On some structural properties of DPIV distribution

Structural properties of a probability model (continuous or discrete) are of paramount importance since they will provide a clear description and characteristic for fitting purposes, as a data set might exhibit various shapes and patterns. Furthermore, since by nature, the majority of the observed phenomena are discrete by nature, and with the fact that existing discrete probability models are not sufficient to address the issue of fitting and forecasting purposes, discrete analogs of well-known continuous probability models, especially in the univariate domain, have received considerable attention over the last decade or so. Among them, discrete Pareto models have received major attraction due to their flexibility in modeling various types of economic data, which is useful for assessing risks associated with an organization’s financial, strategic, and operational risk. For an excellent review on this topic, an interested reader is suggested to read the book by Arnold (2015) and the references cited therein. In this article, we revisit the discrete Pareto (type IV) probability model, which was originally developed and studied involving three parameters in Ghosh (2020). However, several useful structural properties, including but not limited to stochastic ordering, characterization, etc., have not been discussed to date. To address this issue, in this article, we provide some discussion of several of those structural properties, thereby establishing the utility of such a univariate discrete probability model.