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© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.

Abstract

In this article, two new families of distributions are proposed: the generalized log-Lindley-G (GLL-G) and its counterpart, the GLL*-G. These families can be justified by their relation to the log-Lindley model, an important assumption for describing social and economic phenomena. Specific GLL models are introduced and studied. We show that the GLL density is rewritten as a two-member linear combination of the exponentiated G-densities and that, consequently, many of its mathematical properties arise directly, such as moment-based expressions. A maximum likelihood estimation procedure for the GLL parameters is provided and the behavior of the resulting estimates is evaluated by Monte Carlo experiments. An application to repairable data is made. The results argue for the use of the exponential law as the basis for the GLL-G family.

Details

Title
An Extended log-Lindley-G Family: Properties and Experiments in Repairable Data
Author
Ahmed M T Abd El-Bar 1 ; Willams B F da Silva 2 ; Nascimento, Abraão D C 2   VIAFID ORCID Logo 

 Department of Mathematics, Faculty of Science, Tanta University, Tanta 400055, Egypt; Department of Mathematics, College of Science, Taibah University, Madina 41411, Saudi Arabia 
 Department of Statistics, Federal University of Pernambuco, Recife 50670-901, Brazil; [email protected] (W.B.F.d.S.); [email protected] (A.D.C.N.) 
First page
3108
Publication year
2021
Publication date
2021
Publisher
MDPI AG
e-ISSN
22277390
Source type
Scholarly Journal
Language of publication
English
ProQuest document ID
2608132835
Copyright
© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.