Traffic accidents, equipment failures, floods and many other kinds of event occur randomly in time. This chapter describes a few standard distributions that arise with these kinds of processes if a few assumptions can be made about the randomness of the events.

The Poisson distribution describes the number of events that occur in a fixed period of time.

The exponential distribution describes the time until the first event in the process, and also the time between successive events.

The time until the k'th event in the process has an Erlang distribution.

With related assumptions, the lifetime (or survival time) of an item also has an exponential distribution.