On Moments of Order Statistics from a Kappa Distribution

Abstract

The kappa distribution, known as K3D, is a skewed generalization
of the well-known logistic distribution and has many useful
applications in modelling extreme value events occurred usually in
hydrology and environmental sciences. The distribution also nests
the Gumbel distribution in the limiting case of its shape parameter.
In this paper, we consider the order statistics from the
distribution and derive expressions and relations for both single
and product moments of order statistics in computable forms. These
relations can be used effectively in the computation of higher
moments given the lower order ones. The relations also generalize
those relations for the logistic distribution. The moment tables
obtained can be used in the computation of the location-scale
parameter estimation.