Uncertain Gompertz regression model with imprecise observations

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.

[1]  Baoding Liu,et al.  Residual and confidence interval for uncertain regression model with imprecise observations , 2018, J. Intell. Fuzzy Syst..

[2]  F. Galton.  Regression Towards Mediocrity in Hereditary Stature. , 1886 .

[3]  Baoding Liu,et al.  Uncertain regression analysis: an approach for imprecise observations , 2018, Soft Comput..

[4]  Baoding Liu.  Why is There a Need for Uncertainty Theory , 2012 .

[5]  Norberto Corral,et al.  The minimun inaccuracy fuzzy estimation: An extension of the maximum likelihood principle. , 1984 .

[6]  Pierre Nguimkeu.  A simple selection test between the Gompertz and Logistic growth models , 2014 .

[7]  R. Fisher.  Statistical methods for research workers , 1927, Protoplasma.

[8]  Baoding Liu,et al.  Uncertain time series analysis with imprecise observations , 2018, Fuzzy Optimization and Decision Making.

[9]  Baoding Liu,et al.  Uncertainty Theory - A Branch of Mathematics for Modeling Human Uncertainty , 2011, Studies in Computational Intelligence.

[10]  E. S. Pearson,et al.  On the Problem of the Most Efficient Tests of Statistical Hypotheses , 1933 .

[11]  Baoding Liu.  Some Research Problems in Uncertainty Theory , 2009 .

[12]  F. Rombouts,et al.  Modeling of the Bacterial Growth Curve , 1990, Applied and environmental microbiology.

[13]  Student,et al.  THE PROBABLE ERROR OF A MEAN , 1908 .

[14]  S. S. Wilks.  The Large-Sample Distribution of the Likelihood Ratio for Testing Composite Hypotheses , 1938 .

[15]  Baoding Liu,et al.  Uncertainty Theory - A Branch of Mathematics for Modeling Human Uncertainty , 2011, Studies in Computational Intelligence.

[16]  Laird Ak.  DYNAMICS OF TUMOR GROWTH. , 1964 .

[17]  Benjamin Gompertz,et al.  XXIV. 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. In a letter to Francis Baily, Esq. F. R. S. &c , 1825, Philosophical Transactions of the Royal Society of London.