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We study distribution functions $F$ that have the property of rationalinfinite divisibility: there exist some infinitely divisible distributionfunctions $F_1$ and $F_2$ such that $F_1=F*F_2$. We study a class$\boldsymbol{Q}$ of such distribution functions, which is a wide naturalextension of the well-known class of infinitely divisible distributionfunctions. We are interested in general criteria of membership of$\boldsymbol{Q}$. The obtained conditions are formulated in terms ofcharacteristic functions and they seem to be convenient for the application.

Some criteria of rational infinite divisibility for distribution functions