scholarly journals Statistical Ensemble Theory of Gompertz Growth Model

Entropy ◽  
2009 ◽  
Vol 11 (4) ◽  
pp. 807-819 ◽  
Author(s):  
Takuya Yamano
Author(s):  
Majid Asadi ◽  
Antonio Di Crescenzo ◽  
Farkhondeh A. Sajadi ◽  
Serena Spina

AbstractIn this paper, we propose a flexible growth model that constitutes a suitable generalization of the well-known Gompertz model. We perform an analysis of various features of interest, including a sensitivity analysis of the initial value and the three parameters of the model. We show that the considered model provides a good fit to some real datasets concerning the growth of the number of individuals infected during the COVID-19 outbreak, and software failure data. The goodness of fit is established on the ground of the ISRP metric and the $$d_2$$ d 2 -distance. We also analyze two time-inhomogeneous stochastic processes, namely a birth-death process and a birth process, whose means are equal to the proposed growth curve. In the first case we obtain the probability of ultimate extinction, being 0 an absorbing endpoint. We also deal with a threshold crossing problem both for the proposed growth curve and the corresponding birth process. A simulation procedure for the latter process is also exploited.


2019 ◽  
Vol 32 ◽  
pp. 7
Author(s):  
Carlos Goicochea-Vigo ◽  
Enrique Morales-Bojórquez ◽  
Viridiana Y. Zepeda-Benitez ◽  
José Ángel Hidalgo-de-la-Toba ◽  
Hugo Aguirre-Villaseñor ◽  
...  

Mantle length (ML) and age data were analyzed to describe the growth patterns of the flying jumbo squid, Dosidicus gigas, in Peruvian waters. Six non-asymptotic growth models and four asymptotic growth models were fitted. Length-at-age data for males and females were analysed separately to assess the growth pattern. Multi-model inference and Akaike's information criterion were used to identify the best fitting model. For females, the best candidate growth model was the Schnute model with L∞ = 106.96 cm ML (CI 101.23–110.27 cm ML, P < 0.05), age at growth inflection 244.71 days (CI 232.82–284.86 days, P < 0.05), and length at growth inflection 57.26 cm ML (CI 55.42–58.51 cm ML, P < 0.05). The growth pattern in males was best described by a Gompertz growth model with L∞ = 127.58 cm ML (CI 115.27–131.80 cm ML, P < 0.05), t0 = 21.8 (CI 20.06–22.41, P < 0.05), and k = 0.007 (CI 0.006–0.007, P < 0.05). These results contrast with the growth model previously reported for D. gigas in the region, where the growth pattern was identified as non-asymptotic.


2020 ◽  
Author(s):  
Majid Asadi ◽  
Antonio Di Crescenzo ◽  
Farkhondeh A Sajadi ◽  
Serena Spina

Abstract In this paper, we propose a flexible growth model that constitutes a suitable generalization of the well-known Gompertz model. We perform an analysis of various features of interest, including a sensitivity analysis of the initial value and the three parameters of the model. We show that the considered model provides a good fit to some real datasets concerning the growth of the number of individuals infected during the COVID-19 outbreak, and software failure data. The goodness of fit is established on the ground of the ISRP metric and the $d_2$-distance. We also analyze two time-inhomogeneous stochastic processes, namely a birth-death process and a birth process, whose means are equal to the proposed growth curve. In the first case we obtain the probability of ultimate extinction, being 0 an absorbing endpoint. We also deal with a threshold crossing problem both for the proposed growth curve and the corresponding birth process.


2011 ◽  
Vol 56 (1) ◽  
pp. 99-106
Author(s):  
Qiao Bi ◽  
Zu-Tan He ◽  
Jie Liu

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