Asymptotic Expansions for Heavy-Tailed Data

Heavy-tailed distributions are present in the characterization of different modern systems such as high-resolution imaging, cloud computing, and cognitive radio networks. Commonly, the cumulants of these distributions cannot be defined from a certain order, and this restricts the applicability of traditional methods. To fill this gap, the present letter extends the traditional Edgeworth and Cornish–Fisher expansions, which are based on the cumulants, to analogous asymptotic expansions based on the log-cumulants. The proposed expansions inherit the capability of log-cumulants to characterize heavy-tailed distributions and parallel traditional expansions. Thus, they are readily implemented. Interestingly, the proposed expansions are applicable for light-tailed distributions as well.