Criteria for Concentration Functions to Belong to the Domains of Attraction of Stable Laws

1993 ◽  
Vol 37 (3) ◽  
pp. 424-432 ◽  
Author(s):  
V. M. Kruglov
Keyword(s):  
Stable Laws ◽  
Domains Of Attraction ◽  
Concentration Functions

scholarly journals Partial attraction of maxima

1976 ◽  
Vol 13 (01) ◽  
pp. 159-163
Author(s):  
Richard F. Green
Keyword(s):  
Stable Laws ◽  
Domains Of Attraction ◽  
Stable Type ◽  
Domain Of Partial Attraction

There exist three classes of probability laws that are stable for maxima. A number of well-known distributions lie in the domains of attraction of these laws. This fact is sometimes exploited by fitting the distribution of maxima with one of the stable laws. Such a procedure may well be misguided, however, since distributions exist which produce maxima having any desired distribution and not just a stable type. In this paper partial attraction of maxima is defined and it is shown that all distributions have a non-empty domain of partial attraction of maxima. In fact, there exists a distribution that lies simultaneously in the domain of partial attraction of maxima of all distributions.

scholarly journals Stable Laws and Domains of Attraction in Free Probability Theory

1999 ◽  
Vol 149 (3) ◽  
pp. 1023 ◽  
Author(s):  
Hari Bercovici ◽  
Vittorino Pata ◽  
Philippe Biane
Keyword(s):  
Probability Theory ◽  
Free Probability ◽  
Stable Laws ◽  
Domains Of Attraction ◽  
Free Probability Theory

A note on domains of attraction of p-max stable laws

1996 ◽  
Vol 28 (3) ◽  
pp. 279-284 ◽  
Author(s):  
Gerd Christoph ◽  
Michael Falk
Keyword(s):  
Stable Laws ◽  
Domains Of Attraction

Limit distributions of the number of renewals and waiting times

1976 ◽  
Vol 13 (2) ◽  
pp. 301-312
Author(s):  
N. R. Mohan
Keyword(s):  
Distribution Function ◽  
Limit Distribution ◽  
Infinite Sequence ◽  
Waiting Times ◽  
Random Variables ◽  
Stable Laws ◽  
Domains Of Attraction ◽  
Limit Distributions

Let {Xn} be an infinite sequence of independent non-negative random variables. Let the distribution function of Xi, i = 1, 2, …, be either F1 or F2 where F1 and F2 are distinct. Set Sn = X1 + X2 + … + Xn and for t > 0 define and Zt = SN(t)+1 – t. The limit distributions of N(t), Yt and Zt as t → ∞ are obtained when F1 and F2 are in the domains of attraction of stable laws with exponents α1 and α2, respectively and Sn properly normalised has the composition of these two stable laws as its limit distribution.

Limit distributions of the number of renewals and waiting times

1976 ◽  
Vol 13 (02) ◽  
pp. 301-312
Author(s):  
N. R. Mohan
Keyword(s):  
Distribution Function ◽  
Limit Distribution ◽  
Infinite Sequence ◽  
Waiting Times ◽  
Random Variables ◽  
Stable Laws ◽  
Domains Of Attraction ◽  
Limit Distributions

Let {X n} be an infinite sequence of independent non-negative random variables. Let the distribution function of Xi , i = 1, 2, …, be either F 1 or F 2 where F 1 and F 2 are distinct. Set Sn = X 1 + X 2 + … + Xn and for t > 0 define and Zt = SN (t)+1 – t. The limit distributions of N(t), Yt and Zt as t → ∞ are obtained when F 1 and F 2 are in the domains of attraction of stable laws with exponents α 1 and α 2 , respectively and Sn properly normalised has the composition of these two stable laws as its limit distribution.

scholarly journals Partial attraction of maxima

1976 ◽  
Vol 13 (1) ◽  
pp. 159-163 ◽  
Author(s):  
Richard F. Green
Keyword(s):  
Stable Laws ◽  
Domains Of Attraction ◽  
Stable Type ◽  
Domain Of Partial Attraction

There exist three classes of probability laws that are stable for maxima. A number of well-known distributions lie in the domains of attraction of these laws. This fact is sometimes exploited by fitting the distribution of maxima with one of the stable laws. Such a procedure may well be misguided, however, since distributions exist which produce maxima having any desired distribution and not just a stable type. In this paper partial attraction of maxima is defined and it is shown that all distributions have a non-empty domain of partial attraction of maxima. In fact, there exists a distribution that lies simultaneously in the domain of partial attraction of maxima of all distributions.

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