Analysis of a new extension version of the exponential model using improved adaptive progressive censored data and its applications

Author:

Alqasem Ohud A.1,Elshahhat Ahmed2ORCID,Abd Elwahab Maysaa Elmahi1,Nassar Mazen34ORCID

Affiliation:

1. Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University 1 , P.O. Box 84428, Riyadh 11671, Saudi Arabia

2. Faculty of Technology and Development, Zagazig University 2 , Zagazig 44519, Egypt

3. Department of Statistics, Faculty of Science, King Abdulaziz University 3 , Jeddah 21589, Saudi Arabia

4. Department of Statistics, Faculty of Commerce, Zagazig University 4 , Zagazig 44519, Egypt

Abstract

This article covers the issue of evaluating the two shape parameters and reliability metrics of a novel Kumaraswamy-exponential lifetime distribution, whose density exhibits a left-skewed, right-skewed, or symmetric shape, through a type-II improved adaptive progressively censored sample. Both conventional and Bayesian viewpoints are used to evaluate the various parameters, which include point and interval estimations. While the estimation of one of the shape parameters requires a numerical solution, the other shape parameter estimation can be carried out in closed form by the classical method. Besides, the likelihood method’s asymptotic traits are employed to provide interval estimations for all parameters. Leveraging the Markov chain Monte Carlo process, the symmetric squared loss function and independent gamma priors are taken into account for calculating Bayes points and the highest posterior density interval estimations. To illustrate the accuracy, compare estimation methods, and show the applicability of the various suggested methods, a simulation examination and a pair of applications are looked at. In the end, four accuracy indicators are taken into consideration to figure out the best progressive censoring pattern. The numerical results indicate that when collecting samples using the suggested censored procedure, it is advisable to use the Bayesian estimation approach for evaluating the Kumaraswamy-exponential distribution.

Funder

Princess Nourah Bint Abdulrahman University

Publisher

AIP Publishing

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