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where, <math> \{\,N(t) : t \geq 0\,\}</math> is 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 ''Y(t)'' are non-negative discrete random variable,then this compound Poisson distribution is named stuttering Poisson process which has the feature that two or more events occur in a very short time (arrive in group or batches). <ref name=Huiming>{{cite arxiv | first =Zhang | last = Huiming | coauthors = [[Lili Chu]],[[Yu Diao]]| title = Some Properties of the Generalized Stuttering Poisson Distribution and its Applications| eprint = arXiv:1207.6539v1| year = 2012 | class = math.ST }}</ref>
==Properties of the compound Poisson process==
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