Aging and Stochastic Orders of a Wide Family of Continuous Univariate Distributions

The Dg⁺(h) D g + ( h ) family, recently introduced by Koutras and Dafnis (2025, 2026a, b), offers a flexible framework for constructing continuous univariate distributions using generator functions. By selecting appropriate components, this approach enables the development of new distributions with desirable properties. The method establishes systematic conditions for aging properties, including decreasing reversed hazard rates (RHRs) and likelihood ratio properties. It also provides tractable criteria for determining these monotonicity properties. We also derive preservation results under linear combinations of generators and parametric components, thereby providing a unified mechanism for constructing new models while retaining key structural properties. We further investigate stochastic orders and show how structural properties of the underlying functions yield ordering relationships. These findings have practical implications in areas such as reliability analysis, survival studies, and actuarial science, enhancing the tractability and applicability of the proposed distributions.