Translated Titles

The Estimation of Generalized Diversity Index for Geographic Information Data



Key Words

地理資訊系統 ; 辛普森多樣性指數 ; 香農多樣性指數 ; Geographically Information System ; Simpson’s Diversity Index ; Shannon’s Diversity Index



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Chinese Abstract

當研究人員想探索生態圈的生物多樣性時經常使用一些指標作為參考。生物多樣性的常用指標是辛普森多樣性指數和香農多樣性指數。在過去,多樣性指數會忽略地理信息的位置,例如,觀察距離和周圍地理資訊。因此,我們整合辛普森多樣性指數和香農多樣性指數,成為一個廣義多樣性指數,並使其包含地理資訊的物種比例。然後,我們設計一些情況來進行統計模擬,並使用真實數據來計算廣義多樣性指數,並且與過去不考慮地理資訊的多樣性指標一起比較。模擬結果顯示,當樣本數增加,估計變異數會減少; 並且參數的估計量會接近真實值,它們的平均標準誤差和均方根誤差會變小。我們所提出的廣義多樣性指數和比例模型的優點是可以反應物種和目標值之間的距離和物種的地理位置。

English Abstract

This is an interesting issue to explore the biological diversity of ecosphere. Researcher often use some indicators as a reference until now. First, the commonly used indices of biological diversity are Simpson's diversity index and Shannon's diversity index. However, in the past, the indices of the diversity ignore the position of observation or geographically information, for example, the distance and surroundings of observation when we considered the diversity indices of several species. Therefore, we integrate Simpson’s diversity index and Shannon’s diversity index to be a generalized diversity index (GDI) with proportion functions of geographically information. Then, we conduct a statistical simulation by some cases and use a real data for generalized diversity index to compare these diversity indices without considering geographic information data. The simulation results show when sample size increases, the estimation of parameters and GDI are close to true value. Their average standard error and root mean square error become small. The advantage of proposed GDI and function of proportions can reflect about geographical location of species through the distance between species and target value.

Topic Category 基礎與應用科學 > 統計
管理學院 > 統計學系
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