Document Type : Research Manuscript
Author
Department of Statistics, University of Mazandaran, Babolsar, Iran
Abstract
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-19 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.
Keywords
- Bootstrap estimation
- Exponentiation method
- Maximum likelihood estimation
- Moments
- New XLindley distribution
- Simulation
Main Subjects
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