On the Problem of Reconstructing a Summands Distribution by Their Sum
Денис Витальевич Беломестный · Theory of Probability and Its Applications · 2002
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 $0\le p < {\frac{1}{2}}$.