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Generalized renewal sequences and infinitely divisible lattice distributions

Author

Listed:
  • van Harn, K.
  • Steutel, F. W.

Abstract

We introduce an increasing set of classes [Gamma]a (0[less-than-or-equals, slant][alpha][less-than-or-equals, slant]1) of infinitely divisible (i.d.) distributions on {0,1,2,...}, such that [Gamma]0 is the set of all compound-geometric distributions and [Gamma]1 the set of all compound-Poisson distributions, i.e. the set of all i.d. distributions on the non-negative integers. These classes are defined by recursion relations similar to those introduced by Katti [4] for [Gamma]1 and by Steutel [7] for [Gamma]0. These relations can be regarded as generalizations of those defining the so-called renewal sequences (cf. [5] and [2]). Several properties of i.d. distributions now appear as special cases of properties of the [Gamma]a'.

Suggested Citation

  • van Harn, K. & Steutel, F. W., 1977. "Generalized renewal sequences and infinitely divisible lattice distributions," Stochastic Processes and their Applications, Elsevier, vol. 5(1), pages 47-55, February.
    • Handle: RePEc:eee:spapps:v:5:y:1977:i:1:p:47-55
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