混合指数分布顺序统计量的性质(英文)

On properties of order statistics from the mixed exponential distribution

设{Xs,1≤s≤n}独立同分布,X1:n,X2:n,…,Xn:n为其顺序统计量.当Xs服从参数分别为p(0<p<1),λ1,λ2(0<λ1≤λ2)的混合指数分布时,得到了Xs:n的q(q为正整数)阶原点矩E(Xsq:n)(1≤s≤n)的精确表达式.证明了其顺序统计量的样本间隔不独立,且不同分布.此外还研究了其极端顺序统计量X1:n和Xn:n的渐近分布.

Let {Xs,1≤s≤n} be independent and identically distributed,and X1：n,X2：n,…,Xn：n be the corresponding order statistics.When Xs follows the mixed exponential distribution with parameters p（0p1）,λ1,λ2（0λ1 ≤λ2）,the explicit formulas for the q order origin moments of Xs：n are obtained（q is a positive integer and 1 ≤s≤n）.It is proved that the sample intervals of their order statistics are not independent and not identically distributed.What＇s more,the asymptotic distributions of their extreme order statistics X1：n and Xn：n are discussed.