A New Extended Model with Bathtub-Shaped Failure Rate: Properties, Inference, Simulation, and Applications

Alya Al Mutairi, Muhammad Z. Iqbal, Muhammad Z. Arshad, Badr Alnssyan, Hazem Al-Mofleh and Ahmed Z. Afify
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Alya Al Mutairi: Department of Mathematics, Faculty of Science, Taibah University, Medina 42353, Saudi Arabia
Muhammad Z. Iqbal: Department of Mathematics and Statistics, University of Agriculture, Faisalabad, Punjab 38000, Pakistan
Muhammad Z. Arshad: Department of Mathematics and Statistics, University of Agriculture, Faisalabad, Punjab 38000, Pakistan
Badr Alnssyan: Department of Administrative Sciences and Humanities, Community College of Buraydah, Qassim University, Buraydah 51452, Saudi Arabia
Hazem Al-Mofleh: Department of Mathematics, Tafila Technical University, Tafila 66110, Jordan
Ahmed Z. Afify: Department of Statistics, Mathematics and Insurance, Benha University, Benha 13511, Egypt

Mathematics, 2021, vol. 9, issue 17, 1-32

Abstract: Theoretical and applied researchers have been frequently interested in proposing alternative skewed and symmetric lifetime parametric models that provide greater flexibility in modeling real-life data in several applied sciences. To fill this gap, we introduce a three-parameter bounded lifetime model called the exponentiated new power function (E-NPF) distribution. Some of its mathematical and reliability features are discussed. Furthermore, many possible shapes over certain choices of the model parameters are presented to understand the behavior of the density and hazard rate functions. For the estimation of the model parameters, we utilize eight classical approaches of estimation and provide a simulation study to assess and explore the asymptotic behaviors of these estimators. The maximum likelihood approach is used to estimate the E-NPF parameters under the type II censored samples. The efficiency of the E-NPF distribution is evaluated by modeling three lifetime datasets, showing that the E-NPF distribution gives a better fit over its competing models such as the Kumaraswamy-PF, Weibull-PF, generalized-PF, Kumaraswamy, and beta distributions.

Keywords: power function distribution; exponentiated distribution; Rényi entropy; hazard rate function; moments; simulations; type II censoring scheme; maximum likelihood estimation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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