On Bouhadjar distribution: mathematical properties, simulation and applications

Abstract

In this study, we introduce the Bouhadjar Distribution (BoD), a novel extension of the recently proposed new X-Lindley distribution. The BoD model is particularly well-suited for modeling lifetime data, as its hazard rate function accommodates both increasing and bathtub-shaped behaviors. We explore the fundamental statistical properties of the distribution, including moments, incomplete moments, the moment-generating function, mean deviations from the mean and median, Rényi entropy, order statistics, Bonferroni and Lorenz curves, and the mean residual life function. Parameter estimation is addressed using both maximum likelihood and bootstrap techniques. A comprehensive Monte Carlo simulation study is conducted to assess the performance of the proposed estimators. Furthermore, the practical applicability of the BoD distribution is demonstrated through two real-world data analyses, including datasets related to the Marburg virus. Comparative results based on various goodness-of-fit criteria indicate that the BoD model provides a superior fit relative to several existing one- and two-parameter distributions.