The Geometric Generalized Birnbaum–Saunders model with long-Term Survivors

Introduction: A cure rate survival model was developed based on the assumption that the number of competing reasons for the event of interest has the Geometric distribution and the time allocated to the event of interest follows the Generalized Birnbaum-Saunders distribution. Methods: The Geometric Generalized Birnbaum–Saunders distribution was defined and two useful representations were represented for its density function which contributes to the creation of some mathematical properties. Furthermore, the parameters of the model with cure rate were estimated by using the maximum likelihood method. Results: Several simulations were performed and a real data set was analyzed from the medical area for different sample sizes and censoring percentages.In the melanoma data set and regarding the AIC and SBC selection criteria, the Geometric Generalized Birnbaum–Saunders distribution model was preferred and was selected as the appropriate model in the present study. Conclusion: Geometric Generalized Birnbaum–Saunders distribution is a highly flexible lifetime model which allows for different degrees of Kurtosis and asymmetry.by considering the advantages of the Geometric Generalized Birnbaum–Saunders distribution model, the model can be implemented as an appropriate alternative to explain or predict the survival time for long-term individuals.