Characterization of tails through hazard rate and convolution closure properties

TL;DR

This paper investigates the asymptotic behavior of hazard rates in tail distributions, establishing convolution closure for extended rapidly varying tails and relating hazard rate conditions to tail classes.

Contribution

It introduces new asymptotic inequalities for hazard rates using Matuszewska indices and proves convolution closure for extended rapidly varying tail distributions.

Findings

Established asymptotic inequalities for hazard rates.

Linked tail distribution classes to hazard rate conditions.

Proved convolution closure for extended rapidly varying tails.

Abstract

We use the properties of the Matuszewska indices to show asymptotic inequalities for hazard rates. We discuss the relation between membership in the classes of dominatedly or extended rapidly varying tail distributions and corresponding hazard rate conditions. Convolution closure is established for the class of distributions with extended rapidly varying tails.