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Teoriya Veroyatnostei i ee Primeneniya, 1972, Volume 17, Issue 4, Pages 723–732
(Mi tvp4345)
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This article is cited in 38 scientific papers (total in 38 papers)
On an extension of the class of stable distributions
V. M. Kruglov Moscow
Abstract:
Let $\{\xi_n\}$ be a sequence of independent identically distributed random variables. Put
\begin{equation}
\eta_{nj}=\frac{1}{b_j}(\xi_1+\xi_2+\dots+\xi_{nj})\div a_j
\tag{1}
\end{equation}
and assume that
\begin{equation}
n_j<n_{j+1}, \quad \lim_{j\to\infty}\frac{n_{j+1}}{n_j}=r\geq 1, \qquad r<\infty.
\tag{2}
\end{equation}
In the paper, the class of limit distributions for the variables (1) under the conditions (2) is studied. This class is shown to possess some properties of the class of stable distributions. A general form of the spectral function of distributions from this class is given (Theorem 1).
Received: 02.07.1970
Citation:
V. M. Kruglov, “On an extension of the class of stable distributions”, Teor. Veroyatnost. i Primenen., 17:4 (1972), 723–732; Theory Probab. Appl., 17:4 (1973), 685–694
Linking options:
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