Package org.hipparchus.distribution.discrete

Class PoissonDistribution

java.lang.Object
org.hipparchus.distribution.discrete.AbstractIntegerDistribution
org.hipparchus.distribution.discrete.PoissonDistribution
All Implemented Interfaces:
Serializable, IntegerDistribution
public class PoissonDistribution extends AbstractIntegerDistribution
Implementation of the Poisson distribution.
See Also:

  • Field Summary

    Fields
    Modifier and Type
    Field
    Description
    static final double
    DEFAULT_EPSILON
    Default convergence criterion.
    static final int
    DEFAULT_MAX_ITERATIONS
    Default maximum number of iterations for cumulative probability calculations.

  • Constructor Summary

    Constructors
    Constructor
    Description
    PoissonDistribution(double p)
    Creates a new Poisson distribution with specified mean.
    PoissonDistribution(double p, double epsilon)
    Creates a new Poisson distribution with the specified mean and convergence criterion.
    PoissonDistribution(double p, double epsilon, int maxIterations)
    Creates a new Poisson distribution with specified mean, convergence criterion and maximum number of iterations.
    PoissonDistribution(double p, int maxIterations)
    Creates a new Poisson distribution with the specified mean and maximum number of iterations.

  • Method Summary

    Modifier and Type
    Method
    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
    getMean()
    Get the mean for the 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.
    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
    normalApproximateProbability(int x)
    Calculates the Poisson distribution function using a normal approximation.
    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.hipparchus.distribution.discrete.AbstractIntegerDistribution

    inverseCumulativeProbability, probability, solveInverseCumulativeProbability

    Methods inherited from class java.lang.Object

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

  • Field Details

    • DEFAULT_MAX_ITERATIONS

      public static final int DEFAULT_MAX_ITERATIONS
      Default maximum number of iterations for cumulative probability calculations.
      See Also:

    • DEFAULT_EPSILON

      public static final double DEFAULT_EPSILON
      Default convergence criterion.
      See Also:

  • Constructor Details

    • PoissonDistribution

      public PoissonDistribution(double p) throws MathIllegalArgumentException
      Creates a new Poisson distribution with specified mean.
      Parameters:
      p - the Poisson mean
      Throws:
      MathIllegalArgumentException - if p <= 0.

    • PoissonDistribution

      public PoissonDistribution(double p, double epsilon, int maxIterations) throws MathIllegalArgumentException
      Creates a new Poisson distribution with specified mean, convergence criterion and maximum number of iterations.
      Parameters:
      p - Poisson mean.
      epsilon - Convergence criterion for cumulative probabilities.
      maxIterations - the maximum number of iterations for cumulative probabilities.
      Throws:
      MathIllegalArgumentException - if p <= 0.

    • PoissonDistribution

      public PoissonDistribution(double p, double epsilon) throws MathIllegalArgumentException
      Creates a new Poisson distribution with the specified mean and convergence criterion.
      Parameters:
      p - Poisson mean.
      epsilon - Convergence criterion for cumulative probabilities.
      Throws:
      MathIllegalArgumentException - if p <= 0.

    • PoissonDistribution

      public PoissonDistribution(double p, int maxIterations)
      Creates a new Poisson distribution with the specified mean and maximum number of iterations.
      Parameters:
      p - Poisson mean.
      maxIterations - Maximum number of iterations for cumulative probabilities.

  • Method Details

    • getMean

      public double getMean()
      Get the mean for the distribution.
      Returns:
      the mean for the distribution.

    • 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).

      Specified by:
      logProbability in interface IntegerDistribution
      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

    • normalApproximateProbability

      public double normalApproximateProbability(int x)
      Calculates the Poisson distribution function using a normal approximation. The N(mean, sqrt(mean)) distribution is used to approximate the Poisson distribution. The computation uses "half-correction" (evaluating the normal distribution function at x + 0.5).
      Parameters:
      x - Upper bound, inclusive.
      Returns:
      the distribution function value calculated using a normal approximation.

    • getNumericalMean

      public double getNumericalMean()
      Use this method to get the numerical value of the mean of this distribution. For mean parameter p, the mean is 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 mean parameter p, the variance is 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 no matter the mean parameter.
      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 positive infinity, regardless of the parameter values. There is no integer infinity, so this method returns Integer.MAX_VALUE.
      Returns:
      upper bound of the support (always Integer.MAX_VALUE for positive infinity)

    • 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