重覆捕捉實驗是估計母體總數時常用的抽樣方法。在過去離散型資料的估計方法中，當模型考慮時間效應以及行為反應(Mtb模式)時，都必須估計每次捕捉的動物捕捉機率，但我們真正關心的是母體的總數而非捕捉的機率，因此可將每次的捕捉機率視作為干擾參數。本文中我們在假設每次捕取動物數以及已標記的動物數為已知的條件下，用廣義估計方程式(GEE)推導出不須估計捕取機率的方法，並與過去的估計方法作比較，包括最大概似估計量(UMLE)、條件最大概似估計量(CMLE)以及須估計捕捉機率的廣義估計方程式估計量。我們也將此方法推廣至連續型資料的估計，證明此估計方法與輪廓概似估計量是等價的，並證明了當捕捉次數夠大時，此離散型的估計量會等同於連續型估計量。此外關於連續型模式的變異數估計，從輪廓概似估計法以及廣義概似估計方程式的觀點各可產生一種變異數的估計，本文中再從估計方程式的共變異數矩陣來反推出參數估計數的共變異數矩陣，並比較這三種不同的變異數估計方法。在本文的最後，以模擬的方法來比較離散型資料下各估計方法的優劣，觀察捕捉次數增加時離散型估計收斂至連續型估計的情形以及比較三種連續型估計方法的變異數估計，並且以一重複捕捉老鼠的資料來作為實例分析。

[1] Aalen , O. O. (1978) Nonparametric inference for a family of counting process. Annals of statistics 6, 701-726.
[2] Becker, N. G. and Heyde, C. C.(1990) Estimating population size from multiple recapture experiments. Stochastic process and their application 36, 77-83.
[3] Chao, A. and Lee, S.-M. (1992) Estimating the number of classes via sample coverage. Journal of the American Statistical Association 87, 210-217.
[4] Chao, A., Lee S.-M. and Jeng, S-L. (1992) Estimating population size for capture-recapture data when capture probabilities vary by time and individual a nimals. Biometrics 48, 201-216
[5] Chao, A., Chu. W. and Hsu, C-H. (2000). Capture-recapture when time and behavioral affect capture probabilities. Biometrics 56, 427-433.
[6] Chao, A. (2001). An overview of closed capture-recapture models. Journal of Agriculture, Biological, and Environmental Statistics 6, 158-175.
[7] Darroch. J. N. (1958) The Mmultiple-recapture census I: estimation of a closed population. Biometrika 45, 343-359.
[8] Godambe, V. P. and Heyde, C. C. (1987).Quasi-likelihood and optimal estimation. International Statistical Review 55, 231-244.
[9] Godambe, V. P. (1985).The foundations of finite sample estimation in stochastic processes. Biometrika 72, 419-428.
[10] Hwang, W-H., Chao, A. and Yip, P. S. F. (2002). Continuous-time capture-recapture models with time variation and behavioral response. Australian and New Zealand Journal of Statistics 44, 41-54.
[11] McCullagh, P. (1983).Quasi-likelihood functions. The Annals of Statistics 11, 59-67.
[12] Otis, D. L., Burnham, K. P. White G. C. and Anderson, D. R. (1978). Statistical I nference for capture data on closed animal populations. Wildlife Monographs 62, 1-135
[13] Pollock, K. H. (1974). The assumption of equal catchability of animals in tag-recapture experiment. Ph.D. dissertation, Cornell University, Ithaca, New York.
[14] Pollock, K. H. (1991). Modeling capture, recapture, and removal statistics for estimation of demographic parameters for fish and wildlife population: past, present, and future. Journal of the American Statistical Association 86, 225-238.
[15] Wedderburn, R.W.M. (1974). Quasi-likelihood function, generalized linear models, and the Gauss-Newton method. Biometrika 61, 439-447.
[16] Yip, P. (1989). An inference procedure for a capture and recapture experiment with time-dependence capture probabilities. Biometrics 45, 471-479.
[17] Yip, P. (1991). A martingale estimating equation for a capture-recapture experiment in discrete time. Biometrics 47, 1081-1088.
[18] 林淑萍(2001) Comparision of population size estimation between continuous and discrete capture-recapture experiments. [清華大學博士論文]