Marshall–Olkin–Gompertz (MOG) Distribution: Properties, Simulation and Application.

Abstract

The Marshall–Olkin–Gompertz (MOG) distribution extends the classical Gompertz model through the Marshall–Olkin family, introducing an additional parameter that enhances flexibility in lifetime and reliability modeling. Its probability density, cumulative, survival, and hazard functions are derived and analyzed. Graphical studies show that the MOG model can represent increasing, decreasing, or bathtub shaped hazard rates, making it suitable for diverse real world data. Parameter estimation is performed using the maximum likelihood method. Overall, the MOG distribution provides a versatile generalization of the Gompertz law, offering improved adaptability in engineering, biological, and actuarial applications.