Exact nonparametric conditional inference based on k-records, given inter-k-record times

In this paper, we develop exact nonparametric inference for quantiles of the population based on the sequence of k-record values, conditionally on the corresponding observed inter-k-record times, to increase the precision of inference, as compared to nonparametric unconditional procedures. The effect of including the additional information contained in the inter-k-record times is evaluated by means of an empirical study. The conditional tolerance and prediction intervals for a future k-record from another independent sequence are obtained as well. A real data set is also used to illustrate the inferential results developed here.