# On the q-moment determinacy of probability distributions

## TL;DR

This paper investigates conditions under which probability distributions are uniquely determined by their $q$-moments, comparing $q$-moment and classical moment determinacy for absolutely continuous distributions.

## Contribution

It introduces new criteria for $q$-moment determinacy and compares properties of distributions based on classical moments and $q$-moments.

## Key findings

- New conditions for $q$-moment determinacy derived
- Comparison of moment and $q$-moment determinacy properties
- Results on the uniqueness of distributions from $q$-moments

## Abstract

Given $0<q<1,$ every absolutely continuous distribution can be described in two different ways: in terms of a probability density function and also in terms of a $q$-density. Correspondingly, it has a sequence of moments and a sequence of $q$-moments if those exist. In this article, new conditions on the $q$-moment determinacy of probability distributions are derived. In addition, results related to the comparison of the properties of probability distributions with respect to the moment and $q$-moment determinacy are presented.