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Teoriya Veroyatnostei i ee Primeneniya, 1974, Volume 19, Issue 2, Pages 374–382 (Mi tvp2858)  

This article is cited in 3 scientific papers (total in 3 papers)

Short Communications

On the stability of certain characteristic properties of the normal distribution

Yu. R. Gabovich

Moscow
Full-text PDF (524 kB) Citations (3)
Abstract: Consider a set of the random variables (r.v.) $X_1,\dots,X_n$ with the joint distribution function (d.f.) $F$, marginal d.f. $F_1,\dots,F_n$ and the Lévy metric in $R^n$. We denote by $N$ the set of $n$-dimensional normal d.f.
D e f i n i t i o n 1. The r.v. $X_1,\dots,X_n$ are $(L,\varepsilon)$-independent if $L(F,F_1,\dots,F_n)\le\varepsilon$.
D e f i n i t i o n 2. The r.v. $X_1,\dots,X_n$ are $(L,\delta)$-normal if $\inf\limits_NL(F,\Phi)\le\delta$.
Let $\gamma(\varepsilon)=\sup\limits_{\mathfrak M_\varepsilon}\inf\limits_NL(F,\Phi)$, where $\mathfrak M_\varepsilon$ consists of the d.f. $F$ of r.v. $X_1,\dots,X_n$ such that $\mathbf P\{|X_j|>d\}<q$, $j=1,\dots,n$, and that $X_1,\dots,X_n$ are $(L,\varepsilon)$-independent, and $L_1=X_1+\dots+X_n$, $L_2=b_1X_1+\dots+b_nX_n$, $b_j\ne0$, $j=1,\dots,n$, $\sum_1^nb_j=0$ are $(L,\varepsilon)$-independent.
Received: 01.11.1973
English version:
Theory of Probability and its Applications, 1975, Volume 19, Issue 2, Pages 365–371
DOI: https://doi.org/10.1137/1119040
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: Yu. R. Gabovich, “On the stability of certain characteristic properties of the normal distribution”, Teor. Veroyatnost. i Primenen., 19:2 (1974), 374–382; Theory Probab. Appl., 19:2 (1975), 365–371
Citation in format AMSBIB
\Bibitem{Gab74}
\by Yu.~R.~Gabovich
\paper On the stability of certain characteristic properties of the normal distribution
\jour Teor. Veroyatnost. i Primenen.
\yr 1974
\vol 19
\issue 2
\pages 374--382
\mathnet{http://mi.mathnet.ru/tvp2858}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=345161}
\zmath{https://zbmath.org/?q=an:0309.60014}
\transl
\jour Theory Probab. Appl.
\yr 1975
\vol 19
\issue 2
\pages 365--371
\crossref{https://doi.org/10.1137/1119040}
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  • https://www.mathnet.ru/eng/tvp/v19/i2/p374
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теория вероятностей и ее применения Theory of Probability and its Applications
     
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