Abstract
We propose a method for calculating the moments of the so-called apparently infinite mean phenomena, i.e., very fat-tailed phenomena that, when solely examining data, may erroneously appear to possess an infinite mean. This issue arises when a random variable Y exhibits strong variability in an extremely broad yet bounded support, in which the upper bound is so far away that we tend to ignore it.
We introduce the concept of dual distribution, using a log-transformation that smoothly removes the upper bound. The tail of the dual distribution can then be studied using extreme value theory, without making excessive parametric assumptions, and the estimates one obtains can be used to study the original distribution and compute its moments by reverting the transformation.
We show how our methodology can be effectively applied to the study of pandemics, war casualties, solar storms, and climate physical risk.
Organized by: Umberto Cherubini