Modelling Asymmetric Data by Using the Log-Gamma-Normal Regression Model

Abstract

In this paper, we propose a linear regression model in which the error term follows a log-gamma-normal (LGN) distribution. The assumption of LGN distribution gives flexibility to accommodate skew forms to the left and to the right. Kurtosis greater or smaller than the normal model can also be accommodated. The regression model for censored asymmetric data is also considered (censored LGN model). Parameter estimation is implemented using the maximum likelihood approach and a small simulation study is conducted to evaluate parameter recovery. The main conclusion is that the approach is very much satisfactory for moderate and large sample sizes. Results for two applications of the proposed model to real datasets are provided for illustrative purposes.

A Generalized Log Gamma Approach: Theoretical Contributions and an Application to Companies’ Life Expectancy

“…The asymptotic confidence intervals of the ML estimators of the target parameters were produced using the normal approximation to ML and log-transformed ML. The authors of [29] proposed the asymmetric LGN distribution as a flexible option for the error term in linear regression models. The maximum likelihood method was implemented to estimate the parameters of the LGN model, and the Fisher information matrix was derived, showing that it is non-singular.…”