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 在生態方面,估計種類數的估計方式有很多種。例如摺刀估計,拔靴估計,樣本涵蓋估計等等。其中, 利用最大下界估計式估計種類數是一個不錯的方法。其中最常被推薦的是Chao (1987) 建設之下界估計式。Mao (2008) 推廣Chao (1984) 的結果, 提出一組廣義的下界估計式。本文進一步修正Mao (2008) 之方法於森林樹木之種類數估計上, 並以三組實際數據驗證所提之方法。
 There has many ways to estimate species richness of estimation in the ecological aspects. For example, jackknife estimator, bootstrap estimator, abumdance-basedcoverage estimator (ACE) and so on. And, it is good idea that use the greatest lower bound to estimate species richness. In many lower bound estimators, Chao (1987) lower bound estimators are often recommended and famous. Mao (2008) raised the lower bound of a set of generalized estimation by promotion of Chao (1984) results. In this paper, we modify Mao’s (2008) method that the types of trees in the forest was estimated, and three sets of empirical data to validate the method mentioned.
 1 第一章 緒論 12 第二章 模式簡介與文獻回顧 3 2.1抽樣方法與模式假設............................... 3 2.2 符號說明.........................................4 2.3 種類數文獻回顧...................................4 2.3.1 Chao-下界估計式............................. 4 2.3.2 Mao (2008) 的估計方法........................63 第三章種類數估計 10 3.1 廣義下界估計式..................................10 3.2 平滑化fj........................................11 3.3 階次選取........................................12 3.4 估計近似標準差..................................134 第四章模擬研究與實例分析 14 4.1 資料介紹........................................14 4.2 估計量的模擬與條件..............................22 4.3 實例模擬分析與結果..............................235 第五章討論 26參考文獻 27附錄 30
 [1] Burnham, K.P. & Overton, W.S. (1978). Estimation of the size of a closed population when capture probabilities vary ampng animals. Biometrika 65, 625-534[2] C. R. Rao and S. K. Mitra. Generalized Inverse of Matrices and Its Applications. John Wiley & Sons, New York, London, Sidney, Toronto, firrst edition, (1971).[3] Chao, A. (1984). Nonparametric estimation of the number of classes in a population. Scandinavian Journal of Statistics 11, 265-270.[4] Chao, A. (1987). Estimating the population size for capture-recapture data with unequal catchability. Biometrics 43, 783-791.[5] Chao, A. (1989). Estimating population size for sparse data in capturerecapture experiments. Biometrics 45, 427-438.[6] Chao, A. (2001). An overview of closed capture-recapture models. J. Agric. Biol. Environ. Stat 6, 138-155.[7] Chao, A., Shen, T.-J. & Hwang, W.-H. (2006). Application of Laplace''s boundary-mode approximations to estimate species and shared species richness. Aust. N. Z. J. Stat 48, 117-128.[8] Church, K. and W. Gale, (1991), A comparison of the enhanced Good-Turing and deleted estimation methods for estimating probabilities of English bigrams, Computer Speech and Language, v. 5, pp. 19-54.[9] Church, K., W. Gale, J. Kruskal, (1991), Appendix I of (Church and Gale, 1991).R[10] Chao, A., and Lee, S.-M. (1992). Estimating the number of classes via sample coverage. Journal of the American Statistical Association, 87, 210-217.[11] Dorazio, R.M. & Royle, J.A. (2003). Mixture models for estimating the size of a closed population when capture rates vary among individuals. Biometrics 59, 351-364.[12] Efron, B. (1979). Bootstrap methods: Another look at the jackknife. Annals of Statistics 7, 1-26.[13] Donald W. Marquardt (1970). Generalized Inverses, Ridge Regression, Biased Linear Estimation, and Nonlinear Estimation. Technometrics, Vol. 12, No. 3, 591-612.[14] Mao, C.X. (2007). Testing list effects and diagnosing individual catchabilities in the Rasch model. Statist.Methodol 4, 416-422.[15] Mao, C.X., Colwell, R.K. &Chang, J. (2005). Estimating the species accumulation curve usingmixtures. Biometrics 61, 433-441.[16] Mao, C.X. & Lindsay, B.G. (2002). Diagnostics for the homogeneity of capture probabilities in a Bernoulli census. Sankhy‾a 64, 626-639.[17] Mao, C.X. & Lindsay, B.G. (2004). Estimating the number of classes in multiple populations: a geometric analysis. Canad. J. Statist. 32, 303-314.[18] Mao, C.X. & Lindsay, B.G. (2007). Estimating the number of classes. Ann. Statist. 35, 917-930.[19] Margalef, R. (1958) Information theory in ecology. General Systems 3, 36-71.[20] Marquardt, D.W. (1970). Generalized Inverses, Ridge Regression, and Nonlinear Estimation. Technometrics 12, 591-612.[21] Norris, J.L.I. & Pollock, K.H. (1996). Nonparametric MLE under two closed capture-recapture models with heterogeneity. Biometrics 52, 639-649.[22] Pledger, S. (2000). Unified maximum likelihood estimates for closed capturerecapture models using mixtures. Biometrics 56, 434-442.[23] William A. Gale and G. Sampson. Good-turing smoothing without tears, 1995. URL http://citeseer.nj.nec.com/161518.html.[24] Shannon, C. E. (1948), A Mathematical Theory of Communication. Bell System Technical Journal 27, 379-423.[25] Simpson, E.H. (1949) Measurement of diversity. Nature 163, 688.[26] Smith, E. P. and van Belle, G. (1984). Nonparametric estimation of species richness. Biometrics 40, 119-129.[27] Skallioglu, S. & Akdeniz, F. (1998). Generalized Inverse Estimator and Comparison with Least Squares Estimator. Tr. J. Mathematics. 22, 77-84.[28] 林介龍& 蘇聲欣,2005, 馬來西亞森林動態樣區介紹。林業研究專訊Vol. 12 No4. 4-6[29] 孫義方,2006, 森林生態學研究的新潮流-森林動態樣區。林業研究專訊Vol. 13 No2. 1-6[30] http://www.ctfs.si.edu/[31] http://np.cpami.gov.tw/index.php?option=com frontpage&Itemid=9999(臺灣國家公園網站)
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 1 不歸還取樣模式下之種類數估計 2 生物多樣性指標之模擬研究

 1 [28] 林介龍& 蘇聲欣,2005, 馬來西亞森林動態樣區介紹。林業研究專訊Vol. 12 No4. 4-6 2 [29] 孫義方,2006, 森林生態學研究的新潮流-森林動態樣區。林業研究專訊Vol. 13 No2. 1-6

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