Volume 8, Issue 3 (March 2021), Pages: 57-62

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 Original Research Paper

 Title: Comparison of classical and Bayesian estimators to estimate the parameters in Weibull distribution under weighted general entropy loss function

 Author(s): Fuad Alduais ^{1, 2,} *

 Affiliation(s):

 ¹Mathematics Department, College of Humanities and Science in Al Aflaj, Prince Sattam Bin Abdulaziz University, Al-Kharj, Saudi Arabia
 ²Business Administration Department, Administrative Science College, Thamar University, Thamar, Yemen

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 * Corresponding Author. 

  Corresponding author's ORCID profile: https://orcid.org/0000-0002-6798-6295

 Digital Object Identifier: 

 https://doi.org/10.21833/ijaas.2021.03.008

 Abstract:

In this work, we have developed a General Entropy loss function (GE) to estimate parameters of Weibull distribution (WD) based on complete data when both shape and scale parameters are unknown. The development is done by merging weight into GE to produce a new loss function called the weighted General Entropy loss function (WGE). Then, we utilized WGE to derive the parameters of the WD. After, we compared the performance of the developed estimation in this work with the Bayesian estimator using the GE loss function. Bayesian estimator using square error (SE) loss function, Ordinary Least Squares Method (OLS), Weighted Least Squared Method (WLS), and maximum likelihood estimation (MLE). Based on the Monte Carlo simulation method, those estimators are compared depending on the mean squared errors (MSE’s). The results show that the performance of the Bayes estimator under developed method (WGE) loss function is the best for estimating shape parameters in all cases and has good performance for estimating scale parameter. 

 © 2021 The Authors. Published by IASE.

 This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

 Keywords: Weighted general entropy, Bayesian estimation, Weibull distribution, Classical estimation

 Article History: Received 29 August 2020, Received in revised form 19 November 2020, Accepted 21 November 2020

 Acknowledgment:

This Publication was supported by the Deanship of Scientific Research at Prince Sattam bin Abdulaziz University.

 Compliance with ethical standards

 Conflict of interest: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

 Citation:

  Alduais F (2021). Comparison of classical and Bayesian estimators to estimate the parameters in Weibull distribution under weighted general entropy loss function. International Journal of Advanced and Applied Sciences, 8(3): 57-62

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