Transmuted Exponentiated Inverse Weibull Distribution with Applications in Medical Sciences

Transcription

1 ol Jol of Mhmcs Ts Tcholoy JMTT Volm 5 Nmb Ocob 7 Tsm Epo vs Wbll Dsbo wh Applcos Mcl Sccs Uzm J # Kws Fm * SP Ahm # Dpm of Sscs Uvsy of Kshm S Absc: Ths mscp coss h sm mol of h Epo vs Wbll sbo A comphsv scpo of h mhmcl pops of h popos mol s v hs cl Th vos pops whch cl lbly lyss moms l fco m mom fco chcsc fco o sscs hv b scss h pp Th mho of mmm llhoo smo hs b s fo sm h pms of h wly popos sbo Th sflss of h wly vlop mol ov s sb mols fo b f s lls boh by h sml s wll s l lf ss Kywos: Tsm Epo vs Wbll Dsbo lbly lyss Moms Ql fco O Sscs AC HQC NTODUCTON Th Wbll sbo ws oc by Wl Wbll Swsh physcs 95 Ths s o of h mos wly s pobbly mol fo lyz lfm lbly of compos Th bsc mol of vs Wbll sbo ws s by Kll l 98 Fh Dpll 99 wo o vs Wbll mol ss h m s complmy Wbll sbo Ths mol s pplcbl lbly lyss mcl sccs mol f moly w o pos o of mchcl compos c Alm Psh s som ol sbol pops of vs Wbll sbo Mhol l 995 s h Epo Wbll sbo ppl h mol fo h lyss bs moo fl Nss Ess v h l cco of h po Wbll mol p K oc h Epo pol fmly of sbos s l o mm Wbll sbos Al-Hss scss h po fmly of sbos l A lzo of v Wbll sbo cll Epo v Wbll sbo ws oc by Flh l by w shp pm hoh poo o h sbo fco A om vbl s s o follow s po v Wbll sbo f s sbo fco s v s: wh F shp pms Th h pobbly sy fco s of h follow fom: f TANSMUTED EPONENTATED NVETED WEBU DSTBUTON h c ps sfc poss hs b m ows h lzo of som wll ow sbos Ths sbos f h pplco my lfm poblms l fc coomcs bomcl sccs Shw Bcly 9 vs h w c smo mp QTM ch fo lz h ff clsscl mols pov mo flbl so of hs mols fo lf s bs f Acco c smo mp ch QTM ppoch om vbl s s o hv sm sbo f s cmlv sbo fco s v by: F F wh s h cf of h bs sbo whch o ffo yls: f F 4 SSN: -57 hp://wwwmolo P 6

2 ol Jol of Mhmcs Ts Tcholoy JMTT Volm 5 Nmb Ocob 7 H ssoc wh cfs f h cospo pfs F spcvly mh b o ; h mol cs o p sbo Th m m of hs pp s o sy mo flbl so of po v Wbll sbo s h smo mp ch cll sm po v Wbll mol Dff pobbly mols hv b scss h sscl l bs o smo mp ppoch Asho Elhwy oc h sm om sbo Af l 4 foml h sm vs ylh sbo ps comphsv cco of s vos scl pops o o hs Ahm l 5 v h scl pops of sm Wbll sbo Now s h os h cmlv sbo fco cf of h om vbl follow Tsm Epo vs Wbll TEW sbo s v s: 5 Also h pobbly sy fco of h Tsm Epo vs Wbll TEW sbo s h os 4 wh pms s v s: 6 wh h shp pms s h sm pm F pss h possbl shps of h sy fco sbo fco of h popos sm po vs Wbll sbo fo vos possbl vls of h pms EATONSHP WTH OTHE DSTBUTONS Th ff possbl hocl sbos whch c b v fom h popos TEW sbo v s follows: Wh h o 6 cs o wo pm Epo vs Wbll sbo wh pobbly sy fco s: Wh h o6 cs o wo pm Tsm vs Wbll sbo wh pobbly sy fco s: Wh h o 6 cs o o pm vs Wbll sbo wh pobbly sy fco s: 4 Wh h o 6 cs o wo pm sm vs ylh sbo wh pobbly sy fco s: 5 Wh h o 6 cs o o pm vs ylh sbo wh pobbly sy fco s: 6 Wh h o 6 cs o o pm Tsm SSN: -57 hp://wwwmolo P 6

3 ol Jol of Mhmcs Ts Tcholoy JMTT Volm 5 Nmb Ocob 7 S vs ylh sbo wh pobbly sy fco s: 7 Wh h o 6 cs o S vs ylh sbo wh pobbly sy fco s: 8 Wh h o 6 cs o wo pm sm vs Epol sbo wh pobbly sy fco s: 9 Wh h o 6 cs o o pm sm S vs Epol sbo wh pobbly sy fco s: Wh h o 6 cs o o pm vs Epol sbo wh pobbly sy fco s: Wh h o 6 cs o S vs Epol sbo wh pobbly sy fco s: 4 EABTY ANAYSS Ths sco vs comphsv cco of h svvl fco hz vs hz of h sm po v Wbll sbo 4 lbly fco: Th lbly fco of h mol s f s h pobbly h m os o fl po o somm Th oh ms v o lbly fco h svvl o svvo fco of h mol Do by h svvo fco c b mhmclly comp s: 7 4 Hz fco: Th hz of h mol c b v s h o of h pobbly sy fco h lbly fco Do by h s lso m s h hz fl o foc of moly s v s: h h 8 4 vs Hz fco: Th vs hz s v s h o of h pobbly sy fco h cmlv sbo fco s lso ssl co fo chcz lfm s v s: 9 Th phcl pso of svvl fco hz vs hz fo ff vls of pms v f 4 5 spcvly SSN: -57 hp://wwwmolo P 6

4 ol Jol of Mhmcs Ts Tcholoy JMTT Volm 5 Nmb Ocob 7 SSN: -57 hp://wwwmolo P 6 5 STATSTCA POPETES OF THE TEW DSTBUTON hs sco c fml sscl pops of h sm po vs Wbll sbo hv b ob: 5 Moms: Th h moms of h sm po v Wbll sbo comp s follows: E S Ths c b flly ob s: P o w h pc vl of sm po vs Wbll sbo s: Fo ff vls of o w c f h oh moms of h popos mol 5 Hmoc m: Th hmoc m of h popos sm mol c b clcl s: E H M f M H 5 Mom Fco: Th mom fco of h popos sbo c b v s follows: E M = E M 54 Chcsc fco: Th chcsc fco of h sm po Wbll sbo s v s follows: E = E 4 6 QUANTE FUNCTON AND MEDAN Ql fco m Do by Q h l fco c b mhmclly comp s:

5 ol Jol of Mhmcs Ts Tcholoy JMTT Volm 5 Nmb Ocob 7 SSN: -57 hp://wwwmolo P 64 Q wh ~ U Sc h l fco fo TEW sbo s v s: 4 wh lo A A 5 P =5 o w h m of TEW sbo: wh lo A A 6 Oc h l fco s comp w c h om mbs fo h sbo scsso s h l fco 7 ENY ENTOPY Th opy of om vbl wh pobbly sy TEW ; s ms of h vo of h cy Th l h opy cs h cy h Th y opy 96 o by fo s ms of vo of cy s f s: f lo 7 f hs TEWD ; h by sbs o 6 7 w hv: lo Fo h covc l m S h hfo m 8 Us c 8 w hv v m 9 Wh v c v m Now lo lo lo v Th β o -opy oc by Hv Chv 967 s o by H c b comp s: f H wh Sppos hs TEWD ; h by sbs 6 w h β opy s follows: H H v 8 ODE STATSTCS f b om smpl of sz fom TEW sbo wh o vls s h h pobbly sy fco of h o ssc s v s:

6 ol Jol of Mhmcs Ts Tcholoy JMTT Volm 5 Nmb Ocob 7 SSN: -57 hp://wwwmolo P 65 Th sy fco of h h o sscs follow sm po vs Wbll sbo s ob by s h o 5 6 o : Th sy fco of h smlls o sscs s ob by p o s: Smlly by sbs o h sy fco of ls o ssc s follows: 9 PAAMETE ESTMATON hs sco h ow pms of h sm po v Wbll sbo sm by h mmm llhoo smo poc Th smpl coss of obsvos s cos Th llhoo fco of h popos sbo s s follows: 4 Th cospo lo llhoo fco of h o 4 s v s : p lo lo lo lo lo 5 Hc o ff h o 5 wh spc o h ow pms of h TEW mol hs o zo yl h follow h oml os spcvly: p lo p lo lo lo 6 p p lo 7 p p lo 8 c b clly s h h os o plc fom s sch h sms of h ow pms ob by solv h oml os smlosly s h Nwo phso lohm APPCATON hs sco boh h sml s wll s l lf ss cos fo h compso of h flbly of h popos sm mol of po vs Wbll sbo ov s ff sb mols o o comp h ff mols c l AC A fomo co HQC H Q fomo co s Th sbo whch povs s lss vls of AC HQC s s bs Th vls of AC HQC c b comp s follows: AC=-lo HQC=lo lo- lo wh s h mb of pms h pobbly mol s h smpl sz -lo s h mmz vl of h lo-llhoo fco of h mol scsso Th lyss of boh h ss s pfom hoh sofw Th MEs of h pms ob wh s os show phss Moov h cospo lo-llhoo vls AC HQC sply Tbl Sml D S: h smlo sy smpl of sz hs b fom h sofw o vl h pfomc of h popos mol ov s sb mols Choos h vls of h pms s 7 smo

7 ol Jol of Mhmcs Ts Tcholoy JMTT Volm 5 Nmb Ocob 7 pm h s s ob by s h vs cf mho s scss sco 8 Th smmy of h lyss s sply h bl s : Tbl : MEs of h mol pms s l ss h sl SEs phss C fo Compso ollhoo Dsbo AC Tbl : MEs of h mol pms s s h sl SEs phss C fo Compso ollhoo N Dsbo AC HQC TEWD EWD TWD WD TD D TSD TED l f D Ss: o o cofm o sml sls w s wo l ss o show h h sm Epo vs Wbll sbo c b b mol h h sb mols D S : Cos s cospo o msso ms mohs of om smpl of 4 bl cc ps v W Th s s v s follows : D S : Ths pss h svvl ms of ps wh bs cc ob fom l hospl whch s wly po som ls l mos l Ths ss s h oly fo llsv pposs Th mcl vlos c o s sofw D D S TEWD EWD TWD WD TD HQC SSN: -57 hp://wwwmolo P 66

8 ol Jol of Mhmcs Ts Tcholoy JMTT Volm 5 Nmb Ocob 7 D s D TSD TED TEWD EWD TWD WD TD D TSD TED CONCUSON hs pp w hv s h w sbo h s sm po vs Wbll sbo lzo of vs Wbll sbo o mpov h flbly of h p mol by ol sm pm Dff mhmcl pops l lbly lyss moms mom fco chcsc fco v Th pms hv b ob s h mmm llhoo ch o o lyz h flbly pplcbly of h popos sbo boh h sml s wll s l lf ss cos D o h lss vls of AC HQC lyss c b cocl h h wly vlop mol hs spoy ov s sb mols EFEENCES [] A Ahm SP Ahm A Ahm Tsm vs ylh Dsbo: A lzo of h vs ylh Dsbo Mhmcl Thoy Mol Vol 4 No 7 pp [] A Flh H Elslloh E M M Mlov Th po v Wbll sbo Appl Mh f Sc Vol6 No pp67-7 [] A y O Mss of fomo Eopy Poc of h Foh B Sym o Mhs Ss Pob 96pp [4] AZ Kll A Kmh UD P lbly lyss of CNC mch ools le Vol No6 pp [5] Dpll Complmy Wbll sbo: ow o s foo Ql l E Vol 9 pp 8 85 [6] E K A Hss O po clss of sbos J S Th Appl Vol 8 pp 4-6 [7] E T J W W Sscl mhos fo svvl lyss Joh Wly Sos Nw Yo USA [8] S Mhol DK Svsv M Fm Th po Wbll fmly: lyss of h bs-moo fl Tchomcs Vol 7 pp [9] J Hv F Chvá Qfco Mho of Clssfco Pocsss Cocp of Scl Eopy Kyb Vol pp [] K Ahm SP Ahm A Ahm Scl pops of sm Wbll sbo JMASM Vo4 No pp [] M Alm Psh o poc sl moms of o sscs fom vs Wbll sbo Jol of Sscs Vol No pp 7 [] MN Nss F H Ess O po Wbll sbo Comm Ss ThMh Vol pp 7-6 [] MWA mos M Coo PD Mho CB Ds Hm Th Zofos Blsh lo losc sbo: pops pplcos J S Th Appl Vol pp 5-44 [4] D p D K Epo pol fmly: lv o mm Wbll sbos Bomcl Jol Vol 4 pp7- [5] S K Asho M A Elhwy Tsm om Dsbo Am J Appl Mh S Vol No 6 pp-7 [6] Shw W Bcly Th Alchmy of Pobbly Dsbos: Byo m-chl Epsos Sw-Koc-Noml Dsbo fom Tsmo Mp s p 9 SSN: -57 hp://wwwmolo P 67