Poisson Distributions

Definition

A distribution for count data. A lovely history that emerged from seeing how many soldiers died from being kicked by a horse:

where $k$ is the number of occurrences. And $\lambda$ is the rate.

Properties

• Mean: $\lambda$
• Variance: $\lambda$
• The sum of i.id Poisson-distributed random variables is also Poisson distributed.
• The difference between Poisson-distributed random variables follows a Skellam distribution (see Other distributions)

Relationship

• The Poisson distribution is the limit of a Binomial Distribution.
• If data is overdispersed (greater variance than expected), it could be wiser to use the Negative Binomial Distribution

Usage

• I have seen it used with the

History