Summary
The class of discrete distributions of orderk is defined as the class of the generalized discrete distributions with generalizer a discrete distribution truncated at zero and from the right away fromk+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 orderk, leading in particular to the Poisson distribution of orderk, is discussed.
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Charalambides, C.A. On discrete distributions of orderk . Ann Inst Stat Math 38, 557–568 (1986). https://doi.org/10.1007/BF02482543
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DOI: https://doi.org/10.1007/BF02482543