drasys.or.prob
Class PoissonDistribution

java.lang.Object
  |
  +--drasys.or.prob.Distribution
        |
        +--drasys.or.prob.DiscreteDistribution
              |
              +--drasys.or.prob.PoissonDistributionBase
                    |
                    +--drasys.or.prob.PoissonDistribution

public class PoissonDistribution

extends PoissonDistributionBase

implements DiscreteDistributionI

An implementation of the Poisson probability distribution. The Poisson probability distribution models the number of events that occur in a fixed interval. The interval can be measured by time, space, volume, etc. The single parameter is the mean rate that the events happen.

For example, if a street intersection averages two accidents per week, a Poisson distribution to model the intersection would have a mean of 2. The probability distribution function 'pdf(x)' gives the probability that there will be exactly x accidents in one week. The cumulative distribution function 'cdf(x)' gives the probability that there will x or fewer accidents in one week. The method 'getRandomScaler' will return the number of accidents for a random week at the intersection and their average will be 2.

References:

The Art of Computer Programming: Seminumerical Algorithms (Vol 2, 3rd Ed)
    Donald Ervin Knuth; Hardcover
Numerical Recipes in C : The Art of Scientific Computing
    William H. Press, et al / Hardcover / Published 1993
Probability and Statistics
    Morris H. Degroot / Hardcover / Published 1986
Mathematical Statistics With Applications
    Dennis D. Wackerly, et al / Hardcover / Published 1996

See Also:

Serialized Form

Constructor Summary

PoissonDistribution(double mean)

PoissonDistribution(double mean, FunctionsI functions)           The functions objects will be used for the 'lnGamma' and 'lnFactorial' methods.

PoissonDistribution(double mean, long seed)

 

Method Summary
double	cdf(int x)           Returns the value of the cumulative distribution function at x; The standard edition iterates the pdf (x+1) times.
double	probability(int x1, int x2)           Returns the probability that x >= x1 and x <= x2.

 

Methods inherited from class drasys.or.prob.PoissonDistributionBase

equals, getRandomInteger, mean, pdf, setParameters, std, toString, variance

 

Methods inherited from class drasys.or.prob.DiscreteDistribution

cdf, getRandomArray, getRandomArray, getRandomScaler, pdf, probability, probability

 

Methods inherited from class drasys.or.prob.Distribution

getRandomMatrix, getRandomNumberGenerator, getRandomVector, setElements, setElements, setRandomNumberGenerator, setSeed

 

Methods inherited from class java.lang.Object

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

 

Constructor Detail

PoissonDistribution

public PoissonDistribution(double mean)

PoissonDistribution

public PoissonDistribution(double mean,
                           long seed)

PoissonDistribution

public PoissonDistribution(double mean,
                           FunctionsI functions)

The functions objects will be used for the 'lnGamma' and 'lnFactorial' methods.

cdf

public double cdf(int x)

Returns the value of the cumulative distribution function at x; The standard edition iterates the pdf (x+1) times. The professional edition uses the incomplete gamma function.

Specified by:

cdf in interface DiscreteDistributionI

Overrides:

cdf in class PoissonDistributionBase

Throws:

InvalidArgumentError - if x < 0;

probability

public double probability(int x1,
                          int x2)

Returns the probability that x >= x1 and x <= x2. The standard edition iterates the pdf (x2-x1+1) times. The professional edition uses the incomplete gamma function.

Specified by:

probability in interface DiscreteDistributionI

Overrides:

probability in class PoissonDistributionBase

Throws:

InvalidArgumentError - if x2 < x1 or x1 < 0;