評估不同求解Weibull 機率密度函數方法應用於量化臺灣杉人工林林分直徑分布之適用性

Assessment of the applicability of the Weibull probability density function by various stand diameter distribution quantification approaches of a Taiwania (Taiwania cryptomerioides) plantation

Weibull機率密度函數已被廣泛應用於人工林及天然林之直徑分布，而不同的參數求解方法為影響Weibull機率密度函數模擬林分直徑分布良窳的重要因子。本研究目的在於評估Weibull機率密度函數在不同參數求解方法模擬直徑分布之適用性，研究對象為臺灣中部之臺灣杉 (Taiwaniacryptomerioides) 人工林，位於惠蓀林場第3林班。分析方法採用最大概似法 (the maximum likelihoodestimation, MLE)、最小平方法 (the least-squares estimation, LSE)、2種動差法 (the method of momentsestimation, MME-Ⅰ and MME-Ⅱ)、4種百分位數法 (the percentiles estimation, PE I-1, PE I-2, PE Ⅱ-1and PE Ⅱ-2) 與動差百分法 (the moment-percentile estimation, MPE) 等9種方法推估Weibull機率密度函數，並以Kolmogorov-Smirnov (K-S) test、Anderson-Darling (A-D) test 及root mean squared error(RMSE) 3種方法檢定模擬結果。在K-S test結果顯示，除MLE (通過率為75%) 及PE Ⅰ-2 (通過率25%) 兩種方法外，其餘方法的通過率皆為100%，然而僅PE Ⅱ-2經K-S test及A-D test兩者的檢測結果樣本通過率達100%，本研究所得之結果將可提供臺灣杉人工林直徑分布重要量化資訊。

The Weibull probability density function has been widely used in predicting stand diameter distribution for various forests. Predicting stand diameter distribution is influenced by the estimation approaches. The purpose of this study was to assess the application of the Weibull probability density function to quantify stand diameter distribution by various approaches. The data used in this study was collected from a Taiwania (Taiwania cryptomerioides) plantation in the third compartment of Huisun Forest Station located at central Taiwan. We employed 9 approaches, namely, the maximum likelihood estimation (MLE), the least-squares estimation (LSE), two method of moments estimations (MME-Ⅰ and MME-Ⅱ), four percentiles estimations (PE I-1, PE I-2, PE Ⅱ-1 and PE Ⅱ-2) and the moment-percentile estimation (MPE) to predict Weibull functions. The results were examined by the Kolmogorov–Smirnov (K-S) test, Anderson-Darling (A-D) test and root mean squared error (RMSE). We found that the pass rate of the K-S test were 100% for all approaches except MLE (75%) and PE Ⅰ-2 (25%). On the other hand, the pass rate of both K-S test and the A-D test was100% for PE Ⅱ-2 only. Our findings provides valuable information in quantifying diameter distribution for Taiwania plantations.