On The Use of Coefficient of Variation and 1, 2
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1 Samlg Stratege for Fte Poulato Ug Auxlary Iformato O e Ue of oeffet of arato ad, Etmatg Mea of a Fte Poulato B. B. Kare, P. S. Ja ad U. Srvatava Deartmet of Statt, B.H.U, araa-005 Statt Seto, MM, B.H.U, araa-005 bbkare56@yaoo.om Abtrat I t aer te ue of oeffet of varato ad ae arameter ea tratum, te roblem of etmato of oulato of mea a bee odered. e exreo of mea quared error of te rooed etmator derved ad t roerte are dued. Keyword Auxlary formato, MSE, oeffet of varato, tratum, ae arameter. Itroduto e ue of ror formato about te oulato arameter u a oeffet of varato, mea ad kewe ad kurto are very ueful te etmato of te oulato arameter of te tudy arater. I agrultural ad bologal tude formato about te oeffet of varato ad te ae arameter are ofte avalable. If tee arameter rema eetally uaged over te tme ta te kowledge about tem u ae t may roftably be ued to rodue otmum etmate of te arameter Se ad Gerg 975. Searl 96, 67 ad Hrao 97 ave rooed te ue of oeffet of varato te etmato te oulato mea. Searl ad Itaraa 990 ave uggeted te ue of kurto te etmato of varae. Se 978 a rooed te etmator for oulato mea ug te kow value of oeffet of varato. I Stratfed radom amlg, te teory a bee develoed to rovde te otmum etmator of te oulato mea baed o amle mea from ea tratum. We exted t by otrutg a etmator ug te oeffet of varato ad ae arameter,,... from ea tratum ad du t uefule. We alo defe etmator, K 3 ad we te oeffet of varato are ukow but ae arameter are kow ad we eter te oeffet of varato are kow or te ae arameter are kow. Etmator ad ter Mea Square Error Let deote te ze of te t tratum ad deote te ze of te amle to be eleted from te t tratum ad be te umber of trata wt 39
2 Raje Sg Floret Smaradae edtor ad, were ad deote te umber of ut te oulato ad amle reetvely. Let exreed a y j be te j t ut of te t tratum. e te oulato mea Y a be Y Y, were ad Y te oulato mea for te t tratum. Let ut be eleted from te t tratum ad te orreodg amlg mea ad amle varae be deoted by y ad ad te reetvely. e te etmate of Y gve by y 3 f f.. gored, were te oulato varae of y te t tratum. ae : oeffet of varato ad te ae arameter are kow. We defed ad exetato of gve by E { y } Y { Y { Y { Y O 5 Y 8 8 } } } 8 0
3 Samlg Stratege for Fte Poulato Ug Auxlary Iformato were te meaure of kurto te t tratum. 6 e ba of order MSE ad wll be eglgble for large. e mea quare error of te etmator / { } O 3/ Mmg 7 wt reet to, we get te otmum value of gve by were te meaure of kurto te t tratum.. 7 ot, 8 O uttg te otmum value of ot from 8 7 ad o mlfato we get MSE e value of m { } O 3/ ot wll be le ta oe for. 9, w mle tat te dtrbuto ear ormal, oo, egatve bomal ad eyma tye I. e value of wll be equal to oe for e value of wll be greater ta oe for ot ot, w true for gamma ad exoetal dtrbuto., w lkely to te dtrbuto of logormal or vere Gaua. It eay to ee tat wll alway be more effet ta f or, jutfyg te ue of te ae of ear ormal, oo, egatve bomal, eyma tye I ad logormal or vere Gaua dtrbuto. equally effet, f ad o for gamma or exoetal dtrbuto oe may ue or. ow tat rooed etmator uformly ueror to te etmator, toug a omaratvely g effey may be ee ear ormal, oo, egatve bomal ta logormal or vere Gaua dtrbuto.
4 Raje Sg Floret Smaradae edtor ae : are ukow, ad are kow. We are ukow, we ue ter etmate baed o a larger amle of ze from a revou oao. ow we defe a etmator 3 for Y gve by y 3 } { 0 e mea quare error of te etmator 3 a gve by } { / MSE, were } { 3. e otmum value of gve by ot. It eay to ee tat ot m 3 / MSE. 3 It may be remarked tat 3 dffer from 9 by a gle term bot umerator ad deomator. e ature of te etmator 3 mlar to ad t MSE wll overge to MSE for 0. ae 3:, ad are ukow: We, ad are ot kow te tey a be etmated o te ba of a larger amle of ze... from te at data ad we may ave te etmator for te oulato mea Y gve by y } ˆ { ˆ,
5 Samlg Stratege for Fte Poulato Ug Auxlary Iformato ˆ ˆ ˆ were ˆ ot. ˆ ˆ ˆ ˆ It eay to ee tat te MSE wll be ame a MSE 3 beaue after etmatg te ukow arameter te otat ot, te MSE wll rema uaged u to te term of O Srvatava ad Jajj 983. Referee. Searl, D.. 96: e utlzato of oeffet of varato te etmato roedure. Jour. of Amer. Stat. Ao., 59, Searl, D.. 967: A ote o te ue of a aroxmately kow oeffet of varato. e Amer. Statta,, Se, A. R. ad Gerg,. M. 975: Etmato of a oulato mea avg equal oeffet of varato o ueo oao. Bull. It. Stat. It., 6, 3-.. Se, A. R. 978: Etmato of te oulato mea we te oeffet of varato kow. ommu. Stat. eory Met., A7,, Srvatava, S.K. ad Jajj, H.S. 983: A la of etmator of te oulato mea ug mult- auxlary formato. alutta Stat. Ao. Bull, 3, Searl, D.. ad Itaraa R 990: A ote o a etmator for varae tat utlzed te kurto. Amer. Stat.,, Hrao K 97: Ug ome aroxmately kow oeffet of varato etmatg mea. Pro. It. Stat. Mat, 0,
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