Lomax?Bilal Distribution Within the Bilal-G Family: Theoretical Properties and Applications

In this paper, we propose a new flexible modification of the Lomax distribution within the Bilal-G family generated through the T-X framework, referred to as the Lomax?Bilal distribution. The proposed model offers greater flexibility for modeling-skewed and heavytailed phenomena that frequently arise in survival and reliability studies. A comprehensive set of statistical properties is derived, as moments, order statistics, reliability measures, the quantile function, stochastic ordering, and maximum likelihood estimation. Furthermore, several information measures are obtained to characterize the uncertainty structure of the distribution, namely Shannon entropy, R?nyi entropy, extropy, cumulative residual extropy, and generalized weighted extropy. Also, the Lorenz, Bonferroni, Zenga curves and Gini index are presented. The practical applicability and effectiveness of the proposed distribution are illustrated through analyses of two real datasets: survival times of patients with head and neck cancer treated with chemotherapy and radiation therapy, and repair times of an airborne communication transceiver. The empirical results showed that the Lomax?Bilal distribution consistently provides a better fit than several well-established lifetime distributions according to goodness-of-fit statistics and information criteria, particularly in modeling tail behavior. These findings suggest that the Lomax?Bilal distribution constitutes a flexible and competitive alternative for analyzing complex lifetime data in reliability engineering and medical survival studies.