In this paper, the Seismic risk in the middle of the Bayan Har block based on the profile likelihood estimation of the generalized Pareto distribution is studied. Earthquake samples in the middle of the Bayan Har block in the late 60 years are analyzed. The result shows that the area experiences an earthquake above 7.0 every 5 years. The theoretical upper limit of magnitude is 8.7, indicating frequent geological activities in this area. The profile likelihood estimation is consistent with the estimation of the maximum likelihood of the parameters. The confidence interval of the short-term return level is the same for the two methods. But with the increasing return period, the confidence interval obtained by the profile likelihood estimation is shifted to the right as a whole compared to that of the Delt method. The ratio of the confidence interval length on both sides of the return level will increase. This asymmetry is effective for the uncertainty of magnitude prediction.

Objectives. The statistical characteristics of incubation time of COVID-19 are studied comprehensively in this paper. We studied the mean value and tail characteristic of incubation time. Also, the difference in incubation time is studied in different age groups, different genders, and different contact modes. Methods. We analyzed the data by a lognormal distribution. Tail characteristics of incubation time are studied by the excess function. The difference in incubation time between different age groups, different genders, and different contact modes is studied by one-way ANOVA. Results. The results showed that the mean value of incubation time is about 12.6 days, and the standard deviation is about 6.1 days. The incubation time of 95% of patients was within 24 days. Some patients have a very long incubation time according to the excess function. The incubation time was not related to age and gender but related to the suspected contact modes. Conclusions. The mean value of incubation time is consistent with the actual situation. The above results are a reasonable explanation for the phenomenon of super-long incubation time in some patients and the development trend of epidemic situations.

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