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Zapiski Nauchnykh Seminarov LOMI, 1977, Volume 72, Pages 92–97
(Mi znsl1964)
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A class of limit distributions for maximum cumulative sum
V. B. Nevzorov
Abstract:
Let $X_1,X_2,\dots$ be a sequence of independent identically distributed random variables with zero mathematical expectation and finite variances. $S_0=0$ and $S_n\sum^n_{i=1}X_i$. It is proved that $G_a(x)=
\begin{cases}
0, & \text{\rm{ if }}x\leqslant a,\\
\dfrac{\Phi(x)-\Phi(a)}{1-\Phi(a)}, & \text{\rm{ if }}x\geqslant a.
\end{cases}$ is the limit distribution function of the normalized random variable $\overline S_n=\max_{0\leqslant k\leqslant n}\{S_k+a(k,n)\}$ for some sequence of centering constants $a(k,n)$.
Citation:
V. B. Nevzorov, “A class of limit distributions for maximum cumulative sum”, Problems of the theory of probability distributions. Part IV, Zap. Nauchn. Sem. LOMI, 72, "Nauka", Leningrad. Otdel., Leningrad, 1977, 92–97; J. Soviet Math., 23:3 (1983), 2286–2290
Linking options:
https://www.mathnet.ru/eng/znsl1964 https://www.mathnet.ru/eng/znsl/v72/p92
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Abstract page: | 148 | Full-text PDF : | 47 |
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