Some Remarks on the Paper “On the q-type Distributions”

Abstract

A claim is made in the paper Nadarajah and Kotz [On the q-type distributions, Physica A 377:465–468, (2007)] that the many q-densities, which are widely used in physics literature, are special cases of or associated with Burr distributions in classical statistical literature. In the present paper it is pointed out that the q-densities are not coming from Burr distributions or from other classical statistical distributions, and that q-distributions are extensions of the limiting forms for q → 1. It is also shown that a statistical distribution which contains all q-distributions as special cases is the pathway model of Mathai [A pathway to matrix-variate gamma and normal densities, Linear Algebra and Its Applications 396:317–328, (2005)]. Tsallis statistics and superstatistics of Beck and Cohen [Superstatistics, Physica A 322:267–275, (2003)] are also examined here in the light of the discussions.