The Exponentiated Burr–Hatke Distribution and Its Discrete Version: Reliability Properties with CSALT Model, Inference and Applications
Continuous and discrete distributions are essential to model both continuous and discrete lifetime data in several applied sciences. This article introduces two extended versions of the Burr–Hatke model to improve its applicability. The first continuous version is called the exponentiated Burr–Hatke...
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doaj-6e26a214501f4271a73b32570afc79902021-09-26T00:38:24ZengMDPI AGMathematics2227-73902021-09-0192277227710.3390/math9182277The Exponentiated Burr–Hatke Distribution and Its Discrete Version: Reliability Properties with CSALT Model, Inference and ApplicationsMahmoud El-Morshedy0Hassan M. Aljohani1Mohamed S. Eliwa2Mazen Nassar3Mohammed K. Shakhatreh4Ahmed Z. Afify5Department of Mathematics, Faculty of Science, Prince Sattam Bin Abdulaziz University, Al-Kharj 16278, Saudi ArabiaDepartment of Mathematics & Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, EgyptDepartment of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi ArabiaDepartment of Mathematics and Statistics, Jordan University of Science and Technology, P.O. Box 3030, Irbid 22110, JordanDepartment of Statistics, Mathematics and Insurance, Benha University, Benha 13511, EgyptContinuous and discrete distributions are essential to model both continuous and discrete lifetime data in several applied sciences. This article introduces two extended versions of the Burr–Hatke model to improve its applicability. The first continuous version is called the exponentiated Burr–Hatke (EBuH) distribution. We also propose a new discrete analog, namely the discrete exponentiated Burr–Hatke (DEBuH) distribution. The probability density and the hazard rate functions exhibit decreasing or upside-down shapes, whereas the reversed hazard rate function. Some statistical and reliability properties of the EBuH distribution are calculated. The EBuH parameters are estimated using some classical estimation techniques. The simulation results are conducted to explore the behavior of the proposed estimators for small and large samples. The applicability of the EBuH and DEBuH models is studied using two real-life data sets. Moreover, the maximum likelihood approach is adopted to estimate the parameters of the EBuH distribution under constant-stress accelerated life-tests (CSALTs). Furthermore, a real data set is analyzed to validate our results under the CSALT model.https://www.mdpi.com/2227-7390/9/18/2277CSALT modelsurvival discretization approachBurr–Hatke distributionestimation techniquesdata analysis |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Mahmoud El-Morshedy Hassan M. Aljohani Mohamed S. Eliwa Mazen Nassar Mohammed K. Shakhatreh Ahmed Z. Afify |
spellingShingle |
Mahmoud El-Morshedy Hassan M. Aljohani Mohamed S. Eliwa Mazen Nassar Mohammed K. Shakhatreh Ahmed Z. Afify The Exponentiated Burr–Hatke Distribution and Its Discrete Version: Reliability Properties with CSALT Model, Inference and Applications Mathematics CSALT model survival discretization approach Burr–Hatke distribution estimation techniques data analysis |
author_facet |
Mahmoud El-Morshedy Hassan M. Aljohani Mohamed S. Eliwa Mazen Nassar Mohammed K. Shakhatreh Ahmed Z. Afify |
author_sort |
Mahmoud El-Morshedy |
title |
The Exponentiated Burr–Hatke Distribution and Its Discrete Version: Reliability Properties with CSALT Model, Inference and Applications |
title_short |
The Exponentiated Burr–Hatke Distribution and Its Discrete Version: Reliability Properties with CSALT Model, Inference and Applications |
title_full |
The Exponentiated Burr–Hatke Distribution and Its Discrete Version: Reliability Properties with CSALT Model, Inference and Applications |
title_fullStr |
The Exponentiated Burr–Hatke Distribution and Its Discrete Version: Reliability Properties with CSALT Model, Inference and Applications |
title_full_unstemmed |
The Exponentiated Burr–Hatke Distribution and Its Discrete Version: Reliability Properties with CSALT Model, Inference and Applications |
title_sort |
exponentiated burr–hatke distribution and its discrete version: reliability properties with csalt model, inference and applications |
publisher |
MDPI AG |
series |
Mathematics |
issn |
2227-7390 |
publishDate |
2021-09-01 |
description |
Continuous and discrete distributions are essential to model both continuous and discrete lifetime data in several applied sciences. This article introduces two extended versions of the Burr–Hatke model to improve its applicability. The first continuous version is called the exponentiated Burr–Hatke (EBuH) distribution. We also propose a new discrete analog, namely the discrete exponentiated Burr–Hatke (DEBuH) distribution. The probability density and the hazard rate functions exhibit decreasing or upside-down shapes, whereas the reversed hazard rate function. Some statistical and reliability properties of the EBuH distribution are calculated. The EBuH parameters are estimated using some classical estimation techniques. The simulation results are conducted to explore the behavior of the proposed estimators for small and large samples. The applicability of the EBuH and DEBuH models is studied using two real-life data sets. Moreover, the maximum likelihood approach is adopted to estimate the parameters of the EBuH distribution under constant-stress accelerated life-tests (CSALTs). Furthermore, a real data set is analyzed to validate our results under the CSALT model. |
topic |
CSALT model survival discretization approach Burr–Hatke distribution estimation techniques data analysis |
url |
https://www.mdpi.com/2227-7390/9/18/2277 |
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