臺灣博碩士論文加值系統

在本篇中，假設{X_n, n>= 1}為一組獨立的隨機變數，且具有連續的分佈
函數{F_n, n>= 1}。令X_{[1:n]}<= X_{[2:n]}<= ... <= X_{[n:n]}代表
當樣本數為n時所對應出的順序統計量；F_{[kn]}代表X_{[k:n]}的分佈函
數； M_n=max{X_1,...,X_n}。我們考慮當{F_n, n>= 1}是來自一些特殊
的分佈時，該對其分佈的參數給出何種條件，才能給定 a_n和b_n，使得
F_{nn}(a_nx+b_n)收歛到一非退化的分佈函數。當{F_n, n>= 1}是一般的
分佈時，對{F_n, n>= 1}、a_n和b_n設定何種條件，才會使得F_{kn}(
a_nx+b_n)收歛到標準常態分佈；此時k=qn，q in (0,1)。

Let {X_n, n>= 1} be a sequence of independent random variables
with continuous distribution functions {F_n, n>= 1}, and X_{[1:
n]}<= X_{[2:n]}<= ... <= X_{[n:n]} be the corresponding order
statistics for sample size n. For every k (1<= k <= n), let
F_{kn} denote the distribution function of X_{[k:n]} and M_n=
max{X_1,...,X_n}. For this work, when {F_n, n>= 1} come from
some special families with certain parameters, we are
interested in finding some conditions for those parameters to
determine $a_n$ and $b_n$ such that F_{nn}(a_nx+b_n) converges
to a nondegenerate distribution. When {F_n, n>= 1} come from
general families, we also find some conditions for {F_n, n>=
1}, a_n and b_n such that F_{kn}(a_nx+b_n) converges to
standard Normal distribution, where k=qn, q in (0,1).