Geodesic
On an extension of the class of stable distributions
Teoriâ veroâtnostej i ee primeneniâ, Tome 17 (1972) no. 4, pp. 723-732

Voir la notice de l'article provenant de la source Math-Net.Ru

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{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). 
@article{TVP_1972_17_4_a9,
     author = {V. M. Kruglov},
     title = {On an extension of the class of stable distributions},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {723--732},
     publisher = {mathdoc},
     volume = {17},
     number = {4},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1972_17_4_a9/}
}
TY  - JOUR
AU  - V. M. Kruglov
TI  - On an extension of the class of stable distributions
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 1972
SP  - 723
EP  - 732
VL  - 17
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TVP_1972_17_4_a9/
LA  - ru
ID  - TVP_1972_17_4_a9
ER  - 
%0 Journal Article
%A V. M. Kruglov
%T On an extension of the class of stable distributions
%J Teoriâ veroâtnostej i ee primeneniâ
%D 1972
%P 723-732
%V 17
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TVP_1972_17_4_a9/
%G ru
%F TVP_1972_17_4_a9
V. M. Kruglov. On an extension of the class of stable distributions. Teoriâ veroâtnostej i ee primeneniâ, Tome 17 (1972) no. 4, pp. 723-732. http://geodesic.mathdoc.fr/item/TVP_1972_17_4_a9/