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Mat. Zametki, 1976, Volume 19, Issue 4, Pages 635–640 (Mi mz7783)  

Distribution of an analog of Sherman's statistics under rank-censored observations

È. M. Kudlaev

M. V. Lomonosov Moscow State University

Abstract: Let $U_n(1),…,U_n(n)$ be a variational series constructed from a sequence of $n$ aggregate-independent random variables distributed uniformly on $(0,1)$. Let $k_0=0$, $k_1,…,k_m,k_{m+1}=n+1$ be an increasing sequence of nonnegative integers, $\lambda_r=k_{r+1}-k_r$, $r=0,…,m$ and
$$ \xi_n=\frac12\sum^m_{r=0}|U_n(k_{r+1})-U_n(k_r)-\frac{k_{r+1}-k_r}{n+1}|. $$
Under certain restrictions on the numbers $\lambda_r=k_{r+1}-k_r$, in this paper we have shown the asymptotic normality (with an appropriate norming) of the quantity $\xi_n$ as $n,m\to\infty$ such that $\lim\sup(m/\sqrt n)\to\infty$.

Full text: PDF file (450 kB)

English version:
Mathematical Notes, 1976, 19:4, 383–386

Bibliographic databases:

UDC: 519.24
Received: 27.02.1975

Citation: È. M. Kudlaev, “Distribution of an analog of Sherman's statistics under rank-censored observations”, Mat. Zametki, 19:4 (1976), 635–640; Math. Notes, 19:4 (1976), 383–386

Citation in format AMSBIB
\Bibitem{Kud76}
\by \`E.~M.~Kudlaev
\paper Distribution of an analog of Sherman's statistics under rank-censored observations
\jour Mat. Zametki
\yr 1976
\vol 19
\issue 4
\pages 635--640
\mathnet{http://mi.mathnet.ru/mz7783}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=405706}
\zmath{https://zbmath.org/?q=an:0362.62020}
\transl
\jour Math. Notes
\yr 1976
\vol 19
\issue 4
\pages 383--386
\crossref{https://doi.org/10.1007/BF01156803}


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