ESTIMATION OF THE LOCATION AND SCALE PARAMETERS OF MOYAL DISTRIBUTION

Özet

Abstract.In this study, we estimate the parameters of the Moyal distribution by usingwell-known and widely-used maximum likelihood (ML) and method of moments (MoM)methodologies. The ML estimators of the location and scale parameters of the Moyaldistribution cannot be obtained in closed forms therefore iterative methods should beutilized. To make the study complete, modifed ML (MML) estimators for the locationand the scale parameters of the Moyal distribution are also derived. The MML estimatorsare in closed forms and asymptotically equivalent to the ML estimators. Efficiencies of theMML estimators are compared with their ML and MoM counterparts using Monte-Carlo(MC) simulation study. Results of the simulation study show that the ML estimatorsare more efficient than the MML and MoM estimators for small sample sizes. Howeverwhen the sample size increases performances of the ML and MML estimators are almostsame in terms of the Defficiency (Def) criterion as expected. At the end of the study, areal data set is used to show the implementation of the methodology developed in this paper.