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Normality is the most often mathematical supposition used in data modeling.Nonetheless, even based on the law of large numbers (LLN), normality is astrong presumption given that the presence of asymmetry and multi-modality inreal-world problems is expected. Thus, a flexible modification in the Normaldistribution proposed by Elal-Olivero [12] adds a skewness parameter, calledAlpha-skew Normal (ASN) distribution, enabling bimodality and fat-tail, ifneeded, although sometimes not trivial to estimate this third parameter(regardless of the location and scale). This work analyzed seven differentstatistical inferential methods towards the ASNdistribution on synthetic dataand historical data of water flux from 21 rivers (channels) in the Atacamaregion. Moreover, the contribution of this paper is related to the probabilityestimation surrounding the rivers' flux level in Copiapo city neighborhood, themost important economic city of the third Chilean region, and known to belocated in one of the driest areas on Earth, besides the North and the SouthPole

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