Advances and Applications in Statistics
Volume 3, Issue 3, Pages 255 - 266
(December 2003)
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ON DISCRETE STABLE LAWS
K. Jayakumar (India) and P. C. Sreenivas (India)
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R+
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 [
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.