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For discrete distributions, explicit series representations are derived in terms of cumulative probabilities, yielding simple criteria for the existence of moments. Applications are presented for the zeta and Skellam distributions, illustrating how tail behavior determines moment finiteness and how moments can be represented geometrically through cumulative distribution functions. In addition, a representation for logarithmic moments is obtained, linking logarithmic means, Laplace transforms, and the classical Frullani identity.
The results provide a unified perspective on moment representations and establish useful connections between tail probabilities, distribution functions, Laplace transforms, and moment existence.
From: Roberto Vila Gabriel [view email]
[v1]
Fri, 12 Jun 2026 01:40:22 UTC (16 KB)
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