information:classification, linguistic:translation, information:highlighting, structural:expansion
Poisson distribution of point counts

A Poisson point process is characterized via the Poisson distribution. The Poisson distribution is the probability distribution of a random variable N {\textstyle N} (called a Poisson random variable) such that the probability that N {\displaystyle \textstyle N} equals n {\displaystyle \textstyle n} is given by:

where n ! {\textstyle n!} denotes factorial and the parameter Λ {\textstyle \Lambda } determines the shape of the distribution. (In fact, Λ {\textstyle \Lambda } equals the expected value of N {\textstyle N}.)

By definition, a Poisson point process has the property that the number of points in a bounded region of the process's underlying space is a Poisson-distributed random variable.