A New Class of Multivariate Elliptically Contoured Distributions with Inconsistency Property

TL;DR

This paper introduces a novel class of multivariate elliptically symmetric distributions, exploring their properties and demonstrating their flexibility with real data applications.

Contribution

It presents a new class of distributions including logistic and Kotz types, analyzing their probabilistic properties and the inconsistency property.

Findings

New distribution class encompassing logistic and Kotz types

Analysis of marginal, conditional, and transformed distributions

Real data example demonstrating flexibility

Abstract

We introduce a new class of multivariate elliptically symmetric distributions including elliptically symmetric logistic distributions and Kotz type distributions. We investigate the various probabilistic properties including marginal distributions, conditional distributions, linear transformations, characteristic functions and dependence measure in the perspective of the inconsistency property. In addition, we provide a real data example to show that the new distributions have reasonable flexibility.