Max-compound Cox processes. III

TL;DR

This paper investigates the behavior of extreme values in samples with random sizes modeled by mixed Poisson distributions, providing bounds on convergence rates for max-compound Cox processes.

Contribution

It introduces new inequalities that bound the convergence rate in limit theorems for max-compound Cox processes with mixed Poisson sampling.

Findings

Derived inequalities for convergence bounds

Applicable to max-compound Cox processes with mixed Poisson distributions

Enhanced understanding of extreme value behavior in stochastic processes

Abstract

Extreme values are considered in samples with random size that has a mixed Poisson distribution being generated by a doubly stochastic Poisson process. We prove some inequalities providing bounds on the rate of convergence in limit theorems for the distributions of max-compound Cox processes.