Poisson Distribution



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) =
0for 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: