ON STABILITY OF INTERMEDIATE ORDER-STATISTICS

Let X(kn,n), n epsilon N, with the ratio k(n) over n converging to one and the difference n-k(n) converging to infinity for n tending to infinity, respectively, denote a sequence of intermediate order statistics corresponding to i.i.d. random variables X(1),...,X(n). This paper gives necessary and sufficient conditions for weak additive or multiplicative laws of large numbers for such sequences. These conditions are in terms of the tail behaviour of the underlying distribution function, some of them involving the order of convergence of k(n).