Geodesic
On renewal of a distribution by the mean values of the minima of a random number of random variables
Zapiski Nauchnykh Seminarov POMI, Studies in mathematical statistics. Part 8, Tome 166 (1988), pp. 60-62

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It's known that one can reconstruct the distribution of i.i.d.r.v. basing on the mean values of minimums a random number of the above random variables. Some rather general conditions are imposed. 
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     author = {L. B. Klebanov},
     title = {On renewal of a distribution by the mean values of the minima of a random number of random variables},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {60--62},
     publisher = {mathdoc},
     volume = {166},
     year = {1988},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1988_166_a7/}
}
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L. B. Klebanov. On renewal of a distribution by the mean values of the minima of a random number of random variables. Zapiski Nauchnykh Seminarov POMI, Studies in mathematical statistics. Part 8, Tome 166 (1988), pp. 60-62. http://geodesic.mathdoc.fr/item/ZNSL_1988_166_a7/