Generalizing the normality: a novel towards different estimation methods for skewed information

Abstract: Normality is the most often mathematical supposition used in data modeling. Nonetheless, even based on the law of large numbers (LLN), normality is a strong presumption given that the presence of asymmetry and multi-modality in real-world problems is expected. Thus, a flexible modification in the Normal distribution proposed by Elal-Olivero [12] adds a skewness parameter, called Alpha-skew Normal (ASN) distribution, enabling bimodality and fat-tail, if needed, although sometimes not trivial to estimate this third parameter (regardless of the location and scale). This work analyzed seven different statistical inferential methods towards the ASNdistribution on synthetic data and historical data of water flux from 21 rivers (channels) in the Atacama region. Moreover, the contribution of this paper is related to the probability estimation surrounding the rivers' flux level in Copiapo city neighborhood, the most important economic city of the third Chilean region, and known to be located in one of the driest areas on Earth, besides the North and the South Pole