Abstract

Based on record data, the estimation and prediction problems for normal distribution have been investigated by several authors in the frequentist set up. However, these problems have not been discussed in the literature in the Bayesian context. The aim of this paper is to consider a Bayesian analysis in the context of record data from a normal distribution. We obtain Bayes estimators based on squared error and linear-exponential (Linex) loss functions. It is observed that the Bayes estimators can not be obtained in closed forms. We propose using an importance sampling method to obtain Bayes estimators. Further, the importance sampling method is also used to compute Bayesian predictors of future records. Finally, a real data analysis is presented for illustrative purposes and Monte Carlo simulations are performed to compare the performances of the proposed methods. It is shown that Bayes estimators and predictors are superior than frequentist estimators and predictors.

Details

Title
Bayesian Inference and Prediction for Normal Distribution Based on Records
Author
Asgharzadeh, Akbar; Valiollahi, Reza; Fallah, Adeleh; Nadarajah, Saralees
Pages
15-36
Section
Articles
Publication year
2018
Publication date
2018
Publisher
Università degli Studi di Bologna, Department of Statistical Sciences, Alma Mater Studiorum
ISSN
0390590X
e-ISSN
19732201
Source type
Scholarly Journal
Language of publication
English
ProQuest document ID
2068732239
Copyright
© 2018. This work is licensed under http://creativecommons.org/licenses/by/3.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.