The Exponentiated New XLindley Distribution‎: ‎Properties‎, ‎and Applications

‎ In this paper, we introduce a new extension of the XLindley distribution, called the exponentiated new XLindley ‎distribution.‎ The new model has an increasing or bathtub-shaped hazard rate function, making it suitable for modeling real-life phenomena. We study important properties of the new model, such as ‎the ‎moments, moment generating function, incomplete moments, mean deviations from the mean and ‎the ‎median, Bonferroni and Lorenz curves, mean residual life function, Rényi entropy, order statistics, and ‎‎‎k‎‎-record values. We also address the estimation of parameters using ‎the ‎maximum likelihood and bootstrap methods. A Monte Carlo simulation study is conducted to evaluate the estimators discussed in the paper. Additionally, we analyze two real data applications, including rainfall and COVID-۱۹ data sets, to demonstrate the applicability and flexibility of the new distribution. Our results show that the new model fits the data sets better than ‎several ‎other recognized or recently introduced distributions, based on ‎some ‎well-known ‎goodness-‎of-‎fit ‎criteria.

کلیدواژه ها:

Bootstrap estimation‎ ، ‎Exponentiation method‎ ، ‎Maximum likelihood estimation‎ ، ‎Moments‎ ، ‎New XLindley distribution‎ ، Simulation