ASYMPTOTIC PROPERTIES OF MAXIMUM LIKELIHOOD ESTIMATOR FOR SOME DISCRETE DISTRIBUTIONS GENERATED BY CAUCHY STABLE LAW

摘要

In large-scale biomolecular sysrems there are frequency distribuions with properties like Stable Laws. It is of interest to construct such frequency distributions. In the present article we consider Cauchy stable law. The large-sample distribution of the Maximum Likelihood Estimator (M.L.E.) of the scale parameter for some discrete distributions gen-erated by Cauchy stable law are investigated. The existence, strong consistency, asymp-totic normality and asymptotic efficiency of that is established.