Abstract: It
is known that every distribution onR+
is
the weak limit of a sequence of distributions
with rational Laplace-Stieltjes transform (of
mixtures with positive weights of gamma
distribution). Steutel and van Eenige [Comm.
Stat.-Stochastic Models 13 (1997), 271-274]
looked at the discrete analogue of this
result. Here we look into the role of the
discrete Mittag-Leffler distributions in the
study of approximation of distributions on Z+.The
concept of Poisson mixtures is generalized to
discrete stable mixtures. It is shown that
distributions on Z+that
can be approximated by mixtures of generalized
discrete Linnik distributions are discrete
stable mixtures. Discrete semi-stable
autoregressive process is introduced. As a
special case, we study discrete stable
autoregressive process.