Generalizing Normality: Different Estimation Methods for Skewed Information

Abstract

Normality is the most commonly used mathematical supposition 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 adds a skewness parameter called Alpha-skew-normal (ASN) distribution, which enables bimodality and fat-tail, if needed, although it is sometimes not trivial to estimate this third parameter (regardless of the location and scale). This work analyzed seven different statistical inferential methods towards the ASN distribution on synthetic data and historical data of water flux from 21 rivers (channels) in the Atacama region. Moreover, the contributions of this paper are related to the estimations of probability surrounding rivers’ flux levels in the surroundings of Copiapó city, which is the most economically important city of the third Chilean region and is known to be located in one of the driest areas on Earth (excluding the North and the South Poles). The results show the competitiveness of the MPS and RADE methods with respect to the MLE method, as well as their excellent performance.