A heteroscedastic regression model with the generalized normal distribution

In regression analysis, joint modeling mean and dispersion is an essential tool in absence of the variance homogeneity. Moreover, it is known in the literature that the generalized normal (GN) distribution has some features that provide flexibility in modeling thanks to its shape parameter. This paper proposes a joint location and scale model of the GN distribution for modeling location and scale in the presence of heteroscedasticity. We provide maximum likelihood (ML) estimators for the parameters of the proposed model. We also give an estimation procedure to estimate all parameters simultaneously. For the application, some simulation study scenarios and a real-life example are carried out to prove the estimation performance of the proposed model.