Abstract
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.
Highlights
Statistical distributions are very important in predicting and describing different realworld phenomena
This section is devoted to exploring the performance of several estimators by the following algorithm
The simulation results are obtained based on 8 combinations of the parameters, i.e., α = 0.50, 1.50, 3.00 and β = 0.50, 1.50, 3.00
Summary
Statistical distributions are very important in predicting and describing different realworld phenomena. Considerable efforts over the last few years have been expended in constructing more flexible generalized distributions to model several real data sets encountered in different applied fields such as medicine, insurance, economics, engineering, and agriculture, among others. Exponentiated models and their successful applications in several applied sciences have been prevalent in the statistical literature. One of the most widely adopted generalization techniques is the exponentiated-G (Exp-G) class that can be traced back to [1] This technique of generalization has received significant attention in the last three decades, and more than forty Exp-G distributions have been published. Some notable models include the Exp-Weibull [2], Exp-exponential [3], Exp-gamma, Exp-Fréchet and ExpGumbel [4], Exp-generalized modified-Weibull [5], Exp-Weibull Pareto [6], Exp-Weibull family [7], and Exp Chen-G family [8], among others
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