It is well suited for modeling various physical phenomena.
A basic introduction to the concept
Certain events happen at unpredictable intervals. But for some reason, no matter how recent or long ago last event was, the probability that another event will occur within the next hour is exactly the same (say, 10%). The same holds for any other time interval (say, second). Moreover, the number of events within any given time interval is statistically independent of numbers of events in other intervals that do not overlap the given interval. Also, two events never occur simultaneously.
Then the number of events per day is Poisson distributed.
Let X be a stochastic variable taking non-negative integer values with probability density function
Then X follows the Poisson distribution with parameter .
Characteristics of the Poisson distribution
If X is a Poisson distribution stochastic variable with parameter , then
- Binomial distribution
- Exponential distribution
- Probability distribution
- Probability theory