Bayesian Estimates Based On Record Values Under Weighted LINEX Loss Function

Fuad S. Al-Duais; Mohammed Alhagyan

doi:10.18187/pjsor.v16i1.2854

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Bayesian Estimates Based On Record Values Under Weighted LINEX Loss Function

Author(s)

Fuad S. Al-Duais Mathematics Department, College of Humanities and Science in Al Aflaj, Prince Sattam Bin Abdulaziz University, Al Aflaj, Saudia Arabia; Administration Department, Administrative Science College, Thamar University, Thamar, Yemen

Mohammed Alhagyan Mathematics Department, College of Humanities and Science in Al Aflaj, Prince Sattam Bin Abdulaziz University,Al Aflaj, Saudia Arabia

Abstract

In this paper, we developed linear exponential (LINEX) loss function by merging weights to produce weighted linear exponential (WLINEX) loss function. Then we utilized WLINEX to derive scale parameter and reliability function of the Weibull distribution based on record values when the shape parameter is known. After, we estimated scale parameter and reliability function of Weibull distribution by using maximum likelihood (ML) estimation and by several Bayes estimations. The Bayes estimates were obtained with respect to symmetric loss function (squared error loss (SEL)), asymmetric loss function (LINEX) and asymmetric loss function (WLINEX). The ML and the different Bayes estimates were compared via a Monte Carlo simulation study. The result of simulation mentioned that the proposed WLINEX loss function is promising and can be used in real environment especially at the case of underestimate where it revealed better performance than LINEX loss function for estimating scale parameter.

Publication Details

Page(s) 11-19

DOI 10.18187/pjsor.v16i1.2854

Published Journal: Pakistan Journal of Statistics and Operation Research, Volume: 16, Issue: 1, Year: 2020

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Keywords

Reliability, Bayesian estimate, Recorded values, Weighted Linex

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