Kumaraswamy分布顺序统计量的数字特征及渐近性质①

摘要

Let{,1}kX≤k≤nbe independent and identicaly distributed random variables,(1)(2)(),,,nXXLXbe their order statistics. The joint probability density function of its order statistics and the density functions of extreme order statistics were obtained, when(k)X fol-owed Kumaraswamy distribution with parameters(λ,ϕ). The explicit formulas for the moment of order k about(1)Xand(n)Xwere also obtained. What’s more, the asymptotic distributions of the extreme order statistics(1)Xand(n)Xwere discussed.%设{,1}kX≤k≤n独立同分布，(1)(2)(),,,nXXLX为其顺序统计量，当总体服从Kum(λ,ϕ)分布时，得到了其顺序统计量的联合概率密度、极端值顺序统计量的概率密度和k阶矩的表达式。此外还研究了极端值顺序统计量(1)X 和(n)X 的渐近分布。