The Odd Exponentiated Half-Logistic Exponential Distribution: Estimation Methods and Application to Engineering Data

Maha A. D. Aldahlan and Ahmed Z. Afify
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Maha A. D. Aldahlan: Department of Statistics, College of Science, University of Jeddah, Jeddah 21944, Saudi Arabia
Ahmed Z. Afify: Department of Statistics, Mathematics and Insurance, Benha University, Benha 13511, Egypt

Mathematics, 2020, vol. 8, issue 10, 1-26

Abstract: In this paper, we studied the problem of estimating the odd exponentiated half-logistic exponential (OEHLE) parameters using several frequentist estimation methods. Parameter estimation provides a guideline for choosing the best method of estimation for the model parameters, which would be very important for reliability engineers and applied statisticians. We considered eight estimation methods, called maximum likelihood, maximum product of spacing, least squares, Cramér–von Mises, weighted least squares, percentiles, Anderson–Darling, and right-tail Anderson–Darling for estimating its parameters. The finite sample properties of the parameter estimates are discussed using Monte Carlo simulations. In order to obtain the ordering performance of these estimators, we considered the partial and overall ranks of different estimation methods for all parameter combinations. The results illustrate that all classical estimators perform very well and their performance ordering, based on overall ranks, from best to worst, is the maximum product of spacing, maximum likelihood, Anderson–Darling, percentiles, weighted least squares, least squares, right-tail Anderson–Darling, and Cramér–von-Mises estimators for all the studied cases. Finally, the practical importance of the OEHLE model was illustrated by analysing a real data set, proving that the OEHLE distribution can perform better than some well known existing extensions of the exponential distribution.

Keywords: Anderson–Darling estimation; exponential distribution; maximum likelihood; maximum product of spacing; simulation; weighted least squares (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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