Int. Statistical Inst.: Proc. 58th World Statistical Congress, 2011, Dublin (Session CPS019) p.4301
|
|
- Merilyn Day
- 5 years ago
- Views:
Transcription
1 Int. Statistical Inst.: Proc. 58th World Statistical Congress, 0, Dublin (Session CPS RELIABILITY STUDIES OF BIVARIATE LOG-NORMAL DISTRIBUTION Pusha L.Guta Deartment of Mathematics and Statistics Universit of Maine Orono, Maine, U.S.A Ke words and hrases: failure rate, hazard comonents, series and arralel sstems, monotonicit Abstract In this aer, we stud the bivariate log-normal distribution from a reliabilit oint of view. The monotonicit of the hazard rates of the univariate as well as the conditional distributions is discussed. The robabilit distributions, in the case of series and arallel sstems, are derived and the monotonicit of their failure rates is discussed.. INTRODUCTION It has been observed that, in man ractical roblems, the log-normal distribution is widel used to model ositive random variable that exhibits skewness. The log-normal distribution is commonl used in medicine and economics, where the basic rocess under consideration leads to a skewed distribution. Zou et al. (009 comment that the log-normal distribution ma be used to aroximate right skewed data arising in a range of scienti c enquiries, see also Limert et al. (00. In order to test the equalit of means of health care costs in a aired design, Zhou et al. (00 showed that a bivariate log-normal distribution is aroriate to model the outatient costs, six months before and after the Medicaid olic change in the state of Indiana. Hawkins (00 discussed an examle dealing with 56 assa airs of cclosorin from blood samles of organ translant reciients obtained b two di erent methods. In this connection, assuming the bivariate log-normal distribution, Zhou et al. (00 resented ve tests for the equalit of two log-normal means. In this aer, we are interested in studing the class of bivariate log-normal distributions from a reliabilit oint of view. More seci call, we stud the association between the variables and obtain conditions for which this class of distributions is T P ( totall ositive of order or RR ( reverse rule of order. This enables us to stud the deendence roerties of the model. We stud the hazard comonents of the hazard gradient in the sense of Johnson and Kotz (975 and their monotonic structure. In this connection, the conditional distribution of X given Y > is found to be log-skew normal, a class not widel studied in the literature. An association measure (x; de ned b Oakes (989, is investigated for this class of bivariate distributions. Some of the results resented here are general and would be useful in studing the association in other classes of bivariate distributions.
2 Int. Statistical Inst.: Proc. 58th World Statistical Congress, 0, Dublin (Session CPS THE MODEL A random variable (X; Y is said to have bivariate log-normal distribution if (ln X; ln Y has a bivariate normal distribution. It is clear that the marginal and conditional distributions are univariate log-normal. For the bivariate normal distribution, it is well known that the joint densit is T P according as > (<0; see for examle Joe (997. We now state the following result Theorem. Suose the random variable (X; Y has the T P (RR roert. Let h(: be an increasing function. Then (h(x; h(y has the T P (RR roert. Proof. See Shaked ( Bivariate Log-normal Distribution Suose (X; Y has a bivariate log-normal distribution so that (ln X; ln Y has a bivariate normal distribution. It is evident that the conditional distribution of X given Y or of Y given X x is univariate log-normal. Therefore, their reliabilit functions can be easil obtained b using the formulas for log-normal distribution and aroriate values of the arameters. The monotonicit of the failure rate and of the mean residual life function will follow the same attern as of the univariate log-normal distribution. To stud the monotonicit of the failure rate of the conditional distribution of X given Y as a function of ; we emlo the following result due to Shaked (977. Lemma. If f(x; is T P (RR ; the conditional failure rate of X given Y is decreasing(increasing in : Using the above result, we conclude that the failure rate of the conditional distribution of X given Y is decreasing ( increasing in according as > (<0: We now discuss the conditional distribution of X given Y > : Conditional distribution of XjY > Suose (X; Y BV LN( ; ; ; ; : Then the conditional densit of X given Y > is given b
3 Int. Statistical Inst.: Proc. 58th World Statistical Congress, 0, Dublin (Session CPS f XjY > (xjy P (X > xjy Z R f(x; vdvp (Y > xv exf ( [( ln x ( ln x ( ln v +( ln v ]gdv P (Y > x ( ln x [ ( ln [ +((ln x ] ] ( ln : Secial case When 0 and, the above reduces to f XjY > (xjy > f X (x[ ( ln ln x ]P (Y > ; (3. where f X (x is the marginal densit function of a standard log-normal distribution. Thus X given Y > has a log-skew normal distribution. Note that this result is true for standard as well as for non standard bivariate log-normal vectors, see Arnold (009. Hazard comonents and their monotonicit In order to stud the hazard comonents and their monotonicit, it is enough to consider the standard bivariate log-normal model. The hazard rate of the conditional distribution of X given Y > is given b h (x; d dx ln F (x; (3. Z f X (x[ ( f(x; vdvf (x; ln ln x ]F (x; ;. Using equation (3., the distribution of X given Y > is log-skew normal, its hazard rate is of the te U: In a similar manner, we can obtain the conditional densit of Y given X > x and the hazard comonent h (x; : The monotonicit of the conditional hazard of X given Y > as a function of can be determined b emloing the following result due to Shaked (977. Lemma 3. If f(x; is T P (RR ; the conditional failure rate of X given Y > is decreasing( increasing in 3
4 Int. Statistical Inst.: Proc. 58th World Statistical Congress, 0, Dublin (Session CPS As noticed before, the bivariate log-normal distribution is T P (RR according as > (<0: Thus, in the case of bivariate log-normal distribution h (x; is decreasing ( increasing in according as > (<0: Similar statement can be made regarding the other hazard comonent. 4. SERIES AND PARALLEL SYSTEMS In this section, we shall obtain the densit functions of T Min(X; Y and T Max(X; Y : Also we stud the monotonicit of the failure rates of T and T : We know that for an bivariate vector (X; Y, the densit functions of T and T are given b and f T (t f X (tp (Y > tjx t + f Y (tp (X > tjy t (4. f T (t f X (tp (Y < tjx t + f Y (tp (X < tjy t; (4. see Guta and Guta (00. For the bivariate log-normal distribution, using (4., it can be veri ed that f T (t t (ln t [ ( + t (ln t [ ( + ] (4.3 + ]: For the standard bivariate log-normal distribution, it reduces to f T (t r t (ln t[ (ln t ]: (4.4 + Hence T has a log-skew normal distribution. earlier, the failure rate of T is of the te U: Using the result established It can be veri ed that the turning oint of T (t is given b the solution of the equation where ( distribution. ln t + r N ( ln t r 0 N( ln t; (4.5 ( + and r N (: is the failure rate of the standard normal For examle, for ; the maximum value of T (t is achieved at t : Similarl, using (4., it can be veri ed that 4
5 Int. Statistical Inst.: Proc. 58th World Statistical Congress, 0, Dublin (Session CPS f T (t t (ln t [( + t (ln t [( + (4.6 + ]: For the standard bivariate log-normal distribution, the above exression reduces to U: f T (t r t (ln t[(ln t ]: (4.7 + Again, T has a log-skew normal distribution and its failure rate is of the te References [] Arnold, B.C. (009. Flexible univariate and multivariate models based on hidden truncation. Journal of Statistical Planning and Inference, 39, [] Guta, P.L. and Guta, R.C. (00. Failure rate of the minimum and maximum of a multivariate normal distribution. Metrika, 53, [3] Guta, R.C. and Warren, W. (00. Determination of change oint of nonmonotonic failure rates.communications in Statistics. Theor and Methods, 30 (8&9, [4] Hawkins, D.H. (00. Dignostics of conformit of aired quantitative mesurements. Statistics in Medicine,, [5] Joe, H.(997. Multivariate Models and Deendence Concets. Chaman and Hall, New York. [6] Johnson, N.L. and Kotz, S. (975. A vector valued multivariate hazard rate. Journal of Multivariate Analsis 5, [7] Oakes, D. (989. Bivariate survival models induced b fralities. Journal of the American Statistical Association 84, [8] Shaked, M. (977. A famil of concets of deendence for bivariate distributions. Journal of the American Statistical Association 7, [9] Zhou, X.H.,Li, C., Gao, S. and Tierne, W.M. (00. Methods for testing equalit of means of health care costs in a aired design stud. Statistics in Medicine, 0, [0] Zou, G.Y.,Taleban, J. and Huo, C.Y. (009. Con dence interval estimation for log-normal data with alication to health economics. Comutational Statistics and Data Analsis, 53,
ON JARQUE-BERA TESTS FOR ASSESSING MULTIVARIATE NORMALITY
Journal of Statistics: Advances in Theory and Alications Volume, umber, 009, Pages 07-0 O JARQUE-BERA TESTS FOR ASSESSIG MULTIVARIATE ORMALITY KAZUYUKI KOIZUMI, AOYA OKAMOTO and TAKASHI SEO Deartment of
More informationStatistics and Probability Letters. Variance stabilizing transformations of Poisson, binomial and negative binomial distributions
Statistics and Probability Letters 79 (9) 6 69 Contents lists available at ScienceDirect Statistics and Probability Letters journal homeage: www.elsevier.com/locate/staro Variance stabilizing transformations
More informationConfidence Intervals for a Proportion Using Inverse Sampling when the Data is Subject to False-positive Misclassification
Journal of Data Science 13(015), 63-636 Confidence Intervals for a Proortion Using Inverse Samling when the Data is Subject to False-ositive Misclassification Kent Riggs 1 1 Deartment of Mathematics and
More informationSINGLE SAMPLING PLAN FOR VARIABLES UNDER MEASUREMENT ERROR FOR NON-NORMAL DISTRIBUTION
ISSN -58 (Paer) ISSN 5-5 (Online) Vol., No.9, SINGLE SAMPLING PLAN FOR VARIABLES UNDER MEASUREMENT ERROR FOR NON-NORMAL DISTRIBUTION Dr. ketki kulkarni Jayee University of Engineering and Technology Guna
More informationA NOTE ON SKEW-NORMAL DISTRIBUTION APPROXIMATION TO THE NEGATIVE BINOMAL DISTRIBUTION
A NOTE ON SKEW-NORMAL DISTRIBUTION APPROXIMATION TO THE NEGATIVE BINOMAL DISTRIBUTION JYH-JIUAN LIN 1, CHING-HUI CHANG * AND ROSEMARY JOU 1 Deartment of Statistics Tamkang University 151 Ying-Chuan Road,
More informationSupplemental Material: Buyer-Optimal Learning and Monopoly Pricing
Sulemental Material: Buyer-Otimal Learning and Monooly Pricing Anne-Katrin Roesler and Balázs Szentes February 3, 207 The goal of this note is to characterize buyer-otimal outcomes with minimal learning
More informationWorst-case evaluation complexity for unconstrained nonlinear optimization using high-order regularized models
Worst-case evaluation comlexity for unconstrained nonlinear otimization using high-order regularized models E. G. Birgin, J. L. Gardenghi, J. M. Martínez, S. A. Santos and Ph. L. Toint 2 Aril 26 Abstract
More informationOn the Distribution and Its Properties of the Sum of a Normal and a Doubly Truncated Normal
The Korean Communications in Statistics Vol. 13 No. 2, 2006, pp. 255-266 On the Distribution and Its Properties of the Sum of a Normal and a Doubly Truncated Normal Hea-Jung Kim 1) Abstract This paper
More information25 Increasing and Decreasing Functions
- 25 Increasing and Decreasing Functions It is useful in mathematics to define whether a function is increasing or decreasing. In this section we will use the differential of a function to determine this
More informationOn the smallest abundant number not divisible by the first k primes
On the smallest abundant number not divisible by the first k rimes Douglas E. Iannucci Abstract We say a ositive integer n is abundant if σ(n) > 2n, where σ(n) denotes the sum of the ositive divisors of
More informationOrdering a deck of cards... Lecture 3: Binomial Distribution. Example. Permutations & Combinations
Ordering a dec of cards... Lecture 3: Binomial Distribution Sta 111 Colin Rundel May 16, 2014 If you have ever shuffled a dec of cards you have done something no one else has ever done before or will ever
More informationKurtosis of the Topp-Leone distributions
Kurtosis of the Topp-Leone distributions Samuel Kotz Department of Engineering Management and Sstems Engineering, George Washington Universit, 776 G Street, N.W. Washington D.C. 5, USA kotz@gwu.edu Edith
More informationInferences on Correlation Coefficients of Bivariate Log-normal Distributions
Inferences on Correlation Coefficients of Bivariate Log-normal Distributions Guoyi Zhang 1 and Zhongxue Chen 2 Abstract This article considers inference on correlation coefficients of bivariate log-normal
More informationLecture 2. Main Topics: (Part II) Chapter 2 (2-7), Chapter 3. Bayes Theorem: Let A, B be two events, then. The probabilities P ( B), probability of B.
STT315, Section 701, Summer 006 Lecture (Part II) Main Toics: Chater (-7), Chater 3. Bayes Theorem: Let A, B be two events, then B A) = A B) B) A B) B) + A B) B) The robabilities P ( B), B) are called
More informationA Semi-parametric Test for Drift Speci cation in the Di usion Model
A Semi-arametric est for Drift Seci cation in the Di usion Model Lin hu Indiana University Aril 3, 29 Abstract In this aer, we roose a misseci cation test for the drift coe cient in a semi-arametric di
More informationIndividual Comparative Advantage and Human Capital Investment under Uncertainty
Individual Comarative Advantage and Human Caital Investment under Uncertainty Toshihiro Ichida Waseda University July 3, 0 Abstract Secialization and the division of labor are the sources of high roductivity
More informationAsian Economic and Financial Review A MODEL FOR ESTIMATING THE DISTRIBUTION OF FUTURE POPULATION. Ben David Nissim.
Asian Economic and Financial Review journal homeage: htt://www.aessweb.com/journals/5 A MODEL FOR ESTIMATING THE DISTRIBUTION OF FUTURE POPULATION Ben David Nissim Deartment of Economics and Management,
More informationProbability analysis of return period of daily maximum rainfall in annual data set of Ludhiana, Punjab
Indian J. Agric. Res., 49 (2) 2015: 160-164 Print ISSN:0367-8245 / Online ISSN:0976-058X AGRICULTURAL RESEARCH COMMUNICATION CENTRE www.arccjournals.com/www.ijarjournal.com Probabilit analsis of return
More informationInsurance: Mathematics and Economics. Multivariate Tweedie distributions and some related capital-at-risk analyses
Insurance: Mathematics and Economics 46 21 351 361 Contents lists available at ScienceDirect Insurance: Mathematics and Economics ournal homeage: wwwelseviercom/locate/ime Multivariate Tweedie distributions
More informationCapital Allocation Principles
Capital Allocation Principles Maochao Xu Department of Mathematics Illinois State University mxu2@ilstu.edu Capital Dhaene, et al., 2011, Journal of Risk and Insurance The level of the capital held by
More informationC (1,1) (1,2) (2,1) (2,2)
TWO COIN MORRA This game is layed by two layers, R and C. Each layer hides either one or two silver dollars in his/her hand. Simultaneously, each layer guesses how many coins the other layer is holding.
More informationCapital Budgeting: The Valuation of Unusual, Irregular, or Extraordinary Cash Flows
Caital Budgeting: The Valuation of Unusual, Irregular, or Extraordinary Cash Flows ichael C. Ehrhardt Philli R. Daves Finance Deartment, SC 424 University of Tennessee Knoxville, TN 37996-0540 423-974-1717
More informationON THE MEAN VALUE OF THE SCBF FUNCTION
ON THE MEAN VALUE OF THE SCBF FUNCTION Zhang Xiaobeng Deartment of Mathematics, Northwest University Xi an, Shaani, P.R.China Abstract Keywords: The main urose of this aer is using the elementary method
More informationObjectives. 3.3 Toward statistical inference
Objectives 3.3 Toward statistical inference Poulation versus samle (CIS, Chater 6) Toward statistical inference Samling variability Further reading: htt://onlinestatbook.com/2/estimation/characteristics.html
More informationDr. Maddah ENMG 625 Financial Eng g II 10/16/06. Chapter 11 Models of Asset Dynamics (1)
Dr Maddah ENMG 65 Financial Eng g II 0/6/06 Chater Models of Asset Dynamics () Overview Stock rice evolution over time is commonly modeled with one of two rocesses: The binomial lattice and geometric Brownian
More informationStochastic modelling of skewed data exhibiting long range dependence
IUGG XXIV General Assembly 27 Perugia, Italy, 2 3 July 27 International Association of Hydrological Sciences, Session HW23 Analysis of Variability in Hydrological Data Series Stochastic modelling of skewed
More informationINDEX NUMBERS. Introduction
INDEX NUMBERS Introduction Index numbers are the indicators which reflect changes over a secified eriod of time in rices of different commodities industrial roduction (iii) sales (iv) imorts and exorts
More informationWorst-case evaluation complexity of regularization methods for smooth unconstrained optimization using Hölder continuous gradients
Worst-case evaluation comlexity of regularization methods for smooth unconstrained otimization using Hölder continuous gradients C Cartis N I M Gould and Ph L Toint 26 June 205 Abstract The worst-case
More informationWeighted Half Exponential Power Distribution and Associated Inference
Applied Mathematical Sciences, Vol. 0, 206, no. 2, 9-08 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/0.2988/ams.206.5696 Weighted Half Exponential Power Distribution and Associated Inference M. E. Ghitany,
More informationNon-Inferiority Tests for the Ratio of Two Correlated Proportions
Chater 161 Non-Inferiority Tests for the Ratio of Two Correlated Proortions Introduction This module comutes ower and samle size for non-inferiority tests of the ratio in which two dichotomous resonses
More informationInformation and uncertainty in a queueing system
Information and uncertainty in a queueing system Refael Hassin December 7, 7 Abstract This aer deals with the effect of information and uncertainty on rofits in an unobservable single server queueing system.
More informationLECTURE NOTES ON MICROECONOMICS
LECTURE NOTES ON MCROECONOMCS ANALYZNG MARKETS WTH BASC CALCULUS William M. Boal Part : Consumers and demand Chater 5: Demand Section 5.: ndividual demand functions Determinants of choice. As noted in
More informationExtreme Return-Volume Dependence in East-Asian. Stock Markets: A Copula Approach
Extreme Return-Volume Dependence in East-Asian Stock Markets: A Copula Approach Cathy Ning a and Tony S. Wirjanto b a Department of Economics, Ryerson University, 350 Victoria Street, Toronto, ON Canada,
More information508-B (Statistics Camp, Wash U, Summer 2016) Asymptotics. Author: Andrés Hincapié and Linyi Cao. This Version: August 9, 2016
Asymtotics Author: Anrés Hincaié an Linyi Cao This Version: August 9, 2016 Asymtotics 3 In arametric moels, we usually assume that the oulation follows some istribution F (x θ) with unknown θ. Knowing
More informationStatistical inferences and applications of the half exponential power distribution
Statistical inferences and alications of the half exonential ower distribution Wenhao Gui Deartment of Mathematics and Statistics, University of Minnesota Duluth, Duluth MN 558, USA Abstract In this aer,
More informationMidterm Exam: Tuesday 28 March in class Sample exam problems ( Homework 5 ) available tomorrow at the latest
Plan Martingales 1. Basic Definitions 2. Examles 3. Overview of Results Reading: G&S Section 12.1-12.4 Next Time: More Martingales Midterm Exam: Tuesday 28 March in class Samle exam roblems ( Homework
More informationNon-Gaussian Multivariate Statistical Models and their Applications May 19-24, Some Challenges in Portfolio Theory and Asset Pricing
Non-Gaussian Multivariate Statistical Models and their Alications May 19-24, 2013 Some Challenges in Portfolio Theory and Asset Pricing Chris Adcock - 1 Introduction Finance is a very large subject! This
More informationMaximize the Sharpe Ratio and Minimize a VaR 1
Maximize the Share Ratio and Minimize a VaR 1 Robert B. Durand 2 Hedieh Jafarour 3,4 Claudia Klüelberg 5 Ross Maller 6 Aril 28, 2008 Abstract In addition to its role as the otimal ex ante combination of
More informationMossin s Theorem for Upper-Limit Insurance Policies
Mossin s Theorem for Upper-Limit Insurance Policies Harris Schlesinger Department of Finance, University of Alabama, USA Center of Finance & Econometrics, University of Konstanz, Germany E-mail: hschlesi@cba.ua.edu
More informationRisk Neutral Modelling Exercises
Risk Neutral Modelling Exercises Geneviève Gauthier Exercise.. Assume that the rice evolution of a given asset satis es dx t = t X t dt + X t dw t where t = ( + sin (t)) and W = fw t : t g is a (; F; P)
More informationStatistical properties of symmetrized percent change and percent change based on the bivariate power normal distribution
Int. Statistical Inst.: Proc. 58th World Statistical Congress, 2011, Dublin (Session CPS008) p.6061 Statistical properties of symmetrized percent change and percent change based on the bivariate power
More informationApplications of Local Gaussian Correlation in Finance
Applications of Local Gaussian Correlation in Finance and towards a parametric version of the LGC Bård Støve Universit of Bergen, Norwa Department of Mathematics Joint work in progress with Dag Tjøstheim,
More informationSampling Procedure for Performance-Based Road Maintenance Evaluations
Samling Procedure for Performance-Based Road Maintenance Evaluations Jesus M. de la Garza, Juan C. Piñero, and Mehmet E. Ozbek Maintaining the road infrastructure at a high level of condition with generally
More informationEndogenous Income. The consumption-leisure model
Endogenous Income The consumtion-leisure model Modifing consumer s roblem For the moment, assume there is no additional eogenous income Consumer s income is the market value of her initial endowment, (,
More informationInt. Statistical Inst.: Proc. 58th World Statistical Congress, 2011, Dublin (Session CPS048) p.5108
Int. Statistical Inst.: Proc. 58th World Statistical Congress, 2011, Dublin (Session CPS048) p.5108 Aggregate Properties of Two-Staged Price Indices Mehrhoff, Jens Deutsche Bundesbank, Statistics Department
More informationTESTING THE CAPITAL ASSET PRICING MODEL AFTER CURRENCY REFORM: THE CASE OF ZIMBABWE STOCK EXCHANGE
TESTING THE CAPITAL ASSET PRICING MODEL AFTER CURRENCY REFORM: THE CASE OF ZIMBABWE STOCK EXCHANGE Batsirai Winmore Mazviona 1 ABSTRACT The Caital Asset Pricing Model (CAPM) endeavors to exlain the relationshi
More information( ) ( ) β. max. subject to. ( ) β. x S
Intermediate Microeconomic Theory: ECON 5: Alication of Consumer Theory Constrained Maimization In the last set of notes, and based on our earlier discussion, we said that we can characterize individual
More informationDefinition 9.1 A point estimate is any function T (X 1,..., X n ) of a random sample. We often write an estimator of the parameter θ as ˆθ.
9 Point estimation 9.1 Rationale behind point estimation When sampling from a population described by a pdf f(x θ) or probability function P [X = x θ] knowledge of θ gives knowledge of the entire population.
More informationMatching Markets and Social Networks
Matching Markets and Social Networks Tilman Klum Emory University Mary Schroeder University of Iowa Setember 0 Abstract We consider a satial two-sided matching market with a network friction, where exchange
More informationA Skewed Truncated Cauchy Logistic. Distribution and its Moments
International Mathematical Forum, Vol. 11, 2016, no. 20, 975-988 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/imf.2016.6791 A Skewed Truncated Cauchy Logistic Distribution and its Moments Zahra
More informationOn the comparison of the Fisher information of the log-normal and generalized Rayleigh distributions
On the comparison of the Fisher information of the log-normal and generalized Rayleigh distributions Fawziah S. Alshunnar 1, Mohammad Z. Raqab 1 and Debasis Kundu 2 Abstract Surles and Padgett (2001) recently
More informationSUBORDINATION BY ORTHOGONAL MARTINGALES IN L p, 1 < p Introduction: Orthogonal martingales and the Beurling-Ahlfors transform
SUBORDINATION BY ORTHOGONAL MARTINGALES IN L, 1 < PRABHU JANAKIRAMAN AND ALEXANDER VOLBERG 1. Introduction: Orthogonal martingales and the Beurling-Ahlfors transform We are given two martingales on the
More information***SECTION 7.1*** Discrete and Continuous Random Variables
***SECTION 7.*** Discrete and Continuous Random Variables Samle saces need not consist of numbers; tossing coins yields H s and T s. However, in statistics we are most often interested in numerical outcomes
More informationA Skewed Truncated Cauchy Uniform Distribution and Its Moments
Modern Applied Science; Vol. 0, No. 7; 206 ISSN 93-844 E-ISSN 93-852 Published by Canadian Center of Science and Education A Skewed Truncated Cauchy Uniform Distribution and Its Moments Zahra Nazemi Ashani,
More informationA GENERALISED PRICE-SCORING MODEL FOR TENDER EVALUATION
019-026 rice scoring 9/20/05 12:12 PM Page 19 A GENERALISED PRICE-SCORING MODEL FOR TENDER EVALUATION Thum Peng Chew BE (Hons), M Eng Sc, FIEM, P. Eng, MIEEE ABSTRACT This aer rooses a generalised rice-scoring
More informationBivariate Birnbaum-Saunders Distribution
Department of Mathematics & Statistics Indian Institute of Technology Kanpur January 2nd. 2013 Outline 1 Collaborators 2 3 Birnbaum-Saunders Distribution: Introduction & Properties 4 5 Outline 1 Collaborators
More informationBETA DISTRIBUTED CREDIT SCORE - ESTIMATION OF ITS J-DIVERGENCE
The 7 th International Das of Statistics and Economics Prague September 9-2 23 BETA DISTRIBUTED CREDIT SCORE - ESTIMATION OF ITS J-DERGENCE Martin Řezáč Abstract It is known that Beta distribution could
More informationPricing of Stochastic Interest Bonds using Affine Term Structure Models: A Comparative Analysis
Dottorato di Ricerca in Matematica er l Analisi dei Mercati Finanziari - Ciclo XXII - Pricing of Stochastic Interest Bonds using Affine Term Structure Models: A Comarative Analysis Dott.ssa Erica MASTALLI
More informationDiscriminating between the log-normal and generalized exponential distributions
Journal of Statistical Planning and Inference www.elsevier.com/locate/jspi Discriminating between the log-normal and generalized exponential distributions Debasis Kundu a;, Rameshwar D. Gupta b, Anubhav
More informationOn Shewhart Control Charts for Zero-Truncated Negative Binomial Distributions
a. j. eng. technol. sci. Volume 4, No, 204, -2 ISSN: 2222-9930 print ISSN: 2224-2333 online On Shewhart Control Charts for Zero-Truncated Negative Binomial Distributions Anwer Khurshid *, Ashit B. Charaborty
More information18-660: Numerical Methods for Engineering Design and Optimization
18-660: Numerical Methods for Engineering Design and Optimization Xin Li Department of ECE Carnegie Mellon Universit Pittsburgh, PA 15213 Slide 1 Overview Monte Carlo Analsis Latin hpercube sampling Importance
More informationLecture 5: Performance Analysis (part 1)
Lecture 5: Performance Analysis (art 1) 1 Tyical Time Measurements Dark grey: time sent on comutation, decreasing with # of rocessors White: time sent on communication, increasing with # of rocessors Oerations
More informationCS522 - Exotic and Path-Dependent Options
CS522 - Exotic and Path-Deendent Otions Tibor Jánosi May 5, 2005 0. Other Otion Tyes We have studied extensively Euroean and American uts and calls. The class of otions is much larger, however. A digital
More informationDynamic Hedging and PDE Valuation
Dynamic Hedging and PDE Valuation Dynamic Hedging and PDE Valuation 1/ 36 Introduction Asset prices are modeled as following di usion processes, permitting the possibility of continuous trading. This environment
More informationCS 6110 S11 Lecture 8 Inductive Definitions and Least Fixpoints 11 February 2011
CS 6110 S11 Lecture 8 Inductive Definitions and Least Fipoints 11 Februar 2011 1 Set Operators Recall from last time that a rule instance is of the form X 1 X 2... X n, (1) X where X and the X i are members
More information2/20/2013. of Manchester. The University COMP Building a yes / no classifier
COMP4 Lecture 6 Building a yes / no classifier Buildinga feature-basedclassifier Whatis a classifier? What is an information feature? Building a classifier from one feature Probability densities and the
More informationTowards an advanced estimation of Measurement Uncertainty using Monte-Carlo Methods- case study kinematic TLS Observation Process
Towards an advanced estimation of Measurement Uncertainty using Monte-Carlo Methods- case study Hamza ALKHATIB and Hansjörg KUTTERER, Germany Key words: terrestrial laser scanning, GUM, uncertainty, Monte
More informationA Comparative Study of Various Loss Functions in the Economic Tolerance Design
A Comarative Study of Various Loss Functions in the Economic Tolerance Design Jeh-Nan Pan Deartment of Statistics National Chen-Kung University, Tainan, Taiwan 700, ROC Jianbiao Pan Deartment of Industrial
More informationA Test of the Normality Assumption in the Ordered Probit Model *
A Test of the Normality Assumption in the Ordered Probit Model * Paul A. Johnson Working Paper No. 34 March 1996 * Assistant Professor, Vassar College. I thank Jahyeong Koo, Jim Ziliak and an anonymous
More informationA Note on the Pricing of Contingent Claims with a Mixture of Distributions in a Discrete-Time General Equilibrium Framework
A Note on the Pricing of Contingent Claims with a Mixture of Distributions in a Discrete-Time General Equilibrium Framework Luiz Vitiello and Ser-Huang Poon January 5, 200 Corresponding author. Ser-Huang
More informationForeign direct investment in Fiji
Foreign direct investment in Fiji Azmat Gani Senior Economist, Reserve Bank of Fiji One feature of Fiji s investment climate in recent times has been the increased levels of foreign direct investment.
More informationWrite legibly. Unreadable answers are worthless.
MMF 2021 Final Exam 1 December 2016. This is a closed-book exam: no books, no notes, no calculators, no phones, no tablets, no computers (of any kind) allowed. Do NOT turn this page over until you are
More informationFORECASTING EARNINGS PER SHARE FOR COMPANIES IN IT SECTOR USING MARKOV PROCESS MODEL
FORECASTING EARNINGS PER SHARE FOR COMPANIES IN IT SECTOR USING MARKOV PROCESS MODEL 1 M.P. RAJAKUMAR, 2 V. SHANTHI 1 Research Scholar, Sathyabama University, Chennai-119, Tamil Nadu, India 2 Professor,
More informationA Family of Kurtosis Orderings for Multivariate Distributions
A Family of Kurtosis Orderings for Multivariate Distributions Jin Wang Northern Arizona University July 2008 Final preprint version for Journal of Multivariate Analysis, 2008, to appear Department of Mathematics
More informationFeasibilitystudyofconstruction investmentprojectsassessment withregardtoriskandprobability
Feasibilitystudyofconstruction investmentrojectsassessment withregardtoriskandrobability ofnpvreaching Andrzej Minasowicz Warsaw University of Technology, Civil Engineering Faculty, Warsaw, PL a.minasowicz@il.w.edu.l
More informationGENERATION OF STANDARD NORMAL RANDOM NUMBERS. Naveen Kumar Boiroju and M. Krishna Reddy
GENERATION OF STANDARD NORMAL RANDOM NUMBERS Naveen Kumar Boiroju and M. Krishna Reddy Department of Statistics, Osmania University, Hyderabad- 500 007, INDIA Email: nanibyrozu@gmail.com, reddymk54@gmail.com
More informationFinancial Risk Management
Financial Risk Management Professor: Thierry Roncalli Evry University Assistant: Enareta Kurtbegu Evry University Tutorial exercices #4 1 Correlation and copulas 1. The bivariate Gaussian copula is given
More informationEstimating Strategic Complementarity in a State-Dependent Pricing Model
Estimating Strategic Comlementarity in a State-Deendent Pricing Model Marco Bonomo EPGE, Getulio Vargas Foundation marco.bonomo@fgv.br Marcelo Cunha Medeiros Arnildo da Silva Correa Central Bank of Brazil
More informationR-package pendensity - Density Estimation with a Penalized Mixture Approach
R-package pen - Densit Estimation with a Penalized Mixture Approach Christian Schellhase Centre for Statistics, Bielefeld Universit Department for Business Administration and Economics Version 0.2.5 Februar
More informationLindner, Szimayer: A Limit Theorem for Copulas
Lindner, Szimayer: A Limit Theorem for Copulas Sonderforschungsbereich 386, Paper 433 (2005) Online unter: http://epub.ub.uni-muenchen.de/ Projektpartner A Limit Theorem for Copulas Alexander Lindner Alexander
More information: now we have a family of utility functions for wealth increments z indexed by initial wealth w.
Lotteries with Money Payoffs, continued Fix u, let w denote wealth, and set u ( z) u( z w) : now we have a family of utility functions for wealth increments z indexed by initial wealth w. (a) Recall from
More informationOn Shifted Weibull-Pareto Distribution
International Journal of Statistics and Probability; Vol. 5, No. 4; July 206 ISSN 927-7032 E-ISSN 927-7040 Published by Canadian Center of Science and Education On Shifted Weibull-Pareto Distribution Ahmad
More informationHierarchical Bayes Analysis of the Log-normal Distribution
Int. Statistical Inst.: Proc. 58th World Statistical Congress, 2011, Dublin Session CPS066 p.5614 Hierarchical Bayes Analysis of the Log-normal Distribution Fabrizi Enrico DISES, Università Cattolica Via
More informationTHEORETICAL ASPECTS OF THREE-ASSET PORTFOLIO MANAGEMENT
THEORETICAL ASPECTS OF THREE-ASSET PORTFOLIO MANAGEMENT Michal ŠOLTÉS ABSTRACT: The aer deals with three-asset ortfolio It focuses on ordinary investor for whom the Marowitz s theory of selection of otimal
More informationOutline. 1 Introduction. 2 Algorithms. 3 Examples. Algorithm 1 General coordinate minimization framework. 1: Choose x 0 R n and set k 0.
Outline Coordinate Minimization Daniel P. Robinson Department of Applied Mathematics and Statistics Johns Hopkins University November 27, 208 Introduction 2 Algorithms Cyclic order with exact minimization
More informationPORTFOLIO MODELLING USING THE THEORY OF COPULA IN LATVIAN AND AMERICAN EQUITY MARKET
PORTFOLIO MODELLING USING THE THEORY OF COPULA IN LATVIAN AND AMERICAN EQUITY MARKET Vladimirs Jansons Konstantins Kozlovskis Natala Lace Faculty of Engineering Economics Riga Technical University Kalku
More informationMODEL RISK AND DETERMINATION OF SOLVENCY CAPITAL IN THE SOLVENCY 2 FRAMEWORK
MODEL RISK AND DETERMINATION OF SOLVENCY CAPITAL IN THE SOLVENCY 2 FRAMEWORK Frédéric Planchet, Pierre-Emmanuel Thérond To cite this version: Frédéric Planchet, Pierre-Emmanuel Thérond. MODEL RISK AND
More informationInequality and bi-polarization in socioeconomic status and health: Ordinal approaches
Inequalit and bi-olarization in socioeconomic status and health: Ordinal aroaches Bénédicte H. Aoue, Jacques Silber To cite this version: Bénédicte H. Aoue, Jacques Silber. Inequalit and bi-olarization
More informationABSTRACT 1. INTRODUCTION
MULI-LEVEL RISK AGGREGAION BY DAMIR FILIPOVIC * ABSRAC In this paper we compare the current Solvenc II standard and a genuine bottom-up approach to risk aggregation. his is understood to be essential for
More informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY 6.265/15.070J Fall 2013 Lecture 19 11/20/2013. Applications of Ito calculus to finance
MASSACHUSETTS INSTITUTE OF TECHNOLOGY 6.265/15.7J Fall 213 Lecture 19 11/2/213 Applications of Ito calculus to finance Content. 1. Trading strategies 2. Black-Scholes option pricing formula 1 Security
More informationThe Impact of Flexibility And Capacity Allocation On The Performance of Primary Care Practices
University of Massachusetts Amherst ScholarWorks@UMass Amherst Masters Theses 1911 - February 2014 2010 The Imact of Flexibility And Caacity Allocation On The Performance of Primary Care Practices Liang
More informationAsymmetric Information
Asymmetric Information Econ 235, Sring 2013 1 Wilson [1980] What haens when you have adverse selection? What is an equilibrium? What are we assuming when we define equilibrium in one of the ossible ways?
More informationPartially Ordered Preferences in Decision Trees: Computing Strategies with Imprecision in Probabilities
Partially Ordered Preferences in Decision Trees: Comuting trategies with Imrecision in Probabilities Daniel Kikuti scola Politécnica University of ão Paulo daniel.kikuti@oli.us.br Fabio G. Cozman scola
More informationMultivariate Statistics Lecture Notes. Stephen Ansolabehere
Multivariate Statistics Lecture Notes Stephen Ansolabehere Spring 2004 TOPICS. The Basic Regression Model 2. Regression Model in Matrix Algebra 3. Estimation 4. Inference and Prediction 5. Logit and Probit
More information3.4 Copula approach for modeling default dependency. Two aspects of modeling the default times of several obligors
3.4 Copula approach for modeling default dependency Two aspects of modeling the default times of several obligors 1. Default dynamics of a single obligor. 2. Model the dependence structure of defaults
More informationLecture #29: The Greeks
Statistics 441 (Fall 014) November 14, 014 Prof. Michael Kozdron Lecture #9: he Greeks Recall that if V (0,S 0 )denotesthefairrice(attime0)ofaeuroeancallotionwithstrike rice E and exiry date, then the
More informationWe connect the mix-flexibility and dual-sourcing literatures by studying unreliable supply chains that produce
MANUFACTURING & SERVICE OPERATIONS MANAGEMENT Vol. 7, No. 1, Winter 25,. 37 57 issn 1523-4614 eissn 1526-5498 5 71 37 informs doi 1.1287/msom.14.63 25 INFORMS On the Value of Mix Flexibility and Dual Sourcing
More informationProbability and Statistics
Kristel Van Steen, PhD 2 Montefiore Institute - Systems and Modeling GIGA - Bioinformatics ULg kristel.vansteen@ulg.ac.be CHAPTER 3: PARAMETRIC FAMILIES OF UNIVARIATE DISTRIBUTIONS 1 Why do we need distributions?
More informationIntroduction Recently the importance of modelling dependent insurance and reinsurance risks has attracted the attention of actuarial practitioners and
Asymptotic dependence of reinsurance aggregate claim amounts Mata, Ana J. KPMG One Canada Square London E4 5AG Tel: +44-207-694 2933 e-mail: ana.mata@kpmg.co.uk January 26, 200 Abstract In this paper we
More informationOptimum Profit Model for Determining Purchaser s Order Quantity and Producer s Order Quantity and Producer s Process Mean and Warranty Period
International Journal of Operations Research International Journal of Operations Research Vol. 7, No. 3, 4-4 (200) Optimum Profit Model for Determining Purchaser s Order uantit and Producer s Order uantit
More information