Monte Carlo Simulation of a Modified Chi Distribution Considering Asymmetry in the Generating Functions: Application to the Study of Health-Related Variables
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...
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| Format: | Article |
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MDPI AG
2021-05-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/6/924 |
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| author | Nuria Ortigosa Marcos Orellana-Panchame Juan Carlos Castro-Palacio Pedro Fernández de Córdoba J. M. Isidro |
| author_facet | Nuria Ortigosa Marcos Orellana-Panchame Juan Carlos Castro-Palacio Pedro Fernández de Córdoba J. M. Isidro |
| author_sort | Nuria Ortigosa |
| collection | DOAJ |
| description | 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 <i>k</i> 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. |
| first_indexed | 2024-03-10T11:08:24Z |
| format | Article |
| id | doaj.art-7d5a340038f94892b070cb7135f2f073 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T11:08:24Z |
| publishDate | 2021-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-7d5a340038f94892b070cb7135f2f0732023-11-21T20:57:12ZengMDPI AGSymmetry2073-89942021-05-0113692410.3390/sym13060924Monte Carlo Simulation of a Modified Chi Distribution Considering Asymmetry in the Generating Functions: Application to the Study of Health-Related VariablesNuria Ortigosa0Marcos Orellana-Panchame1Juan Carlos Castro-Palacio2Pedro Fernández de Córdoba3J. M. Isidro4Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 Valencia, SpainInstituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 Valencia, SpainDepartamento de Ingeniería Eléctrica, Electrónica, Automática y Física Aplicada, Universidad Politécnica de Madrid, 28012 Madrid, SpainInstituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 Valencia, SpainInstituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, 46022 Valencia, SpainRandom 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 <i>k</i> 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.https://www.mdpi.com/2073-8994/13/6/924skewed distributionex-gaussiannumerical study |
| spellingShingle | Nuria Ortigosa Marcos Orellana-Panchame Juan Carlos Castro-Palacio Pedro Fernández de Córdoba J. M. Isidro Monte Carlo Simulation of a Modified Chi Distribution Considering Asymmetry in the Generating Functions: Application to the Study of Health-Related Variables Symmetry skewed distribution ex-gaussian numerical study |
| title | Monte Carlo Simulation of a Modified Chi Distribution Considering Asymmetry in the Generating Functions: Application to the Study of Health-Related Variables |
| title_full | Monte Carlo Simulation of a Modified Chi Distribution Considering Asymmetry in the Generating Functions: Application to the Study of Health-Related Variables |
| title_fullStr | Monte Carlo Simulation of a Modified Chi Distribution Considering Asymmetry in the Generating Functions: Application to the Study of Health-Related Variables |
| title_full_unstemmed | Monte Carlo Simulation of a Modified Chi Distribution Considering Asymmetry in the Generating Functions: Application to the Study of Health-Related Variables |
| title_short | Monte Carlo Simulation of a Modified Chi Distribution Considering Asymmetry in the Generating Functions: Application to the Study of Health-Related Variables |
| title_sort | monte carlo simulation of a modified chi distribution considering asymmetry in the generating functions application to the study of health related variables |
| topic | skewed distribution ex-gaussian numerical study |
| url | https://www.mdpi.com/2073-8994/13/6/924 |
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