American Journal of Theoretical and Applied Statistics

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Derivation of Inflection Points of Nonlinear Regression Curves - Implications to Statistics

Received: 19 December 2013    Accepted:     Published: 10 January 2014
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Abstract

In this paper, we derive inflection points for the commonly known growth curves, namely, generalized logistic, Richards, Von Bertalanffy, Brody, logistic, Gompertz, generalized Weibull, Weibull, Monomolecular and Mitscherlich functions. The functions often represent the mean part of non-linear regression models in Statistics. Inflection point of a growth curve is the point on the curve at which the rate of growth gets maximum value and it represents an important physical interpretation in the respective application area. Not only the model parameters but also the inflection point of a growth curve is of high statistical interests.

DOI 10.11648/j.ajtas.20130206.25
Published in American Journal of Theoretical and Applied Statistics (Volume 2, Issue 6, November 2013)
Page(s) 268-272
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Inflection Point, Growth Model, Gompertz, Logistic, Richards, Weibull

References
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Author Information
  • School of Mathematical and Statistical Sciences, Hawassa University, Ethiopia

  • School of Mathematical and Statistical Sciences, Hawassa University, Ethiopia

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    Ayele Taye Goshu, Purnachandra Rao Koya. (2014). Derivation of Inflection Points of Nonlinear Regression Curves - Implications to Statistics. American Journal of Theoretical and Applied Statistics, 2(6), 268-272. https://doi.org/10.11648/j.ajtas.20130206.25

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    Ayele Taye Goshu; Purnachandra Rao Koya. Derivation of Inflection Points of Nonlinear Regression Curves - Implications to Statistics. Am. J. Theor. Appl. Stat. 2014, 2(6), 268-272. doi: 10.11648/j.ajtas.20130206.25

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    AMA Style

    Ayele Taye Goshu, Purnachandra Rao Koya. Derivation of Inflection Points of Nonlinear Regression Curves - Implications to Statistics. Am J Theor Appl Stat. 2014;2(6):268-272. doi: 10.11648/j.ajtas.20130206.25

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  • @article{10.11648/j.ajtas.20130206.25,
      author = {Ayele Taye Goshu and Purnachandra Rao Koya},
      title = {Derivation of Inflection Points of Nonlinear Regression Curves - Implications to Statistics},
      journal = {American Journal of Theoretical and Applied Statistics},
      volume = {2},
      number = {6},
      pages = {268-272},
      doi = {10.11648/j.ajtas.20130206.25},
      url = {https://doi.org/10.11648/j.ajtas.20130206.25},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajtas.20130206.25},
      abstract = {In this paper, we derive inflection points for the commonly known growth curves, namely, generalized logistic, Richards, Von Bertalanffy, Brody, logistic, Gompertz, generalized Weibull, Weibull, Monomolecular and Mitscherlich functions. The functions often represent the mean part of non-linear regression models in Statistics. Inflection point of a growth curve is the point on the curve at which the rate of growth gets maximum value and it represents an important physical interpretation in the respective application area. Not only the model parameters but also the inflection point of a growth curve is of high statistical interests.},
     year = {2014}
    }
    

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    T1  - Derivation of Inflection Points of Nonlinear Regression Curves - Implications to Statistics
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    AB  - In this paper, we derive inflection points for the commonly known growth curves, namely, generalized logistic, Richards, Von Bertalanffy, Brody, logistic, Gompertz, generalized Weibull, Weibull, Monomolecular and Mitscherlich functions. The functions often represent the mean part of non-linear regression models in Statistics. Inflection point of a growth curve is the point on the curve at which the rate of growth gets maximum value and it represents an important physical interpretation in the respective application area. Not only the model parameters but also the inflection point of a growth curve is of high statistical interests.
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