poisson

Probability mass function

Distribution

Mean

Variance

The Poisson distribution is a discrete distribution bounded at 0 on the low side and unbounded on the high side. The Poisson distribution is a limiting form of the Hypergeometric distribution.

The Poisson distribution finds frequent use because it represents the infrequent occurrence of events whose rate is constant. This includes many types of events in time or space such as arrivals of telephone calls, defects in semiconductor manufacturing, defects in all aspects of quality control, molecular distributions, stellar distributions, geographical distributions of plants, shot noise, etc. It is an important starting point in queuing theory and reliability theory. Note that the time between arrivals (defects) is Exponentially distributed, which makes this distribution a particularly convenient starting point even when the process is more complex. The Poisson distribution peaks near lambda and falls off rapidly on either side.

Samples

poisson(double lambda)

Description

Generates a sample of the Poisson distribution.

Parameters

Name

Type

Description

lambda

double

the rate of occurrence

Result

Type

Description

int

the generated sample


poisson(double lambda, java.util.Random r)

Description

Generates a sample of the Poisson distribution using the specified random number generator.

Parameters

Name

Type

Description

lambda

double

the rate of occurrence

r

java.util.Random

the random number generator

Result

Type

Description

int

the generated sample

This document includes content from the Stat::Fit User's Manual. Copyright 2016 Geer Mountain Software Corp.