A new discrete pareto type (IV) model: theory, properties and applications

Abstract

Discrete analogue of a continuous distribution (especially in the univariate domain) is not new in the literature. The work of discretizing continuous distributions begun with the paper by Nakagawa and Osaki (1975) to the best of the knowledge of the author. Since then several authors proposed discrete analogues of known continuous models. In this paper, we propose and study a discrete analogue of the continuous Pareto (type IV) distribution, namely the discrete Pareto (type IV) distribution (DPIV, henceforth, in short) that has three parameters. Its probability mass function can be approximately symmetric, right-skewed and left-skewed shapes, and the hazard rate function possesses decreasing and upside-down bathtub shapes. Also, the proposed discrete distribution can be under-, over- or equi- dispersion. The flexibility of the new discrete model is illustrated by means of three applications to real life data sets arising out of various domains affecting our life.