A generalization of random self-decomposability

TL;DR

This paper generalizes the concept of random self-decomposability, explores its connections to other distribution classes, and extends it to discrete distributions, providing a broader framework for probabilistic modeling.

Contribution

It introduces a generalized form of random self-decomposability, linking it to self-decomposability, Harris infinite divisibility, and autoregressive models, extending the concept to discrete distributions.

Findings

Established a generalized framework for random self-decomposability.

Connected the generalized notion to self-decomposability and Harris infinite divisibility.

Extended the concept to distributions on non-negative integers.

Abstract

The notion of random self-decomposability is generalized here. Its relation to self-decomposability, Harris infinite divisibility and its connection with a stationary first order generalized autoregressive model are presented. The notion is then extended to $\mathbf{Z_+}$-valued distributions.