Inference for heavy tailed distributions (Q1378778)

This work develops the statistical inference for stable laws of order \(\alpha\) and an asymmetry parameter \(\beta\), based on an independent sample of size \(n\geq 1\). Three different approaches to the construction of confidence intervals for the mean \(\mu\) are proposed, two of them involving bootstrap. For the parameters \(\alpha\) and \(\beta\) estimators are proposed which are computationally simple and statistically intuitive. The consistency and asymptotic normality of these estimators are also established.