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On a class of discrete distributions arising from the birth-death-with-immigration process. (English) Zbl 0854.60016
Summary: This paper considers a class of distributions which may be regarded as the convolution of a negative binomial and a stopped-sum generalized hypergeometric factorial-moment random variables. Some properties are derived and it is shown that this class of distributions is a subset of distributions for the birth-and-death process with immigration (also reversible counter system). Formulations by mixing, limiting distributions and maximum likelihood equations are also discussed.

60E05 Probability distributions: general theory
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
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