二次极值的分布之重极限律

Double limit laws for distributions of double extremes

｛Ｘｍ，ｚ；ｍ，ｎ≥１｝是两个下标的独立同分布随机序列，ｍ（ｂ）（ｍ，ｎ）表示Ｘｍ，１，…，Ｘｍ，ｚ的第ｋ个最大值，Ｙ（ｌ）（ｍ，ｎ；ｋ）表示Ｍ（ｋ）（１，ｎ），…，Ｍ（ｋ）（ｍ，ｎ）的第ｌ个最大值。研究了当ｍ→∞且ｎ→∞时，Ｙ（ｌ）（ｍ，ｎ；ｋ）的重极限分布，证明了其极限分布是三大经典极值类型之一．

be an I.I.D random sequence with tww subscript,M(k)(m, n) be the k-thmaxima of Xm,1,..,Xm,;Y(l)(m,n;k)be the 1-th maxima of M(k)(1,n),..,M(k) (m, n).The double limit distributions of Y(l)(m,n;k)are studied as m and n both approach to infinite.ItProved that the asymptotic distribution is one of the three classical extreme value types.