org.apache.commons.math3.distribution

## Class GeometricDistribution

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

- All Implemented Interfaces:
    Serializable, IntegerDistribution

      public class GeometricDistribution
      extends AbstractIntegerDistribution

  Implementation of the geometric distribution.
  Since:
    3.3
  See Also:
    Geometric distribution (Wikipedia), Geometric Distribution (MathWorld), Serialized Form

- - ### Field Summary

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

      `random, randomData`

  - ### Constructor Summary

    Constructors
    Constructor and Description
    `GeometricDistribution(double p)` Create a geometric distribution with the given probability of success.
    `GeometricDistribution(RandomGenerator rng, double p)` Creates a geometric distribution.

  - ### 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.
    `double` | `getProbabilityOfSuccess()` Access the probability of success for this distribution.
    `int` | `getSupportLowerBound()` Access the lower bound of the support.
    `int` | `getSupportUpperBound()` Access the upper bound of the support.
    `int` | `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.
    `double` | `logProbability(int x)` For a random variable `X` whose values are distributed according to this distribution, this method returns `log(P(X = x))`, where `log` is the natural logarithm.
    `double` | `probability(int x)` For a random variable `X` whose values are distributed according to this distribution, this method returns `P(X = x)`.

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

      `cumulativeProbability, reseedRandomGenerator, sample, sample, solveInverseCumulativeProbability`

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

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

- - ### Constructor Detail

    - #### GeometricDistribution

          public GeometricDistribution(double p)

      Create a geometric distribution with the given probability of success.

      Note: this constructor will implicitly create an instance of `Well19937c` as random generator to be used for sampling only (see `AbstractIntegerDistribution.sample()` and `AbstractIntegerDistribution.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:
        `p` - probability of success.
      Throws:
        `OutOfRangeException` - if `p <= 0` or `p > 1`.

    - #### GeometricDistribution

          public GeometricDistribution(RandomGenerator rng,
                               double p)

      Creates a geometric distribution.
      Parameters:
        `rng` - Random number generator.
        `p` - Probability of success.
      Throws:
        `OutOfRangeException` - if `p <= 0` or `p > 1`.

  - ### Method Detail

    - #### getProbabilityOfSuccess

          public double getProbabilityOfSuccess()

      Access the probability of success for this distribution.
      Returns:
        the probability of success.

    - #### 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`

    - #### logProbability

          public double logProbability(int x)

      For a random variable `X` whose values are distributed according to this distribution, this method returns `log(P(X = x))`, where `log` is the natural logarithm. In other words, this method represents the logarithm of the probability mass function (PMF) for the distribution. Note that due to the floating point precision and under/overflow issues, this method will for some distributions be more precise and faster than computing the logarithm of `IntegerDistribution.probability(int)`.

      The default implementation simply computes the logarithm of `probability(x)`.

      Overrides:
        `logProbability` in class `AbstractIntegerDistribution`
      Parameters:
        `x` - the point at which the PMF is evaluated
      Returns:
        the logarithm of 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. For probability parameter `p`, the mean is `(1 - p) / p`.
      Returns:
        the mean or `Double.NaN` if it is not defined

    - #### getNumericalVariance

          public double getNumericalVariance()

      Use this method to get the numerical value of the variance of this distribution. For probability parameter `p`, the variance is `(1 - p) / (p * p)`.
      Returns:
        the variance (possibly `Double.POSITIVE_INFINITY` or `Double.NaN` if it is not defined)

    - #### 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}`.

      The lower bound of the support is always 0.
      Returns:
        lower bound of the support (always 0)

    - #### 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}`.

      The upper bound of the support is infinite (which we approximate as `Integer.MAX_VALUE`).
      Returns:
        upper bound of the support (always Integer.MAX_VALUE)

    - #### 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`

    - #### inverseCumulativeProbability

          public int 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 Z | P(X<=x) >= p}` for `0 < p <= 1`,
      - `inf{x in Z | P(X<=x) > 0}` for `p = 0`.
      If the result exceeds the range of the data type `int`, then `Integer.MIN_VALUE` or `Integer.MAX_VALUE` is returned. The default implementation returns
      - `IntegerDistribution.getSupportLowerBound()` for `p = 0`,
      - `IntegerDistribution.getSupportUpperBound()` for `p = 1`, and
      - `AbstractIntegerDistribution.solveInverseCumulativeProbability(double, int, int)` for `0 < p < 1`.
      Specified by:
        `inverseCumulativeProbability` in interface `IntegerDistribution`
      Overrides:
        `inverseCumulativeProbability` in class `AbstractIntegerDistribution`
      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`

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