Bayesian Parameter Estimation for Geometric Process with Rayleigh Distribution

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Bitlis Eren Üniversitesi Fen Bilimleri Dergisi
Volume:13 Issue:2
Bayesian Parameter Estimation for Geometric Process with Rayleigh Distribution

Bayesian Parameter Estimation for Geometric Process with Rayleigh Distribution

Authors : Asuman Yılmaz

Pages : 482-491

Doi:10.17798/bitlisfen.1433870

View : 54 | Download : 64

Publication Date : 2024-06-29

Article Type : Research Paper

Abstract :The main purpose of this study is to deal with the parameter estimation problem for the geometric process (GP) when the distribution of the first occurrence time of an event is assumed to be Rayleigh. For this purpose, maximum likelihood and Bayesian parameter estimation methods are discussed. Lindley and MCMC approximation methods are used in Bayesian calculations. Additionally, a novel method called the Modified-Lindley approximation has been proposed as an alternative to the Lindley approximation. An extensive simulation study was conducted to compare the performances of the prediction methods. Finally, a real data set is analyzed for illustrative purposes.
Keywords : Rayleigh distribution, Geometric process, Maximum likelihood estimator, Bayesian parameter estimation, Simulation study

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