GENERAL RELATIONS AND IDENTITIES FOR ORDER STATISTICS FROM NON-INDEPENDENT NON-IDENTICAL VARIABLES

N. BALAKRISHNAN^{1}, S. M. BENDRE^{1} AND H. J. MALIK^{2}

1Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1 2Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario, Canada N1G 2W1

(Received May 18, 1990; revised November 26, 1990)

Abstract. Some recurrence relations and identities for order statistics are extended to the most general case where the random variables are assumed to be non-independent non-identically distributed. In addition, some new identities are given. The results can be used to reduce the computations considerably and also to establish some interesting combinatorial identities.

Key words and phrases: Order statistics, recurrence relations and identities, non-independent non-identical variables.