@article{Rahmouni2025, 
author = {Mohieddine Rahmouni},
title = {From exponential-geometric to Lomax: A unified survival model via gamma frailty},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {12},
pages = {29927-29954},
keywords = {survival analysis, gamma frailty, geometric distribution, Lomax distribution, mixture model, reliability, first failure time},
url = {https://www.sciopen.com/article/10.3934/math.20251315},
doi = {10.3934/math.20251315},
abstract = {This paper introduces a new flexible lifetime distribution that unifies the exponential-geometric and Lomax models through a random system size and a shared gamma frailty. It models the first failure time in a system with a geometrically distributed number of conditionally exponential components with gamma frailty, producing a geometric mixture of Lomax distributions. The model generalizes classical distributions, reducing to exponential-geometric, Lomax, or exponential under appropriate limits. We derived analytical expressions for the cumulative distribution, survival, and hazard functions, discussed maximum likelihood estimation, and illustrated its competitive and versatile fits on real datasets.}
}