# Background driving distribution functions and series representation for log-gamma selfdecomposable random variables

## TL;DR

This paper explores the background driving distributions of selfdecomposable random variables, specifically deriving series representations for log-gamma distributions and their background variables.

## Contribution

It introduces new series representations for log-gamma selfdecomposable distributions and identifies their background driving probability distributions.

## Key findings

- Background driving distributions are characterized for selfdecomposable variables.
- Series representations are derived for log-gamma distributions.
- The results enhance understanding of the structure of selfdecomposable distributions.

## Abstract

For the selfdecomposable distributions (random variables) we identified background driving probability distributions in their random integral representations. For log-gamma and their background driving random variables series representations are found.