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    National Tsing Hua University Institutional Repository > 理學院 > 統計學研究所 > 期刊論文 >  Nonparametric estimation of Shannon's index of diversity when there are unseen species in sample

    Please use this identifier to cite or link to this item: http://nthur.lib.nthu.edu.tw/dspace/handle/987654321/54102

    Title: Nonparametric estimation of Shannon's index of diversity when there are unseen species in sample
    Authors: Chao A;Shen TJ
    教師: 趙蓮菊
    Date: 2003
    Publisher: Springer Verlag
    Relation: ENVIRONMENTAL AND ECOLOGICAL STATISTICS,Volume: 10,Issue: 4,Pages: 429-443,Published: DEC 2003
    Abstract: A biological community usually has a large number of species with relatively small abundances. When a random sample of individuals is selected and each individual is classified according to species identity, some rare species may not be discovered. This paper is concerned with the estimation of Shannon's index of diversity when the number of species and the species abundances are unknown. The traditional estimator that ignores the missing species underestimates when there is a non-negligible number of unseen species. We provide a different approach based on unequal probability sampling theory because species have different probabilities of being discovered in the sample. No parametric forms are assumed for the species abundances. The proposed estimation procedure combines the Horvitz-Thompson (1952) adjustment for missing species and the concept of sample coverage, which is used to properly estimate the relative abundances of species discovered in the sample. Simulation results show that the proposed estimator works well under various abundance models even when a relatively large fraction of the species is missing. Three real data sets, two from biology and the other one from numismatics, are given for illustration.
    URI: http://pubget.com/paper/pgtmp_2a4ea2424a21d1926199ecfd4a41798d
    Appears in Collections:[統計學研究所] 期刊論文

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