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Teoriya Veroyatnostei i ee Primeneniya, 1975, Volume 20, Issue 2, Pages 402–403 (Mi tvp3151)  
This article is cited in 4 scientific papers (total in 4 papers)

Short Communications

An inequality for moments of a random variable

V. V. Petrov

Leningrad
Full-text PDF (155 kB) Citations (4)
Abstract: Let $X$ be a random variable. For any $r>0$, we set $\beta_r=\mathbf E|X|^r$. The following inequality is proved:
$$ \beta_r^{1/r}\le\gamma^{1/r-1/s}\beta_s^{1/s}\quad(r<s) $$
where $\gamma=\mathbf P(X\ne0)$. This inequality is optimal in a certain sense.
Received: 11.11.1974
English version:
Theory of Probability and its Applications, 1976, Volume 20, Issue 2, Pages 391–392
DOI: https://doi.org/10.1137/1120045
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. V. Petrov, “An inequality for moments of a random variable”, Teor. Veroyatnost. i Primenen., 20:2 (1975), 402–403; Theory Probab. Appl., 20:2 (1976), 391–392
Citation in format AMSBIB
\Bibitem{Pet75}
\by V.~V.~Petrov
\paper An inequality for moments of a~random variable
\jour Teor. Veroyatnost. i Primenen.
\yr 1975
\vol 20
\issue 2
\pages 402--403
\mathnet{http://mi.mathnet.ru/tvp3151}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=380932}
\zmath{https://zbmath.org/?q=an:0336.60005}
\transl
\jour Theory Probab. Appl.
\yr 1976
\vol 20
\issue 2
\pages 391--392
\crossref{https://doi.org/10.1137/1120045}
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  • https://www.mathnet.ru/eng/tvp/v20/i2/p402
    • This publication is cited in the following 4 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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