摘要
ＭＯＮＯＴＯＮＥＣＯＵＰＬＩＮＧＡＮＤＳＴＯＣＨＡＳＴＩＣＯＲＤＥＲＩＮＧＯＦＯＲＤＥＲＳＴＡＴＩＳＴＩＣＳ￥ＨＵＴａｉｚｈｏｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＵｎｉｖｅｒｓｉｔｙｏｆＳｃｉｅｎｃｅａｎｄＴｅｃｈｎｏｌｏｇｙｏｆＣ...
Let Xi, Yj, i, j = 2…, n, be independent nonnegative r.v.'s with Xi～ Fi(t) = 1-exp(-Ri(t)) and Yj～ Gj(t) = 1- exp(-R(t)), j=1,…, n. Two kinds of models are considered, and the monotone coupling of order statistics X(1),…, X(n) and y(1) ,…, Y(n) is established under certain conditions, that is, it is possible to construct on a common probability space r.v.'s X, K, i= 1,… , n, such that for each i, Y Xa.s. and(X,…, X)=d (X1,…, Xn), (Y,…, Y) =d (Y1,…, Yn). The result of Model 1 generalizes the results of Proschan and Sethuraman (1976), Ball (1985) and Barbour et al (1991). We also obtain a result about the stochastic ordering of order statistics. All these results are useful in studying epidemic model and reliability theory.
