{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:06:29Z","timestamp":1760234789805,"version":"build-2065373602"},"reference-count":44,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2021,6,15]],"date-time":"2021-06-15T00:00:00Z","timestamp":1623715200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001807","name":"Funda\u00e7\u00e3o de Amparo \u00e0 Pesquisa do Estado de S\u00e3o Paulo","doi-asserted-by":"publisher","award":["2020\/09174-5"],"award-info":[{"award-number":["2020\/09174-5"]}],"id":[{"id":"10.13039\/501100001807","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>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\u2019 flux levels in the surroundings of Copiap\u00f3 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.<\/jats:p>","DOI":"10.3390\/sym13061067","type":"journal-article","created":{"date-parts":[[2021,6,15]],"date-time":"2021-06-15T21:24:29Z","timestamp":1623792269000},"page":"1067","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Generalizing Normality: Different Estimation Methods for Skewed Information"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3406-4518","authenticated-orcid":false,"given":"Diego Carvalho do","family":"Nascimento","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica, Facultad de Ingenier\u00eda, Universidad de Atacama, Copiap\u00f3 1530000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5387-2457","authenticated-orcid":false,"given":"Pedro Luiz","family":"Ramos","sequence":"additional","affiliation":[{"name":"Institute of Mathematical Science and Computing, University of S\u00e3o Paulo, S\u00e3o Carlos 13566590, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"David","family":"Elal-Olivero","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Facultad de Ingenier\u00eda, Universidad de Atacama, Copiap\u00f3 1530000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Milton","family":"Cortes-Araya","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Facultad de Ingenier\u00eda, Universidad de Atacama, Copiap\u00f3 1530000, Chile"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7815-9554","authenticated-orcid":false,"given":"Francisco","family":"Louzada","sequence":"additional","affiliation":[{"name":"Institute of Mathematical Science and Computing, University of S\u00e3o Paulo, S\u00e3o Carlos 13566590, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/j.spl.2018.02.015","article-title":"Big data: Some statistical issues","volume":"136","author":"Cox","year":"2018","journal-title":"Stat. 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