| Abstract | Let Mn,i be the ith largest of a random sample of size n from a cumulative distribution function F on R=(−∞,∞). Fix r≥1 and let Mn=(Mn,1,...Mn,r)’. If there exist bnand cn> 0 such that as (Formula presented.)G say, a non-degenerate distribution, then as (Formula presented.), where for (Formula presented.) has joint probability density function exp(−zr)on 01<⋯r<∞ and 1r is the r-vector of ones. The moments of Y are given for the three possible forms of G. First approximations for the moments of Mn are obtained when these exist. © 2015, Withers and Nadarajah. |
