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| Title: | 兩相分層抽樣中貝氏最佳解的特例 |
| Authors: | 徐惠莉 |
| Contributors: | 宋傳欽
徐惠莉 |
| Date: | 1990
1989 |
| Issue Date: | 2016-05-03 14:17:40 (UTC+8) |
| Abstract: | (一) Smith & Sedransk ( 1982 )利用雙重抽樣方法研究魚群年齡組成，給定第一階段樣本數nν及其分配nv= (n1ν,...., n1ν),說明如何選取最佳的貝氏子樣本數分配n0∞=( n01∞,...,n01∞), 使得近似風險函數r∞ (nν, nν, n0∞)最小，而後Jinn. Smith |
| Reference: | <註1> Cochran ,W. G. (1977).
Sampling Techniques , 3rd edition 327 - 328. New York:Wiley.
<註2> Smith.P.J. and Sedransk.J. (1982).
Bayesian Optimization of Estimation of the Age Composition of a Fish Population.
Journal of American Statistical Association 77. 707 - 713.
<註3> J.H.Jinn, J.Sedransk and Philip Smith (1987)
Optimal Two-Phase Stratified Sampling f or Estimation of the Age Composition of a Fish Position.
BIOMERTICS 43. 343 - 353.
<註4 > poststratification variable. 在實驗前母體無法被分層，因此可在第一階段抽樣後，利用這個變數觀察所抽取的樣本，將母體分層，因此為一輔助變數。
<註5>因為
fν ({ n1 }∣nν , { P1 }) f ({P1 }∣{b1})=( nν)!Γ(b.)█(I@π@i=1)^ [" " ?P_1?^(n^ν+b-1)/(?n_(?n_1?^ν )?^ν !Γ(b1))]
所以
g({n1ν}∣nν)
=∫??(n^ν ?)! Γ(b.) █(I@π@i=1)^ [" " ?P_1?^(n^ν+b-1)/(?n_(?n_1?^ν )?^ν !Γ(b1))] dP
=((n^ν)! Γ(b.) )/(?π^2?_(i=1) ?? n?_1?^ν∣Γ(b1)) ∫?█(I@π@i=1)^ ?P_1?^(n^ν+b-1) dP
=((n^ν)! Γ(b.) )/(?π^2?_(i=1) ?? n?_1?^ν∣Γ(b1)) (?π^2?_(i=1) ??Γ( n?_1?^ν+b1))/( Γ(n^ν+b.) )
所以
f’’({P1},I nν,{ n1})
=(f^ν ({ n_1 }∣n^(ν ) ,{ P_1 }) f ({P_1 }∣{b_1}))/(g({ ?n_1?^ν }∣n^(ν ) )
=Γ(nν+b.) █(I@π@i=1)^ [" " ?P_1?^(n^ν+b-1)/(Γ(n^ν+b.))]
<註6 >矩陣k 表研究者對於不同母體的重視程度.若對所有母體均有相等的重視，則取kjj =1 j一般視研究的目的來選取{kjj}.
<註7>梁淑真.(1989). 雙重抽樣之貝氏最佳樣本與子樣本數選取的特例. P9.
<註8>DEGROOT,MORRIS H.(1970).
Optimal Statistical Decision. P234.
New York:McGraw-Hill.
<註9 > Rao , J.N.K, and Ghangurde , P.D. (1972)
Baysian Optimization in Sampling Finite Populations. Journal of the American Statistical Association 67.439 - 443.
<註10>同<註7>, P19-P35.
<註11>同<註7>,P28, P35.
<註12>由<註5>知，當I=2, f’’({P1},I nν,{ n1})為Beta分配，所以
E’’(P12)=∫P12Γ(n^ν+b.) █(I@π@i=1)^ [" " ?P_1?^(n^ν+b-1)/(?n_(?n_1?^ν )?^ν !Γ(b1))] dP1
=( ( ?n_1?^ν ?+ b?_1)(?n_1?^ν+b_1+1))/( (n^ν+b.)(n^ν+b.+1))
I=1,2.
<註13> (3.3.1)式的f’(n1∣nν,P1)與(2.2.6)式的g(n1ν∣nν)機率分配的圖形比較,較為陡峭的為前者，較為平緩的為後者.
<註14>Tom M. Apostol.(1977)
Mathematical Analysis. 2nd edition. 354-355.
<註15>同<註7>,P36-P45. |
| Description: | 碩士
國立政治大學
應用數學系 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#B2002005454 |
| Data Type: | thesis |
| Appears in Collections: | [應用數學系] 學位論文
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