drasys.or.prob
Class PoissonDistributionBase

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

Direct Known Subclasses:

PoissonDistribution

public class PoissonDistributionBase

extends DiscreteDistribution

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 'getRandomInteger' 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

PoissonDistributionBase(double mean)

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

PoissonDistributionBase(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.
boolean	equals(java.lang.Object o)
int	getRandomInteger()           Returns a random number from the Poisson distribution.
double	mean()           Returns the mean of the distribution.
double	pdf(int x)           Returns the value of the probability distribution function at x;
double	probability(int x1, int x2)           Returns the probability that x >= x1 and x <= x2.
void	setParameters(double mean)           Sets the distribution parameters.
double	std()           Returns the standard deviation of the distribution.
java.lang.String	toString()
double	variance()           Returns the variance of the distribution.

 

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

PoissonDistributionBase

public PoissonDistributionBase(double mean)

PoissonDistributionBase

public PoissonDistributionBase(double mean,
                               long seed)

PoissonDistributionBase

public PoissonDistributionBase(double mean,
                               FunctionsI functions)

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

setParameters

public void setParameters(double mean)

Sets the distribution parameters.

Throws:

InvalidArgumentError - if mean <= 0.0.

getRandomInteger

public int getRandomInteger()

Returns a random number from the Poisson distribution.

Specified by:

getRandomInteger in interface DiscreteDistributionI

mean

public double mean()

Returns the mean of the distribution.

variance

public double variance()

Returns the variance of the distribution.

std

public double std()

Returns the standard deviation of the distribution.

pdf

public double pdf(int x)

Returns the value of the probability distribution function at x;

Specified by:

pdf in interface DiscreteDistributionI

Throws:

InvalidArgumentError - if x < 0;

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

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

Throws:

InvalidArgumentError - if x2 < x1 or x1 < 0;

equals

public boolean equals(java.lang.Object o)

Overrides:

equals in class java.lang.Object

toString

public java.lang.String toString()

Overrides:

toString in class java.lang.Object