Statistical inference for geometric process with the Rayleigh distribution

Year 2019, Volume: 68 Issue: 1, 149 - 160, 01.02.2019

Cenker Biçer , Hayrinisa Demirci Biçer , Mahmut Kara , Halil Aydoğdu

https://doi.org/10.31801/cfsuasmas.443690

Cited By: 8

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 first occurrence time is assumed to be Rayleigh. Maximum likelihood (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 (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

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