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Estimating Weibull Parameters Using Least Squares and Multilayer Perceptron vs. Bayes Estimation

Walid Aydi1,3,*, Fuad S. Alduais2,4
1 Department of Computer Science, College of Humanities and Science in Al Aflaj, Prince Sattam Bin Abdulaziz University, Al-Aflaj, Saudi Arabia
2 Department of Mathematics, College of Humanities and Science in Al Aflaj, Prince Sattam Bin Abdulaziz University, Al-Aflaj, Saudi Arabia
3 Laboratory of Electronics & Information Technologies, Sfax University, Sfax, Tunisia
4 Department of Administration, Administrative Science College, Thamar University, Yemen
* Corresponding Author: Walid Aydi. Email:
(This article belongs to this Special Issue: Emerging Applications of Artificial Intelligence, Machine learning and Data Science)

Computers, Materials & Continua 2022, 71(2), 4033-4050.

Received 28 August 2021; Accepted 25 October 2021; Issue published 07 December 2021


The Weibull distribution is regarded as among the finest in the family of failure distributions. One of the most commonly used parameters of the Weibull distribution (WD) is the ordinary least squares (OLS) technique, which is useful in reliability and lifetime modeling. In this study, we propose an approach based on the ordinary least squares and the multilayer perceptron (MLP) neural network called the OLSMLP that is based on the resilience of the OLS method. The MLP solves the problem of heteroscedasticity that distorts the estimation of the parameters of the WD due to the presence of outliers, and eases the difficulty of determining weights in case of the weighted least square (WLS). Another method is proposed by incorporating a weight into the general entropy (GE) loss function to estimate the parameters of the WD to obtain a modified loss function (WGE). Furthermore, a Monte Carlo simulation is performed to examine the performance of the proposed OLSMLP method in comparison with approximate Bayesian estimation (BLWGE) by using a weighted GE loss function. The results of the simulation showed that the two proposed methods produced good estimates even for small sample sizes. In addition, the techniques proposed here are typically the preferred options when estimating parameters compared with other available methods, in terms of the mean squared error and requirements related to time.


Weibull distribution; maximum likelihood; ordinary least squares; MLP neural network; weighted general entropy loss function

Cite This Article

W. Aydi and F. S. Alduais, "Estimating weibull parameters using least squares and multilayer perceptron vs. bayes estimation," Computers, Materials & Continua, vol. 71, no.2, pp. 4033–4050, 2022.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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