Equilibrium distributions and discrete Schur-constant models

TL;DR

This paper develops multivariate Schur-constant equilibrium distribution models for non-negative variables, analyzing their properties and correlations, with detailed focus on the Poisson case.

Contribution

It introduces a new class of multivariate equilibrium distribution models based on Schur-constant structures, extending univariate concepts to higher dimensions.

Findings

Analysis of the bivariate case highlights key properties.

Extension to multivariate case broadens applicability.

Explicit results for the distribution of sums and correlations.

Abstract

This paper introduces Schur-constant equilibrium distribution models of dimension n for arithmetic non-negative random variables. Such a model is defined through the (several orders) equilibrium distributions of a univariate survival function. First, the bivariate case is considered and analyzed in depth, stressing the main characteristics of the Poisson case. The analysis is then extended to the multivariate case. Several properties are derived, including the implicit correlation and the distribution of the sum.