Characterization of the special discrete distributions through infinite, noninfinite and finite divisibility

Edward J. Danial

Statistics & Probability Letters, 1989, vol. 8, issue 1, 1-7

Abstract: The negative binomial and the geometric are characterized in terms of the necessary and sufficient conditions for the infinite and finite divisibility of discrete distributions. The Poisson is characterized in terms of the necessary and sufficient conditions for the finite divisibility of discrete distributions. Finally, the binomial, Bernoulli and uniform distributions are characterized in terms of the necessary and sufficient conditions for the noninfinite divisibility of discrete distributions. The significance of these characterizations is briefly discussed.

Keywords: necessary; and; sufficient; conditions; induction; combinatorial; properties; infinite; vectors; and; matrices (search for similar items in EconPapers)
Date: 1989
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