Shannon（1948）所提出的Shannon index即為熱力學第二定律中的「熵」（entropy），
熵的概念最早應用於軍事情報學，代表在情報源中一個字母所平均負擔的情報量，或者

視為一種對於事件（event）選擇結果的不確定程度或尺度（scale），嗣後由MacArthur（1955）

及Margalef（1958）引用於生物物種多樣性的研究。我們假設在七種捕取數及十種不同的

物種種類出現機率的情形下，組合成七十種估計條件。本研究的目的即在於循模擬試驗的

途徑，在不同的估計條件下，針對三種Shannon index估式─最大概度估式（MLE）、樣本

涵蓋估式及摺刀法估式分別比較其估計量的表現。模擬結果發現，隨著捕取數目的增加，

該三種估計量的均方根誤差、樣本標準差及近似標準差均逐漸減少。就不同捕取數而言，

在物種種類數固定於100之條件下，當樣本數小於100時，無論就均方根誤差或95%信賴區

間平均覆蓋率來看，三種估計量中以樣本涵蓋估計量的整體表現為最佳，而最大概度估計

量為最差。我們進一步比較三種估計量的偏差及樣本標準差，發現最大概度估計量的樣本

標準差雖然最小，但是其偏差卻是最大，這正是影響最大概度估計量之估計表現的主要原因。

第二章：Shannon index的估計方法----------------------------- 2

2.1公式及符號簡介----------------------------------------------------- 4

2.2最大概度法----------------------------------------------------------- 4

2.3樣本涵蓋率----------------------------------------------------------- 5

2.4摺刀法----------------------------------------------------------------- 8

第三章：模擬試驗的方法----------------------------------------- 10

3.1捕取樣本數--------------------------------------------------------- 10

3.2物種種類出現機率------------------------------------------------ 10

3.3模擬方法------------------------------------------------------------ 11

第四章：模擬結果與討論----------------------------------------- 12

參考文獻------------------------------------------------------------- 24

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