Moment Determinacy Versus q-moment Determinacy of Probability Distributions

Abstract

Since the classical moment problem is an important issue deeply connected to various mathematical disciplines, its q-analogue based on the notion of q-moments has emerged in the study of q-distributions. For a wide class of probability distributions, both of these problems can be considered. The aim of this work is to establish a connection between the two moment problems. In this paper, the class $${\mathcal A}$$ of probability distributions possessing finite moments of all orders and support on $$(0, \infty )$$ is examined. For each $$q\in (0,1),$$ a distribution $$P\in {\mathcal A}$$ can be characterized with respect to moment-determinacy as well as q-moment determinacy. It is proved that the properties of P regarding these characterizations may differ, and that the q-moment determinacy of P may depend on the value of q.