A New Class of Symmetric Distributions Including the Elliptically Symmetric Logistic

TL;DR

This paper introduces a new broad class of multivariate elliptically symmetric distributions, including the logistic and normal, and explores their probabilistic properties such as marginals, moments, and transformations.

Contribution

It presents a novel, flexible class of elliptically symmetric distributions that encompasses well-known distributions like logistic and normal, with detailed probabilistic analysis.

Findings

Includes the elliptically symmetric logistic within the new class

Provides probabilistic properties such as moments and transformations

Establishes the distribution of linear and marginal transformations

Abstract

We introduce a new broad and exible class of multivariate elliptically symmetric distributions in- cluding the elliptically symmetric logistic and multivariate normal. Various probabilistic properties of the new distribution are studied, including the distribution of linear transformations, marginal distributions, conditional distributions, moments, stochastic representations and characteristic function.