SOME IMPUTATION METHODS IN DOUBLE SAMPLING SCHEME FOR ESTIMATION OF POPULATION MEAN

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1 aoal Joual of Mod Egg Rsach (JMER) ol. ssu. Ja-F 0 pp N: 9- OME MPUTATON METHOD N DOUBLE AMPLNG HEME FOR ETMATON OF POPULATON MEAN ABTRAT Nada gh Thaku Kalpaa adav fo Mahmacal ccs (M) Baashal Uvsy Rajasha-00 NDA ad haad Pahak Dpam of Mahmacs ad ascs D. H.. Gou al Uvsy aga (M.P.) NDA To sma h populao ma wh mpuao.. h chqu of susug mssg daa h a a um of chqus avalal lau lk Rao mhod of mpuao ompomsd mhod of mpuao Ma mhod of mpuao Ahmd s mhods of mpuao F-T mhods of mpuao ad so o. f populao ma of aulay fomao s ukow h hs mhods a o usful ad h wo-phas samplg s usd o oa h populao ma. Ths pap pss som mpuao mhods of fo mssg valus wo-phas samplg. Two dff samplg dsgs wo-phas samplg a compad ud mpud daa. Th as ad m.s. of suggsd smaos a dvd h fom of populao paams usg h cocp of lag sampl appomao. Numcal sudy s pfomd ov wo populaos usg h pssos of as ad m.s. ad ffccy compad wh Ahmd s smaos. Kywods: Esmao Mssg daa Bas Ma squad o (M..E) Two-phas samplg RWOR Lag sampl appomao.. NTRODUTON: To ovcom h polm of mssg osvaos o o-spos sampl suvys h chqu of mpuao s fquly usd o plac h mssg daa. To dal wh mssg valus ffcvly Kalo al. (98) ad ad (979) suggsd mpuao ha mak a compl daa s sucually compl ad s aalyss smpl. mpuao may also cad ou wh h ad of a aulay vaa f s avalal. Fo ampl L al. (99 99) usd h fomao o a aulay vaa fo h pupos of mpuao. La gh ad Ho (000) suggsd a compomsd mhod of mpuao. Ahmd al. (00) suggsd sval w mpuao asd smaos ha us h fomao o a aulay vaa ad compad h pfomacs wh h ma mhod of mpuao. hukla (00) dscussd F-T smao ud wo-phas samplg ad hukla ad Thaku (008) hav poposd smao of ma wh mpuao of mssg daa usg F-T smao. hukla al. (009) hav dscussd o ulzao of o-spos aulay populao ma mpuao fo mssg osvaos ad hukla al. (009a) hav dscussd o smao of ma ud mpuao of mssg daa usg faco yp smao wo-phas samplg. hukla al. (0) suggsd la comao asd mpuao mhod fo mssg daa sampl. Th ojcv of h ps sach wok s o dv som mpuao mhod fo ma smao cas populao paam of aulay fomao s ukow.. NOTATON: L U = (U U U U N ) h f populao of sz N ad h chaac ud sudy dod y y. A lag plmay smpl adom sampl (whou placm) of us s daw fom h populao o U ad a scoday sampl of sz ( < ) s daw h wo ways: O s as a su-sampl fom sampl (dod y dsg ) as fg. ad oh s dpd o sampl (dod y dsg ) as fg. whou placg. Th sampl ca dvdd o wo o-ovlappg su goups h s of spodg us y R ad ha of o- spodg us y R c ad h um of spodg us ou of sampld us dod y (<). Fo vy u R h valu y s osvd u fo h us R h y a mssg ad sad mpud 00 P a g

2 aoal Joual of Mod Egg Rsach (JMER) ol. ssu. Ja-F 0 pp N: 9- valus a dvd. Th h valu R. Assum fo h daa s ad of aulay vaa s usd as a souc of mpuao fo mssg daa wh : ad fo h daa : spcvly. Th followg symols a usd haf: a kow wh ma : h populao ma of ad spcvly; y : h sampl ma of ad spcvly; y : h sampl ma of ad spcvly; : h colao coffc w ad ; : h populao ma squas of ad spcvly; spcvly; ; ; ; ; N N 9 ; D. 0 : h coffc of vaao of ad N ; f. LARGE AMPLE APPROMATON: Populao (N) Populao (N) L ; ; y ad y whch mpls h suls ; ; ad. Now y usg h cocp of wo-phas samplg ad h h mchasm of MAR fo gv ad y R R Fg. [Dsg ] (s Rao ad (99)) w hav: Dsgs E E E E E E y R R Fg. [Dsg ] Dsgs E E E E E 0 E P a g

3 aoal Joual of Mod Egg Rsach (JMER) ol. ssu. Ja-F 0 pp N: 9-. PROPOED TRATEGE: L y j dos h h osvao of h j h suggsd mpuao sagy ad a cosas such ha h vaac of oad smaos of s mmum. W suggs h followg ools of mpuao: () y f R y (.) y f R ud hs sagy h po smao of s gv y y () ud hs h smao of s (.) y f R y (.) y f R f () y f f hc h smao of s y y (.) y f R y (.) R (.). BA AND MEAN QUARED ERROR OF PROPOED ETMATOR: L B(.) ad M(.) do h as ad ma squad o (M..E.) of a smao ud a gv samplg dsg = h h as ad m.s. of ad a dvd h followg homs. Th poofs of all hs suls a smla ad hfo w wll poof oly o of hm.. hom.. Thom.: () Esmao ms of ; ad could pssd: s y gog h ms E E s od of appomao. (.) j j fo s wh s 0... ad ; j whch s fs Poof: y () Bas of Poof: ud dsg ad s: () B 0 () B 0 () B E 0 () B E 0 () Th vaac of ud dsg ad upo fs od of appomao could w as: () () (.) (.) (.) (.) Poof: E E E 0 P a g

4 aoal Joual of Mod Egg Rsach (JMER) ol. ssu. Ja-F 0 pp N: P a g E (.) () Ud Dsg (Usg (.)) () Ud Dsg (Usg (.)) () Th mmum vaac of h s () M wh (.7) () M wh (.8) Poof: () By dffag (.) wh spc o ad qua o zo w g 0 d d Af placg h valu of (.) w oad M () mla o () w pocd fo (.) w hav 0 d d Af placg h valu of (.) w oad M Thom.: () Th smao ms of s ad : (.9) () Th as smao ud dsg ad spcvly s () 0 B (.0) () 0 B (.) (7) Th vaac of ud dsg ad spcvly s: () (.) () (.)

5 aoal Joual of Mod Egg Rsach (JMER) ol. ssu. Ja-F 0 pp N: 9- (8) Th mmum vaac of h () () Thom.: (9) Th smao s wh M M (0) Th as smao wh ms of () B 0 ad s : (.) (.) (.) () B 0 ud dsg ad spcvly s: () Th vaac of ud F ad F s () (.7) (.) (.8) () () Th mmum vaac of h () (). OMPARON: () (.9) s wh M M m m wh N N s ha f 0 0 N whch s always u. m m N N () ha N N s f 0 0 NN whch s always u. m m N N s ha f 0 () (.0) (.) y () m m 0 9 s ha f 0 () m m 9 0 N 0 N N N y P a g

6 aoal Joual of Mod Egg Rsach (JMER) ol. ssu. Ja-F 0 pp N: 9- ha s f 0 N N () m m s ha f 0 D D 7. NUMERAL LLUTRATON: W cosdd wo populaos A ad B fs o s h afcal populao of sz N = 00 [souc hukla al. (009)] ad aoh o s fom Ahmd al. (00) wh h followg paams: Tal 7.0 Paams of Populaos A ad B Populao N A B L = 0 = 0 = fo populao A ad = 000 = 00 = fo populao B spcvly. Th h as ad M..E fo suggsd smaos ud dsg ad usg h pssos of as ad M..E. dvd co fo suggsd smaos a show al 7. ad 7. spcvly. Th as ad M..E. fo Ahmd s smaos (s Appd A) a dsplayd al 7. fo populao A ad B spcvly. Esmaos Tal 7. Bas ad ME (Populao A) DEGN DEGN Bas ME Bas ME Tal 7. Bas ad ME (Populao B) Esmaos DEGN DEGN Bas ME Bas ME Esmaos Tal 7. Bas ad ME fo Ahmd s Esmaos (Populao A ad B) Populao A Populao B Bas ME Bas ME Th samplg ffccy of suggsd smaos ud dsg ad ov Ahmd s smaos s dfd as: 0 P a g

7 aoal Joual of Mod Egg Rsach (JMER) ol. ssu. Ja-F 0 pp N: 9- j Op M E ; ; j (7.) Op M Th ffccy fo populao A ad B spcvly gv al 7.. Tal 7. Effccy of uggsd Esmaos Dsg ad ov Ahmd s Esmaos Effccy Populao A Populao B Dsg Dsg Dsg Dsg E E E DUON: Th da of wo-phas samplg s usd whl cosdg h aulay populao ma s ukow. om sags a suggsd fo mssg osvaos co ad h smaos of populao ma a dvd. Pops of smaos lk as ad m.s. a dscussd h co ad h opmum valu of paams fo mmum ma squad o s oad as wll h sam sco. Ahmd s smaos a cosdd fo lav compaso. Two populaos A ad B cosdd fo umcal sudy fs o fom hukla al. (009) ad aoh o s Ahmd al. (00). Th samplg ffccy of suggsd smao ud dsg ad ov Ahmd s smaos s oad ad suggsd sagy s foud vy clos wh Ahmd al. (00) wh ukow. 9. ONLUON: Th poposd smaos a usful wh som osvaos a mssg h sampl ad populao ma of aulay fomao s ukow. Ovously fom Tal 7. ad 7. all suggsd smaos a dsg ha dsg.. h dsg s ha dsg. Th al 7. shows ha h suggsd smaos ad a vy clos wh Ahmd s smaos ad may usd o sma h populao ma whl populao paam of aulay fomao s ukow. REFERENE. Ahmd M.. Al-T O. Al-Raw Z. ad Au-Dayyh W. (00): Esmao of a populao ma usg dff mpuao mhods ascs Taso Kalo G. Kaspzyk D. ad aos R. (98): ssus of o-spos ad mpuao h uvy of com ad Pogam Pacpao. u Topcs uvy amplg (D. Kwsk R. Plak ad J.N.K. Rao ds.) -80 Acadmc Pss Nw ok.. L H. Racou E. ad adal. E. (99):Epms wh vaac smao fom suvy daa wh mpud valus. Joual of offcal ascs L H. Racou E. ad adal. E. (99): aac smao h psc of mpud daa fo h galzd smao sysm. Poc. of h Am. a. Asso. (ocal uvy Rs. Mhods c.) Rao J. N. K. ad R. R. (99): aac smao ud wo-phas samplg wh applcao o mpuao fo mssg daa Bomca ad. G. (979): A psoal vw of ho dck appoach o auomac d ad mpuao. Joual mpuao Pocdus. uvy Mhodology hukla D. (00): F-T smao ud wo-phas samplg Mo hukla D. ad Thaku N.. (008): Esmao of ma wh mpuao of mssg daa usg faco-yp smao ascs Taso hukla D. Thaku N.. Pahak. ad Rajpu D.. (009): Esmao of ma wh mpuao of mssg daa usg faco- yp smao wo-phas samplg ascs Taso hukla D. Thaku N.. Thaku D.. (009a):Ulzao of o-spos aulay populao ma mpuao fo mssg osvaos Joual of Rlaly ad ascal uds hukla D. Thaku N.. Thaku D.. ad Pahak. (0): La comao asd mpuao mhod fo mssg daa sampl aoal Joual of Mod Egg Rsach (JMER) P a g

8 aoal Joual of Mod Egg Rsach (JMER) ol. ssu. Ja-F 0 pp N: 9-. gh. ad Ho. (000): ompomsd mpuao suvy samplg Mka -7. Poposd Mhods of Ahmd al. (00): APPEND A Ahmd al. (00) poposd som mpuao mhods ad dvd h pops. Auhos a dscussg wh h mhods of hm. L y dos h h avalal osvao fo h j h mpuao ad j s a sualy chos cosa such ha h vaac h sula smao s mmum. mpuao mhods a : () y f R y () y f R ud hs sagy h po smao of s y Thom: Th as vaac ad mmum vaac a () B 0 () () of s gv y () () N () N () m () y f R ud hs sagy h po smao of s y y f R y () Thom: Th as vaac ad mmum vaac a () B 0 (7) of s gv y () (8) (9) N N N () m (0) N N () y f ud hs h smao of s y y f R y () R () Thom: Th as vaac ad mmum vaac a of s gv y () B 0 () () () N m () N () 07 P a g