Class BinomialDistribution

java.lang.Object
org.apache.commons.statistics.distribution.AbstractDiscreteDistribution
org.apache.commons.statistics.distribution.BinomialDistribution
All Implemented Interfaces:
DiscreteDistribution
public final class BinomialDistribution extends AbstractDiscreteDistribution
Implementation of the binomial distribution.

The probability mass function of \( X \) is:

\[ f(k; n, p) = \binom{n}{k} p^k (1-p)^{n-k} \]

for \( n \in \{0, 1, 2, \dots\} \) the number of trials, \( p \in [0, 1] \) the probability of success, \( k \in \{0, 1, \dots, n\} \) the number of successes, and

\[ \binom{n}{k} = \frac{n!}{k! \, (n-k)!} \]

is the binomial coefficient.

See Also:

  • Field Details

    • HALF

      private static final float HALF
      1/2.
      See Also:

    • numberOfTrials

      private final int numberOfTrials
      The number of trials.

    • probabilityOfSuccess

      private final double probabilityOfSuccess
      The probability of success.

    • pmf0

      private final double pmf0
      Cached value for pmf(x=0).

    • pmfn

      private final double pmfn
      Cached value for pmf(x=n).

  • Constructor Details

    • BinomialDistribution

      private BinomialDistribution(int trials, double p)
      Parameters:
      trials - Number of trials.
      p - Probability of success.

  • Method Details

    • of

      public static BinomialDistribution of(int trials, double p)
      Creates a binomial distribution.
      Parameters:
      trials - Number of trials.
      p - Probability of success.
      Returns:
      the distribution
      Throws:
      IllegalArgumentException - if trials < 0, or if p < 0 or p > 1.

    • getNumberOfTrials

      public int getNumberOfTrials()
      Gets the number of trials parameter of this distribution.
      Returns:
      the number of trials.

    • getProbabilityOfSuccess

      public double getProbabilityOfSuccess()
      Gets the probability of success parameter of 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 - 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.
      Parameters:
      x - 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 - 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.

    • survivalProbability

      public double survivalProbability(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 complementary cumulative distribution function.

      By default, this is defined as 1 - cumulativeProbability(x), but the specific implementation may be more accurate.

      Parameters:
      x - Point at which the survival function is evaluated.
      Returns:
      the probability that a random variable with this distribution takes a value greater than x.

    • getMean

      public double getMean()
      Gets the mean of this distribution.

      For number of trials \( n \) and probability of success \( p \), the mean is \( np \).

      Returns:
      the mean.

    • getVariance

      public double getVariance()
      Gets the variance of this distribution.

      For number of trials \( n \) and probability of success \( p \), the variance is \( np (1 - p) \).

      Returns:
      the variance.

    • getSupportLowerBound

      public int getSupportLowerBound()
      Gets the lower bound of the support. This method must return the same value as inverseCumulativeProbability(0), i.e. \( \inf \{ x \in \mathbb Z : P(X \le x) \gt 0 \} \). By convention, Integer.MIN_VALUE should be substituted for negative infinity.

      The lower bound of the support is always 0 except for the probability parameter p = 1.

      Returns:
      0 or the number of trials.

    • getSupportUpperBound

      public int getSupportUpperBound()
      Gets the upper bound of the support. This method must return the same value as inverseCumulativeProbability(1), i.e. \( \inf \{ x \in \mathbb Z : P(X \le x) = 1 \} \). By convention, Integer.MAX_VALUE should be substituted for positive infinity.

      The upper bound of the support is the number of trials except for the probability parameter p = 0.

      Returns:
      number of trials or 0.

    • getMedian

      int getMedian()
      Gets the median. This is used to determine if the arguments to the AbstractDiscreteDistribution.probability(int, int) function are in the upper or lower domain.

      The default implementation calls AbstractDiscreteDistribution.inverseCumulativeProbability(double) with a value of 0.5.

      Overrides:
      getMedian in class AbstractDiscreteDistribution
      Returns:
      the median