Nonparametric methods of statistical inference for double-censored data with applications

This article introduces new nonparametric statistical methods for prediction in case of data containing right-censored observations and left-censored observations simultaneously. The methods can be considered as new versions of Hill’s A ( n ) {A}_{\left(n)} assumption for double-censored data. Two bounds are derived to predict the survival function for one future observation X n + 1 {X}_{n+1} based on each version, and these bounds are compared through two examples. Two interesting features are provided based on the proposed methods. The first one is the detailed graphical presentation of the effects of right and left censoring. The second feature is that the lower and upper survival functions can be derived.