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.

中文翻译：

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新的扩展正态回归模型：仿真和应用

自然科学中的各种应用要求模型比众所周知的分布更准确。在这种情况下，最近提出了几种分布的产生器。我们引入了一种新的四参数扩展正态（EN）分布，与在实际数据的两种应用中通过经验证明的偏态正态分布和β正态分布相比，它可以提供更好的拟合。我们提出了蒙特卡洛模拟，以研究使用Kullback-Leibler发散准则的EN分布的有效性。不建议在大多数实际应用中使用经典回归模型，因为它过分简化了现实世界中的问题。我们提出一个EN回归模型，并通过与其他回归模型进行比较来展示其实用性。