Regression model under skew-normal error with applications in predicting groundwater arsenic level in the Mekong Delta Region

Abstract

Recently there has been some renewed interest in skew-normal distribution (SND) because it provides a nice and natural generalization (in terms of accommodating skewed data) over the usual normal distribution. In this study we have used the SND error in a regression set-up, discussed a step by step approach on how to estimate all the model parameters, and show how naturally the resultant SND-based regression model can lead to a superior fitting to a given dataset. This generalization enhances the precision in predicting the future value of the response variable when the values of the independent (or input) variables are available. We validate the applicability of our proposed SND-based regression model by using a recently acquired dataset from the Mekong Delta Region (MDR) of Vietnam which had necessitated this study from a public health perspective. Using the existing survey data our proposed model allows all the stakeholders to better predict the groundwater arsenic level at a site easily, based on its geographic characteristics, in lieu of costly chemical analyses, which can be very beneficial to developing countries due to their resource constraints.