# Poisson Distribution

 Probability Home Poisson Distribution

The cumulative distribution function of a random variable X distributed according to the Poisson distribution with shape parameter λ (the mean) has zero slope everywhere except where a jump occurs, F(x) = P(X ≤ x), given by
F(x) =
 0 for x < 0 e- λ  Σi=0[x]  λi / i! for 0 ≤ x

The corresponding probability point distribution, f(i), i = 0,..., is
 f(i) = e- λ λi / i! for i = 0,...,

#### Function List

• double Poisson_Cumulative_Distribution( int k, double mu )

This function returns F(k) where F(k) is described above.

• double Poisson_Point_Distribution( int n, int k, double p )

This function returns f(k) where f(k) is described above.

• void Poisson_Distribution_Tables( int size, double mu, double* pr, double* cumulative )

This function returns f(k) where f(k) is described above for k = 0,...,n in the array pr and returns F(k) where F(k) is described above for k = 0,...,n in the array cumulative.

#### Source Code

C source code is available for these routines: