A new extended normal regression model: simulations and applications

Abstract

Various applications in natural science require models more accurate than well-known distributions. In this context, several generators of distributions have been recently proposed. We introduce a new four-parameter extended normal (EN) distribution, which can provide better fits than the skew-normal and beta normal distributions as proved empirically in two applications to real data. We present Monte Carlo simulations to investigate the effectiveness of the EN distribution using the Kullback-Leibler divergence criterion. The classical regression model is not recommended for most practical applications because it oversimplifies real world problems. We propose an EN regression model and show its usefulness in practice by comparing with other regression models. We adopt maximum likelihood method for estimating the model parameters of both proposed distribution and regression model.