Mathematical Analysis and Convex Optimization
آنالیز ریاضی و بهینه سازی محدب
MACO
Basic Sciences
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2022
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Objective Bayesian Analysis For a Two-parameters Exponential Distribution
Applied Mathematics
Applied Mathematics
پژوهشي
Research Article
In any Bayesian inference problem, the posterior distribution is a product of the<br>
likelihood and the prior: thus, it is a ected by both in cases where one possesses little or no<br>
information about the target parameters in advance. In the case of an objective Bayesian<br>
analysis, the resulting posterior should be expected to be universally agreed upon by ev-<br>
eryone, whereas . subjective Bayesianism would argue that probability corresponds to the<br>
degree of personal belief. In this paper, we consider Bayesian estimation of two-parameter<br>
exponential distribution using the Bayes approach needs a prior distribution for parame-<br>
ters. However, it is dicult to use the joint prior distributions. Sometimes, by using linear<br>
transformation of reliability function of two-parameter exponential distribution in order to<br>
get simple linear regression model to estimation of parameters. Here, we propose to make<br>
Bayesian inferences for the parameters using non-informative priors, namely the (depen-<br>
dent and independent) Je reys' prior and the reference prior. The Bayesian estimation was<br>
assessed using the Monte Carlo method. The criteria mean square error was determined<br>
evaluate the possible impact of prior speci cation on estimation. Finally, an application on<br>
a real dataset illustrated the developed procedures.
Jeffreys' prior, two-parameters exponential distribution, objective Bayesian analysis, posterior distribution, MSE
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http://maco.lu.ac.ir/browse.php?a_code=A-10-138-1&slc_lang=en&sid=1
Mehdi
Jabbari Nooghabi
jabbarinm@um.ac.ir
`10031947532846001095`

10031947532846001095
Yes
Department of Statistics, Ferdowsi University of Mashhad, Mashhad, Iran.
Ali
Soori
ali.sori50@gmail.com
`10031947532846001096`

10031947532846001096
No
Department of Mathematics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran.
Parviz
Nasiri
pnasiri45@pnasiri@pnu.ac.ir
`10031947532846001097`

10031947532846001097
No
Department of Statistics, University of Payam Noor, 19395-4697 Tehran, Iran.
Farshin
Hormozinejad
hormozi-nejad@iauahvaz.ac.ir
`10031947532846001098`

10031947532846001098
No
Department of Mathematics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran.
Mohammadreza
Ghalani
m_ghalani@yahoo.com
`10031947532846001099`

10031947532846001099
No
Department of Mathematics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran.