Statistical inference for geometric process with the Rayleigh distribution

Authors : Cenker BİÇER, Hayrinisa DEMİRCİ BİÇER, Mahmut KARA, Halil AYDOĞDU

Pages : 149-160

Doi:10.31801/cfsuasmas.443690

View : 16 | Download : 8

Publication Date : 2019-02-01

Article Type : Research Paper

Abstract :The aim of this study is to investigate the solution of the statistical inference problem for the geometric process insert ignore into journalissuearticles values(GP); when the distribution of first occurrence time is assumed to be Rayleigh. Maximum likelihood insert ignore into journalissuearticles values(ML); estimators for the parameters of GP, where a and λ 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 different parameter values to compare the estimation performances of the obtained ML estimators with the non-parametric modified moment insert ignore into journalissuearticles values(MM); estimators. The results of the simulation studies show that the obtained estimators are more efficient than the MM estimators.
Keywords : Parameter estimation, geometric process, maximum likelihood estimators, asymptotic distribution