A NEW GENERALISATION OF SAM-SOLAI S MULTIVARIATE ADDITIVE GAMMA DISTRIBUTION*
|
|
- Emory Anthony
- 6 years ago
- Views:
Transcription
1 A NEW GENERALISATION OF SAM-SOLAI S MULTIVARIATE ADDITIVE GAMMA DISTRIBUTION* Dr. G.S. Davd Sam Jayakumar, Assstant Profssor, Jamal Insttut of Managmnt, Jamal Mohamd Collg, Truchraall , South Inda, Inda. E-mal: samjaya77@gmal.com Dr. A. Solaraju, Assocat Profssor, Dt. of Mathmatcs, Jamal Mohamd Collg, Truchraall , South Inda, Inda. E-mal:Solarama@yahoo.co.n A.Sulthan, Rsarch scholar, Jamal Insttut of Managmnt, Truchraall South Inda, Inda, E-mal: Sulthan90@gmal.com Abstract: Ths ar roosd a nw gnralzaton of boundd Contnuous multvarat symmtrc robablty dstrbutons. In ths ar, w vsualz a nw gnralzaton of Sam-Sola s Multvarat addtv Gamma dstrbuton from th un-varat two aramtrs Gamma dstrbuton. Furthr, w fnd ts Margnal, Multvarat Condtonal dstrbutons, Multvarat Gnratng functons, Multvarat survval, hazard functons and also dscussd t s scal cass. Th scal cass ncluds th transformaton of Sam-Sola s Multvarat addtv Gamma dstrbuton nto Multvarat Ch-squar dstrbuton, Multvarat Erlang dstrbuton, Two aramtr Multvarat Gamma dstrbuton, Multvarat Invrs Gamma dstrbuton, Multvarat log Gamma dstrbuton and Multvarat Nagakam-m dstrbuton. Morovr, t s found that th bvarat corrlaton btwn two Gamma random varabls urly dnds on th sha aramtr and w smulatd and stablshd slctd standard bvarat gamma corrlaton bounds from 900 dffrnt combnatons of valus for sha aramtr. Kywords: Sam-Sola s Multvarat Gamma dstrbuton, Transformaton, Multvarat Ch-squar dstrbuton, Multvarat Erlang dstrbuton, Two aramtr Multvarat Gamma dstrbuton, Multvarat Invrs Gamma dstrbuton, Multvarat log Gamma dstrbuton, Multvarat Nagakam-m dstrbuton, corrlaton bounds Introducton: Chryan (94) ntroducd a b-varat Gamma ty dstrbuton functon wth assumton of th Gamma random varabls ar corrlatd and smlarly Ramabhadran [95] roosd a multvarat Gamma ty dstrbuton n th xonntal famly of functons. Morovr Krshnamoorthy t al. (95) contnud th work of chryan, Ramabhadran and roosd a smlar ty of multvarat Gamma dstrbuton. On th othr hand, Sarmanov (968) roosd a gnralzd Gamma dstrbuton wth th assumton of symmtrcty among random varabls and Gavr (970) stablshd th mxtur of multvarat Gamma dstrbuton. Johnson t al (972, 2000) hghlghtd th Multvarat systm of Gamma dstrbuton and Dussauchoy t al (975) ntroducd a Multvarat Gamma dstrbuton whos margnal ar also followd a unvarat Gamma laws. Bckr t al(98) studd th xtnson of gamma dstrbuton for th bvarat cas and smlarly D Est(98) also dscrbd th Morgnstrn ty Gnralzaton of bvarat Gamma dstrbuton.kowalczyk t al(989) conductd a n-dth study about th rorts of Multvarat Gamma dstrbuton namly thr sha, stmaton of aramtrs and Matha(99,992) studd a dffrnt form of multvarat Gamma dstrbuton. Basd on th ast and rsnt ltraturs, th authors roosd a nw gnralzaton of boundd Contnuous multvarat symmtrc robablty dstrbutons wth scal rfrnc to th Gamma law and t s dscussd n th nxt scton. Thus th logcal gnralzaton of unvarat robablty dstrbuton for a Multvarat cas s an ntrstng task on th art of statstcans. Th gnralzaton of unvarat two aramtr Gamma dstrbuton to ts Multvarat cas basd on th addtv ty dstrbuton s dscussd. *Mathmatcs Subjct Classfcaton. Prmary 62H0; Scondary 62E5 Global Publshng Comany 39
2 G. S. DAVID SAM JAYAKUMAR, A. SOLAIRAJU, A. SULTHAN Scton : Sam-Sola s Multvarat Addtv Gamma dstrbuton Dfnton.: Lt X, X 2, X3, X b th random varabls followd Contnuous unvarat Gamma dstrbuton wth sha aramtr k and scal aramtr for all (= to ). Thn th dnsty functon of th Multvarat Sam Sola s addtv Gamma dstrbuton s dfnd as x f ( x, x, x, x ) {( ) ( )} k k x -- () whr 0, k 0. x Thorm.2: Th cumulatv dstrbuton functon of th Sam-Sola s Multvarat addtv Gamma dstrbuton s dfnd by x x2 x x 3 k u ( u ) k F( x, x, x, x ) {( ) ( )} du du du du -- (2) Whr 0 u x, k 0 x k k u x u x k 0 F( x, x, x, x ) ( ){ ( du ) ( ))} (,, ) x x k F( x, x2, x3, x ) ( ){ ( ) ( )} x whr x k k u u ( x,, k ) du k 0 s th lowr ncomlt Gamma ntgral of th random varabl. Thorm.3: Th Probablty dnsty functon of Sam-Sola s Multvarat addtv Condtonal Gamma dstrbuton of X on X 2, X 3, X s P ( x ) {( ) ( )} k k k ( x) f ( x / x, x, x ) ( ) ( 2) k 2 x -- (3) whr 0 x, k 0 Proof: It s obtand from f ( x / x, x, x ) f ( x, x, x, x ) f ( x, x, x ) 2 3 Global Publshng Comany 40
3 A NEW GENERALIZATION Thorm.4: Man and Varanc of Sam - Sola s Multvarat addtv Condtonal Gamma dstrbuton ar k { ( k ) ( )} 2 k k ( x) E( x / x, x, x ) 2 ( x ) ( ) ( 2) k -- (4) V ( x / x, x, x ) E( x / x, x, x ) ( E( x / x, x, x )) (5) whr k ( ) 2 { ( ) (2 x k k ) 2( )} 2 2 k E( x / x2, x3, x ) k ( x) ( ) ( 2)) k th Proof: Th n ordr momnt of th dstrbuton s 2 n n E( x / x, x, x ) x f ( x / x, x, x ) dx 0 k x {( ) ( )} n n k k ( ) 0 x 2 ( x ) E( x / x, x, x ) x dx ( ) ( 2) k ( nk ) ( x ) k { ( ){( n n ) ( )}} n k 2 k k ( x) E( x / x, x, x ) ( ) ( 2)) k 2 If n=, thn th Condtonal xctaton s k { ( k ) ( )} 2 k k ( x) E( x / x, x, x ) 2 ( x ) ( ) ( 2) k If n=2, thn th scond ordr momnt s k 2 { ( ) 2( k k ) 2( )} 2 2 k k ( x) E( x / x, x, x ) 2 ( x ) ( ) ( 2)) k Th condtonal varanc of th dstrbuton s obtand by Substtutng th frst and scond momnts n (5). Global Publshng Comany 4
4 G. S. DAVID SAM JAYAKUMAR, A. SOLAIRAJU, A. SULTHAN Thorm.5: If thr ar = (q + k) random varabls, such that q random varabls X, X, X, X X, X 2, X3, X q condtonally dnds on th k varabls,thn th dnsty functon of Sam-Sola s q q2 q3 qk multvarat addtv condtonal Gamma dstrbuton s ( x ) {( ) ( q k )} k q qk k q q q2 q3 qk k qk ( x ) f ( x, x, x, x / x, x, x, x ) ( ) ( k ) q k q x -- (6) whr 0, k 0 x Proof: Lt th multvarat condtonal law for q random varabls k varabls X, X, X, X q q2 q3 qk s gvn as X, X 2, X3, X q condtonally dndng on th f ( x, x, x, x / x, x, x, x ) q q q2 q3 qk f ( x, x, x, x, x, x, x, x ) q q q2 q3 qk f ( x, x, x, x ) q q2 q3 qk qk k x qk qk ( x ) {( ) ( q k )} k q q q2 q3 qk qk k x qk qk ( x ) q {( ) ( )} k q k x q qk ( x ) {( ) ( q k )} k f ( x, x, x, x / x, x, x, x ) q q q2 q3 qk k qk ( x ) f ( x, x, x, x / x, x, x, x ) whr 0, k 0 x q k dx ( ) ( k ) q k Scton 2: Constants of Sam-Sola s multvarat addtv Gamma dstrbuton Thorm 2.: Th Margnal roduct momnts, Co-varanc and Poulaton Corrlaton Co-ffcnt btwn th Gamma random varabls X and X ar gvn as k E( x x ) k -- (7) ( k)( k2) COV ( x, x2) -- (8) ( k)( k2) ( x, x2) kk -- (9) whr ( x, x ) Global Publshng Comany 42
5 A NEW GENERALIZATION Proof: Assum that x and x 2 ar random varabls from Sam-Sola s multvarat addtv Gamma dstrbuton. Lt th roduct momnt of th dstrbuton s E( x x ) x x f ( x, x, x, x ) dx Its Co-varanc s COV ( x, x ) E( x x ) E( x ) E( x ) -- (0) Thn k x ( x ) k E( x x ) x x {( ) ( )} dx By valuaton, t follows that k E( x x ) k Th Margnal xctaton of Gamma varabls x and x 2 ar k / and k 2 / 2 rsctvly. Th Margnal Product momnt for E(x x 2 ) s obtand by substtutng th abov Margnal xctatons for x and x 2 n (0). Thus ( k)( k2) COV ( x, x2) -- () Corrlaton coffcnt of a dstrbuton s COV ( x, x2) ( x, x2) --(2a) It obsrvs that = k / and 2 = k 2 / 2 --(2b) From (), (2a) and (2b), t follows that ( k)( k2) ( x, x2) kk --(3) whr ( x, x ) Rmark 2.: Th Product momnts, Co-varanc and oulaton Corrlaton Co-ffcnt btwn th th and th j of Sam-Sola s multvarat addtv Gamma dstrbuton random varabl ar gvn as Global Publshng Comany 43
6 G. S. DAVID SAM JAYAKUMAR, A. SOLAIRAJU, A. SULTHAN k kj E( xx j) j ( k)( kj) COV ( x, x j) ( k)( kj) ( x, xj) kk j j --(4) --(5) --(6) whr j ; ( x, x ) Thorm 2.2: Th Momnt gnratng functon of Sam-Sola s Multvarat addtv Gamma dstrbuton s M t t t t k x, x2, x ( 3, x, 2, 3, ) ( ){( ( ) ) ( 2)} t t --(7) Proof: Lt th momnt gnratng functon of a Multvarat dstrbuton s gvn as tx M ( t, t, t t ) f ( x, x, x, x ) dx x, x2, x3, x, tx k x ( ) x x, x2, x ( 3, x, 2, 3, ) {( ) ( )} k M t t t t dx M t t t t k x, x2, x ( 3, x, 2, 3, ) ( ){( ( ) ) ( 2)} t t by ntgratng th abov quaton. Thorm 2.3: Th Cumulant of th Momnt gnratng functon of th Sam-Sola s Multvarat addtv Gamma dstrbuton s C t t t t k x, x2, x ( 3, x, 2, 3, ) log( ) log{( ( ) ) ( )} t t --(8) Proof: It s found from. C ( t, t, t t ) log( M ( t, t, t t )) x, x2, x3, x, x, x2, x3, x, Global Publshng Comany 44
7 A NEW GENERALIZATION Thorm 2.4: Th Charactrstc functon of th Sam-Sola s Multvarat addtv Gamma dstrbuton s j j k j ( t, t, t t ) ( ){( ( ) ) ( )} t t x, x2, x3, x, j j j j j j --(9) Proof: Lt th charactrstc functon of a multvarat dstrbuton s gvn as t x j j j x, x2, x ( 3, x t, t2, t3, t ) (, 2, 3, ) f x x x x dx j j t x j j k j ( ) jxj j jx j j x, x2, x ( 3, x t, t2, t3, t ) {( ) ( )} j dx j j j k j j j j k j ( t, t, t t ) ( ){( ( ) ) ( )} t t x, x2, x3, x, j j j j j j by ntgratng th abov quaton. Thorm 2.5: Th survval functon of th Sam-Sola s Multvarat addtv Gamma dstrbuton s (,, ) x x k S( x, x2, x3, x) ( )( ( ) ( )) x --(20) Proof: Lt th survval functon of a multvarat dstrbuton s gvn as S( x, x, x, x ) F( x, x, x, x ) x x2 x x 3 k ( ) u u k S( x, x, x, x ) ( ( )) du du du du x k k u x u x k 0 S( x, x, x, x ) ( )( ( du ) ( )) (,, ) x x k S( x, x2, x3, x) ( )( ( ) ( )) x Whr varabl. x k k u u ( x,, k ) du k 0 s th lowr ncomlt Gamma ntgral of th random Global Publshng Comany 45
8 G. S. DAVID SAM JAYAKUMAR, A. SOLAIRAJU, A. SULTHAN Thorm 2.6: Th hazard functon of th Sam-Sola s Multvarat addtv Gamma dstrbuton s h( x, x, x, x ) k x x {( ) ( )} k (,, ) x x k x ( )( ( ) ( )) --(2) Proof: It s obtand from h( x, x, x, x ) f ( x, x, x, x ) S( x, x, x, x ) and S( x, x, x, x ) F( x, x, x, x ) Thorm 2.7: Th Cumulatv hazard functon of th Sam-Sola s Multvarat addtv Gamma dstrbuton s (,, ) x x k H( x, x2, x3, x) log( ( )( ( ) ( ))) x --(22) Proof: Lt th Cumulatv hazard functon of a multvarat dstrbuton s gvn as H( x, x, x, x ) log( F( x, x, x, x ) H( x, x, x, x ) log( S( x, x, x, x )) (,, ) x x k H( x, x2, x3, x) log( ( )( ( ) ( ))) x Scton 3: Som Scal Cass Rsult 3.: Th un-varat margnal of th Sam-Sola s multvarat addtv Gamma dstrbuton s th un-varat two aramtr Gamma dstrbutons. Rsult 3.2: If P = n (), th Sam-Sola s multvarat addtv Gamma dnsty s rducd to dnsty of un-varat two aramtr Gamma dstrbuton. Rsult 3.3: If P = 2 n (), thn th dnsty of Sam-Sola s Multvarat Gamma dstrbuton was rducd nto x x f ( x, x ) ( ) k k k2 k2 2 k k2 ( x x2 ) --(23) Global Publshng Comany 46
9 A NEW GENERALIZATION whr 0, x x2, k k2,,, 0 Ths s calld th dnsty of Sam-Sola s B-varat addtv Gamma dstrbuton. Rsult 3.4: Th tabls, tabl 2 and B-varat robablty surfac for (23) show th slctd smulatd standard Bvarat corrlatons btwn two Gamma random varabls whch ar boundd btwn - and + calculatd from 900 dffrnt combnatons of sha aramtr ( k, k ). Tabl : Smulaton runs for slctd valus of sha aramtr wth oulaton corrlaton bounds Runs K K ( x, x ) Tabl 2: Smulaton runs and combnaton of sha aramtrs of Bvarat Gamma dstrbuton whn ( x, x2) =0 Runs K K 2 Runs K K 2 Runs K K Global Publshng Comany 47
10 G. S. DAVID SAM JAYAKUMAR, A. SOLAIRAJU, A. SULTHAN Fgur 2 Fg. Fg.2 Fg.3 Fg. 4 Fg.5 Fg.6 Global Publshng Comany 48
11 A NEW GENERALIZATION Fg. 7 Fg.8 Fg.9 Fg.0 Fg. Fg.2 Global Publshng Comany 49
12 G. S. DAVID SAM JAYAKUMAR, A. SOLAIRAJU, A. SULTHAN Rsult 3.6: From () and f k =, thn th oulaton corrlaton btwn th th and th j random varabl s gvn as ( x, xj) =0 and th dnsty of Sam-Sola s Multvarat addtv Gamma dstrbuton s rducd as roduct of unvarat xonntal dstrbuton, and ts dnsty functon s f ( x, x2, x3, x) ( ) x x f ( x, x, x, x ) -- (24) whr 0 x 0 Rsult 3.7: From() and f =, th Sam-sola s Multvarat addtv Gamma dstrbuton s rducd nto Sam- sola s Multvarat on aramtr addtv Gamma dstrbuton wth aramtrs as k and ts dnsty functon s gvn k x f ( x, x2, x3, x) {( ) ( )} k x -- (25) k whr 0 k 0 k x Rsult 3.8: From () and f and, thn th Sam-sola s Multvarat addtv Gamma dstrbuton s rducd nto Sam-sola s Multvarat two aramtr addtv Gamma dstrbuton wth aramtrs, k and ts dnsty functon s gvn as f x x x x x k k (, 2, 3, ) {( ) ( )} k x -- (26) Rsult 3.9: From () and f n, k 2 2 whr 0, k 0 dstrbuton s modfd nto Sam-sola s Multvarat addtv ch-squar and ts dnsty functon s gvn as x, thn th Sam-sola s Multvarat two aramtr addtv Gamma 2 -dstrbuton wth n dgrs frdom Global Publshng Comany 50
13 A NEW GENERALIZATION n x 2 ( ) f ( x 2, x2, x3, x) ( ) {( ) ( )} 2 n 2 2 x --(27) whr 0 x n 0 k Rsult 3.0: From () and f, thn th Sam-sola s Multvarat two aramtr addtv Gamma dstrbuton s altrd nto Sam-sola s Multvarat addtv Erlang-k dstrbuton and ts dnsty functon s gvn as k ( kx) f ( x, x, x, x ) ( k ){( ) ( )} k kx -- (28) y x whr 0 x, k 0 Rsult 3.: From () and f, thn th Sam-sola s Multvarat two aramtr addtv Gamma dstrbuton s transformd nto Sam-sola s Multvarat addtv Invrs Gamma dstrbuton and ts dnsty functon s gvn as k ( ) y f ( y, y, y, y ) ( ){( ) ( )} k 2 y ( ) y -- (29) Rsult 3.2: From () and f y x whr 0, k 0 y, thn th Sam-sola s Multvarat two aramtr addtv Gamma dstrbuton s transformd nto Sam-sola s Multvarat addtv log-gamma dstrbuton and ts dnsty functon s gvn as k log y ( log y ) f ( y, y2, y3, y ) ( ){( ) ( )} y k -- (30) Rsult 3.3: From () and fk m, whr m and y, k 0 y x, thn th Sam-sola s Multvarat two aramtr addtv Gamma dstrbuton s transformd nto Sam-sola s Multvarat Nagakam-m dstrbuton and ts dnsty functon s gvn as Global Publshng Comany 5
14 G. S. DAVID SAM JAYAKUMAR, A. SOLAIRAJU, A. SULTHAN m m ( ) 2 m y m y m y m m f ( y, y, y, y ) 2 ( ( )) -- (3) whr 0 y, 0 m 0.5 Concluson: Th multvarat gnralzaton of two aramtr Gamma dstrbuton s an addtv form of Sam- Sola s gnralzaton havng som ntrstng faturs. At frst, th margnal un-varat dstrbutons of th Sam- Sola s Multvarat addtv Gamma dstrbuton ar un-varat and njoyd th symmtrc rorty. Scondly, th Poulaton Corrlaton co-ffcnt of th roosd dstrbuton s boundd btwn - and + for crtan valus of sha aramtr and th authors stablshd th smulatd standard bvarat corrlatons. Thrdly, th Condtonal varanc of Sam-Sola s Multvarat addtv condtonal Gamma dstrbuton s htroscdastc n natur and ths fatur s a unqu for th roosd dstrbuton. Fnally, th multvarat gnralzaton of two aramtr Gamma dstrbuton n an addtv form on th way for th sam addtv form of th gnralzaton of th xonntal famly of Sam-Sola s Multvarat Ch-squar dstrbuton, Multvarat Erlang dstrbuton, Multvarat Invrs Gamma dstrbuton, Multvarat log Gamma dstrbuton and Multvarat Nagakam-m dstrbuton. REFERENCES: []Chryan, K. C. A bvarat corrlatd gamma-ty dstrbuton functon, Journal of th Indan Mathmatcal Socty, 5, (94), [2]Krshnamoorthy, A. S., and Parthasarathy, M. A multvarat gamma- ty dstrbuton, Annals of Mathmatcal Statstcs, 22, (95), 3, 229 [3]Ramabhadran,V. R.A multvarat gamma-ty dstrbuton, Sankhya,, (95), [4]Krshnaah, P. R., and Rao, M. M. Rmarks on a multvarat gamma dstrbuton, Amrcan Mathmatcal Monthly, 68, (96), [5]Sarmanov, I. O.A gnralzd symmtrc gamma corrlaton, Doklady Akadm Nauk SSSR, 79, ; Sovt Mathmatcs Doklady, 9, (968), [6]Gavr, D. P. Multvarat gamma dstrbutons gnratd by mxtur, Sankhya, Srs A, 32, (970), [7]Johnson, N. L., and Kotz, S. Contnuous Multvarat Dstrbutons, frst dton, Nw York: John Wly &: Sons, 972. [8]Dussauchoy, A., and Brland, R. A multvarat gamma dstrbuton whos margnal laws ar gamma, In Statstcal Dstrbutons n Scntfc Work, Vol. (G. P. Patl, S. Kotz, and J. K. Ord, ds.), (975), [9]Bckr, P. J., and Roux, J. J. J. A bvarat xtnson of th gamma dstrbuton, South Afrcan Statstcal Journal, 5, (98), -2. [0]D'Est, G. M. A Morgnstrn-ty bvarat gamma dstrbuton, Bomtrka, 68, (98) []Kowalczyk, T., and Tyrcha, J.Multvarat gamma dstrbutons, rorts and sha stmaton, Statstcs, J. Math. Bol. 26, , 20, (989) [2]Matha, A. M., and Moschooulos, P. G. On a multvarat gamma, Journal of Multvarat Analyss, 39, (99) [3]Matha, A. M., and Moschooulos, P. G. A form of multvarat gamma dstrbuton, Annals of th Insttut of Statstcal Mathmatcs, 44, (992), Global Publshng Comany 52
Research Journal of Pure Algebra -2(12), 2012, Page: Available online through ISSN
Research Journal of Pure Algebra (, 0, Page: 37038 Avalable onlne through www.rja.nfo ISSN 48 9037 A NEW GENERALISATION OF SAMSOLAI S MULTIVARIATE ADDITIVE EXPONENTIAL DISTRIBUTION* Dr. G. S. Davd Sam
More informationFolding of Regular CW-Complexes
Ald Mathmatcal Scncs, Vol. 6,, no. 83, 437-446 Foldng of Rgular CW-Comlxs E. M. El-Kholy and S N. Daoud,3. Dartmnt of Mathmatcs, Faculty of Scnc Tanta Unvrsty,Tanta,Egyt. Dartmnt of Mathmatcs, Faculty
More informationA Note on Estimability in Linear Models
Intrnatonal Journal of Statstcs and Applcatons 2014, 4(4): 212-216 DOI: 10.5923/j.statstcs.20140404.06 A Not on Estmablty n Lnar Modls S. O. Adymo 1,*, F. N. Nwob 2 1 Dpartmnt of Mathmatcs and Statstcs,
More informationOn Properties of the difference between two modified C p statistics in the nested multivariate linear regression models
Global Journal o Pur Ald Mathatcs. ISSN 0973-1768 Volu 1, Nubr 1 (016),. 481-491 Rsarch Inda Publcatons htt://www.rublcaton.co On Prorts o th drnc btwn two odd C statstcs n th nstd ultvarat lnar rgrsson
More informationGrand Canonical Ensemble
Th nsmbl of systms mmrsd n a partcl-hat rsrvor at constant tmpratur T, prssur P, and chmcal potntal. Consdr an nsmbl of M dntcal systms (M =,, 3,...M).. Thy ar mutually sharng th total numbr of partcls
More informationAnalyzing Frequencies
Frquncy (# ndvduals) Frquncy (# ndvduals) /3/16 H o : No dffrnc n obsrvd sz frquncs and that prdctd by growth modl How would you analyz ths data? 15 Obsrvd Numbr 15 Expctd Numbr from growth modl 1 1 5
More informationCOMPLEX NUMBER PAIRWISE COMPARISON AND COMPLEX NUMBER AHP
ISAHP 00, Bal, Indonsa, August -9, 00 COMPLEX NUMBER PAIRWISE COMPARISON AND COMPLEX NUMBER AHP Chkako MIYAKE, Kkch OHSAWA, Masahro KITO, and Masaak SHINOHARA Dpartmnt of Mathmatcal Informaton Engnrng
More informationThe Hyperelastic material is examined in this section.
4. Hyprlastcty h Hyprlastc matral s xad n ths scton. 4..1 Consttutv Equatons h rat of chang of ntrnal nrgy W pr unt rfrnc volum s gvn by th strss powr, whch can b xprssd n a numbr of dffrnt ways (s 3.7.6):
More informationON THE COMPLEXITY OF K-STEP AND K-HOP DOMINATING SETS IN GRAPHS
MATEMATICA MONTISNIRI Vol XL (2017) MATEMATICS ON TE COMPLEXITY OF K-STEP AN K-OP OMINATIN SETS IN RAPS M FARAI JALALVAN AN N JAFARI RA partmnt of Mathmatcs Shahrood Unrsty of Tchnology Shahrood Iran Emals:
More informationST 524 NCSU - Fall 2008 One way Analysis of variance Variances not homogeneous
ST 54 NCSU - Fall 008 On way Analyss of varanc Varancs not homognous On way Analyss of varanc Exampl (Yandll, 997) A plant scntst masurd th concntraton of a partcular vrus n plant sap usng ELISA (nzym-lnkd
More informationReview - Probabilistic Classification
Mmoral Unvrsty of wfoundland Pattrn Rcognton Lctur 8 May 5, 6 http://www.ngr.mun.ca/~charlsr Offc Hours: Tusdays Thursdays 8:3-9:3 PM E- (untl furthr notc) Gvn lablld sampls { ɛc,,,..., } {. Estmat Rvw
More information10/7/14. Mixture Models. Comp 135 Introduction to Machine Learning and Data Mining. Maximum likelihood estimation. Mixture of Normals in 1D
Comp 35 Introducton to Machn Larnng and Data Mnng Fall 204 rofssor: Ron Khardon Mxtur Modls Motvatd by soft k-mans w dvlopd a gnratv modl for clustrng. Assum thr ar k clustrs Clustrs ar not rqurd to hav
More informationChapter 6 Student Lecture Notes 6-1
Chaptr 6 Studnt Lctur Nots 6-1 Chaptr Goals QM353: Busnss Statstcs Chaptr 6 Goodnss-of-Ft Tsts and Contngncy Analyss Aftr compltng ths chaptr, you should b abl to: Us th ch-squar goodnss-of-ft tst to dtrmn
More informationte Finance (4th Edition), July 2017.
Appndx Chaptr. Tchncal Background Gnral Mathmatcal and Statstcal Background Fndng a bas: 3 2 = 9 3 = 9 1 /2 x a = b x = b 1/a A powr of 1 / 2 s also quvalnt to th squar root opraton. Fndng an xponnt: 3
More informationLucas Test is based on Euler s theorem which states that if n is any integer and a is coprime to n, then a φ(n) 1modn.
Modul 10 Addtonal Topcs 10.1 Lctur 1 Prambl: Dtrmnng whthr a gvn ntgr s prm or compost s known as prmalty tstng. Thr ar prmalty tsts whch mrly tll us whthr a gvn ntgr s prm or not, wthout gvng us th factors
More informationPARTIAL DISTRIBUTION FUNCTION AND RADIAL STATISTICAL COEFFICIENTS FOR Be-ATOM
Journal of Krbala Unvrsty, Vol. 7 o.4 Scntfc. 009 PARTIAL DISTRIBUTIO FUCTIO AD RADIAL STATISTICAL COEFFICIETS FOR B-ATOM Mohammd Abdulhussan Al-Kaab Dpartmnt of Physcs, collg of Scnc, Krbala Unvrsty ABSTRACT
More informationUNIT 8 TWO-WAY ANOVA WITH m OBSERVATIONS PER CELL
UNIT 8 TWO-WAY ANOVA WITH OBSERVATIONS PER CELL Two-Way Anova wth Obsrvatons Pr Cll Structur 81 Introducton Obctvs 8 ANOVA Modl for Two-way Classfd Data wth Obsrvatons r Cll 83 Basc Assutons 84 Estaton
More informationJournal of Theoretical and Applied Information Technology 10 th January Vol. 47 No JATIT & LLS. All rights reserved.
Journal o Thortcal and Appld Inormaton Tchnology th January 3. Vol. 47 No. 5-3 JATIT & LLS. All rghts rsrvd. ISSN: 99-8645 www.att.org E-ISSN: 87-395 RESEARCH ON PROPERTIES OF E-PARTIAL DERIVATIVE OF LOGIC
More informationStress-Based Finite Element Methods for Dynamics Analysis of Euler-Bernoulli Beams with Various Boundary Conditions
9 Strss-Basd Fnt Elmnt Mthods for Dynamcs Analyss of Eulr-Brnoull Bams wth Varous Boundary Condtons Abstract In ths rsarch, two strss-basd fnt lmnt mthods ncludng th curvatur-basd fnt lmnt mthod (CFE)
More informationThe Equitable Dominating Graph
Intrnational Journal of Enginring Rsarch and Tchnology. ISSN 0974-3154 Volum 8, Numbr 1 (015), pp. 35-4 Intrnational Rsarch Publication Hous http://www.irphous.com Th Equitabl Dominating Graph P.N. Vinay
More informationarxiv: v1 [math.pr] 28 Jan 2019
CRAMÉR-TYPE MODERATE DEVIATION OF NORMAL APPROXIMATION FOR EXCHANGEABLE PAIRS arxv:190109526v1 [mathpr] 28 Jan 2019 ZHUO-SONG ZHANG Abstract In Stn s mthod, an xchangabl par approach s commonly usd to
More informationVISUALIZATION OF DIFFERENTIAL GEOMETRY UDC 514.7(045) : : Eberhard Malkowsky 1, Vesna Veličković 2
FACTA UNIVERSITATIS Srs: Mchancs, Automatc Control Robotcs Vol.3, N o, 00, pp. 7-33 VISUALIZATION OF DIFFERENTIAL GEOMETRY UDC 54.7(045)54.75.6:59.688:59.673 Ebrhard Malkowsky, Vsna Vlčkovć Dpartmnt of
More informationHORIZONTAL IMPEDANCE FUNCTION OF SINGLE PILE IN SOIL LAYER WITH VARIABLE PROPERTIES
13 th World Confrnc on Earthquak Engnrng Vancouvr, B.C., Canada August 1-6, 4 Papr No. 485 ORIZONTAL IMPEDANCE FUNCTION OF SINGLE PILE IN SOIL LAYER WIT VARIABLE PROPERTIES Mngln Lou 1 and Wnan Wang Abstract:
More informationNEW APPLICATIONS OF THE ABEL-LIOUVILLE FORMULA
NE APPLICATIONS OF THE ABEL-LIOUVILLE FORMULA Mirca I CÎRNU Ph Dp o Mathmatics III Faculty o Applid Scincs Univrsity Polithnica o Bucharst Cirnumirca @yahoocom Abstract In a rcnt papr [] 5 th indinit intgrals
More informationDecision-making with Distance-based Operators in Fuzzy Logic Control
Dcson-makng wth Dstanc-basd Oprators n Fuzzy Logc Control Márta Takács Polytchncal Engnrng Collg, Subotca 24000 Subotca, Marka Orškovća 16., Yugoslava marta@vts.su.ac.yu Abstract: Th norms and conorms
More informationANALYTICITY THEOREM FOR FRACTIONAL LAPLACE TRANSFORM
Sc. Rs. hm. ommn.: (3, 0, 77-8 ISSN 77-669 ANALYTIITY THEOREM FOR FRATIONAL LAPLAE TRANSFORM P. R. DESHMUH * and A. S. GUDADHE a Prof. Ram Mgh Insttt of Tchnology & Rsarch, Badnra, AMRAVATI (M.S. INDIA
More informationPROOF OF FIRST STANDARD FORM OF NONELEMENTARY FUNCTIONS
Intrnational Journal Of Advanc Rsarch In Scinc And Enginring http://www.ijars.com IJARSE, Vol. No., Issu No., Fbruary, 013 ISSN-319-8354(E) PROOF OF FIRST STANDARD FORM OF NONELEMENTARY FUNCTIONS 1 Dharmndra
More information4.8 Huffman Codes. Wordle. Encoding Text. Encoding Text. Prefix Codes. Encoding Text
2/26/2 Word A word a word coag. A word contrctd ot of on of th ntrctor ar: 4.8 Hffan Cod word contrctd ng th java at at word.nt word a randozd grdy agorth to ov th ackng rob Encodng Txt Q. Gvn a txt that
More information2. Grundlegende Verfahren zur Übertragung digitaler Signale (Zusammenfassung) Informationstechnik Universität Ulm
. Grundlgnd Vrfahrn zur Übrtragung dgtalr Sgnal (Zusammnfassung) wt Dc. 5 Transmsson of Dgtal Sourc Sgnals Sourc COD SC COD MOD MOD CC dg RF s rado transmsson mdum Snk DC SC DC CC DM dg DM RF g physcal
More informationEconomics 600: August, 2007 Dynamic Part: Problem Set 5. Problems on Differential Equations and Continuous Time Optimization
THE UNIVERSITY OF MARYLAND COLLEGE PARK, MARYLAND Economcs 600: August, 007 Dynamc Part: Problm St 5 Problms on Dffrntal Equatons and Contnuous Tm Optmzaton Quston Solv th followng two dffrntal quatons.
More informationSCITECH Volume 5, Issue 1 RESEARCH ORGANISATION November 17, 2015
Journal of Informaton Scncs and Computng Tchnologs(JISCT) ISSN: 394-966 SCITECH Volum 5, Issu RESEARCH ORGANISATION Novmbr 7, 5 Journal of Informaton Scncs and Computng Tchnologs www.sctcrsarch.com/journals
More informationReliability of time dependent stress-strength system for various distributions
IOS Joural of Mathmatcs (IOS-JM ISSN: 78-578. Volum 3, Issu 6 (Sp-Oct., PP -7 www.osrjourals.org lablty of tm dpdt strss-strgth systm for varous dstrbutos N.Swath, T.S.Uma Mahswar,, Dpartmt of Mathmatcs,
More informationIndependent Domination in Line Graphs
Itratoal Joural of Sctfc & Egrg Rsarch Volum 3 Issu 6 Ju-1 1 ISSN 9-5518 Iddt Domato L Grahs M H Muddbhal ad D Basavarajaa Abstract - For ay grah G th l grah L G H s th trscto grah Thus th vrtcs of LG
More informationSoft k-means Clustering. Comp 135 Machine Learning Computer Science Tufts University. Mixture Models. Mixture of Normals in 1D
Comp 35 Machn Larnng Computr Scnc Tufts Unvrsty Fall 207 Ron Khardon Th EM Algorthm Mxtur Modls Sm-Suprvsd Larnng Soft k-mans Clustrng ck k clustr cntrs : Assocat xampls wth cntrs p,j ~~ smlarty b/w cntr
More informationExternal Equivalent. EE 521 Analysis of Power Systems. Chen-Ching Liu, Boeing Distinguished Professor Washington State University
xtrnal quvalnt 5 Analyss of Powr Systms Chn-Chng Lu, ong Dstngushd Profssor Washngton Stat Unvrsty XTRNAL UALNT ach powr systm (ara) s part of an ntrconnctd systm. Montorng dvcs ar nstalld and data ar
More informationSeptember 27, Introduction to Ordinary Differential Equations. ME 501A Seminar in Engineering Analysis Page 1. Outline
Introucton to Ornar Dffrntal Equatons Sptmbr 7, 7 Introucton to Ornar Dffrntal Equatons Larr artto Mchancal Engnrng AB Smnar n Engnrng Analss Sptmbr 7, 7 Outln Rvw numrcal solutons Bascs of ffrntal quatons
More informationMatched Quick Switching Variable Sampling System with Quick Switching Attribute Sampling System
Natur and Sn 9;7( g v, t al, Samlng Systm Mathd Quk Swthng Varabl Samlng Systm wth Quk Swthng Attrbut Samlng Systm Srramahandran G.V, Palanvl.M Dartmnt of Mathmats, Dr.Mahalngam Collg of Engnrng and Thnology,
More informationLevel crossing rate of relay system over LOS multipath fading channel with one and two clusters in the presence of co-channel interference
INFOTEHJAHORINA Vol 5, March 6 Lvl crossng rat of rla sstm ovr LOS multath fadng channl th on and to clustrs n th rsnc of cochannl ntrfrnc Goran Ptovć, Zorca Nolć Facult of Elctronc Engnrng Unvrst of Nš
More informationCHAPTER 7d. DIFFERENTIATION AND INTEGRATION
CHAPTER 7d. DIFFERENTIATION AND INTEGRATION A. J. Clark School o Engnrng Dpartmnt o Cvl and Envronmntal Engnrng by Dr. Ibrahm A. Assakka Sprng ENCE - Computaton Mthods n Cvl Engnrng II Dpartmnt o Cvl and
More informationHeisenberg Model. Sayed Mohammad Mahdi Sadrnezhaad. Supervisor: Prof. Abdollah Langari
snbrg Modl Sad Mohammad Mahd Sadrnhaad Survsor: Prof. bdollah Langar bstract: n ths rsarch w tr to calculat analtcall gnvalus and gnvctors of fnt chan wth ½-sn artcls snbrg modl. W drov gnfuctons for closd
More informationLOGIT ANALYSIS. A.K. VASISHT Indian Agricultural Statistics Research Institute, Library Avenue, New Delhi
LOGIT ANALYSIS A.K. VASISHT Indan Agrcultural Statstcs Research Insttute, Lbrary Avenue, New Delh-0 02 amtvassht@asr.res.n. Introducton In dummy regresson varable models, t s assumed mplctly that the dependent
More informationFrom Structural Analysis to FEM. Dhiman Basu
From Structural Analyss to FEM Dhman Basu Acknowldgmnt Followng txt books wr consultd whl prparng ths lctur nots: Znkwcz, OC O.C. andtaylor Taylor, R.L. (000). Th FntElmnt Mthod, Vol. : Th Bass, Ffth dton,
More informationGroup Codes Define Over Dihedral Groups of Small Order
Malaysan Journal of Mathmatcal Scncs 7(S): 0- (0) Spcal Issu: Th rd Intrnatonal Confrnc on Cryptology & Computr Scurty 0 (CRYPTOLOGY0) MALAYSIA JOURAL OF MATHEMATICAL SCIECES Journal hompag: http://nspm.upm.du.my/ournal
More informationCHAPTER 33: PARTICLE PHYSICS
Collg Physcs Studnt s Manual Chaptr 33 CHAPTER 33: PARTICLE PHYSICS 33. THE FOUR BASIC FORCES 4. (a) Fnd th rato of th strngths of th wak and lctromagntc forcs undr ordnary crcumstancs. (b) What dos that
More information8-node quadrilateral element. Numerical integration
Fnt Elmnt Mthod lctur nots _nod quadrlatral lmnt Pag of 0 -nod quadrlatral lmnt. Numrcal ntgraton h tchnqu usd for th formulaton of th lnar trangl can b formall tndd to construct quadrlatral lmnts as wll
More informationOutlier-tolerant parameter estimation
Outlr-tolrant paramtr stmaton Baysan thods n physcs statstcs machn larnng and sgnal procssng (SS 003 Frdrch Fraundorfr fraunfr@cg.tu-graz.ac.at Computr Graphcs and Vson Graz Unvrsty of Tchnology Outln
More informationA NON-LINEAR MODEL FOR STUDYING THE MOTION OF A HUMAN BODY. Piteşti, , Romania 2 Department of Automotive, University of Piteşti
ICSV Carns ustrala 9- July 7 NON-LINER MOEL FOR STUYING THE MOTION OF HUMN OY Ncola-oru Stănscu Marna Pandra nl Popa Sorn Il Ştfan-Lucan Tabacu partnt of ppld Mchancs Unvrsty of Ptşt Ptşt 7 Roana partnt
More informationCase Study of Cascade Reliability with weibull Distribution
ISSN: 77-3754 ISO 900:008 Certfed Internatonal Journal of Engneerng and Innovatve Technology (IJEIT) Volume, Issue 6, June 0 Case Study of Cascade Relablty wth webull Dstrbuton Dr.T.Shyam Sundar Abstract
More informationDr. Shalabh Department of Mathematics and Statistics Indian Institute of Technology Kanpur
Analyss of Varance and Desgn of Exerments-I MODULE III LECTURE - 2 EXPERIMENTAL DESIGN MODELS Dr. Shalabh Deartment of Mathematcs and Statstcs Indan Insttute of Technology Kanur 2 We consder the models
More informationFREE VIBRATION ANALYSIS OF FUNCTIONALLY GRADED BEAMS
Journal of Appl Mathatcs an Coputatonal Mchancs, (), 9- FREE VIBRATION ANAYSIS OF FNCTIONAY GRADED BEAMS Stansław Kukla, Jowta Rychlwska Insttut of Mathatcs, Czstochowa nvrsty of Tchnology Czstochowa,
More informationSCHUR S THEOREM REU SUMMER 2005
SCHUR S THEOREM REU SUMMER 2005 1. Combinatorial aroach Prhas th first rsult in th subjct blongs to I. Schur and dats back to 1916. On of his motivation was to study th local vrsion of th famous quation
More information(Upside-Down o Direct Rotation) β - Numbers
Amrican Journal of Mathmatics and Statistics 014, 4(): 58-64 DOI: 10593/jajms0140400 (Upsid-Down o Dirct Rotation) β - Numbrs Ammar Sddiq Mahmood 1, Shukriyah Sabir Ali,* 1 Dpartmnt of Mathmatics, Collg
More informationHere is the rationale: If X and y have a strong positive relationship to one another, then ( x x) will tend to be positive when ( y y)
Secton 1.5 Correlaton In the prevous sectons, we looked at regresson and the value r was a measurement of how much of the varaton n y can be attrbuted to the lnear relatonshp between y and x. In ths secton,
More informationLecture 14. Relic neutrinos Temperature at neutrino decoupling and today Effective degeneracy factor Neutrino mass limits Saha equation
Lctur Rlc nutrnos mpratur at nutrno dcoupln and today Effctv dnracy factor Nutrno mass lmts Saha quaton Physcal Cosmoloy Lnt 005 Rlc Nutrnos Nutrnos ar wakly ntractn partcls (lptons),,,,,,, typcal ractons
More informationLogistic Regression I. HRP 261 2/10/ am
Logstc Rgrsson I HRP 26 2/0/03 0- am Outln Introducton/rvw Th smplst logstc rgrsson from a 2x2 tabl llustrats how th math works Stp-by-stp xampls to b contnud nxt tm Dummy varabls Confoundng and ntracton
More informationΕρωτήσεις και ασκησεις Κεφ. 10 (για μόρια) ΠΑΡΑΔΟΣΗ 29/11/2016. (d)
Ερωτήσεις και ασκησεις Κεφ 0 (για μόρια ΠΑΡΑΔΟΣΗ 9//06 Th coffcnt A of th van r Waals ntracton s: (a A r r / ( r r ( (c a a a a A r r / ( r r ( a a a a A r r / ( r r a a a a A r r / ( r r 4 a a a a 0 Th
More informationMP IN BLOCK QUASI-INCOHERENT DICTIONARIES
CHOOL O ENGINEERING - TI IGNAL PROCEING INTITUTE Lornzo Potta and Prr Vandrghynst CH-1015 LAUANNE Tlphon: 4121 6932601 Tlfax: 4121 6937600 -mal: lornzo.potta@pfl.ch ÉCOLE POLYTECHNIQUE ÉDÉRALE DE LAUANNE
More informationStrategies evaluation on the attempts to gain access to a service system (the second problem of an impatient customer)
h ublcaton aard n Sostk R.: Stratgs valuaton on th attmts to gan accss to a vc systm th scond roblm of an matnt customr, Intrnatonal Journal of Elctroncs and lcommuncatons Quartrly 54, no, PN, Warsa 8,.
More informationLecture 3: Phasor notation, Transfer Functions. Context
EECS 5 Fall 4, ctur 3 ctur 3: Phasor notaton, Transfr Functons EECS 5 Fall 3, ctur 3 Contxt In th last lctur, w dscussd: how to convrt a lnar crcut nto a st of dffrntal quatons, How to convrt th st of
More information4D SIMPLICIAL QUANTUM GRAVITY
T.YUKAWA and S.HORATA Soknda/KEK D SIMPLICIAL QUATUM GRAITY Plan of th talk Rvw of th D slcal quantu gravty Rvw of nurcal thods urcal rsult and dscusson Whr dos th slcal quantu gravty stand? In short dstanc
More informationOptimal Ordering Policy in a Two-Level Supply Chain with Budget Constraint
Optmal Ordrng Polcy n a Two-Lvl Supply Chan wth Budgt Constrant Rasoul aj Alrza aj Babak aj ABSTRACT Ths papr consdrs a two- lvl supply chan whch consst of a vndor and svral rtalrs. Unsatsfd dmands n rtalrs
More informationA Probabilistic Characterization of Simulation Model Uncertainties
A Proalstc Charactrzaton of Sulaton Modl Uncrtants Vctor Ontvros Mohaad Modarrs Cntr for Rsk and Rlalty Unvrsty of Maryland 1 Introducton Thr s uncrtanty n odl prdctons as wll as uncrtanty n xprnts Th
More informationThe Fourier Transform
/9/ Th ourr Transform Jan Baptst Josph ourr 768-83 Effcnt Data Rprsntaton Data can b rprsntd n many ways. Advantag usng an approprat rprsntaton. Eampls: osy ponts along a ln Color spac rd/grn/blu v.s.
More informationDiscrete Shells Simulation
Dscrt Shlls Smulaton Xaofng M hs proct s an mplmntaton of Grnspun s dscrt shlls, th modl of whch s govrnd by nonlnar mmbran and flxural nrgs. hs nrgs masur dffrncs btwns th undformd confguraton and th
More informationBasic Electrical Engineering for Welding [ ] --- Introduction ---
Basc Elctrcal Engnrng for Wldng [] --- Introducton --- akayosh OHJI Profssor Ertus, Osaka Unrsty Dr. of Engnrng VIUAL WELD CO.,LD t-ohj@alc.co.jp OK 15 Ex. Basc A.C. crcut h fgurs n A-group show thr typcal
More informationSpecial Random Variables: Part 1
Spcl Rndom Vrbls: Prt Dscrt Rndom Vrbls Brnoull Rndom Vrbl (wth prmtr p) Th rndom vrbl x dnots th succss from trl. Th probblty mss functon of th rndom vrbl X s gvn by p X () p X () p p ( E[X ]p Th momnt
More informationNaresuan University Journal: Science and Technology 2018; (26)1
Narsuan Unvrsty Journal: Scnc and Tchnology 018; (6)1 Th Dvlopmnt o a Corrcton Mthod or Ensurng a Contnuty Valu o Th Ch-squar Tst wth a Small Expctd Cll Frquncy Kajta Matchma 1 *, Jumlong Vongprasrt and
More informationRelate p and T at equilibrium between two phases. An open system where a new phase may form or a new component can be added
4.3, 4.4 Phas Equlbrum Dtrmn th slops of th f lns Rlat p and at qulbrum btwn two phass ts consdr th Gbbs functon dg η + V Appls to a homognous systm An opn systm whr a nw phas may form or a nw componnt
More information3.1 Expectation of Functions of Several Random Variables. )' be a k-dimensional discrete or continuous random vector, with joint PMF p (, E X E X1 E X
Statstcs 1: Probablty Theory II 37 3 EPECTATION OF SEVERAL RANDOM VARIABLES As n Probablty Theory I, the nterest n most stuatons les not on the actual dstrbuton of a random vector, but rather on a number
More informationComparing two Quantiles: the Burr Type X and Weibull Cases
IOSR Journal of Mathematcs (IOSR-JM) e-issn: 78-578, -ISSN: 39-765X. Volume, Issue 5 Ver. VII (Se. - Oct.06), PP 8-40 www.osrjournals.org Comarng two Quantles: the Burr Tye X and Webull Cases Mohammed
More informationEEC 686/785 Modeling & Performance Evaluation of Computer Systems. Lecture 12
EEC 686/785 Modlng & Prformanc Evaluaton of Computr Systms Lctur Dpartmnt of Elctrcal and Computr Engnrng Clvland Stat Unvrsty wnbng@.org (basd on Dr. Ra Jan s lctur nots) Outln Rvw of lctur k r Factoral
More informationGreen Functions, the Generating Functional and Propagators in the Canonical Quantization Approach
Grn Functons, th Gnratng Functonal and Propagators n th Canoncal Quantzaton Approach by Robrt D. Klaubr 15, 16 www.quantumfldthory.nfo Mnor Rv: Spt, 16 Sgnfcant Rv: Fb 3, 16 Orgnal: Fbruary, 15 Th followng
More informationj) = 1 (note sigma notation) ii. Continuous random variable (e.g. Normal distribution) 1. density function: f ( x) 0 and f ( x) dx = 1
Random varables Measure of central tendences and varablty (means and varances) Jont densty functons and ndependence Measures of assocaton (covarance and correlaton) Interestng result Condtonal dstrbutons
More informationIV. Transport Phenomena Lecture 35: Porous Electrodes (I. Supercapacitors)
IV. Transort Phnomna Lctur 35: Porous Elctrods (I. Surcaactors) MIT Studnt (and MZB) 1. Effctv Equatons for Thn Doubl Layrs For surcaactor lctrods, convcton s usually nglgbl, and w dro out convcton trms
More informationThe graph of y = x (or y = ) consists of two branches, As x 0, y + ; as x 0, y +. x = 0 is the
Copyright itutcom 005 Fr download & print from wwwitutcom Do not rproduc by othr mans Functions and graphs Powr functions Th graph of n y, for n Q (st of rational numbrs) y is a straight lin through th
More information3.4 Properties of the Stress Tensor
cto.4.4 Proprts of th trss sor.4. trss rasformato Lt th compots of th Cauchy strss tsor a coordat systm wth bas vctors b. h compots a scod coordat systm wth bas vctors j,, ar gv by th tsor trasformato
More information10. The Discrete-Time Fourier Transform (DTFT)
Th Discrt-Tim Fourir Transform (DTFT Dfinition of th discrt-tim Fourir transform Th Fourir rprsntation of signals plays an important rol in both continuous and discrt signal procssing In this sction w
More information:2;$-$(01*%<*=,-./-*=0;"%/;"-*
!"#$%'()%"*#%*+,-./-*+01.2(.*3+456789*!"#$%"'()'*+,-."/0.%+1'23"45'46'7.89:89'/' ;8-,"$4351415,8:+#9' Dr. Ptr T. Gallaghr Astrphyscs Rsarch Grup Trnty Cllg Dubln :2;$-$(01*%
More information26 The University of Texas at Austin
Rlaxng th Multvarat Normalty Assumpton n th Smulaton of Transportaton Systm Dpndncs ManWo Ng (corrspondng author) Ph.D. Canddat Th Unvrsty of Txas at Austn Dpartmnt of Cvl, Archtctural, and Envronmntal
More informationON THE INTEGRAL INVARIANTS OF KINEMATICALLY GENERATED RULED SURFACES *
Iranan Journal of Scnc & Tchnology Transacton A ol 9 No A Prntd n Th Islamc Rpublc of Iran 5 Shraz Unvrsty ON TH INTGRAL INARIANTS OF KINMATICALLY GNRATD RULD SURFACS H B KARADAG AND S KLS Dpartmnt of
More informationEstimation: Part 2. Chapter GREG estimation
Chapter 9 Estmaton: Part 2 9. GREG estmaton In Chapter 8, we have seen that the regresson estmator s an effcent estmator when there s a lnear relatonshp between y and x. In ths chapter, we generalzed the
More informationHardy-Littlewood Conjecture and Exceptional real Zero. JinHua Fei. ChangLing Company of Electronic Technology Baoji Shannxi P.R.
Hardy-Littlwood Conjctur and Excptional ral Zro JinHua Fi ChangLing Company of Elctronic Tchnology Baoji Shannxi P.R.China E-mail: fijinhuayoujian@msn.com Abstract. In this papr, w assum that Hardy-Littlwood
More informationFirst Year Examination Department of Statistics, University of Florida
Frst Year Examnaton Department of Statstcs, Unversty of Florda May 7, 010, 8:00 am - 1:00 noon Instructons: 1. You have four hours to answer questons n ths examnaton.. You must show your work to receve
More informationAvailable online at ScienceDirect. Procedia Economics and Finance 17 ( 2014 ) 39 46
Avalabl onln at www.scncdrct.com ScncDrct Procda Economcs and Fnanc 7 ( 204 ) 39 46 Innovaton and Socty 203 Confrnc, IES 203 A masur of ordnal concordanc for th valuaton of Unvrsty courss Donata arasn
More informationThe root mean square value of the distribution is the square root of the mean square value of x: 1/2. Xrms
Background and Rfrnc Matral Probablty and Statstcs Probablty Dstrbuton P(X) s a robablty dstrbuton for obsrvng a valu X n a data st of multl obsrvatons. It can dscrb thr a dscrt ( = 1 to N) data st or
More information1) They represent a continuum of energies (there is no energy quantization). where all values of p are allowed so there is a continuum of energies.
Unbound Stats OK, u untl now, w a dalt solly wt stats tat ar bound nsd a otntal wll. [Wll, ct for our tratnt of t fr artcl and w want to tat n nd r.] W want to now consdr wat ans f t artcl s unbound. Rbr
More informationANALYSIS IN THE FREQUENCY DOMAIN
ANALYSIS IN THE FREQUENCY DOMAIN SPECTRAL DENSITY Dfinition Th spctral dnsit of a S.S.P. t also calld th spctrum of t is dfind as: + { γ }. jτ γ τ F τ τ In othr words, of th covarianc function. is dfind
More informationFitting bivariate losses with phase-type distributions
Scandnavan Actuaral Journal ISSN: 346-238 (Prnt) 65-23 (Onln) Journal hompag: http://www.tandfonln.com/lo/sact2 Fttng bvarat losss wth phas-typ dstrbutons Amn Hassan Zadh & Martn Blodau To ct ths artcl:
More informationOn Parameter Estimation of the Envelope Gaussian Mixture Model
Australan Communcatons Thory Worsho (AusCTW) On Paramtr Estmaton of th Envlo Gaussan Mtur Modl Lnyun Huang Dartmnt of ECSE Monash Unvrsty, Australa Lnyun.Huang@monash.du Y Hong Dartmnt of ECSE Monash Unvrsty,
More informationSupplementary material: Margin based PU Learning. Matrix Concentration Inequalities
Supplementary materal: Margn based PU Learnng We gve the complete proofs of Theorem and n Secton We frst ntroduce the well-known concentraton nequalty, so the covarance estmator can be bounded Then we
More informationSPECTRUM ESTIMATION (2)
SPECTRUM ESTIMATION () PARAMETRIC METHODS FOR POWER SPECTRUM ESTIMATION Gnral consdraton of aramtrc modl sctrum stmaton: Autorgrssv sctrum stmaton: A. Th autocorrlaton mthod B. Th covaranc mthod C. Modfd
More informationChat eld, C. and A.J.Collins, Introduction to multivariate analysis. Chapman & Hall, 1980
MT07: Multvarate Statstcal Methods Mke Tso: emal mke.tso@manchester.ac.uk Webpage for notes: http://www.maths.manchester.ac.uk/~mkt/new_teachng.htm. Introducton to multvarate data. Books Chat eld, C. and
More information1973 AP Calculus AB: Section I
97 AP Calculus AB: Sction I 9 Minuts No Calculator Not: In this amination, ln dnots th natural logarithm of (that is, logarithm to th bas ).. ( ) d= + C 6 + C + C + C + C. If f ( ) = + + + and ( ), g=
More information1- Summary of Kinetic Theory of Gases
Dr. Kasra Etmad Octobr 5, 011 1- Summary of Kntc Thory of Gass - Radaton 3- E4 4- Plasma Proprts f(v f ( v m 4 ( kt 3/ v xp( mv kt V v v m v 1 rms V kt v m ( m 1/ v 8kT m 3kT v rms ( m 1/ E3: Prcntag of
More informationLINEAR REGRESSION ANALYSIS. MODULE VIII Lecture Indicator Variables
LINEAR REGRESSION ANALYSIS MODULE VIII Lecture - 7 Indcator Varables Dr. Shalabh Department of Maematcs and Statstcs Indan Insttute of Technology Kanpur Indcator varables versus quanttatve explanatory
More informationMODEL QUESTION. Statistics (Theory) (New Syllabus) dx OR, If M is the mode of a discrete probability distribution with mass function f
MODEL QUESTION Statstcs (Thory) (Nw Syllabus) GROUP A d θ. ) Wrt dow th rsult of ( ) ) d OR, If M s th mod of a dscrt robablty dstrbuto wth mass fucto f th f().. at M. d d ( θ ) θ θ OR, f() mamum valu
More informationON EISENSTEIN-DUMAS AND GENERALIZED SCHÖNEMANN POLYNOMIALS
ON EISENSTEIN-DUMAS AND GENERALIZED SCHÖNEMANN POLYNOMIALS Anuj Bshno and Sudsh K. Khanduja Dpartmnt of Mathmatcs, Panjab Unvrsty, Chandgarh-160014, Inda. E-mal: anuj.bshn@gmal.com, skhand@pu.ac.n ABSTRACT.
More informationOn Selection of Best Sensitive Logistic Estimator in the Presence of Collinearity
Amrcan Journal of Appld Mathmatcs and Statstcs, 05, Vol. 3, No., 7- Avalabl onln at http://pubs.scpub.com/ajams/3// Scnc and Educaton Publshng DOI:0.69/ajams-3-- On Slcton of Bst Snstv Logstc Estmator
More informationStatistics and Probability Theory in Civil, Surveying and Environmental Engineering
Statstcs and Probablty Theory n Cvl, Surveyng and Envronmental Engneerng Pro. Dr. Mchael Havbro Faber ETH Zurch, Swtzerland Contents o Todays Lecture Overvew o Uncertanty Modelng Random Varables - propertes
More informationΑ complete processing methodology for 3D monitoring using GNSS receivers
7-5-5 NATIONA TECHNICA UNIVERSITY OF ATHENS SCHOO OF RURA AND SURVEYING ENGINEERING DEPARTMENT OF TOPOGRAPHY AORATORY OF GENERA GEODESY Α complt procssng mthodology for D montorng usng GNSS rcvrs Gorg
More information