Two non-closure properties on the class of subexponential densities

TL;DR

This paper investigates the properties of subexponential densities, revealing that they are not closed under convolution roots or asymptotic equivalence, and discusses closure properties for related distribution classes.

Contribution

It demonstrates non-closure of subexponential densities under convolution roots and asymptotic equivalence, providing new insights into their structural properties.

Findings

Subexponential densities are not closed under convolution roots.

They are not closed under asymptotic equivalence.

Remarks on closure properties for convolution equivalent distributions.

Abstract

Relations between subexponential densities and locally subexponential distributions are discussed. It is shown that the class of subexponential densities is neither closed under convolution roots nor closed under asymptotic equivalence. A remark is given on the closure under convolution roots for the class of convolution equivalent distributions.