A class of efficient Ratio type estimators for the Estimation of Population Mean Using the auxilliary information in survey sampling
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1 0 IJE olume Iue IN: - A la o eet ato tpe etmator or te Etmato o Populato Mea Ug te aullar ormato urve amplg Mr uzar. Maqool ad T. A. aja vo o Agrultural tatt KUAT-Kamr 00 Ida. Atrat: - Etmato o te populato mea te pertet ue amplg prate ad ma eort ave ee made varou tatta to mprove te preo o te etmate ug te aullar ormato. I t paper we propoed a la o eet etmator or etmatg te populato mea W O ug te aullar ormato o oeet o ewe ad populato dele o te aullar varale. Te properte aoated wt te propoed etmator are aaled troug ME ad a. We alo provde a empral tud or llutrato ad verato. Keword: oeet o ewe; Populato ele; ato -tpe etmator; Mea quare error; a; Ee.. INTOUTION Te ue o aular ormato urve amplg a t ow emet role ot at deg ad etmato tage. It well ow tat te ue o aular ormato at te etmato tage mprove te preo o etmate o te populato mea or total. ato produt ad regreo metod o etmato are good eample t otet. I te orrelato etwee tud vara te ad te aular varate potve g te rato metod o etmato evaged ora ued. o t paper we alo tae te advatage o orrelato etwee tud varale ad aullar varale ad tu propog te rato tpe etmator ug te aullar ormato o oeet o ewe ad populato dele o aullar varale. oder a te populato U U U U... U } o N dtt ad detale ut. Let e te tud varale wt value populato mea meaured o N N { N U... N gvg a vetor... } { N. Te ojetve to etmate o te a o a radom ample. We te populato parameter o te aular varale u a populato mea urto ewe oeet o varato meda quartle orrelato oeet dele et. are ow rato etmator ad ter modato are avalale te lterature w perorm etter ta te uual ample me a uder te mple radom amplg wtout replaemet W O. Te otato ued t paper a e dered a ollow: NOMENLATUE ome N Populato ze ample ze N amplg rato tud varale Au lar vara le Populato mea ample mea ample total Populato tadard devato Populato ovarae etwee oeet o varato orrelato oeet. a o te Etmator. Etg moded rato etmator o ME Mea quare error o te etmator Propoed moded rato etmator o...0 ele Kurto ` urpt For etg etmator j For propoed etmator aed o te aove metoed otato te mea rato etmator or etmatg te Populato mea o te tud varale deed a r ewe Te a related otat ad te mea quared error ME o te rato etmator are repetvel gve r ME r IJE0 Iteratoal Joural o Egeerg evelopmet ad eear
2 0 IJE olume Iue IN: - IJE0 Iteratoal Joural o Egeerg evelopmet ad eear Te rato etmator gve ued or mprovg te preo o te etmate o te populato mea a ompared to u ual ample mea etmator weever a potve orrelato et etwee te tud varale ad te aular varale. ora 0 uggeted a laal rato tpe etmator or te etmato o te populato mea ug oe aular varale u der mple radom amplg eme. Murt propoed a produt tpe etmator to etmate te populato mea or total o tud varale ug aular ormato we oeet o orrelato egatve. ao trodued deree tp e rato etmator tat outperorm ovetoal rato ad lear regreo etmator. Upadaa & g moded rato tpe etmator ug oeet o varato ad oeet o urto o te aular varate. g & Talor 00 propo ed a aml o etmator ug ow value o ome parameter ug WO or etmato o populato mea o te tud varale. oda & wved ad g et al. 00 utlzed oeet o varato o te aular varate. Furter mprovemet are aeved trodug a large umer o moded rato etmator wt te ue o ow oeet o varato urto ewe meda oeet o orrelato dele ee urama ad Kumarpada 0 a ad. Te orgazato o te ret o te artle a ollow: eto provde a derpto o te etg etmator. Te truture o uggeted moded lear regreo tpe rato etmator ad te ee omparo o te uggeted etmator wt te etg etmator are preeted eto. eto ot o a empral tud o propoed etmator. Fall e to ummarze te dg o te tud.. Etg ato Etmator Kadlar ad g 00 uggeted rato tpe etmator or te populato mea te mple radom amplg ug ome ow aular ormato o oeet o urto ad oeet o varato. Te owed tat ter uggeted etmator are more eet ta tradtoal rato etmator te etmato o te populato mea. Kadlar & g 00 etmator are gve Te ae related otat ad te ME or Kadlar ad g 00 etmator are repetvel a ollow: ME ME ME ME. ME Kadlar ad g 00 developed ome moded rato etmator ug ow value o oeet o orrelato urto ad oeet o varato a ollow:. 0 Te ae related otat ad te ME or Kadlar ad g 00 etmator are repetvel gve ME ME ME
3 0 IJE olume Iue IN: - IJE0 Iteratoal Joural o Egeerg evelopmet ad eear ME ME a ad Ta 00 propoed ome moded rato etmator ug oeet o ewe ad urto a ollow:. Te ae related otat ad te ME or a ad Ta 00 etmator are repetvel gve. ME. ME a ad Ta 00 owed tat te ue o oeet o ewe ad oeet o urto repetvel provde etter etmate or te populato mea omparo to te uual rato etmator ad umerou etg etmator.. Propoed Moded ato Etmator Motvated te metoed etmator eto we propoe ew la o eet rato tpe etmator ug te lear omato o oeet o ewe ad populato dele. Te propoed etmator gve elow:. p. p. p. p. p. p. p. p. p p Te a related otat ad te ME or te rt propoed etmator a e otaed a ollow: ME o t etmator a e oud ug Talor ere metod deed a d d d. Were ad. A ow Wolter. a e appled to te propoed etmator order to ota ME equato a ollow: / / ov ov E
4 0 IJE olume Iue IN: - IJE0 Iteratoal Joural o Egeerg evelopmet ad eear Were. Note tat we omt te deree o E. ov ov E ME ME mlarl te a otaed a j a Tu te a ad ME o te propoed etmator gve elow: j j j ME Were 0... j ad..... Ee omparo.. omparo wt etg rato etmator From te epreo o te ME o te propoed etmator ad te etg etmator we ave derved te odto or w te propoed etmator are more eet ta te etg moded rato etmator a ollow: ME ME Were 0... j ad..... Empral tud Te perormae o te uggeted rato etmator are evaluated ad ompared wt te uual rato etmator ad te meto ed rato etmator eto ug atural Populato. Te peretage relatve ee PE o te propoed etmator p wt repetve to te etg etmator e are omputed a 00 propoed etmator ME o Etmator Etg ME o PE Te tatt o populato tae rom g ad audar gve tale Tale Parameter Populato Parameter Populato Parameter Populato N
5 Etmator Etmator 0 IJE olume Iue IN: Tale : Te tattal Aal o te Etmator or t Populato Pop I Pop I otat a M E otat a M E p...0 p.. 0. p... p... p p p p p... Tale : PE o te Propoed Etmator wt te Etmator Lterature or t populato p0 p p p p p p p p p p IJE0 Iteratoal Joural o Egeerg evelopmet ad eear 0
6 0 IJE olume Iue IN: - oluo From te aove empral tud we reveal tat propog te la o rato tpe etmator WO ug te populato dele ad oeet o ewe a aullar ormato are oud more eet ta te etg etmator a ter ME ad a lower ta te etg etmator ad ee we trogl reommed tat our propoed etmator preerred over etg etmator or pratal applato. eeree ora W. G. 0. Te Etmato o te eld o te ereal Epermet amplg or te ato o Gra to Total Produe. Te Joural o Agr ee Kadlar. & g H. 00 ato etmator mple radom amplg Appled Matemat ad omputato 0. Kadlar. & g H. 00 A mprovemet etmatg te populato mea ug te orrelato oeet Haettepe Joural o Matemat ad tatt 0 0. Murt M. amplg Teor ad Metod ed tattal Pulg oet Ida. ao T. J. O erta metod o mprovg rato ad regreo etmator ommuato tatt-teor ad Metod g. & audar F.. Teor ad Aal o ample urve eg ed New Age Iteratoal Puler Ida. g H. P. & Talor. 00 Ue o ow orrelato oeet etmatg te te populato mea tatt Trato 0. g H. P. Talor. Talor. & Kara M. 00 A mproved etmator o populato mea ug power traormato Joural o te Ida oet o Agrultural tatt 0. oda... & wved. K. A moded rato e tmator ug oeet o varato o aular varale Joural o te Ida oet o Agrultural tatt. urama J. & Kumarapada G. 0a Etmato o populato mea ug o - eet o varato ad meda o a aular varale Iteratoal Joural o Proalt ad tatt. urama J. & Kumarapada G. 0 Etmato o populato mea ug ow meda ad o-eet o ewe Amera Joural o Matemat ad tatt 0 0. urama J. & Kumarapada G. 0 Moded rato etmator ug ow meda ad o-eet o urto Amera Joural o Matemat ad tatt 00. Upadaa L. N. & g H. Ue o traormed aular varale etmatg te te populato mea ometral Joural. Wolter K.M.. Itroduto to arae Etmato prger-erlag. a Z. & Ta. 00 ato metod to te mea etmato ug oeet o ewe o aular varale Iormato omputg ad Applato IJE0 Iteratoal Joural o Egeerg evelopmet ad eear
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