An inductive proof for a closed form formula in truncated inverse sampling
|
|
- Ethelbert Nelson
- 5 years ago
- Views:
Transcription
1 Journal of Proagatons n Probablty and Statstcs Vol. No. August Internatonal ed.. 7- An nductve roof for a closed for forula n truncated nverse salng Kuang-Chao Chang Fu Jen Catholc Unversty Abstract Inverse salng s a seuental salng rocedure such that salng s contnued untl a redeterned nuber of unts ossessng certan attrbute are ncluded n the sale. Ths salng rocedure does not have control over the total sale sze n artcular when the attrbute under consderaton revals wth rare freuency. A reedy for ths shortcong s to truncate the salng rocedure when the total sale sze reaches a secfed axu nuber. We roose a closed for forula to coute the exected total sale sze n ths truncated verson of nverse salng and we rove the forula by atheatcal nducton. Keywords: Inverse salng Truncated nverse salng atheatcal nducton. Kuang-Chao Chang s Assocate Professor Deartent of Statstcs and Inforaton Scence Fu Jen Catholc Unversty Tae Tawan ROC. -al: stat6@als.fu.edu.tw
2 JPPS Volue Nuber August. 7-. Introducton In sale survey theory and ethodology nverse salng s often used to estate the roorton of a certan rare te n the oulaton. In so-called standard nverse salng sales are taen randoly and seuentally untl a secfed nuber of the rare te has been observed see Haldane 945 or Cochran 977. A drawbac n such salng rocedure s the lac of control on the fnal rando sale sze whch ay be very large f the value of the roorton to be estated s very sall. To overcoe ths drawbac we ay consder truncatng the nverse salng rocedure when the rando total sale sze reaches a redeterned ostve nteger. Ths odfed verson of nverse salng wll be called the truncated nverse salng TIS. In ths aer we roose a closed for forula to coute the exected fnal rando total sale sze n TIS under the assuton of nfnte oulaton and we rove the forula by the ethod of atheatcal nducton. The contents of ths artcle ay be used as suleentary teachng ateral for teachers of robablty statstcs atheatcs and other related felds.. A closed for forula n TIS We begn ths secton wth the followng lea. Lea. Let X be dstrbuted as Bnoaln then n Pr X n where. Proof. Let Y be dstrbuted as Bnoaln then n Pr X n Pr Y Y n snce Y s nonnegatve and nteger-valued see Karr Corollary 4.4. Q..D. Next n the followng theore we gve the closed for forula to coute the exected fnal rando total sale sze n TIS assung the oulaton s nfnte. Theore. Let Z have negatve bnoal dstrbuton wth..f. z z f z z L and let Z be the rando varable defned by Z n{z } where s a ostve nteger and. Then the exected value of Z denoted by s - 8 -
3 A closed for forula n truncated nverse salng Kuang-Chao Chang f > f. Proof. The case that s trval. If > we rove by nducton on. Let U be the rando varable defned by otherwse. results n a success the frst tral f U Then when we have U PrU U PrU [ ].. [ ] L L /. Next we assue that the theore s true f the araeter value of the reured nuber of successes for Z s. Then when the araeter value s we have U PrU U PrU [ ]. [ ]. { } { } - 9 -
4 JPPS Volue Nuber August. 7-. Now and see Feller 968 Vol. I.64 euaton.8. Thus where. Let XBnoal then by Lea.. Pr X Cobnng all the above results we obtan { } - -
5 A closed for forula n truncated nverse salng Kuang-Chao Chang. Q..D. The dstrbuton of Z n Theore. ay be consdered as a rght truncated negatve bnoal dstrbuton dfferng fro those left truncated ones largely dscussed n lterature see Saford 955 Rder 955 Cacoullos and Charalabdes 975 Johnson Kotz and Ke etc.. 3. Concluson In ths aer we roosed a closed for forula to coute the exected fnal rando total sale sze n TIS and we roved the forula by atheatcal nducton. The ethod of atheatcal nducton ay be used to rove any forulas n salng theory. We conclude ths aer by ntroducng the followng Lea 3. n whch a well-nown forula n cature-recature salng s gven see Sngh and Chaudhary or Chaan 95. The nductve roof of the forula s left as an exercse for readers. Lea 3. Let N be the sze of a fnte oulaton consstng of two strata and let th N h be the h stratu sze h. Sales are taen seuentally wthout relaceent untl observatons are obtaned fro the frst stratu. Then the exected value of the fnal rando sale sze denoted by N N N s where N. N N N N N The roof wll be gven n the next ssue of ths ournal. Acnowledgeents The author would le to than Professor Chen-Pa Han and Professor Shaw-Hwa Lo for ther careful readng and helful coents. References Cacoullos T. and Charalabdes C. A On VU for truncated bnoal and negatve bnoal dstrbutons Annals of the Insttute of Statstcal atheatcs
6 JPPS Volue Nuber August. 7- Chaan D. G. 95. Inverse ultle and seuental sale censuses Boetrcs Cochran W. G Salng Technues 3 rd ed. Wley. Feller W An Introducton to Probablty Theory and Its Alcatons Vol. I 3 rd ed. Wley. Haldane J. B. S On a ethod of estatng freuences Boetra Johnson N. L. Kotz S. and Ke A. W. 99. Unvarate Dscrete Dstrbutons nd ed. Wley. Karr A. F Probablty. Srnger-Verlag. Rder Paul R.955. Truncated bnoal and negatve bnoal dstrbutons Journal of the Aercan Statstcal Assocaton Saford. R The truncated negatve bnoal dstrbuton Boetra Sngh D. and Chaudhary F. S Theory and Analyss of Sale Survey Desgns Wley. - -
Inference on Reliability in the Gamma and Inverted Gamma Distributions
Statstcs n the Twenty-Frst Century: Specal Volue In Honour of Dstngushed Professor Dr. Mr Masoo Al On the Occason of hs 75th Brthday Annversary PJSOR, Vol. 8, No. 3, pages 635-643, July Jungsoo Woo Departent
More informationEconomic Design of Short-Run CSP-1 Plan Under Linear Inspection Cost
Tamkang Journal of Scence and Engneerng, Vol. 9, No 1, pp. 19 23 (2006) 19 Economc Desgn of Short-Run CSP-1 Plan Under Lnear Inspecton Cost Chung-Ho Chen 1 * and Chao-Yu Chou 2 1 Department of Industral
More informationCyclic Scheduling in a Job shop with Multiple Assembly Firms
Proceedngs of the 0 Internatonal Conference on Industral Engneerng and Operatons Management Kuala Lumpur, Malaysa, January 4, 0 Cyclc Schedulng n a Job shop wth Multple Assembly Frms Tetsuya Kana and Koch
More informationEstimating Long-Run PD, Asset Correlation, and Portfolio Level PD by Vasicek Models
MPRA Munch Personal RePEc Archve Estatng Long-Run PD, Asset Correlaton, and Portfolo Level PD by Vasce Models Bll Huajan Yang. July 3 Onlne at http://pra.ub.un-uenchen.de/5744/ MPRA Paper No. 5744, posted.
More informationarxiv: v1 [math.nt] 29 Oct 2015
A DIGITAL BINOMIAL THEOREM FOR SHEFFER SEQUENCES TOUFIK MANSOUR AND HIEU D. NGUYEN arxv:1510.08529v1 [math.nt] 29 Oct 2015 Abstract. We extend the dgtal bnomal theorem to Sheffer polynomal sequences by
More informationMgtOp 215 Chapter 13 Dr. Ahn
MgtOp 5 Chapter 3 Dr Ahn Consder two random varables X and Y wth,,, In order to study the relatonshp between the two random varables, we need a numercal measure that descrbes the relatonshp The covarance
More information15-451/651: Design & Analysis of Algorithms January 22, 2019 Lecture #3: Amortized Analysis last changed: January 18, 2019
5-45/65: Desgn & Analyss of Algorthms January, 09 Lecture #3: Amortzed Analyss last changed: January 8, 09 Introducton In ths lecture we dscuss a useful form of analyss, called amortzed analyss, for problems
More informationTests for Two Correlations
PASS Sample Sze Software Chapter 805 Tests for Two Correlatons Introducton The correlaton coeffcent (or correlaton), ρ, s a popular parameter for descrbng the strength of the assocaton between two varables.
More informationTests for Two Ordered Categorical Variables
Chapter 253 Tests for Two Ordered Categorcal Varables Introducton Ths module computes power and sample sze for tests of ordered categorcal data such as Lkert scale data. Assumng proportonal odds, such
More informationPrice and Quantity Competition Revisited. Abstract
rce and uantty Competton Revsted X. Henry Wang Unversty of Mssour - Columba Abstract By enlargng the parameter space orgnally consdered by Sngh and Vves (984 to allow for a wder range of cost asymmetry,
More informationIn this appendix, we present some theoretical aspects of game theory that would be followed by players in a restructured energy market.
Market Operatons n Electrc Power Systes: Forecastng, Schedulng, and Rsk Manageentg Mohaad Shahdehpour, Hat Yan, Zuy L Copyrght 2002 John Wley & Sons, Inc. ISBNs: 0-47-44337-9 (Hardback); 0-47-2242-X (Electronc)
More informationOPERATIONS RESEARCH. Game Theory
OPERATIONS RESEARCH Chapter 2 Game Theory Prof. Bbhas C. Gr Department of Mathematcs Jadavpur Unversty Kolkata, Inda Emal: bcgr.umath@gmal.com 1.0 Introducton Game theory was developed for decson makng
More informationMode is the value which occurs most frequency. The mode may not exist, and even if it does, it may not be unique.
1.7.4 Mode Mode s the value whch occurs most frequency. The mode may not exst, and even f t does, t may not be unque. For ungrouped data, we smply count the largest frequency of the gven value. If all
More informationTopics on the Border of Economics and Computation November 6, Lecture 2
Topcs on the Border of Economcs and Computaton November 6, 2005 Lecturer: Noam Nsan Lecture 2 Scrbe: Arel Procacca 1 Introducton Last week we dscussed the bascs of zero-sum games n strategc form. We characterzed
More informationHomework 9: due Monday, 27 October, 2008
PROBLEM ONE Homework 9: due Monday, 7 October, 008. (Exercses from the book, 6 th edton, 6.6, -3.) Determne the number of dstnct orderngs of the letters gven: (a) GUIDE (b) SCHOOL (c) SALESPERSONS. (Exercses
More informationAnalysis of Variance and Design of Experiments-II
Analyss of Varance and Desgn of Experments-II MODULE VI LECTURE - 4 SPLIT-PLOT AND STRIP-PLOT DESIGNS Dr. Shalabh Department of Mathematcs & Statstcs Indan Insttute of Technology Kanpur An example to motvate
More informationReal Exchange Rate Fluctuations, Wage Stickiness and Markup Adjustments
Real Exchange Rate Fluctuatons, Wage Stckness and Markup Adjustments Yothn Jnjarak and Kanda Nakno Nanyang Technologcal Unversty and Purdue Unversty January 2009 Abstract Motvated by emprcal evdence on
More information3/3/2014. CDS M Phil Econometrics. Vijayamohanan Pillai N. Truncated standard normal distribution for a = 0.5, 0, and 0.5. CDS Mphil Econometrics
Lmted Dependent Varable Models: Tobt an Plla N 1 CDS Mphl Econometrcs Introducton Lmted Dependent Varable Models: Truncaton and Censorng Maddala, G. 1983. Lmted Dependent and Qualtatve Varables n Econometrcs.
More informationParallel Prefix addition
Marcelo Kryger Sudent ID 015629850 Parallel Prefx addton The parallel prefx adder presented next, performs the addton of two bnary numbers n tme of complexty O(log n) and lnear cost O(n). Lets notce the
More informationChapter 3 Descriptive Statistics: Numerical Measures Part B
Sldes Prepared by JOHN S. LOUCKS St. Edward s Unversty Slde 1 Chapter 3 Descrptve Statstcs: Numercal Measures Part B Measures of Dstrbuton Shape, Relatve Locaton, and Detectng Outlers Eploratory Data Analyss
More informationTest Bank to accompany Modern Portfolio Theory and Investment Analysis, 9 th Edition
Test ank to accopany Modern ortfolo Theory and Investent Analyss, 9 th Edton Test ank to accopany Modern ortfolo Theory and Investent Analyss, 9th Edton Copleted download lnk: https://testbankarea.co/download/odern-portfolotheory-nvestent-analyss-9th-edton-test-bank-eltongruber-brown-goetzann/
More informationLinear Combinations of Random Variables and Sampling (100 points)
Economcs 30330: Statstcs for Economcs Problem Set 6 Unversty of Notre Dame Instructor: Julo Garín Sprng 2012 Lnear Combnatons of Random Varables and Samplng 100 ponts 1. Four-part problem. Go get some
More informationNotes are not permitted in this examination. Do not turn over until you are told to do so by the Invigilator.
UNIVERSITY OF EAST ANGLIA School of Economcs Man Seres PG Examnaton 2016-17 BANKING ECONOMETRICS ECO-7014A Tme allowed: 2 HOURS Answer ALL FOUR questons. Queston 1 carres a weght of 30%; queston 2 carres
More informationCreating a zero coupon curve by bootstrapping with cubic splines.
MMA 708 Analytcal Fnance II Creatng a zero coupon curve by bootstrappng wth cubc splnes. erg Gryshkevych Professor: Jan R. M. Röman 0.2.200 Dvson of Appled Mathematcs chool of Educaton, Culture and Communcaton
More informationChapter 3 Student Lecture Notes 3-1
Chapter 3 Student Lecture otes 3-1 Busness Statstcs: A Decson-Makng Approach 6 th Edton Chapter 3 Descrbng Data Usng umercal Measures 005 Prentce-Hall, Inc. Chap 3-1 Chapter Goals After completng ths chapter,
More informationWages as Anti-Corruption Strategy: A Note
DISCUSSION PAPER November 200 No. 46 Wages as Ant-Corrupton Strategy: A Note by dek SAO Faculty of Economcs, Kyushu-Sangyo Unversty Wages as ant-corrupton strategy: A Note dek Sato Kyushu-Sangyo Unversty
More informationChapter 5 Student Lecture Notes 5-1
Chapter 5 Student Lecture Notes 5-1 Basc Busness Statstcs (9 th Edton) Chapter 5 Some Important Dscrete Probablty Dstrbutons 004 Prentce-Hall, Inc. Chap 5-1 Chapter Topcs The Probablty Dstrbuton of a Dscrete
More informationDr. A. Sudhakaraiah* V. Rama Latha E.Gnana Deepika
Internatonal Journal Of Scentfc & Engneerng Research, Volume, Issue 6, June-0 ISSN - Splt Domnatng Set of an Interval Graph Usng an Algorthm. Dr. A. Sudhakaraah* V. Rama Latha E.Gnana Deepka Abstract :
More informationThe Integration of the Israel Labour Force Survey with the National Insurance File
The Integraton of the Israel Labour Force Survey wth the Natonal Insurance Fle Natale SHLOMO Central Bureau of Statstcs Kanfey Nesharm St. 66, corner of Bach Street, Jerusalem Natales@cbs.gov.l Abstact:
More informationreferences Chapters on game theory in Mas-Colell, Whinston and Green
Syllabus. Prelmnares. Role of game theory n economcs. Normal and extensve form of a game. Game-tree. Informaton partton. Perfect recall. Perfect and mperfect nformaton. Strategy.. Statc games of complete
More informationCS 286r: Matching and Market Design Lecture 2 Combinatorial Markets, Walrasian Equilibrium, Tâtonnement
CS 286r: Matchng and Market Desgn Lecture 2 Combnatoral Markets, Walrasan Equlbrum, Tâtonnement Matchng and Money Recall: Last tme we descrbed the Hungaran Method for computng a maxmumweght bpartte matchng.
More informationA Bootstrap Confidence Limit for Process Capability Indices
A ootstrap Confdence Lmt for Process Capablty Indces YANG Janfeng School of usness, Zhengzhou Unversty, P.R.Chna, 450001 Abstract The process capablty ndces are wdely used by qualty professonals as an
More informationA DUAL EXTERIOR POINT SIMPLEX TYPE ALGORITHM FOR THE MINIMUM COST NETWORK FLOW PROBLEM
Yugoslav Journal of Operatons Research Vol 19 (2009), Number 1, 157-170 DOI:10.2298/YUJOR0901157G A DUAL EXTERIOR POINT SIMPLEX TYPE ALGORITHM FOR THE MINIMUM COST NETWORK FLOW PROBLEM George GERANIS Konstantnos
More informationRandom Variables. b 2.
Random Varables Generally the object of an nvestgators nterest s not necessarly the acton n the sample space but rather some functon of t. Techncally a real valued functon or mappng whose doman s the sample
More informationTesting for Omitted Variables
Testng for Omtted Varables Jeroen Weese Department of Socology Unversty of Utrecht The Netherlands emal J.weese@fss.uu.nl tel +31 30 2531922 fax+31 30 2534405 Prepared for North Amercan Stata users meetng
More informationEquilibrium in Prediction Markets with Buyers and Sellers
Equlbrum n Predcton Markets wth Buyers and Sellers Shpra Agrawal Nmrod Megddo Benamn Armbruster Abstract Predcton markets wth buyers and sellers of contracts on multple outcomes are shown to have unque
More informationOn the Block-cut Transformation Graphs
Journal of Couter and Matheatal Senes, Vol.66,354-36, June 015 An Internatonal Researh Journal, www.oath-ournal.org ISSN 0976-577 Prnt ISSN 319-8133 Onlne On the Blok-ut Transforaton Grahs B. Basaanagoud
More informationWhich of the following provides the most reasonable approximation to the least squares regression line? (a) y=50+10x (b) Y=50+x (d) Y=1+50x
Whch of the followng provdes the most reasonable approxmaton to the least squares regresson lne? (a) y=50+10x (b) Y=50+x (c) Y=10+50x (d) Y=1+50x (e) Y=10+x In smple lnear regresson the model that s begn
More informationTo find a non-split strong dominating set of an interval graph using an algorithm
IOSR Journal of Mathematcs (IOSR-JM) e-issn: 2278-5728,p-ISSN: 219-765X, Volume 6, Issue 2 (Mar - Apr 201), PP 05-10 To fnd a non-splt rong domnatng set of an nterval graph usng an algorthm Dr A Sudhakaraah*,
More informationMeasures of Spread IQR and Deviation. For exam X, calculate the mean, median and mode. For exam Y, calculate the mean, median and mode.
Part 4 Measures of Spread IQR and Devaton In Part we learned how the three measures of center offer dfferent ways of provdng us wth a sngle representatve value for a data set. However, consder the followng
More informationBasket Default Swaps Pricing Based on the Normal Inverse Gaussian Distribution
Councatons n Matheatcal Fnance, vol. 2, no. 3, 23, 4-54 ISSN: 224-968 (prnt, 224 95X (onlne Scenpress Ltd, 23 Baset Default Swaps Prcng Based on the Noral Inverse Gaussan Dstrbuton Xuen Zhao, Maoun Zhang,2
More informationECE 586GT: Problem Set 2: Problems and Solutions Uniqueness of Nash equilibria, zero sum games, evolutionary dynamics
Unversty of Illnos Fall 08 ECE 586GT: Problem Set : Problems and Solutons Unqueness of Nash equlbra, zero sum games, evolutonary dynamcs Due: Tuesday, Sept. 5, at begnnng of class Readng: Course notes,
More informationA Comparison of Statistical Methods in Interrupted Time Series Analysis to Estimate an Intervention Effect
Transport and Road Safety (TARS) Research Joanna Wang A Comparson of Statstcal Methods n Interrupted Tme Seres Analyss to Estmate an Interventon Effect Research Fellow at Transport & Road Safety (TARS)
More informationFoundations of Machine Learning II TP1: Entropy
Foundatons of Machne Learnng II TP1: Entropy Gullaume Charpat (Teacher) & Gaétan Marceau Caron (Scrbe) Problem 1 (Gbbs nequalty). Let p and q two probablty measures over a fnte alphabet X. Prove that KL(p
More informationTCOM501 Networking: Theory & Fundamentals Final Examination Professor Yannis A. Korilis April 26, 2002
TO5 Networng: Theory & undamentals nal xamnaton Professor Yanns. orls prl, Problem [ ponts]: onsder a rng networ wth nodes,,,. In ths networ, a customer that completes servce at node exts the networ wth
More informationPrivatization and government preference in an international Cournot triopoly
Fernanda A Ferrera Flávo Ferrera Prvatzaton and government preference n an nternatonal Cournot tropoly FERNANDA A FERREIRA and FLÁVIO FERREIRA Appled Management Research Unt (UNIAG School of Hosptalty
More informationYORK UNIVERSITY Faculty of Science Department of Mathematics and Statistics MATH A Test #2 November 03, 2014
Famly Name prnt): YORK UNIVERSITY Faculty of Scence Department of Mathematcs and Statstcs MATH 2280.00 A Test #2 November 0, 2014 Solutons Gven Name: Student No: Sgnature: INSTRUCTIONS: 1. Please wrte
More informationA REAL OPTIONS DESIGN FOR PRODUCT OUTSOURCING. Mehmet Aktan
Proceedngs of the 2001 Wnter Smulaton Conference B. A. Peters, J. S. Smth, D. J. Mederos, and M. W. Rohrer, eds. A REAL OPTIONS DESIGN FOR PRODUCT OUTSOURCING Harret Black Nembhard Leyuan Sh Department
More informationUNIVERSITY OF VICTORIA Midterm June 6, 2018 Solutions
UIVERSITY OF VICTORIA Mdterm June 6, 08 Solutons Econ 45 Summer A0 08 age AME: STUDET UMBER: V00 Course ame & o. Descrptve Statstcs and robablty Economcs 45 Secton(s) A0 CR: 3067 Instructor: Betty Johnson
More information4. Greek Letters, Value-at-Risk
4 Greek Letters, Value-at-Rsk 4 Value-at-Rsk (Hull s, Chapter 8) Math443 W08, HM Zhu Outlne (Hull, Chap 8) What s Value at Rsk (VaR)? Hstorcal smulatons Monte Carlo smulatons Model based approach Varance-covarance
More informationCHAPTER 3: BAYESIAN DECISION THEORY
CHATER 3: BAYESIAN DECISION THEORY Decson makng under uncertanty 3 rogrammng computers to make nference from data requres nterdscplnary knowledge from statstcs and computer scence Knowledge of statstcs
More informationSIMPLE FIXED-POINT ITERATION
SIMPLE FIXED-POINT ITERATION The fed-pont teraton method s an open root fndng method. The method starts wth the equaton f ( The equaton s then rearranged so that one s one the left hand sde of the equaton
More informationFinancial mathematics
Fnancal mathematcs Jean-Luc Bouchot jean-luc.bouchot@drexel.edu February 19, 2013 Warnng Ths s a work n progress. I can not ensure t to be mstake free at the moment. It s also lackng some nformaton. But
More informationAppendix for Solving Asset Pricing Models when the Price-Dividend Function is Analytic
Appendx for Solvng Asset Prcng Models when the Prce-Dvdend Functon s Analytc Ovdu L. Caln Yu Chen Thomas F. Cosmano and Alex A. Hmonas January 3, 5 Ths appendx provdes proofs of some results stated n our
More informationAbstract The R chart is often used to monitor for changes in the process variability. However, the standard
An Alternatve to the Stanar Chart chael B.C. Khoo an H.C. Lo School of athematcal Scences, Unverst Sans alaysa, 800 nen, Penang, alaysa Emal: mkbc@usm.my & hclo@cs.usm.my Abstract The chart s often use
More informationAn introduction to quasi-random numbers
An ntroducton to quas-random numbers By George Levy, umercal Algorthms Grou Ltd. Introducton Monte-Carlo smulaton and random number generaton are technques that are wdely used n fnancal engneerng as a
More informationHow Likely Is Contagion in Financial Networks?
OFFICE OF FINANCIAL RESEARCH How Lkely Is Contagon n Fnancal Networks? Paul Glasserman & Peyton Young Systemc Rsk: Models and Mechansms Isaac Newton Insttute, Unversty of Cambrdge August 26-29, 2014 Ths
More informationAnswers to exercises in Macroeconomics by Nils Gottfries 2013
. a) C C b C C s the ntercept o the consumpton uncton, how much consumpton wll be at zero ncome. We can thnk that, at zero ncome, the typcal consumer would consume out o hs assets. The slope b s the margnal
More informationEDC Introduction
.0 Introducton EDC3 In the last set of notes (EDC), we saw how to use penalty factors n solvng the EDC problem wth losses. In ths set of notes, we want to address two closely related ssues. What are, exactly,
More informationCOS 511: Theoretical Machine Learning. Lecturer: Rob Schapire Lecture #21 Scribe: Lawrence Diao April 23, 2013
COS 511: Theoretcal Machne Learnng Lecturer: Rob Schapre Lecture #21 Scrbe: Lawrence Dao Aprl 23, 2013 1 On-Lne Log Loss To recap the end of the last lecture, we have the followng on-lne problem wth N
More informationProblem Set 6 Finance 1,
Carnege Mellon Unversty Graduate School of Industral Admnstraton Chrs Telmer Wnter 2006 Problem Set 6 Fnance, 47-720. (representatve agent constructon) Consder the followng two-perod, two-agent economy.
More informationSolutions to Odd-Numbered End-of-Chapter Exercises: Chapter 12
Introducton to Econometrcs (3 rd Updated Edton) by James H. Stock and Mark W. Watson Solutons to Odd-Numbered End-of-Chapter Exercses: Chapter 1 (Ths verson July 0, 014) Stock/Watson - Introducton to Econometrcs
More informationoccurrence of a larger storm than our culvert or bridge is barely capable of handling? (what is The main question is: What is the possibility of
Module 8: Probablty and Statstcal Methods n Water Resources Engneerng Bob Ptt Unversty of Alabama Tuscaloosa, AL Flow data are avalable from numerous USGS operated flow recordng statons. Data s usually
More informationOn the Moments of the Traces of Unitary and Orthogonal Random Matrices
Proceedngs of Insttute of Mathematcs of NAS of Ukrane 2004 Vol. 50 Part 3 1207 1213 On the Moments of the Traces of Untary and Orthogonal Random Matrces Vladmr VASILCHU B. Verkn Insttute for Low Temperature
More informationInterval Estimation for a Linear Function of. Variances of Nonnormal Distributions. that Utilize the Kurtosis
Appled Mathematcal Scences, Vol. 7, 013, no. 99, 4909-4918 HIKARI Ltd, www.m-hkar.com http://dx.do.org/10.1988/ams.013.37366 Interval Estmaton for a Lnear Functon of Varances of Nonnormal Dstrbutons that
More informationMaximum Likelihood Estimation of Isotonic Normal Means with Unknown Variances*
Journal of Multvarate Analyss 64, 183195 (1998) Artcle No. MV971717 Maxmum Lelhood Estmaton of Isotonc Normal Means wth Unnown Varances* Nng-Zhong Sh and Hua Jang Northeast Normal Unversty, Changchun,Chna
More informationConsumption Based Asset Pricing
Consumpton Based Asset Prcng Mchael Bar Aprl 25, 208 Contents Introducton 2 Model 2. Prcng rsk-free asset............................... 3 2.2 Prcng rsky assets................................ 4 2.3 Bubbles......................................
More informationAppendix - Normally Distributed Admissible Choices are Optimal
Appendx - Normally Dstrbuted Admssble Choces are Optmal James N. Bodurtha, Jr. McDonough School of Busness Georgetown Unversty and Q Shen Stafford Partners Aprl 994 latest revson September 00 Abstract
More informationComparison of Singular Spectrum Analysis and ARIMA
Int. Statstcal Inst.: Proc. 58th World Statstcal Congress, 0, Dubln (Sesson CPS009) p.99 Comparson of Sngular Spectrum Analss and ARIMA Models Zokae, Mohammad Shahd Behesht Unverst, Department of Statstcs
More informationHedging Greeks for a portfolio of options using linear and quadratic programming
MPRA Munch Personal RePEc Archve Hedgng reeks for a of otons usng lnear and quadratc rogrammng Panka Snha and Archt Johar Faculty of Management Studes, Unversty of elh, elh 5. February 200 Onlne at htt://mra.ub.un-muenchen.de/20834/
More informationMidterm Exam. Use the end of month price data for the S&P 500 index in the table below to answer the following questions.
Unversty of Washngton Summer 2001 Department of Economcs Erc Zvot Economcs 483 Mdterm Exam Ths s a closed book and closed note exam. However, you are allowed one page of handwrtten notes. Answer all questons
More informationFinancial Risk Management in Portfolio Optimization with Lower Partial Moment
Amercan Journal of Busness and Socety Vol., o., 26, pp. 2-2 http://www.ascence.org/journal/ajbs Fnancal Rsk Management n Portfolo Optmzaton wth Lower Partal Moment Lam Weng Sew, 2, *, Lam Weng Hoe, 2 Department
More informationLecture 7. We now use Brouwer s fixed point theorem to prove Nash s theorem.
Topcs on the Border of Economcs and Computaton December 11, 2005 Lecturer: Noam Nsan Lecture 7 Scrbe: Yoram Bachrach 1 Nash s Theorem We begn by provng Nash s Theorem about the exstance of a mxed strategy
More informationA further generalization of the Solow growth model: the role of the public sector
Econocs Letters 68 (2000) 79 84 www.elsever.co/ locate/ econbase A further generalzaton of the Solow growth odel: the role of the publc sector Oscar Bajo-Rubo* Departaento de Econoıa, Unversdad Publca
More informationCofactorisation strategies for the number field sieve and an estimate for the sieving step for factoring 1024-bit integers
Cofactorsaton strateges for the number feld seve and an estmate for the sevng step for factorng 1024-bt ntegers Thorsten Klenjung Unversty of Bonn, Department of Mathematcs, Berngstraße 1, D-53115 Bonn,
More informationBootstrap and Permutation tests in ANOVA for directional data
strap and utaton tests n ANOVA for drectonal data Adelade Fgueredo Faculty of Economcs of Unversty of Porto and LIAAD-INESC TEC Porto - PORTUGAL Abstract. The problem of testng the null hypothess of a
More informationElements of Economic Analysis II Lecture VI: Industry Supply
Elements of Economc Analyss II Lecture VI: Industry Supply Ka Hao Yang 10/12/2017 In the prevous lecture, we analyzed the frm s supply decson usng a set of smple graphcal analyses. In fact, the dscusson
More informationAvailable online: 20 Dec 2011
Ths artcle was downloaded by: [UVA Unverstetsbblotheek SZ] On: 16 May 212, At: 6:32 Publsher: Taylor & Francs Informa Ltd Regstered n England and Wales Regstered Number: 172954 Regstered offce: Mortmer
More informationBayes Nets Representing and Reasoning about Uncertainty (Continued)
Bayes Nets Representng and Reasonng about Uncertanty ontnued) obnng the wo Eaples I a at work y neghbor John calls to say that y alar went off y neghbor Mary doesn t call. Soetes the alar s set off by
More informationEvaluating Performance
5 Chapter Evaluatng Performance In Ths Chapter Dollar-Weghted Rate of Return Tme-Weghted Rate of Return Income Rate of Return Prncpal Rate of Return Daly Returns MPT Statstcs 5- Measurng Rates of Return
More informationInternational ejournals
Avalable onlne at www.nternatonalejournals.com ISSN 0976 1411 Internatonal ejournals Internatonal ejournal of Mathematcs and Engneerng 7 (010) 86-95 MODELING AND PREDICTING URBAN MALE POPULATION OF BANGLADESH:
More informationMorningstar After-Tax Return Methodology
Mornngstar After-Tax Return Methodology Mornngstar Research Report 24 October 2003 2003 Mornngstar, Inc. All rghts reserved. The nformaton n ths document s the property of Mornngstar, Inc. Reproducton
More informationGames and Decisions. Part I: Basic Theorems. Contents. 1 Introduction. Jane Yuxin Wang. 1 Introduction 1. 2 Two-player Games 2
Games and Decsons Part I: Basc Theorems Jane Yuxn Wang Contents 1 Introducton 1 2 Two-player Games 2 2.1 Zero-sum Games................................ 3 2.1.1 Pure Strateges.............................
More information3: Central Limit Theorem, Systematic Errors
3: Central Lmt Theorem, Systematc Errors 1 Errors 1.1 Central Lmt Theorem Ths theorem s of prme mportance when measurng physcal quanttes because usually the mperfectons n the measurements are due to several
More informationTechnological inefficiency and the skewness of the error component in stochastic frontier analysis
Economcs Letters 77 (00) 101 107 www.elsever.com/ locate/ econbase Technologcal neffcency and the skewness of the error component n stochastc fronter analyss Martn A. Carree a,b, * a Erasmus Unversty Rotterdam,
More informationAn Economic Analysis of Interconnection Arrangements between Internet Backbone Providers
ONLINE SUPPLEMENT TO An Eonom Analyss of Interonneton Arrangements between Internet Bakbone Provders Yong Tan Unversty of Washngton Busness Shool Box 353 Seattle Washngton 9895-3 ytan@uwashngtonedu I Robert
More informationDomestic Savings and International Capital Flows
Domestc Savngs and Internatonal Captal Flows Martn Feldsten and Charles Horoka The Economc Journal, June 1980 Presented by Mchael Mbate and Chrstoph Schnke Introducton The 2 Vews of Internatonal Captal
More informationA Dynamic Inventory Control Policy Under Demand, Yield and Lead Time Uncertainties
A Dynamc Inventory Control Polcy Under Demand, Yeld and ead Tme Uncertantes Z. Baba, Yves Dallery To cte ths verson: Z. Baba, Yves Dallery. A Dynamc Inventory Control Polcy Under Demand, Yeld and ead Tme
More information332 Mathematical Induction Solutions for Chapter 14. for every positive integer n. Proof. We will prove this with mathematical induction.
33 Mathematcal Inducton. Solutons for Chapter. Prove that 3 n n n for every postve nteger n. Proof. We wll prove ths wth mathematcal nducton. Observe that f n, ths statement s, whch s obvously true. Consder
More information02_EBA2eSolutionsChapter2.pdf 02_EBA2e Case Soln Chapter2.pdf
0_EBAeSolutonsChapter.pdf 0_EBAe Case Soln Chapter.pdf Chapter Solutons: 1. a. Quanttatve b. Categorcal c. Categorcal d. Quanttatve e. Categorcal. a. The top 10 countres accordng to GDP are lsted below.
More informationXiaoli Lu VA Cooperative Studies Program, Perry Point, MD
A SAS Program to Construct Smultaneous Confdence Intervals for Relatve Rsk Xaol Lu VA Cooperatve Studes Program, Perry Pont, MD ABSTRACT Assessng adverse effects s crtcal n any clncal tral or nterventonal
More informationA MODEL OF COMPETITION AMONG TELECOMMUNICATION SERVICE PROVIDERS BASED ON REPEATED GAME
A MODEL OF COMPETITION AMONG TELECOMMUNICATION SERVICE PROVIDERS BASED ON REPEATED GAME Vesna Radonć Đogatovć, Valentna Radočć Unversty of Belgrade Faculty of Transport and Traffc Engneerng Belgrade, Serba
More informationREGULATORY REFORM IN THE JAPANESE ELECTRIC POWER INDUSTRY AN EVENT STUDY ANALYSIS IAEE 2017 Conference, Singapore 20 th June 2017 Koichiro Tezuka,
REGULATORY REFORM IN THE JAPANESE ELECTRIC POWER INDUSTRY AN EVENT STUDY ANALYSIS IAEE 2017 Conference, Sngapore 20 th June 2017 Kochro Tezuka, Nhon Unversty, Masahro Ish, Sopha Unversty, Satoru Hashmoto,
More informationHarmonised Labour Cost Index. Methodology
Harmonsed Labour Cost Index Methodology March 2013 Index 1 Introducton 3 2 Scope, coverage and reference perod 4 3 Defntons 5 4 Sources of nformaton 7 5 Formulae employed 9 6 Results obtaned 10 7 Seres
More informationON GETTING MEANINGFUL BOCR RESULTS WITH ANP S SUPER DECISIONS SOFTWARE
SAHP 2007, Vña del Mar, hle, August 3-6, 2007 N GETTNG MEANNGFUL ESULTS WTH ANP S SUPE DESNS SFTWAE Dederk J.D. Wjnalen TN rganzaton for Aled Scentfc esearch, Det. for eratonal Analyss P ox 96864, 2509
More informationGraphical Methods for Survival Distribution Fitting
Graphcal Methods for Survval Dstrbuton Fttng In ths Chapter we dscuss the followng two graphcal methods for survval dstrbuton fttng: 1. Probablty Plot, 2. Cox-Snell Resdual Method. Probablty Plot: The
More informationσ σ σ = = im i im is constant and then βi If is constant and ρim R i -rf σ ρ If i = M-V efficient portfolio p then Rp = = =
F8000 Valuaton of Fnancal Assets Srng Seester 2010 Dr. Isabel Tkatch Assstant Professor of Fnance Today The Catal Asset Prcng Model Catal allocaton n rsky assets one rsk free asset CAPM equlbru β - A new
More informationCombined overbooking and seat inventory control for two-class revenue management model
Songklanakarn J. Sc. Technol. 38 (6), 657-665, Nov. - Dec. 06 http://www.sjst.psu.ac.th Orgnal Artcle Combned overbookng and seat nventory control for two-class revenue management model Murat Somboon and
More informationOn estimating the location parameter of the selected exponential population under the LINEX loss function
On estmatng the locaton parameter of the selected exponental populaton under the LINEX loss functon Mohd. Arshad 1 and Omer Abdalghan Department of Statstcs and Operatons Research Algarh Muslm Unversty,
More informationImprovement of Order Promise With Material Constraints and Finite Capacity
Iproveent of Order Prose Wth Materal Constrants and Fnte Capacty Iproveent of Order Prose Wth Materal Constrants and Fnte Capacty Jun-Han Chen Departent of Industral Engneerng and Manageent, Cheng Shu
More information