Geometric Gamma Max-Infinitely Divisible Models

TL;DR

This paper introduces geometric gamma max-infinitely divisible laws, explores their properties, and develops related extremal processes and models demonstrating new invariance under geometric maxima.

Contribution

It presents the concept of geometric gamma max-infinitely divisible laws, analyzes their properties, and introduces a max-AR(1) model with invariance under geometric maxima.

Findings

Distributional and divisibility properties analyzed

A new invariance (stability) under geometric maxima proved

A max-AR(1) model developed

Abstract

A transformation of gamma max-infinitely divisible laws viz. geometric gamma max-infinitely divisible laws is considered in this paper. Some of its distributional and divisibility properties are discussed and a random time changed extremal process corresponding to this distribution is presented. A new kind of invariance (stability) under geometric maxima is proved and a max-AR(1) model corresponding to it is also discussed.