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研究生:張力慶
研究生(外文):Li-Ching Chang
論文名稱:環狀均衡餘數系統抽樣
論文名稱(外文):The Circular Balanced Remainder Systematic Sampling
指導教授:呂金河呂金河引用關係
指導教授(外文):Ching-Ho Leu
學位類別:碩士
校院名稱:國立成功大學
系所名稱:統計學系碩博士班
學門:數學及統計學門
學類:統計學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:中文
論文頁數:75
中文關鍵詞:線性系統抽樣均衡系統抽樣包含機率環狀餘數系統抽樣餘數線性系統抽樣
外文關鍵詞:inclusion probabilitylinear systematic samplingremainder circular systematic samplingbalanced systematic samplingremainder linear systematic sampling
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  • 被引用被引用:0
  • 點閱點閱:151
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  • 下載下載:14
  • 收藏至我的研究室書目清單書目收藏:0
  文中首先提出兩種對於線性系統抽樣作修正的抽樣方法, 均衡餘數系統抽樣是結合均衡系統抽樣與餘數線性系統抽樣方式的抽樣方法, 而環狀均衡餘數系統抽樣是結合均衡系統抽樣與環狀餘數系統抽樣方式的抽樣方法。這兩種抽樣方法皆可用於母體數被樣本數整除或不整除的情況。我們推導出這兩種新抽樣方法的包含機率並導出母體均值的不偏估計式與其變異數估計。將這兩種抽樣方法與餘數線性系統抽樣、環狀餘數系統抽樣與簡單隨機抽樣在數種母體比較其有效性。由於, 環狀餘數系統抽樣的有效性不盡理想, 因此再對環狀餘數系統抽樣作了一些修正。
  In this paper, we propose two sampling procedures to modify linear systematic sampling. One is balanced remainder systematic sampling which is a combination of remainder linear systematic sampling and balanced systematic sampling, and another is circular balanced remainder systematic sampling which is a modification of remainder circular systematic sampling and balanced systematic sampling. All procedures can be used when the population size is not a multiple of the sample size or N=nk. The inclusion probability of the two sampling procedures and the corresponding estimator of population mean and its variance estimator are derived. We discuss the efficiency of the proposed sampling design with respect to simple random sampling, remainder linear systematic sampling, and remainder circular systematic sampling under various types of populations. However, efficiency of circular balanced remainder systematic sampling is not good enough. A slight modification of circular balanced remainder systematic sampling at end.
1 序論..................................................................1
1.1 研究動機與背景....................................................1
1.2 論文回顧..........................................................1
1.3 研究目的..........................................................2

2 均衡餘數系統抽樣與環狀均衡餘數系統抽樣................................3
2.1 均衡餘數系統抽樣方法..............................................3
2.2 均衡餘數系統抽樣之母體均值估計與其變異數..........................8
2.3 環狀均衡餘數系統抽樣方法.........................................10
2.4 環狀均衡餘數系統抽樣之母體均值估計與其變異數.....................14

3 各種抽樣方法有效性的比較.............................................30
3.1 隨機順序排列母體 (Population in random order)....................30
3.2 拋物線與線性趨勢母體 (Population in parabolic or linear trend)...32
3.3 自我相關母體 (Autocorrelated population).........................46

4 修正的環狀均衡餘數系統抽樣...........................................59
4.1 修正的環狀均衡餘數系統抽樣方法...................................59
4.2 修正的環狀均衡餘數系統抽樣之母體均值估計與其變異數...............62
4.3 修正的環狀均衡餘數系統抽樣估計式的變異數模擬結果.................65

5 結論與未來研究方向...................................................72
5.1 結論.............................................................72
5.2 未來研究方向.....................................................73

參考文獻...............................................................74
1. Chang, H. J. and Huang, K. C. (2000), Remainder
linear systematic sampling. Sankhy ‾a , B62, 249-256.
2. Cochran, W. G. (1942), Sampling theory when the
sampling units are of unequal sizes. Jour. Amer.
Stat. Assoc., 37, 199-212
3. Cochran, W. G. (1977), Sampling Techniques. 3rd ed.
Wiley, New York.
4. Deming, W. E. (1960), Sampling Design in Business
Research. Wiley, New York.
5. Gautschi, W. (1957), Some remarks on systematic
sampling. AMS 28, 385-394.
6. Leu, C. H. (2001), Remainder circular systematic
sampling, NCKU Technical Report.
7. Murthy, M. N. (1967), Sampling Theory and Methods.
Calcutta: Statistical Publishing Society.
8. Murthy, M. N. and Rao, T. J. (1988),Systmatic
sampling with illustrative examples. Handbook of
Statistics Vol.6, 147-185.
9. Sethi, V. K. (1965), On optimum pairing of units.
Sankhy‾a B27, 315-320.
10. Singh, D., Jindal, K. K. and Garg, J. N. (1968),
On modified systematic sampling. Biometrika 55, 541-546.
11. Yates, F., and Grundy, P. M. (1953), Selection
without replacement from within strata with probability
proportional to size. Jour. Roy. Stat. Soc., B15, 253-261.
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