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Variations of Poisson Process

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Multivariate Poisson Process

 

Variable Rate Poisson Process

 

Compound Poisson Process

One of the conditions of the simple Poisson process is that "events occur singly", i.e. that the probability of two events occurring in a time interval is disapearingly small as the length of the interval tends to zero.

To introduce a model which gets round this restriction, consider a (simple) Poisson process, where each event consists of a random number of "sub-events", being at least one sub-event to each event. The distribution of the number of sub-events per event would have to be specified. Typically we would be interested in the total number of sub-events in a given time period.