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جامعة القاهرة كلية الا قتصاد والعلوم السياسية قسم الا حصاء استخدام برمجة الهدف لا ختيار المتغيرات في تحليل التمايز العنقودي بالتطبيق علي مشكلة توزيع السلع الغذاي ية المدعومة رسالة للحصول علي درجة دكتوراة الفلسفة في الا حصاء ا عداد محمد ا بو العنين ا حمد ا شراف ا.د نادية مكاري جرجس ا ستاذ الا حصاء بكلية الا قتصاد والعلوم السياسية جامعة القاهرة د. محمود مصطفي رشوان د. زينب يوسف محمود ا ستاذ الا حصاء المساعد - كلية الا قتصاد مدرس الا حصاء كلية الاقتصاد والعلوم السياسية جامعة القاهرة والعلوم السياسية جامعة القاهرة 2012

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א المحتويات א 1... 2...1-1 3...א א 1-2 4...א1-3 א א א 7.. א א א א 8... CDAא אאא א 10...אאאא א א א... 27 28...א 3-1 33... א3-2 37... 3-3 39... Uniquenessאא3-4 40... א אא א3-5 41... אא3-6 א א א א א א א... 43 44... א א א 4-1 46... א א4-2 47...אא א4-3 48... א4-4 א א א א א א א א א א... 54 55...אא5-1 58....א א5-2 58... אאאאא א 5-3 61......א אא 5-4 66... א5-5 74...אא א א5-6 77...א אאאא(A) 82 אא א א (B) א א... א א... 93

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אא אאא א א א א א א א א א א א א א א א א א א אאא אא אא א.א א א א : 1-1 [41] :Discriminant Analysis (DA) א א אא א א אא DAא א. א..א א א א אאא א א א א א א אא א א אא אא dependent variablepredictors א א א א א א א. א אא א א אא א Discriminant function (DF) א א א א אא א. א א אCA) ) :[43] Cluster Analysis Clusters א א CAא א א אא א אא א א. 2

[42] : Clusterwise Discriminant Analysis (CDA)א א א אא אא א א א א א א אאאא א א א א א א.א א א א.א (א )א א( א ) א א א CDA א א א א א א א א א א א א א א א א א א א א א א א א א א א אא אא.א... :Selection of variablesאא א אא א אא א א א א א א א א א א. א אא א אא א א אא אאא א אא. אא אא א [35] א א א א. :א א1-2 אא א א אאא אאא 3

א א.CDAא אא אא א א אא אאא אא2009/2008א אא א אא א א א א () אא א א א אאא. א אא א א א א אאא א א אאאאא א א אא א א א א א א א א א א א א א א א א. א אא אא א 1-3 :א :א א א א א א א א א א א א א. א א : א א א אא אא אא א א א א. אא א אא א א א א א א א א אא א אא אא א א א א. 4

א א : א א א א א א א א א א א א א א א אאאא אא אא Lau אא א א א. א א א א 1999 א א א א 2001 אGlen א א א א א א Decision variable א אאאא. אא א.אא אא Uniqueness test א א א א א א Classification rule אאא א א א א א א א.אא א א א :א א א Simulationאאא א א א א אאאא א : :א א: א א א א א אא א 50א 20. 100 : א א א א א. 5

:א אאא א 5 אא :אא א א א 10א א א 15 א 60 א א א א א אא א א א א א אא 60 א א א א. Stepwise Discriminant א אא אא Analysis (SDA) א א א אSDA א א :א א א א א א א :א א א א :א א א א א א א :א א א א א א :א א א א א :א א א א א א א א א א. א א :א א א א א א א א א א א א א () אאא א א א א א אאאאאא SDAא א א א : א א א א א א אא א אא אא א א א א אא א א א אאא א א א א. אא 6

א א אא א

: א א א א א אא א א א א א אvariables א masking א א א א א א א א א א א א א א א א [35] א א א א א א א א א א א אDA.CAא א א א CDA א א א א א א א א א א א א א א א א א א א א א א א א א א א. א א א א א א א א CDA א א א DA א א א א א א.CA CDA א אאא א [42] 1999 Lau א א א א א א Lau א א א א א א א אא אא(heterogeneity)א א א א א א א א א א א א א א א א א א א א א 8

א א אCDA א Min s. t s א אא א א א א ( y i ) א א א א א א א א א א א categorical א א א א א א א א א א א א א א א א א א א א א א א א א א א א א. א א א א א Lau א א א Lau א א א א א א א א : : א א + z2is2i ) + ( z א א א + z ( z1 is1i 1i s1 i 2is2i ) i { yki = 1} i { y ki = 0} z ki s ki a kj ( 2 1) 3 a j= 1 3 a j= 1 kj kj x x ji ji + s s ki k i ε ε, k = 1,2, k = 1,2, i = 1,2,..., n, i = 1,2,..., n z z 1, i = 1,2,..., n z 1 i + 2 i = 1i, z2i 0 i = 1,2,..., n, k = 1, 2 { y ki ; y 1} for all i = ki { y ki ; y 0} for all i = ki ( 2 2) ( 2 3) ( 2 4) ( 2 5) 9

z ki 1 = 0 k א א i א א א א אא א א א א א א: א א k = 1,2 i = 1, 2,..., n i = 1,2,..., n k א אא א אאא א א א א א א j i = 1,2,3 k = 1,2 אא y i s ki a kj ε אאאא א אא א א אא אא א א א DA א א א א :CA [37] DA א אאא א: א אא אאא א אאא אאdependent variablepredictors א אאאא א א א א אאא א א. אאDA א אאא א א א א א א א א א א :א א א א א normal dist. א א אא Canonical א א Stepwiseא א א : אVariate 10

[37] Stepwise method א -1 אאאא א א א אא א Minitab SAS SPSSאא א א א א א א א א א א א א א : [37]The Forward Stepwise Processes א א : א א א א ( ).אאא א אאאא אא א א א א א א r א. א א א א א א א א DA א א א א א X X, X,..., X 1, 2 3 e r+1.123... r between-groups א r א א א א א h r+1.123... r X r+1 X r+ 1 א א within-group א Fr +.123... r = ( n E r) hr+ 1.123... r /( nh er+ 1.123... 1 r ) (2 6) k = 1,2,..., m α k א ( nh, ne r, α ) m א F n k n H n אא א א א אא = m 1 : E F = m k = 1 n k m א א א א א א x r+1 11

[37]The Backward Stepwise Processes א א : א אאא אא א א א א אא אא א א א א א א א אא א א א א א א א Combining Forward and א א א א א [37] :Backward Stepwise Processes : א אאא אא א אאא א א אאא אא א אא אא אאא א א אא א א אאא א א א אאאא א אאא א א א א אאאא א אאאא א אאא אא א[37]Sharma א א א א א. 12

The Canonical Variate Method א א א 2 א א[37] א א א א א א אאא א א א א א principal component אfactor analysis א א H א אא The Canonical Variateאאא E א א א א א א E 1 H א H א Within א א א E Eigen roots א א j = 1,2,..., s j אgroups between groups 1 λ ( E H ) אא א λ א E 1 H Eigen vectorsאא f discriminant j j א א א א j = 1,2,..., s λ f Ef = n t j X 1, X 2,..., j X p E j j (.) E 1 H 1, f 2 f s f,..., 1 א א ( ( E H א א אא canonical variates אאאfunction אאא א אאא :אא א א אא א א א א א א א א א ( f j א ) The Canonical Variate א א א א א א א. א א א.א א 13

אאאSmith and Huberty [37] א אאThe Canonical Variateאאא א. א א א א r א א 1982 McKay and Campbell Q = R r f j א א א R א א א א : H E א א אאא E E = E rr Qr E E rq QQ H rr H rq H = H Qr H QQ :אא E Q. r = E QQ E Qr E 1 rr E rq ( 2 7) H Q. r = 1 ( EQQ + H QQ ) ( EQr + H Qr )( Err + H rr ) ( ErQ + H rq ) EQr (2 : אא 8) W ( E + H E ) 1 Q. r = Q. r Q. r / Q. r ( 2 9) n H n E R F א א α ( nh, ne r, α ) א א א א א F א א F א א Q = R r א א א 14