Simultaneous Closeness of k-Records

In this article, we study the simultaneous Pitman closeness of upper (and lower) k-records to a common parameter of the parent distribution and obtain general expressions for the corresponding probabilities. Since the usual record values are contained in the k-records, the corresponding results for the usual records can be deduced as special cases. The results are then applied to location-scale families with an emphasis on population quantiles. Exact expressions are derived for some common distributions such as exponential and uniform. In each case, the simultaneous closest k-record to a population quantile is determined.