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

Ayele Taye Goshu; Purnachandra Rao Koya

doi:doi:10.11648/j.ajtas.20130206.25

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

Ayele Taye Goshu, Purnachandra Rao Koya

Published in American Journal of Theoretical and Applied Statistics (Volume 2, Issue 6)

Received: 19 December 2013 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.

Published in	American Journal of Theoretical and Applied Statistics (Volume 2, Issue 6)
DOI	10.11648/j.ajtas.20130206.25
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), 2014. Published by Science Publishing Group

Keywords

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

References

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APA Style

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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ACS 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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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://article.sciencepublishinggroup.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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TY  - JOUR
T1  - Derivation of Inflection Points of Nonlinear Regression Curves - Implications to Statistics
AU  - Ayele Taye Goshu
AU  - Purnachandra Rao Koya
Y1  - 2014/01/10
PY  - 2014
N1  - https://doi.org/10.11648/j.ajtas.20130206.25
DO  - 10.11648/j.ajtas.20130206.25
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 268
EP  - 272
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20130206.25
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.
VL  - 2
IS  - 6
ER  -

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Author Information

Ayele Taye Goshu

School of Mathematical and Statistical Sciences, Hawassa University, Ethiopia
Purnachandra Rao Koya

School of Mathematical and Statistical Sciences, Hawassa University, Ethiopia

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APA Style

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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ACS 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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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

Copy | Download

@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://article.sciencepublishinggroup.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}
}

Copy | Download

TY  - JOUR
T1  - Derivation of Inflection Points of Nonlinear Regression Curves - Implications to Statistics
AU  - Ayele Taye Goshu
AU  - Purnachandra Rao Koya
Y1  - 2014/01/10
PY  - 2014
N1  - https://doi.org/10.11648/j.ajtas.20130206.25
DO  - 10.11648/j.ajtas.20130206.25
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 268
EP  - 272
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20130206.25
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.
VL  - 2
IS  - 6
ER  -

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