On discrete distributions of order k. (English) Zbl 0611.60016

Charalambides, Ch. A.

Ann. Inst. Stat. Math. 38, 557-568 (1986).

The class of discrete distributions of order k is defined as the class of the generalized discrete distributions with generalizer a discrete distribution truncated at zero and from the right away from \(k+1\). The probability function and factorial moments of these distributions are expressed in terms of the (right) truncated Bell (partition) polynomials and several special cases are briefly examined. Finally a Poisson process of order k, leading in particular to the Poisson distribution of order k, is discussed.

MSC:

60E05	Probability distributions: general theory
62E10	Characterization and structure theory of statistical distributions

Keywords:

reliability models; generalized negative binomial distribution; truncated Bell polynomials; discrete distributions; factorial moments

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