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| Title: | 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 |
| Authors: | 蔡政珈 |
| Contributors: | 余清祥
蔡政珈 |
| Keywords: | 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 |
| Date: | 2012 |
| Issue Date: | 2013-07-11 16:36:56 (UTC+8) |
| Abstract: | 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. |
| Reference: | 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。 |
| Description: | 碩士
國立政治大學
統計研究所
100354024
101 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0100354024 |
| Data Type: | thesis |
| Appears in Collections: | [統計學系] 學位論文
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