Taipei : Graduate Institute of Management Science, Tamkang University
摘要:
Let $X$ be a random variable on the interval $[a,b]$ with continuous distribution function $F$. If $E(X\vert X>c) = {b+c\over 2}$ for $a < c < b$, then $X$ has an uniform distribution on $[a,b]$. Also let $X_{1:n}<X_{2:n}<\cdots <X_{n:n}$ be the order statistics of a random sample of size $n$ from $F$ , the relation $E(X_{k+1:n}-X_{k:n}\vert X_{k:n}=c)={b-c\over n-k+1}$, for any $1 \le k < n$, and $a < c < b$, characterizes the uniform distribution
關聯:
International Journal of Information and Management Sciences 4(1), pp.107-111
