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Teoriya Veroyatnostei i ee Primeneniya, 1977, Volume 22, Issue 3, Pages 466–481
(Mi tvp3248)
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This article is cited in 3 scientific papers (total in 3 papers)
Inequalities for the distribution of the length of random vector sums
G. О. H. Katona Institute of Mathematics, Hungary Academy of Sciences
Abstract:
Starting from a combinatorial proof of the inequality
$$
\mathbf P(|\xi+\eta|\ge x)\ge\frac{1}{2}\mathbf P^2(|\xi|\ge x).
$$
where $\xi$ and $\eta$ are independent random vectors in a $d$-dimensional Euclidean space, continuous analogues of the combinatorial model are constructed, which enable to deduce inequalities similar to the above.
Received: 14.02.1975
Citation:
G. О. H. Katona, “Inequalities for the distribution of the length of random vector sums”, Teor. Veroyatnost. i Primenen., 22:3 (1977), 466–481; Theory Probab. Appl., 22:3 (1978), 450–464
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https://www.mathnet.ru/eng/tvp3248 https://www.mathnet.ru/eng/tvp/v22/i3/p466
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Abstract page: | 191 | Full-text PDF : | 93 |
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