An exponentiated XLindley distribution with properties, inference and applications

Abdullah M Alomair; Mukhtar Ahmed; Saadia Tariq; Muhammad Ahsan-Ul-Haq; Junaid Talib

doi:10.1016/j.heliyon.2024.e25472

An exponentiated XLindley distribution with properties, inference and applications

Heliyon. 2024 Jan 29;10(3):e25472. doi: 10.1016/j.heliyon.2024.e25472. eCollection 2024 Feb 15.

Authors

Abdullah M Alomair¹, Mukhtar Ahmed², Saadia Tariq², Muhammad Ahsan-Ul-Haq³, Junaid Talib²

Affiliations

¹ Department of Quantitative Methods, School of Business, King Faisal University, 31982, Al-Ahsa, Saudi Arabia.
² School of Statistics, Minhaj University Lahore, Lahore, Pakistan.
³ College of Statistical Sciences, University of the Punjab, Lahore, Pakistan.

Abstract

In this paper, we propose exponentiated XLindley (EXL) distribution. The novel model is adaptable due to the mixt shapes of its density and failure rate functions. The following key statistical properties of EXL distribution are derived: quantile function, moments, hazard function, mean residual life, and Rényi entropy. The parameters are estimated using the maximum likelihood, Anderson Darling, Cramer von Misses, maximum product spacing, ordinary and weighted least square estimation procedures. To examine the behavior of the estimate, Monte Carlo simulation is used. Further Bayesian technique is also utilized to estimate the EXL parameters. The traceplot and Geweke diagnostics are used to track the convergence of simulated processes. The applicability of the EXL distribution is demonstrated by three datasets from different domains such as mortality rate due to COVID-19, precipitation in inches, and failure time for repairable items. The proposed distribution provides efficient results as compared to renowned competitive distributions.

Keywords: Bayesian; Data analysis; Generalization; Inference; Reliability measures; XLindley distribution.