Distributions and moments

The goal of this talk will be to analyze important properties of distributions in terms of their moments. A lot of attention will be paid to conditions under which a distribution is, or is not, uniquely determined by the moment sequence. This will be related to characterizing the distributions of non-linear (Box-Cox) transformations of random data. Besides well-known classical results, several recent results will be reported. The results will be well-illustrated by examples involving popular distributions. Some of them are new, not so well-known, and look even shocking. If time allows, a few open questions will be outlined.
The talk will be addressed not only to professionals in probability and statistics but also to Master and Doctoral students in this area.