Kullback–Leibler Divergence of the γ–ordered Normal over t–distribution

Abstract

The aim of this paper is to evaluate and study the Kullback–Leibler divergence of the γ–ordered Normal distribution, a generalization of Normal distribution emerged from the generalized Fisher’s information measure, over the scaled t–distribution. We investigate this evaluation through a series of bounds and approximations while the asymptotic behavior of the divergence is also studied. Moreover, we obtain a generalization of the known Kullback–Leibler information measure between two normal distributions, as well as the K–L divergence between Uniform or Laplace distribution over Normal distribution.