On the nearness of record values to order statistics from Pitman’s measure of closeness

In the two-sample prediction problem, record values from the present sample may be used as predictors of order statistics from a future sample. In this paper, we investigate the nearness of record statistics (upper and lower) to order statistics from a location-scale family of distributions in the sense of Pitman closeness and discuss the corresponding monotonicity properties. We then determine the closest record value to a specific order statistic from a future sample. Even though in general it depends on the parent distribution, exact and explicit expressions are derived for the required probabilities in the case of exponential and uniform distributions, and some computational results are presented as well. Finally, we consider the mean squared error criterion and examine the corresponding results in the exponential case.