probability mass function enumeration.
    `EnumeratedRealDistribution(RandomGenerator rng, double[] data)` Create a discrete real-valued distribution from the input data.
    `EnumeratedRealDistribution(RandomGenerator rng, double[] singletons, double[] probabilities)` Create a discrete real-valued distribution using the given random number generator and probability mass function enumeration.

  - ### Method Summary

    Methods
    Modifier and Type | Method and Description
    --- | ---
    `double` | `cumulativeProbability(double x)` For a random variable `X` whose values are distributed according to this distribution, this method returns `P(X <= x)`.
    `double` | `density(double 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.
    `double` | `getSupportLowerBound()` Access the lower bound of the support.
    `double` | `getSupportUpperBound()` Access the upper bound of the support.
    `double` | `inverseCumulativeProbability(double p)` Computes the quantile function of this distribution.
    `boolean` | `isSupportConnected()` Use this method to get information about whether the support is connected, i.e.
    `boolean` | `isSupportLowerBoundInclusive()` Whether or not the lower bound of support is in the domain of the density function.
    `boolean` | `isSupportUpperBoundInclusive()` Whether or not the upper bound of support is in the domain of the density function.
    `double` | `probability(double x)` For a random variable `X` whose values are distributed according to this distribution, this method returns `P(X = x)`.
    `double` | `sample()` Generate a random value sampled from this distribution.

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

      `cumulativeProbability, getSolverAbsoluteAccuracy, logDensity, probability, reseedRandomGenerator, sample`

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

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

- - ### Field Detail

    - #### innerDistribution

          protected final EnumeratedDistribution<Double> innerDistribution

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

  - ### Constructor Detail

    - #### EnumeratedRealDistribution

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

      Create a discrete real-valued distribution using the given probability mass function enumeration.

      Note: this constructor will implicitly create an instance of `Well19937c` as random generator to be used for sampling only (see `sample()` and `AbstractRealDistribution.sample(int)`). In case no sampling is needed for the created distribution, it is advised to pass `null` as random generator via the appropriate constructors to avoid the additional initialisation overhead.

      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.

    - #### EnumeratedRealDistribution

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

      Create a discrete real-valued distribution using the given random number generator and probability mass function enumeration.
      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.

    - #### EnumeratedRealDistribution

          public EnumeratedRealDistribution(RandomGenerator rng,
                                    double[] data)

      Create a discrete real-valued distribution from the input data. Values are assigned mass based on their frequency.
      Parameters:
        `rng` - random number generator used for sampling
        `data` - input dataset
      Since:
        3.6

    - #### EnumeratedRealDistribution

          public EnumeratedRealDistribution(double[] data)

      Create a discrete real-valued distribution from the input data. Values are assigned mass based on their frequency. For example, [0,1,1,2] as input creates a distribution with values 0, 1 and 2 having probability masses 0.25, 0.5 and 0.25 respectively,
      Parameters:
        `data` - input dataset
      Since:
        3.6

  - ### Method Detail

    - #### probability

          public double probability(double 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.
      Specified by:
        `probability` in interface `RealDistribution`
      Overrides:
        `probability` in class `AbstractRealDistribution`
      Parameters:
        `x` - the point at which the PMF is evaluated
      Returns:
        zero.

    - #### density

          public double density(double 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 point `x`

    - #### cumulativeProbability

          public double cumulativeProbability(double 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`

    - #### inverseCumulativeProbability

          public double inverseCumulativeProbability(double p)
                                              throws OutOfRangeException

      Computes the quantile function of this distribution. For a random variable `X` distributed according to this distribution, the returned value is
      - `inf{x in R | P(X<=x) >= p}` for `0 < p <= 1`,
      - `inf{x in R | P(X<=x) > 0}` for `p = 0`.
      The default implementation returns
      - `RealDistribution.getSupportLowerBound()` for `p = 0`,
      - `RealDistribution.getSupportUpperBound()` for `p = 1`.
      Specified by:
        `inverseCumulativeProbability` in interface `RealDistribution`
      Overrides:
        `inverseCumulativeProbability` in class `AbstractRealDistribution`
      Parameters:
        `p` - the cumulative probability
      Returns:
        the smallest `p`-quantile of this distribution (largest 0-quantile for `p = 0`)
      Throws:
        `OutOfRangeException` - if `p < 0` or `p > 1`

    - #### 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 double 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 R | P(X <= x) > 0}`.

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

    - #### getSupportUpperBound

          public double 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.

    - #### isSupportLowerBoundInclusive

          public boolean isSupportLowerBoundInclusive()

      Whether or not the lower bound of support is in the domain of the density function. Returns true iff `getSupporLowerBound()` is finite and `density(getSupportLowerBound())` returns a non-NaN, non-infinite value. The support of this distribution includes the lower bound.
      Returns:
        `true`

    - #### isSupportUpperBoundInclusive

          public boolean isSupportUpperBoundInclusive()

      Whether or not the upper bound of support is in the domain of the density function. Returns true iff `getSupportUpperBound()` is finite and `density(getSupportUpperBound())` returns a non-NaN, non-infinite value. The support of this distribution includes the upper bound.
      Returns:
        `true`

    - #### isSupportConnected

          public boolean isSupportConnected()

      Use this method to get information about whether the support is connected, i.e. whether all values 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 double sample()

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

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