混合機率分布於水文頻率分析適用性之研究

由於理論上混合機率分布之累積機率呈反曲或S型，且水文資料常因其長度不足或資料特性之關係，點繪於機率紙上亦常呈現反曲或S型，此時，吾人易將資料判定爲滿足某一特性之混合機率分布。因此，若一資料點繪於機率紙上呈現反曲或是S型時，資料是否滿足某一特定之機率分布或混合機率分布爲本研究探討之主題。故，本研究以統計特性已知之合成資料，探討當資料以混合機率分布及傳統上常用之單一機率分布（NOR、LN2、EV1及PT3）分別擬合後，其推估值與理論值以及推估值與樣本本身兩者間之差異，並針對不同樣本大小進行分析，以了解混合機率分布之適用性。研究中並分析台灣地區資料記錄年至少30年之年一日、二日及三日最大降雨量資料，共計250站，以供規劃之參考。研究結果顯示，由於資料的特性與樣本數過小，其常易被判定為混合機率分布，其中，又以資料為極端値I型分布及皮爾遜III型分布時，造成資料誤判為混合機率分布的比例較高。應用於台灣地區年一日、二日及三日最大降雨資料時發現，混合對數常態分布十分不適宜，然，最佳分布以皮爾遜III型分布及混合常態分布所佔的比例最多，且若當混合常態分布爲最佳分布時，次佳分布大都爲皮爾遜III型分布，同時，此現象均發生於小樣本時。因此，依據合成資料之研究結果可知，台灣地區年一日、二日、三日最大暴雨資料仍採用皮爾遜III型分布，而非混合常態分布。

關鍵字

頻率分析；混合機率分布

並列摘要

The theoretical cumulative probability of the mixture distributions shows reverse curvatures. For the real hydrological data, however, due to the small sample size and the characteristics of data, data that draw on the probability paper often shows the reverse curvatures. By this time, it tends to identify it to mixture distributions. Consequently, when the data shows reverse curvatures on probability paper, would it satisfy a single probability distribution or mixture distributions is the major objection of this study. First of all, the synthetic data which is statistical property is known is fitted by mixture probability distribution (NOR, LN) and single probability distribution (NOR, LN2, EV1 and PT3) to yield estimated values separately. The difference between the comparison of estimated value and theoretical value and the comparison of estimated value and sample itself has been discussed with the different sample sizes to examine the aptness of the mixture distributions. Furthermore, the record of hydrology data of Taiwan area, at least thirty years of the annual maximum 1-day, 2-day, and 3-day rainfall (total 250 stations), is also analyzed in this study. From this research result, the hydrology data inclined to be misidentified as a mixture distribution because of property of the data and its small sample. However, most of the cases are belonged to Type I extreme distribution or Pearson type III distribution. For the annual maximum 1-day, 2-day and 3-day rainfall data, it was found that the mixture log-normal distribution is not appropriate. The most appropriate distributions are Pearson Type III and mixture normal distributions for the real data. However when the best distribution is mixture normal, most of the second best one are Pearson Type III distribution, particularly for the small sample size. Therefore, according to the results obtained by the synthetic data study, the Pearson Type III distribution is an appropriate for the annual maximum rainfall data in Taiwan area.

並列關鍵字

Frequency analysis ； Mixture distribution

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