On the Regression Model for Generalized Normal Distributions |
| |
Authors: | Ayman Alzaatreh Mohammad Aljarrah Ayanna Almagambetova Nazgul Zakiyeva |
| |
Affiliation: | 1.Department of Mathematics and Statistics, American University of Sharjah, Sharjah P.O. Box 26666, United Arab Emirates;2.Department of Mathematics, Tafila Technical University, Tafila 66110, Jordan;3.Department of Mathematics, University of Amsterdam, 1098 XH Amsterdam, The Netherlands;4.Zuse Institute Berlin, 14195 Berlin, Germany; |
| |
Abstract: | The traditional linear regression model that assumes normal residuals is applied extensively in engineering and science. However, the normality assumption of the model residuals is often ineffective. This drawback can be overcome by using a generalized normal regression model that assumes a non-normal response. In this paper, we propose regression models based on generalizations of the normal distribution. The proposed regression models can be used effectively in modeling data with a highly skewed response. Furthermore, we study in some details the structural properties of the proposed generalizations of the normal distribution. The maximum likelihood method is used for estimating the parameters of the proposed method. The performance of the maximum likelihood estimators in estimating the distributional parameters is assessed through a small simulation study. Applications to two real datasets are given to illustrate the flexibility and the usefulness of the proposed distributions and their regression models. |
| |
Keywords: | T-X family logistic distribution normal distribution moments estimation regression |
|
|