Log-cumulant matching approximation of heavy-tailed-distributed aggregate interference

The Method of Moments (MoM) and Method of Log-cumulants (MoLC) estimate the distribution parameters in terms of First Kind Statistics (FKS) and Second Kind Statistics (SKS), respectively. Although SKS offer a suitable framework to analyze heavy-tailed (and asymmetric) distributions, which are commonly-found in aggregate interference modeling, statistical methods developed within this framework has been understudied. For networks following point processes of varying regularity, this paper evaluates the MoM and MoLC methods to estimate the distribution parameters of interference under Rayleigh fading and log-normal shadowing. The results confirm that the gamma and log-normal models offer accurate approximations only when the interference does not present a heavy-tail. For heavy-tailed interference, the MoLC allows an accurate and fast estimation for the α-stable model.