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.