A cumulative poisson distribution is used to calculate the probability of getting atleast n successes in a poisson experiment. Here, n is the poisson random variable which refers to the number of success.
P(x = 0) and P(x = 1) is calculated using poisson distribution formula.
Consider, in an office 2 customers arrived today. Calculate the possibility for atleast 3 customers to be arrived on tomorrow.
λ=2 , e=2.718 and x=3. P(x < 3) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) = e-2 λ0 / 0! + e-2 λ1 / 1! + e-2 λ2 / 2! + e-2 λ3 / 3! = 0.135 + 0.271 + 0.271 + 0.18 = 0.857 Hence there are atleast 85.7% possibilities for atleast 3 customers to be arrived on tomorrow.
Online tutorial on how to calculate the cumulative poisson distribution with definition, formula and example.