Representation of order statistics based on exponential variables with different scale parameters

Let $X_k(1\leqslant k\leqslant n)$ be independent random variables with distribution functions $F_k(x)=\max\{0,1-e^{-\lambda_kx}\}$, $(\lambda_k>0)$ and $X_{k,n}(1\leqslant k\leqslant n)$ be corresponding order statistics. Somre representations via mixtures of sums of independent exponential variables are obtained for $X_{nk}$ and their linear combinations.