The Poisson Distribution

The Poisson distribution models the number of occurrences of an event where each event has a constant probability of occurring. It is closely related to the The Exponential Distribution, which models the time between successive occurrences.

The Poisson distribution has one parameter, μ ('mu'), which specifies the mean number of occurrences per unit time.

Examples of applications of the Poisson distribution are:

• The number of cars passing a road that is not too busy.

• The number of failures of a piece of equipment that is replaced with identical copies when it fails.

The Poisson distribution is often used as an approximation for the The Binomial Distribution when the number of trials is very large and the probability of success is small.

The Poisson distribution is implemented by the PoissonDistribution class. It has one constructor which takes one argument: the mean number of events per unit time. The following constructs a Poisson distribution with mean 4.4:

var poisson = new PoissonDistribution(4.4);

Dim poisson = New PoissonDistribution(4.4)

let poisson = PoissonDistribution(4.4)

The PoissonDistribution class has no specific properties. The mean number of events per unit time is returned by the Mean property.

PoissonDistribution has one static (Shared in Visual Basic) method, Sample, which generates a random sample using a user-supplied uniform random number generator.

var random = new MersenneTwister();
int sample = PoissonDistribution.Sample(random, 4.4);

Dim random = New MersenneTwister()
Dim sample = PoissonDistribution.Sample(random, 4.4)

let random = MersenneTwister()
let sample = PoissonDistribution.Sample(random, 4.4)

The above example uses the MersenneTwister class to generate uniform random numbers.

For details of the properties and methods common to all discrete probability distribution classes, see the topic on Discrete Distributions.