Abstract
Regression is widely applied in many fields. Regardless of the types of regression, we often assume that the observations are precise. However, in real-life circumstances, this assumption can only be met sometimes, which means the traditional regression methods can result in significant imprecise or biased predictions. Consequently, uncertain regression models might provide more accurate and meaningful results under these circumstances. In this article, we provide the residual analysis of uncertain Gompertz regression model, as well as the corresponding forecast value and confidence interval. Finally, we give a numerical example of uncertain Gompertz regression model.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Corral N, Gil MA (1984) The minimum inaccuracy fuzzy estimation: an extension of the maximum likelihood principle. Stochastica 8:63–81
Fisher RA (1925) Statistical methods for research workers. Oliver and Boyd, Edinburgh
Galton F (1885) Regression towards mediocrity in hereditary stature. J Anthropol Inst 15:246–263
Gompertz B (1825) On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philos Trans B 115:513585
Laird AK (1964) Dynamics of tumor growth. Br J Cancer 18:490502
Legendre AM (1805) New methods for the determination of the orbits of comets. Firmin Didot, Paris
Lio W, Liu B (2018) Residual and confidence interval for uncertain regression model with imprecise observations. J Intell Fuzzy Syst 35:2573–83
Liu B (2007) Uncertainty theory, 2nd edn. Springer, Berlin
Liu B (2009) Some research problems in uncertainty theory. J Uncertain Syst 3:3–10
Liu B (2010) Uncertainty theory: a branch of mathematics for modeling human uncertainty. Springer, Berlin
Liu B (2012) Why is there a need for uncertainty theory. J Uncertain Syst 6:3–10
Neyman J, Pearson ES (1933) On the problem of the most efficient tests of statistical hypotheses. Philos Trans R Soc A Math Phys Eng Sci 231:289–337
Nguimkeu P (2014) A simple selection test between the Gompertz and logistic growth models. Technol Forecast Soc Change 88:98–105
Student (1908) The probable error of a mean. Biometrika 6:1–25
Tanaka H, Uejima S, Asai K (1982) Linear regression analysis with fuzzy model. IEEE Trans Syst Man Cybern 12:903–907
Wilks SS (1938) The large-sample distribution of the likelihood ratio for testing composite hypotheses. Ann Math Stat 9:60–62
Yang X, Liu B (2017) Uncertain time series analysis with imprecise observations. Fuzzy Optim Decis Mak (in press)
Yao K, Liu B (2018) Uncertain regression analysis: an approach for imprecise observations. Soft Comput 22:557982
Zwietering MH, Jongenburger I, Rombouts FM, VanT Rie TK (1990) Modeling of the bacterial growth curve. Appl Environ Micriobiol 56:197581
Acknowledgements
This work was supported by National Natural Science Foundation of China (Grant No. 61374082).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that there is no conflict of interest regarding the publication of this paper.
Ethical Approval
This article does not contain any studies with human participants performed by any of the authors.
Additional information
Communicated by Y. Ni.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Hu, Z., Gao, J. Uncertain Gompertz regression model with imprecise observations. Soft Comput 24, 2543–2549 (2020). https://doi.org/10.1007/s00500-018-3611-1
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-018-3611-1