Asymptotic properties of maximum likelihood estimator for some discrete distributions generated by

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 generated by Cauchy stable law are investigated. The existence, strong consistency, asymptotic normality and asymptotic efficiency of that is established