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    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/53390


    Title: 多重社群的相似指數研究
    Other Titles: A Similarity Index among Multiple Populations
    Authors: 余清祥
    Contributors: 國立政治大學統計學系
    行政院國家科學委員會
    Keywords: 相似指數;生物多樣性;Jaccard 指數;Simpson 指數;Shannon 指數;最大概似估計;Delta法
    Similarity index;Species diversity;Jaccard Index;Simpson index;Shannon Index;Maximum likelihood estimator;Delta method
    Date: 2007
    Issue Date: 2012-08-30 09:59:00 (UTC+8)
    Abstract: 物種相似性為兩個族群中有物種的相似程度測量值，可用於比較兩個地區生態環境的 相似程度，或是評估某族群在不同時間的變遷。過去，生態學家曾使用物種重複評估諸如 珊瑚、水鳥等生物族群間的相似性及其變遷；近年來也應用於網際網路搜尋引擎，查詢比 對資料的相似性。較為常用的相似指數為Jaccard 指數，其定義為相同品種個數的比例，並 未將品種在族群中佔有的比例及可能遷移的特性列入考慮，無法反映各品種間的生態競爭 問題，參考Yue等人(2001, 2005)的討論。 本研究以探討多重社群的相似指數為目的，首先研究回顧現有的兩兩社群間的相似指 數，並將其延伸至多重社群。第一年計畫將探討如何將變異數分析延伸至多重社群的相似 指數，並以最大概似估計求取相似指數的估計量，以理論及電腦模擬研究估計量的在大樣 本及小樣本的特性。 第二年計畫著重於推廣相似指數的應用，尤其在適合度檢定。一般適合度檢定多考慮 卡方檢定，因其使用時較有彈性，但需要滿足期望個數不小於5 的規定。因為相似指數沒 有這種限制，我們將以電腦模擬為主，研究常見的Jaccard、Simpson、Shannon 等指數，將 其用於適合度檢定。
    Most species diversity indices are designed to measure the species diversity of one population or two populations. For example, the Shannon and Simpson indices are for one population and the Jaccard index is for two populations. There are only a few for the similarity among three or more populations. In this study, we propose a class of similarity indices for multiple populations, to measure the ratio of between-population characteristics and within-population characteristics. We will also use the similarity index as a tool for the goodness-of-fit test. The focus of the first year project is to review the similarity indices and propose a similarity index for measuring 3 or more populations. The proposed index will adapt the idea of Analysis of Variance in measuring treatment effect. We will use the Maximum likelihood estimation to find the estimator and study its asymptotic properties. The focus of the second year project is to study the goodness-of-fit and use the similarity indices (e.g., Jaccard, Simpson, and Shannon indices) as a tool for testing. Although the frequently used chi-square test has the advantages of flexibility, there are certain restrictions for using it. The similarity indices do not have those restrictions and we will use simulations to study the performances of frequently used indices.
    Relation: 基礎研究
    學術補助
    研究期間:9608~ 9707
    研究經費:460仟元
    Data Type: report
    Appears in Collections:[統計學系] 國科會研究計畫

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