"Estimation of the Survival and Hazard Functions for the Inverse Gompertz Model with a Simulation-Based Application"

Abstract

The interest of statisticians in studying probability distributions arises from the role these statistical tools play in describing the behavior of data and understanding their characteristics. Phenomena can be expressed through random variables, and each random variable is represented by a probability distribution that contains important information about that variable.

The Inverse Gompertz distribution has been widely used among classical distributions over the past decades for modeling univariate and bivariate data in fields such as engineering, actuarial and environmental sciences, medicine, biological studies, demography, economics, finance, and insurance.

In this study, the survival and hazard functions were estimated using the maximum likelihood method and the Kaplan–Meier method. To demonstrate the applicability of this model and to evaluate which method performs better, sample sizes of n=5,10,30,80,120n = 5, 10, 30, 80, 120n=5,10,30,80,120 were generated. The comparison criterion employed was the Integrated Mean Squared Error (IMSE).