Calibration Approach Based Estimators of Finite Population Mean in Two - Stage Stratified Random Sampling
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1 I.J.Curr.crobol.App.Sc (08) 7(): Ieraoal Joural of Curre crobolog ad Appled Scece ISS: olue 7 uber 0 (08) Joural hoepage: hp:// Orgal Reearch Arcle hp://do.org/0.0546/jca Calbrao Approach Baed Eaor of Fe Populao ea Two - Sage Srafed Rado Saplg Sadeep Kuar * Depare of Agrculural Sac aredra Deva Uver of Agrculure ad Techolog Kuargaj Fazabad-49 (UP) Ida *Correpodg auhor A B S T R A C T K e w o r d Fe populao Aular forao Two-age rafed rado aplg Calbrao eaor Populao ea Arcle Ifo Acceped: 4 Deceber 07 Avalable Ole: 0 Jauar 08 Devlle ad Sardal (99) developed calbrao eaor b ug he aular forao o oba a beer eae of he populao oal of ud varae ad aular varable. hle calbrao approach doe o aue a eplc relaohp bewee ad bu aue ol ha he populao oal of kow followg Devlle ad Sardal (99) calbrao approach calbrao eaor of fe populao ea wo-age rafed rado aplg have bee developed. The varace ad ubaed eaor of her varace have bee derved. I he pree paper a aep ha bee ade o coduc a led ulao ud o eae he relave perforace of calbrao approach baed eaor. The real daa ha bee ake fro Apped-C of Sardal e al. (003). The ud varae ad he aular varae are he populao of he Swede ear 985 ad ear 975 whch dvded 84 ucpale (U84). The reul have bee foud ha he calbrao eaor have ouperfored he uual eaor of fe populao ea wo-age rafed rado aplg. Iroduco The aular forao ha bee effecvel ued aple urve a eleco rafcao ad eao age for brgg abou he provee he eae of populao paraeer. The dffere fudaeal approache are ued fe populao urve aplg. Thee are deg baed approache odel baed approach ad odel aed approach. Uder deg baed approach he o coo ubaed eaor of fe populao oal Y of ud varable he well-kow Horvz-Thopo (HT) eaor gve b Ŷ d () HT h varace Y D HT j j () j 808
2 I.J.Curr.crobol.App.Sc (08) 7(): j j j d / beg he cluo of probabl of h u he aple whch ha bee draw fro he fe populao of ze b a probabl D aplg deg P () ad he oberved value of correpodg o he h u eleced aple. Devlle ad Sardal (99) developed calbrao eaor of fe populao oal gve b C where d q (3) dq hch equvale o GREG eaor of Y (See Cael e al. 976). A approae varace of Y C of Y for a large aple gve b (Devlle ad Sardal 99) Y D d E d E C j j j (4) j E d q ad d q A aep ha bee ade he pree paper o develop calbrao eaor of fe populao ea wo-age rafed rado aplg. Followg he calbrao approach of Devlle ad Sardal (99) & calbrao baed eaor wo-age aplg Ada e al. (06) whe aular forao o a gle aular varable relaed o ud varable kow a fr age u (fu) level ha ea he oal of.e. I a h fu level kow. The uual eaor of populao ea of he ud varae wo-age rafed rado aplg ha bee developed eco-. The calbrao eaor of he populao ea wo-age rafed rado aplg b calbrag he deg wegh have bee developed he eco-3. The varace ad varace eaor of he calbrao eaor have bee developed he eco- 4 ad a led ulao ud ha bee coduced he eco-5. The uual eaor of populao ea wo-age rafed rado aplg Coder he fe populao ( U U U U3... U ) co of fr age u (fu) ad rafed o raa uch ha U co of fu ad.e alo coder ha each fu h rau ( 3... ) ha uber of ecod age u (u). ow he followg er are defe a Y value of he characerc uder ud j o j h u j 3... ) correpodg ( o he h fu ( 3... ) he h rau. Y. j j of h fu h rau. Y.. j of h rau. j ea of u he populao ea 809
3 I.J.Curr.crobol.App.Sc (08) 7(): he populao. S S b ( ) j he populao ea of Y j.... ad ow coder ha a aple of ze fu ou of fu eleced fro h rau ad ub-aple of ze ou of u fro he eleced fu are draw b SRSOR (ple rado aplg whou replacee). Th proce carred ou depedel each rau. e furher defe = j j ( 3... aple ea fro h eleced fu ) h rau. = rau. b he overall aple ea h j j Obvoul he.the varace of.. a ubaed eaor of obaed a b w (5) S S S w S A ubaed eaor of ) obaed a ( ( ) b w (6) w A ubaed eaor of rafed wo age rado aplg gve b (7) uch ha The varace of obaed a = Sb Sw (8) A ubaed eaor of obaed a = b w (9) 80
4 I.J.Curr.crobol.App.Sc (08) 7(): Propoed calbrao eaor of populao ea wo-age rafed rado aplg e have decrbed deal of develope of a eaor of populao ea j j 0 0 ug ple rado aplg whou replacee (SRSOR) depedel each rau. The eaor of gve b Such ha (0).The wegh deg wegh ad gve b ad The varace of. obaed a S S elf b w () A ubaed eaor of obaed a b w () The wegh ca be calbraed f he forao of a aular varable relaed o he ud varae avalable order o prove he effcec of he eaor. The forao of a aular varable relaed o a be avalable a fu level woage rafed rado aplg. I h cae he populao ea of he aular varable ca eal be obaed.e. 0 (3) he value of he aular varable correpodg o h fu he h rau. e be calbraed wegh.the calbrao eaor of Y herefore gve b c (4) calbraed wegh obaed b zg a dace eaure q where q pove qua urelaed o ubjec o calbrao cora (5) a eaor of developed larl a. For he read referece gve b The followg fuco j j (6) (7) q I zed wh repec o where agraga ulpler. Th eld a 8
5 I.J.Curr.crobol.App.Sc (08) 7(): q (8) q The developed calbrao eaor gve b c q q (9) hch a cobed regreo eaor rafed rado aplg. a cla of c eaor depedg upo he value of q. For q we ge a eaor a SC (0) hch a cobed regreo eaor wo-age rafed rado aplg. For SC q = we ge aoher eaor a () hch a cobed rao eaor woage rafed rado aplg. arace ad varace eaor of propoed calbrao eaor The approae varace of ha bee c derved followg he procedure gve b Sardal e al. (003 chaper 4&8) ad gve b ( ) c pu u () Ij j pu j I Ij Ij D D D Y Y B ad B u U I kl / I U kl / j j j / j / Y ad j / The eaor of varace of SC followg Sardal e al. (003) obaed a SC d B d d j j j (3) B ad 8
6 I.J.Curr.crobol.App.Sc (08) 7(): Table. The eae of Y baed o c ad c alog wh her eae of varace Eaor Eae %RB Eae of PSE varace c c B: Acual populao ea of Y The approae varace of c followg Sardal e al. (003) ad Sgh e al. (998) obaed a c S E E Y Y B B Y f E. S E (4) f ad The approae coe ad ubaed eaor of c obaed a e B c e B a eae of rado aplg. Sulao e f e (5) ad wo-age rafed A led ulao ud ha bee carred ou wh real daa. The populao U84 gve Apped-C of Sardal e al. (003) ha bee ued. There are 50 fu of varg ze. The varable uder ud populao of 985 ad a aular varable he populao of 975. The 50 fu are rafed o 4 raa coderg he value of acedg order. The rau I co of 3 fu rau II co of 4 fu rau III co of fu rau I co of fu repecvel. The aple of ze 4 fu were draw b SRSOR depedel fro raa o 4 repecvel. Th proce ha bee repeaed 300 e depedel. Tha ea we obaed 300 aple of ze 4 fu fro each rau. Sub aple of ze 3 u are draw b SRSOR fro each aple of fu each rau. The value of ad ub aple were ued o copue he populao ea. I h proce we ge 300 Y eae of fro 300 ub aple each rau. The value of ad ub aple were ued o copue he populao ea of Y. I h proce we ge 300 eae of fro 300 ub-aple each rau. The average of hee 300 eae fro each rau are ued o ge he eae of Y. aheacall le Y be he eae of fro h rau. e copue Y 83
7 I.J.Curr.crobol.App.Sc (08) 7(): (6) The average of 300 ub-aple he h rau. So we ge ulaed eae of Y a follow (7) The perce relave ba (%RB) of he eae ha bee copued a follow % RB 00 (8) Slarl he approae varace of he uual eaor c ad c are copued. The perce adard error (PSE) of he eae ha bee copued a follow: 00 SE PSE (9) The ulao ude reul are preeed he Table. I ha bee foud fro he reul of he Table ha he regreo pe calbrao eaor c c ad rao pe calbrao eaor have perfored beer ha he uual eaor wo-age rafed rado c aplg. However eaor ha bee c foud be coparo o eaor a ha u PSE of 9.74 a aga.4 for c. I a be oed ha he calbrao c eaor equvale o cobed c weghed regreo eaor ad he uual cobed rao eaor. I ha alo bee foud ha he calbrao eaor c c relavel le baed ha eaor ad Referece Ada K. Sud U.C. Chadra H. ad Bwa A. 06. Calbrao baed regreo pe eaor of he populao oal uder wo-age aplg deg. Joural of Ida Soce of Agrculural Sac ol. 70() pp Cael C.. Sardal C.E. ad rea J.H Soe reul o geeralzed dfferece eao ad geeralzed regreo eao for fe populao Boerka ol. 63 pp Devlle J.C. ad Sardal C.E. 99. Calbrao eaor urve aplg. Joural of he Aerca Sacal Aocao ol. 87 pp Horvz D.G. ad Thopo D.J. 95. A geeralzao of aplg whou replacee fro a fe uvere. Joural of he Aerca Sacal Aocao ol. 47 pp K J.K. ad Park. 00. Calbrao eao urve aplg. Ieraoal Sacal Revew ol oura K.K. Soda B..S. ad Chadra H. 06. Calbrao approach for eag fe populao paraeer wo-age aplg. Joural of Sacal Theor ad Pracce ol. 0(3) pp Sardal C.E. Sweo B. ad rea J odel-aed urve aplg. Sprger-erlag ew York Ic. (Reved Edo). Sgh S. Hor S. ad Yu F Eao of varace of he geeral 84
8 I.J.Curr.crobol.App.Sc (08) 7(): regreo eaor: Hgher level calbrao approach. Surve ehodolog ol. 4() pp Sha. Soda B..S. Sgh S. ad Sgh S. K. 06. Calbrao approach eao of ea rafed aplg ad double rafed aplg. Coucao Sac- Theor ad ehod 46(0) pp Sud U.C. Chadra H. ad Gupa.K. 04. Calbrao baed produc eaor gle ad wo phae aplg. Joural of Sacal Theor ad Pracce 8 pp. -. Trac D.S. Sgh S. ad Arab R oe o calbrao eaor rafed ad double aplg. Surve ehodolog 9 pp How o ce h arcle: Sadeep Kuar. 08. Calbrao Approach Baed Eaor of Fe Populao ea Two - Sage Srafed Rado Saplg. I.J.Curr.crobol.App.Sc. 7(0): do: hp://do.org/0.0546/jca
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