  Let $X_{1},\ldots ,X_{n}$ be $n$ real-valued dependent random variables. With
motivation from Mitra and Resnick (2009), we derive the tail asymptotic
expansion for the weighted sum of order statistics $X_{1:n}\leq \cdots \leq
X_{n:n}$ of $X_{1},\ldots ,X_{n}$ under the general case in which the
distribution function of $X_{n:n}$ is long-tailed or rapidly varying and $%
X_{1},\ldots ,X_{n}$ may not be comparable in terms of their tail probability.
We also present two examples and an application of our results in risk theory.
