Prats’ovytyj, M. V.; Kosopl’otkina, O. V. The fractal properties of the spectrum of the superposition of singular distribution functions. (Ukrainian, English) Zbl 1050.60013 Teor. Jmovirn. Mat. Stat. 67, 122-129 (2002); translation in Theory Probab. Math. Stat. 67, 135-144 (2003). The relation between the spectrum of the superposition of two distribution functions (d.f.) and the spectra of each component is studied. Sufficient conditions for the singularity of the superposition are obtained. It is proved that any continuous d.f. of random variables with independent \(s\)-adic digitals can be represented as a superposition of two singular d.f. The fractal properties of the superposition of two identical Cantor type d.f. are investigated in details. Reviewer: N. M. Zinchenko (Kyïv) MSC: 60E99 Distribution theory Keywords:distribution function; superposition; singularity; Cantor type distribution function; fractal properties PDFBibTeX XMLCite \textit{M. V. Prats'ovytyj} and \textit{O. V. Kosopl'otkina}, Teor. Ĭmovirn. Mat. Stat. 67, 122--129 (2002; Zbl 1050.60013); translation in Theory Probab. Math. Stat. 67, 135--144 (2003)