The digital characteristics and the asymptotic properties of order statistics from Kumaraswamy distribution

Let {Xk,1≤ k ≤n}be independent and identically distributed random variables,X(1),X(2),······ X(n) be their order statistics. The joint probability density function of its order statistics and the density functions of extreme order statistics were obtained, whenX( k) followed Kumaraswamy distribution with parameters(λ,φ). The explicit formulas for the moment of order k aboutX(1) andX( n) were also obtained. What's more, the asymptotic distributions of the extreme order statisticsX(1) andX( n) were discussed.