分布函数间一种新的散布序

A New Dispersive Ordering of Distributions

设Ｆ是一分布函数，对α∈（０，１），记Ｘ_Ｆ~＋（α）＝ｓｕｐ｛ｘ；Ｆ（ｘ）＜α｝，Ｘ_Ｆ~－（α）＝ｉｎｆ｛ｘ；Ｆ（ｘ）＞α｝，ＸＦ（α）＝（Ｘ_Ｆ~＋（α）＋Ｘ_Ｆ~－（α））／２．本文给出了分布函数Ｆ和Ｇ之间的一种散布序，记作；对α，β∈（０，１），α＜β，ＸＦ（β）－ＸＦ（α）＋ＸＦ（１－α）－ＸＦ（１－β）≤ＸＧ（β）－ＸＧ（α）＋ＸＧ（１－α）－ＸＧ（１－β），得到了这种序关系的若干性质，并与Ｌｅｗｉｓ Ｔ和Ｔｈｏｍｐｓｏｎ Ｍ（１９８２）给出的散布序作了比较，我们的序关系弱于Ｌｅｗｉｓ Ｔ和Ｔｈｏｍｐｓｏｎ Ｍ给出的散布序关系．

Let F is a distribution function,X_F￣+(α)=sup {x,F(x) <α},X_F￣-(α)=inf{x, F (x) >α},X_F (α)=(X_F￣+(α) +X_F￣- (α))/2, α∈ (0,1).In this paper, a new dispersive ordering of distributions is proposed. We denote it by.F G if and only if.for every α,β∈(0, 1), α< β, X_F(β) -X_F (α) + X_F(1-α) -X_F (1-β)≤X_G(β) X_G (α) +X_G (1-α)- X_G (1-β). The properties of it are derived and it is compared with the dispersive ordering that was proposed by Lewis J. and Thompson M. in 1982.