  We propose an approach to compute the conditional moments of fat-tailed
phenomena that, only looking at data, could be mistakenly considered as having
infinite mean. This type of problems manifests itself when a random variable Y
has a heavy- tailed distribution with an extremely wide yet bounded support. We
introduce the concept of dual distribution, by means of a log-transformation
that 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 log- transformation. The
central difference between our approach and a simple truncation is in the
smoothness of the transformation between the original and the dual
distribution, allowing use of extreme value theory. War casualties, operational
risk, environment blight, complex networks and many other econophysics
phenomena are possible fields of application.
