Evaluation of the Applicability of the Weibull Probability Density Function with Different Approaches for Diameter Distributions of Plantations of Four Conifer Species

評估不同方法推估之Weibull函數在四種針葉樹人工林直徑分布之適用性

黃凱洛(Kai-Luo Huang) ； 王兆桓(Chao-Huan Wang) ； 顏添明(Tian-Ming Yen) ； 李隆恩(Long-En Li)

《台灣林業科學》 30卷1期 (2015/03) Pp. 1-13

https://doi.org/10.7075/TJFS.201503_30(1).0001

摘要

本研究旨在探討應用Weibull機率密度函數應用於臺灣四種主要針葉樹種－杉木、柳杉、紅檜及臺灣杉林分直徑分布之適用性。此四種針葉樹過去廣泛地栽植於臺灣各地區，本研究主要以此四種針葉樹人工林為研究對象，研究區域分布於整個臺灣，所採用之資料主要來自於國有林事業區森林經營計畫檢訂調查之永久樣區系統，林分直徑分布建模係採用最大概似法（the maximum likelihood estimator,MLE）和兩種百分位數法［the percentile estimators, PE（I） and PE（II）］配適Weibull機率密度函數，建模後以Kolmogorov-Smirnov測驗檢測觀測值和由三種方法模擬所得之Weibull分布之適合度，所得結果以PE（II）模擬結果最佳，其樣本通過檢測比例在杉木、柳杉、紅檜及臺灣杉分別為100、96.6、85.5及97.2%。此外研究結果也發現三種推估方法在模擬不同樹種呈現一致性趨勢，即樣本通過檢測比例：PE（II）＞ PE（I）＞ MLE，此結果顯示PE（II）之推估結果最適合四種樹種之直徑分布。

關鍵字

Weibull機率密度函數 ； 針葉樹人工林 ； 最大概似法 ； 百分位數法

並列摘要

The purpose of this research was to quantify diameter distributions of stands using the Weibull probability density function for 4 conifers, namely China fir (Cunninghamia lanceolata), Japanese cedar (Cryptomeria japonica), Taiwan red cypress (Chamaecyparis formosensis), and Taiwania (Taiwania cryptomerioides). These 4 conifers are widely planted in mountain areas of Taiwan, and we focused on plantation forests. The study area included all of Taiwan, and the data were from a system of permanent sample plots of the National Forest Management Plan Revision. We utilized the Weibull function to model diameter distributions based on 3 approaches of the maximum likelihood estimator (MLE) and 2 percentile estimators [PE(I) and PE(II)]. After examining the goodness- of-fit for the observed data and the Weibull distribution estimated using the 3 approaches with the Kolmogorov-Smirnov (K-S) test, we found that PE(II) was superior to the other approaches, and the respective pass rates of samples were 100, 96.6, 85.5, and 97.2% for China fir, Japanese cedar, Taiwan red cypress and Taiwania. A similar trend of pass rates of samples indicated that PE(II) ＞ PE(I) ＞ MLE for each species. The results implied that PE(II) was the best estimator among the 3 approaches for these 4 conifers.

並列關鍵字

Weibull probability density function ； conifer plantations ； maximum likelihood estimators ； percentile estimators