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Article

Generalizing Normality: Different Estimation Methods for Skewed Information

1
Departamento de Matemática, Facultad de Ingeniería, Universidad de Atacama, Copiapó 1530000, Chile
2
Institute of Mathematical Science and Computing, University of São Paulo, São Carlos 13566590, Brazil
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editor: Giuseppe Bagliesi
Symmetry 2021, 13(6), 1067; https://doi.org/10.3390/sym13061067
Received: 6 May 2021 / Revised: 8 June 2021 / Accepted: 10 June 2021 / Published: 15 June 2021
(This article belongs to the Special Issue Symmetric and Asymmetric Bimodal Distributions with Applications)
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. View Full-Text
Keywords: Alpha-skew-normal; bimodal distribution; asymmetry accommodation; water monitoring Alpha-skew-normal; bimodal distribution; asymmetry accommodation; water monitoring
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MDPI and ACS Style

Nascimento, D.C.d.; Ramos, P.L.; Elal-Olivero, D.; Cortes-Araya, M.; Louzada, F. Generalizing Normality: Different Estimation Methods for Skewed Information. Symmetry 2021, 13, 1067. https://doi.org/10.3390/sym13061067

AMA Style

Nascimento DCd, Ramos PL, Elal-Olivero D, Cortes-Araya M, Louzada F. Generalizing Normality: Different Estimation Methods for Skewed Information. Symmetry. 2021; 13(6):1067. https://doi.org/10.3390/sym13061067

Chicago/Turabian Style

Nascimento, Diego C.d., Pedro L. Ramos, David Elal-Olivero, Milton Cortes-Araya, and Francisco Louzada. 2021. "Generalizing Normality: Different Estimation Methods for Skewed Information" Symmetry 13, no. 6: 1067. https://doi.org/10.3390/sym13061067

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