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.