Geodesic
Representation of order statistics based on exponential variables with different scale parameters
Zapiski Nauchnykh Seminarov POMI, Studies in mathematical statistics. Part VI, Tome 136 (1984), pp. 162-164

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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. 
@article{ZNSL_1984_136_a11,
     author = {V. B. Nevzorov},
     title = {Representation of order statistics based on exponential variables with different scale parameters},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {162--164},
     publisher = {mathdoc},
     volume = {136},
     year = {1984},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1984_136_a11/}
}
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V. B. Nevzorov. Representation of order statistics based on exponential variables with different scale parameters. Zapiski Nauchnykh Seminarov POMI, Studies in mathematical statistics. Part VI, Tome 136 (1984), pp. 162-164. http://geodesic.mathdoc.fr/item/ZNSL_1984_136_a11/