Nonparametric Predictive Inference for Two Future Observations with Right-Censored Data

In reliability and survival analyses, right-censored observations are common. This type of data occurs when an event of interest is not fully observed during an experiment and there is no information provided about a random quantity, except that it exceeds a certain value. Nonparametric Predictive Inference (NPI) is a frequentist statistical method that relies on only few assumptions. It quantifies uncertainty by using imprecise probabilities based on Hill’s assumption $$A_{(n)}$$ and focuses specifically on future observations. NPI has been developed for various types of data, including right-censored data, for some inferences such as multiple group comparisons, uncertainty quantification of the survival function, and in the context of competing risks. However, NPI with right-censored data has only considered a single future observation. This paper aims to extend this method by considering two future observations and taking into account that in the NPI approach, such multiple future observations are not conditionally independent given the data. Specifically, we present NPI lower and upper probabilities for the event that both future observations are greater than a particular time. Examples are provided for illustration and an application to system reliability is presented.