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:
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:
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
f f \ exp P R exp P R=,, =,,, =,,, = ax {\ > 0} M M M /
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
Digaa Fucio ML L ML ML L ML... 5 0 6 4 L Maxiu Lielihood Esiaios MLEs ewo-raphso Mehod i 4 i i i i g g g ML g
i i i i i ML i M, Develope of ho Mehod ho ho L 4y /3, 4y L ho L L / ML
0 / 6 L L L 4 / 3 4 Siha Develope of Siha Mehod Siha L, y Siha L
ML L ] [ ML ML L L s L s s s
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
= e e e... i X i Z e 3 e f f ; \ 33 \,,,, f L exp 34
LL M LL M LL L ML LL 0 0 0 35 A 36 M A M A A 37
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 ]
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 =,,,
=6, = =,,, =6 =,,, 6 =0 4- اختيار قين املعلواث االفرتاضيت: Ivese asfo 0, xi,,,..., x i i,,..., i Logu, i i,,..., Coiuous Uifo Vaiae 43 44 u i
38 L MSE i L MSE 4 i L =6 Model s bl sh 0.8066.849.3490.958.58030 30.08993.09045.044303.469.067377 50.04854.048776.00645.076054.0570 00.0307.030648 0.98450.046986.007584 0.9364.93790.46558.388.7074 30.9373.9388.46660.535.7070 50.837.8473.0856.4433.04865 00.05534.0568.00548.06568.0908 0 3.466788 3.466856 3.4955 3.49059 3.443056 30 3.303605 3.30367 3.56079 3.387 3.79875 50 3.6837 3.68385 3.0806 3.8039 3.44595 00 3.093468 3.093536 3.045960 3.099038 3.069748
Model 3 = 6 s MSE bl sh 0 0.960 0.9598 0.04508 0.35964 0.58 30 0.0973 0.0947 0.09646 0.4936 0.09954 50 0.046000 0.045986 0.043455 0.05340 0.04488 00 0.03558 0.03554 0.0766 0.07795 0.068 0 0.7348 0.7345 0.70544 0.749495 0.77889 30 0.40874 0.40855 0.39858 0.45460 0.399499 50 0.789 0.7883 0.0779 0.3373 0.80 00 0.088964 0.088957 0.0863 0.09566 0.086983 0.635.6335.569675.66847.590438 30 0.86749 0.86740 0.835807 0.898 0.848707 50 0.447087 0.447079 0.4334 0.469963 0.439544 00 0.9575 0.95749 0.8905 0.05979 0.98 =6 Model 3 s bl sh 0.94603.95096.4834.3398.778 30.09895.099449.0594.3368.07686 50.0509.0563.005388.078905.0850 00.03345.033974 0.987699.050349.00837 0.5685.5759.8056.6433.39908 30.003.00387.076705.97.088546 50.068009.068083.044399.076006.0564 00.07479.07553.00393.0358.05738 0.59968.5999.44076.67975.5033 30.0583.05853.089933.859.097893 50.058069.05809.0495.0603.05043 00.03088.030.0636.033976.0473
Model =6 MSE s bl sh 3 0 0.4343 0.436 0.589 0.64597 0.337 30 0.638 0.69 0.07993 0.30088 0.565 50 0.05586 0.05580 0.04986 0.06045 0.050396 00 0.06605 0.06607 0.058 0.030977 0.05407 0 0.98553 0.98546 0.943 0.03909 0.94847 30 0.0836 0.083 0.0386 0.79 0.05933 50 0.05964 0.0596 0.056765 0.06370 0.058053 00 0.03487 0.03486 0.0663 0.056 0.0935 0 0.906 0.905 0.85054 0.9645 0.8756 30 0.03539 0.03538 0.006 0.07 0.0837 50 0.050805 0.050805 0.0495 0.053348 0.04995 00 0.0655 0.0655 0.0853 0.03890 0.09 = Model s bl sh 3 0.50498.5077.863.7789.34467 30.094805.095085.06494.97.078790 50.055664.05594.03354.079.039648 00.0309.03369 0.999787.04876.06078 0.338.33898.99765.36875.3633 30.96489.96568.63445.363.80006 50.4595.4673.08557.363.0985 00.056454.05653.0340.05995.039976 0 3.50888 3.50896 3.475607 3.5783 3.496 30 3.86676 3.867 3.5343 3.303935 3.70063 50 3.00047 3.0008 3.6678 3.05076 3.8343 00 3.089478 3.08954 3.0569 3.09590 3.07867
Model = s MSE bl sh 3 0 0.870 0.854 0.75 0.90090 0.76487 30 0.0865 0.0860 0.0337 0.759 0.05698 50 0.046087 0.04608 0.04348 0.050 0.044485 00 0.0584 0.0583 0.0494 0.05 0.0773 0 0.80876 0.808749 0.787537 0.84644 0.797868 30 0.398460 0.398450 0.386374 0.49959 0.3938 50 0.0363 0.0357 0.94769 0.06300 0.97789 00 0.08467 0.08465 0.08476 0.087750 0.08547 0.85380.85370.80.889703.836468 30 0.90387 0.90386 0.8857 0.935539 0.894509 50 0.4730 0.47308 0.46000 0.476940 0.465877 00 0.0840 0.0838 0.05940 0.79 0.08 = Model s bl sh 3 0.6003.60478.769.878.44049 30.09697.09707.06455.069.080879 50.058863.0594.06446.074605.04794 00.03456.034805.005.04594.08478 0.7009.7030.53496.8445.683 30.0854.0894.08576.07.093585 50.059657.059696.0430.064009.05399 00.0985.0934.0749.03044.0036 0.73486.73498.6358.79734.6798 30.09865.09867.087500.0436.093064 50.067553.067565.056454.06993.06009 00.030546.030558.09453.03675.05005
Model = s MSE bl sh 3 0 0.00 0.00 0.90769 0.0934 0.95663 30 0.4 0.409 0.0846 0.4037 0.044 50 0.049788 0.049786 0.04674 0.055407 0.04798 00 0.0508 0.0509 0.03664 0.07646 0.04079 0 0.07934 0.0793 0.0369 0.6578 0.0508 30 0.0404 0.040 0.00863 0.09059 0.044 50 0.053044 0.05304 0.0557 0.054334 0.0508 00 0.090 0.0909 0.077 0.0849 0.0474 0 0.657 0.656 0.0880 0.6438 0.0707 30 0.05057 0.05056 0.093 0.0859 0.03954 50 0.053677 0.053677 0.0568 0.054073 0.0594 00 0.04364 0.04364 0.03789 0.0537 0.04046
: 4 االستنتاجاث والتوصياث, MSE Siha, ho Bowa, Sheo ad La
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.47-88.. 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. 683-690.. Coi, D.W., ad Dey, K.A. 999, Aalysis of Gouped Daa fo Field- Failue Repoig Syses, Reliabiliy Egieeig ad Syse Safey, 65, 95-0.. Coi, D.W., ad JI,. 000, Gaa Disibuio Paaee Esiaio fo Field Reliabiliy Daa wih Missig Failue ies, IEEE asacios, 3, 6-66.. Dey, K.A. 98, Saisical Aalysis of oisy ad Icoplee Failue Daa i Poceedigs Aual Reliabiliy ad Maiaiabiliy Syposiu RAMS, IEEE, Piscaaway. J. PP. 93-97.. 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. 54-60.