{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T05:44:43Z","timestamp":1761975883559,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2021,5,22]],"date-time":"2021-05-22T00:00:00Z","timestamp":1621641600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","award":["RTI2018-102256-B-100 (Spain)."],"award-info":[{"award-number":["RTI2018-102256-B-100 (Spain)."]}]},{"name":"Generalitat Valenciana, Spain","award":["Prometeo\/2017\/102"],"award-info":[{"award-number":["Prometeo\/2017\/102"]}]},{"name":"Spanish MINECO","award":["MTM2016-76647-P"],"award-info":[{"award-number":["MTM2016-76647-P"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Random variables in biology, social and health sciences commonly follow skewed distributions. Many of these variables can be represented by exGaussian functions; however, in practice, they are sometimes considered as Gaussian functions when statistical analysis is carried out. The asymmetry can play a fundamental role which can not be captured by central tendency estimators such as the mean. By means of Monte Carlo simulations, the effect of a small asymmetry in the generating functions of the chi distribution is studied. To this end, the k generating functions are taken as exGaussian functions. The limits of this approximation are tested numerically for the practical case of three health-related variables: one physical (body mass index) and two cognitive (verbal fluency and short-term memory). This work is in line with our previous works on a physics-inspired mathematical model to represent the reaction times of a group of individuals.<\/jats:p>","DOI":"10.3390\/sym13060924","type":"journal-article","created":{"date-parts":[[2021,5,24]],"date-time":"2021-05-24T02:32:43Z","timestamp":1621823563000},"page":"924","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Monte Carlo Simulation of a Modified Chi Distribution Considering Asymmetry in the Generating Functions: Application to the Study of Health-Related Variables"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5272-7661","authenticated-orcid":false,"given":"Nuria","family":"Ortigosa","sequence":"first","affiliation":[{"name":"Instituto Universitario de Matem\u00e1tica Pura y Aplicada, Universitat Polit\u00e8cnica de Val\u00e8ncia, 46022 Valencia, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8578-4574","authenticated-orcid":false,"given":"Marcos","family":"Orellana-Panchame","sequence":"additional","affiliation":[{"name":"Instituto Universitario de Matem\u00e1tica Pura y Aplicada, Universitat Polit\u00e8cnica de Val\u00e8ncia, 46022 Valencia, Spain"},{"name":"Departamento de Matem\u00e1tica, Valle de Sula, Universidad Nacional Aut\u00f3noma de Honduras (UNAH), Sector Pedregal, 21102 San Pedro Sula, Honduras"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0132-9989","authenticated-orcid":false,"given":"Juan Carlos","family":"Castro-Palacio","sequence":"additional","affiliation":[{"name":"Departamento de Ingenier\u00eda El\u00e9ctrica, Electr\u00f3nica, Autom\u00e1tica y F\u00edsica Aplicada, Universidad Polit\u00e9cnica de Madrid, 28012 Madrid, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0347-7280","authenticated-orcid":false,"given":"Pedro Fern\u00e1ndez de","family":"C\u00f3rdoba","sequence":"additional","affiliation":[{"name":"Instituto Universitario de Matem\u00e1tica Pura y Aplicada, Universitat Polit\u00e8cnica de Val\u00e8ncia, 46022 Valencia, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0720-9945","authenticated-orcid":false,"given":"J. M.","family":"Isidro","sequence":"additional","affiliation":[{"name":"Instituto Universitario de Matem\u00e1tica Pura y Aplicada, Universitat Polit\u00e8cnica de Val\u00e8ncia, 46022 Valencia, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2021,5,22]]},"reference":[{"key":"ref_1","unstructured":"Montgomery, D.C., and Runger, G.C. (2014). Applied Statistics and Probability for Engineers, John Wiley & Sons, Inc.. [6th ed.]."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1080\/14786440009463897","article-title":"On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling","volume":"50","author":"Pearson","year":"1900","journal-title":"Lond. Edinb. Dublin Philos. Mag. J. 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