SIMULATING SURFACE ENERGY FLUX AND SOIL MOISTURE AT THE WENJIANG PBL SITE USING THE LAND DATA ASSIMILATION SYSTEM OF THE UNIVERSITY OF TOKYO

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "SIMULATING SURFACE ENERGY FLUX AND SOIL MOISTURE AT THE WENJIANG PBL SITE USING THE LAND DATA ASSIMILATION SYSTEM OF THE UNIVERSITY OF TOKYO"

Transcription

1 Aual Joural of Hydraulc Egeerg, JSCE, Vol.53, 9, February SIMULATING SURFACE ENERGY FLUX AND SOIL MOISTURE AT THE WENJIANG PBL SITE USING THE LAND DATA ASSIMILATION SYSTEM OF THE UNIVERSITY OF TOKYO Hu LU, Tosho KOIKE, Ku YANG 3, Xagde Xu 4, X LI 5, Hroyuk TSUTSUI, Yueqg LI 6, Xgbg ZHAO 6, ad Katsuor TAMAGAWA 7 Member of JSCE, Ph.D., Researcher, Dept. of Cvl Eg., Uv. of Tokyo (Bukyo-ku, Tokyo , Japa) Member of JSCE, Dr. Eg., Professor, Dept. of Cvl Eg., Uv. of Tokyo (Bukyo-ku, Tokyo , Japa) 3 Member of JSCE, Ph.D., Professor, Ist. of Tbet, Cha Academy of Sceces (Bejg 85, Cha) 4 Professor, Chese Academy of Met. Scece., Cha Met. Adm. (Bejg 8, Cha) 5 Ph.D., Professor, Cold ad Ard Regos Ev. ad Eg. Research Ist., CAS (Lazhou 73, Cha) 6 Professor, Isttute of Plateau Meteorology, Cha Met. Adm. (Chegdu 67, Cha) 7 Researcher, Dept. of Cvl Eg., Uv. of Tokyo (Bukyo-ku, Tokyo , Japa) Ths paper reports a applcato of a Lad Data Assmlato System (LDAS) to the Wejag ste located ear Chegdu, Cha, for the perod from Jauary to March, 8. The LDAS was frst drve by -stu observed mcrometeorologcal data. Smulated eergy fluxes were compared to hourly drect measuremets ad smulated sol mosture cotet was compared to the -stu sol mosture observatos at a depth of 4 cm. The results show that the LDAS well smulated those varables ad thus valdated the capablty of LDAS. To check the possblty of applyg LDAS globally ad smulatg surface eergy ad water budget worldwde, two sets of model output data were used as the drvg data of the LDAS: the Japa Meteorology Agecy (JMA) Model Output Local Tme Seres (), ad the Modfed JMA. The LDAS performace was ot so good whe drve by the orgal JMA data, but mproved after we used modfed data wth some smple lear regresso equatos. Ths result demostrated the feasblty of relably smulatg lad surface fluxes wth a LDAS drve by model outputs. Key Words: Lad Data Assmlato System, Eergy Fluxes, Sol Mosture, Feld Expermets. INTRODUCTION Lad surface processes through whch exchages of water, eergy ad carbo betwee the lad surface ad the atmosphere are realzed, remarkably affect weather ad clmate. Clmate smulatos are especally sestve to the dural ad seasoal cycles of the surface eergy balace ). Lad surface eergy budgets are also very mportat hydrologcal ad ecologcal modelg. The eergy flux ca be measured at a patch scale wth some specal strumets such as traxal soc aemometers, krypto hygrometers ad fe-wre thermocouples. It also ca be estmated at a regoal scale from satellte observatos whe frared mages ad acllary data are avalable. Lad surface models (LSMs) are developed to predct temporal ad spatal patters of lad surface varables,3), but the qualty of the predctos are usually ot so good because of model talzato, parameter ad forcg errors, ad adequate model physcs ad/or resoluto 4,5). The Lad Data Assmlato System (LDAS), developed by mergg observato formato (from groud-based statos, satelltes ad so o) to dyamc models (.e. LSMs), s expected to provde hgh qualty surface eergy ad water flux estmates wth adequate coverage ad resoluto. I ths study, we appled a LDAS developed at the Uversty of Tokyo (LDASUT) 6) for the Wejag ste of a JICA project where a PBL tower had bee bult. The objectves of ths study are: () to evaluate LDASUT a vegetated lad surface usg -stu observatos, ad () to check the feasblty of estmatg areal lad surface eergy ad water fluxes relably usg LDASUT drve by spatally-

2 dstrbuted forcg data. I ths study, LDASUT was drve by Japa Meteorology Agecy (JMA) Model Output Local Tme Seres () data ad smulato results were compared wth drect measuremets. I the followg secto, we brefly descrbe the materals ad methods used ths study, cludg the expermetal ste ad troduce the LDASUT. The smulato results of LDASUT drve by -stu data are descrbed secto 3. I secto 4, the LDASUT was frst drve by data, ad the by modfed MOTLS data to mprove the qualty of the smulato. Fally, we fsh ths paper wth some coclusos.. MATERIALS AND METHODS. Expermetal ste descrpto The Wejag ste s located o a flat farm feld approxmately 9 km west of Chedu cty of Schua provce, Cha. The ste has a elevato of 53 m ad s cetered at 3 44'N lattude, 3 5'E logtude. It s ear the edge of Tbeta Plateau ad the water vapor corrdor of the Asa mosoo. A PBL tower, establshed by a JICA project, was bult ths ste Feb. 7. Observatos at the PBL tower clude wd speed ad drecto at four levels, ar temperature ad humdty, turbuleces, fluxes of eergy ad CO, sol mosture ad temperature profles, sol heat flux, solar ad atmospherc radato, ad precptato.. LDASUT I ths study, the lad surface eergy ad water budget was smulated usg the LDASUT 6). Ths system cossts of a LSM to calculate surface fluxes ad sol mosture, a radatve trasfer model (RTM) to estmate mcrowave brghtess temperature, ad a optmzato scheme to search for optmal values of sol mosture through mmzg the dfferece betwee modeled ad observed brghtess temperature. The LSM s a Smple Bosphere model (SB) ). The RTM used the LDASUT has two compoets: volume scatterg ad surface scatterg parts 7). The volume scatterg part smulates the radatve trasfer process sde the sol layer by a 4-stream based RTM whch the multply scatterg effects of a dry sol medum s calculated by the dese meda radatve trasfer model (DMRT) 8). The surface scatterg part smulates the surface scatterg effects at the ladatmosphere terface by the Advaced Itegral Equato Method (AIEM) 9). The mmzato scheme s a shuffled complex evoluto method. The tal parameters of LDASUT are obtaed from a global data set; for example, the leaf area dex (LAI) from Moderate Resoluto Imagg Spectroradometer (MODIS) data; ad the sol ad vegetato parameters from The Iteratoal Satellte Lad Surface Clmatology Project (ISLSCP). The satellte observato data s from the Advaced Mcrowave Scag Radometer for the Earth Observg System (AMSR-E) brghtess temperature data. The meteorologcal drvg data of the LDASUT ca be ether weather model outputs or -stu observato..3 Statstcal aalyss of the smulato results The smulato results (M ) of the LDASUT are compared agast the -stu feld measuremets (O ), o the bass of three statstcal aalyses: MBE = ( M O ) / () RMSE = NSEE = = = = ( M O ) / () ( M O ) / ( O ) (3) = where s the total hourly observato pots; MBE s the mea bas error; RMSE s the Root Mea Square Error; ad NSEE s the Normalzed Stadard Error of the Estmato, deotg a estmato of relatve ucertaty. 3. SIMULATION DRIVEN BY IN-SITU DATA As the frst step ths study, we performed seaso log rus from Ja. to Mar. 8 (9 days) wth PBL observato as the forcg data of the LDASUT. Agrculture/C3 grasslad the stadard SB parameters for vegetato was used for the smulato. The default sol parameters (texture, thermal ad hydraulc propertes) were derved from the ISLSCP Itatve II sol data. Ths smulato s called PBL. To avod aomalous results, data are rejected whe () latet heat flux was less tha - W/m or () the resdual eergy was less tha - W/m. After data flterg, we retaed 99 data sets from the orgal 6 data sets. 3. Surface Eergy Budget Fgure shows the mothly mea dural chages of et radato (hereafter referred to as R), latet heat flux (le), sesble heat flux (Hs), ad sol heat flux (G), from the top to the bottom row, respectvely. The ope cycle represets the drect measuremets ad the sold le represets the results of PBL. From fgure a, t s clear that PBL smulated R wth hgh accuracy for both the peak ad dural patters. Ths was because -stu observed dowward radato was used as forcg data ad

3 le(w/m/m) Hs(w/m/m) G(w/m/m) 3 - R(w/m/m) (a) Mothly Mea Dural Chage of R Measurmets PBL (b) Mothly Mea Dural Chage of le (c) Mothly Mea Dural Chage of Hs (d) Mothly Mea Dural Chage of G Fg. Comparso of mothly mea dural chage of (a) R, (b) le, (c) Hs ad (d) G of PBL agast drect measuremet. SB calculates R from the four compoets of radato budgets. As show fgure b-d, t s obvous that PBL captured the temporal varato characterstcs of le, Hs ad G. Smulated_R_PBL Smulated_lE_PBL Measured R Measured le Fg. Scatterplots of R, le, Hs ad G of PBL agast drect measuremets. Fgure shows scatterplots of smulated R, G, le, ad Hs, agast drect measuremets. The squared correlato coeffcets are.99,.8,.89 ad.85. As show table, PBL slghtly overestmated G ad uderestmated le, whle t well estmated R. The overestmato of G may be to the result of measuremet errors of sol heat flux ad the uderestmato of eergy storage the upper sol layer above the heat flux plate where the heterogeety creased as crop roots developed. The dscrepaces le may be partly to the result of strumet errors. Accordg to Mauder et al. ), the accuracy of sesble heat flux measuremet s Smulated_G_PBL Smulated_Hs_PBL Measured G Measured Hs aroud -3 W/m, ad -4 W/m for latet heat flux. Moreover, cosderg the fact that PBL smulato ad -stu observato have dfferet scales, ad the fact that the resdual eergy (Re) of drect measuremet (Re=R-lE-Hs-G, show table ) s comparable to the largest RMSE of eergy compoets, the qualty of surface eergy budget smulato of PBL s acceptable. The capablty of LDASUT to smulate lad surface fluxes relably s the valdated. Table. Three moths averaged eergy compoets (ut: W/m ) R le Hs G Re PBL Surface temperature ad upward log-wave radato Temperature s a very mportat progostc state varable o the lad surface. LDASUT s able to provde vegetato, groud surface ad deep sol temperatures. Ufortuately, the frared thermometer used at the Wejag ste was broke durg the study perod ad so we do ot have drect groud surface temperature measuremets. Accordg to the Stefa-Boltzma law, upward log-wave radato (ULR) s a good surrogate of lad surface temperature. We therefore compared the smulated ULR wth the drect measuremets. ULR (W/m/m) Table. Statstc aalyss of eergy compoets of PBL MBE RMSE NSEE R (W/m ) % le (W/m ) % Hs (W/m ) % G (W/m )..9 65% Upward Logwave Radato PBL Fg. 3 Comparso of hourly log-wave radato of PBL agast drect measuremets. Fgure 3 shows a comparso of hourly ULR. It s apparet that PBL geerated cosstet temporal varatos of ULR. The squared correlato coeffcet was.88; MBE -4. W/m ; RMSE.8 W/m ad NSEE 3%. 3.3 Sol Water Cotet Fgure 4 shows a tme seres of the volumetrc sol mosture cotet observed at 4 cm depth (th le) ad those geerated by PBL (thck le). I-stu observed precptato s also plotted. We foud that the observed sol mosture dd ot chage much

4 durg ths perod, ragg from.3 to.33. PBL predcted the mosture peak good agreemet wth drect measuremets, for both the occurrg tme ad values. The gaps betwee PBL sol mosture ad observed oes get larger the dryg processes. Ths s partly due because -stu sol mosture s measured at a depth of 4 cm, whch s geerally deeper tha the peetrato depth of AMSR-E. The scale dfferece of the AMSR-E observatos ad -stu oes also cotrbute to such dscrepaces. Geerally ad statstcally, PBL estmated sol mosture wth hgh qualty, cosderg that MBE s -.; RMSE s. ad NSEE s 9%. Mv.4.3. Ra_Obs Measurmets(4cm) PBL SIMULATION DRIVEN BY MODEL OUTPUT From a aalyss of the PBL smulato secto 3, t s clear that LDASUT ca correctly smulate the surface eergy ad water budget whe t s drve by -stu observed forcg data. I clmate studes ad umercal weather predctos, the spatal dstrbuto formato of eergy ad water fluxes s very essetal. To smulate lad surface fluxes at a regoal or global scale, spatallydstrbuted meteorologcal forcg data are eeded. Such forcg data were oly avalable from model outputs, ad, as metoed secto, JMA data was selected ths study. Same as the PBL smulato, a smulato was coducted by usg the orgal as meteorologcal forcg data ad s called M_O. 4. Surface Eergy Budget of M_O Table 3 shows the statstcal results of the eergy fluxes of M_O. It s clear that the qualty of M_O s much worse tha that of PBL. The MBE of R s larger tha 5 W/m, whch s the accuracy Table. 3 Statstc aalyss of radato compoets of M_O MBE RMSE NSEE Fg. 4 Comparg smulated sol mosture cotet wth drect measuremets R (W/m ) % le (W/m ) % Hs (W/m ) % G (W/m ) % Ra(mm) of solar radato measuremet. The NSEE of Hs ad G are larger tha %. Therefore, the qualty of M_O s ot acceptable ad we ca ot drectly apply data as forcg data for LDASUT. 4. Modfcato to data To ascerta the reaso why M_O performace s ot so good, we compared forcg data wth -stu observatos (a) Mothly mea dual chage shortwave dowward radato Measuremet (b) Mothly Ja. mea dual 4 chage logwave Feb. dowward 48 radato Mar Measuremet Fg. 5 Mothly mea dural chages dow ward radato of ad -stu PBL observato From a aalyss of mothly mea dural radato (see Fg. 5a), t s clear that the peak of the dowward short wave radato of was much bgger tha that of -stu observatos, whle the dowward log-wave radato of was aroud W/m smaller tha that of PBL observatos(fg. 5b). The pressure of was slghtly larger (mea hpa) tha that of PBL observato (mea 956.9hPa). The mea ar temperature of was 8.8K, almost the same as that of PBL observato, 8.5K (a) Comparso of Precptato (mm/hour) (b) Comparso of accumulated precptato (mm) Fg. 6 Hourly precptato ad accumulated values of ad -stu observato There are some obvous dffereces betwee MOTLS precptato data ad PBL observato (see Fg. 6). gave a larger precptato tha PBL observato. The accumulated precptato of ths perod was 3.3 mm, whle that of PBL observato was just 56. mm. Fortuately,

5 as demostrated by Yag et al. 6), LDASUT s able to partly overcome such bases put precptato data, because t drectly assmlates AMSR-E brghtess data to correct the sol mosture states. Through a comparso of forcg data ad -stu observed data, t was clear that the large overestmato dowward radato s the ma reaso that M_O faled to correctly smulate the lad surface eergy budget. To mtgate such a obvous overestmato, we modfed the JMA dowward shortwave radato data by usg lear equatos acqured from the regresso aalyss of the mothly mea dural cycle data. Aalogously, the dowward log-wave radato data was modfed usg a lear regresso equato of all three moth data. The correcto equatos are as follows: RSW _ C = max[,( RSW_ O 5.) /.6435] (4) RLW _ C = ( RLW_ O ) /.9557 (5) where RSW s the dowward short wave radato, RLW s the dowward log-wave radato, _C meas the modfed value, ad _O meas the orgal value. After applyg equatos 4 ad 5 to all dowward radato data, a ew data set, modfed, was created. Aalogously, the smulato drve by the modfed data s called M_C. 4.3 Results of M_O ad M_C As show table 4, comparg table 3, t s clear that M_C estmates surface eergy fluxes better tha M_O ; as all tems table 4 are smaller tha those table 3. Ths meas that the performace of LDASUT s mproved usg the modfed stead of the orgal. Table. 4 Statstcal aalyss of radato compoets of M_C MBE RMSE NSEE R (W/m ) % le (W/m ) % Hs (W/m ) % G (W/m ) % Fgure 7 shows the mothly mea dural chages of the surface eergy compoets. Comparg M_O (dash le) ad M_C (sold le) agast the drect measuremets (ope cycles), t s clear that M_C geerally produced better results tha M_O. Ths meas the performace of the eergy budget smulato ca be mproved through a smple lear modfcato. Wth cosderg measuremet accuracy ad scale problems, the qualty of M_C s reasoable for the bg doma smulatos. Fgure 8 shows a comparso of the mothly mea dural chages of ULR. It s clear that M_O uderestmated ULR at ght tme, wth a MBE of - 7. W/m ; whle M_C estmated ULR wth better accuracy, wth a MBE of -4.4 W/m. Fgure 9 shows a tme seres of the hourly sol mosture of M_O (dash le), M_C (thck le) ad -stu observato (th le). The results of M_O ad M_C are acceptable, because the stregth of LDASUT, whch optmzed sol parameters ad assmlatg sol mosture. But sometmes M_O ad M_C dd ot follow the R(w/m/m) le(w/m/m) Hs(w/m/m) G(w/m/m) (a) Mothly Mea Dural Chage of R Measurmets M_O M_C (b) Mothly Mea Dural Chage of le (c) Mothly Mea Dural Chage of Hs (d) Mothly Mea Dural Chage of G Fg. 7 Comparso of mothly mea dural chage of (a) R, (b) le, (c) Hs ad (d) G of M_O ad M_C agast drect measuremet. ULR (w/m/m) Ra_ Obs(4cm) 7 8 M_O M_C Mv Mothly Mea Dural Chage of ULR M_O M_C Ja Feb Mar Fg. 8 Comparso of mothly mea dural chage of ULR of M_O ad M_C agast drect measuremet. Fg. 9 Comparg smulated sol mosture cotet wth drect measuremets Ra(mm)

6 tedecy of the drect measuremets. Ths s partly to the result of the bg dfferece betwee precptato ad the observed oe, as show fgure 6. Statstcally, M_O estmates sol mosture wth a MBE of., a RMSE of. ad NSEE of 8%, whle those of M_C are -.,. ad 7%, respectvely. By comparg M_O ad M_C results wth -stu measuremets, the advatages of modfed were verfed. Thus the possblty of geeratg relable spatal dstrbuto of lad surface fluxes wth LDASUT drve by modfed data ca be cofrmed. 5. CONCLUSIONS LDAS s expected to provde accurate temporal ad spatal cotuous lad surface varables that wll promote research felds such as clmate chage, weather forecastg, ad hydrologcal modelg. I ths study, the LDASUT was frstly drve by -stu observato data to valdate ts capablty to estmate lad surface fluxes (PBL). The, to check the feasblty to estmate the spatal patter of lad surface fluxes wth usg LDASUT ad model output forcg data, LDASUT was drve by two model output data sets: the orgal (M_O) ad a modfed (M_C). Smulato results of R, le, Hs, G, ULR ad sol mosture cotet were compared agast the drect measuremets. Our results show that the smulato results of PBL geerally well agreed wth the drect measuremet, ad the dffereces betwee -stu observato ad smulato are geerally smaller tha strumetal observato errors. Therefore, we valdated that LDASUT ca relably smulate lad surface fluxes. The dscrepaces betwee the smulated fluxes of M_O ad the drect measuremets are apprecable; whle M_C, a smple modfcato from M_O usg lear regresso equatos, estmated those fluxes wth mproved accuracy. Because of the uque feature of the LDASUT to optmze sol parameters ad the assmlate sol mosture, the smulated sol mosture of M_O ad M_C were good qualty. From these ecouragg results, t s possble to relably estmate lad surface varables usg the LDAS drve by model outputs. It s especally mportat for rug the GCM ad for studes remote areas where -stu mcrometeorologcal observato s ot avalable. We also foud that the qualty of the le ad G smulatos was ot as good as that of R. Ths could be the result of strumetal errors, dfferet scales of the LDASUT ad -stu observato, the heterogeety problem the calculato of eergy storage, ad the model defceces the structure ad parameters. Further efforts are eeded both expermetal ad model research. ACKNOWLEDGMENTS: Ths study was carred out as part of a JICA project; for whch the authors express ther great grattude. We also thak our local colleagues at the Wejag ste ad JMA for provdg ecessary data set. REFERENCES ) Betts AK, Ball JH, Beljaars ACM et al.: The lad surfaceatmosphere teracto: a revew based o observatoal ad global modelg perspectves. J. Geophys. Res.,, 79 75, 996. ) Sellers PJ, Radall DA, Collatz GJ et al.: A revsed lad surface parameterzato (SB) for atmospherc GCMs. Part I: model formulato. J. of Clmate, 9, , ) Gao, Z., N. Chae, J. Km, J. Hog, T. Cho, ad H. Lee: Modelg of surface eergy parttog, surface temperature, ad sol wetess the Tbeta prare usg the Smple Bosphere Model (SB), J. Geophys. Res., 9, D6, do:.9/3jd489, 4. 4) Ptma, A.J ad PILPS team co-authors: Key results ad mplcatos from phase (c) of the project for tercomparso of lad-surface parameterzato schemes, Clm. Dyamcs, , ) Ku Yag ad co-authors: Ital CEOP-based revew of the predcto skll of operatoal geeral crculato models ad lad surface models, JMSJ, Vol. 85A, pp 9-4, 7. 6) Ku YANG, Takahro WATANABE, et al: A Autocalbrato System to Assmlate AMSR-E data to a Lad Surface Model for Estmatg Sol Mosture ad Surface Eergy Budget, JMSJ, Vol. 85A, pp 9-4, 7. 7) Lu, H., T. Koke, N. Hrose, M. Morta, H. Fuj, D.N. Kura, T. Graf, ad H. Tsutsu: A basc study o sol mosture algorthm usg groud based observatos uder dry codtos. JSCE, 5, 7-, 6. 8) We, B, L. Tsag, D. P. Webreer, ad A. Ishmura: Dese meda radatve trasfer theory: comparso wth expermet ad applcato to mcrowave remote sesg ad polarmetry, IEEE Tras. o Geosc. Remote Sesg, 8, 46-59, 99. 9) K. S. Che, T. D. Wu, L. Tsag, Q. L, J. C. Sh, ad A. K. Fug: Emsso of rough surfaces calculated by the tegral equato method wth comparso to three-dmesoal momet method Smulatos, IEEE Tras. o Geosc. Remote Sesg, vol. 4, pp. 9-, 3. ) Mauder, M., C. Lebethal, M. Gockede, J.-P. Leps, F. Beyrch, ad T. Foke: Processg ad qualty cotrol of flux data durg LITFASS-3. Boudary-Layer Meteorology :67 88, 6. (Receved September 3, 8)

SPATIAL RAINFALL FIELD SIMULATION WITH RANDOM CASCADE INTRODUCING OROGRAPHIC EFFECTS ON RAINFAL

SPATIAL RAINFALL FIELD SIMULATION WITH RANDOM CASCADE INTRODUCING OROGRAPHIC EFFECTS ON RAINFAL Proc. of the d Asa Pacfc Assocato of Hydrology ad Water Resources (APHW) Coferece, July 5-8, 4, Sutec Sgapore Iteratoal Coveto Exhbto Cetre, Sgapore, vol., pp. 67-64, 4 SPATIAL RAINFALL FIELD SIMULATION

More information

Lecture 7. Confidence Intervals and Hypothesis Tests in the Simple CLR Model

Lecture 7. Confidence Intervals and Hypothesis Tests in the Simple CLR Model Lecture 7. Cofdece Itervals ad Hypothess Tests the Smple CLR Model I lecture 6 we troduced the Classcal Lear Regresso (CLR) model that s the radom expermet of whch the data Y,,, K, are the outcomes. The

More information

Bootstrap Method for Testing of Equality of Several Coefficients of Variation

Bootstrap Method for Testing of Equality of Several Coefficients of Variation Cloud Publcatos Iteratoal Joural of Advaced Mathematcs ad Statstcs Volume, pp. -6, Artcle ID Sc- Research Artcle Ope Access Bootstrap Method for Testg of Equalty of Several Coeffcets of Varato Dr. Navee

More information

Functions of Random Variables

Functions of Random Variables Fuctos of Radom Varables Chapter Fve Fuctos of Radom Varables 5. Itroducto A geeral egeerg aalyss model s show Fg. 5.. The model output (respose) cotas the performaces of a system or product, such as weght,

More information

Chapter Business Statistics: A First Course Fifth Edition. Learning Objectives. Correlation vs. Regression. In this chapter, you learn:

Chapter Business Statistics: A First Course Fifth Edition. Learning Objectives. Correlation vs. Regression. In this chapter, you learn: Chapter 3 3- Busess Statstcs: A Frst Course Ffth Edto Chapter 2 Correlato ad Smple Lear Regresso Busess Statstcs: A Frst Course, 5e 29 Pretce-Hall, Ic. Chap 2- Learg Objectves I ths chapter, you lear:

More information

best estimate (mean) for X uncertainty or error in the measurement (systematic, random or statistical) best

best estimate (mean) for X uncertainty or error in the measurement (systematic, random or statistical) best Error Aalyss Preamble Wheever a measuremet s made, the result followg from that measuremet s always subject to ucertaty The ucertaty ca be reduced by makg several measuremets of the same quatty or by mprovg

More information

Research on SVM Prediction Model Based on Chaos Theory

Research on SVM Prediction Model Based on Chaos Theory Advaced Scece ad Techology Letters Vol.3 (SoftTech 06, pp.59-63 http://dx.do.org/0.457/astl.06.3.3 Research o SVM Predcto Model Based o Chaos Theory Sog Lagog, Wu Hux, Zhag Zezhog 3, College of Iformato

More information

Multiple Regression. More than 2 variables! Grade on Final. Multiple Regression 11/21/2012. Exam 2 Grades. Exam 2 Re-grades

Multiple Regression. More than 2 variables! Grade on Final. Multiple Regression 11/21/2012. Exam 2 Grades. Exam 2 Re-grades STAT 101 Dr. Kar Lock Morga 11/20/12 Exam 2 Grades Multple Regresso SECTIONS 9.2, 10.1, 10.2 Multple explaatory varables (10.1) Parttog varablty R 2, ANOVA (9.2) Codtos resdual plot (10.2) Trasformatos

More information

Statistics Descriptive and Inferential Statistics. Instructor: Daisuke Nagakura

Statistics Descriptive and Inferential Statistics. Instructor: Daisuke Nagakura Statstcs Descrptve ad Iferetal Statstcs Istructor: Dasuke Nagakura (agakura@z7.keo.jp) 1 Today s topc Today, I talk about two categores of statstcal aalyses, descrptve statstcs ad feretal statstcs, ad

More information

Journal of Water and Soil Vol. 26, No. 1, Mar-Apr 2012, p Kriging. (

Journal of Water and Soil Vol. 26, No. 1, Mar-Apr 2012, p Kriging. ( Joural of Water ad Sol Vol. 26, No. 1, Mar-Apr 212, p. 53-64 ( ) 53-64. 1391 1 26 *2 1-89/7/26: 9/8/15:.. (1386-87 1361-62) 26 32.. (GPI) (IDW). (Co-Krgg) (Krgg) (RBF) (LPI) 64/46 6/49 77/2 66/86 IDW RBF.

More information

Statistics MINITAB - Lab 5

Statistics MINITAB - Lab 5 Statstcs 10010 MINITAB - Lab 5 PART I: The Correlato Coeffcet Qute ofte statstcs we are preseted wth data that suggests that a lear relatoshp exsts betwee two varables. For example the plot below s of

More information

Convergence of the Desroziers scheme and its relation to the lag innovation diagnostic

Convergence of the Desroziers scheme and its relation to the lag innovation diagnostic Covergece of the Desrozers scheme ad ts relato to the lag ovato dagostc chard Méard Evromet Caada, Ar Qualty esearch Dvso World Weather Ope Scece Coferece Motreal, August 9, 04 o t t O x x x y x y Oservato

More information

2006 Jamie Trahan, Autar Kaw, Kevin Martin University of South Florida United States of America

2006 Jamie Trahan, Autar Kaw, Kevin Martin University of South Florida United States of America SOLUTION OF SYSTEMS OF SIMULTANEOUS LINEAR EQUATIONS Gauss-Sedel Method 006 Jame Traha, Autar Kaw, Kev Mart Uversty of South Florda Uted States of Amerca kaw@eg.usf.edu Itroducto Ths worksheet demostrates

More information

A Helmholtz energy equation of state for calculating the thermodynamic properties of fluid mixtures

A Helmholtz energy equation of state for calculating the thermodynamic properties of fluid mixtures A Helmholtz eergy equato of state for calculatg the thermodyamc propertes of flud mxtures Erc W. Lemmo, Reer Tller-Roth Abstract New Approach based o hghly accurate EOS for the pure compoets combed at

More information

A Combination of Adaptive and Line Intercept Sampling Applicable in Agricultural and Environmental Studies

A Combination of Adaptive and Line Intercept Sampling Applicable in Agricultural and Environmental Studies ISSN 1684-8403 Joural of Statstcs Volume 15, 008, pp. 44-53 Abstract A Combato of Adaptve ad Le Itercept Samplg Applcable Agrcultural ad Evrometal Studes Azmer Kha 1 A adaptve procedure s descrbed for

More information

Quantitative analysis requires : sound knowledge of chemistry : possibility of interferences WHY do we need to use STATISTICS in Anal. Chem.?

Quantitative analysis requires : sound knowledge of chemistry : possibility of interferences WHY do we need to use STATISTICS in Anal. Chem.? Ch 4. Statstcs 4.1 Quattatve aalyss requres : soud kowledge of chemstry : possblty of terfereces WHY do we eed to use STATISTICS Aal. Chem.? ucertaty ests. wll we accept ucertaty always? f ot, from how

More information

Comparison of Parameters of Lognormal Distribution Based On the Classical and Posterior Estimates

Comparison of Parameters of Lognormal Distribution Based On the Classical and Posterior Estimates Joural of Moder Appled Statstcal Methods Volume Issue Artcle 8 --03 Comparso of Parameters of Logormal Dstrbuto Based O the Classcal ad Posteror Estmates Raja Sulta Uversty of Kashmr, Sragar, Ida, hamzasulta8@yahoo.com

More information

VOL. 3, NO. 11, November 2013 ISSN ARPN Journal of Science and Technology All rights reserved.

VOL. 3, NO. 11, November 2013 ISSN ARPN Journal of Science and Technology All rights reserved. VOL., NO., November 0 ISSN 5-77 ARPN Joural of Scece ad Techology 0-0. All rghts reserved. http://www.ejouralofscece.org Usg Square-Root Iverted Gamma Dstrbuto as Pror to Draw Iferece o the Raylegh Dstrbuto

More information

residual. (Note that usually in descriptions of regression analysis, upper-case

residual. (Note that usually in descriptions of regression analysis, upper-case Regresso Aalyss Regresso aalyss fts or derves a model that descres the varato of a respose (or depedet ) varale as a fucto of oe or more predctor (or depedet ) varales. The geeral regresso model s oe of

More information

: At least two means differ SST

: At least two means differ SST Formula Card for Eam 3 STA33 ANOVA F-Test: Completely Radomzed Desg ( total umber of observatos, k = Number of treatmets,& T = total for treatmet ) Step : Epress the Clam Step : The ypotheses: :... 0 A

More information

Correlation and Regression Analysis

Correlation and Regression Analysis Chapter V Correlato ad Regresso Aalss R. 5.. So far we have cosdered ol uvarate dstrbutos. Ma a tme, however, we come across problems whch volve two or more varables. Ths wll be the subject matter of the

More information

Statistics: Unlocking the Power of Data Lock 5

Statistics: Unlocking the Power of Data Lock 5 STAT 0 Dr. Kar Lock Morga Exam 2 Grades: I- Class Multple Regresso SECTIONS 9.2, 0., 0.2 Multple explaatory varables (0.) Parttog varablty R 2, ANOVA (9.2) Codtos resdual plot (0.2) Exam 2 Re- grades Re-

More information

Lecture Notes Types of economic variables

Lecture Notes Types of economic variables Lecture Notes 3 1. Types of ecoomc varables () Cotuous varable takes o a cotuum the sample space, such as all pots o a le or all real umbers Example: GDP, Polluto cocetrato, etc. () Dscrete varables fte

More information

Analysis of System Performance IN2072 Chapter 5 Analysis of Non Markov Systems

Analysis of System Performance IN2072 Chapter 5 Analysis of Non Markov Systems Char for Network Archtectures ad Servces Prof. Carle Departmet of Computer Scece U Müche Aalyss of System Performace IN2072 Chapter 5 Aalyss of No Markov Systems Dr. Alexader Kle Prof. Dr.-Ig. Georg Carle

More information

Econometric Methods. Review of Estimation

Econometric Methods. Review of Estimation Ecoometrc Methods Revew of Estmato Estmatg the populato mea Radom samplg Pot ad terval estmators Lear estmators Ubased estmators Lear Ubased Estmators (LUEs) Effcecy (mmum varace) ad Best Lear Ubased Estmators

More information

(Monte Carlo) Resampling Technique in Validity Testing and Reliability Testing

(Monte Carlo) Resampling Technique in Validity Testing and Reliability Testing Iteratoal Joural of Computer Applcatos (0975 8887) (Mote Carlo) Resamplg Techque Valdty Testg ad Relablty Testg Ad Setawa Departmet of Mathematcs, Faculty of Scece ad Mathematcs, Satya Wacaa Chrsta Uversty

More information

Simple Linear Regression - Scalar Form

Simple Linear Regression - Scalar Form Smple Lear Regresso - Scalar Form Q.. Model Y X,..., p..a. Derve the ormal equatos that mmze Q. p..b. Solve for the ordary least squares estmators, p..c. Derve E, V, E, V, COV, p..d. Derve the mea ad varace

More information

Ordinary Least Squares Regression. Simple Regression. Algebra and Assumptions.

Ordinary Least Squares Regression. Simple Regression. Algebra and Assumptions. Ordary Least Squares egresso. Smple egresso. Algebra ad Assumptos. I ths part of the course we are gog to study a techque for aalysg the lear relatoshp betwee two varables Y ad X. We have pars of observatos

More information

Comparative Analysis of Single and Mixed Spatial Interpolation Methods for Variability Prediction of Temperature Prediction

Comparative Analysis of Single and Mixed Spatial Interpolation Methods for Variability Prediction of Temperature Prediction Vol. 6, No. 1, Jauary, 2013 Comparatve Aalyss of Sgle ad Mxed Spatal Iterpolato Methods for Varablty Predcto of Temperature Predcto Yuhua Gu, Lgme Su ad J Wag Jagsu Egeerg Ceter of Network Motorg, School

More information

12.2 Estimating Model parameters Assumptions: ox and y are related according to the simple linear regression model

12.2 Estimating Model parameters Assumptions: ox and y are related according to the simple linear regression model 1. Estmatg Model parameters Assumptos: ox ad y are related accordg to the smple lear regresso model (The lear regresso model s the model that says that x ad y are related a lear fasho, but the observed

More information

PGE 310: Formulation and Solution in Geosystems Engineering. Dr. Balhoff. Interpolation

PGE 310: Formulation and Solution in Geosystems Engineering. Dr. Balhoff. Interpolation PGE 30: Formulato ad Soluto Geosystems Egeerg Dr. Balhoff Iterpolato Numercal Methods wth MATLAB, Recktewald, Chapter 0 ad Numercal Methods for Egeers, Chapra ad Caale, 5 th Ed., Part Fve, Chapter 8 ad

More information

Chapter Statistics Background of Regression Analysis

Chapter Statistics Background of Regression Analysis Chapter 06.0 Statstcs Backgroud of Regresso Aalyss After readg ths chapter, you should be able to:. revew the statstcs backgroud eeded for learg regresso, ad. kow a bref hstory of regresso. Revew of Statstcal

More information

Generating Multivariate Nonnormal Distribution Random Numbers Based on Copula Function

Generating Multivariate Nonnormal Distribution Random Numbers Based on Copula Function 7659, Eglad, UK Joural of Iformato ad Computg Scece Vol. 2, No. 3, 2007, pp. 9-96 Geeratg Multvarate Noormal Dstrbuto Radom Numbers Based o Copula Fucto Xaopg Hu +, Jam He ad Hogsheg Ly School of Ecoomcs

More information

Comparative study of four methods for estimating Weibull parameters for Halabja, Iraq

Comparative study of four methods for estimating Weibull parameters for Halabja, Iraq Iteratoal Joural of Physcal Sceces ol. 8(5), pp. 86-9, 9 February, 3 Avalable ole at http://www.academcjourals.org/ijps DOI:.5897/IJPS.697 ISSN 99-95 3 Academc Jourals Full Legth Research Paper Comparatve

More information

Global Warming and Caspian Sea Level Fluctuations

Global Warming and Caspian Sea Level Fluctuations Iteratoal Coferece o Water Resources ad Clmate Chage the MENA Rego -4 November 008, Muscat, Oma Global Warmg ad Caspa Sea Level Fluctuatos Reza Ardakaa, Seyed Hamed Alemohammad Asssstat Professor, Departmet

More information

ε. Therefore, the estimate

ε. Therefore, the estimate Suggested Aswers, Problem Set 3 ECON 333 Da Hugerma. Ths s ot a very good dea. We kow from the secod FOC problem b) that ( ) SSE / = y x x = ( ) Whch ca be reduced to read y x x = ε x = ( ) The OLS model

More information

i 2 σ ) i = 1,2,...,n , and = 3.01 = 4.01

i 2 σ ) i = 1,2,...,n , and = 3.01 = 4.01 ECO 745, Homework 6 Le Cabrera. Assume that the followg data come from the lear model: ε ε ~ N, σ,,..., -6. -.5 7. 6.9 -. -. -.9. -..6.4.. -.6 -.7.7 Fd the mamum lkelhood estmates of,, ad σ ε s.6. 4. ε

More information

PROJECTION PROBLEM FOR REGULAR POLYGONS

PROJECTION PROBLEM FOR REGULAR POLYGONS Joural of Mathematcal Sceces: Advaces ad Applcatos Volume, Number, 008, Pages 95-50 PROJECTION PROBLEM FOR REGULAR POLYGONS College of Scece Bejg Forestry Uversty Bejg 0008 P. R. Cha e-mal: sl@bjfu.edu.c

More information

Analysis of Variance with Weibull Data

Analysis of Variance with Weibull Data Aalyss of Varace wth Webull Data Lahaa Watthaacheewaul Abstract I statstcal data aalyss by aalyss of varace, the usual basc assumptos are that the model s addtve ad the errors are radomly, depedetly, ad

More information

Chapter 11 Systematic Sampling

Chapter 11 Systematic Sampling Chapter stematc amplg The sstematc samplg techue s operatoall more coveet tha the smple radom samplg. It also esures at the same tme that each ut has eual probablt of cluso the sample. I ths method of

More information

Chapter 4 (Part 1): Non-Parametric Classification (Sections ) Pattern Classification 4.3) Announcements

Chapter 4 (Part 1): Non-Parametric Classification (Sections ) Pattern Classification 4.3) Announcements Aoucemets No-Parametrc Desty Estmato Techques HW assged Most of ths lecture was o the blacboard. These sldes cover the same materal as preseted DHS Bometrcs CSE 90-a Lecture 7 CSE90a Fall 06 CSE90a Fall

More information

STA 108 Applied Linear Models: Regression Analysis Spring Solution for Homework #1

STA 108 Applied Linear Models: Regression Analysis Spring Solution for Homework #1 STA 08 Appled Lear Models: Regresso Aalyss Sprg 0 Soluto for Homework #. Let Y the dollar cost per year, X the umber of vsts per year. The the mathematcal relato betwee X ad Y s: Y 300 + X. Ths s a fuctoal

More information

Generalized Convex Functions on Fractal Sets and Two Related Inequalities

Generalized Convex Functions on Fractal Sets and Two Related Inequalities Geeralzed Covex Fuctos o Fractal Sets ad Two Related Iequaltes Huxa Mo, X Su ad Dogya Yu 3,,3School of Scece, Bejg Uversty of Posts ad Telecommucatos, Bejg,00876, Cha, Correspodece should be addressed

More information

PTAS for Bin-Packing

PTAS for Bin-Packing CS 663: Patter Matchg Algorthms Scrbe: Che Jag /9/00. Itroducto PTAS for B-Packg The B-Packg problem s NP-hard. If we use approxmato algorthms, the B-Packg problem could be solved polyomal tme. For example,

More information

Chapter 11 The Analysis of Variance

Chapter 11 The Analysis of Variance Chapter The Aalyss of Varace. Oe Factor Aalyss of Varace. Radomzed Bloc Desgs (ot for ths course) NIPRL . Oe Factor Aalyss of Varace.. Oe Factor Layouts (/4) Suppose that a expermeter s terested populatos

More information

We have already referred to a certain reaction, which takes place at high temperature after rich combustion.

We have already referred to a certain reaction, which takes place at high temperature after rich combustion. ME 41 Day 13 Topcs Chemcal Equlbrum - Theory Chemcal Equlbrum Example #1 Equlbrum Costats Chemcal Equlbrum Example #2 Chemcal Equlbrum of Hot Bured Gas 1. Chemcal Equlbrum We have already referred to a

More information

9.1 Introduction to the probit and logit models

9.1 Introduction to the probit and logit models EC3000 Ecoometrcs Lecture 9 Probt & Logt Aalss 9. Itroducto to the probt ad logt models 9. The logt model 9.3 The probt model Appedx 9. Itroducto to the probt ad logt models These models are used regressos

More information

Estimation of the Loss and Risk Functions of Parameter of Maxwell Distribution

Estimation of the Loss and Risk Functions of Parameter of Maxwell Distribution Scece Joural of Appled Mathematcs ad Statstcs 06; 4(4): 9- http://www.scecepublshggroup.com/j/sjams do: 0.648/j.sjams.060404. ISSN: 76-949 (Prt); ISSN: 76-95 (Ole) Estmato of the Loss ad Rsk Fuctos of

More information

Unsupervised Learning and Other Neural Networks

Unsupervised Learning and Other Neural Networks CSE 53 Soft Computg NOT PART OF THE FINAL Usupervsed Learg ad Other Neural Networs Itroducto Mture Destes ad Idetfablty ML Estmates Applcato to Normal Mtures Other Neural Networs Itroducto Prevously, all

More information

Arithmetic Mean and Geometric Mean

Arithmetic Mean and Geometric Mean Acta Mathematca Ntresa Vol, No, p 43 48 ISSN 453-6083 Arthmetc Mea ad Geometrc Mea Mare Varga a * Peter Mchalča b a Departmet of Mathematcs, Faculty of Natural Sceces, Costate the Phlosopher Uversty Ntra,

More information

A Remark on the Uniform Convergence of Some Sequences of Functions

A Remark on the Uniform Convergence of Some Sequences of Functions Advaces Pure Mathematcs 05 5 57-533 Publshed Ole July 05 ScRes. http://www.scrp.org/joural/apm http://dx.do.org/0.436/apm.05.59048 A Remark o the Uform Covergece of Some Sequeces of Fuctos Guy Degla Isttut

More information

Nonlinear Blind Source Separation Using Hybrid Neural Networks*

Nonlinear Blind Source Separation Using Hybrid Neural Networks* Nolear Bld Source Separato Usg Hybrd Neural Networks* Chu-Hou Zheg,2, Zh-Ka Huag,2, chael R. Lyu 3, ad Tat-g Lok 4 Itellget Computg Lab, Isttute of Itellget aches, Chese Academy of Sceces, P.O.Box 3, Hefe,

More information

LINEAR REGRESSION ANALYSIS

LINEAR REGRESSION ANALYSIS LINEAR REGRESSION ANALYSIS MODULE V Lecture - Correctg Model Iadequaces Through Trasformato ad Weghtg Dr. Shalabh Departmet of Mathematcs ad Statstcs Ida Isttute of Techology Kapur Aalytcal methods for

More information

The TDT. (Transmission Disequilibrium Test) (Qualitative and quantitative traits) D M D 1 M 1 D 2 M 2 M 2D1 M 1

The TDT. (Transmission Disequilibrium Test) (Qualitative and quantitative traits) D M D 1 M 1 D 2 M 2 M 2D1 M 1 The TDT (Trasmsso Dsequlbrum Test) (Qualtatve ad quattatve trats) Our am s to test for lkage (ad maybe ad/or assocato) betwee a dsease locus D ad a marker locus M. We kow where (.e. o what chromosome,

More information

GEOID IN THE WEST UKRAINE AREA DERIVED BY MEANS OF NON-CENTRAL MULTIPOLE ANALYSIS TECHNIQUE

GEOID IN THE WEST UKRAINE AREA DERIVED BY MEANS OF NON-CENTRAL MULTIPOLE ANALYSIS TECHNIQUE GEOID IN THE WEST UKRAINE AREA DERIVED BY MEANS OF NON-CENTRAL MULTIPOLE ANALYSIS TECHNIQUE INTRODUCTION Alexader Marcheko ad Oleg Abrkosov Faculty of Geodesy State Uversty "Lvv Polytechc" SBadera St 90646

More information

A Note on Ratio Estimators in two Stage Sampling

A Note on Ratio Estimators in two Stage Sampling Iteratoal Joural of Scetfc ad Research Publcatos, Volume, Issue, December 0 ISS 0- A ote o Rato Estmators two Stage Samplg Stashu Shekhar Mshra Lecturer Statstcs, Trdet Academy of Creatve Techology (TACT),

More information

Collocation Extraction Using Square Mutual Information Approaches. Received December 2010; revised January 2011

Collocation Extraction Using Square Mutual Information Approaches. Received December 2010; revised January 2011 Iteratoal Joural of Kowledge www.jklp.org ad Laguage Processg KLP Iteratoal c2011 ISSN 2191-2734 Volume 2, Number 1, Jauary 2011 pp. 53-58 Collocato Extracto Usg Square Mutual Iformato Approaches Huaru

More information

CHAPTER 4 RADICAL EXPRESSIONS

CHAPTER 4 RADICAL EXPRESSIONS 6 CHAPTER RADICAL EXPRESSIONS. The th Root of a Real Number A real umber a s called the th root of a real umber b f Thus, for example: s a square root of sce. s also a square root of sce ( ). s a cube

More information

Dimensionality reduction Feature selection

Dimensionality reduction Feature selection CS 750 Mache Learg Lecture 3 Dmesoalty reducto Feature selecto Mlos Hauskrecht mlos@cs.ptt.edu 539 Seott Square CS 750 Mache Learg Dmesoalty reducto. Motvato. Classfcato problem eample: We have a put data

More information

Measures of Dispersion

Measures of Dispersion Chapter 8 Measures of Dsperso Defto of Measures of Dsperso (page 31) A measure of dsperso s a descrptve summary measure that helps us characterze the data set terms of how vared the observatos are from

More information

On Fuzzy Arithmetic, Possibility Theory and Theory of Evidence

On Fuzzy Arithmetic, Possibility Theory and Theory of Evidence O Fuzzy rthmetc, Possblty Theory ad Theory of Evdece suco P. Cucala, Jose Vllar Isttute of Research Techology Uversdad Potfca Comllas C/ Sata Cruz de Marceado 6 8 Madrd. Spa bstract Ths paper explores

More information

Johns Hopkins University Department of Biostatistics Math Review for Introductory Courses

Johns Hopkins University Department of Biostatistics Math Review for Introductory Courses Johs Hopks Uverst Departmet of Bostatstcs Math Revew for Itroductor Courses Ratoale Bostatstcs courses wll rel o some fudametal mathematcal relatoshps, fuctos ad otato. The purpose of ths Math Revew s

More information

Logistic regression (continued)

Logistic regression (continued) STAT562 page 138 Logstc regresso (cotued) Suppose we ow cosder more complex models to descrbe the relatoshp betwee a categorcal respose varable (Y) that takes o two (2) possble outcomes ad a set of p explaatory

More information

Study on a Fire Detection System Based on Support Vector Machine

Study on a Fire Detection System Based on Support Vector Machine Sesors & Trasducers, Vol. 8, Issue, November 04, pp. 57-6 Sesors & Trasducers 04 by IFSA Publshg, S. L. http://www.sesorsportal.com Study o a Fre Detecto System Based o Support Vector Mache Ye Xaotg, Wu

More information

Exponentiated Pareto Distribution: Different Method of Estimations

Exponentiated Pareto Distribution: Different Method of Estimations It. J. Cotemp. Math. Sceces, Vol. 4, 009, o. 14, 677-693 Expoetated Pareto Dstrbuto: Dfferet Method of Estmatos A. I. Shawky * ad Haaa H. Abu-Zadah ** Grls College of Educato Jeddah, Scetfc Secto, Kg Abdulazz

More information

Lecture 02: Bounding tail distributions of a random variable

Lecture 02: Bounding tail distributions of a random variable CSCI-B609: A Theorst s Toolkt, Fall 206 Aug 25 Lecture 02: Boudg tal dstrbutos of a radom varable Lecturer: Yua Zhou Scrbe: Yua Xe & Yua Zhou Let us cosder the ubased co flps aga. I.e. let the outcome

More information

Statistical modelling and latent variables (2)

Statistical modelling and latent variables (2) Statstcal modellg ad latet varables (2 Mxg latet varables ad parameters statstcal erece Trod Reta (Dvso o statstcs ad surace mathematcs, Departmet o Mathematcs, Uversty o Oslo State spaces We typcally

More information

Processing of Information with Uncertain Boundaries Fuzzy Sets and Vague Sets

Processing of Information with Uncertain Boundaries Fuzzy Sets and Vague Sets Processg of Iformato wth Ucerta odares Fzzy Sets ad Vage Sets JIUCHENG XU JUNYI SHEN School of Electroc ad Iformato Egeerg X'a Jaotog Uversty X'a 70049 PRCHIN bstract: - I the paper we aalyze the relatoshps

More information

Cloud formation by condensation

Cloud formation by condensation Cloud formato by codesato U ( r) SV r m RT r: radus of droplet : surface teso of lqud ( ) - 80 - N/m : desty of lqud ( ) (r): vapor pressure over covex surface e Clouds develop from codesato of water vapor

More information

Image Decomposition of Partly Noisy Images

Image Decomposition of Partly Noisy Images Avalable ole at wwwscecedrectcom Proceda Egeerg 9 () 6 66 Iteratoal Workshop o Iformato ad Electrocs Egeerg (IWIEE) Image Decomposto of Partly Nosy Images Ruhua u ab** Ruzh Ja a ad yu Su a a School of

More information

On the Modeling and Simulation of Collision and Collision-Free Motion for Planar Robotic Arm Galia V. Tzvetkova

On the Modeling and Simulation of Collision and Collision-Free Motion for Planar Robotic Arm Galia V. Tzvetkova Iteratoal Joural of Egeerg Research & Scece (IJOER [Vol-, Issue-9, December- 25] O the Modelg ad Smulato of Collso ad Collso-Free Moto for Plaar Robotc Arm Gala V. Tzvetova Isttute of mechacs, Bulgara

More information

Statistical characteristics of the normalized Stokes parameters

Statistical characteristics of the normalized Stokes parameters Scece Cha Seres F: Iformato Sceces 008 SCIENCE IN CHINA PRESS Sprger www.sccha.com fo.sccha.com www.sprgerlk.com Statstcal characterstcs of the ormalzed Stokes parameters LIU Tao 1 WANG XueSog 1 & XIAO

More information

Probabilistic Meanings of Numerical Characteristics for Single Birth Processes

Probabilistic Meanings of Numerical Characteristics for Single Birth Processes A^VÇÚO 32 ò 5 Ï 206 c 0 Chese Joural of Appled Probablty ad Statstcs Oct 206 Vol 32 No 5 pp 452-462 do: 03969/jss00-426820605002 Probablstc Meags of Numercal Characterstcs for Sgle Brth Processes LIAO

More information

C.11 Bang-bang Control

C.11 Bang-bang Control Itroucto to Cotrol heory Iclug Optmal Cotrol Nguye a e -.5 C. Bag-bag Cotrol. Itroucto hs chapter eals wth the cotrol wth restrctos: s boue a mght well be possble to have scotutes. o llustrate some of

More information

THE EFFICIENCY OF EMPIRICAL LIKELIHOOD WITH NUISANCE PARAMETERS

THE EFFICIENCY OF EMPIRICAL LIKELIHOOD WITH NUISANCE PARAMETERS Joural of Mathematcs ad Statstcs (: 5-9, 4 ISSN: 549-3644 4 Scece Publcatos do:.3844/jmssp.4.5.9 Publshed Ole ( 4 (http://www.thescpub.com/jmss.toc THE EFFICIENCY OF EMPIRICAL LIKELIHOOD WITH NUISANCE

More information

Chapter -2 Simple Random Sampling

Chapter -2 Simple Random Sampling Chapter - Smple Radom Samplg Smple radom samplg (SRS) s a method of selecto of a sample comprsg of umber of samplg uts out of the populato havg umber of samplg uts such that every samplg ut has a equal

More information

Entropy ISSN by MDPI

Entropy ISSN by MDPI Etropy 2003, 5, 233-238 Etropy ISSN 1099-4300 2003 by MDPI www.mdp.org/etropy O the Measure Etropy of Addtve Cellular Automata Hasa Aı Arts ad Sceces Faculty, Departmet of Mathematcs, Harra Uversty; 63100,

More information

DIFFERENTIAL GEOMETRIC APPROACH TO HAMILTONIAN MECHANICS

DIFFERENTIAL GEOMETRIC APPROACH TO HAMILTONIAN MECHANICS DIFFERENTIAL GEOMETRIC APPROACH TO HAMILTONIAN MECHANICS Course Project: Classcal Mechacs (PHY 40) Suja Dabholkar (Y430) Sul Yeshwath (Y444). Itroducto Hamltoa mechacs s geometry phase space. It deals

More information

Chapter 3 Sampling For Proportions and Percentages

Chapter 3 Sampling For Proportions and Percentages Chapter 3 Samplg For Proportos ad Percetages I may stuatos, the characterstc uder study o whch the observatos are collected are qualtatve ature For example, the resposes of customers may marketg surveys

More information

"It is the mark of a truly intelligent person to be moved by statistics." George Bernard Shaw

It is the mark of a truly intelligent person to be moved by statistics. George Bernard Shaw Chapter 0 Chapter 0 Lear Regresso ad Correlato "It s the mark of a truly tellget perso to be moved by statstcs." George Berard Shaw Source: https://www.google.com.ph/search?q=house+ad+car+pctures&bw=366&bh=667&tbm

More information

MATH 247/Winter Notes on the adjoint and on normal operators.

MATH 247/Winter Notes on the adjoint and on normal operators. MATH 47/Wter 00 Notes o the adjot ad o ormal operators I these otes, V s a fte dmesoal er product space over, wth gve er * product uv, T, S, T, are lear operators o V U, W are subspaces of V Whe we say

More information

C. Statistics. X = n geometric the n th root of the product of numerical data ln X GM = or ln GM = X 2. X n X 1

C. Statistics. X = n geometric the n th root of the product of numerical data ln X GM = or ln GM = X 2. X n X 1 C. Statstcs a. Descrbe the stages the desg of a clcal tral, takg to accout the: research questos ad hypothess, lterature revew, statstcal advce, choce of study protocol, ethcal ssues, data collecto ad

More information

Linear Regression Linear Regression with Shrinkage. Some slides are due to Tommi Jaakkola, MIT AI Lab

Linear Regression Linear Regression with Shrinkage. Some slides are due to Tommi Jaakkola, MIT AI Lab Lear Regresso Lear Regresso th Shrkage Some sldes are due to Tomm Jaakkola, MIT AI Lab Itroducto The goal of regresso s to make quattatve real valued predctos o the bass of a vector of features or attrbutes.

More information

Kangwon National University, South Korea

Kangwon National University, South Korea Evaluato of WAT Auto-calbrato usg Dverse Effcecy Crtera 0 Iteratoal WAT Coferece Hyuwoo Kag Kagwo Natoal Uversty, outh Korea Itroducto Calbrato ad Valdato of hydrologcal model Nash-utclffe Model Effcecy

More information

Reliability Based Design Optimization with Correlated Input Variables

Reliability Based Design Optimization with Correlated Input Variables 7--55 Relablty Based Desg Optmzato wth Correlated Iput Varables Copyrght 7 SAE Iteratoal Kyug K. Cho, Yoojeog Noh, ad Lu Du Departmet of Mechacal & Idustral Egeerg & Ceter for Computer Aded Desg, College

More information

COMPROMISE HYPERSPHERE FOR STOCHASTIC DOMINANCE MODEL

COMPROMISE HYPERSPHERE FOR STOCHASTIC DOMINANCE MODEL Sebasta Starz COMPROMISE HYPERSPHERE FOR STOCHASTIC DOMINANCE MODEL Abstract The am of the work s to preset a method of rakg a fte set of dscrete radom varables. The proposed method s based o two approaches:

More information

1 Lyapunov Stability Theory

1 Lyapunov Stability Theory Lyapuov Stablty heory I ths secto we cosder proofs of stablty of equlbra of autoomous systems. hs s stadard theory for olear systems, ad oe of the most mportat tools the aalyss of olear systems. It may

More information

Lecture 3. Sampling, sampling distributions, and parameter estimation

Lecture 3. Sampling, sampling distributions, and parameter estimation Lecture 3 Samplg, samplg dstrbutos, ad parameter estmato Samplg Defto Populato s defed as the collecto of all the possble observatos of terest. The collecto of observatos we take from the populato s called

More information

Risk management of hazardous material transportation

Risk management of hazardous material transportation Maagemet of atural Resources, Sustaable Developmet ad Ecologcal azards 393 Rs maagemet of hazardous materal trasportato J. Auguts, E. Uspuras & V. Matuzas Lthuaa Eergy Isttute, Lthuaa Abstract I recet

More information

General Method for Calculating Chemical Equilibrium Composition

General Method for Calculating Chemical Equilibrium Composition AE 6766/Setzma Sprg 004 Geeral Metod for Calculatg Cemcal Equlbrum Composto For gve tal codtos (e.g., for gve reactats, coose te speces to be cluded te products. As a example, for combusto of ydroge wt

More information

STA 105-M BASIC STATISTICS (This is a multiple choice paper.)

STA 105-M BASIC STATISTICS (This is a multiple choice paper.) DCDM BUSINESS SCHOOL September Mock Eamatos STA 0-M BASIC STATISTICS (Ths s a multple choce paper.) Tme: hours 0 mutes INSTRUCTIONS TO CANDIDATES Do ot ope ths questo paper utl you have bee told to do

More information

3. Basic Concepts: Consequences and Properties

3. Basic Concepts: Consequences and Properties : 3. Basc Cocepts: Cosequeces ad Propertes Markku Jutt Overvew More advaced cosequeces ad propertes of the basc cocepts troduced the prevous lecture are derved. Source The materal s maly based o Sectos.6.8

More information

Recall MLR 5 Homskedasticity error u has the same variance given any values of the explanatory variables Var(u x1,...,xk) = 2 or E(UU ) = 2 I

Recall MLR 5 Homskedasticity error u has the same variance given any values of the explanatory variables Var(u x1,...,xk) = 2 or E(UU ) = 2 I Chapter 8 Heterosedastcty Recall MLR 5 Homsedastcty error u has the same varace gve ay values of the eplaatory varables Varu,..., = or EUU = I Suppose other GM assumptos hold but have heterosedastcty.

More information

Lecture 1. (Part II) The number of ways of partitioning n distinct objects into k distinct groups containing n 1,

Lecture 1. (Part II) The number of ways of partitioning n distinct objects into k distinct groups containing n 1, Lecture (Part II) Materals Covered Ths Lecture: Chapter 2 (2.6 --- 2.0) The umber of ways of parttog dstct obects to dstct groups cotag, 2,, obects, respectvely, where each obect appears exactly oe group

More information

Applied Mathematics and Computation

Applied Mathematics and Computation Appled Mathematcs ad Computato 215 (2010) 4198 4202 Cotets lsts avalable at SceceDrect Appled Mathematcs ad Computato joural homepage: www.elsever.com/locate/amc Improvemet estmatg the populato mea smple

More information

The E vs k diagrams are in general a function of the k -space direction in a crystal

The E vs k diagrams are in general a function of the k -space direction in a crystal vs dagram p m m he parameter s called the crystal mometum ad s a parameter that results from applyg Schrödger wave equato to a sgle-crystal lattce. lectros travelg dfferet drectos ecouter dfferet potetal

More information

Estimation and Testing for Rank Size Rule Regression under Pareto Distribution

Estimation and Testing for Rank Size Rule Regression under Pareto Distribution Estmato ad Testg for Ra Sze Rule Regresso uder Pareto Dstrbuto Y Nshyama a S Osada a ad K Mormue b a Kyoto Isttute of ecoomc Research Kyoto Uversty Kyoto 66-85 Japa b Graduate School of Ecoomcs Kyoto Uversty

More information

Part I: Background on the Binomial Distribution

Part I: Background on the Binomial Distribution Part I: Bacgroud o the Bomal Dstrbuto A radom varable s sad to have a Beroull dstrbuto f t taes o the value wth probablt "p" ad the value wth probablt " - p". The umber of "successes" "" depedet Beroull

More information

Answer key to problem set # 2 ECON 342 J. Marcelo Ochoa Spring, 2009

Answer key to problem set # 2 ECON 342 J. Marcelo Ochoa Spring, 2009 Aswer key to problem set # ECON 34 J. Marcelo Ochoa Sprg, 009 Problem. For T cosder the stadard pael data model: y t x t β + α + ǫ t a Numercally compare the fxed effect ad frst dfferece estmates. b Compare

More information

Lecture notes on epidemiology

Lecture notes on epidemiology Bostatstcs 2002, ÅS Lecture otes o epdemology The ams of epdemology: Epdemology s the study of the dstrbuto ad determats of health related states or evets specfed populatos ad the applcato of ths study

More information