随机比较系数的若干极限性质

SOME LIMIT PROPERTIES OF RANDOM COMPARISON COFFICIENT

设｛Ｘｎ，ｎ≥１｝是在Ｓ＝（１，２，…，ｍ｝中取值的一列随机变量，其联合分布为Ｐ（Ｘ１＝ｘ１，，…，Ｘｎ＝Ｘｎ）＝Ｐ（ｘ１，…，Ｘｎ）＞０，（Ｐｎ１，Ｐｎ２，…，Ｐｎｍ）（ｎ＝１，２，…）是Ｓ上的一列分布，Ｋ∈Ｓ，Ｓｎ（ｋ，ｗ）是在序列Ｘ１（ｗ），…，Ｘｎ（ｗ）中出现ｋ的次数，ｒｎ（ｗ）＝称为（Ｘｉ，１≤ｉ≤ｎ｝相对于乘积分布的随机比较系数，Ｓｎ（ｋ，ｗ）─为Ｓｎ（ｋ，ｗ）与ｋ相对于乘积分布的期望出现次数之差．本文的目的是要研究ｒｎ（ｗ）与Ｓｎ（ｋ，ｗ）之间的某些极限关系．

Let {Xn,n≥1} be a Sequence variables taking values in S= (1, 2, …,m}with joint distribution P(X1=x1,…=, Xn=xn) = p(x1,…, xn)>0, and (Pn1,pn2, …,, pnm) (n= 1, 2,…) be a sequence of distributions on S, k∈s.sn(k,w) be the number of k in the sequence X1(w), …,Xn(w),rn(w) = is called random comparison cofficient of {Xi, 1≤i≤n), relative to the product destribution sn(k,w) - pik is the difference between Sn(k,w) and the expected numbers of relatine to the product distribution the purpose of this pater is to study the between rn(w) and Sn(k,w)-pik.