Some Notes on Arcsine Exponentiated-X Family

Abstract

In 2020, He, Ahmad, Afify and Goual proposed a new family based on classical Arcsine distribution and exponentiated family named Arcsine Exponentiated-X family. The main purpose of this work is to continue studying the intrinsic properties of these families, namely to study the “saturation”—d to the horizontal asymptote in the Hausdorff sense. We obtain precious estimates for the value of the Hausdorff distance that can be used as an additional criterion in practice. We consider Hausdorff approximation of two submodels from the proposed family with baseline distribution—some extensions of the classical Weibull distribution. In this study, we also define a new “adaptive ASE-W model with polynomial variable transfer”. We develop several simple dynamic programming modules implemented within the programming environment CAS Wolfram Mathematica. All new results are illustrated with suitable numerical experiments with real cumulative data.