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:<math>Y(t) = \sum_{i=1}^{N(t)} D_i</math>
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 .
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