An Evaluation of the Extended Logistic, Simple Logistic, and Gompertz Models for Forecasting Short Lifecycle Products and Services


 Alban Oswald Moody
 2 years ago
 Views:
Transcription
1 An Evaluaton of the Extended Logstc, Smple Logstc, and Gompertz Models for Forecastng Short Lfecycle Products and Servces Charles V. Trappey a,1, Hsnyng Wu b a Professor (Management Scence), Natonal Chao Tung Unversty, Hsnchu, Tawan. b PhD student, Natonal Chao Tung Unversty, Hsnchu, Tawan. Abstract. Many successful technology forecastng models have been developed but lttle research has explored the relatonshp between sample set sze and forecast predcton accuracy. Ths research studes the forecast accuracy of large and small data sets usng the smple logstcl, Gompertz, and the extended logstc models. The performance of the models were evaluated usng the mean absolute devaton and the root mean square error. A tme seres dataset of four electronc products and servces were used to evaluate the model performance. The result shows that the extended logstc model fts large and small datasets better than the smple logstc and Gompertz models. The fndngs also show that that the extended logstc model s well suted to predct market growth wth lmted hstorcal data as s typcally the case for short lfecycle products and servces. Keywords. Extended logstc model, Technology forecastng 1 Introducton Wth the rapd ntroducton of new technologes, electronc products and servces are often replaced wthn a year. The product lfe cycle for electronc goods, whch used to be about ten years n the 1960 s, fell to about 5 years n the 1980 s and s now less than two years for cell phones and computer games. As product lfe cycles become shorter, less data becomes avalable for analyss. Gven ths market stuaton, t s mportant to use smaller data sets to forecast future trends of new electronc products and servces as they are ntroduced. A product lfe cycle s typcally dvded nto four stages: ntroducton, growth, maturty and declne stage [3]. At ntroducton stage, the product s new to the market and the product awareness has not been bult, so the feature of ths stage s 1 Professor (Management Scence), Natonal Chao Tung Unversty, 1001 Ta Hsueh Road, Hsnchu, Tawan 300; Tel: +886 (3) ; Fax: +886 (3) ; Emal:
2 2 C. Trappey, HY. Wu slow sales growth. The growth stage s a perod of rapd sales growth snce the product s accepted wdely by the market and the sales volume wll boost. As the sales growth begn to slow down, the mature stage start. Therefore, the product lfe cycle curve can be llustrated wth Sshaped curve from ntroducton stage to begnnng of mature stage. Snce lfecycle curve grow as sgmod curve, growth curve method could be appled to forecast the future trend of products. Growth curves are wdely used n technology forecastng [4, 610] and are referred to as Sshaped curves. Technology product growth follows ths curve snce the ntal growth s often very slow (e.g., a new product replacng a mature product), followed by rapd exponental growth when barrers to adopton fall, whch then falls off as a lmt to market share s approached. The lmt reflects the saturaton of the marketplace wth the product or the replacement of the product wth another. The curve also models an nflecton or break pont where growth ends and declne begns. Many growth curve models have been developed to forecast the adopton rate of technology based products wth the smple logstc curve and the Gompertz curve the most frequently referenced [1, 6]. However, when usng these two models to forecast market share growth, care must be taken to set the upper lmt of the curve correctly or the predcton wll become naccurate. Settng the upper lmt to growth can dffcult and ambguous. If the product s a necessty or wll lkely be popular for decades, then the upper lmt can be set to 100% of the market share. Ths means that the product wll be completely replaced only after everyone n the market has purchased the product. However, when marketers consder new technology products such as a computer game or a new model cell phone, the value for the upper lmt to market share growth can be dffcult to estmate. That s, a computer game can be quckly replaced by another game after only reachng 10% market share. In order to avod the problem of estmatng the market share growth capacty for the smple logstc and the Gompertz models, Meyer and Ausubel [8] proposed the extended logstc model. Under ths model, the capacty (or upper lmt) of the curve s not constant but s dynamc over tme. Meyer and Ausubel also proposed that technology nnovatons do not occur evenly through tme but nstead appear n clusters or nnovaton waves. Thus, they formulated an extended logstcs model whch s a smple logstcs model wth a carryng capacty K ( t) that s tself a logstcs functon of tme. Therefore, the saturaton or celng value becomes dynamc and can model pulses from blogstc growth. Blogstc growth represents growth where market share seems to reach a lmt but then growth s suddenly rejuvenated or reborn and begns agan. Therefore, the researchers extend the constant capacty ( K ) of the smple logstc model to the carryng capacty ( K() t ). Ths study apples ths dea to the study of electroncs products wth K() t representng an extended logstc model. The proposton of ths research s that the extended logstc model wth a tmevaryng capacty feature wll be better than the smple logstc model and the Gompertz model whch requre a set constant capacty. Therefore, ths research studes the forecast accuracy of large and small data sets usng the smple logstc, Gompertz, and extended logstc models. A tmeseres dataset descrbng the
3 An Evaluaton of the Extended Logstc, Smple Logstc, and Gompertz Models for Forecastng Short Lfecycle Products and Servces 3 Tawan market growth rates for two types of electronc products and two types of servces were used to evaluate model performance. 2 Technologcal Forecastng Models 2.1 Smple Logstc Curve Model Most bologcal growth follows an Sshape curve or logstc curve whch best models growth and declne over tme [8]. Snce the adopton of technology and technology based products s smlar to bologcal growth, the smple logstc model s wdely used for technology forecastng. L The model of smple logstc curve s expressed as y = T 1 bt + ae where L s the upper bound of yt, a descrbes the locaton of the curve, and b controls the shape of the curve. To estmate the parameters for a and b, the equaton of the smple logstc model s transformed nto lnear functon usng natural logarthms. The lnear model s expressed as Yt = ln ( yt L yt ) = ln( a) + bt and the parameter a and b are then estmated usng a smple lnear regresson. 2.2 Gompertz Model The Gompertz model was frst used to calculate mortalty rates n 1825 but has snce been appled to technology forecastng [5]. Although the Gompertz curve s smlar to the smple logstc curve, t s not symmetrcal about the nfllecton pont whch occurs at t = ( ln() b k). Gompertz s model reaches the pont of nflcton = bt ae early n the growth trend and s expressed as y t = Le, where L s the upper bound whch should be set before estmatng the parameters a and b. Smlar to the parameters of the smple logstc model, natural logarthms are used to transform the orgnal Gompertz model to lnear equatony = ln ln L y = ln a and then the parameters are estmated. t ( ( )) ( ) bt 2.3 Extended Logstc Model t The smple logstc model and the Gompertz model assume that the capacty of technology adopton s fxed and there s an a upper bound to growth for these models. However, the adopton of new technology s seldom constant and changes over tme. As shown by Meyer & Ausubel [8], the orgnal form of smple logstc df model = y df by 1 s extended to = by dt k () 1 y, where k s the upper dt k t lmt of the logstc curve and k ( t) s the tmevaryng capacty and s the functon whch s smlar to logstc curve.
4 4 C. Trappey, HY. Wu Ths research uses the extended logstc model and assumes that k t = 1 D e, where the value of D can be any number and the value of A () at larger than zero. The settng of k( t) comes from Chen s study [2]. Ths research also assumes that the capacty wll fluctuate wth tme and the saturaton level of a product could be 100% but may also just be 60% or 80% because some new products could be ntroduced to the market and substtute older products. Thus, a product may not acheve the 100% penetraton of the market and may be replaced earler than expected. Fnally, the extended logstc model can be expressed ( t) at k 1 D e as yt = = bt bt 1+ C e 1+ C e tme, and a, b, C, D are the parameters computed usng a nonlnear estmaton method provded by a statstc software package lke SYSTAT., where k ( t) s the capacty that s fluctuate wth 2.4 The Measurements of Ft and Forecast Performance There are many statstcs used to measure forecast accuracy. In ths study, the Mean Absolute Devaton (MAD) and Root Mean Square Error (RMSE) are used to measure performance. The mathematcal representatons are shown below: n f fˆ = MAD = 1 n n ( f fˆ ) 2 = 1 RMSE = n where f s the actual value at tme t, fˆ s the estmate at tme t, and n s the number of observatons. These measurements are based on the resduals, whch represent the dstance between real data and predcted data. Consequently, f the values of these measurements are small, then the ft and predcted performance s acceptable. 3 Data Collecton and Data Analyss The Tawan market growth rate for color TVs, telephones, Asymmetrc Dgtal Subscrber Lnes (ASDL) and mobl nternet subscrbers were collected to test the forecast accuracy of the smple logstc model, the Gompertz model and the extended logstc model. ADSL s a type of data communcatons technology whch enables the use of the Internet over copper telephone lnes. ADSL users must sgn up for accounts so the applcaton data models the growth rate of adopton of the technology servce. Mobl nternet subscrbers also apply for accounts and the subscrptons for WAP, GPRS, and PHS represent ths class of data servce.
5 An Evaluaton of the Extended Logstc, Smple Logstc, and Gompertz Models for Forecastng Short Lfecycle Products and Servces 5 There are 31 data ponts for color TV set purchases (from 1974 to 2004) and 35 data ponts for telephone purchases (1964 to 2004). Twenty sx quarterly data ponts for ADSL subscrpton were collected from the second quarter n 2000 to the thrd quarter n 2006 and 19 quarterly data ponts for moble nternet subscrpton were collected from the thrd quarter n 2000 to the thrd quarter n Fgure 1 shows the saturaton rate for the four products. The growth rate for color TVs and telephones follows as Sshape curve and the curves for ADSL and moble nternet subscrptons also have basc sgmod curve. As can be seen n Fgure 1, t spent 20 years ( ) for telephone gettng nto the mature stage whose characterstc s slower growth rate than that at the growth stage n product lfecycle. Further, color TV also spent 10 years ( ) enterng the mature stage. However, for ADSL and moble nternet subscrptons, t only took 5 years to begn the mature stage. Therefore, the data for color TV and telephones were categorzed as long lfe cycle products, whle the data for ADSL and moble nternet were as short lfe cycle products. These four data are ftted to the models after removng the last fve data ponts. The last 5 data ponts were reserved to test the predcton accuracy of the models. Further, to compare the performance of the three models usng large and small data sets, the data for color TV and telephones were used to represent longer lfecycles (larger data sets) snce these two products have more than 30 years hstorc data. Compared to color TV and telephones, the data for ADSL and moble nternet subscrptons rely on small data sets of less than 6 years and represent shorter lfecycles. Fgure 1. Market growth for Color TVs, telephones, ADSL subscrpton, and moble Internet subscrpton Saturaton (%) Color TV Telephone ADSL Moble nternet Tme
6 6 C. Trappey, HY. Wu 4 Analyss The frst step s to ft the data to the smple logstc, Gompertz, and the extended logstc models. After reservng the last fve data ponts, the coeffcents of the models and the statstcs for MAD and RMSE are computed. The second step uses the derved models to forecast the fve data ponts and compare the forecast wth the true observatons and compare. Table 1 summarzes the ft and predcton performance of the three models. The evaluaton rule s that the smaller the value for MAD and RMSE, then the better the predcton performance. Therefore, the results show that the extended logstc model has the best ft and predcton performance for both long and short data sets. Thus, the extended logstc model s sutable for predctng both long and short lfecycle products. The smple logstc and the Gompertz model requre that the values for the upper lmt be set correctly, otherwse the accuracy of the models can be suffer. For the long data sets, the upper lmt for color TVs and telephones s easy to see and s set at 100%. However, for the short data sets, the capacty for ADSL and moble Internet servce s dffcult to determne. Thus, for the smple logstc and the Gompertz model, dfferent upper lmts are set for the short data sets. The upper lmt for the saturaton rate of ADSL s set to 100%, 50% or 30% whereas and the upper bound for moble Internet s set to ether 100% or 50%. As shown n Table 1, the extended logstc model wth tmevaryng capacty yelds the best ft and predcton performance. Table 1. Performance measures for the extended logstc, Gompertz, and the smple logstc models Data length Model Long data Short data Statstc Ft Forecast Extended Gompertz Smple Extended Gompertz Smple logstc logstc logstc logstc MAD Color TV RMSE Phone MAD RMSE ADSL MAD % RMSE ADSL MAD % RMSE ADSL MAD % RMSE Moble MAD Internet 100% RMSE
7 An Evaluaton of the Extended Logstc, Smple Logstc, and Gompertz Models for Forecastng Short Lfecycle Products and Servces 7 Moble MAD Internet 50% RMSE Dscusson and Concluson Ths study compares the ft and predcton performance of the smple logstc, Gompertz, and the extended logstc models for four electronc products. Snce the smple logstc and Gompertz curves requre the correct settng of upper lmts for accurate market growth rate predctons, these two models may not be sutable for short lfe cycle products wth lmted data. Therefore, to solve ths problem, the extended logstc model proposed by Meyer and Ausubel was used n ths study. Snce the extended logstc model estmates the tmevaryng capacty from the data, t tends to perform better for long data sets and for short data sets. Besdes, the extended logstc model s also sutable for predctng both long and short lfecycle products. There are lmtatons to the use of the extended logstc model. For example, Meade & Islam [6] use telephone data from Sweden to compare the smple logstc, extended logstc, and the local logstc models. They concluded that the extended logstc model had the worst performance. However, the growth curve of ther data set was resembled a lnear curve, not lke sgmod curve. Snce the capacty of extended logstc model s tmevaryng and s a logstcs functon of tme, t s not sutable for the data wth lnear curve. Therefore, we suggest that f forecasters wsh to apply the extended logstc model, then they should confrm that the data s not lnear. Ths research s concerned wth accurate market predctons for short lfe cycle, small data set problems. For ths study, we conclude that the extended logstc model s most sutable and research s planned to conduct a more rgorous and systematc testng of the model as proposed by Meade and Islam [8]. 5 Reference [1] Bengsu M, Nekhl R. Forecastng emergng technologes wth the ad of scence and technology databases. Technologcal Forecastng and Socal Change 2006;73: [2] Chen CP. The Test of Technologcal Forecastng Models: Comparson between Extended Logstc Model, FsherPry Model, and Gompertz Model. Master thess, Natonal Chao Tung Unversty, [3] Kotlor P. Marketng management. 11 th ed. 2003, New Jersey: Prentce Hall. [4] Levary RR, Han D. Choosng a technologcal forecastng method. Industral Management 1995;37:14. [5] Martno JP. Technologcal Forecastng for Decson Makng. 3 rd ed. 1993, New York: McGrawHll. [6] Meade N, Islam T. Forecastng wth growth curves: An emprcal comparson. Internatonal Journal of Forecastng 1995;11: [7] Meade N, Islam T. Technologcal forecastngmodel selecton, model stablty, and combnng models. Management Scence 1998;44:1115.
8 8 C. Trappey, HY. Wu [8] Meyer PS, Ausubel JH. Carryng Capacty A Model wth Logstcally Varyng Lmts. Technologcal Forecastng and Socal Change 1999;61: [9] Meyer PS, Yung JW, Ausubel JH. A Prmer on Logstc Growth and Substtuton. Technologcal Forecastng and Socal Change 1999;61: [10] Ra LP, Kumar N. Development and applcaton of mathematcal models for technology substtuton. PRANJANA 2003;6:
Forecasting the Direction and Strength of Stock Market Movement
Forecastng the Drecton and Strength of Stock Market Movement Jngwe Chen Mng Chen Nan Ye cjngwe@stanford.edu mchen5@stanford.edu nanye@stanford.edu Abstract  Stock market s one of the most complcated systems
More informationUsing Series to Analyze Financial Situations: Present Value
2.8 Usng Seres to Analyze Fnancal Stuatons: Present Value In the prevous secton, you learned how to calculate the amount, or future value, of an ordnary smple annuty. The amount s the sum of the accumulated
More informationForecasting the Demand of Emergency Supplies: Based on the CBR Theory and BP Neural Network
700 Proceedngs of the 8th Internatonal Conference on Innovaton & Management Forecastng the Demand of Emergency Supples: Based on the CBR Theory and BP Neural Network Fu Deqang, Lu Yun, L Changbng School
More informationCausal, Explanatory Forecasting. Analysis. Regression Analysis. Simple Linear Regression. Which is Independent? Forecasting
Causal, Explanatory Forecastng Assumes causeandeffect relatonshp between system nputs and ts output Forecastng wth Regresson Analyss Rchard S. Barr Inputs System Cause + Effect Relatonshp The job of
More informationThe Development of Web Log Mining Based on ImproveKMeans Clustering Analysis
The Development of Web Log Mnng Based on ImproveKMeans Clusterng Analyss TngZhong Wang * College of Informaton Technology, Luoyang Normal Unversty, Luoyang, 471022, Chna wangtngzhong2@sna.cn Abstract.
More informationStudy on CET4 Marks in China s Graded English Teaching
Study on CET4 Marks n Chna s Graded Englsh Teachng CHE We College of Foregn Studes, Shandong Insttute of Busness and Technology, P.R.Chna, 264005 Abstract: Ths paper deploys Logt model, and decomposes
More informationCalculating the high frequency transmission line parameters of power cables
< ' Calculatng the hgh frequency transmsson lne parameters of power cables Authors: Dr. John Dcknson, Laboratory Servces Manager, N 0 RW E B Communcatons Mr. Peter J. Ncholson, Project Assgnment Manager,
More informationSolution of Algebraic and Transcendental Equations
CHAPTER Soluton of Algerac and Transcendental Equatons. INTRODUCTION One of the most common prolem encountered n engneerng analyss s that gven a functon f (, fnd the values of for whch f ( = 0. The soluton
More informationU.C. Berkeley CS270: Algorithms Lecture 4 Professor Vazirani and Professor Rao Jan 27,2011 Lecturer: Umesh Vazirani Last revised February 10, 2012
U.C. Berkeley CS270: Algorthms Lecture 4 Professor Vazran and Professor Rao Jan 27,2011 Lecturer: Umesh Vazran Last revsed February 10, 2012 Lecture 4 1 The multplcatve weghts update method The multplcatve
More informationb) The mean of the fitted (predicted) values of Y is equal to the mean of the Y values: c) The residuals of the regression line sum up to zero: = ei
Mathematcal Propertes of the Least Squares Regresson The least squares regresson lne obeys certan mathematcal propertes whch are useful to know n practce. The followng propertes can be establshed algebracally:
More informationSPEE Recommended Evaluation Practice #6 Definition of Decline Curve Parameters Background:
SPEE Recommended Evaluaton Practce #6 efnton of eclne Curve Parameters Background: The producton hstores of ol and gas wells can be analyzed to estmate reserves and future ol and gas producton rates and
More informationHYPOTHESIS TESTING OF PARAMETERS FOR ORDINARY LINEAR CIRCULAR REGRESSION
HYPOTHESIS TESTING OF PARAMETERS FOR ORDINARY LINEAR CIRCULAR REGRESSION Abdul Ghapor Hussn Centre for Foundaton Studes n Scence Unversty of Malaya 563 KUALA LUMPUR Emal: ghapor@umedumy Abstract Ths paper
More information7.5. Present Value of an Annuity. Investigate
7.5 Present Value of an Annuty Owen and Anna are approachng retrement and are puttng ther fnances n order. They have worked hard and nvested ther earnngs so that they now have a large amount of money on
More information9.1 The Cumulative Sum Control Chart
Learnng Objectves 9.1 The Cumulatve Sum Control Chart 9.1.1 Basc Prncples: Cusum Control Chart for Montorng the Process Mean If s the target for the process mean, then the cumulatve sum control chart s
More informationIntroduction to Regression
Introducton to Regresson Regresson a means of predctng a dependent varable based one or more ndependent varables. Ths s done by fttng a lne or surface to the data ponts that mnmzes the total error. 
More informationAn Alternative Way to Measure Private Equity Performance
An Alternatve Way to Measure Prvate Equty Performance Peter Todd Parlux Investment Technology LLC Summary Internal Rate of Return (IRR) s probably the most common way to measure the performance of prvate
More informationBinary Dependent Variables. In some cases the outcome of interest rather than one of the right hand side variables is discrete rather than continuous
Bnary Dependent Varables In some cases the outcome of nterest rather than one of the rght hand sde varables s dscrete rather than contnuous The smplest example of ths s when the Y varable s bnary so that
More informationFORECASTING TELECOMMUNICATION NEW SERVICE DEMAND BY ANALOGY METHOD AND COMBINED FORECAST
Yugoslav Journal of Operatons Research 5 (005), Number, 9707 FORECAING ELECOMMUNICAION NEW ERVICE DEMAND BY ANALOGY MEHOD AND COMBINED FORECA FengJenq LIN Department of Appled Economcs Natonal ILan
More informationThe Analysis of Outliers in Statistical Data
THALES Project No. xxxx The Analyss of Outlers n Statstcal Data Research Team Chrysses Caron, Assocate Professor (P.I.) Vaslk Karot, Doctoral canddate Polychrons Economou, Chrstna Perrakou, Postgraduate
More informationPrediction of Wind Energy with Limited Observed Data
Predcton of Wnd Energy wth Lmted Observed Data Shgeto HIRI, khro HOND Nagasak R&D Center, MITSISHI HEVY INDSTRIES, LTD, Nagasak, 8539 JPN Masaak SHIT Nagasak Shpyard & Machnery Works, MITSISHI HEVY INDSTRIES,
More informationThe Application of Fractional Brownian Motion in Option Pricing
Vol. 0, No. (05), pp. 738 http://dx.do.org/0.457/jmue.05.0..6 The Applcaton of Fractonal Brownan Moton n Opton Prcng Qngxn Zhou School of Basc Scence,arbn Unversty of Commerce,arbn zhouqngxn98@6.com
More informationbenefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ).
REVIEW OF RISK MANAGEMENT CONCEPTS LOSS DISTRIBUTIONS AND INSURANCE Loss and nsurance: When someone s subject to the rsk of ncurrng a fnancal loss, the loss s generally modeled usng a random varable or
More informationA Novel Methodology of Working Capital Management for Large. Public Constructions by Using Fuzzy Scurve Regression
Novel Methodology of Workng Captal Management for Large Publc Constructons by Usng Fuzzy Scurve Regresson ChengWu Chen, Morrs H. L. Wang and TngYa Hseh Department of Cvl Engneerng, Natonal Central Unversty,
More informationModule 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module LOSSLESS IMAGE COMPRESSION SYSTEMS Lesson 3 Lossless Compresson: Huffman Codng Instructonal Objectves At the end of ths lesson, the students should be able to:. Defne and measure source entropy..
More informationCHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES
CHAPTER 5 RELATIONSHIPS BETWEEN QUANTITATIVE VARIABLES In ths chapter, we wll learn how to descrbe the relatonshp between two quanttatve varables. Remember (from Chapter 2) that the terms quanttatve varable
More informationCHAPTER 14 MORE ABOUT REGRESSION
CHAPTER 14 MORE ABOUT REGRESSION We learned n Chapter 5 that often a straght lne descrbes the pattern of a relatonshp between two quanttatve varables. For nstance, n Example 5.1 we explored the relatonshp
More informationInequality and The Accounting Period. Quentin Wodon and Shlomo Yitzhaki. World Bank and Hebrew University. September 2001.
Inequalty and The Accountng Perod Quentn Wodon and Shlomo Ytzha World Ban and Hebrew Unversty September Abstract Income nequalty typcally declnes wth the length of tme taen nto account for measurement.
More informationSIMPLE LINEAR CORRELATION
SIMPLE LINEAR CORRELATION Smple lnear correlaton s a measure of the degree to whch two varables vary together, or a measure of the ntensty of the assocaton between two varables. Correlaton often s abused.
More informationQuality Adjustment of Secondhand Motor Vehicle Application of Hedonic Approach in Hong Kong s Consumer Price Index
Qualty Adustment of Secondhand Motor Vehcle Applcaton of Hedonc Approach n Hong Kong s Consumer Prce Index Prepared for the 14 th Meetng of the Ottawa Group on Prce Indces 20 22 May 2015, Tokyo, Japan
More informationStatistical Methods to Develop Rating Models
Statstcal Methods to Develop Ratng Models [Evelyn Hayden and Danel Porath, Österrechsche Natonalbank and Unversty of Appled Scences at Manz] Source: The Basel II Rsk Parameters Estmaton, Valdaton, and
More informationProceedings of the Annual Meeting of the American Statistical Association, August 59, 2001
Proceedngs of the Annual Meetng of the Amercan Statstcal Assocaton, August 59, 2001 LISTASSISTED SAMPLING: THE EFFECT OF TELEPHONE SYSTEM CHANGES ON DESIGN 1 Clyde Tucker, Bureau of Labor Statstcs James
More informationCalculation of Sampling Weights
Perre Foy Statstcs Canada 4 Calculaton of Samplng Weghts 4.1 OVERVIEW The basc sample desgn used n TIMSS Populatons 1 and 2 was a twostage stratfed cluster desgn. 1 The frst stage conssted of a sample
More informationThe eigenvalue derivatives of linear damped systems
Control and Cybernetcs vol. 32 (2003) No. 4 The egenvalue dervatves of lnear damped systems by YeongJeu Sun Department of Electrcal Engneerng IShou Unversty Kaohsung, Tawan 840, R.O.C emal: yjsun@su.edu.tw
More informationBinomial Link Functions. Lori Murray, Phil Munz
Bnomal Lnk Functons Lor Murray, Phl Munz Bnomal Lnk Functons Logt Lnk functon: ( p) p ln 1 p Probt Lnk functon: ( p) 1 ( p) Complentary Log Log functon: ( p) ln( ln(1 p)) Motvatng Example A researcher
More informationSection 5.4 Annuities, Present Value, and Amortization
Secton 5.4 Annutes, Present Value, and Amortzaton Present Value In Secton 5.2, we saw that the present value of A dollars at nterest rate per perod for n perods s the amount that must be deposted today
More informationA study on the ability of Support Vector Regression and Neural Networks to Forecast Basic Time Series Patterns
A study on the ablty of Support Vector Regresson and Neural Networks to Forecast Basc Tme Seres Patterns Sven F. Crone, Jose Guajardo 2, and Rchard Weber 2 Lancaster Unversty, Department of Management
More informationProject Networks With MixedTime Constraints
Project Networs Wth MxedTme Constrants L Caccetta and B Wattananon Western Australan Centre of Excellence n Industral Optmsaton (WACEIO) Curtn Unversty of Technology GPO Box U1987 Perth Western Australa
More information9 Arithmetic and Geometric Sequence
AAU  Busness Mathematcs I Lecture #5, Aprl 4, 010 9 Arthmetc and Geometrc Sequence Fnte sequence: 1, 5, 9, 13, 17 Fnte seres: 1 + 5 + 9 + 13 +17 Infnte sequence: 1,, 4, 8, 16,... Infnte seres: 1 + + 4
More information1. Measuring association using correlation and regression
How to measure assocaton I: Correlaton. 1. Measurng assocaton usng correlaton and regresson We often would lke to know how one varable, such as a mother's weght, s related to another varable, such as a
More informationCan Auto Liability Insurance Purchases Signal Risk Attitude?
Internatonal Journal of Busness and Economcs, 2011, Vol. 10, No. 2, 159164 Can Auto Lablty Insurance Purchases Sgnal Rsk Atttude? ChuShu L Department of Internatonal Busness, Asa Unversty, Tawan ShengChang
More informationA hybrid global optimization algorithm based on parallel chaos optimization and outlook algorithm
Avalable onlne www.ocpr.com Journal of Chemcal and Pharmaceutcal Research, 2014, 6(7):18841889 Research Artcle ISSN : 09757384 CODEN(USA) : JCPRC5 A hybrd global optmzaton algorthm based on parallel
More informationIntroduction: Analysis of Electronic Circuits
/30/008 ntroducton / ntroducton: Analyss of Electronc Crcuts Readng Assgnment: KVL and KCL text from EECS Just lke EECS, the majorty of problems (hw and exam) n EECS 3 wll be crcut analyss problems. Thus,
More informationQuestions that we may have about the variables
Antono Olmos, 01 Multple Regresson Problem: we want to determne the effect of Desre for control, Famly support, Number of frends, and Score on the BDI test on Perceved Support of Latno women. Dependent
More informationTHE TITANIC SHIPWRECK: WHO WAS
THE TITANIC SHIPWRECK: WHO WAS MOST LIKELY TO SURVIVE? A STATISTICAL ANALYSIS Ths paper examnes the probablty of survvng the Ttanc shpwreck usng lmted dependent varable regresson analyss. Ths appled analyss
More informationTime Value of Money. Types of Interest. Compounding and Discounting Single Sums. Page 1. Ch. 6  The Time Value of Money. The Time Value of Money
Ch. 6  The Tme Value of Money Tme Value of Money The Interest Rate Smple Interest Compound Interest Amortzng a Loan FIN21 Ahmed Y, Dasht TIME VALUE OF MONEY OR DISCOUNTED CASH FLOW ANALYSIS Very Important
More informationFuzzy Regression and the Term Structure of Interest Rates Revisited
Fuzzy Regresson and the Term Structure of Interest Rates Revsted Arnold F. Shapro Penn State Unversty Smeal College of Busness, Unversty Park, PA 68, USA Phone: 84865396, Fax: 84865684, Emal: afs@psu.edu
More informationAn empirical study for credit card approvals in the Greek banking sector
An emprcal study for credt card approvals n the Greek bankng sector Mara Mavr George Ioannou Bergamo, Italy 1721 May 2004 Management Scences Laboratory Department of Management Scence & Technology Athens
More informationThe Effect of Mean Stress on Damage Predictions for Spectral Loading of Fiberglass Composite Coupons 1
EWEA, Specal Topc Conference 24: The Scence of Makng Torque from the Wnd, Delft, Aprl 92, 24, pp. 546555. The Effect of Mean Stress on Damage Predctons for Spectral Loadng of Fberglass Composte Coupons
More informationMarginal Benefit Incidence Analysis Using a Single Crosssection of Data. Mohamed Ihsan Ajwad and Quentin Wodon 1. World Bank.
Margnal Beneft Incdence Analyss Usng a Sngle Crosssecton of Data Mohamed Ihsan Ajwad and uentn Wodon World Bank August 200 Abstract In a recent paper, Lanjouw and Ravallon proposed an attractve and smple
More informationREVISED CRITERIA FOR CHOICE OF SUBSET SIZE IN TREND ANALYSIS AND PREDICTION
Journal of Informaton, Control and Management Systems, Vol. 4, (006), No. 69 REVISED CRITERIA FOR CHOICE OF SUBSET SIZE IN TREND ANALYSIS AND PREDICTION Vanya MARKOVA Insttute of Control and System Research,
More informationMultivariate EWMA Control Chart
Multvarate EWMA Control Chart Summary The Multvarate EWMA Control Chart procedure creates control charts for two or more numerc varables. Examnng the varables n a multvarate sense s extremely mportant
More informationNonlinear data mapping by neural networks
Nonlnear data mappng by neural networks R.P.W. Dun Delft Unversty of Technology, Netherlands Abstract A revew s gven of the use of neural networks for nonlnear mappng of hgh dmensonal data on lower dmensonal
More informationIDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS
IDENTIFICATION AND CORRECTION OF A COMMON ERROR IN GENERAL ANNUITY CALCULATIONS Chrs Deeley* Last revsed: September 22, 200 * Chrs Deeley s a Senor Lecturer n the School of Accountng, Charles Sturt Unversty,
More informationANALYZING THE RELATIONSHIPS BETWEEN QUALITY, TIME, AND COST IN PROJECT MANAGEMENT DECISION MAKING
ANALYZING THE RELATIONSHIPS BETWEEN QUALITY, TIME, AND COST IN PROJECT MANAGEMENT DECISION MAKING Matthew J. Lberatore, Department of Management and Operatons, Vllanova Unversty, Vllanova, PA 19085, 6105194390,
More informationJoe Pimbley, unpublished, 2005. Yield Curve Calculations
Joe Pmbley, unpublshed, 005. Yeld Curve Calculatons Background: Everythng s dscount factors Yeld curve calculatons nclude valuaton of forward rate agreements (FRAs), swaps, nterest rate optons, and forward
More informationVRT012 User s guide V0.1. Address: Žirmūnų g. 27, Vilnius LT09105, Phone: (3705) 2127472, Fax: (3705) 276 1380, Email: info@teltonika.
VRT012 User s gude V0.1 Thank you for purchasng our product. We hope ths userfrendly devce wll be helpful n realsng your deas and brngng comfort to your lfe. Please take few mnutes to read ths manual
More informationAPPLICATION OF PROBE DATA COLLECTED VIA INFRARED BEACONS TO TRAFFIC MANEGEMENT
APPLICATION OF PROBE DATA COLLECTED VIA INFRARED BEACONS TO TRAFFIC MANEGEMENT Toshhko Oda (1), Kochro Iwaoka (2) (1), (2) Infrastructure Systems Busness Unt, Panasonc System Networks Co., Ltd. Saedocho
More informationErrorPropagation.nb 1. Error Propagation
ErrorPropagaton.nb Error Propagaton Suppose that we make observatons of a quantty x that s subject to random fluctuatons or measurement errors. Our best estmate of the true value for ths quantty s then
More informationProperties of Indoor Received Signal Strength for WLAN Location Fingerprinting
Propertes of Indoor Receved Sgnal Strength for WLAN Locaton Fngerprntng Kamol Kaemarungs and Prashant Krshnamurthy Telecommuncatons Program, School of Informaton Scences, Unversty of Pttsburgh Emal: kakst2,prashk@ptt.edu
More informationDescriptive Models. Cluster Analysis. Example. General Applications of Clustering. Examples of Clustering Applications
CMSC828G Prncples of Data Mnng Lecture #9 Today s Readng: HMS, chapter 9 Today s Lecture: Descrptve Modelng Clusterng Algorthms Descrptve Models model presents the man features of the data, a global summary
More informationDEFINING %COMPLETE IN MICROSOFT PROJECT
CelersSystems DEFINING %COMPLETE IN MICROSOFT PROJECT PREPARED BY James E Aksel, PMP, PMISP, MVP For Addtonal Informaton about Earned Value Management Systems and reportng, please contact: CelersSystems,
More informationSection 5.3 Annuities, Future Value, and Sinking Funds
Secton 5.3 Annutes, Future Value, and Snkng Funds Ordnary Annutes A sequence of equal payments made at equal perods of tme s called an annuty. The tme between payments s the payment perod, and the tme
More informationSupport Vector Machines
Support Vector Machnes Max Wellng Department of Computer Scence Unversty of Toronto 10 Kng s College Road Toronto, M5S 3G5 Canada wellng@cs.toronto.edu Abstract Ths s a note to explan support vector machnes.
More informationADVERSE SELECTION IN INSURANCE MARKETS: POLICYHOLDER EVIDENCE FROM THE U.K. ANNUITY MARKET *
ADVERSE SELECTION IN INSURANCE MARKETS: POLICYHOLDER EVIDENCE FROM THE U.K. ANNUITY MARKET * Amy Fnkelsten Harvard Unversty and NBER James Poterba MIT and NBER * We are grateful to Jeffrey Brown, PerreAndre
More informationGraph Theory and Cayley s Formula
Graph Theory and Cayley s Formula Chad Casarotto August 10, 2006 Contents 1 Introducton 1 2 Bascs and Defntons 1 Cayley s Formula 4 4 Prüfer Encodng A Forest of Trees 7 1 Introducton In ths paper, I wll
More informationPRIVATE SCHOOL CHOICE: THE EFFECTS OF RELIGIOUS AFFILIATION AND PARTICIPATION
PRIVATE SCHOOL CHOICE: THE EFFECTS OF RELIIOUS AFFILIATION AND PARTICIPATION Danny CohenZada Department of Economcs, Benuron Unversty, BeerSheva 84105, Israel Wllam Sander Department of Economcs, DePaul
More informationTraffic State Estimation in the Traffic Management Center of Berlin
Traffc State Estmaton n the Traffc Management Center of Berln Authors: Peter Vortsch, PTV AG, Stumpfstrasse, D763 Karlsruhe, Germany phone ++49/72/965/35, emal peter.vortsch@ptv.de Peter Möhl, PTV AG,
More informationDescribing Communities. Species Diversity Concepts. Species Richness. Species Richness. SpeciesArea Curve. SpeciesArea Curve
peces versty Concepts peces Rchness pecesarea Curves versty Indces  mpson's Index  hannonwener Index  rlloun Index peces Abundance Models escrbng Communtes There are two mportant descrptors of a communty:
More informationOn the correct model specification for estimating the structure of a currency basket
On the correct model specfcaton for estmatng the structure of a currency basket JyhDean Hwang Department of Internatonal Busness Natonal Tawan Unversty 85 Roosevelt Road Sect. 4, Tape 106, Tawan jdhwang@ntu.edu.tw
More informationAnalysis of Premium Liabilities for Australian Lines of Business
Summary of Analyss of Premum Labltes for Australan Lnes of Busness Emly Tao Honours Research Paper, The Unversty of Melbourne Emly Tao Acknowledgements I am grateful to the Australan Prudental Regulaton
More informationOn the Optimal Control of a Cascade of HydroElectric Power Stations
On the Optmal Control of a Cascade of HydroElectrc Power Statons M.C.M. Guedes a, A.F. Rbero a, G.V. Smrnov b and S. Vlela c a Department of Mathematcs, School of Scences, Unversty of Porto, Portugal;
More informationThe Analysis of Covariance. ERSH 8310 Keppel and Wickens Chapter 15
The Analyss of Covarance ERSH 830 Keppel and Wckens Chapter 5 Today s Class Intal Consderatons Covarance and Lnear Regresson The Lnear Regresson Equaton TheAnalyss of Covarance Assumptons Underlyng the
More informationBrigid Mullany, Ph.D University of North Carolina, Charlotte
Evaluaton And Comparson Of The Dfferent Standards Used To Defne The Postonal Accuracy And Repeatablty Of Numercally Controlled Machnng Center Axes Brgd Mullany, Ph.D Unversty of North Carolna, Charlotte
More informationIdentifying Workloads in Mixed Applications
, pp.395400 http://dx.do.org/0.4257/astl.203.29.8 Identfyng Workloads n Mxed Applcatons Jeong Seok Oh, Hyo Jung Bang, Yong Do Cho, Insttute of Gas Safety R&D, Korea Gas Safety Corporaton, ShghungSh,
More informationPerformance Analysis of Energy Consumption of Smartphone Running Mobile Hotspot Application
Internatonal Journal of mart Grd and lean Energy Performance Analyss of Energy onsumpton of martphone Runnng Moble Hotspot Applcaton Yun on hung a chool of Electronc Engneerng, oongsl Unversty, 511 angdodong,
More informationSolution: Let i = 10% and d = 5%. By definition, the respective forces of interest on funds A and B are. i 1 + it. S A (t) = d (1 dt) 2 1. = d 1 dt.
Chapter 9 Revew problems 9.1 Interest rate measurement Example 9.1. Fund A accumulates at a smple nterest rate of 10%. Fund B accumulates at a smple dscount rate of 5%. Fnd the pont n tme at whch the forces
More informationUnderstanding the Impact of Marketing Actions in Traditional Channels on the Internet: Evidence from a Large Scale Field Experiment
A research and educaton ntatve at the MT Sloan School of Management Understandng the mpact of Marketng Actons n Tradtonal Channels on the nternet: Evdence from a Large Scale Feld Experment Paper 216 Erc
More informationPROFIT RATIO AND MARKET STRUCTURE
POFIT ATIO AND MAKET STUCTUE By Yong Yun Introducton: Industral economsts followng from Mason and Ban have run nnumerable tests of the relaton between varous market structural varables and varous dmensons
More informationAn Integrated Framework for Responsive Supply Chain Management
1 An Integrated Framework for Responsve Supply Chan Management 1 Darsht Parmar 1 Teresa Wu 1 John Fowler Tom Callarman 3 Vncent Hargaden 4 Eamonn Ambrose 1 Phlp Wolfe 1 Department of Industral Engneerng
More informationA Computer Technique for Solving LP Problems with Bounded Variables
Dhaka Unv. J. Sc. 60(2): 163168, 2012 (July) A Computer Technque for Solvng LP Problems wth Bounded Varables S. M. Atqur Rahman Chowdhury * and Sanwar Uddn Ahmad Department of Mathematcs; Unversty of
More informationIMPACT ANALYSIS OF A CELLULAR PHONE
4 th ASA & μeta Internatonal Conference IMPACT AALYSIS OF A CELLULAR PHOE We Lu, 2 Hongy L Bejng FEAonlne Engneerng Co.,Ltd. Bejng, Chna ABSTRACT Drop test smulaton plays an mportant role n nvestgatng
More informationTime Series Analysis in Studies of AGN Variability. Bradley M. Peterson The Ohio State University
Tme Seres Analyss n Studes of AGN Varablty Bradley M. Peterson The Oho State Unversty 1 Lnear Correlaton Degree to whch two parameters are lnearly correlated can be expressed n terms of the lnear correlaton
More informationEstimating the Development Effort of Web Projects in Chile
Estmatng the Development Effort of Web Projects n Chle Sergo F. Ochoa Computer Scences Department Unversty of Chle (56 2) 6784364 sochoa@dcc.uchle.cl M. Cecla Bastarrca Computer Scences Department Unversty
More informationCHOLESTEROL REFERENCE METHOD LABORATORY NETWORK. Sample Stability Protocol
CHOLESTEROL REFERENCE METHOD LABORATORY NETWORK Sample Stablty Protocol Background The Cholesterol Reference Method Laboratory Network (CRMLN) developed certfcaton protocols for total cholesterol, HDL
More information1. Fundamentals of probability theory 2. Emergence of communication traffic 3. Stochastic & Markovian Processes (SP & MP)
6.3 /  Communcaton Networks II (Görg) SS20  www.comnets.unbremen.de Communcaton Networks II Contents. Fundamentals of probablty theory 2. Emergence of communcaton traffc 3. Stochastc & Markovan Processes
More information"Research Note" APPLICATION OF CHARGE SIMULATION METHOD TO ELECTRIC FIELD CALCULATION IN THE POWER CABLES *
Iranan Journal of Scence & Technology, Transacton B, Engneerng, ol. 30, No. B6, 789794 rnted n The Islamc Republc of Iran, 006 Shraz Unversty "Research Note" ALICATION OF CHARGE SIMULATION METHOD TO ELECTRIC
More information8.5 UNITARY AND HERMITIAN MATRICES. The conjugate transpose of a complex matrix A, denoted by A*, is given by
6 CHAPTER 8 COMPLEX VECTOR SPACES 5. Fnd the kernel of the lnear transformaton gven n Exercse 5. In Exercses 55 and 56, fnd the mage of v, for the ndcated composton, where and are gven by the followng
More informationA COLLABORATIVE TRADING MODEL BY SUPPORT VECTOR REGRESSION AND TS FUZZY RULE FOR DAILY STOCK TURNING POINTS DETECTION
A COLLABORATIVE TRADING MODEL BY SUPPORT VECTOR REGRESSION AND TS FUZZY RULE FOR DAILY STOCK TURNING POINTS DETECTION JHENGLONG WU, PEICHANN CHANG, KAITING CHANG Department of Informaton Management,
More informationRecurrence. 1 Definitions and main statements
Recurrence 1 Defntons and man statements Let X n, n = 0, 1, 2,... be a MC wth the state space S = (1, 2,...), transton probabltes p j = P {X n+1 = j X n = }, and the transton matrx P = (p j ),j S def.
More informationLecture 10: Linear Regression Approach, Assumptions and Diagnostics
Approach to Modelng I Lecture 1: Lnear Regresson Approach, Assumptons and Dagnostcs Sandy Eckel seckel@jhsph.edu 8 May 8 General approach for most statstcal modelng: Defne the populaton of nterest State
More informationCommunication Networks II Contents
8 / 1  Communcaton Networs II (Görg)  www.comnets.unbremen.de Communcaton Networs II Contents 1 Fundamentals of probablty theory 2 Traffc n communcaton networs 3 Stochastc & Marovan Processes (SP
More informationOnline Appendix Supplemental Material for Market Microstructure Invariance: Empirical Hypotheses
Onlne Appendx Supplemental Materal for Market Mcrostructure Invarance: Emprcal Hypotheses Albert S. Kyle Unversty of Maryland akyle@rhsmth.umd.edu Anna A. Obzhaeva New Economc School aobzhaeva@nes.ru Table
More information1. Math 210 Finite Mathematics
1. ath 210 Fnte athematcs Chapter 5.2 and 5.3 Annutes ortgages Amortzaton Professor Rchard Blecksmth Dept. of athematcal Scences Northern Illnos Unversty ath 210 Webste: http://math.nu.edu/courses/math210
More informationSingle and multiple stage classifiers implementing logistic discrimination
Sngle and multple stage classfers mplementng logstc dscrmnaton Hélo Radke Bttencourt 1 Dens Alter de Olvera Moraes 2 Vctor Haertel 2 1 Pontfíca Unversdade Católca do Ro Grande do Sul  PUCRS Av. Ipranga,
More informationLinear Circuits Analysis. Superposition, Thevenin /Norton Equivalent circuits
Lnear Crcuts Analyss. Superposton, Theenn /Norton Equalent crcuts So far we hae explored tmendependent (resste) elements that are also lnear. A tmendependent elements s one for whch we can plot an / cure.
More informationThe OC Curve of Attribute Acceptance Plans
The OC Curve of Attrbute Acceptance Plans The Operatng Characterstc (OC) curve descrbes the probablty of acceptng a lot as a functon of the lot s qualty. Fgure 1 shows a typcal OC Curve. 10 8 6 4 1 3 4
More informationConversion between the vector and raster data structures using Fuzzy Geographical Entities
Converson between the vector and raster data structures usng Fuzzy Geographcal Enttes Cdála Fonte Department of Mathematcs Faculty of Scences and Technology Unversty of Combra, Apartado 38, 3 454 Combra,
More informationNumber of Levels Cumulative Annual operating Income per year construction costs costs ($) ($) ($) 1 600,000 35,000 100,000 2 2,200,000 60,000 350,000
Problem Set 5 Solutons 1 MIT s consderng buldng a new car park near Kendall Square. o unversty funds are avalable (overhead rates are under pressure and the new faclty would have to pay for tself from
More informationJ. Parallel Distrib. Comput.
J. Parallel Dstrb. Comput. 71 (2011) 62 76 Contents lsts avalable at ScenceDrect J. Parallel Dstrb. Comput. journal homepage: www.elsever.com/locate/jpdc Optmzng server placement n dstrbuted systems n
More informationAn InterestOriented Network Evolution Mechanism for Online Communities
An InterestOrented Network Evoluton Mechansm for Onlne Communtes Cahong Sun and Xaopng Yang School of Informaton, Renmn Unversty of Chna, Bejng 100872, P.R. Chna {chsun,yang}@ruc.edu.cn Abstract. Onlne
More information