Affiliations: [a]
School of Reliability and Systems Engineering, Beihang University, Beijing, China
| [b]
School of Economics, Shanghai University, Shanghai, China
Correspondence:
[*]
Corresponding author. Haoran Zheng, School of Economics, Shanghai University, Shanghai 200444, China. E-mail: [email protected].
Abstract: Uncertain statistics is a set of mathematical techniques to collect, analyze and interpret data based on uncertainty theory. In addition, probability statistics is another set of mathematical techniques based on probability theory. In practice, when to use uncertain statistics and when to use probability statistics to model some quality depends on whether the distribution function of the quality is close enough to the actual frequency. If it is close enough, then probability statistics may be used. Otherwise, uncertain statistics is recommended. In order to illustrate it, this paper employs uncertain statistics, including uncertain time series analysis, uncertain regression analysis and uncertain differential equation, to model the birth rate in China, and explains the reason why uncertain statistics is used instead of probability statistics by analyzing the characteristics of the residual plot. In addition, uncertain hypothesis test is used to determine whether the estimated uncertain statistical models are appropriate.
Keywords: Uncertainty theory, uncertain time series analysis, uncertain regression
analysis, uncertain differential equation, birth rate
