Inference for heavy tailed distributions

Let X₁, X₂, ... be a sequence of independent and identically distributed random variables in the domain of attraction of a stable law of order α and asymmetry parameter β. This paper develops some large sample inference procedures for the population mean μ and parameters α and β. Three different approaches to the construction of confidence intervals for μ are proposed, two of them involving bootstrap. For the parameters α and β estimators are proposed that are straightforward, computationally simple and statistically intuitive. The consistency and asymptotically normality of these estimators are also established. It is shown that in addition to these estimators being simple their accuracy is comparable to that of more complicated estimators available in the current literature.