Modified generalized Weibull distribution: theory and applications.

Autor: Shama MS; Department of Basic Sciences, CFY, King Saud University, Riyadh, 12373, Saudi Arabia.; Department of Mathematics and Statistics, Osim Higher Institute of Administrative Science, Osim, 12961, Egypt., Alharthi AS; Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif, 21944, Saudi Arabia., Almulhim FA; Department of Mathematical Sciences, College of Sciences, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh, 11671, Saudi Arabia., Gemeay AM; Department of Mathematics, Faculty of Science, Tanta University, Tanta, 31527, Egypt., Meraou MA; Laboratory of Statistics and Stochastic Processes, University of Djillali Liabes, BP 89, 22000, Sidi Bel Abbès, Algeria., Mustafa MS; Department of Statistics, Faculty of Science, University of Tabuk, Tabuk, Saudi Arabia., Hussam E; Department of Mathematics, Faculty of Science, Helwan University, Cairo, Egypt. eslmhussam1986@gmail.com., Aljohani HM; Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif, 21944, Saudi Arabia.
Jazyk: angličtina
Zdroj: Scientific reports [Sci Rep] 2023 Aug 07; Vol. 13 (1), pp. 12828. Date of Electronic Publication: 2023 Aug 07.
DOI: 10.1038/s41598-023-38942-9
Abstrakt: This article presents and investigates a modified version of the Weibull distribution that incorporates four parameters and can effectively represent a hazard rate function with a shape resembling a bathtub. Its significance in the fields of lifetime and reliability stems from its ability to model both increasing and decreasing failure rates. The proposed distribution encompasses several well-known models such as the Weibull, extreme value, exponentiated Weibull, generalized Rayleigh, and modified Weibull distributions. The paper derives key mathematical statistics of the proposed distribution, including the quantile function, moments, moment-generating function, and order statistics density. Various mathematical properties of the proposed model are established, and the unknown parameters of the distribution are estimated using different estimation techniques. Furthermore, the effectiveness of these estimators is assessed through numerical simulation studies. Finally, the paper applies the new model and compares it with various existing distributions by analyzing two real-life time data sets.
(© 2023. Springer Nature Limited.)
Databáze: MEDLINE
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