Monte Carlo Simulation of a Modified Chi Distribution Considering Asymmetry in the Generating Functions: Application to the Study of Health-Related Variables
Abstract
:1. Introduction
2. Methodology
2.1. Generalities on the Chi Distribution
2.2. Monte Carlo Simulations for Non-Gaussian Generating Distributions
2.3. Measurement of Goodness of Fit between Data and Models
3. Results and Discussion
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Set | τ1 | τ2 | τ3 | eτ (%) | 〈γ〉 | 〈〉 | 〈 | ||
---|---|---|---|---|---|---|---|---|---|
1 | 0.5 | 0.8 | 1.45 | 97.44 | 0.67 | 5.27 | 5.00 | 0.9863 | 4.84 |
0.5 | 1 | 1.45 | 97.44 | 5.12 | 4.87 | ||||
0.5 | 1.2 | 1.45 | 97.44 | 5.26 | 5.04 | ||||
2 | 0.7 | 0.9 | 1.4 | 66.67 | 0.73 | 4.55 | 4.31 | 0.9885 | 4.89 |
0.7 | 1 | 1.4 | 66.67 | 4.14 | 3.94 | ||||
0.7 | 1.2 | 1.4 | 66.67 | 4.25 | 4.07 | ||||
3 | 0.9 | 0.95 | 1.2 | 28.57 | 0.74 | 4.14 | 3.93 | 0.9891 | 4.74 |
0.9 | 1 | 1.2 | 28.57 | 3.97 | 3.79 | ||||
0.9 | 1.1 | 1.2 | 28.57 | 4.02 | 3.84 | ||||
4 | 1 | 1.5 | 2.8 | 94.74 | 1.26 | 3.44 | 3.60 | 0.9462 | 4.06 |
1 | 2 | 2.8 | 94.74 | 3.26 | 3.51 | ||||
1 | 2.5 | 2.8 | 94.74 | 3.47 | 3.48 | ||||
5 | 1.3 | 1.5 | 2.5 | 63.16 | 1.32 | 3.52 | 3.58 | 0.9439 | 3.43 |
1.3 | 2 | 2.5 | 63.16 | 3.32 | 3.49 | ||||
1.3 | 2.3 | 2.5 | 63.16 | 3.59 | 3.72 | ||||
6 | 1.7 | 1.8 | 2.1 | 21.05 | 1.38 | 3.02 | 3.28 | 0.9412 | 8.68 |
1.7 | 1.9 | 2.1 | 21.05 | 3.01 | 3.28 | ||||
1.7 | 2 | 2.1 | 21.05 | 2.94 | 3.24 |
Set | (%) | 〈〉 | 〈〉 | 〈〉 | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|
1 | 0.5 | 0.8 | 0.9 | 1.0 | 1.45 | 97.44 | 0.74 | 4.55 | 4.50 | 0.9744 | 1.61 |
0.5 | 1.0 | 1.1 | 1.2 | 1.45 | 4.48 | 4.53 | |||||
0.5 | 1.2 | 1.3 | 1.4 | 1.45 | 4.69 | 4.83 | |||||
2 | 0.7 | 0.9 | 1.0 | 1.2 | 1.4 | 66.67 | 0.80 | 4.15 | 4.14 | 0.9753 | 1.15 |
0.7 | 1.0 | 1.1 | 1.2 | 1.4 | 3.91 | 3.94 | |||||
0.7 | 1.2 | 1.3 | 1.35 | 1.4 | 4.05 | 4.15 | |||||
3 | 0.9 | 0.95 | 1.0 | 1.1 | 1.2 | 28.57 | 0.77 | 3.85 | 3.84 | 0.9788 | 0.72 |
0.9 | 1.0 | 1.1 | 1.15 | 1.2 | 3.77 | 3.80 | |||||
0.9 | 1.1 | 1.15 | 1.16 | 1.2 | 3.79 | 3.84 | |||||
4 | 1.0 | 1.5 | 1.6 | 1.8 | 2.8 | 94.74 | 1.35 | 3.21 | 3.68 | 0.8951 | 18.01 |
1.0 | 2.0 | 2.2 | 2.4 | 2.8 | 3.14 | 3.88 | |||||
1.0 | 2.5 | 2.6 | 2.7 | 2.8 | 4.02 | 4.88 | |||||
5 | 1.3 | 1.5 | 1.8 | 2.0 | 2.5 | 63.16 | 1.39 | 3.19 | 3.84 | 0.8954 | 22.55 |
1.3 | 2.0 | 2.1 | 2.2 | 2.5 | 3.05 | 3.90 | |||||
1.3 | 2.3 | 2.35 | 2.4 | 2.5 | 3.30 | 4.24 | |||||
6 | 1.7 | 1.8 | 1.9 | 2.0 | 2.1 | 21.05 | 1.40 | 2.89 | 3.70 | 0.8979 | 25.61 |
1.7 | 1.9 | 1.95 | 2.0 | 2.1 | 2.90 | 3.72 | |||||
1.7 | 2.0 | 2.05 | 2.08 | 2.1 | 2.84 | 3.73 |
Variable | |||||||
---|---|---|---|---|---|---|---|
B.M.I | 23.274 | 0.235 | 2.8314 | 0.1971 | 3.8610 | 0.4428 | 0.9735 |
Verbal fluency | 17.063 | 0.485 | 6.1891 | 0.2964 | 4.8408 | 0.7148 | 0.9883 |
Short term mem. | 5.4995 | 0.4108 | 1.5475 | 0.1351 | 0.58533 | 0.48266 | 0.9947 |
MB parameter | 0.07370 | 0.00025 | 0.9853 | 0.07918 | 7.17 |
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Ortigosa, N.; Orellana-Panchame, M.; Castro-Palacio, J.C.; Córdoba, P.F.d.; Isidro, J.M. Monte Carlo Simulation of a Modified Chi Distribution Considering Asymmetry in the Generating Functions: Application to the Study of Health-Related Variables. Symmetry 2021, 13, 924. https://doi.org/10.3390/sym13060924
Ortigosa N, Orellana-Panchame M, Castro-Palacio JC, Córdoba PFd, Isidro JM. Monte Carlo Simulation of a Modified Chi Distribution Considering Asymmetry in the Generating Functions: Application to the Study of Health-Related Variables. Symmetry. 2021; 13(6):924. https://doi.org/10.3390/sym13060924
Chicago/Turabian StyleOrtigosa, Nuria, Marcos Orellana-Panchame, Juan Carlos Castro-Palacio, Pedro Fernández de Córdoba, and J. M. Isidro. 2021. "Monte Carlo Simulation of a Modified Chi Distribution Considering Asymmetry in the Generating Functions: Application to the Study of Health-Related Variables" Symmetry 13, no. 6: 924. https://doi.org/10.3390/sym13060924
APA StyleOrtigosa, N., Orellana-Panchame, M., Castro-Palacio, J. C., Córdoba, P. F. d., & Isidro, J. M. (2021). Monte Carlo Simulation of a Modified Chi Distribution Considering Asymmetry in the Generating Functions: Application to the Study of Health-Related Variables. Symmetry, 13(6), 924. https://doi.org/10.3390/sym13060924