I propose the Risk Analysis（Method of Yearly Maxima）as the 2nd solution for the secure marriage age, but this method has some problems which are not easy to be described. The Risk Analysis is part of the earthquake theory in Civil Engineering, and the seismic design code takes it to calculate the seismic forces. The theory can be used to calculate the maximal possible period for the marriage age, but it cannot describe the other conditions or situations. Let's see the formal formula of Risk Analysis as follow:
The general design mode takes the exceedance probability Rd = 10% and the working life Td = 50 years, so that you can derive the return period Tr = 475 years for buildings. In the secure marriage age, you can choose Rd = 1~10%, and you can take the same Tr values, 5~200, as the computer program of "Statistical Methods in Hydrology（on-line）". Hence, you can get the Td values, and you can know when you shall marriage for the maxima age.
What's the meaning of Td in the secure marriage age? It means "the future years", so that your secure marriage age shall be less than the return period of Tr with the possibility of Rd. The return period of Tr is the maxima value, but your future years Td has to achieve the maxima value to meet the failure mode. Hence, you can use return age of Tr minus Td to find the desired secure marriage age as follow:
I choose the male Taiwanese data, and I take Rd = 1% and Tr = 5, 10, 25, 50, 100, 200. Therefore, I can get the results of return period analysis, and calculate the Td values of various Tr values.
What's the problem in the Risk Analysis? The Risk Analysis just can be described for the MAXIMAL DATA MODE, but analyzed for the other distribution modes. After you get a data, you should analyize which kind of distribution mode is. And then, you can try to predict the possible value and its possibility. Hence, the so-called possibility of the Risk Analysis means the happening possibility of the maximal data, not the general possibility concepts in statistics. Of course, the return period can find the maximal data for the period, but you cannot always do the same mode for different modes of distribution data. Besides, it just can be predict to marry at a late age, but to marry at an early age.
I have proposed the 2nd solution for the secure marriage age, but this solution just can be used for the prediction of the maxima value. Actually, the Risk Analysis is one kind of Gumbel distribution, so that the distribution mode is the same as the male Taiwanese data. I suggest the male Taiwanese that you can choose Rd = 1% and Tr = 100 years, and the reasonable secure marriage age shall be 32.175 years old. In Hydraulic engineering, the developed land always take the return period Tr = 100 years for the hydrology analysis, so that it makes sense really, Deliberation Standards of Agricultural District of Urban Planning Area, for example.
References
The general design mode takes the exceedance probability Rd = 10% and the working life Td = 50 years, so that you can derive the return period Tr = 475 years for buildings. In the secure marriage age, you can choose Rd = 1~10%, and you can take the same Tr values, 5~200, as the computer program of "Statistical Methods in Hydrology（on-line）". Hence, you can get the Td values, and you can know when you shall marriage for the maxima age.
What's the meaning of Td in the secure marriage age? It means "the future years", so that your secure marriage age shall be less than the return period of Tr with the possibility of Rd. The return period of Tr is the maxima value, but your future years Td has to achieve the maxima value to meet the failure mode. Hence, you can use return age of Tr minus Td to find the desired secure marriage age as follow:
I choose the male Taiwanese data, and I take Rd = 1% and Tr = 5, 10, 25, 50, 100, 200. Therefore, I can get the results of return period analysis, and calculate the Td values of various Tr values.
| Tr | Return Age/td> | Td | Age |
| 5 | 31.37284191 | 0.315307598 | 31.05753431 |
| 10 | 31.64606514 | 0.318053583 | 31.32801156 |
| 25 | 31.99128343 | 0.321523143 | 31.66976029 |
| 50 | 32.24738607 | 0.324097060 | 31.92328901 |
| 100 | 32.50159770 | 0.326651973 | 32.17494572 |
| 200 | 32.75488174 | 0.329197562 | 32.42568418 |
What's the problem in the Risk Analysis? The Risk Analysis just can be described for the MAXIMAL DATA MODE, but analyzed for the other distribution modes. After you get a data, you should analyize which kind of distribution mode is. And then, you can try to predict the possible value and its possibility. Hence, the so-called possibility of the Risk Analysis means the happening possibility of the maximal data, not the general possibility concepts in statistics. Of course, the return period can find the maximal data for the period, but you cannot always do the same mode for different modes of distribution data. Besides, it just can be predict to marry at a late age, but to marry at an early age.
I have proposed the 2nd solution for the secure marriage age, but this solution just can be used for the prediction of the maxima value. Actually, the Risk Analysis is one kind of Gumbel distribution, so that the distribution mode is the same as the male Taiwanese data. I suggest the male Taiwanese that you can choose Rd = 1% and Tr = 100 years, and the reasonable secure marriage age shall be 32.175 years old. In Hydraulic engineering, the developed land always take the return period Tr = 100 years for the hydrology analysis, so that it makes sense really, Deliberation Standards of Agricultural District of Urban Planning Area, for example.
References
- 李景亮、梁英文（2000）結構耐震設計，文笙書局
- MOI，統計處性別統計專區/性別統計指標/參、婚姻與家庭/初婚按年齡及教育程度分，http://www.moi.gov.tw/stat/gender.aspx
- 鄭子璉，Statistical Methods in Hydrology，http://tlcheng.twbbs.org/Tools/stat/stat.asp
- Wikipedia, Gumbel distribution, http://en.wikipedia.org/wiki/Gumbel_distribution
- CPAMI, Deliberation Standards of Agricultural District of Urban Planning Area, http://www.cpami.gov.tw
