Beta Linear Failure Rate Geometric Distribution with Applications

Transcription

1 Gog Souh Us Dg Souh Mhmc Sccs Fcu Pucos Dpm o Mhmc Sccs 4-6 L Fu R Gomc Dsuo wh Appcos odc O Oud Gog Souh Us oud@gogsouhdu Ihm E A Imm Mohmmd I Sud Ismc Us Shuo Hug Us o Houso Foow hs d ddo wos : hps://dgcommosgogsouhdu/mh-sc-cpus P o h Mhmcs Commos Rcommdd Co Oud odc O Ihm E Shuo Hug 6 " L Fu R Gomc Dsuo wh Appcos" Jou o D Scc 4 : hps://dgcommosgogsouhdu/mh-sc-cpus/63 Ths c s ough o ou o d op ccss h Dpm o Mhmc Sccs Dg Commos@Gog Souh I hs ccpd o cuso Mhmc Sccs Fcu Pucos uhozd dmso o Dg Commos@Gog Souh Fo mo omo ps coc dgcommos@gogsouhdu

2 Jou o D Scc L Fu R Gomc Dsuo wh Appcos odc O Oud Ihm E Shuo Hug 3 Dpm o Mhmc Sccs Gog Souh Us Dpm o Mhmcs d Sscs A Imm Mohmmd I Sud Ismc Us 3 Dpm o Mhmcs Us o Houso Asc: Ths pp oducs h u gomc dsuo whch cos um o dsuos cudg h pod u gomc u gomc u po gomc Rgh gomc Rgh d po dsuos s spc css Th mod uh gzs h u dsuo A comphs sgo o h mod pops cudg moms codo moms dos Loz d oo cus d op psd Esms o mod pms g R d mps psd o us h ususs d ppc o h dsuo K wods: u dsuo L u gomc dsuo Moms Mmum hood smo Ioduco L G φ h cumu dsuo uco cd o sou couous dom X wh ϕ Ω s h pm co A g css gd om h og o dom ws oducd Eug Th cd o h -G dsuo hs h om F ϕ Gφ I Gφ wh > d > wo ddo pms whos o s o oduc swss d o wgh G ϕ s p/s cd w w dw s h comp uco wh d I s h comp uco o O mo o hs css o dsuos s s o g swd d h co pop d sg dsuos I w h F [ G ] whch s cd h pod G dsuo o h Lhm p-i dsuo S o mp h pod Wu P 6 Mudho 995 d pod po Gup d Kudu 999 dsuos Idd Z s dsud dom wh pms d h h cd o X G Z gs wh h cd g quo As usu dom X wh h cd s

3 38 L Fu R Gomc Dsuo G sd o h G dsuo d w dod X ~ G φ Som spc css o G dsuos g dm 3 d Th csss o dsuos od wh quo cd spc h pm d sc pm ms wh udg dsuo S Msh d O 7 C o pos g us o G h G cd wh s h cd o ss p ssm wh G dpd compos hg h cd S w-ow dsuos h og o h sc pm m cud h pod Wu EW dsuo s Mudho 995 gzd o pod po dsuo poposd Gup d Kudu 999 d pod p dsuos oducd Ndh d Koz 6 Th gzd po-gomc GEG dsuo o S so ogs o h sc pm m Fo g d w c pss h cd g quo ms o h wow hpgomc uco h s [ G ] F F G wh F o < d α Γα+ αα + α + dos h scdg co o W c Γα o h pops o F o - G dsuo dd om p G dsuo quo whch pcp oow om h pops o h hpgomc uco h w sshd h u s o mp sco 9 o Gdsh d Rzh Th po ds uco pd d hzd u ucos o G dsuo cospodg o h cd quo g ϕ gϕ G φ { G φ} 3 d g G h I G G spc wh I I F s h su G G uco o G dsuo cospodg o h cd quo Th Gzd -G dsuo modd Wu MW dsuo oducd S s ch css o gzd dsuos Ths css hs cpud cosd o o h s w s Sps d Kog 7 ppd h - G dsuo o mod h sz dsuo o com Ths dsuo hs sudd h u o ous oms o h s dsuo G Th -G dsuos h

4 O Oud I E S Hug 39 h pod cud h om N Eug F c h F dsuo Ndh d Koz 4 po E dsuo Ndh d Koz 6 h Wu W dsuo L 7 Wu-gomc dsuo Codo gzd h om dsuo Pscm dd h-om mod Codo 4 u XII dsuo Pí o-souz oducd h gzd po GE dsuo Th gzd Ld dsuo ws psd Oud d Yg 5 d s Wu IW ws dopd Kh Oud 5 oducd d sudd h og gzd Ld-Wu dsuo d ppd h mod o m d Rc Codo oducd h - Wu gomc dsuo whch quo ws o h cd o h G Wu-gomc dsuo o o-souz dm poposd h po-gomc dsuo h dg h po-gomc dsuo o Admds d Lous 998 Aso dm 3 oducd w dsuo h cuds h Wu-gomc dsuo o o-souz Pco 3 oducd d dscussd h pops o h Wu Posso dsuo Codo 4 psd h pops o Kumm gzd gmm dsuo I hs c w mp o gzd h u gomc LFRG dsuo o Mhmoud d J 4 g G quo o h cd o LFRG dsuo wh Cθ θ θ < θ < Mhmoud d J 4 compoudd h u dsuo wh gomc dsuo o od w m dsuo wh poss shps o h hzd uco h s csg dcsg upsd - dow hu umod hu d csg - dcsg - csg shpd whch commo d oogc suds Rc gzos o h u dsuos cud h gmm u dsuo Codo 4 d h Posso gzd u mod Codo 5 Th md o h pp s ogzd s oows I Sco w d h u gomc dsuo pso o h cumu d ds ucos hzd d s hzd ucos d som spc css psd Moms mom gg uco d codo moms dscussd Sco 3 I Sco 4 w o h m dos ou h m d h md oo d Loz cus Sco 5 cos h dsuo o h od sscs d uc msus cudg Ré d s-ops Mmum hood smo s pomd Sco 6 Appcos g sco 7 oowd cocudg ms L Fu R Gomc Dsuo Cosd h u gomc LFRG dsuo o Mhmoud d J 4 wh h cd

5 3 L Fu R Gomc Dsuo > G 4 wh > > d Rpcg G wh quo h LFRG cd quo 4 o ds w cd dw w w F I G 5 o > > > > > d A dom X wh h cd quo 5 s sd o h u gomc dsuo d w dod X : Th cospodg pd o hs w dsuo s g 6 o > wh h pms > d > shp pms whch chcz h swss uoss d umod o h dsuo Gphs o h pd o dsuo g h Fgu Th pos show h h LFR pd c dcsg o gh swd mog s oh poss shps s s h gu Th dsuo hs pos smm

6 O Oud I E S Hug 3 Fgu : Gphs o pd o Scd Pms Th su uco RF o h dsuo dod R s g R F I G Th hzd d s hzd ucos o h dsuo g h R 7

7 3 L Fu R Gomc Dsuo I G 8 d F I G 9 spc Th ds d hzd ucos c h d ho dpdg o h us o h pms wh chos o pos s show hs pos How s hd o z h shp o oh h ds d hzd uco du o h compcd oms Pos o h hzd uco o d comos o h pm us g Fgu Th po shows ous shps cudg moooc csg d hu shps o comos o h us o h pms Ths ms h hzd uco su o oh moooc d o-moooc mpc hzd hos h o coud suos

8 O Oud I E S Hug 33 Fgu : Gphs o Hzd Fuco o Scd Pms Spc Css o h Dsuo Th dsuo s mod h ppochs d dsuos wh s pms chgd Th dsuo cos s spc-mods cudg h oowg dsuos I h dsuo ducs o h m dsuo cd po gomc EG dsuo whch ws poposd dm Th po gomc EG dsuo s od wh d I ddo h po dsuo wh pm > s od

9 34 L Fu R Gomc Dsuo Wh h dsuo ducs o h u gomc LFRG dsuo Wh w g u LFR dsuo whch ws oducd Mhmoud d J 4 Gzd u GLFR dsuo ss wh d whch ws g Sh d Kudu 9 I ddo wh u LFR dsuo s od Wh w g h Rgh gomc RG dsuo I ddo h wh h Rgh R dsuo s od Rgh gomc RG dsuo ss s spc cs o g d Wh d Rgh dsuo s od wh w o h po E dsuo d Epod u gomc dsuo ELFRG s od wh Qu Fuco I hs susco w ps h qu uco o h dsuo Th qu o h dsuo s od sog h o quo IG U wh G / d U s uom o h u [] I oows h h X h oos o h quo h s X X Iu X og I u Iu og I u Iu og Iu o > d X d > wh I u dos h s o h comp uco o Qus o h dsuo o scd us o h mod pms g T A R gohm o h compuo o h qus o h dsuo s g h ppd

10 O Oud I E S Hug 35 T Qus o Scd Pm Vus α β θ u 3 Epso o h Cumu d Ds Fucos I hs susco w ps som ss psos o h cd d pd o h dsuo Th mhmc o g ow w usu susqu scos H d hcoh w X dom hg h dsuo W o som pssos o h cd F d pd o h dsuo Th oowg ss psos w usu sudg h pops o h dsuo I s pos o-g d z < h F z z Appg h ss pso o c -w h cd s oows: G FGLFRG 3 Cosqu h cd c pssd s mu o gzd u gomc GLFRG dsuos wh pms d Aso wh > s g h d h ss pso sops Usg h ss pso ow: z z z < d > 4

11 36 L Fu R Gomc Dsuo h pd c pssd s LFR 5 wh LFR s h pd o h LFR dsuo h ws oducd Mhmoud d J 4 Aoh om o quo 5 s s oows: 6 Now sc < < d usg To pso o h uco g quo 6 coms w 7 wh w 3 Moms d Codo Moms

12 O Oud I E S Hug 37 I hs sco w ps h moms d codo moms o h dsuo Moms css d mpo ssc ss spc ppcos I c usd o sud h mos mpo us d chcscs o dsuo g dc dspso swss d uoss A o h s s moms d d sscs o scd us o h mod pms s so psd 3 Moms I X hs h dsuo h h h mom o X s g w ' 8 No h d w ' ] [ w 9 Th cocs o o swss d uoss o h dsuo c d od ccodg o h oowg o SD μ μ CV μ μ CS μ 3 3μ μ +μ 3 [μ μ ] 3 d CK μ 4 4μ μ 3 +6μ μ 3μ 4 [μ μ ] T T o Moms d Rd Sscs α β θ EX EX EX EX EX EX SD CV

13 38 L Fu R Gomc Dsuo CS CK Codo Moms Fo m mods s so o s o d h codo moms d h m sdu m uco Th h codo moms o dsuo s g d F X X E > d F w ] [ F w ] [ wh d s s s h upp comp gmm uco Th m sdu m uco s g > F w X X E 3 ] [ 4 M Dos oo d Loz Cus I hs sco w o m do ou h m d h m do ou h md s w s oo d Loz cus o h dsuo 4 M Dos Th mou o sc popuo s d msud o som h o o dos om h m d md Ths ow s h m do ou h m d h m do ou h md Th dd d M d d

14 spc wh E X O Oud I E S Hug 39 d M Md X d c ccud usg h oshps d spc Wh No h F d M d quo?? w g h m w d d M d g dos h md Th msus E X s w d [ ] 3 d w d M M [ ] 3 M spc so h h m do ou h m s w F [ ] 3 d h m do ou h md s w M [ ] 3 M 4 oo d Loz Cus I hs susco w ps oo d Loz Cus oo d Loz cus oo 93 h ppcos o o coomcs o h sud com d po u so oh ds such s dmogph suc d mdc oo d Loz cus g 3

15 33 L Fu R Gomc Dsuo d p p q q w p 3 ] [ q d d p L q q w 3 ] [ q spc wh d s h ow comp gmm uco 5 Od Sscs d Msus o Uc I hs sco h dsuo o od sscs d msus o uc o h dsuo psd Th cocp o op ps o omo ho Th op o dom s dd ms o s po dsuo d c show o good msu o domss o uc 5 Dsuo o Od Sscs Suppos h X X s dom smp o sz om couous pd L X X X : : : < < < do h cospodg od sscs I X X s dom smp om dsuo oows om h quos 5 d 6 h h pd o h h od sscs s X Y : s g G

16 O Oud I E S Hug 33 ] [ ] [ G Th cospodg cd o Y s F F ] [ G ] [ G 5 Ré Eop Ré op 96 s so o Sho op Ré op s dd o og d H wh > d Ré op ds o Sho op s No h usg h ss psos quos d 5 w h ] [ s s s s s Now

17 33 L Fu R Gomc Dsuo [ s d s s s s [ ] ] s Cosqu Ré op o h dsuo s H og[ o 53 s -Eop H > s s s s [ /] s ] s [ ] Th s -op o dsuo s dd s [ d] s s > s E[ og X ] s s wh s d s g ow: p s s s [ s d s p s p s s s p p [ s] 6 Esmo d Ic s ] I hs sco w ps h mmum hood sms MLEs o h pms o h dsuo om comp smps o L dom smp o sz T om dsuo wh s h co o mod pms Th og-hood uco c w s p og L o h co o pms

18 O Oud I E S Hug 333 og og og og og og L og og 4 wh Th ssocd sco uco s g T U Th og-hood c mmzd h dc o sog h o hood quos od dg h og hood uco Th compos o h sco co g og og og 8 d og og 9 spc Th mmum hood sm MLE o s φ s od sog h o ssm U Ths quos co sod c d ssc

19 334 L Fu R Gomc Dsuo sow c usd o so hm umc mhods W c us chqus such s Nwo-Rphso p gohm o o h sm φ Th cogc o h smo pocdus o dpds o h choc o sg o us o h pms so o hs o cuous o c mus wh og h umc ppomos o h pcd omo m Fo mhods such s h FGS ppomo o h Hss m s usd o h compuos o ch o d hs ppomo m o wh cogc o h mhods occus oo s h dg o u ppom Hss m Oh mhods o smo such s gzd mhod o moms o o us oowd Nwo o qus- Nwo mhods o o d pm sms m usd I hs pp w mmz h hood uco usg NLmd SAS d m R Th uco ws ppd d cud o wd g o us Ths pocss o sus o d o mo h o mmum how hs css w h MLEs cospodg o h gs u o h mm I w css o mmum ws dd o h scd us I hs css w u ws d od o o mmum Fo smo d hpohss ss o h mod pms w qu h omo m Th Fsh omo m s g og L J [ J ] 5X 5 E 345 c umc od Th o Fsh omo m J c ppomd I ˆ [ ˆ ] 5X Fo g s o osos h m g h quo o s od h cogc o h Nwo-Rphso pocdu Appg h usu g smp ppomo MLE o h s φ c d s g ppom N J wh J EI Ud codos h ud o pms h o o h pm spc u o o h oud h smpoc dsuo o φ φ s N 5 J wh J m I s h u omo m Ths smpoc ho ms d J s pcd h g smp omo m ud φ s I φ Th smd smpoc mu om N 5 φ I φ dsuo o φ c usd o cosuc ppom codc s o h pms d o h hzd d su ucos A % smpoc codc o ch pm s g ACI ˆ z Iˆ ˆ z Iˆ 5

20 Î O Oud I E S Hug 335 wh s h dgo m o I ˆ o 345 d zζ s h ζ qu o h sdd om dsuo W c us h hood o LR s o comp h o h dsuo wh s su-mods o g d s Fo mp o s h LR ssc s ~ ~ [ L ˆ ˆ ˆ ˆ ˆ L ~ ] wh d h uscd sms d d ~ h scd sms Th LR s cs h u hpohss > wh dgs o dom 7 Smuo ~ ~ wh do h upp ˆ ˆ ˆ â % po o h ˆ dsuo I hs sco w m h pomc o h dsuo coducg ous smuos o d smp szs W smu smps o h u pms us I : d II : T 3 ss h m MLEs o h mod pms og wh h spc oo m squd os RMSE d s o smp szs 5 4 d 8 Fo pm d s sm ˆ Th oo-m-squ o RMSE o h MLE ˆ s g ˆ RMSE N Th g s o h MLE ˆ o h pm s g ˆ s ˆ N Fom h sus T 3 w c h s h smp sz css h RMSEs dc owd zo W so os h o h pmc us h ss dcs s h smp sz css T 3 Mo Co Smuo Rsus: M Esms ss d RMSEs I II M RMSE s M RMSE s α N N

21 336 L Fu R Gomc Dsuo β θ Appcos I hs sco w ps mps o us h o h dsuo d s su-mods o d modg W so comp h pms dsuo o h -Wu-gomc WG dsuo dm 3 Th cd d pd o WG dsuo g d F p p p p p d spc wh > > d p Th mmum hood sms MLEs o h pms compud mmzg h oc uco h suou NLMIXED SAS Th smd us o h pms sdd o phss -og-hood ssc 3 3 d

22 O Oud I E S Hug 337 A Iomo Co AIC p L s Iomo Co IC p L d Coss A Iomo Co p p AICC AIC wh s h u o h hood uco ud p h pm sms s h um o osos d s h um o smd pms psd Ts 4 d 5 spc Aso psd us o h h * * goodss-o- sscs W d A dscd Ch d sh 995 Ths sscs c usd o whch dsuo s o h d I g h sm h us o d h h L h cd wh h om o G s ow u h -dmso pm co s Δ s uow W c o h sscs * * W d A s oows: W * A * L L ˆ Compu u G Δˆ wh h Compu u wh s G Δ p s scdg od s h sdd om cd d Compu / s wh d s Ccu W { / } / d A Mod A * A W { og og } * o W W 5/ d A o 75/ 5/ Th sum o squs SS G ˆ ˆ ˆ ˆ ˆ h od om h po pos so g h s Ths sscs usd o comp h dsuos psd Ts 4 d 5 Pos o h d dss h hsogm d po pos Chms 983 o h d g Fgus 3 d 4 Fo h po po w pod G ˆ ˆ ˆ ˆ ˆ gs wh h odd us o h osd d s 8 Tm o u o 49/po sds sd ous sss Th d cosss o mp s om Coo d Ad 8 wh d pos ps h sss-upu o 49/po sds whch sucd

23 338 L Fu R Gomc Dsuo o cos susd pssu h 9% sss u h d so h h comp d s wh h c ms o u s codd Ths u ms hous og g Adws d Hzg 985 d ow 984 I u o mod h R cod 5 Esms o h pms o dsuo d s d su-mods sdd o phss AIC AICC IC 4 * W * A d SS o sss-upu o 49/po sds d g T T 4 Esms o Mods o Fu Tms o K D S Esms Sscs Mod α β θ og L AIC AICC IC W A SS ELFRG LFRG EG E R R α β p WG Th smpoc coc m o h MLEs o h mod pms whch s h s o h osd Fsh omo m I s g :

24 O Oud I E S Hug 339 d h 95% smpoc codc s o h mod pms g d spc Pos o h d dss d h hsogm osd po s pdcd po d mpc su uco o h d g Fgu 3 Fgu 3: Fd Dss d Po Pos gs Th LR s ssc o h hpohss H H : R gs H : d H : LFRG : 3 p-u 56 d 38 p-u 485 W c cocud h h s sgc dc w d R dsuos Cosdg h us o h sscs AIC IC d h us o SS g T 4 w os h h dsuo gs o h d Th us o h goodsso- sscs * W d * A W * shows h h dsuo s h s sumods cp o h sscs o h R d R dsuos Wh h dsuo s compd o h o-sd pm WG dsuo s s h h dsuo s comp dsuo 8 Fgu cu o 373/po Th d s s o h o gu cu o K 373/po h suc o cos pssu h 9% sss u hd d Th comp d wh h c ms o u ws so sudd Adws d Hzg 985 d ow Tod d Fm 984 I u o mod h R cod 3 4 Esms o h pms o dsuo d s

25 34 L Fu R Gomc Dsuo d su-mods sdd o phss AIC AICC IC gu cu o K 373/po d g T 5 * W * A d SS o h T 5 Esms o Mods o Fu Tms o K D S Esms Sscs Mod α β θ og L AIC AICC IC W A SS ELFRG LFRG GLFR LFR E RG R E RG R α β p WG Th smpoc coc m o h MLEs o h mod pms whch s h s o h osd Fsh omo m I s g :

26 O Oud I E S Hug d h 95% smpoc codc s o h mod pms g d spc Pos o h d dss d h hsogm osd po s pdcd po d mpc su uco o h d g Fgu 4 Fgu 4: Fd Dss d Po Pos Th LR s ssc o h hpohss H : R gs H : d H : LFRG gs H : 99 p-u 7 d 79 p-u 486 W c cocud h h sgc dcs w d R dsuos s w s w * * d LFRG dsuos Cosdg h us o h sscs AIC IC W A d h us o SS g T 5 w os h h dsuo gs o h d Wh h dsuo s compd o h o-sd pm WG dsuo s s h h dsuo s

27 34 L Fu R Gomc Dsuo 9 Cocudg Rms A w d gzd u dsuo cd h u gomc dsuo s poposd d sudd Th dsuo hs s w ow dsuos cudg h LFRG LFR EG RG Rgh d po dsuos s spc css Th ds o hs w css o dsuos c pssd s como o LFR ds ucos Th dsuo posssss hzd uco wh ho W so o cosd om pssos o h moms m d md dos dsuo o od sscs d op Mmum hood smo chqu s usd o sm h mod pms F h dsuo s d o d ss o us s ppc d ususs Acowdgms Th uhos woud o h h do d h s o cu dg h pp d o h u comms whch g mpod h pso o hs pp Rcs [] Admds K d Lous S 998 A Lm Dsuo wh Dcsg Fu R Sscs d Po Ls [] A W H 964 R Egg ARINC Pc H Nw Js [3] Adws A D d Hzg A M 985 D: A Coco o Poms om M Fds o h Sud d Rsch Wo Spg Ss Sscs Nw Yo [4] ow R E Tod R H d Fm T 984 A s Ass o Sss- Rupu L o K 49/po Sphc Pssu Vss I D Dwd Ed Pocdgs o h Cd Coc Appd Sscs Mc D Nw Yo [5] o-souz W Mos A L Codo G M Th Wu-Gomc Dsuo Jou o Ssc Compuo d Smuo [6] o-souz W Sos A H S Codo G M Th Gzd Epo Dsuo Jou o Ssc Compuo d Smuo [7] dm H hood J d Towhd M 3 Th Wu-Gomc Dsuo Jou o Ssc Compuo d Smuo [8] dm H Th Epo-Gomc Dsuo Commucos Sscs-Smuo d Compuo

28 O Oud I E S Hug 343 [9] oo C E 93 Em d Ssc G S Fz [] Chms JM Cd WS K d Tu PA 983 Gphc Mhods o D Ass mo CA Wdswoh 983 [] Ch G d sh N 995 A G Pupos Appom Goodss-o- Ts Jou o Qu Tchoog [] Coo K d Ad M 8 A Gzo o h H-Nom Dsuo wh Appco o Lm D Commucos Sscs-Tho d Mhods [3] Codo G M Pscm R R Dméo C G d Og E M M 4 Th Kumm Gzd Gmm Dsuo Jou o D Scc [4] Codo G M S G O Og E M M Th -Wu Gomc Dsuo Sscs DOI: 8/ [5] Codo G M S G O Pscm R R d Og E M M 4 G Pops o h Edd H-Nom Mod Jou o Ssc Compuo d Smuo [6] Codo G M Og E M M d Popoc V 4 Th Gmm L Fu R Dsuo Jou o Ssc Compuo d Smuo [7] Codo G M Og E M M d Lmo A J 5 Th Posso Gzd L Fu R Mod Commucos Sscs-Tho d Mhods [8] Codo G M S G O Og E E M C L C Rgo L C Th -Wu Gomc Dsuo Sscs: A Jou o Thoc d Appd Sscs -8 DOI: 8/ [9] Eug N L C d Fmo F -Nom Dsuo d Is Appcos Commucos Sscs-Tho d Mhods [] Gdsh I S d Rzh I M T o Igs Ss d Poducs sh do S Dgo: Acdmc Pss [] Gup R D d Kudu D 999 Gzd Epo Dsuo Aus d Nw Zd Jou o Sscs [] J A d Mhmoud E -L Fu R Dsuo d s Appcos X:565 [sme]

29 344 L Fu R Gomc Dsuo [3] Kh M S Th Is Wu Dsuo Io Tscos Mhmc Sccs d Compu [4] L C Fmo F Oumod O 7 -Wu Dsuo: Som Pops d Appcos o Csod D Jou o Mod Appd Ssc Mhods [5] Mhmoud E d J A 4 Th Compoud Css o L Fu R-Pow Ss Dsuos: Mod Pops d Appcos X:458 [sco] [6] Msh A W d O I 7 L Dsuos: Sucu o Nopmc Sm pmc d Pmc Fms Nw Yo: Spg [7] Mudho G S Ss D K d Fm M 995 Th Epod Wu Fm: A Rss o h us-moo Fu D Tchomcs [8] Ndh S d Koz S 4 Th Gum Dsuo Mhmc Poms Egg [9] Ndh S d Koz S 6 Th Epo Dsuo R Egg d Ssm S [3] Oud O Muso F d Hug S 5 Th Log Gzd Ld-Wu Dsuo wh Appco Jou o D Scc [3] Oud O d Yg T 5 A Nw Css o Gzd Ld Dsuo wh Appcos Jou o Ssc Compuo d Smuos [3] P M Msso A M Woo J 6 O h Epod Wu Dsuo Ssc [33] Pco A s d Codo G M 3 Th Wu Posso Dsuo Ch Jou o Sscs 4: 3-6 [34] Pscm R R Dméo CG Codo G M Og E M M d Uo M R Th Gzd H-Nom Dsuo Compuo Sscs d D Ass [35] Pí P F Og E M M Codo G M d Pscm R R Th u XII Dsuo wh Appcos o Lm D Compuo Sscs d D Ass [36] Posch F 963 Thoc Epo o Osd Dcsg Fu Rs Tchomcs

30 O Oud I E S Hug 345 [37] Ré A 96 O Msus o Eop d Iomo Pocdgs o h Fouh Smposum o Mhmc Sscs d Po [38] Sh M d Kudu D 9 Gzd L Fu R Dsuo Commucos Sscs-Tho d Mhods [39] Sps J H d Kog L A 7 Fm o Gzd Dsuos o Icom /X:7464S [s ME] [4] S G O Og E M M d Codo G M Th Modd Wu dsuo Lm D Ass Rcd Ju 5 4 ccpd Spm 8 4 odc O Oud Dpm o Mhmc Sccs Gog Souh Us GA 346 USA oud@gogsouhdu Ihm E Dpm o Mhmcs d Sscs A Imm Mohmmd I Sud Ismc Us Sud Shuo Hug Dpm o Mhmcs Us o Houso Houso TX USA zsh54@mhuhdu

31 346 L Fu R Gomc Dsuo