What is Poisson distribution?

Data Science, AI and ML
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The Poisson distribution, named after the French mathematician Denis Simon Poisson, is a discrete distribution function describing the probability that an event will occur a certain number of times in a fixed time (or space) interval.

Poisson Distribution Formula

Central to the Poisson distribution is the parameter lambda, which describes the rate at which events are happening. For a Poisson random variable X, lambda is simply the mean number of events x happening per interval. The probability mass function is

Example:

  • Number of arrivals at a restaurant
  • Number of calls per hour in a call center

Conditions for Poisson Distribution:

  • An event can occur any number of times in the defined period of time
  • All the events are independent
  • The rate of occurrence of events is constant

f(x,λ)=P(X=x)= [(λ^x). (e)^(−λ)/x!]

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