Poisson Distribution Calculator, Formula and Examples

Poisson Distribution is a discrete probability function used to estimate the probability of x-success events in very large n-number of trials in probability and statistics experiments. It's often related to rare events where the number of trials are indefinitely large and the probability of success P(x) is very small. This discrete probability function follows the laws of exponent. Since P(x) is very small, the negative probability becomes very large which almost equals to 1. The parameter λ = m = np equals to mean and variance of Poisson distribution and the standard deviation equals to √λ where n is the number of trials and p is the probability of success.

The assumptions for Poisson distribution are
(i) The events are exclusive and non-mutual. Any event does not affect the occurance of other events.
(ii) The probability of more than one success is negligible.
(iii) The time interval for probability of success P(x) is directly proportional to the time interval for the length n independent trials.

The below formula is the mathematical representation for Poisson probability distribution to find P(x) in n number of large trials where the probability of success rate is very small. Users can refer the below Poisson formula to know what are all the input parameters are being used to find P(x) in the statistical experiments and use this calculator to verify the results of manual computations or generate the step by step calculation for the corresponding input values.