| Summary: | 碩士 === 淡江大學 === 水資源及環境工程學系 === 90 === Probability estimation in hydrological frequency analysis is an essential procedure, and also a significant factor of accuracy. This study is to solve the dispute on plotting position formula by numerically solving the analytic solutions of order statistics. It is shown in the results that the median corresponding to the plotting position formula is independent of the probability distributions of samples. On the other hand, the parameter α of distribution-free plotting position formula is the function of n and k. The variation of parameter’s value (α) in numerical analytic solutions is dependent on the sample size (n), the exceedence probability (p) and order (k). However, it is not convenient to use the analytic solutions in the practical application. By comparing the analytic solutions of the distribution-free plotting position formula and the other plotting positions, it is found that the Chegodayev plotting position formula is the optimum plotting position formula.
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