Chapter 11 Systematic Sampling
|
|
- Meagan Walsh
- 7 years ago
- Views:
Transcription
1 Chapter Sstematc Samplg 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 samplg, the frst ut s selected wth the help of radom umbers ad the remag uts are selected automatcall accordg to a predetermed patter. Ths method s ow as sstematc samplg. Suppose the uts the populato are umbered to some order. Suppose further that s expressble as a product of two tegers ad, so that. To draw a sample of sze, - select a radom umber betwee ad. - Suppose t s. - Select the frst ut whose seral umber s. - Select ever th ut after th ut. - Sample wll cota,,,..., ( ) seral umber uts. So frst ut s selected at radom ad other uts are selected sstematcall. Ths sstematc sample s called th sstematc sample ad s termed as samplg terval. Ths s also ow as lear sstematc samplg. The observatos the sstematc samplg are arraged as the followg table: Sstematc sample umber Sample composto 3 ( ) Probablt ( ) 3 3 ( ) 3 ( ) Sample mea 3
2 Example: Let 50 ad 5. So 0. Suppose frst selected umber betwee ad 0 s 3. The sstematc sample cossts of uts wth followg seral umber 3, 3, 3, 33, 43. Sstematc samplg two dmesos: Assume that the uts a populato are arraged the form of m rows ad each row cotas uts. A sample of sze m s reured. The - select a par of radom umbers (, j ) such that ad j. - Select the (, j ) th ut,.e., - The the rows to be selected are,,,..., ( m) ad colums to be selected are j, j, j,..., j( ). th j ut th row as the frst ut. - The pots at whch the m selected rows ad selected colums tersect determe the posto of m selected uts the sample. Such a sample s called a alged sample. Alteratve approach to select the sample s - depedetl select radom tegers,,..., such that each of them s less tha or eual to. - Idepedetl select m radom tegers j, j,..., j m such that each of them s less tha or eual to. - The uts selected the sample wll have followg coordates: ( r, j ),( r, j ),( r, j ),...,( r, j ( ) ). r r 3 r r Such a sample s called a ualged sample. Uder certa codtos, a ualged sample s ofte superor to a alged sample as well as a stratfed radom sample.
3 Advatages of sstematc samplg:. It s easer to draw a sample ad ofte easer to execute t wthout mstaes. Ths s more advatageous whe the drawg s doe felds ad offces as there ma be substatal savg tme.. The cost s low ad the selecto of uts s smple. Much less trag s eeded for surveors to collect uts through sstematc samplg. 3. The sstematc sample s spread more evel over the populato. So o large part wll fal to be represeted the sample. The sample s evel spread ad cross secto s better. Sstematc samplg fals case of too ma blas. Relato to the cluster samplg The sstematc sample ca be vewed from the cluster samplg pot of vew. Wth, there are possble sstematc samples. The same populato ca be vewed as f dvded to large samplg uts, each of whch cotas of the orgal uts. The operato of choosg a sstematc sample s euvalet to choosg oe of the large samplg ut at radom whch costtutes the whole sample. A sstematc sample s thus a smple radom sample of oe cluster ut from a populato of cluster uts. Estmato of populato mea : Whe = : Let : observato o the ut bearg the seral umber ( j ) the populato, j,,...,, j,,...,. Suppose the draw radom umber s. th Sample cossts of colum ( earler table). Cosder the sample mea gve b s j j as a estmator of the populato mea gve b Y j. Probablt of selectg j th colum as sstematc sample. 3
4 So E( s ) Y. Thus s s a ubased estmator of Y. Further, Cosder where Var( ) ( Y ) s. j j ( ) S ( Y) ( j ) ( Y) j ( j ) ( Y) j ws ( ) S ( Y) S ws ( j ) ( ) j s the varato amog the uts that le wth the same sstematc sample. Thus ( ) Var( s ) S S ( ) S S ws ws Varato Pooled wth as a varato of the whole sstematc sample wth. Ths expresso dcates that whe the wth varato s large, the Var( ) becomes smaller. Thus hgher heterogeet maes the estmator more effcet ad hgher heterogeet s well expected sstematc sample. 4
5 Alteratve form of varace: Var( s ) ( Y ) j Y j ( ) j Y j ( j Y) ( j Y)( Y) j j( ) ( ) S ( j Y )( Y ). j( ) The traclass correlato betwee the pars of uts that are the same sstematc sample s E( j Y)( Y) w ; E( j Y) ( j Y)( Y) ( ) j( ). S So substtutg j( ) Var( ) gves ( Y)( Y) ( )( ) S j w S Var( s ) w( ) S w( ). Comparso wth WOR: For a WOR sample of sze, Var( ) S S S. 5
6 Sce Thus Var( s ) S Sws Var( ) Var( ) S S ( Sws S ). s s s ws - more effcet tha whe S S. ws - less effcet tha whe S S. ws - euall effcet as S S whe ws. Also, the relatve effcec of s relatve to s Var( ) RE Var( ) s S S w( ) w( ) ( ) ;. ( ) w( ) Thus s s - more effcet tha whe - less effcet tha whe - euall effcet as whe w w w. 6
7 Comparso wth stratfed samplg: The sstematc sample ca also be vewed as f arsg as a stratfed sample. If populato of uts s dvded to strata ad suppose oe ut s radoml draw from each of the strata. The we get a stratfed sample of sze. I dog so, just cosder each row of the followg arragemet as a stratum. Sstematc sample umber Sample composto 3 ( ) Probablt ( ) 3 3 ( ) 3 ( ) Sample mea 3 Recall that case of stratfed samplg wth strata, the stratum mea st jj j s a ubased estmator of populato mea. Cosderg the set up of stratfed sample the set up of sstematc sample, we have - umber of strata = - Sze of strata = (row sze) - Sample sze to be draw from each stratum = ad st becomes st j j j j 7
8 where Var( st ) Var( ) j j usg ( ) Sj Var S j. j S S S wst j wst S j ( j j) s the mea sum of suares of uts the th j stratum. S wst Sj j ( ) j ( ) s the mea sum of suares wth strata (or rows). j j The varace of sstematc sample mea s Var( s ) ( Y ) j j j j ( j j ) j ( j j ) ( j j )( ). j j ow we smplf ad express ths expresso terms of traclass correlato coeffcet. The traclass correlato coeffcet betwee the pars of devatos of uts whch le alog the same row measured from ther stratum meas s defed as 8
9 So Thus ( ) j wst j j ( )( ) ( ) ( )( ) ( )( ) S j j j j j wst Var( s ) ( ) S ( )( ) wst wstswst S wst ( ) wst. (usg ) j Var( st) Var( s) ( ) wstswst ad the relatve effcec of sstematc samplg relatve to euvalet stratfed samplg s gve b RE ( ). wst So the sstematc samplg s - more effcet tha the correspodg euvalet stratfed sample whe wst 0. - less effcet tha the correspodg euvalet stratfed sample whe wst 0 - euall effcet tha the correspodg euvalet stratfed sample whe wst 0. Comparso of sstematc samplg, stratfed samplg ad wth populato wth lear tred: We assume that the values of uts the populato crease accordg to lear tred. So the values of successve uts the populato crease accordace wth a lear model so that ab,,,...,. ow we determe the varaces of, ad st uder ths lear tred. s 9
10 Uder WOR V( ) Here Y ab ( ) ab ab S Y S. ( ) abab b b b ( )( ) ( ) 6 4 ( ) b ( ) Var( ) b. b ( )( ). 0
11 Uder sstematc samplg Earler j deoted the value of stud varable wth the th j ut the th sstematc sample. ow j th represets the value of ( j ) ut of the populato, so j j ab ( j),,,..., ; j,,...,. s Var( s ) ( Y ) j a b ( j ) j ab ( Y) ab ab b b b ( )() ( ) b ( ) 6 ( ) Var b b ( s ) ( ) ( ).
12 Uder stratfed samplg where S st ab ( j),,,...,, j,,..., j Var( ) S S st wst wst wst Sj j ( ) j ( ) j ab( j) ab ( j) ( ) j b ( ) b ( ) ( ) b ( ) ( ) Var( st ) b b j j If s large, so that s eglgble, the comparg Var( st ), Var( s ) ad V ( ), Var( st ) : Var( ) : Var( ) s or or or ( ) : : : ( )( ) : : : : Thus Var( st ) : Var( s ) : Var( ) :: : : So stratfed samplg s best for learl treded populato. ext best s sstematc samplg.
13 Estmato of varace: As such there s ol oe cluster, so varace prcple, caot be estmated. Some approxmatos have bee suggested.. Treat sstematc sample as f t were a radom sample. I ths case, a estmate of varace s Var( s ) swc where s ( ). wc j j0 Ths estmator uder-estmates the true varace.. Use of successve dffereces of the values gves the estmate of varace as Var s j ( j) ( ). ( ) j0 Ths estmator s a based estmator of true varace. 3. Use the balaced dfferece of,,..., to get the estmate of varace as Var( s ) 5( ) or 4 4 Var( s ) 3. 5( 4) 4. The terpeetratg subsamples ca be utlzed b dvdg the sample to C groups each of sze. c The the group meas are,,..., c. ow fd c c t t c Var( s ) ( t ). cc ( ) t 3
14 Sstematc samplg whe. Whe s ot expressble as the suppose ca be expressed as p; p. The cosder the followg sample mea as a estmator of populato mea j f p j j f p. j s I ths case p E( ) j j j p j Y. So s s a based estmator of Y. A ubased estmator of Y s * s j C j where C s the total of values of the th colum. * ( s ) E( C ) E. Y C Var( ) * * s S c where S * c Y. 4
15 ow we cosder aother procedure whch s opted whe. [Referece: Theor of Sample Surves, A.K. Gupta, D.G. Kabe, 0, World Scetfc Publshg Co.] Whe populato sze s ot expressble as the product of ad, the let r. The tae the samplg terval as f f r. r Let If M g M deotes the largest teger cotaed. g * ( or ), the the umber of uts expected sample wth probablt * * * wth probablt. * * * If *, the we get * Smlarl, f r r r wth probablt r r r wth probablt *, the. * r ( r) r wth probablt ( ) r r ( r) wth probablt. ( ) Example: Let 7 ad 5. The 3 ad r. Sce r, 3. The sample szes would be * r r r 5 wth probablt 3 r r r 6 wth probablt. 3 5
16 Ths ca be verfed from the followg example: Sstematc sample umber Sstematc sample Probablt 3 Y, Y4, Y7, Y0, Y3, Y 6 Y4, Y5, Y8, Y, Y4, Y 7 Y, Y, Y, Y, Y /3 /3 /3 We ow prove the followg theorem whch shows how to obta a ubased estmator of the populato mea whe. Theorem: I sstematc samplg wth samplg terval from a populato wth sze, a ubased estmator of the populato mea Y s gve b ' ˆ Y where stads for the th sstematc sample,,,..., ad ' deotes the sze of th sstematc sample. Proof. Each sstematc sample has probablt. Hece ' ˆ EY ( ). '. ow, each ut occurs ol oe of the possble sstematc samples. Hece ' whch o substtuto Y, EY ( ˆ ) proves the theorem. Whe, the sstematc samples are ot of the same sze ad the sample mea s ot a ubased estmator of the populato mea. To overcome these dsadvatages of sstematc samplg whe, crcular sstematc samplg s proposed. Crcular sstematc samplg cossts of selectg a radom umber from to ad the selectg Thereafter ever the earest teger to. the ut correspodg to ths radom umber. th ut a cclcal maer s selected tll a sample of uts s obtaed, beg 6
17 I other words, f s a umber selected at radom from to, the the crcular sstematc sample cossts of uts wth seral umbers j, f j j 0,,,...,( ). j, f j Ths samplg scheme esures eual probablt of cluso the sample for ever ut. Example: Let 4 ad 5. The, earest teger to 4 3. Let the frst umber selected at radom 5 from to 4 be 7. The, the crcular sstematc sample cossts of uts wth seral umbers 7,0,3, 6-4=, 9-4=5. Ths procedure s llustrated dagrammatcall followg fgure
18 Theorem: I crcular sstematc samplg, the sample mea s a ubased estmator of the populato mea. Proof: If s the umber selected at radom, the the crcular sstematc sample mea s where, deotes the total of values the th crcular sstematc sample,,,...,. We ote here that crcular sstematc samplg, there are crcular sstematc samples, each havg probablt of ts selecto. Hece, E( ) Clearl, each ut of the populato occurs of the possble crcular sstematc sample meas. Hece, Y, whch o substtuto E( ) proves the theorem. What to do whe Oe of the followg possble procedures ma be adopted whe. () Drop oe ut at radom f sample has ( ) uts. () Elmate some uts so that. () Adopt crcular sstematc samplg scheme. (v) Roud off the fractoal terval. 8
ANOVA Notes Page 1. Analysis of Variance for a One-Way Classification of Data
ANOVA Notes Page Aalss of Varace for a Oe-Wa Classfcato of Data Cosder a sgle factor or treatmet doe at levels (e, there are,, 3, dfferet varatos o the prescrbed treatmet) Wth a gve treatmet level there
More informationSTATISTICAL PROPERTIES OF LEAST SQUARES ESTIMATORS. x, where. = y - ˆ " 1
STATISTICAL PROPERTIES OF LEAST SQUARES ESTIMATORS Recall Assumpto E(Y x) η 0 + η x (lear codtoal mea fucto) Data (x, y ), (x 2, y 2 ),, (x, y ) Least squares estmator ˆ E (Y x) ˆ " 0 + ˆ " x, where ˆ
More informationSimple Linear Regression
Smple Lear Regresso Regresso equato a equato that descrbes the average relatoshp betwee a respose (depedet) ad a eplaator (depedet) varable. 6 8 Slope-tercept equato for a le m b (,6) slope. (,) 6 6 8
More information6.7 Network analysis. 6.7.1 Introduction. References - Network analysis. Topological analysis
6.7 Network aalyss Le data that explctly store topologcal formato are called etwork data. Besdes spatal operatos, several methods of spatal aalyss are applcable to etwork data. Fgure: Network data Refereces
More informationThe simple linear Regression Model
The smple lear Regresso Model Correlato coeffcet s o-parametrc ad just dcates that two varables are assocated wth oe aother, but t does ot gve a deas of the kd of relatoshp. Regresso models help vestgatg
More informationPreprocess a planar map S. Given a query point p, report the face of S containing p. Goal: O(n)-size data structure that enables O(log n) query time.
Computatoal Geometry Chapter 6 Pot Locato 1 Problem Defto Preprocess a plaar map S. Gve a query pot p, report the face of S cotag p. S Goal: O()-sze data structure that eables O(log ) query tme. C p E
More informationAbraham Zaks. Technion I.I.T. Haifa ISRAEL. and. University of Haifa, Haifa ISRAEL. Abstract
Preset Value of Autes Uder Radom Rates of Iterest By Abraham Zas Techo I.I.T. Hafa ISRAEL ad Uversty of Hafa, Hafa ISRAEL Abstract Some attempts were made to evaluate the future value (FV) of the expected
More informationIDENTIFICATION OF THE DYNAMICS OF THE GOOGLE S RANKING ALGORITHM. A. Khaki Sedigh, Mehdi Roudaki
IDENIFICAION OF HE DYNAMICS OF HE GOOGLE S RANKING ALGORIHM A. Khak Sedgh, Mehd Roudak Cotrol Dvso, Departmet of Electrcal Egeerg, K.N.oos Uversty of echology P. O. Box: 16315-1355, ehra, Ira sedgh@eetd.ktu.ac.r,
More informationSHAPIRO-WILK TEST FOR NORMALITY WITH KNOWN MEAN
SHAPIRO-WILK TEST FOR NORMALITY WITH KNOWN MEAN Wojcech Zelńsk Departmet of Ecoometrcs ad Statstcs Warsaw Uversty of Lfe Sceces Nowoursyowska 66, -787 Warszawa e-mal: wojtekzelsk@statystykafo Zofa Hausz,
More informationAPPENDIX III THE ENVELOPE PROPERTY
Apped III APPENDIX III THE ENVELOPE PROPERTY Optmzato mposes a very strog structure o the problem cosdered Ths s the reaso why eoclasscal ecoomcs whch assumes optmzg behavour has bee the most successful
More informationCSSE463: Image Recognition Day 27
CSSE463: Image Recogto Da 27 Ths week Toda: Alcatos of PCA Suda ght: roject las ad relm work due Questos? Prcal Comoets Aalss weght grth c ( )( ) ( )( ( )( ) ) heght sze Gve a set of samles, fd the drecto(s)
More informationSettlement Prediction by Spatial-temporal Random Process
Safety, Relablty ad Rs of Structures, Ifrastructures ad Egeerg Systems Furuta, Fragopol & Shozua (eds Taylor & Fracs Group, Lodo, ISBN 978---77- Settlemet Predcto by Spatal-temporal Radom Process P. Rugbaapha
More informationChapter 3. AMORTIZATION OF LOAN. SINKING FUNDS R =
Chapter 3. AMORTIZATION OF LOAN. SINKING FUNDS Objectves of the Topc: Beg able to formalse ad solve practcal ad mathematcal problems, whch the subjects of loa amortsato ad maagemet of cumulatve fuds are
More informationNumerical Methods with MS Excel
TMME, vol4, o.1, p.84 Numercal Methods wth MS Excel M. El-Gebely & B. Yushau 1 Departmet of Mathematcal Sceces Kg Fahd Uversty of Petroleum & Merals. Dhahra, Saud Araba. Abstract: I ths ote we show how
More informationCurve Fitting and Solution of Equation
UNIT V Curve Fttg ad Soluto of Equato 5. CURVE FITTING I ma braches of appled mathematcs ad egeerg sceces we come across epermets ad problems, whch volve two varables. For eample, t s kow that the speed
More informationThe analysis of annuities relies on the formula for geometric sums: r k = rn+1 1 r 1. (2.1) k=0
Chapter 2 Autes ad loas A auty s a sequece of paymets wth fxed frequecy. The term auty orgally referred to aual paymets (hece the ame), but t s ow also used for paymets wth ay frequecy. Autes appear may
More informationM. Salahi, F. Mehrdoust, F. Piri. CVaR Robust Mean-CVaR Portfolio Optimization
M. Salah, F. Mehrdoust, F. Pr Uversty of Gula, Rasht, Ira CVaR Robust Mea-CVaR Portfolo Optmzato Abstract: Oe of the most mportat problems faced by every vestor s asset allocato. A vestor durg makg vestmet
More informationFractal-Structured Karatsuba`s Algorithm for Binary Field Multiplication: FK
Fractal-Structured Karatsuba`s Algorthm for Bary Feld Multplcato: FK *The authors are worg at the Isttute of Mathematcs The Academy of Sceces of DPR Korea. **Address : U Jog dstrct Kwahadog Number Pyogyag
More informationStatistical Pattern Recognition (CE-725) Department of Computer Engineering Sharif University of Technology
I The Name of God, The Compassoate, The ercful Name: Problems' eys Studet ID#:. Statstcal Patter Recogto (CE-725) Departmet of Computer Egeerg Sharf Uversty of Techology Fal Exam Soluto - Sprg 202 (50
More informationChapter 3 0.06 = 3000 ( 1.015 ( 1 ) Present Value of an Annuity. Section 4 Present Value of an Annuity; Amortization
Chapter 3 Mathematcs of Face Secto 4 Preset Value of a Auty; Amortzato Preset Value of a Auty I ths secto, we wll address the problem of determg the amout that should be deposted to a accout ow at a gve
More informationECONOMIC CHOICE OF OPTIMUM FEEDER CABLE CONSIDERING RISK ANALYSIS. University of Brasilia (UnB) and The Brazilian Regulatory Agency (ANEEL), Brazil
ECONOMIC CHOICE OF OPTIMUM FEEDER CABE CONSIDERING RISK ANAYSIS I Camargo, F Fgueredo, M De Olvera Uversty of Brasla (UB) ad The Brazla Regulatory Agecy (ANEE), Brazl The choce of the approprate cable
More information10.5 Future Value and Present Value of a General Annuity Due
Chapter 10 Autes 371 5. Thomas leases a car worth $4,000 at.99% compouded mothly. He agrees to make 36 lease paymets of $330 each at the begg of every moth. What s the buyout prce (resdual value of the
More informationSpeeding up k-means Clustering by Bootstrap Averaging
Speedg up -meas Clusterg by Bootstrap Averagg Ia Davdso ad Ashw Satyaarayaa Computer Scece Dept, SUNY Albay, NY, USA,. {davdso, ashw}@cs.albay.edu Abstract K-meas clusterg s oe of the most popular clusterg
More informationThe Gompertz-Makeham distribution. Fredrik Norström. Supervisor: Yuri Belyaev
The Gompertz-Makeham dstrbuto by Fredrk Norström Master s thess Mathematcal Statstcs, Umeå Uversty, 997 Supervsor: Yur Belyaev Abstract Ths work s about the Gompertz-Makeham dstrbuto. The dstrbuto has
More informationAn Effectiveness of Integrated Portfolio in Bancassurance
A Effectveess of Itegrated Portfolo Bacassurace Taea Karya Research Ceter for Facal Egeerg Isttute of Ecoomc Research Kyoto versty Sayouu Kyoto 606-850 Japa arya@eryoto-uacp Itroducto As s well ow the
More informationMDM 4U PRACTICE EXAMINATION
MDM 4U RCTICE EXMINTION Ths s a ractce eam. It does ot cover all the materal ths course ad should ot be the oly revew that you do rearato for your fal eam. Your eam may cota questos that do ot aear o ths
More informationChapter Eight. f : R R
Chapter Eght f : R R 8. Itroducto We shall ow tur our atteto to the very mportat specal case of fuctos that are real, or scalar, valued. These are sometmes called scalar felds. I the very, but mportat,
More informationADAPTATION OF SHAPIRO-WILK TEST TO THE CASE OF KNOWN MEAN
Colloquum Bometrcum 4 ADAPTATION OF SHAPIRO-WILK TEST TO THE CASE OF KNOWN MEAN Zofa Hausz, Joaa Tarasńska Departmet of Appled Mathematcs ad Computer Scece Uversty of Lfe Sceces Lubl Akademcka 3, -95 Lubl
More informationRegression Analysis. 1. Introduction
. Itroducto Regresso aalyss s a statstcal methodology that utlzes the relato betwee two or more quattatve varables so that oe varable ca be predcted from the other, or others. Ths methodology s wdely used
More informationOnline Appendix: Measured Aggregate Gains from International Trade
Ole Appedx: Measured Aggregate Gas from Iteratoal Trade Arel Burste UCLA ad NBER Javer Cravo Uversty of Mchga March 3, 2014 I ths ole appedx we derve addtoal results dscussed the paper. I the frst secto,
More informationOptimal multi-degree reduction of Bézier curves with constraints of endpoints continuity
Computer Aded Geometrc Desg 19 (2002 365 377 wwwelsevercom/locate/comad Optmal mult-degree reducto of Bézer curves wth costrats of edpots cotuty Guo-Dog Che, Guo-J Wag State Key Laboratory of CAD&CG, Isttute
More informationThe Analysis of Development of Insurance Contract Premiums of General Liability Insurance in the Business Insurance Risk
The Aalyss of Developmet of Isurace Cotract Premums of Geeral Lablty Isurace the Busess Isurace Rsk the Frame of the Czech Isurace Market 1998 011 Scetfc Coferece Jue, 10. - 14. 013 Pavla Kubová Departmet
More informationAverage Price Ratios
Average Prce Ratos Morgstar Methodology Paper August 3, 2005 2005 Morgstar, Ic. All rghts reserved. The formato ths documet s the property of Morgstar, Ic. Reproducto or trascrpto by ay meas, whole or
More informationCredibility Premium Calculation in Motor Third-Party Liability Insurance
Advaces Mathematcal ad Computatoal Methods Credblty remum Calculato Motor Thrd-arty Lablty Isurace BOHA LIA, JAA KUBAOVÁ epartmet of Mathematcs ad Quattatve Methods Uversty of ardubce Studetská 95, 53
More informationn. We know that the sum of squares of p independent standard normal variables has a chi square distribution with p degrees of freedom.
UMEÅ UNIVERSITET Matematsk-statstska sttutoe Multvarat dataaalys för tekologer MSTB0 PA TENTAMEN 004-0-9 LÖSNINGSFÖRSLAG TILL TENTAMEN I MATEMATISK STATISTIK Multvarat dataaalys för tekologer B, 5 poäg.
More informationConstrained Cubic Spline Interpolation for Chemical Engineering Applications
Costraed Cubc Sple Iterpolato or Chemcal Egeerg Applcatos b CJC Kruger Summar Cubc sple terpolato s a useul techque to terpolate betwee kow data pots due to ts stable ad smooth characterstcs. Uortuatel
More informationCH. V ME256 STATICS Center of Gravity, Centroid, and Moment of Inertia CENTER OF GRAVITY AND CENTROID
CH. ME56 STTICS Ceter of Gravt, Cetrod, ad Momet of Ierta CENTE OF GITY ND CENTOID 5. CENTE OF GITY ND CENTE OF MSS FO SYSTEM OF PTICES Ceter of Gravt. The ceter of gravt G s a pot whch locates the resultat
More informationRUSSIAN ROULETTE AND PARTICLE SPLITTING
RUSSAN ROULETTE AND PARTCLE SPLTTNG M. Ragheb 3/7/203 NTRODUCTON To stuatos are ecoutered partcle trasport smulatos:. a multplyg medum, a partcle such as a eutro a cosmc ray partcle or a photo may geerate
More information1. The Time Value of Money
Corporate Face [00-0345]. The Tme Value of Moey. Compoudg ad Dscoutg Captalzato (compoudg, fdg future values) s a process of movg a value forward tme. It yelds the future value gve the relevat compoudg
More informationReinsurance and the distribution of term insurance claims
Resurace ad the dstrbuto of term surace clams By Rchard Bruyel FIAA, FNZSA Preseted to the NZ Socety of Actuares Coferece Queestow - November 006 1 1 Itroducto Ths paper vestgates the effect of resurace
More informationCHAPTER 13. Simple Linear Regression LEARNING OBJECTIVES. USING STATISTICS @ Sunflowers Apparel
CHAPTER 3 Smple Lear Regresso USING STATISTICS @ Suflowers Apparel 3 TYPES OF REGRESSION MODELS 3 DETERMINING THE SIMPLE LINEAR REGRESSION EQUATION The Least-Squares Method Vsual Exploratos: Explorg Smple
More informationA Study of Unrelated Parallel-Machine Scheduling with Deteriorating Maintenance Activities to Minimize the Total Completion Time
Joural of Na Ka, Vol. 0, No., pp.5-9 (20) 5 A Study of Urelated Parallel-Mache Schedulg wth Deteroratg Mateace Actvtes to Mze the Total Copleto Te Suh-Jeq Yag, Ja-Yuar Guo, Hs-Tao Lee Departet of Idustral
More informationFundamentals of Mass Transfer
Chapter Fudametals of Mass Trasfer Whe a sgle phase system cotas two or more speces whose cocetratos are ot uform, mass s trasferred to mmze the cocetrato dffereces wth the system. I a mult-phase system
More informationThe Digital Signature Scheme MQQ-SIG
The Dgtal Sgature Scheme MQQ-SIG Itellectual Property Statemet ad Techcal Descrpto Frst publshed: 10 October 2010, Last update: 20 December 2010 Dalo Glgorosk 1 ad Rue Stesmo Ødegård 2 ad Rue Erled Jese
More informationModels for Selecting an ERP System with Intuitionistic Trapezoidal Fuzzy Information
JOURNAL OF SOFWARE, VOL 5, NO 3, MARCH 00 75 Models for Selectg a ERP System wth Itutostc rapezodal Fuzzy Iformato Guwu We, Ru L Departmet of Ecoomcs ad Maagemet, Chogqg Uversty of Arts ad Sceces, Yogchua,
More informationLecture 7. Norms and Condition Numbers
Lecture 7 Norms ad Codto Numbers To dscuss the errors umerca probems vovg vectors, t s usefu to empo orms. Vector Norm O a vector space V, a orm s a fucto from V to the set of o-egatve reas that obes three
More informationOn Error Detection with Block Codes
BULGARIAN ACADEMY OF SCIENCES CYBERNETICS AND INFORMATION TECHNOLOGIES Volume 9, No 3 Sofa 2009 O Error Detecto wth Block Codes Rostza Doduekova Chalmers Uversty of Techology ad the Uversty of Gotheburg,
More informationMaintenance Scheduling of Distribution System with Optimal Economy and Reliability
Egeerg, 203, 5, 4-8 http://dx.do.org/0.4236/eg.203.59b003 Publshed Ole September 203 (http://www.scrp.org/joural/eg) Mateace Schedulg of Dstrbuto System wth Optmal Ecoomy ad Relablty Syua Hog, Hafeg L,
More informationUSEFULNESS OF BOOTSTRAPPING IN PORTFOLIO MANAGEMENT
USEFULNESS OF BOOTSTRAPPING IN PORTFOLIO MANAGEMENT Radovaov Bors Faculty of Ecoomcs Subotca Segedsk put 9-11 Subotca 24000 E-mal: radovaovb@ef.us.ac.rs Marckć Aleksadra Faculty of Ecoomcs Subotca Segedsk
More informationIntegrating Production Scheduling and Maintenance: Practical Implications
Proceedgs of the 2012 Iteratoal Coferece o Idustral Egeerg ad Operatos Maagemet Istabul, Turkey, uly 3 6, 2012 Itegratg Producto Schedulg ad Mateace: Practcal Implcatos Lath A. Hadd ad Umar M. Al-Turk
More informationBasic statistics formulas
Wth complmet of tattcmetor.com, the te for ole tattc help Set De Morga Law Bac tattc formula Meaure of Locato Sample mea (AUB) c A c B c Commutatvty & (A B) c A c U B c A U B B U A ad A B B A Aocatvty
More informationClassic Problems at a Glance using the TVM Solver
C H A P T E R 2 Classc Problems at a Glace usg the TVM Solver The table below llustrates the most commo types of classc face problems. The formulas are gve for each calculato. A bref troducto to usg the
More informationA particle swarm optimization to vehicle routing problem with fuzzy demands
A partcle swarm optmzato to vehcle routg problem wth fuzzy demads Yag Peg, Ye-me Qa A partcle swarm optmzato to vehcle routg problem wth fuzzy demads Yag Peg 1,Ye-me Qa 1 School of computer ad formato
More informationFINANCIAL MATHEMATICS 12 MARCH 2014
FINNCIL MTHEMTICS 12 MRCH 2014 I ths lesso we: Lesso Descrpto Make use of logarthms to calculate the value of, the tme perod, the equato P1 or P1. Solve problems volvg preset value ad future value autes.
More informationBanking (Early Repayment of Housing Loans) Order, 5762 2002 1
akg (Early Repaymet of Housg Loas) Order, 5762 2002 y vrtue of the power vested me uder Secto 3 of the akg Ordace 94 (hereafter, the Ordace ), followg cosultato wth the Commttee, ad wth the approval of
More informationDynamic Two-phase Truncated Rayleigh Model for Release Date Prediction of Software
J. Software Egeerg & Applcatos 3 63-69 do:.436/jsea..367 Publshed Ole Jue (http://www.scrp.org/joural/jsea) Dyamc Two-phase Trucated Raylegh Model for Release Date Predcto of Software Lafe Qa Qgchua Yao
More informationReport 52 Fixed Maturity EUR Industrial Bond Funds
Rep52, Computed & Prted: 17/06/2015 11:53 Report 52 Fxed Maturty EUR Idustral Bod Fuds From Dec 2008 to Dec 2014 31/12/2008 31 December 1999 31/12/2014 Bechmark Noe Defto of the frm ad geeral formato:
More informationHow To Value An Annuity
Future Value of a Auty After payg all your blls, you have $200 left each payday (at the ed of each moth) that you wll put to savgs order to save up a dow paymet for a house. If you vest ths moey at 5%
More informationApproximation Algorithms for Scheduling with Rejection on Two Unrelated Parallel Machines
(ICS) Iteratoal oural of dvaced Comuter Scece ad lcatos Vol 6 No 05 romato lgorthms for Schedulg wth eecto o wo Urelated Parallel aches Feg Xahao Zhag Zega Ca College of Scece y Uversty y Shadog Cha 76005
More informationDECISION MAKING WITH THE OWA OPERATOR IN SPORT MANAGEMENT
ESTYLF08, Cuecas Meras (Meres - Lagreo), 7-9 de Septembre de 2008 DECISION MAKING WITH THE OWA OPERATOR IN SPORT MANAGEMENT José M. Mergó Aa M. Gl-Lafuete Departmet of Busess Admstrato, Uversty of Barceloa
More informationof the relationship between time and the value of money.
TIME AND THE VALUE OF MONEY Most agrbusess maagers are famlar wth the terms compoudg, dscoutg, auty, ad captalzato. That s, most agrbusess maagers have a tutve uderstadg that each term mples some relatoshp
More informationThe Time Value of Money
The Tme Value of Moey 1 Iversemet Optos Year: 1624 Property Traded: Mahatta Islad Prce : $24.00, FV of $24 @ 6%: FV = $24 (1+0.06) 388 = $158.08 bllo Opto 1 0 1 2 3 4 5 t ($519.37) 0 0 0 0 $1,000 Opto
More informationA Parallel Transmission Remote Backup System
2012 2d Iteratoal Coferece o Idustral Techology ad Maagemet (ICITM 2012) IPCSIT vol 49 (2012) (2012) IACSIT Press, Sgapore DOI: 107763/IPCSIT2012V495 2 A Parallel Trasmsso Remote Backup System Che Yu College
More informationSecurity Analysis of RAPP: An RFID Authentication Protocol based on Permutation
Securty Aalyss of RAPP: A RFID Authetcato Protocol based o Permutato Wag Shao-hu,,, Ha Zhje,, Lu Sujua,, Che Da-we, {College of Computer, Najg Uversty of Posts ad Telecommucatos, Najg 004, Cha Jagsu Hgh
More informationEfficient Traceback of DoS Attacks using Small Worlds in MANET
Effcet Traceback of DoS Attacks usg Small Worlds MANET Yog Km, Vshal Sakhla, Ahmed Helmy Departmet. of Electrcal Egeerg, Uversty of Souther Calfora, U.S.A {yogkm, sakhla, helmy}@ceg.usc.edu Abstract Moble
More informationMathematics of Finance
CATE Mathematcs of ace.. TODUCTO ths chapter we wll dscuss mathematcal methods ad formulae whch are helpful busess ad persoal face. Oe of the fudametal cocepts the mathematcs of face s the tme value of
More informationTaylor & Francis, Ltd. is collaborating with JSTOR to digitize, preserve and extend access to The Journal of Experimental Education.
The Statstcal Iterpretato of Degrees of Freedom Author(s): Wllam J. Mooa Source: The Joural of Expermetal Educato, Vol. 21, No. 3 (Mar., 1953), pp. 259264 Publshed by: Taylor & Fracs, Ltd. Stable URL:
More informationISyE 512 Chapter 7. Control Charts for Attributes. Instructor: Prof. Kaibo Liu. Department of Industrial and Systems Engineering UW-Madison
ISyE 512 Chapter 7 Cotrol Charts for Attrbutes Istructor: Prof. Kabo Lu Departmet of Idustral ad Systems Egeerg UW-Madso Emal: klu8@wsc.edu Offce: Room 3017 (Mechacal Egeerg Buldg) 1 Lst of Topcs Chapter
More informationRobust Realtime Face Recognition And Tracking System
JCS& Vol. 9 No. October 9 Robust Realtme Face Recogto Ad rackg System Ka Che,Le Ju Zhao East Cha Uversty of Scece ad echology Emal:asa85@hotmal.com Abstract here s some very mportat meag the study of realtme
More informationROULETTE-TOURNAMENT SELECTION FOR SHRIMP DIET FORMULATION PROBLEM
28-30 August, 2013 Sarawak, Malaysa. Uverst Utara Malaysa (http://www.uum.edu.my ) ROULETTE-TOURNAMENT SELECTION FOR SHRIMP DIET FORMULATION PROBLEM Rosshary Abd. Rahma 1 ad Razam Raml 2 1,2 Uverst Utara
More informationANALYTICAL MODEL FOR TCP FILE TRANSFERS OVER UMTS. Janne Peisa Ericsson Research 02420 Jorvas, Finland. Michael Meyer Ericsson Research, Germany
ANALYTICAL MODEL FOR TCP FILE TRANSFERS OVER UMTS Jae Pesa Erco Research 4 Jorvas, Flad Mchael Meyer Erco Research, Germay Abstract Ths paper proposes a farly complex model to aalyze the performace of
More informationOn formula to compute primes and the n th prime
Joural's Ttle, Vol., 00, o., - O formula to compute prmes ad the th prme Issam Kaddoura Lebaese Iteratoal Uversty Faculty of Arts ad ceces, Lebao Emal: ssam.addoura@lu.edu.lb amh Abdul-Nab Lebaese Iteratoal
More informationCHAPTER 2. Time Value of Money 6-1
CHAPTER 2 Tme Value of Moey 6- Tme Value of Moey (TVM) Tme Les Future value & Preset value Rates of retur Autes & Perpetutes Ueve cash Flow Streams Amortzato 6-2 Tme les 0 2 3 % CF 0 CF CF 2 CF 3 Show
More informationOptimal replacement and overhaul decisions with imperfect maintenance and warranty contracts
Optmal replacemet ad overhaul decsos wth mperfect mateace ad warraty cotracts R. Pascual Departmet of Mechacal Egeerg, Uversdad de Chle, Caslla 2777, Satago, Chle Phoe: +56-2-6784591 Fax:+56-2-689657 rpascual@g.uchle.cl
More informationA New Bayesian Network Method for Computing Bottom Event's Structural Importance Degree using Jointree
, pp.277-288 http://dx.do.org/10.14257/juesst.2015.8.1.25 A New Bayesa Network Method for Computg Bottom Evet's Structural Importace Degree usg Jotree Wag Yao ad Su Q School of Aeroautcs, Northwester Polytechcal
More informationWe present a new approach to pricing American-style derivatives that is applicable to any Markovian setting
MANAGEMENT SCIENCE Vol. 52, No., Jauary 26, pp. 95 ss 25-99 ess 526-55 6 52 95 forms do.287/msc.5.447 26 INFORMS Prcg Amerca-Style Dervatves wth Europea Call Optos Scott B. Laprse BAE Systems, Advaced
More informationSTOCHASTIC approximation algorithms have several
IEEE TRANSACTIONS ON INFORMATION THEORY, VOL 60, NO 10, OCTOBER 2014 6609 Trackg a Markov-Modulated Statoary Degree Dstrbuto of a Dyamc Radom Graph Mazyar Hamd, Vkram Krshamurthy, Fellow, IEEE, ad George
More informationMeasures of Central Tendency: Basic Statistics Refresher. Topic 1 Point Estimates
Basc Statstcs Refresher Basc Statstcs: A Revew by Alla T. Mese, Ph.D., PE, CRE Ths s ot a tetbook o statstcs. Ths s a refresher that presumes the reader has had some statstcs backgroud. There are some
More informationCIS603 - Artificial Intelligence. Logistic regression. (some material adopted from notes by M. Hauskrecht) CIS603 - AI. Supervised learning
CIS63 - Artfcal Itellgece Logstc regresso Vasleos Megalookoomou some materal adopted from otes b M. Hauskrecht Supervsed learg Data: D { d d.. d} a set of eamples d < > s put vector ad s desred output
More informationImpact of Interference on the GPRS Multislot Link Level Performance
Impact of Iterferece o the GPRS Multslot Lk Level Performace Javer Gozalvez ad Joh Dulop Uversty of Strathclyde - Departmet of Electroc ad Electrcal Egeerg - George St - Glasgow G-XW- Scotlad Ph.: + 8
More informationAN ALGORITHM ABOUT PARTNER SELECTION PROBLEM ON CLOUD SERVICE PROVIDER BASED ON GENETIC
Joural of Theoretcal ad Appled Iformato Techology 0 th Aprl 204. Vol. 62 No. 2005-204 JATIT & LLS. All rghts reserved. ISSN: 992-8645 www.jatt.org E-ISSN: 87-395 AN ALGORITHM ABOUT PARTNER SELECTION PROBLEM
More informationSequences and Series
Secto 9. Sequeces d Seres You c thk of sequece s fucto whose dom s the set of postve tegers. f ( ), f (), f (),... f ( ),... Defto of Sequece A fte sequece s fucto whose dom s the set of postve tegers.
More informationSoftware Aging Prediction based on Extreme Learning Machine
TELKOMNIKA, Vol.11, No.11, November 2013, pp. 6547~6555 e-issn: 2087-278X 6547 Software Agg Predcto based o Extreme Learg Mache Xaozh Du 1, Hum Lu* 2, Gag Lu 2 1 School of Software Egeerg, X a Jaotog Uversty,
More informationAP Statistics 2006 Free-Response Questions Form B
AP Statstcs 006 Free-Respose Questos Form B The College Board: Coectg Studets to College Success The College Board s a ot-for-proft membershp assocato whose msso s to coect studets to college success ad
More informationReal-Time Scheduling Models: an Experimental Approach
Real-Tme Schedulg Models: a Expermetal Approach (Techcal Report - Nov. 2000) Atóo J. Pessoa de Magalhães a.p.magalhaes@fe.up.pt Fax: 22 207 4247 SAI DEMEGI Faculdade de Egehara da Uversdade do Porto -
More informationOptimal Packetization Interval for VoIP Applications Over IEEE 802.16 Networks
Optmal Packetzato Iterval for VoIP Applcatos Over IEEE 802.16 Networks Sheha Perera Harsha Srsea Krzysztof Pawlkowsk Departmet of Electrcal & Computer Egeerg Uversty of Caterbury New Zealad sheha@elec.caterbury.ac.z
More informationAn Approach to Evaluating the Computer Network Security with Hesitant Fuzzy Information
A Approach to Evaluatg the Computer Network Securty wth Hestat Fuzzy Iformato Jafeg Dog A Approach to Evaluatg the Computer Network Securty wth Hestat Fuzzy Iformato Jafeg Dog, Frst ad Correspodg Author
More informationStatistical Techniques for Sampling and Monitoring Natural Resources
Uted States Departmet of Agrculture Forest Servce Statstcal Techques for Samplg ad Motorg Natural Resources Rocky Mouta Research Stato Geeral Techcal Report RMRS-GTR-6 Has T. Schreuder, Rchard Erst, ad
More informationA probabilistic part-of-speech tagger for Swedish
A probablstc part-of-speech tagger for Swedsh eter Nlsso Departmet of Computer Scece Uversty of Lud Lud, Swede dat00pe@ludat.lth.se Abstract Ths paper presets a project for mplemetg ad evaluatg a probablstc
More informationUsing Phase Swapping to Solve Load Phase Balancing by ADSCHNN in LV Distribution Network
Iteratoal Joural of Cotrol ad Automato Vol.7, No.7 (204), pp.-4 http://dx.do.org/0.4257/jca.204.7.7.0 Usg Phase Swappg to Solve Load Phase Balacg by ADSCHNN LV Dstrbuto Network Chu-guo Fe ad Ru Wag College
More informationNumerical Comparisons of Quality Control Charts for Variables
Global Vrtual Coferece Aprl, 8. - 2. 203 Nuercal Coparsos of Qualty Cotrol Charts for Varables J.F. Muñoz-Rosas, M.N. Pérez-Aróstegu Uversty of Graada Facultad de Cecas Ecoócas y Epresarales Graada, pa
More informationImpact of Mobility Prediction on the Temporal Stability of MANET Clustering Algorithms *
Impact of Moblty Predcto o the Temporal Stablty of MANET Clusterg Algorthms * Aravdha Vekateswara, Vekatesh Saraga, Nataraa Gautam 1, Ra Acharya Departmet of Comp. Sc. & Egr. Pesylvaa State Uversty Uversty
More informationSP Betting as a Self-Enforcing Implicit Cartel
SP Bettg as a Self-Eforcg Implct Cartel by Ad Schytzer ad Avcha Sr Departmet of Ecoomcs Bar-Ila Uversty Ramat Ga Israel 52800 e-mal: schyta@mal.bu.ac.l srav@mal.bu.ac.l Abstract A large share of the UK
More informationCyber Journals: Multidisciplinary Journals in Science and Technology, Journal of Selected Areas in Telecommunications (JSAT), January Edition, 2011
Cyber Jourals: Multdscplary Jourals cece ad Techology, Joural of elected Areas Telecommucatos (JAT), Jauary dto, 2011 A ovel rtual etwork Mappg Algorthm for Cost Mmzg ZHAG hu-l, QIU Xue-sog tate Key Laboratory
More informationForecasting Trend and Stock Price with Adaptive Extended Kalman Filter Data Fusion
2011 Iteratoal Coferece o Ecoomcs ad Face Research IPEDR vol.4 (2011 (2011 IACSIT Press, Sgapore Forecastg Tred ad Stoc Prce wth Adaptve Exteded alma Flter Data Fuso Betollah Abar Moghaddam Faculty of
More information10/19/2011. Financial Mathematics. Lecture 24 Annuities. Ana NoraEvans 403 Kerchof AnaNEvans@virginia.edu http://people.virginia.
Math 40 Lecture 24 Autes Facal Mathematcs How ready do you feel for the quz o Frday: A) Brg t o B) I wll be by Frday C) I eed aother week D) I eed aother moth Aa NoraEvas 403 Kerchof AaNEvas@vrga.edu http://people.vrga.edu/~as5k/
More informationRQM: A new rate-based active queue management algorithm
: A ew rate-based actve queue maagemet algorthm Jeff Edmods, Suprakash Datta, Patrck Dymod, Kashf Al Computer Scece ad Egeerg Departmet, York Uversty, Toroto, Caada Abstract I ths paper, we propose a ew
More informationLow-Cost Side Channel Remote Traffic Analysis Attack in Packet Networks
Low-Cost Sde Chael Remote Traffc Aalyss Attack Packet Networks Sach Kadloor, Xu Gog, Negar Kyavash, Tolga Tezca, Nkta Borsov ECE Departmet ad Coordated Scece Lab. IESE Departmet ad Coordated Scece Lab.
More informationTHE McELIECE CRYPTOSYSTEM WITH ARRAY CODES. MATRİS KODLAR İLE McELIECE ŞİFRELEME SİSTEMİ
SAÜ e Blmler Dergs, 5 Clt, 2 Sayı, THE McELIECE CRYPTOSYSTEM WITH ARRAY CODES Vedat ŞİAP* *Departmet of Mathematcs, aculty of Scece ad Art, Sakarya Uversty, 5487, Serdva, Sakarya-TURKEY vedatsap@gmalcom
More informationT = 1/freq, T = 2/freq, T = i/freq, T = n (number of cash flows = freq n) are :
Bullets bods Let s descrbe frst a fxed rate bod wthout amortzg a more geeral way : Let s ote : C the aual fxed rate t s a percetage N the otoal freq ( 2 4 ) the umber of coupo per year R the redempto of
More information