Rates of convergence to stable and discrete stable laws

Discrete analogues of self-decomposability and stability were introduced in (Steutel and van Harn, 1979), where discrete stable laws occur with discrete domains of attraction. In the present paper rates of convergence for the distribution functions of certain sums or random sums of non-negative integer valued random variables to discrete stable as well as (continuous) stable limit laws are considered and discussed. Discrete Mittag-Leffler discrete Linnik as well as the Sibuya distributions are considered as examples. (orig.)Available from TIB Hannover: RR 4487(1998,36) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman