هقارنت طرائق تقذير هعلواث توزيع كاها ري املعلوتني

Transcription

1 هقارنت طرائق تقذير هعلواث توزيع كاها ري املعلوتني يف حالت البياناث املفقودة باستخذام احملاكاة د أ. الباحثة ظافر حسين رشيد جامعة بغداد- كمية االدارة واالقتصاد قسم االحصاء آوات سردار وادي املستخلص Maxiu Lielihood Mehod Shiage Mehod Siha ho Bowa, Sheo ad La Moe Calo MSE Absac he esiaio of he paaees of wo Paaees Gaa Disibuio i case of issig daa has bee ade by usig wo ipoa ehods: he Maxiu Lielihood Mehod ad he Shiage Mehod. he foe oe cosiss of hee ehods o solve he MLE o-liea equaio by which he esiaos of he axiu lielihood ca be obaied: ewo-raphso, ho ad Siha ehods. ho ad Siha ehods ae developed by he eseache o be suiable i case of issig daa. Fuheoe, he Bowa, Sheo ad La Mehod, which depeds o he hee Paaees Gaa Disibuio o ge he axiu lielihood esiaos, has bee developed. A copaiso has bee ade bewee he ehods i he expeieal aspec o fid he bes ehod hough siulaio by usig he Moe Calo Mehod. Seveal expeieaios have bee ade by usig he ipoa saisical easue: Mea Squae Eo MSE. : املقذهت واهلذف:

2 Icoplee Dey Coi ad Dey Coi ad JI Maxiu Lielihood Mehod Siha ho Shiage Mehod Siha, Bowa, Sheo ad La Moe Calo MSE : تقذير هعلواث توزيع كاها ري املعلوتني يف حالت البياناث املفقودة:

3 Disibuio of Cuulaive ie- o- Failue Lielihood Fucio MLEs Maxiu Lielihood Esiaio, = X + X + +X ;=,,, X i X i ~ i.i.d gaa, X i i ~ gaa, ; =,,, ; =,,, f f \ exp X i f f \ P R PR= Mixue Model

4 f f \ exp P R exp P R=,, =,,, =,,, = ax {\ > 0} M M M /

5 Esiaig by Maxiu Lielihood Mehod i i i exp L, i i L, f exp, \ f \ LL, M ML L L L L M : LL, M 0 : LL, ML L LL

6 Digaa Fucio ML L ML ML L ML L Maxiu Lielihood Esiaios MLEs ewo-raphso Mehod i 4 i i i i g g g ML g

7 i i i i i ML i M, Develope of ho Mehod ho ho L 4y /3, 4y L ho L L / ML

8 0 / 6 L L L 4 / 3 4 Siha Develope of Siha Mehod Siha L, y Siha L

9 ML L ] [ ML ML L L s L s s s

10 Bowa, Sheo ad La Develope of Bowa, Sheo ad La Mehod Bowa, Sheo ad La, 3, X i Rado Vaiable 0 0,, ;, x I e x x f x X 30 i X i Moe Geeaig Fucio X = Ee X dx e x e x x y = x X e 3 Z = Z Z Ee X X X Ee... ] ]...[ ][ [ X X X

11 = e e e... i X i Z e 3 e f f ; \ 33 \,,,, f L exp 34

12 LL M LL M LL L ML LL A 36 M A M A A 37

13 A M A =0 bl bl bl 38 M, bl bl 3- التقذير باستخذام طريقت التقلص طريقت هقرتحت: Esiaio by Shiage Mehod Poposed Mehod Siha ho ho Siha hopso ~ h h 0 h 39 ~ ~ h h ~ MSE ~ E E[ h h ]

14 h MSE ~ h MSE h h B h h h [ MSE ~ h h ] 40 0 h 4 [ MSE h 4 ] h 3: اجلانب التجريبي: = 6, =0,30,50,00 =,,,

15 =6, = =,,, =6 =,,, 6 =0 4- اختيار قين املعلواث االفرتاضيت: Ivese asfo 0, xi,,,..., x i i,,..., i Logu, i i,,..., Coiuous Uifo Vaiae u i

16 38 L MSE i L MSE 4 i L =6 Model s bl sh

17 Model 3 = 6 s MSE bl sh =6 Model 3 s bl sh

18 Model =6 MSE s bl sh = Model s bl sh

19 Model = s MSE bl sh = Model s bl sh

20 Model = s MSE bl sh

21 : 4 االستنتاجاث والتوصياث, MSE Siha, ho Bowa, Sheo ad La

22 املصادر العربيت: املصادر األجنبيت:. Bowa, K.O., Sheo, L.R. ad La, H.K. 987 Siulaio ad Easiaio Pobles Associaed wih he 3-Paaee Gaa Desiy. Couicaios i Saisics, Seies B- Siulaio ad Copuaio, Vol.6, o.4, PP Choi, S.C., ad Wee, R. 969, Maxiu Lielihood Esiaio of he Paaees of he Gaa Disibuio ad hei Bias, echoeics, Vol., o. 4, PP Coi, D.W., ad Dey, K.A. 999, Aalysis of Gouped Daa fo Field- Failue Repoig Syses, Reliabiliy Egieeig ad Syse Safey, 65, Coi, D.W., ad JI,. 000, Gaa Disibuio Paaee Esiaio fo Field Reliabiliy Daa wih Missig Failue ies, IEEE asacios, 3, Dey, K.A. 98, Saisical Aalysis of oisy ad Icoplee Failue Daa i Poceedigs Aual Reliabiliy ad Maiaiabiliy Syposiu RAMS, IEEE, Piscaaway. J. PP Lawless. J. F. 003, Saisical Models ad Mehods fo Lifeie Daa, d ed., ew Jesey, Joh Wiley & Sos, Ic.. Sheo, L. R., ad Bowa, K.O. 970, Reas o ho s Esiaos fo he Gaa Disibuio, Mohly Weahe Review, Vol. 98, o., PP