Abstract
A common method of testing the reasonableness of estimates of unknown parameters in uncertain differential equations is to judge them by the \(\alpha \)-path of the differential equation. If all observations fall between the \(\alpha \)-paths, the estimates are considered reasonable. This paper introduces uncertain hypothesis testing into uncertain differential equations to test the reasonableness of the estimates, which is another new approach. Further, the concept of interval estimation of unknown parameters for uncertain differential equations is introduced. Some numerical examples are given to verify the feasibility of the method. The uncertain differential equations are also used to model global average temperature data, and the results are satisfactory.
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Acknowledgements
This work was funded by the National Natural Science Foundation of China (Grant Nos. 12061072 and 62162059) and the Xinjiang Key Laboratory of Applied Mathematics (Grant No. XJDX1401).
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Funding was provided by Natural Science Foundation of Xin-jiang Province (Grant No. 2020D01C017).
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Zhang, G., Shi, Y. & Sheng, Y. Uncertain hypothesis testing and its application. Soft Comput 27, 2357–2367 (2023). https://doi.org/10.1007/s00500-022-07748-8
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DOI: https://doi.org/10.1007/s00500-022-07748-8