Bayesian Estimation of the Logormal Distrbution Mean Using Ranked SET Sampling

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1 Basrah ournal o Sn Vol.5-7 Basan Estaton o th ooral Dstrbuton Man Usn Ran SET Sapln R.. h bstrat Bas staton or onoral an usn Ran St Sapln s onsr n ths papr an opar to that usn Spl Rano Sapln. It as sho that th Bas stator s bttr than Bas stator n trs o th Bas rs. lso th rato btn Bas rs to Bas rs s shon to b alas ratr than on. ريكان عبد العزيز احمد جامعة البصرة/ كلية الا دارة والاقتصاد/قسم الاحصاء الملخص لقد تم تقدير بييز للوسط الحسابي في حالة توزيع اللوغارتمي الطبيعي باستخدام طريقة المعاينة المرتبة ومقارنته بتقدير بييز بطريقة المعاينة العشواي ية البسيطة. وقد وجد ان تقدير بييز للمعاينة المرتبة ا فضل منه للمعاينة العشواي ية البسيطة من حيث الخطورة في تقدير بييز. وقد وجد ان النسبة بين خطورة تقدير بييز للمعاينة العشواي ية البسيطة الى خطورة بييز للمعاينة المرتبة داي ما اكبر من الواحد. Introuton Snha an Wu 994 nvstat th proran o n th staton o othr paratrs not ssntall th an hn th populaton s partall non. Th shap an th sal paratr o th to paratrs Wbull strbuton ar onsr n thr stu. Stos 995 µ onsr th loaton sal al th non stu σ ME ro both an or to ass snl paratr s unnon an both paratrs ar unnon. Bal Snha an Sutra 995 nvstat so provnts o µ th sutabl

2 Basrah ournal o Sn Vol.5-7 oatons o or staton o µ hn s noral an ponntal. In ths papr assu that th populaton unr stu s a onoral populaton th paratr an unnon an varan σ non an has a pror nst unton as. s an attpt to stat usn Basan staton a spl rano sapl o s s tan ro th populaton on th othr han a spl rano sapl o s s also tan ro th populaton to obtan th ran st sapl. or ah sapl th Basan stator s oun th rspt to th Conjuat an r prors. Th proran o th to stators ar opar usn thr Bas rss th to stators ar pn on th onjuat pror or opar usn thr rs unton th to stators ar pn on th r pror. n not that th squar rror loss unton SE ll b us n ths papr that ans a a rprsnt th loss that rsult ro stator b a. Th Bas stators th rspt to th Conjuat pror: Th onjuat prors hav th ntutvl appaln atur o allon on to bn th a rtan untonal or or th pror an n up th a postror o th sa untonal or but th upat paratrs b th sapl noraton as O.Brr. Th onjuat pror n ths as s noral strbuton an thout loss o nralt ll assu that t s ~ N. Th Bas stators pn on. N hr t b a ro lo σ σ non thn thout loss o nralt ta σ nst unton s. thn th probablt lo ~ > < <

3 R.. h Basan Estaton o 3 an th jont nst unton s. an th nst unton o th onjuat pror s Th postror nst unton o s thn Th Bas stator o s E baus th Bas stat th rspt to SE s th postror an thn lo an th Bas rs o th stator s Th Bas stators pn on. W assu that hav rano sapls ah o s sn. M M M lo < < lo lo ~ N Var E r

4 Basrah ournal o Sn Vol hr j N j lo ~. No lt Y Y Y b th hr n Y n n Y a Y.. Y s th th orr statst o th st. Thn th p o s vn b. hr Usn th transoraton lo thn ~ N.Thn p o s ba as. hr s a p o N an s a CD o N sn ar npnnt thr jont nst s. No t < < ;!!! < < > lo!!!!!!!!!

5 R.. h Basan Estaton o 5 & Thn Th postror nst unton o s vn b. Th Bas stator o s E n th postror varan s Th Bas rs Var E r Var

6 Basrah ournal o Sn Vol.5-7 Th nral Bas stators th rspt to th r pror: Th Basan approah an b us vn hn no pror noraton s avalabl n suh stuatons a non-noraton pror s us an b all r pror. Th Bas rs has no ann hr nnt so opar pn on th rs unton. Th nral Bas stators pn on. t b a ro lo N an lt th r pror n ths as s ~.Baus th s alloaton paratr s as O.Brr thn th postror nst s vn b. lo lo sn ~ N Hn th nral Bas stator o s. E Th rs unton s lo lo R bas Var Th nral Bas stators pn on. t Y Y Y b th ro lo N an lt th r pror n ths as s also ~. Usn th transoraton lo thn ~ N. Thn p o s ba as.!!! 6

7 R.. h Basan Estaton o 7 Thn th jont nst unton o 's s Thn th postror nst s vn b. thror Thus th nral Bas stator Th rs unton s vn b Proprts o th nral Bas stator usn. t b a onstant thn Proo: R

8 Basrah ournal o Sn Vol t thn Th rs unton o s r o. Proo: Usn proprt on. lt E R!!!!!!

9 R.. h Basan Estaton o 9 hh s r o. 3 proo: But. Thn t an j thn 4 s unbas stator or ; E Rss. proo: & j j Rss Rss E

10 Basrah ournal o Sn Vol.5-7 Usn proprt on an lt thn E!!! u an lt j usn th transoraton an usn th proprt thr hav. E u u u u j u u j rna u u rsptvl b thn E j j E Thus E E E E E E Thus s unbas stator or. Nural oparson. In ths ston ll usn th sulaton to obtan th valus o th Bas rs { r r } an rs unton { R R } pn on th onjuat pror an r pror rsptvl an also opar th to stators b usn n sn. Th n o th rspt to pn on th onjuat r pror s n b r Th n o th rspt to pn on th r pror s n b R R Tabl on ontans valus or & r r R R

11 R.. h Basan Estaton o alon th th n or slt valus o nubr o ls an s th st s. r & hr r s th Tabl :Bas rs { r r } an rs unton { R R } an n th rspt to th onjuat pror an r pror rsptvl Conluson.. Th Bas rs usn s alas lss than th Bas rs usn or all th ass onsr.

12 Basrah ournal o Sn Vol.5-7. Th rs unton usn th nral Bas stator s alas lss than that usn th nral Bas stator. 3. Both th Bas rs usn an rass as n r nrass. 4. Both th rss unton rass as r n nrass. 5. Th n s alas ratr than on. 6. Th n s nrasn thn a l as nrass. Rrns. Barr C. rnol & N. Balashnan rst Cours n Orr Statsts. ohn Wl & Sons. Bal K. Snha & Sutra On so aspts o ran st sapln or staton o noral an ponntal paratrs. Statsts an Dsons.. H. Snha B.K. an Wu's.994. Estaton o paratrs n to paratr Wbull an tr-valu strbutons usn ran st sapln. ournal o Statstal Rsarh as O. Brr 985. Statstal Dson Thor an Basan nalss. Son Eton. ohn Wl & Sons. Noran. ohnson 997.vans n th Thor an Prat o Statsts. ohn Wl & Sons Stos S Paratr ran st sapln. nnals o Insttut o Mathatal Statsts