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Was this proposition on cumulants of compound Poisson distributions known before I put it in...

\end{align} (These properties plus one trivial property characterize the cumulants. … (So in particular, for example, the cumulants of even order of a compound Poisson distribution are nonnegative.) …
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cumulant problem

sequence of cumulants of some probability distribution? … In one sense, this is trivially equivalent to the problem of moments: the $n$th moment is a polynomial in the first $n$ cumulants and vice-versa. …