Criteria for Evaluating Probability Distribution Models in Hydrologic Frequency Analysis

This paper proposes a new framework for evaluating probability distribution models used in hydrologic frequency analysis. In the framework, the variance (standard deviation) in estimation of T-year events (quantiles) obtained by the model is incorporated as an evaluation criterion as well as some goodness-of-fit criteria; resampling methods such as the jackknife and the bootstrap are also incorporated to quantify the variance. Using the existing extreme data (annual maxima of κ-day precipitation, κ=1, 2, 3), the authors reveal the insufficiency of the conventional model evaluation which is based on only the goodness of fit. The proposed framework evaluates ten distributions with two or three parameters. Additionally, the relation between the amount of data and the variance (estimation accuracy) is investigated through bootstrap-type resampling.