scholarly journals Statistical Ensemble Theory of Gompertz Growth Model

Entropy ◽  
2009 ◽  
Vol 11 (4) ◽  
pp. 807-819 ◽  
Author(s):  
Takuya Yamano
Keyword(s):  
Growth Model ◽  
Statistical Ensemble ◽  
Ensemble Theory ◽  
Gompertz Growth Model

scholarly journals A generalized Gompertz growth model with applications and related birth-death processes

2020 ◽  
Author(s):  
Majid Asadi ◽  
Antonio Di Crescenzo ◽  
Farkhondeh A. Sajadi ◽  
Serena Spina
Keyword(s):  
Growth Model ◽  
Growth Curve ◽  
Goodness Of Fit ◽  
Gompertz Model ◽  
Death Process ◽  
Birth Process ◽  
Failure Data ◽  
First Case ◽  
Gompertz Growth Model ◽  
Birth Death

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.

Age and growth estimates of the jumbo flying squid (Dosidicus gigas) off Peru

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 ◽  
...  
Keyword(s):  
Growth Model ◽  
Growth Pattern ◽  
Growth Models ◽  
Information Criterion ◽  
Growth Patterns ◽  
Age And Growth ◽  
Dosidicus Gigas ◽  
Asymptotic Growth ◽  
Schnute Model ◽  
Gompertz Growth Model

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.

scholarly journals A generalized Gompertz growth model with applications and related birth-death processes

2020 ◽  
Author(s):  
Majid Asadi ◽  
Antonio Di Crescenzo ◽  
Farkhondeh A Sajadi ◽  
Serena Spina
Keyword(s):  
Growth Model ◽  
Growth Curve ◽  
Goodness Of Fit ◽  
Gompertz Model ◽  
Death Process ◽  
Birth Process ◽  
Failure Data ◽  
First Case ◽  
Gompertz Growth Model ◽  
Birth Death

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.

A Framework for Non-Equilibrium Statistical Ensemble Theory

2011 ◽  
Vol 56 (1) ◽  
pp. 99-106
Author(s):  
Qiao Bi ◽  
Zu-Tan He ◽  
Jie Liu
Keyword(s):  
Statistical Ensemble ◽  
Ensemble Theory ◽  
Non Equilibrium
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