Jordan Stoyanov

We describe diverse stochastic inference problems whose solution essentially depends on the moment determinacy of some distributions involved. For a variety of stochastic models we ask questions such as “how to identify a distribution if knowing its moments?” “how asymmetric can be a distribution with zero odd order moments?” “is any mixture model identifiable?” For specific models we provide answers, motivating arguments, and illustrations. Some challenging open questions are outlined.

We study the class of logarithmic skew-normal (LSN) distributions. They have heavy tails; however, all their moments of positive integer orders are finite. We are interested in the problem of moments for such distributions. We show that the LSN distributions are all nonunique (moment-indeterminate). Moreover, we explicitly describe Stieltjes classes for some LSN distributions; they are families of infinitely many distributions, which are different but have the same moment sequence as a fixed LSN distribution.