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.

**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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