org.apache.commons.math3.distribution

## Class BinomialDistribution

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

- All Implemented Interfaces:
    Serializable, IntegerDistribution

      public class BinomialDistribution
      extends AbstractIntegerDistribution

  Implementation of the binomial distribution.
  See Also:
    Binomial distribution (Wikipedia), Binomial Distribution (MathWorld), Serialized Form

- - ### Field Summary

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

      `random, randomData`

  - ### Constructor Summary

    Constructors
    Constructor and Description
    `BinomialDistribution(int trials, double p)` Create a binomial distribution with the given number of trials and probability of success.
    `BinomialDistribution(RandomGenerator rng, int trials, double p)` Creates a binomial 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)`.
    `int` | `getNumberOfTrials()` Access the number of trials for this distribution.
    `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.
    `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, inverseCumulativeProbability, reseedRandomGenerator, sample, sample, solveInverseCumulativeProbability`

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

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

- - ### Constructor Detail

    - #### BinomialDistribution

          public BinomialDistribution(int trials,
                              double p)

      Create a binomial distribution with the given number of trials and 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:
        `trials` - Number of trials.
        `p` - Probability of success.
      Throws:
        `NotPositiveException` - if `trials < 0`.
        `OutOfRangeException` - if `p < 0` or `p > 1`.

    - #### BinomialDistribution

          public BinomialDistribution(RandomGenerator rng,
                              int trials,
                              double p)

      Creates a binomial distribution.
      Parameters:
        `rng` - Random number generator.
        `trials` - Number of trials.
        `p` - Probability of success.
      Throws:
        `NotPositiveException` - if `trials < 0`.
        `OutOfRangeException` - if `p < 0` or `p > 1`.
      Since:
        3.1

  - ### Method Detail

    - #### getNumberOfTrials

          public int getNumberOfTrials()

      Access the number of trials for this distribution.
      Returns:
        the number of trials.

    - #### 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 `n` trials and probability parameter `p`, the mean is `n * 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 `n` trials and probability parameter `p`, the variance is `n * p * (1 - 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 except for the probability parameter `p = 1`.
      Returns:
        lower bound of the support (0 or the number of trials)

    - #### 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 the number of trials except for the probability parameter `p = 0`.
      Returns:
        upper bound of the support (number of trials or 0)

    - #### 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`

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