STATISTICAL INFERENCE FOR GEOMETRIC PROCESS WITH THE RAYLEIGH DISTRIBUTION

Abstract

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