Narrow Zones of Local Normal Attraction

1991 ◽  
Vol 35 (1) ◽  
pp. 140-145
Author(s):  
N. N. Amosova
Keyword(s):  
Normal Attraction

A Note on Normal Attraction to a Stable Law

1971 ◽  
Vol 14 (3) ◽  
pp. 451-452
Author(s):  
M. V. Menon ◽  
V. Seshadri
Keyword(s):  
Distribution Function ◽  
Sufficient Conditions ◽  
Characteristic Exponent ◽  
Random Variables ◽  
Stable Law ◽  
Common Distribution ◽  
Normal Attraction ◽  
Common Distribution Function ◽  
The Common ◽  
Necessary And Sufficient

Let X1, X2, …, be a sequence of independent and identically distributed random variables, with the common distribution function F(x). The sequence is said to be normally attracted to a stable law V with characteristic exponent α, if for some an (converges in distribution to V). Necessary and sufficient conditions for normal attraction are known (cf [1, p. 181]).

The Bounds Based on the Functions of Observations for Maximum of Stable Law

1972 ◽  
Vol 15 (2) ◽  
pp. 285-287
Author(s):  
A. K. Basu ◽  
M. T. Wasan
Keyword(s):  
Stable Law ◽  
Partial Sum ◽  
Normal Attraction ◽  
Image Position ◽  
Domain Of Normal Attraction

Gnedenko and Kolmogorov [3, pp. 181-182] have shown that if Xn with law F(x) belong to the domain of normal attraction of a stable law of index 0<α<2, i.e. if partial sum Sn/an1/α converges in distribution to some stable law Vα, a>0 then there exist c1 and c2 such thatand

Narrow integral zones of normal attraction

1981 ◽  
Vol 21 (1) ◽  
pp. 1-8 ◽  
Author(s):  
N. Amosova
Keyword(s):  
Normal Attraction

A local limit theorem for attractions under a stable law

1980 ◽  
Vol 87 (1) ◽  
pp. 179-187 ◽  
Author(s):  
Sujit K. Basu ◽  
Makoto Maejima
Keyword(s):  
Limit Theorem ◽  
Local Limit Theorem ◽  
Random Variables ◽  
Local Limit ◽  
Independent Random Variables ◽  
Stable Law ◽  
Absolutely Continuous ◽  
Normal Attraction ◽  
Image Position ◽  
Domain Of Normal Attraction

AbstractLet {Xn} be a sequence of independent random variables each having a common d.f. V1. Suppose that V1 belongs to the domain of normal attraction of a stable d.f. V0 of index α 0 ≤ α ≤ 2. Here we prove that, if the c.f. of X1 is absolutely integrable in rth power for some integer r > 1, then for all large n the d.f. of the normalized sum Zn of X1, X2, …, Xn is absolutely continuous with a p.d.f. vn such thatas n → ∞, where v0 is the p.d.f. of Vo.

scholarly journals The Domain of Normal Attraction of an Operator-Stable Law

1983 ◽  
Vol 11 (1) ◽  
pp. 178-184 ◽  
Author(s):  
William N. Hudson ◽  
J. David Mason ◽  
Jerry Alan Veeh
Keyword(s):  
Stable Law ◽  
Normal Attraction ◽  
Operator Stable ◽  
Domain Of Normal Attraction
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