Package org.apache.commons.math.distribution

Class PoissonDistributionImpl

    • Field Detail

      • DEFAULT_MAX_ITERATIONS

        public static final int DEFAULT_MAX_ITERATIONS
        Default maximum number of iterations for cumulative probability calculations.
        Since:
        2.1
        See Also:
        Constant Field Values

      • DEFAULT_EPSILON

        public static final double DEFAULT_EPSILON
        Default convergence criterion.
        Since:
        2.1
        See Also:
        Constant Field Values

    • Constructor Detail

      • PoissonDistributionImpl

        public PoissonDistributionImpl​(double p)
        Create a new Poisson distribution with the given the mean. The mean value must be positive; otherwise an IllegalArgument is thrown.
        Parameters:
        p - the Poisson mean
        Throws:
        java.lang.IllegalArgumentException - if p ≤ 0

      • PoissonDistributionImpl

        public PoissonDistributionImpl​(double p,
                               double epsilon,
                               int maxIterations)
        Create a new Poisson distribution with the given mean, convergence criterion and maximum number of iterations.
        Parameters:
        p - the Poisson mean
        epsilon - the convergence criteria for cumulative probabilites
        maxIterations - the maximum number of iterations for cumulative probabilites
        Since:
        2.1

      • PoissonDistributionImpl

        public PoissonDistributionImpl​(double p,
                               double epsilon)
        Create a new Poisson distribution with the given mean and convergence criterion.
        Parameters:
        p - the Poisson mean
        epsilon - the convergence criteria for cumulative probabilites
        Since:
        2.1

      • PoissonDistributionImpl

        public PoissonDistributionImpl​(double p,
                               int maxIterations)
        Create a new Poisson distribution with the given mean and maximum number of iterations.
        Parameters:
        p - the Poisson mean
        maxIterations - the maximum number of iterations for cumulative probabilites
        Since:
        2.1

      • PoissonDistributionImpl

        @Deprecated
public PoissonDistributionImpl​(double p,
                               NormalDistribution z)
        Deprecated.
        as of 2.1 (to avoid possibly inconsistent state, the "NormalDistribution" will be instantiated internally)
        Create a new Poisson distribution with the given the mean. The mean value must be positive; otherwise an IllegalArgument is thrown.
        Parameters:
        p - the Poisson mean
        z - a normal distribution used to compute normal approximations.
        Throws:
        java.lang.IllegalArgumentException - if p ≤ 0
        Since:
        1.2

    • Method Detail

      • getMean

        public double getMean()
        Get the Poisson mean for the distribution.
        Specified by:
        getMean in interface PoissonDistribution
        Returns:
        the Poisson mean for the distribution.

      • setMean

        @Deprecated
public void setMean​(double p)
        Deprecated.
        as of 2.1 (class will become immutable in 3.0)
        Set the Poisson mean for the distribution. The mean value must be positive; otherwise an IllegalArgument is thrown.
        Specified by:
        setMean in interface PoissonDistribution
        Parameters:
        p - the Poisson mean value
        Throws:
        java.lang.IllegalArgumentException - if p ≤ 0

      • probability

        public double probability​(int x)
        The probability mass function P(X = x) for a Poisson distribution.
        Specified by:
        probability in interface IntegerDistribution
        Parameters:
        x - the value at which the probability density function is evaluated.
        Returns:
        the value of the probability mass function at x

      • normalApproximateProbability

        public double normalApproximateProbability​(int x)
                                    throws MathException
        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

        Specified by:
        normalApproximateProbability in interface PoissonDistribution
        Parameters:
        x - the upper bound, inclusive
        Returns:
        the distribution function value calculated using a normal approximation
        Throws:
        MathException - if an error occurs computing the normal approximation

      • sample

        public int sample()
           throws MathException
        Generates a random value sampled from this distribution.

        Algorithm Description:

        • For small means, uses simulation of a Poisson process using Uniform deviates, as described here. The Poisson process (and hence value returned) is bounded by 1000 * mean.
          • <
        • For large means, uses the rejection algorithm described in
          Devroye, Luc. (1981).The Computer Generation of Poisson Random Variables Computing vol. 26 pp. 197-207.

        Overrides:
        sample in class AbstractIntegerDistribution
        Returns:
        random value
        Throws:
        MathException - if an error occurs generating the random value
        Since:
        2.2

      • setNormal

        @Deprecated
public void setNormal​(NormalDistribution value)
        Deprecated.
        as of 2.1 (class will become immutable in 3.0)
        Modify the normal distribution used to compute normal approximations. The caller is responsible for insuring the normal distribution has the proper parameter settings.
        Parameters:
        value - the new distribution
        Since:
        1.2

      • getSupportLowerBound

        public int getSupportLowerBound()
        Returns the lower bound of the support for the distribution. The lower bound of the support is always 0 no matter the mean parameter.
        Returns:
        lower bound of the support (always 0)
        Since:
        2.2

      • getSupportUpperBound

        public int getSupportUpperBound()
        Returns the upper bound of the support for the distribution. 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 and AbstractIntegerDistribution.isSupportUpperBoundInclusive() returns true.
        Returns:
        upper bound of the support (always Integer.MAX_VALUE for positive infinity)
        Since:
        2.2

      • getNumericalVariance

        public double getNumericalVariance()
        Returns the variance of the distribution. For mean parameter p, the variance is p
        Returns:
        the variance
        Since:
        2.2