On the Maximum Likelihood Estimators for some Generalized Pareto-like Frequency Distribution

In this paper we consider some four-parametric, so-called Generalized Pareto-like Frequency Distribution, which have been constructed using stochastic Birth-Death Process in order to model phenomena arising in Bioinformatics (Astola and Danielian, 2007). As examples, two ”real data” sets on the number of proteins and number of residues for analyzing such distribution are given. The conditions of coincidence of solution for the system of Likelihood Equations with the Maximum Likelihood Estimators (MLE) for the parameters of this distribution are also investigated. In addition, we propose Accumulation Method as a recurrence method for approximate computation of the MLE of the parameters. Simulation studies are done.