The Poisson distribution is a probability distribution . In probability theory and statistics , the Poisson distribution ( pronounced ) ( or Poisson law of small numbers ) is a discrete probability distribution that expresses the probability of a number of events occurring in a fixed period of time if these events occur with a known average rate and independently of the time since the last event . ( The Poisson distribution can also be used for the number of events in other specified intervals such as distance , area or volume . )