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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 41, Fasc. 2,
pages 321 - 345
DOI: 10.37190/0208-4147.41.2.7
Published online 20.9.2021
 

On tails of symmetric and totally asymmetric $\alpha$-stable~distributions

Witold M. Bednorz
Rafał M. Łochowski
Rafał Martynek

Abstract:

We estimate up to universal constants tails of symmetric and totally asymmetric 1-dimensional α-stable distributions in terms of functions of the parameters of these distributions. In particular, for values of \(\alpha\) close to \(2\) we specify where exactly the tail changes from being Gaussian and starts to behave like in the Pareto distribution.

2010 AMS Mathematics Subject Classification: Primary 60E07; Secondary 60E15, 60E10.

Keywords and phrases: alpha-stable distributions, tail estimates.

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