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