In probability and statistics, Poisson distribution is a probability distribution. It is named after Siméon Denis Poisson. It measures the probability that a certain number of events occur within a certain period of time. The events need to be unrelated to each other. They also need to occur with a known average rate, represented by the symbol (lambda).[1]
More specifically, if a random variable follows Poisson distribution with rate , then the probability of the different values of can be described as follows:[2][3]
for
Examples of Poisson distribution include:
The numbers of cars that pass on a certain road in a certain time
The number of telephone calls a call center receives per minute
The number of light bulbs that burn out (fail) in a certain amount of time
The number of mutations in a given stretch of DNA after a certain amount of radiation
The number of errors that occur in a system
The number of Property & Casualty insurance claims experienced in a given period of time