Poisson distribution is a discrete distribution, one of the most important limiting cases of binomial distribution. The binomial distribution converges towards the Poisson distribution as the number of trials goes to infinity while the product np=λ remains fixed. Therefore, random variable having Poisson distribution with parameter λ takes non-negative values with probability

Cumulative distribution function is

Parameter λ is both mean and variance of a random variable.

Classical example of a random variable having Poisson distribution is a number of cars which pass through a road section in a given period of time. We can also mention such examples as a number of stars in the given area of the sky, a number of errors in the text of a given length, a number of phone calls in a call-center, number of web-server requests in a given period of time.

Algorithms

PoissonDistribution and PoissonCDistribution are used to calculate the areas under the left and right tails of the graph (i.e. to calculate the cumulative distribution function and its own complement). InvPoissonDistribution subroutine calculates the inverse cumulative distribution function (finds such λ that F_λ (x)=y).

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C#

C# 1.0 source.
poissondistr.csharp.zip - Poisson distribution

C++

C++ source.
poissondistr.cpp.zip - Poisson distribution
ablas.zip - optimized basic linear algebra subroutines with SSE2 support (for C++ sources only)

Delphi

Delphi source.
Can be compiled under FPC (in Delphi compatibility mode).
poissondistr.delphi.zip - Poisson distribution

Visual Basic 6

Visual Basic 6 source.
poissondistr.vb6.zip - Poisson distribution

Zonnon ^beta

Zonnon source.
Zonnon is an experimental language developed at ETH Zurich.
See www.zonnon.ethz.ch for more information.
poissondistr.zonnon.zip - Poisson distribution