The shortage of extreme rainfall data gives substantial uncertainty to design rainfalls and causes predictions for torrential rainfall to deviate strongly from adopted probability distributions used in river planning. These torrential rainfalls are treated as outliers which existing studies do not evaluate. However, probability limit method test which its acceptance region expresses with high accuracy the range where observed ith order statistics could realize. Confidence interval which quantifies uncertainty of adopted distributions can be constructed by assuming that these critical values in both sides of the adopted region follow the same function form applied to actual observed data. Furthermore, its validity is proved through comparison of confidence interval derived from ensemble downscaling calculations. In addition, these critical values are almost in accordance with outliers in samples from the ensemble downscaling calculations. Therefore, prediction interval which expresses the range that an unknown observed datum can take is constructed by extrapolating the critical values for limit estimation of a future datum. In this paper, quantification method of uncertainty of design rainfall and occurrence risk of outliers in the traditional framework, using the proposed confidence interval and prediction interval, is shown. Moreover, their application to future climate by using Bayesian statistics is explained.
Calculation of critical values of several probability distributions using standard numerical methods