in probability theory and statistics, the poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event.[1] it is named after french mathematician siméon denis poisson (/ˈpwɑːsɒn/; french pronunciation: ​[pwasɔ̃]). the poisson distribution can also be used for the number of events in other specified interval types such as distance, area or volume.

for instance, a call center receives an average of 180 calls per hour, 24 hours a day. the calls are independent; receiving one does not change the probability of when the next one will arrive. the number of calls received during any minute has a poisson probability distribution: the most likely numbers are 2 and 3 but 1 and 4 are also likely and there is a small probability of it being as low as zero and a very small probability it could be 10. another example is the number of decay events that occur from a radioactive source during a defined observation period.

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