Approximate moments of extremes

Christopher S Withers, Saralees Nadarajah
2015 Journal of Inequalities and Applications  
Let M n,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 M n = (M n,1 , . . . , M n,r ) . If there exist b n and . . , Z r ) has joint probability density function exp(-z r ) on 0 < z 1 < · · · < z r < ∞ and  r 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 M n are obtained when these exist.
doi:10.1186/s13660-015-0771-8 fatcat:6q6d5lcvynck7jyfuzloqyzzma