Compound Poisson process: Difference between revisions

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where, <math> \{\,N(t) : t \geq 0\,\}</math> is a counting of a [[Poisson process]] with rate <math>\lambda</math>, and <math> \{\,D_i : i \geq 1\,\}</math> are independent and identically distributed random variables, with distribution function ''G'', which are also independent of <math> \{\,N(t) : t \geq 0\,\}.\,</math>

When <math> D_i </math> are non-negative integer-valued random variables, then this compound Poisson process is known as a '''stuttering Poisson process which has the feature that two or more events occur in a very short time.{{vague|reason=How is "a very short time" defined?|date=January 2023}}'''

==Properties of the compound Poisson process==