Poisson Distribution Calculator

Definition

The Poisson distribution, the discrete probability function, is used to estimate the extent to which propagation occurs with a known average rate. When an experimental situation occurs, a large number of possible events occur, and the Poisson distribution specifies the probability of a given data set or the number of fixed-time events. It is an asymmetrical function and is applied in conjunction with hypergeometric distribution, binomial distribution and exponential distribution.

Poisson distribution, where k = 0, 1, 2, ..., n can be calculated from the following formula

\(f((k;λ)= \frac {λ^ke^{-λ}}{k!}\)

Where?

e is the cardinality of the natural logarithm equal to 2.71828..

k is the number of events that occur; the probability is given by the given function

K is the factorial of k

λ is a positive real number equal to the expected number of occurrences within a given time interval. For example, if an event occurs on average 3 times per minute, and one is a probability event that wants to occur k times at a 10-minute interval, one would use the Poisson distribution model λ=10×3=30.