Some Notes on the Omega Distribution and the Pliant Probability Distribution Family

Abstract

In 2020 Dombi and Jónás (Acta Polytechnica Hungarica 17:1, 2020) introduced a new four parameter probability distribution which they named the pliant probability distribution family. One of the special members of this family is the so-called omega probability distribution. This paper deals with one of the important characteristic “saturation” of these new cumulative functions to the horizontal asymptote with respect to Hausdorff metric. We obtain upper and lower estimates for the value of the Hausdorff distance. A simple dynamic software module using CAS Mathematica and Wolfram Cloud Open Access is developed. Numerical examples are given to illustrate the applicability of obtained results.

On Topp-Leone-G Power Series: Saturation in the Hausdorff Sense and Applications

“…The proposed methodology can be successfully applied to other sub-models of Topp-Leone-G power series as well as other commonly used CDFs in practice. Some related results can be found in [35][36][37][38][39] . Several dynamic modules implemented in CAS Wolfram Mathematica are included.…”