Bayesian Estimation of the Kumaraswamy Inverse Weibull Distribution
|
|
- Stephen Lane
- 5 years ago
- Views:
Transcription
1 Journal of Sascal Theory and Applcaons, Vol 16, No 2 June 217) Bayesan Esmaon of he Kumaraswamy Inverse Webull Dsrbuon Felpe R S de Gusmão Deparmen of Sascs, Federal Unversy of São Carlos, Brazl felpe556@gmalcom Vera L D Tomazella Deparmen of Sascs, Federal Unversy of São Carlos, Brazl vera@ufscarbr Rcardo S Ehlers Deparmen of Appled Mahemacs and Sascs, Unversy of São Paulo, Brazl ehlers@cmcuspbr Receved 25 Sepember 215 Acceped 23 Augus 216 The Kumaraswamy Inverse Webull dsrbuon has he ably o model falure raes ha have unmodal shapes and are que common n relably and bologcal sudes The hree-parameer Kumaraswamy Inverse Webull dsrbuon wh decreasng and unmodal falure rae s nroduced We provde a comprehensve reamen of he mahemacal properes of he Kumaraswany Inverse Webull dsrbuon and derve expressons for s momen generang funcon and he r-h generalzed momen Some properes of he model wh some graphs of densy and hazard funcon are dscussed We also dscuss a Bayesan approach for hs dsrbuon and an applcaon was made for a real daa se Keywords: Kumaraswamy dsrbuon; Webull dsrbuon; Survval; Bayesan analyss 2 Mahemacs Subjec Classfcaon: 22E46, 53C35, 57S2 1 Inroducon In hs paper we propose a new probably dsrbuon o handle he problem of survval daa Movaed by research developed n recen years, we nroduce he Kumaraswany Inverse Webull dsrbuon ha ncludes several well known dsrbuons used n survval analyss Recenly, many auhors have proposed new classes of dsrbuons, whch are modfcaons of dsrbuon funcons whch provde hazard raos conemplang varous shapes We can ce for example he Webull exponenal 6], whch has also he hazard rae funcon wh a unmodal form, see also 13]) 1] proposed a four-parameer dsrbuon denoed generalzed modfed Webull Copyrgh 217, he Auhors Publshed by Alans Press Ths s an open access arcle under he CC BY-NC lcense hp://creavecommonsorg/lcenses/by-nc/4/) 248
2 Journal of Sascal Theory and Applcaons, Vol 16, No 2 June 217) GMW) dsrbuon, 3] nroduced and suded he r-paramerc nverse Webull generalzed dsrbuon ha possesses falure rae wh unmodal, ncreasng and decreasng forms 9] proposed a dsrbuon wh four parameers, called bea generalzed half normal dsrbuon Underexplored n he leraure and rarely used by sascans, he Kumaraswamy dsrbuon 8] has a doman n he real nerval,1) Ths propery urns he Kumaraswamy dsrbuon a naural canddae o combne wh oher dsrbuons o produce a more general one Is cumulave dsrbuon funcon cdf) s gven by, and s probably densy funcon pdf) s gven by, F x;a,b) = 1 1 x a ] b, 11) f x;a,b) = abx a 1 1 x a ] b 1, < x < 1, where a > and b > Ths densy can be unmodal, ncreasng, decreasng or consan Recenly, 2] proposed o use he Kumaraswamy o generalze oher dsrbuons Consderng ha a random varable X has dsrbuon G, hey sugges o apply he Kumarasawamy dsrbuon o Gx) Noe ha, snce < Gx) < 1 for any dsrbuon funcon G, hen evaluang Eq 11) a Gx) we oban, F G x;a,b) = 1 1 Gx) a ] b 12) where F G s he cdf of he generalzed Kumaraswamy-G dsrbuon Based on hese deas, we consder he Inverse Webull Dsrbuon as a canddae for G, usng Eq 12) Then, performng some adjusmens and mahemacal manpulaons, we oban he Kumaraswamy nverse Webull Kum-IW) dsrbuon The res of he paper s organzed as follows In Secon 2, we develop he Kum-IW dsrbuon Secon 3 s devoed o descrbe basc properes of he dsrbuon Inference procedures va maxmum lkelhood and Bayesan approaches are presened n Secon 4 Secon 5 s devoed o analyze a real daa se and n Secon 6 we presen some conclusons of hs work 2 Kumaraswamy nverse Webull dsrbuon Le T a random varable wh nverse Webull dsrbuon Then s cdf can be wren as, α ) ] G) = exp, >, 21) where α >, >, and s pdf s gven by, g) = α +1) exp α ) ] Inserng he G funcon of Eq 21) n Eq 12) follows ha, { α ) ]} b F G ;a,b,α,) = 1 1 exp a 22) We noe ha he parameers a and α n 22) are no denfable and we adop he reparameerzaon c = αa 1/ so ha he Kum-IW cdf s rewren as, { c ) ]} b F G ;b,c,) = 1 1 exp, 23) 249
3 Journal of Sascal Theory and Applcaons, Vol 16, No 2 June 217) where b > and c > are he shape and scale paremeers respecvely Accordngly, he Kum-IW pdf s now gven by, c ) ]{ c ) ]} b 1 f G ;b,c,) = bc +1) exp 1 exp 24) I can be easly seen ha when b = 1 we oban he pdf of he Inverse Webull IW) dsrbuon gven by, α ) ] g) = α +1) exp Fnally, he correspondng survval and hazard funcons are respecvely gven by, { c ) ]} b S G ;b,c,) = 1 exp and h G ;b,c,) = whle he quanle funcon, Qu), of he Kum-IW dsrbuon s gven by, bc +1) exp 1 exp c ) ] c ) ] Qu) = F 1 u;b,c,) = c log1 1 u) 1 b )) 1 21 Some specal classes of he Kum-IW The followng well known and new dsrbuons are specal sub-classes of he Kum-IW dsrbuon Kumaraswamy nverse Raylegh dsrbuon Kum-IR) If = 2, he Kum-IW dsrbuon reduces o he Kumaraswamy nverse Raylegh dsrbuon Kum-IR) Then, wh = 2 he densy funcon of Kum-IW s expressed by: { c ) ]} 2 b F G ;b,c) = 1 1 exp, where b > s he shape parameer, and c > s he scale parameer Hence, he KR dsrbuon has wo parameers, and s pdf s gven by c ) ]{ 2 c ) ]} 2 b 1 f G ;b,c) = 2bc 2 3 exp 1 exp The correspondng survval and hazard funcons are gven respecvely by, { c ) ]} 2 b S G ;b,c) = 1 exp and h G ;b,c) = Inverse Raylegh dsrbuon IR) 2bc 2 3 exp 1 exp ) ] c 2 ) ] 2 c 25
4 Journal of Sascal Theory and Applcaons, Vol 16, No 2 June 217) If = 2 and b = 1, he Kum-IW dsrbuon reduces o he nverse Raylegh dsrbuon Kum-IR) Then, wh = 2 and b = 1 he densy funcon of Kum-IW s expressed by: α ) ] 2 G) = exp, >, where α >, and s pdf s α ) ] 2 g) = 2α 2 3 exp Kumaraswamy nverse Exponenal dsrbuon Kum-IE) If = 1, he Kum-IW dsrbuon reduces o he Kumaraswamy nverse Exponenal dsrbuon Kum-IE) Then, wh = 1 he densy funcon of Kum-IW s expressed by: { c )]} b F G ;b,c) = 1 1 exp, where b > s he shape parameer, and c > s he scale parameer Hence, he KIE dsrbuon has wo parameers, and s pdf s gven by c )]{ c )]} b 1 f G ;b,c) = bc 2 exp 1 exp The correspondng survval and hazard funcons are respecvely { c )]} b S G ;b,c) = 1 exp and h G ;b,c) = bc 2 exp )] c 1 exp )] c Inverse Exponenal dsrbuon IE) If = 1 and b = 1, he Kum-IW dsrbuon reduces o he Inverse Exponenal dsrbuon IE) Then, wh = 1 and b = 1 he densy funcon of Kum-IW s expressed by: )] λ G) = exp, >, where λ > and s pdf s )] λ g) = λ 2 exp 3 Basc Properes In hs secon we descrbe n deal some properes lke expansons, momens, mean devaons, Bonferron and Lorenz curves, order sascs and enropes whch mgh be useful n any applcaon of he dsrbuon 251
5 Journal of Sascal Theory and Applcaons, Vol 16, No 2 June 217) f) b = 2 ; c = 1 ; = 1 b = 3 ; c = 26 ; = 28 b = 4 ; c = 48 ; = 23 b = 5 ; c = 62 ; = 25 f) b = 22 ; c = 8 ; = 1 b = 35 ; c = 23 ; = 28 b = 5 ; c = 4 ; = 23 b = 4 ; c = 72 ; = a) b) Fg 1 Kumaraswamy nverse Webull densy funcons S) b = 2 ; c = 1 ; = 15 b = 3 ; c = 29 ; = 18 b = 4 ; c = 49 ; = 22 b = 5 ; c = 62 ; = 25 S) b = 22 ; c = 1 ; = 15 b = 2 ; c = 4 ; = 18 b = 4 ; c = 47 ; = 25 b = 55 ; c = 7 ; = a) b) Fg 2 Kumaraswamy nverse Webull survval funcons 31 Expansons for he dsrbuon and densy funcons We now gve smple expansons for he cdf of he Kumaraswamy Inverse Webull dsrbuon If x < 1 and ψ > s a non-neger real number, we have 1 x) ψ = = 1) ψ!)x 31) 252
6 Journal of Sascal Theory and Applcaons, Vol 16, No 2 June 217) h) b = 2 ; c = 1 ; = 25 b = 3 ; c = 25 ; = 3 b = 4 ; c = 82 ; = 35 b = 12 ; c = 12 ; = 1 h) b = 2 ; c = 5 ; = 1 b = 35 ; c = 23 ; = 28 b = 5 ; c = 4 ; = 23 b = 4 ; c = 72 ; = a) b) Fg 3 Kumaraswamy nverse Webull hazard funcons If ψ s a posve neger, he seres sops a = ψ Usng expanson n Eq 31) follows ha, f ;b,c,) = bc +1) 1) Γb) c ) ]!)Γb ) exp + 1) 32) and F ;b,c,) = 1 = = 1) Γb + 1)!)Γb + 1 ) exp c ) ] Because he negrals nvolved n he compuaon of momens, Bonferron and Lorenz curves, relably, Shannon and Rény enropes and oher nferenal resuls do no have analycal soluons, hese expansons are necessary 32 A general formula for he momens of he Kum-IW We hardly need o emphasze he need and mporance of he momens n any sascal analyses, especally n appled work Some of he mos mporan feaures and characerscs of a dsrbuon can be suded usng her momens eg endency, dsperson, skewness and kuross) If he random varable T follows he Kum-IW dsrbuon, s k-h momen abou zero s gven by, E k) = k bc +1) exp = bc k c ) ] 1) r Γb) Γb r)r! r + 1) k 1 Γ The momen generang funcon Mz) of T for z < 1 s, M z) = { n k= z k k! bck 1 exp ) 1 k c ) ]] b 1 d 1) r Γb) Γb r)r! r + 1) k 1 Γ 1 k ) } 253
7 Journal of Sascal Theory and Applcaons, Vol 16, No 2 June 217) Hence, for z < 1, he cumulave generang funcon of T s K z) = log n k= k! bck 1)r Γb) Γb r)r! r + 1) k 1 Γ 1 k )] ] z k We noe ha was necessary o use he expansons prevously presened for he resuls of hs secon 33 Mean devaons The amoun of scaerng n a populaon may be measured by all he absolue values of he devaons from he mean or he medan If X s a random varable wh Kum-IW dsrbuon wh mean µ = EX] and medan M, hen he average devaon from he average and he average devaon o he medan are defned respecvely by, δ 1 X) = x µ f x)dx and δ 2 X) = Usng he densy of exended Kum-IW and gven ha, µ x f x)dx = bc 1) r ) 1 Γb) 1 1 γ Γb r)r! 1 + r x M f x)dx 1 where γa,x) s he lower ncomplee Gamma funcon, follows ha 1) δ 1 X) = 2µFµ) 2µ + 2bc r ) 1 Γb) 1 1 γ Γb r)r! 1 + r ), c 1 + r), µ 1 ), c 1 + r) µ and δ 2 X) = 2µFµ) 2µ + 2bc 1) r ) 1 Γb) 1 1 γ Γb r)r! 1 + r 1 ), c 1 + r) M 34 Bonferron and Lorenz curves Bonferron and Lorenz curves are wdely appled no only n economcs o sudy ncome and povery, bu also n oher felds such as relably, demography, nsurance and medcne Le hen µ = EX) e q = F 1 p;θ), where F 1 ) s he nverse funcon of he cumulave funcon of a random varable X Bonferron and Lorenz curves are defned by, Then, usng he expanded densy, q Bp) = 1 q x f x)dx and Lp) = 1 q x f x)dx pµ µ x f x)dx = bc 1) r ) 1 Γb) 1 1 Γ Γb r)r! 1 + r 1 where Γa,x) s he upper ncomplee gamma funcon Therefore, we have, ), c 1 + r), q 254
8 Journal of Sascal Theory and Applcaons, Vol 16, No 2 June 217) he Bonferron curve whch s gven by: Bp) = bc pµ he Lorenz curve whch s gven by: Lp) = bc µ 1) r ) 1 Γb) 1 1 Γ Γb r)r! 1 + r 1) r ) 1 Γb) 1 1 Γ Γb r)r! 1 + r 1 1 ), c 1 + r) ; q ), c 1 + r) q 35 Order sascs and Shannon enropy Le T 1:n T 2:n T n:n be he order sascs obaned from he Kum-IW dsrbuon The random varable T r:n, for r = 1,,n, denoes he r-h order sasc n a sample of sze n The pdf of T r:n wren as, f r:n ) = C r:n F) r 1 1 F)] n r f ), >, where f ) and F) are gven by Eq 24) and 23) and C r:n = n!/r 1)!n r)!] The k-h momen µ k) r:n of he rh order sasc s for k = 1,2,, and 1 r n Hence, µ r:n k) = ETr:n) k = k C r:n F)] r 1 1 F)] n r f )d, µ k) r:n = C r:n 1 and we oban an expresson for he momen gven by, ET k r:n) = C r:n bc j= = j n r 1 j) n 1 d j 1) + j Γbn br + b j + b)! j!γr j)γbn br + b ) + 1) k 1 Γ 1 k ) The Shannon enropy of a random varable T s defned as a measure of he quany of nformaon A ceran message has more quany of nformaon he greaer degree of uncerany and s defned mahemacally by E{ log f )]}, where f ) s he fdp of T In parcular, for a random varable T whch follows he Kum-IW dsrbuon we have, ) E { log f )]} = log bc + b + 1)logc) 1 b + 1)b 1) r Γb) Γb r)r! = 1) r Γb) Γb r)r! 1 γ logr + 1)] + c 1 r + 1) 1 r + 1) 1) r Γb) Γb r)r! r + 1) 1 1 Γ 1 1 ) + 1) +r Γb)Γb + 1)!r!Γb r)γb + 1 j) j + 1)2, j > 1 33) where γ = log j)exp{ j}d j s he approxmae value of he Euler s consan 255
9 Journal of Sascal Theory and Applcaons, Vol 16, No 2 June 217) Rény enropy The enropy of a random varable X wh densy funcon 32) measurng he uncerany of he varaon The Rény enropy s gven by, I r ρ) = 1 { 1 ρ log f x) dx} ρ where ρ > and ρ 1 In nformaon heory, Rény enropy generalzes he Shannon enropy Ths form of enropy s mporan especally n ecology and sascs, where can be used as an ndex of dversy In quanum nformaon, can be used as a measure of enanglemen If X s a random varable and follows he Kum-IW dsrbuon, hen he Rény enropy s gven by I r ρ) = 1 1 ρ log 4 Inference for Censored Daa { ρ 1 bc 1 ρ 1) Γρb ρ + 1)!)Γρb ρ + 1 ) r + ) 1 ρ = 41 Maxmum lkelhood esmaon ) 1+ 1 ρ Γ + ρ 1 ) } Le T be a random varable wh Kum-IW dsrbuon wh parameer vecor θ = b,c,) The daa n survval analyss and relably sudes are generally censored A very smple random censorng mechansm ha s ofen realsc s one n whch each ndvdual s assumed o have a lfeme T and a censorng me C, where T and C are ndependen random varables Suppose he daa se consss of n ndependen observaons = mnt,c ) for = 1,,n The dsrbuon of C does no depend on any of he unknown parameers of T Paramerc nference for such daa are usually based on lkelhood mehods and her asympoc heory The censored log-lkelhood lθ) for he model parameers s ) ) 1 ) ]] c lθ) = r log bc c + 1) F log ) + b 1) log 1 exp + F F b log C 1 exp ) ]] c, 41) where F = 1,r] and C = r + 1,n]; sll, C represens he censored daa and F represens he falure daa The maxmum lkelhood esmae MLE) θ of θ s obaned by solvng he nonlnear lkelhood equaons U b θ) = lθ) b =, U c θ) = lθ) c = and U θ) = lθ) = These equaons canno be solved analycally and sascal sofware can be used o solve he equaons numercally For nerval esmaon of b, c and, and ess of hypoheses on hese parameers, we mus oban he 3 3 observed nformaon marx Jθ) whch s gven by, J bb θ) J bc θ) J b θ) Jθ) = J cb θ) J cc θ) J c θ), J b θ) J c θ) J θ) 256
10 Journal of Sascal Theory and Applcaons, Vol 16, No 2 June 217) Under condons me for parameers obeyng he paramerc space and no consderng he lms of he same, he asympoc dsrbuon of n θ θ) s N 3,Iθ) 1 ), where Iθ) s he expeced nformaon marx Ths asympoc behavor s vald f Iθ) s replaced by J θ), he observed nformaon marx evaluaed a θ The asympoc mulvarae normal dsrbuon N 3,J θ) 1 ) can be used o consruc approxmae confdence nervals and confdence regons for he ndvdual parameers and for he hazard and survval funcons The asympoc normaly s also useful for esng goodness of f of he hree parameers he Kum-IW dsrbuon and for comparng hs dsrbuon wh some of s specal submodels usng one of he wo well-known asympocally equvalen es sascs - namely, he lkelhood rao LR) sasc and he Wald and Rao score sascs 42 Bayesan approach Followng he Bayesan paradgm, we need o complee he model specfcaon by specfyng a pror dsrbuon for he parameers By Bayes Theorem, he poseror dsrbuon s hen proporonal o he produc of he lkelhood funcon by he pror densy Subjevsm s he predomnan phlosophcal foundaon n Bayesan nference, alhough n pracce nonnformave pror denses bul on some formal rule) are frequenly used 7]) Snce he parameers n he Kum-IW dsrbuon are all posve quanes and due o he flexbly generaed by he wo-parameer Gamma dsrbuon hs s adoped as pror dsrbuon So, b Gammam,w), c Gammaa,s) and Gammax,l) Assumng ndependence among he pror denses, he poseror densy s expressed by, ] hθ ) b m+n 1 c a+n 1 x+n 1 exp n =1 1 wb sc l c n =1 { ) ]} c b 1 1 exp 42) Ths jon densy has no known analycal form bu we can provde an approxmae soluon based on he complee condonal dsrbuons of b, c and These are gven by he followng expressons, hb c,,) b m+n 1 exp hc b,,) c a+n 1 exp h b,c,) x+n 1 exp wb c sc c l c n =1 n =1 n =1 ] ] ] n =1 n =1 n = { c 1 exp { c 1 exp { c 1 exp ) ]} b 1, ) ]} b 1, ) ]} b 1 257
11 Journal of Sascal Theory and Applcaons, Vol 16, No 2 June 217) Applcaon In hs secon, we presen esmaon resuls for parameers of he Kum-IW dsrbuon under a Bayesan approach usng a real daa se The commercal producon of cale mea n Brazl, whch usually comes from cale of he Nelore race, seeks o opmze he process ryng o oban a me for he cale o reach he specfc wegh n he perod from he brh unl weans For a daa se wh 69 bulls of he Nelore race, he mes n days) unl he anmals reached he wegh of 16kg relave o he perod from brh unl weans were observed We hen compared he classcal Kaplan-Meyer and Bayesan survval funcons hrough wo graphc mehods We used Markov chan Mone Carlo MCMC) smulaon o esmae he parameers θ = b,c,) T of he Kum-IW dsrbuon Usng he expresson for he log-lkelhood lθ) and Gamma prors for he parameers a roune was wren for he package Wnbugs see 11]) The resuls appear n Table 1 n erms of poseror mean, sandard devaon SD), medan and 95% credble nervals of he hree parameer Fgure 4 show he race plos of smulaed parameer values and esmaes of margnal poseror denses Table 1 Resuls of he Bayesan approach o he Kum-IW dsrbuon Parameer Mean SD 25% Medan 975% b c One of he mehods a our dsposal o check f our model s well adjused o he daa consss of a comparson of he survval funcon of he proposed paramerc model wh he Kaplan-Meer esmaor Anoher mehod consss of skechng he survval funcon of he paramerc model versus he Kaplan-Meer esmae for he survval funcon, f hs curves s close o he sragh lne y = x we wll have a good adjusmen see Fgure 5) 6 Conclusons We worked ou a hree parameer lfeme dsrbuon called he Kumaraswamy Inverse Webull Kum-IW) dsrbuon whch exends Inverse Webull dsrbuon proposed and wdely used n he lfeme leraure The model s much more flexble han he nverse Webull The Kum-IW dsrbuon could have ncreasng, decreasng and unmodal hazard raes We provde a mahemacal overvew of hs dsrbuon ncludng he denses of he order sascs, Rény enropy, Shannon enropy, Bonferron and Lorenz curves and Mean devaons Also, we derve an explc algebrac formula for he r-h momen, expressons for he order sascs, and he maxmum lkelhood esmaon for he censored daa The performance of he model was analzed usng real daa ses where he Kum-IW dsrbuon performng very well and he esmaon was gven by Bayes mehod 258
12 Journal of Sascal Theory and Applcaons, Vol 16, No 2 June 217) Trace of c Trace of bea Trace of b Ieraons Densy of b Densy of c Densy of bea 2 N = Ieraons 2 Ieraons 5 14 Bandwdh = N = Bandwdh = N = Bandwdh = Fg 4 Trace plos of smulaed parameer values of he Kumaraswamy nverse Webull dsrbuon Lnear Bayesan 2 4 S) S) 6 8 Kaplan Meer Bayesan me weeks) S) Kaplan Meer a) b) Fg 5 a) Comparson beween survval funcons generaed by he Bayesan mehod and Kaplan-Meer esmaor descrbed by plong S) versus me b) Comparson beween survval funcons generaed by he Bayesan mehod descrbed by plong S) versus Kaplan-Meer esmae 259
13 Journal of Sascal Theory and Applcaons, Vol 16, No 2 June 217) References 1] Carrasco, J F, Orega, E M M, and Cordero, G M 28) A generalzed modfed Webull dsrbuon for lfeme modelng Compuaonal Sascs & Daa Analyss, 532): ] Cordero, G M and de Casro, M 211) A new famly of generalzed dsrbuons Journal of Sascal Compuaon and Smulaon, 817): ] Gusmão, F R S, Orega, E M M, and Cordero, G M 211) The generalzed nverse Webull dsrbuon Sascal Papers, 52: ] Gusmão, F R S, Orega, E M M, and Cordero, G M 212) Reply o he Leer o he Edor of M C Jones Sascal Papers, 53: ] Gupa, RD, Kundu, D 1999) Generalzed exponenal dsrbuon Ausralan and New Zealand Journal of Sascs 412): ] Mudholkar, G S, Srvasava, D K, and Fremer, M 1995) The exponenaed Webull famly: A reanalyss of he bus-moor-falure daa Technomercs, 374): ] Kass, RE, Wasserman, L 1996) The Selecon of Pror Dsrbuons by Formal Rules Journal of he Amercan Sascal Assocaon, 91: ] Kumaraswamy, P 198) A generalzed probably densy funcon for double-bounded random processes Journal of Hydrology, 461?2): ] Pescm, R R, Deméro, C G B, Cordero, G M, Orega, E M M, and Urbano, M R 21) The bea generalzed half-normal dsrbuon Compuaonal Sascs & Daa Analyss, 544): ] Pollard, W E 1986) Bayesan sascs for evaluaon research An Inroducon Sage Publcaons New Delh, 241p 11] Spegelhaler, D, Thomas, A, Bes, N, Lunn, D 27) Wnbugs user manual, Verson ] R Core Team 212) R: A Language and Envronmen for Sascal Compung R Foundaon for Sascal Compung, Venna, Ausra ISBN: ] Xe, M and La, C D 1996) Relably analyss usng an addve Webull model wh bahub-shaped falure rae funcon Relably Engneerng & Sysem Safey, 521):
V.Abramov - FURTHER ANALYSIS OF CONFIDENCE INTERVALS FOR LARGE CLIENT/SERVER COMPUTER NETWORKS
R&RATA # Vol.) 8, March FURTHER AALYSIS OF COFIDECE ITERVALS FOR LARGE CLIET/SERVER COMPUTER ETWORKS Vyacheslav Abramov School of Mahemacal Scences, Monash Unversy, Buldng 8, Level 4, Clayon Campus, Wellngon
More information( t) Outline of program: BGC1: Survival and event history analysis Oslo, March-May Recapitulation. The additive regression model
BGC1: Survval and even hsory analyss Oslo, March-May 212 Monday May 7h and Tuesday May 8h The addve regresson model Ørnulf Borgan Deparmen of Mahemacs Unversy of Oslo Oulne of program: Recapulaon Counng
More informationSurvival Analysis and Reliability. A Note on the Mean Residual Life Function of a Parallel System
Communcaons n Sascs Theory and Mehods, 34: 475 484, 2005 Copyrgh Taylor & Francs, Inc. ISSN: 0361-0926 prn/1532-415x onlne DOI: 10.1081/STA-200047430 Survval Analyss and Relably A Noe on he Mean Resdual
More informationApproximate Analytic Solution of (2+1) - Dimensional Zakharov-Kuznetsov(Zk) Equations Using Homotopy
Arcle Inernaonal Journal of Modern Mahemacal Scences, 4, (): - Inernaonal Journal of Modern Mahemacal Scences Journal homepage: www.modernscenfcpress.com/journals/jmms.aspx ISSN: 66-86X Florda, USA Approxmae
More informationGENERATING CERTAIN QUINTIC IRREDUCIBLE POLYNOMIALS OVER FINITE FIELDS. Youngwoo Ahn and Kitae Kim
Korean J. Mah. 19 (2011), No. 3, pp. 263 272 GENERATING CERTAIN QUINTIC IRREDUCIBLE POLYNOMIALS OVER FINITE FIELDS Youngwoo Ahn and Kae Km Absrac. In he paper [1], an explc correspondence beween ceran
More information5th International Conference on Advanced Design and Manufacturing Engineering (ICADME 2015)
5h Inernaonal onference on Advanced Desgn and Manufacurng Engneerng (IADME 5 The Falure Rae Expermenal Sudy of Specal N Machne Tool hunshan He, a, *, La Pan,b and Bng Hu 3,c,,3 ollege of Mechancal and
More informationJohn Geweke a and Gianni Amisano b a Departments of Economics and Statistics, University of Iowa, USA b European Central Bank, Frankfurt, Germany
Herarchcal Markov Normal Mxure models wh Applcaons o Fnancal Asse Reurns Appendx: Proofs of Theorems and Condonal Poseror Dsrbuons John Geweke a and Gann Amsano b a Deparmens of Economcs and Sascs, Unversy
More informationDepartment of Economics University of Toronto
Deparmen of Economcs Unversy of Torono ECO408F M.A. Economercs Lecure Noes on Heeroskedascy Heeroskedascy o Ths lecure nvolves lookng a modfcaons we need o make o deal wh he regresson model when some of
More informationTools for Analysis of Accelerated Life and Degradation Test Data
Acceleraed Sress Tesng and Relably Tools for Analyss of Acceleraed Lfe and Degradaon Tes Daa Presened by: Reuel Smh Unversy of Maryland College Park smhrc@umd.edu Sepember-5-6 Sepember 28-30 206, Pensacola
More informationNew M-Estimator Objective Function. in Simultaneous Equations Model. (A Comparative Study)
Inernaonal Mahemacal Forum, Vol. 8, 3, no., 7 - HIKARI Ld, www.m-hkar.com hp://dx.do.org/.988/mf.3.3488 New M-Esmaor Objecve Funcon n Smulaneous Equaons Model (A Comparave Sudy) Ahmed H. Youssef Professor
More informationFall 2010 Graduate Course on Dynamic Learning
Fall 200 Graduae Course on Dynamc Learnng Chaper 4: Parcle Flers Sepember 27, 200 Byoung-Tak Zhang School of Compuer Scence and Engneerng & Cognve Scence and Bran Scence Programs Seoul aonal Unversy hp://b.snu.ac.kr/~bzhang/
More informationThe Log-Kumaraswamy Generalized Gamma Regression Model with Application to Chemical Dependency Data
Journal of Daa Scence 112013), 781-818 The Log-Kumaraswamy Generalzed Gamma Regresson Model wh Applcaon o Chemcal Dependency Daa Marcelno A. R. Pascoa 1, Clauda M. M. de Pava 2, Gauss M. Cordero 3 and
More informationIn the complete model, these slopes are ANALYSIS OF VARIANCE FOR THE COMPLETE TWO-WAY MODEL. (! i+1 -! i ) + [(!") i+1,q - [(!
ANALYSIS OF VARIANCE FOR THE COMPLETE TWO-WAY MODEL The frs hng o es n wo-way ANOVA: Is here neracon? "No neracon" means: The man effecs model would f. Ths n urn means: In he neracon plo (wh A on he horzonal
More information( ) () we define the interaction representation by the unitary transformation () = ()
Hgher Order Perurbaon Theory Mchael Fowler 3/7/6 The neracon Represenaon Recall ha n he frs par of hs course sequence, we dscussed he chrödnger and Hesenberg represenaons of quanum mechancs here n he chrödnger
More informationAppendix H: Rarefaction and extrapolation of Hill numbers for incidence data
Anne Chao Ncholas J Goell C seh lzabeh L ander K Ma Rober K Colwell and Aaron M llson 03 Rarefacon and erapolaon wh ll numbers: a framewor for samplng and esmaon n speces dversy sudes cology Monographs
More informationPerformance Analysis for a Network having Standby Redundant Unit with Waiting in Repair
TECHNI Inernaonal Journal of Compung Scence Communcaon Technologes VOL.5 NO. July 22 (ISSN 974-3375 erformance nalyss for a Nework havng Sby edundan Un wh ang n epar Jendra Sngh 2 abns orwal 2 Deparmen
More informationRobustness Experiments with Two Variance Components
Naonal Insue of Sandards and Technology (NIST) Informaon Technology Laboraory (ITL) Sascal Engneerng Dvson (SED) Robusness Expermens wh Two Varance Componens by Ana Ivelsse Avlés avles@ns.gov Conference
More informationExistence and Uniqueness Results for Random Impulsive Integro-Differential Equation
Global Journal of Pure and Appled Mahemacs. ISSN 973-768 Volume 4, Number 6 (8), pp. 89-87 Research Inda Publcaons hp://www.rpublcaon.com Exsence and Unqueness Resuls for Random Impulsve Inegro-Dfferenal
More informationSOME NOISELESS CODING THEOREMS OF INACCURACY MEASURE OF ORDER α AND TYPE β
SARAJEVO JOURNAL OF MATHEMATICS Vol.3 (15) (2007), 137 143 SOME NOISELESS CODING THEOREMS OF INACCURACY MEASURE OF ORDER α AND TYPE β M. A. K. BAIG AND RAYEES AHMAD DAR Absrac. In hs paper, we propose
More informationTime-interval analysis of β decay. V. Horvat and J. C. Hardy
Tme-nerval analyss of β decay V. Horva and J. C. Hardy Work on he even analyss of β decay [1] connued and resuled n he developmen of a novel mehod of bea-decay me-nerval analyss ha produces hghly accurae
More informationOn One Analytic Method of. Constructing Program Controls
Appled Mahemacal Scences, Vol. 9, 05, no. 8, 409-407 HIKARI Ld, www.m-hkar.com hp://dx.do.org/0.988/ams.05.54349 On One Analyc Mehod of Consrucng Program Conrols A. N. Kvko, S. V. Chsyakov and Yu. E. Balyna
More informationCS434a/541a: Pattern Recognition Prof. Olga Veksler. Lecture 4
CS434a/54a: Paern Recognon Prof. Olga Veksler Lecure 4 Oulne Normal Random Varable Properes Dscrmnan funcons Why Normal Random Varables? Analycally racable Works well when observaon comes form a corruped
More informationRELATIONSHIP BETWEEN VOLATILITY AND TRADING VOLUME: THE CASE OF HSI STOCK RETURNS DATA
RELATIONSHIP BETWEEN VOLATILITY AND TRADING VOLUME: THE CASE OF HSI STOCK RETURNS DATA Mchaela Chocholaá Unversy of Economcs Braslava, Slovaka Inroducon (1) one of he characersc feaures of sock reurns
More informatione-journal Reliability: Theory& Applications No 2 (Vol.2) Vyacheslav Abramov
June 7 e-ournal Relably: Theory& Applcaons No (Vol. CONFIDENCE INTERVALS ASSOCIATED WITH PERFORMANCE ANALYSIS OF SYMMETRIC LARGE CLOSED CLIENT/SERVER COMPUTER NETWORKS Absrac Vyacheslav Abramov School
More informationCubic Bezier Homotopy Function for Solving Exponential Equations
Penerb Journal of Advanced Research n Compung and Applcaons ISSN (onlne: 46-97 Vol. 4, No.. Pages -8, 6 omoopy Funcon for Solvng Eponenal Equaons S. S. Raml *,,. Mohamad Nor,a, N. S. Saharzan,b and M.
More informationOrdinary Differential Equations in Neuroscience with Matlab examples. Aim 1- Gain understanding of how to set up and solve ODE s
Ordnary Dfferenal Equaons n Neuroscence wh Malab eamples. Am - Gan undersandng of how o se up and solve ODE s Am Undersand how o se up an solve a smple eample of he Hebb rule n D Our goal a end of class
More informationBayesian Inference of the GARCH model with Rational Errors
0 Inernaonal Conference on Economcs, Busness and Markeng Managemen IPEDR vol.9 (0) (0) IACSIT Press, Sngapore Bayesan Inference of he GARCH model wh Raonal Errors Tesuya Takash + and Tng Tng Chen Hroshma
More informationDensity Matrix Description of NMR BCMB/CHEM 8190
Densy Marx Descrpon of NMR BCMBCHEM 89 Operaors n Marx Noaon Alernae approach o second order specra: ask abou x magnezaon nsead of energes and ranson probables. If we say wh one bass se, properes vary
More information( ) [ ] MAP Decision Rule
Announcemens Bayes Decson Theory wh Normal Dsrbuons HW0 due oday HW o be assgned soon Proec descrpon posed Bomercs CSE 90 Lecure 4 CSE90, Sprng 04 CSE90, Sprng 04 Key Probables 4 ω class label X feaure
More informationComparison of Differences between Power Means 1
In. Journal of Mah. Analyss, Vol. 7, 203, no., 5-55 Comparson of Dfferences beween Power Means Chang-An Tan, Guanghua Sh and Fe Zuo College of Mahemacs and Informaon Scence Henan Normal Unversy, 453007,
More informationHEAT CONDUCTION PROBLEM IN A TWO-LAYERED HOLLOW CYLINDER BY USING THE GREEN S FUNCTION METHOD
Journal of Appled Mahemacs and Compuaonal Mechancs 3, (), 45-5 HEAT CONDUCTION PROBLEM IN A TWO-LAYERED HOLLOW CYLINDER BY USING THE GREEN S FUNCTION METHOD Sansław Kukla, Urszula Sedlecka Insue of Mahemacs,
More informationComparison of Weibayes and Markov Chain Monte Carlo methods for the reliability analysis of turbine nozzle components with right censored data only
Comparson of Webayes and Markov Chan Mone Carlo mehods for he relably analyss of urbne nozzle componens wh rgh censored daa only Francesco Cannarle,2, Mchele Compare,2, Sara Maafrr 3, Fauso Carlevaro 3,
More informationFI 3103 Quantum Physics
/9/4 FI 33 Quanum Physcs Aleander A. Iskandar Physcs of Magnesm and Phooncs Research Grou Insu Teknolog Bandung Basc Conces n Quanum Physcs Probably and Eecaon Value Hesenberg Uncerany Prncle Wave Funcon
More informationP R = P 0. The system is shown on the next figure:
TPG460 Reservor Smulaon 08 page of INTRODUCTION TO RESERVOIR SIMULATION Analycal and numercal soluons of smple one-dmensonal, one-phase flow equaons As an nroducon o reservor smulaon, we wll revew he smples
More informationABSTRACT KEYWORDS. Bonus-malus systems, frequency component, severity component. 1. INTRODUCTION
EERAIED BU-MAU YTEM ITH A FREQUECY AD A EVERITY CMET A IDIVIDUA BAI I AUTMBIE IURACE* BY RAHIM MAHMUDVAD AD HEI HAAI ABTRACT Frangos and Vronos (2001) proposed an opmal bonus-malus sysems wh a frequency
More informationStandard Error of Technical Cost Incorporating Parameter Uncertainty
Sandard rror of echncal Cos Incorporang Parameer Uncerany Chrsopher Moron Insurance Ausrala Group Presened o he Acuares Insue General Insurance Semnar 3 ovember 0 Sydney hs paper has been prepared for
More informationDensity Matrix Description of NMR BCMB/CHEM 8190
Densy Marx Descrpon of NMR BCMBCHEM 89 Operaors n Marx Noaon If we say wh one bass se, properes vary only because of changes n he coeffcens weghng each bass se funcon x = h< Ix > - hs s how we calculae
More informationOn computing differential transform of nonlinear non-autonomous functions and its applications
On compung dfferenal ransform of nonlnear non-auonomous funcons and s applcaons Essam. R. El-Zahar, and Abdelhalm Ebad Deparmen of Mahemacs, Faculy of Scences and Humanes, Prnce Saam Bn Abdulazz Unversy,
More informationM. Y. Adamu Mathematical Sciences Programme, AbubakarTafawaBalewa University, Bauchi, Nigeria
IOSR Journal of Mahemacs (IOSR-JM e-issn: 78-578, p-issn: 9-765X. Volume 0, Issue 4 Ver. IV (Jul-Aug. 04, PP 40-44 Mulple SolonSoluons for a (+-dmensonalhroa-sasuma shallow waer wave equaon UsngPanlevé-Bӓclund
More informationF-Tests and Analysis of Variance (ANOVA) in the Simple Linear Regression Model. 1. Introduction
ECOOMICS 35* -- OTE 9 ECO 35* -- OTE 9 F-Tess and Analyss of Varance (AOVA n he Smple Lnear Regresson Model Inroducon The smple lnear regresson model s gven by he followng populaon regresson equaon, or
More informationCHAPTER 10: LINEAR DISCRIMINATION
CHAPER : LINEAR DISCRIMINAION Dscrmnan-based Classfcaon 3 In classfcaon h K classes (C,C,, C k ) We defned dscrmnan funcon g j (), j=,,,k hen gven an es eample, e chose (predced) s class label as C f g
More informationNotes on the stability of dynamic systems and the use of Eigen Values.
Noes on he sabl of dnamc ssems and he use of Egen Values. Source: Macro II course noes, Dr. Davd Bessler s Tme Seres course noes, zarads (999) Ineremporal Macroeconomcs chaper 4 & Techncal ppend, and Hamlon
More informationRelative controllability of nonlinear systems with delays in control
Relave conrollably o nonlnear sysems wh delays n conrol Jerzy Klamka Insue o Conrol Engneerng, Slesan Techncal Unversy, 44- Glwce, Poland. phone/ax : 48 32 37227, {jklamka}@a.polsl.glwce.pl Keywor: Conrollably.
More informationA NEW TECHNIQUE FOR SOLVING THE 1-D BURGERS EQUATION
S19 A NEW TECHNIQUE FOR SOLVING THE 1-D BURGERS EQUATION by Xaojun YANG a,b, Yugu YANG a*, Carlo CATTANI c, and Mngzheng ZHU b a Sae Key Laboraory for Geomechancs and Deep Underground Engneerng, Chna Unversy
More informationChapter Lagrangian Interpolation
Chaper 5.4 agrangan Inerpolaon Afer readng hs chaper you should be able o:. dere agrangan mehod of nerpolaon. sole problems usng agrangan mehod of nerpolaon and. use agrangan nerpolans o fnd deraes and
More informationMath 128b Project. Jude Yuen
Mah 8b Proec Jude Yuen . Inroducon Le { Z } be a sequence of observed ndependen vecor varables. If he elemens of Z have a on normal dsrbuon hen { Z } has a mean vecor Z and a varancecovarance marx z. Geomercally
More informationVariants of Pegasos. December 11, 2009
Inroducon Varans of Pegasos SooWoong Ryu bshboy@sanford.edu December, 009 Youngsoo Cho yc344@sanford.edu Developng a new SVM algorhm s ongong research opc. Among many exng SVM algorhms, we wll focus on
More informationInverse Joint Moments of Multivariate. Random Variables
In J Conem Mah Scences Vol 7 0 no 46 45-5 Inverse Jon Momens of Mulvarae Rom Varables M A Hussan Dearmen of Mahemacal Sascs Insue of Sascal Sudes Research ISSR Caro Unversy Egy Curren address: Kng Saud
More informationSolution in semi infinite diffusion couples (error function analysis)
Soluon n sem nfne dffuson couples (error funcon analyss) Le us consder now he sem nfne dffuson couple of wo blocks wh concenraon of and I means ha, n a A- bnary sysem, s bondng beween wo blocks made of
More informationLet s treat the problem of the response of a system to an applied external force. Again,
Page 33 QUANTUM LNEAR RESPONSE FUNCTON Le s rea he problem of he response of a sysem o an appled exernal force. Agan, H() H f () A H + V () Exernal agen acng on nernal varable Hamlonan for equlbrum sysem
More informationLinear Response Theory: The connection between QFT and experiments
Phys540.nb 39 3 Lnear Response Theory: The connecon beween QFT and expermens 3.1. Basc conceps and deas Q: ow do we measure he conducvy of a meal? A: we frs nroduce a weak elecrc feld E, and hen measure
More informationImplementation of Quantized State Systems in MATLAB/Simulink
SNE T ECHNICAL N OTE Implemenaon of Quanzed Sae Sysems n MATLAB/Smulnk Parck Grabher, Mahas Rößler 2*, Bernhard Henzl 3 Ins. of Analyss and Scenfc Compung, Venna Unversy of Technology, Wedner Haupsraße
More informationAn Extended Gamma Function Involving a Generalized Hypergeometric Function
World Appled cences Journal 8 (): 79-799, IN 88-495 IDOI Publcaons, DOI:.589/dos.wasj..8..366 An Exended Gamma Funcon Involvng a Generalzed Hypergeomerc Funcon Abdus aboor Deparmen of Mahemacs, Koha Unversy
More informationChapter 6: AC Circuits
Chaper 6: AC Crcus Chaper 6: Oulne Phasors and he AC Seady Sae AC Crcus A sable, lnear crcu operang n he seady sae wh snusodal excaon (.e., snusodal seady sae. Complee response forced response naural response.
More informationJanuary Examinations 2012
Page of 5 EC79 January Examnaons No. of Pages: 5 No. of Quesons: 8 Subjec ECONOMICS (POSTGRADUATE) Tle of Paper EC79 QUANTITATIVE METHODS FOR BUSINESS AND FINANCE Tme Allowed Two Hours ( hours) Insrucons
More informationDEEP UNFOLDING FOR MULTICHANNEL SOURCE SEPARATION SUPPLEMENTARY MATERIAL
DEEP UNFOLDING FOR MULTICHANNEL SOURCE SEPARATION SUPPLEMENTARY MATERIAL Sco Wsdom, John Hershey 2, Jonahan Le Roux 2, and Shnj Waanabe 2 Deparmen o Elecrcal Engneerng, Unversy o Washngon, Seale, WA, USA
More informationFTCS Solution to the Heat Equation
FTCS Soluon o he Hea Equaon ME 448/548 Noes Gerald Reckenwald Porland Sae Unversy Deparmen of Mechancal Engneerng gerry@pdxedu ME 448/548: FTCS Soluon o he Hea Equaon Overvew Use he forward fne d erence
More informationBayes rule for a classification problem INF Discriminant functions for the normal density. Euclidean distance. Mahalanobis distance
INF 43 3.. Repeon Anne Solberg (anne@f.uo.no Bayes rule for a classfcaon problem Suppose we have J, =,...J classes. s he class label for a pxel, and x s he observed feaure vecor. We can use Bayes rule
More information[Link to MIT-Lab 6P.1 goes here.] After completing the lab, fill in the following blanks: Numerical. Simulation s Calculations
Chaper 6: Ordnary Leas Squares Esmaon Procedure he Properes Chaper 6 Oulne Cln s Assgnmen: Assess he Effec of Sudyng on Quz Scores Revew o Regresson Model o Ordnary Leas Squares () Esmaon Procedure o he
More informationGraduate Macroeconomics 2 Problem set 5. - Solutions
Graduae Macroeconomcs 2 Problem se. - Soluons Queson 1 To answer hs queson we need he frms frs order condons and he equaon ha deermnes he number of frms n equlbrum. The frms frs order condons are: F K
More informationLecture 2 M/G/1 queues. M/G/1-queue
Lecure M/G/ queues M/G/-queue Posson arrval process Arbrary servce me dsrbuon Sngle server To deermne he sae of he sysem a me, we mus now The number of cusomers n he sysems N() Tme ha he cusomer currenly
More informationOptimal environmental charges under imperfect compliance
ISSN 1 746-7233, England, UK World Journal of Modellng and Smulaon Vol. 4 (28) No. 2, pp. 131-139 Opmal envronmenal charges under mperfec complance Dajn Lu 1, Ya Wang 2 Tazhou Insue of Scence and Technology,
More informationTHE PREDICTION OF COMPETITIVE ENVIRONMENT IN BUSINESS
THE PREICTION OF COMPETITIVE ENVIRONMENT IN BUSINESS INTROUCTION The wo dmensonal paral dfferenal equaons of second order can be used for he smulaon of compeve envronmen n busness The arcle presens he
More informationAnalysis And Evaluation of Econometric Time Series Models: Dynamic Transfer Function Approach
1 Appeared n Proceedng of he 62 h Annual Sesson of he SLAAS (2006) pp 96. Analyss And Evaluaon of Economerc Tme Seres Models: Dynamc Transfer Funcon Approach T.M.J.A.COORAY Deparmen of Mahemacs Unversy
More informationCS286.2 Lecture 14: Quantum de Finetti Theorems II
CS286.2 Lecure 14: Quanum de Fne Theorems II Scrbe: Mara Okounkova 1 Saemen of he heorem Recall he las saemen of he quanum de Fne heorem from he prevous lecure. Theorem 1 Quanum de Fne). Le ρ Dens C 2
More information[ ] 2. [ ]3 + (Δx i + Δx i 1 ) / 2. Δx i-1 Δx i Δx i+1. TPG4160 Reservoir Simulation 2018 Lecture note 3. page 1 of 5
TPG460 Reservor Smulaon 08 page of 5 DISCRETIZATIO OF THE FOW EQUATIOS As we already have seen, fne dfference appromaons of he paral dervaves appearng n he flow equaons may be obaned from Taylor seres
More informationOnline Appendix for. Strategic safety stocks in supply chains with evolving forecasts
Onlne Appendx for Sraegc safey socs n supply chans wh evolvng forecass Tor Schoenmeyr Sephen C. Graves Opsolar, Inc. 332 Hunwood Avenue Hayward, CA 94544 A. P. Sloan School of Managemen Massachuses Insue
More informationSampling Procedure of the Sum of two Binary Markov Process Realizations
Samplng Procedure of he Sum of wo Bnary Markov Process Realzaons YURY GORITSKIY Dep. of Mahemacal Modelng of Moscow Power Insue (Techncal Unversy), Moscow, RUSSIA, E-mal: gorsky@yandex.ru VLADIMIR KAZAKOV
More informationMethod of upper lower solutions for nonlinear system of fractional differential equations and applications
Malaya Journal of Maemak, Vol. 6, No. 3, 467-472, 218 hps://do.org/1.26637/mjm63/1 Mehod of upper lower soluons for nonlnear sysem of fraconal dfferenal equaons and applcaons D.B. Dhagude1 *, N.B. Jadhav2
More informationCHAPTER 5: MULTIVARIATE METHODS
CHAPER 5: MULIVARIAE MEHODS Mulvarae Daa 3 Mulple measuremens (sensors) npus/feaures/arbues: -varae N nsances/observaons/eamples Each row s an eample Each column represens a feaure X a b correspons o he
More informationRobustness of DEWMA versus EWMA Control Charts to Non-Normal Processes
Journal of Modern Appled Sascal Mehods Volume Issue Arcle 8 5--3 Robusness of D versus Conrol Chars o Non- Processes Saad Saeed Alkahan Performance Measuremen Cener of Governmen Agences, Insue of Publc
More informationAn introduction to Support Vector Machine
An nroducon o Suppor Vecor Machne 報告者 : 黃立德 References: Smon Haykn, "Neural Neworks: a comprehensve foundaon, second edon, 999, Chaper 2,6 Nello Chrsann, John Shawe-Tayer, An Inroducon o Suppor Vecor Machnes,
More informationTight results for Next Fit and Worst Fit with resource augmentation
Tgh resuls for Nex F and Wors F wh resource augmenaon Joan Boyar Leah Epsen Asaf Levn Asrac I s well known ha he wo smple algorhms for he classc n packng prolem, NF and WF oh have an approxmaon rao of
More informationNormal Random Variable and its discriminant functions
Noral Rando Varable and s dscrnan funcons Oulne Noral Rando Varable Properes Dscrnan funcons Why Noral Rando Varables? Analycally racable Works well when observaon coes for a corruped snle prooype 3 The
More informationTSS = SST + SSE An orthogonal partition of the total SS
ANOVA: Topc 4. Orhogonal conrass [ST&D p. 183] H 0 : µ 1 = µ =... = µ H 1 : The mean of a leas one reamen group s dfferen To es hs hypohess, a basc ANOVA allocaes he varaon among reamen means (SST) equally
More informationEcon107 Applied Econometrics Topic 5: Specification: Choosing Independent Variables (Studenmund, Chapter 6)
Econ7 Appled Economercs Topc 5: Specfcaon: Choosng Independen Varables (Sudenmund, Chaper 6 Specfcaon errors ha we wll deal wh: wrong ndependen varable; wrong funconal form. Ths lecure deals wh wrong ndependen
More informationAttribute Reduction Algorithm Based on Discernibility Matrix with Algebraic Method GAO Jing1,a, Ma Hui1, Han Zhidong2,b
Inernaonal Indusral Informacs and Compuer Engneerng Conference (IIICEC 05) Arbue educon Algorhm Based on Dscernbly Marx wh Algebrac Mehod GAO Jng,a, Ma Hu, Han Zhdong,b Informaon School, Capal Unversy
More informationRobust and Accurate Cancer Classification with Gene Expression Profiling
Robus and Accurae Cancer Classfcaon wh Gene Expresson Proflng (Compuaonal ysems Bology, 2005) Auhor: Hafeng L, Keshu Zhang, ao Jang Oulne Background LDA (lnear dscrmnan analyss) and small sample sze problem
More information@FMI c Kyung Moon Sa Co.
Annals of Fuzzy Mahemacs and Informacs Volume 8, No. 2, (Augus 2014), pp. 245 257 ISSN: 2093 9310 (prn verson) ISSN: 2287 6235 (elecronc verson) hp://www.afm.or.kr @FMI c Kyung Moon Sa Co. hp://www.kyungmoon.com
More informationCH.3. COMPATIBILITY EQUATIONS. Continuum Mechanics Course (MMC) - ETSECCPB - UPC
CH.3. COMPATIBILITY EQUATIONS Connuum Mechancs Course (MMC) - ETSECCPB - UPC Overvew Compably Condons Compably Equaons of a Poenal Vecor Feld Compably Condons for Infnesmal Srans Inegraon of he Infnesmal
More informationMixture Model. A dissertation presented to. the faculty of. In partial fulfillment. of the requirements for the degree. Doctor of Philosophy.
Sem-paramerc Bayesan Inference of Acceleraed Lfe Tes Usng Drchle Process Mure Model A dsseraon presened o he faculy of he Russ College of Engneerng and Technology of Oho Unversy In paral fulfllmen of he
More informationThis document is downloaded from DR-NTU, Nanyang Technological University Library, Singapore.
Ths documen s downloaded from DR-NTU, Nanyang Technologcal Unversy Lbrary, Sngapore. Tle A smplfed verb machng algorhm for word paron n vsual speech processng( Acceped verson ) Auhor(s) Foo, Say We; Yong,
More informationComb Filters. Comb Filters
The smple flers dscussed so far are characered eher by a sngle passband and/or a sngle sopband There are applcaons where flers wh mulple passbands and sopbands are requred Thecomb fler s an example of
More informationESTIMATIONS OF RESIDUAL LIFETIME OF ALTERNATING PROCESS. COMMON APPROACH TO ESTIMATIONS OF RESIDUAL LIFETIME
Srucural relably. The heory and pracce Chumakov I.A., Chepurko V.A., Anonov A.V. ESTIMATIONS OF RESIDUAL LIFETIME OF ALTERNATING PROCESS. COMMON APPROACH TO ESTIMATIONS OF RESIDUAL LIFETIME The paper descrbes
More informationJournal of Theoretical and Applied Information Technology.
Journal of heorecal and Appled Informaon echnology 5-9 JAI. All rghs reserved. www.ja.org NEW APPROXIMAION FOR ANDOFF RAE AND NUMBER OF ANDOFF PROBABILIY IN CELLULAR SYSEMS UNDER GENERAL DISRIBUIONS OF
More informationImprovement in Estimating Population Mean using Two Auxiliary Variables in Two-Phase Sampling
Rajesh ngh Deparmen of ascs, Banaras Hndu Unvers(U.P.), Inda Pankaj Chauhan, Nrmala awan chool of ascs, DAVV, Indore (M.P.), Inda Florenn marandache Deparmen of Mahemacs, Unvers of New Meco, Gallup, UA
More informationGenetic Algorithm in Parameter Estimation of Nonlinear Dynamic Systems
Genec Algorhm n Parameer Esmaon of Nonlnear Dynamc Sysems E. Paeraks manos@egnaa.ee.auh.gr V. Perds perds@vergna.eng.auh.gr Ah. ehagas kehagas@egnaa.ee.auh.gr hp://skron.conrol.ee.auh.gr/kehagas/ndex.hm
More informationSingle-loop System Reliability-Based Design & Topology Optimization (SRBDO/SRBTO): A Matrix-based System Reliability (MSR) Method
10 h US Naonal Congress on Compuaonal Mechancs Columbus, Oho 16-19, 2009 Sngle-loop Sysem Relably-Based Desgn & Topology Opmzaon (SRBDO/SRBTO): A Marx-based Sysem Relably (MSR) Mehod Tam Nguyen, Junho
More informationCHAPTER FOUR REPEATED MEASURES IN TOXICITY TESTING
CHAPTER FOUR REPEATED MEASURES IN TOXICITY TESTING 4. Inroducon The repeaed measures sudy s a very commonly used expermenal desgn n oxcy esng because no only allows one o nvesgae he effecs of he oxcans,
More informationDiscussion Paper No Multivariate Time Series Model with Hierarchical Structure for Over-dispersed Discrete Outcomes
Dscusson Paper No. 113 Mulvarae Tme Seres Model wh Herarchcal Srucure for Over-dspersed Dscree Oucomes Nobuhko Teru and Masaaka Ban Augus, 213 January, 213 (Frs verson) TOHOKU MANAGEMENT & ACCOUNTING RESEARCH
More informationDegradation data analysis using the Probability Integral Transformation and a linear degradation path model with Weibull distributed random effects
Ro de Janero, Brazl Degradaon daa analyss usng he Probably Inegral Transformaon and a lnear degradaon pah model wh Webull dsrbued random effecs Clódo de Almeda Deparameno de Esaísca - UFMG Av. Presdene
More informationACEI working paper series RETRANSFORMATION BIAS IN THE ADJACENT ART PRICE INDEX
ACEI workng paper seres RETRANSFORMATION BIAS IN THE ADJACENT ART PRICE INDEX Andrew M. Jones Robero Zanola AWP-01-2011 Dae: July 2011 Reransformaon bas n he adjacen ar prce ndex * Andrew M. Jones and
More informationKayode Ayinde Department of Pure and Applied Mathematics, Ladoke Akintola University of Technology P. M. B. 4000, Ogbomoso, Oyo State, Nigeria
Journal of Mahemacs and Sascs 3 (4): 96-, 7 ISSN 549-3644 7 Scence Publcaons A Comparave Sudy of he Performances of he OLS and some GLS Esmaors when Sochasc egressors are boh Collnear and Correlaed wh
More informationELASTIC MODULUS ESTIMATION OF CHOPPED CARBON FIBER TAPE REINFORCED THERMOPLASTICS USING THE MONTE CARLO SIMULATION
THE 19 TH INTERNATIONAL ONFERENE ON OMPOSITE MATERIALS ELASTI MODULUS ESTIMATION OF HOPPED ARBON FIBER TAPE REINFORED THERMOPLASTIS USING THE MONTE ARLO SIMULATION Y. Sao 1*, J. Takahash 1, T. Masuo 1,
More informationVolatility Interpolation
Volaly Inerpolaon Prelmnary Verson March 00 Jesper Andreasen and Bran Huge Danse Mares, Copenhagen wan.daddy@danseban.com brno@danseban.com Elecronc copy avalable a: hp://ssrn.com/absrac=69497 Inro Local
More information12d Model. Civil and Surveying Software. Drainage Analysis Module Detention/Retention Basins. Owen Thornton BE (Mech), 12d Model Programmer
d Model Cvl and Surveyng Soware Dranage Analyss Module Deenon/Reenon Basns Owen Thornon BE (Mech), d Model Programmer owen.hornon@d.com 4 January 007 Revsed: 04 Aprl 007 9 February 008 (8Cp) Ths documen
More informationResource Sharing Models
ESA / T. Reer Mahemacal Deals on Resource Sharng Models Auhors: Güner Wmann, Maser of Mahemacs Andreas Wolfsener, Maser of Economcs save-he-clmae@onlne.ms (mal o) Verson: 7 h December 216 Mahemacal Deals
More informationShould Exact Index Numbers have Standard Errors? Theory and Application to Asian Growth
Should Exac Index umbers have Sandard Errors? Theory and Applcaon o Asan Growh Rober C. Feensra Marshall B. Rensdorf ovember 003 Proof of Proposon APPEDIX () Frs, we wll derve he convenonal Sao-Vara prce
More informationComputing Relevance, Similarity: The Vector Space Model
Compung Relevance, Smlary: The Vecor Space Model Based on Larson and Hears s sldes a UC-Bereley hp://.sms.bereley.edu/courses/s0/f00/ aabase Managemen Sysems, R. Ramarshnan ocumen Vecors v ocumens are
More informationUNIVERSITAT AUTÒNOMA DE BARCELONA MARCH 2017 EXAMINATION
INTERNATIONAL TRADE T. J. KEHOE UNIVERSITAT AUTÒNOMA DE BARCELONA MARCH 27 EXAMINATION Please answer wo of he hree quesons. You can consul class noes, workng papers, and arcles whle you are workng on he
More information