Geodesic
On the Problem of Reconstructing a Summands Distribution by Their Sum
Teoriâ veroâtnostej i ee primeneniâ, Tome 46 (2001) no. 2, pp. 366-370

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This paper considers the problem of reconstructing a distribution of independent identically distributed random variables by the distribution of their sum in which each summand is included with a probability $1-p$. We show the ambiguity of this reconstruction in the case of an arbitrary (including odd) number of summands for $0\le p\frac12$.
Keywords: summands, sum, components.
Mots-clés : distribution, decomposition, convolution 
@article{TVP_2001_46_2_a9,
     author = {D. V. Belomestny},
     title = {On the {Problem} of {Reconstructing} a {Summands} {Distribution} by {Their} {Sum}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {366--370},
     publisher = {mathdoc},
     volume = {46},
     number = {2},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2001_46_2_a9/}
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D. V. Belomestny. On the Problem of Reconstructing a Summands Distribution by Their Sum. Teoriâ veroâtnostej i ee primeneniâ, Tome 46 (2001) no. 2, pp. 366-370. http://geodesic.mathdoc.fr/item/TVP_2001_46_2_a9/