@article{Castro-Palacio2025, 
author = {Juan Carlos Castro-Palacio and Pedro Fernández de Córdoba and Álvaro González-Cortés and J. M. Isidro and A. Noverques and Marcos Orellana-Panchame and Sarira Sahu and Enrique A. Sánchez-Pérez},
title = {Generalized Chi distribution for non-integer degrees of freedom in modelling biological collectivities},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {10},
pages = {25033-25048},
keywords = {Chi distribution, Gamma distribution, non-integer degrees of freedom, survival time data, statistical modelin},
url = {https://www.sciopen.com/article/10.3934/math.20251109},
doi = {10.3934/math.20251109},
abstract = {This article aims to expand the practical potential of the Chi and Chi-square distributions by extending their applicability to non-integer degrees of freedom,    k. The study has two main objectives: first, to explore and leverage the relationship between the Chi, Chi-square, and Gamma distributions to interpret non-integer degrees of freedom; and second, to apply this framework to real survival-time data in the context of biological and health sciences. Three specific cases are analyzed: the germination times of Pinus tropicalis Morelet seeds cultivated in western Cuba; the interval between infection by virulent tuberculous bacilli and death from tuberculosis in guinea pigs; and the period from the onset of symptoms to death due to COVID-19 in patients in Mexico during 2020. A parameter estimation was performed by maximum likelihood (MLE), and the optimal value of    k was found to be non-integer in all cases.}
}