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

TL;DR

This paper explores the Alpha-skew Normal distribution to better model skewed data, analyzing seven inference methods on synthetic and real river flux data to improve probability estimation in arid regions.

Contribution

It introduces a comprehensive analysis of inference methods for the ASN distribution applied to real-world water flux data, addressing estimation challenges in skewed distributions.

Findings

Seven inference methods evaluated on synthetic data.

Improved probability estimates for river flux levels.

Application to water data from Atacama rivers.

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