An exponentiated XLindley distribution with properties, inference and applications

Area of Science:

• Statistics
• Probability Distributions

Background:

• The development of novel statistical distributions is crucial for modeling complex phenomena.
• Existing distributions may not adequately capture the characteristics of all data types.

Purpose of the Study:

• To propose and characterize a new statistical distribution, the exponentiated XLindley (EXL) distribution.
• To investigate the statistical properties and estimation methods for the EXL distribution.
• To demonstrate the practical utility of the EXL distribution across various applications.

Main Methods:

• Derivation of key statistical properties: quantile function, moments, hazard function, mean residual life, and Rényi entropy.
• Parameter estimation using maximum likelihood, Anderson Darling, Cramer von Misses, maximum product spacing, and least square methods.
• Validation through Monte Carlo simulations and Bayesian inference with traceplot and Geweke diagnostics.

Main Results:

• The exponentiated XLindley (EXL) distribution exhibits adaptable density and failure rate functions.
• Various estimation techniques were applied, and their behavior was examined via simulation.
• Bayesian methods were successfully employed for parameter estimation, with convergence confirmed.

Conclusions:

• The EXL distribution is a versatile and efficient statistical model.
• Its applicability is validated across diverse datasets including COVID-19 mortality, precipitation, and repairable item failure times.
• The proposed EXL distribution offers competitive performance compared to established distributions.