It is very important to estimate the parameters of a risk prediction model in the case of small samples. This paper proposed an improved method for predicting water shortage risk in situations when insufficient data are available. The new method (maximum entropy estimation, MEE) does not require the data about water shortage risk but only a few data about the risk factors. Twelve simulations or experiments were made to evaluate the performance of MEE under different small sample size and compared with the maximum likelihood estimation (MLE) which requires a large amount of data about risk and its factors, and two models which require small samples about risk and risk factors. The result shows that MEE performs much better than MLE, and has an advantage over the two models. Water shortage risks in 2020 in all the districts or counties of Tianjin were predicted by using the new method. The result shows that the values of water shortage risk in most of the districts or counties of Tianjin are very high when the transferred and unconventional water are not used. After using the transferred and unconventional water, all the values of water shortage risk decline considerably.
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The study was supported by National Natural Science Foundation of China (Grant No. 51609254).
Communicated by Subimal Ghosh
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Qian, L., Wang, Z., Wang, H. et al. An improved method for predicting water shortage risk in the case of insufficient data and its application in Tianjin, China. J Earth Syst Sci 129, 48 (2020). https://doi.org/10.1007/s12040-019-1299-y
- Maximum entropy estimation
- maximum likelihood estimation
- small samples
- water shortage risk