Application of MML methodology to an $alpha$ series process with Weibull distribution

Abstract

In an $alpha$ -series process, explicit estimators of the parameters $alpha$ , $mu$ and $sigma^2$ are obtained by using the methodology of modified maximum likelihood (MML) when the distribution of the first occurrence time of an event is assumed to be Weibull. Monte Carlo simulations are performed to compare the efficiencies of the MML estimators with the corresponding nonparametric (NP) estimators. We also apply the MML methodol- ogy to two real life data sets to show the performance of the MML estimators compared to the NP estimators.