THE ASYMPTOTIC PROPERTIES OF SOME DISCRETE DISTRIBUTIONS GENERATED BY LEVY’S LAW

Davood Farbod (Armenia)

Received April 6, 2008

Abstract

There are some frequency distributions in large-scale biomolecular systems having properties like stable densities. It is of interest to construct such frequency distributions. This paper is devoted to a special case of stable densities. The large sample distributions of the maximum-likelihood estimates (M.L.E.) of the scale parameter for some discrete distributions generated by Levy’s law are studied. It is shown the existence, strong consistency and asymptotic normality of that.

Keywords and phrases: stable laws, Levy’s law, maximum likelihood estimate (M.L.E.), asymptotic properties.