The difference between the average of the top $k$ out of $n$ order statistics and the population mean expressed in population standard deviation units is known as the selection differential. This paper obtains some nondegenerate limit laws for this quantity. The results are applied to the construction of tables used in testing for outliers.
"Some Nondegenerate Limit Laws for the Selection Differential." Ann. Statist. 10 (4) 1306 - 1310, December, 1982. https://doi.org/10.1214/aos/1176345997