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.

中文翻译：

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新的离散pareto类型（IV）模型：理论，属性和应用

连续分布的离散类似物（尤其是在单变量域中）在文献中并不新鲜。离散分布的离散化工作从中川和大崎（1975）的论文开始，据作者所知。从那以后，几位作者提出了已知连续模型的离散类似物。在本文中，我们提出并研究了连续帕累托（IV型）分布的离散类似物，即具有三个参数的离散帕累托（IV型）分布（以下简称DPIV）。它的概率质量函数可以是近似对称的，右偏和左偏的形状，而危险率函数具有递减和倒置的浴缸形状。而且，建议的离散分布可以是欠分散，过分散或等分散的。