An extended normal distribution for skewed and bimodal data: New properties and a new regression model

Rodrigues G.M.; Ortega E.M.M.; Vila R.; Cordeiro G.M.; Cóndor C.M.R. · Communications in Statistics - Theory and Methods (2026) · DOI: 10.1080/03610926.2025.2538538

Resumen

We introduce and study a new distribution based on the composition of the generalized odd log-logistic-G family and the normal distribution, which can be used to model asymmetric and bimodal data. So, we propose a new heteroskedasticity regression model based on the odd log-logistic normal distribution under two systematic components easily interpreted. The maximum likelihood method is used for estimating the parameters of the proposed model, and several simulations are done to verify the accuracy of the estimators. We report diagnostic measures and residual analysis. The newly developed procedures are illustrated by considering two real data sets and empirically comparing the results found with the skew-normal regression model.

Instituciones: Universidad Nacional Mayor de San Marcos