Analysis of Survival Data by a Weibull-generalized Sibuya Distribution

Abstract

In this paper, we consider a survival model of a series system with random sample size, Z. Such a situation arises in competing risk analysis where the number of causes of failure is random and only the minimum of the survival times due to various causes is observed. Considering the distribution of Z as generalized Sibuya and the baseline distribution as Weibull, a Weibull-generalized Sibuya distribution is derived. The structural properties of the proposed model are studied along with the maximum likelihood estimation of the parameters. Extensive simulation studies are carried out to study the performance of the estimators. For illustration, two real data sets are analyzed and it is shown that the proposed model fits better than some of the existing models.