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題名 兩母體共有物種數的估計及最佳停止點
The optimal stopping rule for estimating the number of shared species of two populations作者 蔡政珈 貢獻者 余清祥
蔡政珈關鍵詞 生物多樣性
共有物種數
摺刀估計法
最適停止規則
電腦模擬
Biodiversity
Number of shared species
Jackknife estimate
Optimal stopping rule
Computer simulation日期 2012 上傳時間 11-Jul-2013 16:36:56 (UTC+8) 摘要 在生態學與生物學上，物種數常作為生物多樣性的指標，以估計單一群體物種數為例，較知名的方法首推Good (1953)以在樣本中出現一次的物種為基礎，提出的物種數估計方法堪稱的先驅，隨後許多文獻延伸Good的想法，發展出許多的估計方法，例如Burham and Overton (1978)的摺刀估計法，Chao and Lee (1992)則以涵蓋機率方式估計。相對而言，兩群體的共有物種數的研究少有人探討，目前以Chao et al. (2000)的估計式較為知名。本研究參考Good (1953)提出估計未發現物種出現機率的想法，估計未發現共有物種的機率，並以Burham and Overton (1978)中應用摺刀法估計物種數的概念，建立一階摺刀估計式與變異數，且另行以多項分配公式推導變異數估計式，進行電腦模擬與實際資料驗證並與Chao et al. (2000)提出的共有物種估計式比較。最後根據Rasmussen and Starr (1979)以抽樣成本建立最適停止規則的概念，應用於本研究所提出的估計式，並經由電腦模擬找出抽樣成本與物種分佈均勻程度的關聯，可作為設定停止規則的依據。
The number of species is often used to measure the biodiversity of a population in ecology and biology. Good (1953) proposed a famous estimate for the number of species based on the probability of unseen species. Subsequently, many studies applied Good’s idea to create new estimation methods, For example, the Jackknife estimate by Burham and Overton (1978), and the estimate by using the sample coverage probability in Chao and Lee (1992) are two famous examples. However, not many studies focus on estimating the number of shared species of two populations, except the method by Chao et al. (2000).In this study, we modify Good’s idea and extend the Jackknife method of Burham and Overton (1978) to develop the estimate for the number of shared species of two populations. In addition, we also establish the variance formula of the estimator by using the multinomial distribution. Subsequently, we use computer simulation and real data sets to evaluate the proposed method, and compare them with the estimator by Chao et al. (2000). Finally, we adapt the idea of optimal stopping rule by Rasmussen and Starr (1979) and combine it with the proposed jackknife estimate. We found that using the sampling cost as the stopping rule is a feasible approach for estimating the number of shared species.參考文獻 英文部分：Bunge, J. and Fitzpatrick, M. (1993). Estimating the number of species : A Review. Journal of the American Statistical Association, 88, pp. 364-373.Burnham, P. K. and Overton, S. W. (1978). Estimation of the size of a closed population when capture probabilities vary among animals. Biometrika, 65, pp. 625-633.Chao, A. and Lee, S-M. (1992). Estimating the number of classes via sample coverage. Journal of American Statistical Association, 87, pp. 210-217.Chao, A., Hwang, W-H, Chen, Y-C., and Kuo, C-Y. (2000). Estimating the number of shared species in two communities. Statistica Sinica, 10, pp. 227-246.Chao, A., Ma, M.C., and Yang, M.C.K. (1993). Stopping rule and estimation for recapture debugging with unequal detection rates. Biometrika, 80, pp. 193-201.Chuang, C.J. (2012). Estimation of similarity indices via two-sample jackknife procedure. Journal of Applied Science and Engineering, 15, 3, pp. 301-310.Darroch, J. N., and Ratcliff, D. (1980). A note on capture-recapture estimation. Biometrics, 36, pp. 149-153.Efron, B. and Thisted, R. (1976). Estimation the number of unseen species: How many words did Shakespeare now? Biometrika, 63, pp. 435-447.Good, I. J. (1953). The population frequencies of species and the estimation of population parameters. Biometrika, 40, pp. 237-264.Quenouille, M. H. (1949). Approximate tests of correlation in time-series. Journal of the Royal Statistical Society. Series B, 11, pp. 68-84.Quenouille, M. H. (1956). Notes on bias in estimation. Biometrika, 43, pp. 353-360.Rasmussen, S.L. and Starr, N. (1979) Optimal and adaptive stopping in the search for new species. Journal of the American Statistical Association, 74, 367, pp. 661-667.Schechtman, E. and Wang, S. (2004). Jackknifng two-sample statistics. Journal of Statistical Planning and Inference, 119, pp. 329 – 340.Schucany, W. R., Gray, H. L., and Owen, D. B. (1971). On bias Reduction in Estimation. Journal of the American Statistical Association, 66, pp. 524-533.Sharot, T. (1976) The Generalized Jackknife: Finite Samples and Subsample Sizes. Journal of the American Statistical Association, 71, 354, pp. 451-454.Tuckey J. W. (1958). Bias and confidence in not quite large samples. Annals of Mathematical statistics, 29, pp. 614.Yue, J.C. and Clayton, M.K. (2001). A nonparametric estimator of species overlap. Biometrics, 57, 3, pp. 743-749.Yue, J.C. and Clayton, M.K. (2005). Similarity Measures based on Species Proportions. Communications in Statistics: Theory and Methods, 34, pp. 2123-2131.Yue, J.C. and Clayton, M.K. (2012). Sequential Sampling in the Search for New Shared Species. Journal of Statistical Planning and Inference, 142(5), pp. 1031-1039.中文部分：余清祥(1998)，統計在紅樓夢的應用，國立政治大學學報，第76期，頁303-327。 描述 碩士
國立政治大學
統計研究所
100354024
101資料來源 http://thesis.lib.nccu.edu.tw/record/#G0100354024 資料類型 thesis dc.contributor.advisor 余清祥 zh_TW dc.contributor.author (Authors) 蔡政珈 zh_TW dc.creator (作者) 蔡政珈 zh_TW dc.date (日期) 2012 en_US dc.date.accessioned 11-Jul-2013 16:36:56 (UTC+8) - dc.date.available 11-Jul-2013 16:36:56 (UTC+8) - dc.date.issued (上傳時間) 11-Jul-2013 16:36:56 (UTC+8) - dc.identifier (Other Identifiers) G0100354024 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/58785 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 統計研究所 zh_TW dc.description (描述) 100354024 zh_TW dc.description (描述) 101 zh_TW dc.description.abstract (摘要) 在生態學與生物學上，物種數常作為生物多樣性的指標，以估計單一群體物種數為例，較知名的方法首推Good (1953)以在樣本中出現一次的物種為基礎，提出的物種數估計方法堪稱的先驅，隨後許多文獻延伸Good的想法，發展出許多的估計方法，例如Burham and Overton (1978)的摺刀估計法，Chao and Lee (1992)則以涵蓋機率方式估計。相對而言，兩群體的共有物種數的研究少有人探討，目前以Chao et al. (2000)的估計式較為知名。本研究參考Good (1953)提出估計未發現物種出現機率的想法，估計未發現共有物種的機率，並以Burham and Overton (1978)中應用摺刀法估計物種數的概念，建立一階摺刀估計式與變異數，且另行以多項分配公式推導變異數估計式，進行電腦模擬與實際資料驗證並與Chao et al. (2000)提出的共有物種估計式比較。最後根據Rasmussen and Starr (1979)以抽樣成本建立最適停止規則的概念，應用於本研究所提出的估計式，並經由電腦模擬找出抽樣成本與物種分佈均勻程度的關聯，可作為設定停止規則的依據。 zh_TW dc.description.abstract (摘要) The number of species is often used to measure the biodiversity of a population in ecology and biology. Good (1953) proposed a famous estimate for the number of species based on the probability of unseen species. Subsequently, many studies applied Good’s idea to create new estimation methods, For example, the Jackknife estimate by Burham and Overton (1978), and the estimate by using the sample coverage probability in Chao and Lee (1992) are two famous examples. However, not many studies focus on estimating the number of shared species of two populations, except the method by Chao et al. (2000).In this study, we modify Good’s idea and extend the Jackknife method of Burham and Overton (1978) to develop the estimate for the number of shared species of two populations. In addition, we also establish the variance formula of the estimator by using the multinomial distribution. Subsequently, we use computer simulation and real data sets to evaluate the proposed method, and compare them with the estimator by Chao et al. (2000). Finally, we adapt the idea of optimal stopping rule by Rasmussen and Starr (1979) and combine it with the proposed jackknife estimate. We found that using the sampling cost as the stopping rule is a feasible approach for estimating the number of shared species. en_US dc.description.tableofcontents 第一章、 緒論.................................1第二章、 文獻回顧..............................3 第一節、 抽樣方法與假設.........................3 第二節、 符號定義..............................4 第三節、 未出現物種發現機率-Good估計式............5 第四節、 單一群體物種數估計......................6 壹、 Burham and Overton 估計式.............6 貳、 Chao估計式............................8 第五節、 共有物種數估計-Chao估計式...............9 第六節、 估計新物種的最適停止點..................11第三章、 研究方法.............................13 第一節、 共有物種摺刀估計式- J1.................13 第二節、 共有物種摺刀估計式- J2.................16 第三節、 電腦模擬驗證..........................17 壹、 未發現共有物種機率.....................18 貳、 共有物種一階摺刀估計式..................19 參、 變異數估計式..........................21第四章、 摺刀估計式與Chao估計式.................25 第一節、 電腦模擬驗證..........................25 第二節、 實際資料驗證..........................30第五章、 最適停止規則..........................35 第一節、 抽樣停止點............................35 第二節、 以共有物種數建立停止規則.................38第六章、 結論與建議............................43 第一節、 結論.................................43 第二節、 未來研究方向與建議......................45參考文獻......................................47附錄.........................................49 附錄一、 摺刀估計式變異數推導....................49 附錄二、 未發現共有物種機率估計值與真實值比值.......52 附錄三、 幾何分配Type1，參數α為0.3與0.4時涵蓋率...53 附錄四、 實際資料不均勻程度......................54 zh_TW dc.format.extent 1185351 bytes - dc.format.mimetype application/pdf - dc.language.iso en_US - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0100354024 en_US dc.subject (關鍵詞) 生物多樣性 zh_TW dc.subject (關鍵詞) 共有物種數 zh_TW dc.subject (關鍵詞) 摺刀估計法 zh_TW dc.subject (關鍵詞) 最適停止規則 zh_TW dc.subject (關鍵詞) 電腦模擬 zh_TW dc.subject (關鍵詞) Biodiversity en_US dc.subject (關鍵詞) Number of shared species en_US dc.subject (關鍵詞) Jackknife estimate en_US dc.subject (關鍵詞) Optimal stopping rule en_US dc.subject (關鍵詞) Computer simulation en_US dc.title (題名) 兩母體共有物種數的估計及最佳停止點 zh_TW dc.title (題名) The optimal stopping rule for estimating the number of shared species of two populations en_US dc.type (資料類型) thesis en dc.relation.reference (參考文獻) 英文部分：Bunge, J. and Fitzpatrick, M. (1993). Estimating the number of species : A Review. Journal of the American Statistical Association, 88, pp. 364-373.Burnham, P. K. and Overton, S. W. (1978). Estimation of the size of a closed population when capture probabilities vary among animals. Biometrika, 65, pp. 625-633.Chao, A. and Lee, S-M. (1992). Estimating the number of classes via sample coverage. Journal of American Statistical Association, 87, pp. 210-217.Chao, A., Hwang, W-H, Chen, Y-C., and Kuo, C-Y. (2000). Estimating the number of shared species in two communities. Statistica Sinica, 10, pp. 227-246.Chao, A., Ma, M.C., and Yang, M.C.K. (1993). Stopping rule and estimation for recapture debugging with unequal detection rates. Biometrika, 80, pp. 193-201.Chuang, C.J. (2012). Estimation of similarity indices via two-sample jackknife procedure. Journal of Applied Science and Engineering, 15, 3, pp. 301-310.Darroch, J. N., and Ratcliff, D. (1980). A note on capture-recapture estimation. Biometrics, 36, pp. 149-153.Efron, B. and Thisted, R. (1976). Estimation the number of unseen species: How many words did Shakespeare now? Biometrika, 63, pp. 435-447.Good, I. J. (1953). The population frequencies of species and the estimation of population parameters. Biometrika, 40, pp. 237-264.Quenouille, M. H. (1949). Approximate tests of correlation in time-series. Journal of the Royal Statistical Society. Series B, 11, pp. 68-84.Quenouille, M. H. (1956). Notes on bias in estimation. Biometrika, 43, pp. 353-360.Rasmussen, S.L. and Starr, N. (1979) Optimal and adaptive stopping in the search for new species. Journal of the American Statistical Association, 74, 367, pp. 661-667.Schechtman, E. and Wang, S. (2004). Jackknifng two-sample statistics. Journal of Statistical Planning and Inference, 119, pp. 329 – 340.Schucany, W. R., Gray, H. L., and Owen, D. B. (1971). On bias Reduction in Estimation. Journal of the American Statistical Association, 66, pp. 524-533.Sharot, T. (1976) The Generalized Jackknife: Finite Samples and Subsample Sizes. Journal of the American Statistical Association, 71, 354, pp. 451-454.Tuckey J. W. (1958). Bias and confidence in not quite large samples. Annals of Mathematical statistics, 29, pp. 614.Yue, J.C. and Clayton, M.K. (2001). A nonparametric estimator of species overlap. Biometrics, 57, 3, pp. 743-749.Yue, J.C. and Clayton, M.K. (2005). Similarity Measures based on Species Proportions. Communications in Statistics: Theory and Methods, 34, pp. 2123-2131.Yue, J.C. and Clayton, M.K. (2012). Sequential Sampling in the Search for New Shared Species. Journal of Statistical Planning and Inference, 142(5), pp. 1031-1039.中文部分：余清祥(1998)，統計在紅樓夢的應用，國立政治大學學報，第76期，頁303-327。 zh_TW
