Improvd Epoal Emaor for Populao Varac Ug Two Aular Varabl Rajh gh Dparm of ac,baara Hdu Uvr(U.P., Ida (rgha@ahoo.com Pakaj Chauha ad rmala awa chool of ac, DAVV, Idor (M.P., Ida Flor maradach Dparm of Mahmac, Uvr of w Mco, Gallup, UA (marad@um.du Abrac I h papr poal rao ad poal produc p maor ug wo aular varabl ar propod for mag ukow populao varac. Problm dd o h ca of wo-pha amplg. Thorcal rul ar uppord b a mprcal ud. K word: Aular formao, poal maor, ma quard rror.. Iroduco I commo pracc o u h aular varabl for mprovg h prco of h ma of a paramr. Ou of ma rao ad produc mhod of mao ar good ampl h co. Wh h corrlao bw h ud vara ad h aular vara pov (hgh rao mhod of mao qu ffcv. O h ohr had, wh h corrlao gav (hgh produc mhod of mao ca b mplod ffcvl. L ad (, do h ud vara ad aular vara akg h valu ad (, rpcvl, o h u U (,,,, whr povl corrlad wh ad gavl corrlad wh. To ma (, aumd
ha ( X ad ( Z ar kow. Aum ha populao larg o ha h f populao corrco rm ar gord. Aum ha a mpl radom ampl of draw whou rplacm (RWOR from U. Th uual ubad maor of whr ( (. h ampl ma of. Wh h populao varac rao maor for a ( X kow, Iak (983 propod a k (. whr ( X a ubad maor of. Upo h fr ordr of appromao, h varac of populao corrco (fpc rm ar rpcvl gv b ad ME of k (gorg h f (.3 ( [ ] var ME (. ( [ ] k μ pqr whr δ pqr, p / q / r / μ μ μ μ pqr p q r ( Y ( X ( Z ; p, q, r bg h o-gav gr.
Followg Bahl ad Tuja (99, w propo poal rao p ad poal produc p maor for mag populao varac a p (.5 p (.6. Ba ad ME of propod maor To oba h ba ad ME of, w wr (, ( uch ha E( E( E E Afr mplfcao w g h ba ad ME of a ad (, (, ( (. E 3 B (. 8 8 ME (. To oba h ba ad ME of, w wr (, ( uch ha E( E( E( (, ( ( E Afr mplfcao w g h ba ad ME of a 5 B( (.3 8 8 9 ( (. ME 3. Improvd Emaor Followg Kadlar ad Cg (6 ad gh. al. (7, w propo a mprovd maor for mag populao varac a-
α p ( αp (3. whr α a ral coa o b drmd uch ha h ME of mmum. Eprg rm of, w hav ( α α p p (3. Epadg h rgh had d of (3. ad rag rm up o cod powr of, w hav 8 α 8 α 8 α α (3.3 8 8 Takg pcao of boh d of (3.3 ad h ubracg h ba of h maor, up o h fr ordr of appromao, a ( α ( α ( α ( ( 8 8 B From (3., w hav ( α α from boh d, w g α ( (3. (3.5 quarg boh h d of (3.5 ad h akg pcao, w g ME of h maor, up o h fr ordr of appromao, a α α ( ( ME ( α ( α α( ( α( (3.6 Mmao of (3.6 wh rpc o α ld opmum valu a { ( 6} ( α α (a (3.7 ubuo of α from (3.7 o (3.6 gv mmum valu of ME of.
. Propod maor wo-pha amplg I cra praccal uao wh o kow a pror, h chqu of wopha or doubl amplg ud. Th chm rqur collco of formao o ad h fr pha ampl of ( < ad o for h cod pha ampl of (< from h fr pha ampl. Th maor, ad wo-pha amplg wll ak h followg form, rpcvl ' d p (. ' ' d p (. ' ' ' d k p ( kp (.3 ' ' To oba h ba ad ME of d, d, d, w wr (, (, ' ( ' (, ' ( ' ' whr ' ( ', ' ' ' Alo, E( E(, ', E(' ' ' ' ' (, (' ( E(' ' ' (, E ' ( ' Eprg d, d, ad d rm of ad followg h procdur plad co ad co3 w g h ME of h maor, rpcvl a-
ME( d ' ( ( (. ' ( ME( d ' ( ( (.5 ' ( ( d k ' k ' ( ME ' ' ( ( k ( k k(k ( (.6 ' Mmao of (.6 wh rpc o k ld opmum valu a { ( 6} ( k k (a (.7 ubuo of k from (.7 o (.6 gv mmum valu of ME of d. 5. Emprcal ud To llura h prformac of varou maor of Murh(967, p.-6. Th vara ar: : oupu, : umbr of workr, : fd capal, 8, 5,., w codr h daa gv.667, 3. 65,. 866,. 3377,. 8, 3. Th prc rlav ffcc (PRE of varou maor of wh rpc o covoal maor ha b compud ad dplad abl 5..
Tabl 5. : PRE of,, ad m. ME ( wh rpc o Emaor PRE(.,.35.9 5.7 I abl 5. PRE of varou maor of wo-pha amplg wh rpc o dplad. Tabl 5. : PRE of, d, d ad m.me ( d wh rpc o Emaor PRE (., d 7.76 d 53.86 d 7.77 ar 6. Cocluo From abl 5. ad 5., w fr ha h propod maor prform br ha covoal maor ad ohr mod maor. Rfrc Iak, C. T. (983: Varac mao ug aular formao. Joural of Amrca acal Aocao. Bahl,. ad Tuja, R.K. (99: Rao ad Produc p poal maor, Iformao ad Opmao cc, Vol.XII, I, 59-63. Kadlar,C. ad Cg,H. (6 : Improvm mag h populao ma mpl radom amplg. Appld Mahmac Lr 9 (6 75 79.
gh, R. Chauha, P. awa,. ad maradach, F. (7: Aular formao ad a pror valu coruco of mprovd maor. Raac hgh pr, UA. Murh, M..(967: amplg Thor ad Mhod. acal Publhg oc, Calcua, Ida.