A Parsimonious Quadratic-Exponential Submodel of the Kummer–Beta-G Family: Properties and Regression Modeling

Abstract

Bounded continuous data arise in many areas of applied probability and statistics, particularly when the underlying variable is restricted to a finite interval and the density is expected to vanish at the endpoints. This paper studies a parsimonious fixed-shape submodel of the Kummer–beta-G family, referred to as the asymmetric quadratic-exponential bounded generator model, abbreviated as AQEB-G. The model is obtained by fixing the two beta shape parameters at a=b=2, which yields the unit quadratic-exponential kernel wβ(u)=u(1−u)exp(−βu), 0