STATISTICAL INFERENCE FOR GEOMETRIC PROCESS WITH THE RAYLEIGH DISTRIBUTION

Abstract

The aim of this study is to investigate the solution of the statisticalinference problem for the geometric process (GP) when the distribution of Örstoccurrence time is assumed to be Rayleigh. Maximum likelihood (ML) estimators for the parameters of GP, where a and are the ratio parameter of GP andscale parameter of Rayleigh distribution, respectively, are obtained. In addition, we derive some important asymptotic properties of these estimators suchas normality and consistency. Then we run some simulation studies by di§erent parameter values to compare the estimation performances of the obtainedML estimators with the non-parametric modiÖed moment (MM) estimators.The results of the simulation studies show that the obtained estimators aremore e¢ cient than the MM estimators.