Estimation of extremes for heavy-tailed and light-tailed distributions in the presence of random censoring

In this paper, the flexible semi-parametric model introduced in is considered for conducting tail inference of censored data. Both the censored and censoring variables are supposed to belong to this family of distributions, and thus solutions for modelling the tail of censored data which are between Weibull-tail and Pareto-tail behaviours are proposed. Estimators of the tail parameters and extreme quantiles are defined without prior knowledge of censoring strength and asymptotic normality results are proved. Various combinations of the tails of censored and censoring distributions are covered, ranging from rather mild censoring to severe censoring in the tail, i.e., when the ultimate probability of censoring in the tail is zero. Finite sample behaviour is presented via some simulations and an illustration on real data is also provided.