系統識別號 U0026-0812200913434570 論文名稱(中文) 捕取歷史記錄失誤下的母體總數估計方法 論文名稱(英文) Estimating the Closed Population Size for Capture History with Missing Data 校院名稱 成功大學 系所名稱(中) 統計學系碩博士班 系所名稱(英) Department of Statistics 學年度 95 學期 2 出版年 96 研究生(中文) 鄭宜珊 研究生(英文) Yi-Shan Zheng 學號 r2694408 學位類別 碩士 語文別 英文 論文頁數 60頁 口試委員 口試委員-陳俞成口試委員-鄭順林指導教授-馬瀰嘉口試委員-趙昌泰 中文關鍵字 母體總數估計  失誤值  隨機失誤  樣本涵蓋率  變異係數 英文關鍵字 Population size estimator  Missing value  Missing at random  Sample coverage  Coefficient of variation 學科別分類 中文摘要 有關母體總數估計研究至今已有一段很長的歷史，且已廣為應用，在此研究領域中，一般可分為封閉性母體與開放性母體兩種。在封閉母體下，通常假設動物的捕取歷史是完整的(completely data)，然而在實務上，卻可能因為被捕取動物缺失記號，或調查者記號登錄錯誤、記錄缺失，而造成捕取歷史的不完整。故本文針對在封閉母體下，假設動物捕取機率不同，研究當資料有紀錄失誤時，失誤機率值對既有的估計量所造成的偏差，以及如果捕取歷史資料是完全隨機失誤(missing completely at random )或是隨機失誤(missing at random)時，對母體總數的估計是否有影響，並提出修正的估計方法來彌補因失誤值所造成的偏差。 英文摘要 The analysis of the population size estimation has a long history and has been widely used in many applications. In this research field, it usually can be divided into the open population and the closed population. Under the closed population, we often assumed capture history of animals is the completely data. However, in the practical applications, animals maybe lose marks during sampling periods, records mistake of the marks or records lost. It causes the capture history of animals incomplete. Therefore, this paper studies the estimators of population size for the closed population. The bias of the estimators under complete capture-recapture data and capture history with missing data are compared. Two biases will be compared when capture history data are generated with missing completely at random and the probability that capture history data is missing depends on the capture-recapture data value. Finally, a bias corrected estimator is proposed. 論文目次 CONTENTS ABSTRACT ………………………………………………………………………….I CONTENTS………………………………………………………………………...IV LIST OF TABLES………………………………………………………………….. V LIST OF FIGURES……………………………………………………………….. VI 1. INTRODUCTION…………………………………………………………………1 2. LITERATURE REVIEW…………………………………………………………3 2.1 Notation……………………………………………………………………….. 3 2.2 Literature review…………………………………………………………….....4 3. PROPOSED ESTIMATORS…………………………………………………….11 3.1 Sample coverage……………………………………………………………….11 3.2 The usual handle methods under capture history with missing data ………….12 3.3 The bias-corrected estimators………………………………………………….14 4. SIMULATION STUDY ………………………………………………………….19 4.1 Simulation procedure………………………………………………………….19 4.2 Simulation results ……………………………………………………………..21 4.3 Numerical Example……………………………………………………………27 5. CONCLUSION …………………………………………………………………..30 REFERENCE ……………………………………………………………………....32 APPENDIX A ……………………………………………………………………..35 APPENDIX B ……………………………………………………………………..38 參考文獻 [1] Burnham, K. P., and Overton. W. S. (1978). “Estimating the Size of a Closed Population when Capture Probabilities vary Among Animals.” Biometrika, 65, 625 -633. 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