Linear regression model with generalized new symmetric error distribution

Abstract

Linear models play a dominant role in analyzing several data sets arising at places like agricultural experiments, space experiments, biological experiments, financial modeling and a wide range other practical problems. One of the major strings in the development of the regression model is the assumption of the error. It is often assumed that the random error of the linear regression model is normally distributed. In numerous situations, however, it is nearly impossible to find a data set that satisfies the normality assumption due to various reasons, such as multivariate skewed and/or heavy-tailed distributions. This problem has been addressed by specifying a different parametric distribution family for the error terms. In this paper, a linear regression model with generalized new symmetric errors is developed and analyzed. The Maximum Likelihood (ML) estimators of the model parameters are derived and their properties with respect to the generalized new symmetric distributed errors are discussed. Simulations were carried out to study the performance of the proposed model with that of Gaussian errors and found that the proposed model perform well when the variables are platykurtic. Some applications of the developed model are also pointed.   

Key Words: Generalized new symmetric distribution, Regression model, Simulation