Aldossari, ShaykhahShaykhahAldossariHugo Salinas PerezBakouch, Hassan S.Hassan S.BakouchÇetinkaya, ÇağatayÇağatayÇetinkaya2026-10-082026-10-082026-08-28Aldossari, Shaykhah; Salinas, Hugo S.; Bakouch, Hassan S.; Çetinkaya, Çağatay (2026-08-28). A Parsimonious Quadratic-Exponential Submodel of the Kummer–Beta-G Family: Properties and Regression Modeling. Mathematics, 14(17), 3102. https://doi.org/10.3390/math141731022227-7390https://hdl.handle.net/20.500.12740/24948Bounded 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<u<1, where β∈R is a dimensionless tilting parameter. Composing its normalized distribution function with an absolutely continuous baseline cdf G produces the corresponding fixed-shape Kummer–beta-G specialization on the support inherited from G. The bounded AQEB distribution on (0,α) is obtained by using the uniform baseline G(x;α)=x/α and the endpoint-scale parametrization β=λα. We derive the cumulative distribution, density, survival, hazard and reversed hazard functions. We also show that, after standardization, the bounded AQEB model is exactly the natural exponential tilt of a beta(2,2) distribution, and, hence, its version on (0,α) is a scaled exponentially tilted beta(2,2) model. Several mathematical properties are obtained, including ordinary and incomplete moments, generating functions, entropy measures, Lorenz and Bonferroni curves, shape properties, stochastic representations and ordering results. Likelihood-based inference is also discussed with attention to the support-dependent endpoint parameter. The finite-sample behavior of the estimators is examined through a Monte Carlo simulation study, and two empirical applications illustrate the practical use of the AQEB model. In the examples considered, the AQEB model performs competitively relative to the evaluated alternatives according to the reported likelihood-based criteria, goodness-of-fit statistics, and residual diagnostics.http://purl.org/coar/access_right/c_abf2https://creativecommons.org/licenses/by/4.0/Statistical Distribution Estimation and ApplicationsProbability and Statistical ResearchMathematical functions and polynomialsArticulohttps://doi.org/10.3390/math14173102