在環境生態學中，生態學家往往會利用相似性指標來探討兩個群落中的物種分佈結構，然而部份生態學家認為相似性指標並非唯一可行的方法；利用兩群落物種間的相異程度也可得到物種的分佈結構，以此想法衍生出了距離指標。
本文探討距離指標中的Hellinger 距離指標，並利用動差法求出其估計量。而在電腦模擬中可發現此估計量有高估的情形，因此本文使用三次圓滑曲線逼近法進行修正，再利用矩陣條件數分析所採用的逼近法；並藉由電腦模擬觀察在改變共同種種類數以及總物種數的情況下，新估計量的表現情形。最後，本文所提出之指標將以嘉義縣好美里海岸線水生生物的資料加以應用分析。

In environmental ecology, the ecologists often use similarity index to explore the species structure of two communities. But some ecologists think that the similarity index is not the only feasible way, using the difference between the two communities is also available to explore the of species structure. So the distance index can be derived from this idea.
In this thesis, we discusses the index of Hellinger distance from the distance index, and find its estimator by the method of moments. From the simulation results can be found the estimation is overestimated, so we need to correct the estimation by Cubic Spline Interpolation, and use condition number of matrix to analyze the approach. We evaluated the performance of corrected estimation by changing the sample size and the number of shared species in the simulation result.
Finally, we will use the estimation to analysis the marine organism in Haomei Village, Chiayi County, Taiwan.

第一章 緒論 1
第二章 符號說明及文獻回顧 4
2.1 符號與模式介紹 4
2.2 距離指標文獻回顧 6
2.2.1 距離指標 6
2.2.2 圓滑曲線逼近法 10
第三章 Hellinger 距離指標與其估計量之探討 13
3.1 估計量之探討 13
3.1.1 估計量之推導 13
3.1.2 三次圓滑曲線逼近法修正估計量 14
3.1.3 比較二次、三次與四次圓滑曲線逼近法 19
3.2估計量 之標準化與探討 23
第四章 模擬研究與分析 26
4.1模擬條件 26
4.2 估計量模擬結果 28
第五章 實例分析-嘉義縣好美里水生生態資料 20
第六章 結論與未來研究 34

中文文獻

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英文文獻

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