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Teor. Veroyatnost. i Primenen., 1969, Volume 14, Issue 4, Pages 715–718 (Mi tvp1483)  

Short Communications

On the stability of decompositions of the unit distribution function

J. Macys

Institute of Mathematics and Informatics, AS of Lithuanian SSR, Vilnius

Abstract: Let $E$ be the unit distribution function
$$ E(x)= \begin{cases} 0,&x\le0
1,&x>0 \end{cases} $$
and $F=F_1*F_2$ be a distribution function such that in the uniform metric
$$ \rho(F,E)\le\varepsilon\le1/4. $$
Let $F_1$ have median 0. We show that
$$ \rho(F_1,E)\le\frac{1-\sqrt{1-4\varepsilon}}2. $$
and this estimate can not be improved.

Full text: PDF file (214 kB)

English version:
Theory of Probability and its Applications, 1969, 14:4, 688–690

Bibliographic databases:

Received: 03.03.1969

Citation: J. Macys, “On the stability of decompositions of the unit distribution function”, Teor. Veroyatnost. i Primenen., 14:4 (1969), 715–718; Theory Probab. Appl., 14:4 (1969), 688–690

Citation in format AMSBIB
\Bibitem{Mac69}
\by J.~Macys
\paper On the stability of decompositions of the unit distribution function
\jour Teor. Veroyatnost. i Primenen.
\yr 1969
\vol 14
\issue 4
\pages 715--718
\mathnet{http://mi.mathnet.ru/tvp1483}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=261660}
\zmath{https://zbmath.org/?q=an:0204.51402|0188.23903}
\transl
\jour Theory Probab. Appl.
\yr 1969
\vol 14
\issue 4
\pages 688--690
\crossref{https://doi.org/10.1137/1114084}


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