在防洪及排水工程規劃設計中，洪水歷線是重要的考慮因素之一，然而以往對於洪水歷線的處理，不論是實測或是設計洪水歷線，均採用離散式的紀錄方式，即一個時刻一個時刻的紀錄。若洪水歷線較長則需紀錄較多的數據，而時刻與時刻之間未紀錄的數據也無從得知。利用機率密度函數來模擬直接逕流歷線的形狀，則可以改善此一缺點。本文之研究目的為利用常用的機率密度函數，如gamma、beta、lognormal、Gumbel及Weibull等五種不同的分佈，來模擬直接逕流歷線，並比較兩種不同的參數推估方式，包括形狀變數法(以形狀平均值與形狀變異數推估)和洪峰法(以洪峰量與洪峰時間推估)，所得模擬直接逕流歷線與實測值之差異。文末以濁水溪流域桶頭(2)流量站五場實測颱風洪水歷線進行檢驗，結果顯示gamma分佈配合洪峰法參數推估方式所得之模擬直接逕流歷線最佳。 The flood hydrograph is an essential factor in flood control planning and design. Traditional treatments of flood hydrographs use discrete type records. The data between time intervals are not available, however. Using the probability density function to model the flood hydrographs can overcome this problem and thus become continuous recording. The major purpose of this study is applying the probability density function to model the direct runoff hydrograph. The probability density functions considered in this study include gamma, beta, lognormal, Gumbel, and Weibull. Two different parameter-estimation schemes, one using shape variables and the other using flood peak and time to peak, are employed to investigate the effects on differences between the derived and observed flood hydrographs. The proposed methodology is demonstrated with an application to the Tungtou gauge station in Choshui Creek, Taiwan. The results show that the gamma probability density function associated with flood peak and time to peak parameter-estimation scheme has the best fitting to the observed flood hydrographs.