Detecting Auto Insurance Fraud by Data Mining Techniques

Size: px
Start display at page:

Download "Detecting Auto Insurance Fraud by Data Mining Techniques"

Transcription

1 Detectig Auto Isurace Fraud by Data Miig Techiques Rekha Bhowmik Computer Sciece Departmet Uiversity of Texas at Dallas, USA ABSTRACT The paper presets fraud detectio method to predict ad aalyze fraud patters from data. To geerate classifiers, we apply the Naïve Bayesia Classificatio, ad Decisio Tree-Based algorithms. A brief descriptio of the algorithm is provided alog with its applicatio i detectig fraud. The same data is used for both the techiques. We aalyze ad iterpret the classifier predictios. The model predictio is supported by Bayesia Naïve Visualizatio, Decisio Tree visualizatio, ad Rule-Based Classificatio. We evaluate techiques to solve fraud detectio i automobile isurace. Keywords: Rule-based Algorithm, Bayesia Network, C4.5, Fraud Detectio 1. INTRODUCTION There are a umber of data miig techiques like clusterig, eural etworks, regressio, multiple predictive models. Here, we discuss oly few techiques of data miig which would be cosidered importat to hadle fraud detectio. Data Miig is associated with (a) supervised learig based o traiig data of kow fraud ad legal cases ad (b) usupervised learig with data that are ot labeled to be fraud or legal. Bedford s law ca be iterpreted as a example of usupervised learig [1]. Isurace fraud, credit card fraud, telecommuicatios fraud, ad check forgery are some of the mai types of fraud. Isurace fraud is commo i automobile, travel. Fraud detectio ivolves three types of offeders: i) Crimial offeders, ii) orgaized crimial offeders who are resposible for major fraud, ad iii) offeders who commit fraud (called soft fraud) whe sufferig from fiacial hardship. Soft fraud is the hardest to lesse because the cost for each suspected icidet is usually higher tha the cost of the fraud. Types i) ad ii) offeders, called hard fraud, avoid ati-fraud measures [2]. We preset data miig techiques which are most appropriate for fraud aalysis. We preset automobile isurace example. Here, the data miig techiques used for fraud aalysis are: i) Bayesia etwork, ad ii) Decisio tree. Bayesia etwork is the techique used for classificatio task. Classificatio, give a set of predefied categorical classes, determies which of these classes a specific data belogs to. Decisio trees are used to create descriptive models. Descriptive models are created to describe the characteristics of fault. The remaider of this paper is orgaized as follows. I Sectio 2, we preset the existig fraud detectio systems ad techiques. Sectio 3 icludes the algorithms ad applicatio. Sectio 4 presets the model. Fially, i sectio 5, we discuss the importat features of our work. 2. EXISTING FRAUD DETECTION SYSTEMS The hot spots methodology[3] performed a three step process: i) k-meas clusterig algorithm for cluster detectio is used because the other clusterig algorithms ted to be expesive for very large datasets, ii) C4.5 algorithm, the resultig decisio tree ca be coverted to a rule set ad prued, ad iii) visualizatio tools for rule evaluatio, buildig statistical summaries of the etities associated with each rule. The credit fraud model[4] suggested a classificatio techique with fraud/legal attribute, ad a clusterig followed by a classificatio techique with o fraud/legal attribute. Kohoe's Self-Orgaizig Feature Map [5] was used to categorize automobile ijury claims depedig o the type of fraud. Classificatio techiques have proved to be very effective i fraud detectio[6] ad therefore, ca be applied to categorize crime data. The distributed data miig model[6] uses a realistic cost model to evaluate C4.5, CART, ad aïve Bayesia classificatio models. The method was applied to credit card trasactios. The eural data miig approach[7] uses rule-based associatio rules to mie symbolic data. The approach discusses the importace of use of o-umeric data i fraud detectio. SAS Eterprise Mier Software[8] depeds o associatio rules, cluster detectio ad classificatio techiques to detect fraudulet claims. The Bayesia Belief Network (BBN) ad Artificial Neural Network (ANN) study used the STAGE algorithm for BBN i fraud detectio ad backpropagatio for ANN[9]. The result shows that BBNs were much faster to trai, but were slower whe applied to ew istaces. The ASPECT group[10] focused o eural etworks to trai curret user profiles ad user profiles histories. A caller s curret profile ad the profile history are compared to fid probable fraud. [11] build o the adaptive fraud detectio framework[12, 13], by applyig a evet-drive approach of assigig fraud scores to detect fraud. The [11] framework ca also detect types of fraud usig rules. [14] 156

2 used dyamic BBNs called Mass Detectio tool to detect fraudulet claims, which the used a rule geerator called Suspicio Buildig Tool. Iteral fraud detectio cosists i determiig fraudulet fiacial reportig by maagemet[15], ad abormal retail trasactios by employees[16]. There are four types of isurace fraud detectio: home isurace[17], crop isurace [18], automobile isurace fraud detectio[19], ad health isurace[20]. A sigle meta-classifier[21] is used to select the best base classifiers, ad the combied with these base classifiers predictios to improve cost savigs. Credit card fraud detectio refers to screeig credit applicatios, ad/or logged credit card trasactios [22]. Credit trasactioal fraud detectio has bee preseted by [22]. Literature focus o video-o-demad websites[23] ad IP-based telecommuicatio services[24]. Olie sellers[25] ad olie buyers[26] ca be moitored by automated systems. Fraud detectio i govermet orgaisatios such as tax[27] ad customs[28] has also bee reported. 2.1 Bayesia Belief Networks Naïve Bayesia classificatio assumes that the attributes of a istace are idepedet, give the target attribute[29]. The aim is to assig a ew istace to the class that has the highest posterior probability. The algorithm is very effective ad ca give better predictive accuracy whe compared to C4.5 decisio trees ad backpropagatio 2.2 Decisio Trees Decisio trees are machie learig techiques that express idepedet attributes ad a depedet attribute i a tree-shaped structure. Classificatio rules, extracted from decisio trees, are IF-THEN expressios i which the precoditios are logically ANDed ad all the tests have to succeed if each rule is to be geerated. The related applicatios iclude the aalysis of istaces from drug smugglig, govermetal fiacial trasactios[30], ad customs declaratio fraud[28] to more serious crimes such as drug related homicides, serial sex crimes[31], ad homelad security[31, 30]. C4.5 [32] is used to divide data ito segmets based ad to geerate descriptive classificatio rules that ca be used to classify a ew istace. C4.5 ca help to make predictios ad to extract crime patters. It geerates rules from trees [33] ad hadles umeric attributes, missig values, pruig, ad estimatig error rates. The learig ad classificatio steps are geerally fast. However, performace decrease ca occur whe C4.5 is applied to large datasets. C5.0 shows margial improvemets to decisio tree iductio. 3. APPLICATION The steps i crime detectio are: i) classifiers, ii) itegrate multiple classifiers, iii) ANN approach to clusterig, ad iv) visualizatio techiques to describe the patters. 3.1 Bayesia Network For the purpose of fraud detectio, we costruct two Bayesia etworks to describe the behavior of auto isurace. First, a Bayesia etwork is costructed to model behavior uder the assumptio that the driver is fraudulet ad aother model uder the assumptio the driver is a legal. The fraud et is set up by usig expert kowledge. The legal et is set up by usig data from legal drivers. By isertig evidece i these etworks, we ca get the probability of the measuremet E uder two above metioed hypotheses. This meas, we obtai judgmets to what degree a observed user behavior meets typical fraudulet or legal behavior. These quatities we call P(E output = legal) ad P(E output = fraud). By postulatig the probability of fraud P(output = fraud ) ad P(output = legal) = 1 - P(output = fraud ) i geeral ad by applyig Bayes rule, we get the probability of fraud, give the measuremet E, P(output = fraud E) = P(output = fraud ) P(E output = fraud) / P(E) where, the deomiator P(E) ca be calculated as: P(E) = P(output = fraud) P(E output = fraud) + P(output = legal) P(E output = legal) The chai rule of probabilities is: Suppose there are two outputs O 1, O 2 for fraud ad legal respectively. Give a istace E = (E 1, E 2,, E ), each row is represeted by a attribute A = (A 1, A 2,, A ) The classificatio is to derive the maximum P(O i X) which ca be derived from Bayes theorem Applicatio We preset Bayesia learig algorithm to predict occurrece of fraud. Cosider the two output attributes, fraud ad legal. The geeral equatio for computig the probability that the output attribute is legal or fraud is: i) P(output = fraud E) = [P(E output = fraud) P(output = fraud)] / P(E P(output = legal E) = [P(E output = legal) P(output = legal)] / P(E) ii) The a priori probability, show as P(output=fraud), is the probability of a fraud customer without kowig the history of the istace. Here, the a priori probability is the fractio of the total populatio that is fraud, that is: P(fraud) = d i / d d is the total populatio ad d i is the umber of fraud. iii) A simplified assumptio of o depedet relatioships betwee attributes is made. Thus, 157

3 P(E output = fraud) = k1 P(x k output = fraud) P(E output = legal) = P(x k output = legal) k1 The probabilities P(x 1 output = fraud), P(x 2 output = fraud) ca be estimated from the database usig: P(x k output = fraud) = d ik / d i Here, d i is the umber of records for output fraud ad d ik is the umber of records of output class fraud havig the value x k for the attributes. iv) Repeat step iii) for computig P(E output = legal) [P(E output = fraud) P(output = fraud)] ad [P(E output = legal) P(output = legal)] eed to be optimized as P(E ) is costat. Cosider the data i Table 1, which is a subset of auto isurace database. We use Output attribute whose value is to be predicted. E= (policyholder = 1, driverratig = 0, reportfiled = 0.33) to be either fraud or legal. P(fraud) = d i / d = 3/20 = 0.15 P(legal) = d i / d = 17/20 = 0.85 From step iii) of the algorithm, P(policyHolder = 1/ output=fraud) = 3/3 = 1 P(E output = fraud) = P(x k output = fraud) = 0 k1 From step iv) of the algorithm, P(policyholder = 1/ output=legal) = 12/17= P(E output = fraud) = P(x k output = legal) k1 = Therefore, [P(E output = fraud) P(output = fraud)] = 0 [P(E output = legal) P(output = legal)] = Based o these probabilities, we classify the ew tuple as legal. The probabilities for P(E output = fraud) is always 0. The Laplace estimator improves the value by addig 1 to the umerator ad the total umber of attribute value types to the deomiator of P(E output = fraud) ad P(E output = fraud) [33] Based o step iii) of the algorithm, P(policyHolder = 1/ output=fraud) = 0.8 From step iv) of the algorithm, P(policyholder = 1/ output=legal) = [P(E output = fraud) P(output = fraud)] = [P(E output = legal) P(output = legal)] = Thus, istace E is more likely to be Fraud. Likelihood of beig legal = Likelihood of beig fraud = We estimate P(E) by summig up these idividuals likelihood values sice E will be either legal of fraud: P(E) = = Fially, we obtai the actual probabilities of each evet: P(output = legal E) = (0.039 *0.9)/ = P(output = fraud E) = (0.500 *0.1)/ = Bayesia classifier ca hadle missig values i traiig datasets. To demostrate this, seve missig values appear i dataset. The Naïve Bayes approach is easy to use ad oly oe sca of the data is required. The approach ca hadle missig values by simply omittig that probability whe calculatig the likelihoods of membership i each class. 3.2 Decisio Tree-Based Algorithm Solvig the classificatio problem is a two-step process: i) decisio tree iductio- costruct a Decisio Tree(DT), ad ii) apply the DT to determie its class. Rules ca be geerated that are easy to iterpret. The basic algorithm for decisio tree is as follows: i) Suppose there are two outputs, fraud ad legal. The tree starts as a sigle ode N represetig the dataset. If the istaces are of the same type fraud, the the ode becomes a leaf ad is labeled as fraud. ii) Otherwise, the algorithm uses a Etropy, Gii Idex, ad Classificatio Error to measure degree of impurity for selectig the attribute that will best separate the data ito idividual classes. iii) Etropy is calculated as the sum of the coditioal probabilities of a evet (p i ) times its iformatio required for the evet i subsets (b i ). Note that b i = - log 2 p i i the cases of a simple (biary) split ito two classes. Etropy(p 1,p 2,...,p ) = p 1 * b 1 + p 2 * b p * b = - p 1 logp 1 - p 2 logp p logp Table 1a. Data for Bayes Classifier istace Policy Driver Report Output Holder Ratig Filed legal fraud legal legal legal E ? 158

4 Table 1b. Data for Bayes Classifier istace Policy Driver Report Vehicle Output Holder Ratig Filed AgePrice legal fraud legal legal legal E ? C4.5 Algorithm The Etropy, or expected iformatio eeded to classify a give istace is: P(fraud, legal)= (fraudistaces / Istaces) log 2 (fraudistaces / Istaces) (legalistaces / Istaces) log 2 (legalistaces / Istaces) Expected iformatio or etropy by attribute: E(A)= [{(fraudattributes / Istaces) + (legalattributes/ Istaces)} * {E(fraudAttributes, legalattributes)}] iv) The value (or cotributio to iformatio) of a attribute is calculated as gai(attr) = (iformatio before split) - (iformatio after split) Expected reductio i etropy is: gai(attr) = Etropy of paret table E(A) The algorithm computes the iformatio gai of each attribute. The attribute with the highest iformatio gai is the oe selected for test attribute. v) A brach is created for each kow value of the test attribute. The algorithm uses the same process iteratively to form a decisio tree at each partitio. Oce a attribute has occurred at a ode, it eed ot be cosidered i ay of the ode s descedets. vi) The iterative partitioig stops whe oe of the coditios is true: a) all examples for a give ode belog to the same class, or b) there are o remaiig attributes o which samples may be further partitioed, ad c) there are o samples for the brach test-attribute Applicatio From Table 1b, the probability of each output class is: etropy = -0.1 log (0.1) 0.9log(0.9) = - 0.1* * =0.469 E(vehicleAgePrice) = (9/20) etropy(1, 8) = (9/20) (-1/9 log 2 1/9-8/9 log 2 8/9) =.225 The iformatio gai of attribute VehicleAgePrice is computed as follows: [(9/20) (-1/9 log 2 1/9-8/9 log 2 8/9)] = prob(output = fraud) = 2/20 = gii idex = 1 (prob) j j = ( ) = 0.18 Classificatio error = 1- max{prob j } = 1- max{0.1, 0.9} = 0.9 Etropy, Gii Idex, ad Classificatio Error Idex of sigle class is zero. They reach maximum value whe all the classes i the table have equal probability. The attribute VehicleAgePrice has four values. Based o step v) of C4.5 algorithm, a decisio tree ca be created. Each ode is either i) a leaf ode - (output class), or ii)a decisio ode 3.3 Rule Based Algorithm Oe way to perform classificatio is to geerate if-the rules Geeratig Rules from a Decisio Tree The followig rules are geerated for the Decisio Tree: If (driver_age 40) ) (driver_ratig =1) ) (vehicle_age =2), the class = fraud If (driver_age > 40) ) (driver_age 50) ) (driver_ratig = 0.33), the class = legal 4. MODEL PERFORMANCE Cofusio Matrix There are two ways to examie the performace of classifiers: i) cofusio matrix, ad ii) to use a ROC graph. Give a class, C j, ad a tuple, t i, that tuple may or may ot be assiged to that class while its actual membership may or may ot be i that class. With two classes, there are four possible outcomes with the classificatio as: i) true positives (hits), ii) false positives (false alarms), iii) true egatives (correct rejectios), ad iv) false egatives. Table 2a, cotais iformatio about actual ad predicted classificatios. Performace is evaluated usig the data i the matrix. Table 2b shows cofusio matrix built o simulated data. The model commits some errors ad has a accuracy of 78%. We also applied the model to the same data, but to the egative class with respect to class skew i the data. The quality of a model highly depeds o the choice of the test data. A umber of model performace metrics ca be derived from the cofusio matrix. Table 2a. Cofusio Matrix Observed legal fraud predicted legal TP FP fraud FN TN 159

5 Table 2b. Cofusio matrix of a model applied to test dataset Observed legal fraud accuracy: 0.78 predicted legal recall: 0.86 fraud precisio: 0.70 The accuracy determied i (Table 2b) may ot be a adequate performace measure whe the umber of egative cases is much greater tha the umber of positive cases. Suppose there are 1500 cases, 1460 of which are egative cases ad 40 of which are positive cases. If the system classifies them all as egative, the accuracy would be 97.3%, eve though the classifier missed all positive cases. Other performace measures are geometric mea (g-mea), ad F-Measure. For calculatig F-measure, β has a value from 0 to ad is used to cotrol the weight assiged to TP ad P. Ay classifier evaluated usig g- mea or F-measure will have a value of 0, if all positive cases are classified icorrectly. To easily view ad uderstad the output, visualizatio of the results is helpful. Naïve Bayesia visualizatio provides a iteractive view of the predictio results. The attributes ca be sorted by the predictor ad evidece items ca be sorted by the umber of items i its storage bi. Attribute colum graphs help to fid the sigificat attributes i eural etworks. Decisio tree visualizatio builds trees by splittig attributes from C4.5 classifiers. Cumulative gais ad lift charts are visual aids for measurig model performace. Lift is a measure of a predictive model calculated as the ratio betwee the results obtaied with or without the predictive model. For istace, if 105 of all samples are actually fraud ad a aïve Bayesia classifier could correctly predict 20 fraud samples per 100 samples, the that correspods to a lift of 4. Table 3c: Performace metrics model performace metrics Accuracy(AC) Recall or true positive rate(tp) False positive rate(fp) True egative rate(tn) False egative rate(fn) Precisio(P) geometric mea(g-mea) F-measure Classificatio models are ofte evaluated o accuracy rates, error rates, false egative rates, ad false positive rates. Table 3 shows that True Positives (hits) ad False Positives (false alarms) require cost per ivestigatio. False alarms cost are the most expesive because both ivestigatio ad claim costs are required. False Negatives (misses) ad True Negatives(correct rejectio) are the cost of claim. Table 3: Cost/ Beefit Decisio Summary of Predictios fraud True Positive(Hit) cost = umber of hits * average cost per ivestigatio False Negative(miss) cost = umber of misses * average cost per claim 5. CONCLUSIONS legal False Positive(False alarm) cost =umber of false alarms * (Average cost per ivestigatio + average cost per claim) True Negative(correct rejectio) cost = umber of correct rejectio claims * average cost per claim We studied the existig fraud detectio systems. To predict ad preset fraud we used Naïve Bayesia classifier ad Decisio Tree-Based algorithms. We looked at model performace metrics derived from the cofusio matrix. Performace metrics such as accuracy, recall, ad precisio are derived from the cofusio matrix. It is strog with respect to class skew, makig it a reliable performace metric i may importat fraud detectio applicatio areas. REFERENCES [1] Bolto, R., Had, D.: Statistical Fraud Detectio: A Review. Statistical Sciece 17(3): (2002). [2] Sparrow, M. K.: Fraud Cotrol i the Health Care Idustry: Assessig the State of the Art, i Shichor et al(eds), Readigs i white-collar Crime, Wavelad Press, Illiois(2002). [3] Williams, G.: Evolutioary Hot Spots Data Miig: A Architecture for Explorig for Iterestig Discoveries. I: 3rd Pacific-Asia Coferece i Kowledge Discovery ad Data Miig, Beijig, Chia(1999). [4] Groth, R.: Data Miig: A Hads-o Approach for Busiess Professioals, Pretice Hall, pp (1998). 160

6 [5] Brockett, P., Derrig, R., Golde, L., Levie, A. & Alpert, M.: Fraud Classificatio usig Pricipal Compoet Aalysis of RIDITs. Joural of Risk ad Isurace 69(3): (2002). [6] Che, R., Chiu, M., Huag, Y., Che, L.: Detectig Credit Card Fraud by Usig Questioaire-Respoded Trasactio Model Based o Support Vector Machies. I: IDEAL2004, (2004). [7] Brause, R., Lagsdorf, T., Hepp, M.: Neural Data Miig for Credit Card Fraud Detectio. I: 11th IEEE Iteratioal Coferece o Tools with Artificial Itelligece(1999). [8] SAS, e-itelligecedata Miig i the Isurace idustry: Solvig Busiess problems usig SAS Eterprise Mier Software. White Paper(2000). [9] Maes, S., Tuyls, K., Vaschoewikel, B. & Maderick, B.: Credit Card Fraud Detectio usig Bayesia ad Neural Networks. Proc. of the 1st Iteratioal NAISO Cogress o Neuro Fuzzy Techologies (2002). [10] Weatherford, M.: Miig for Fraud. I: IEEE Itelliget Systems(2002). [11] Cahill, M., Che, F., Lambert, D., Piheiro, J. & Su, D.: Detectig Fraud i the Real World. Hadbook of Massive Datasets (2002) [12] Fawcett, T.: ROC graphs: Notes ad practical cosideratios for researchers. Machie Learig, 3(2004). [13] Fawcett, T., Flach, P. A.: A respose to web ad Tig s o the applicatio of ROC aalysis to predict classificatio performace uder varyig class distributios. Machie Learig, 58(1), (2005). [14] Ormerod T., Morley N., Ball L., Lagley C., Speser C.: Usig Ethography To Desig a Mass Detectio Tool (MDT) for the Early Discovery of Isurace Fraud. Computer Huma Iteractio, Ft. Lauderdale, Florida(2003). [15] Li, J., Hwag, M., Becker, J.: A Fuzzy Neural Network for Assessig the Risk of Fraudulet Fiacial Reportig. J. of Maagerial Auditig, 18(8), (2003). [16] Kim, H., Pag, S., Je, H., Kim, D. & Bag, S.: Costructig Support Vector Machie Esemble. Patter Recogitio 36: (2003).Kim, J., Og, A. & Overill, R. (2003). Desig of a Artificial Immue System as a Novel Aomaly Detector for Combatig Fiacial Fraud i Retail Sector. Cogress o Evolutioary Computatio. [17]Betley, P., Kim, J., Jug., G., Choi, J.: Fuzzy Darwiia Detectio of Credit Card Fraud. I: 14th Aual Fall Symposium of the Korea Iformatio Processig Society(2000). [18] Little, B., Johsto, W., Lovell, A., Rejesus, R. & Steed, S.: Collusio i the US Crop Isurace Program: Applied Data Miig. Proc. of SIGKDD02, (2002). [19] Viaee, S., Derrig, R., Dedee, G.: A Case Study of Applyig Boostig Naive Bayes to Claim Fraud Diagosis. I: IEEE Trasactios o Kowledge ad Data Egieerig, 16(5), (2004). [20] Yamaishi, K., Takeuchi, J., Williams, G., Mile, P.: O-Lie Usupervised Outlier Detectio Usig Fiite Mixtures with Discoutig Learig Algorithms. Data Miig ad Kowledge Discovery, 8, (2004). [21] Phua, C., Alahakoo, D., Lee, V.: Miority Report i Fraud Detectio: Classificatio of Skewed Data. I: SIGKDD Exploratios, 6(1), (2004). [22] Foster, D. & Stie, R.: Variable Selectio i Data Miig: Buildig a Predictive Model for Bakruptcy. J. of America Statistical Associatio 99, (2004). [23] Barse, E., Kvarstrom, H., Josso, E.: Sythesizig Test Data for Fraud Detectio Systems. I: 19th Aual Computer Security Applicatios Coferece, (2003). [24] McGibey, J., Heare, S.: A Approach to Rulesbased Fraud Maagemet i Emergig Coverged Networks. I: IEI/IEEE ITSRS (2003). [25] Bhargava, B., Zhog, Y., Lu, Y.: Fraud Formalizatio ad Detectio. I: DaWaK2003, (2003). [26] Sherma, E.: Fightig Web Fraud. Newsweek, Jue 10(2002). [27] Bochi, F., Giaotti, F., Maietto, G., Pedreschi, D.: A Classificatio-based Methodology for Plaig Auditig Strategies i Fraud Detectio. I: SIGKDD99, (1999). [28] Shao, H., Zhao, H., Chag, G.: Applyig Data Miig to Detect Fraud Behavior i Customs Declaratio. I: 1 st Iteratioal Coferece o Machie Learig ad Cyberetics, (2002). [29] Feelders, A. J.: Statistical Cocepts. Berthold M. ad Had D. (eds), Itelliget Data Aalysis, Spriger- Verlag, Berli, Germay, pp ,

7 [30] Mea J.: Data miig for Homelad Security. Executive Briefig, VA(2003). Mea J.: Ivestigative Data Miig for Security ad Crimial Detectio, Butterworth Heiema, MA(2003). [31] SPSS: Data miig ad Crime aalysis i the Richmod Police Departmet, White Paper, Virgiia(2003). [32] Quila, J. R.: C4.5 Programs for Machie Learig, Morga Kauffma, CA, USA(1993). [33] Witte, I., Frak, E.: Data Miig: Practical Machie Learig Tools ad Techiques, 2d Editio, Morga Kaufma(2005). [31]James F.: FBI has eye o busiess databases. Chicago Tribue, Kight Ridder/ Tribue Busiess News(2002). 162

Review: Classification Outline

Review: Classification Outline Data Miig CS 341, Sprig 2007 Decisio Trees Neural etworks Review: Lecture 6: Classificatio issues, regressio, bayesia classificatio Pretice Hall 2 Data Miig Core Techiques Classificatio Clusterig Associatio

More information

Ordinal Classification Method for the Evaluation Of Thai Non-life Insurance Companies

Ordinal Classification Method for the Evaluation Of Thai Non-life Insurance Companies Ordial Method for the Evaluatio Of Thai No-life Isurace Compaies Phaiboo Jhopita, Sukree Sithupiyo 2 ad Thitivadee Chaiyawat 3 Techopreeurship ad Iovatio Maagemet Program Graduate School, Chulalogkor Uiversity,

More information

I. Chi-squared Distributions

I. Chi-squared Distributions 1 M 358K Supplemet to Chapter 23: CHI-SQUARED DISTRIBUTIONS, T-DISTRIBUTIONS, AND DEGREES OF FREEDOM To uderstad t-distributios, we first eed to look at aother family of distributios, the chi-squared distributios.

More information

Department of Computer Science, University of Otago

Department of Computer Science, University of Otago Departmet of Computer Sciece, Uiversity of Otago Techical Report OUCS-2006-09 Permutatios Cotaiig May Patters Authors: M.H. Albert Departmet of Computer Sciece, Uiversity of Otago Micah Colema, Rya Fly

More information

CHAPTER 3 THE TIME VALUE OF MONEY

CHAPTER 3 THE TIME VALUE OF MONEY CHAPTER 3 THE TIME VALUE OF MONEY OVERVIEW A dollar i the had today is worth more tha a dollar to be received i the future because, if you had it ow, you could ivest that dollar ad ear iterest. Of all

More information

INVESTMENT PERFORMANCE COUNCIL (IPC) Guidance Statement on Calculation Methodology

INVESTMENT PERFORMANCE COUNCIL (IPC) Guidance Statement on Calculation Methodology Adoptio Date: 4 March 2004 Effective Date: 1 Jue 2004 Retroactive Applicatio: No Public Commet Period: Aug Nov 2002 INVESTMENT PERFORMANCE COUNCIL (IPC) Preface Guidace Statemet o Calculatio Methodology

More information

Confidence Intervals for One Mean

Confidence Intervals for One Mean Chapter 420 Cofidece Itervals for Oe Mea Itroductio This routie calculates the sample size ecessary to achieve a specified distace from the mea to the cofidece limit(s) at a stated cofidece level for a

More information

Analyzing Longitudinal Data from Complex Surveys Using SUDAAN

Analyzing Longitudinal Data from Complex Surveys Using SUDAAN Aalyzig Logitudial Data from Complex Surveys Usig SUDAAN Darryl Creel Statistics ad Epidemiology, RTI Iteratioal, 312 Trotter Farm Drive, Rockville, MD, 20850 Abstract SUDAAN: Software for the Statistical

More information

INVESTMENT PERFORMANCE COUNCIL (IPC)

INVESTMENT PERFORMANCE COUNCIL (IPC) INVESTMENT PEFOMANCE COUNCIL (IPC) INVITATION TO COMMENT: Global Ivestmet Performace Stadards (GIPS ) Guidace Statemet o Calculatio Methodology The Associatio for Ivestmet Maagemet ad esearch (AIM) seeks

More information

where: T = number of years of cash flow in investment's life n = the year in which the cash flow X n i = IRR = the internal rate of return

where: T = number of years of cash flow in investment's life n = the year in which the cash flow X n i = IRR = the internal rate of return EVALUATING ALTERNATIVE CAPITAL INVESTMENT PROGRAMS By Ke D. Duft, Extesio Ecoomist I the March 98 issue of this publicatio we reviewed the procedure by which a capital ivestmet project was assessed. The

More information

In nite Sequences. Dr. Philippe B. Laval Kennesaw State University. October 9, 2008

In nite Sequences. Dr. Philippe B. Laval Kennesaw State University. October 9, 2008 I ite Sequeces Dr. Philippe B. Laval Keesaw State Uiversity October 9, 2008 Abstract This had out is a itroductio to i ite sequeces. mai de itios ad presets some elemetary results. It gives the I ite Sequeces

More information

Lesson 15 ANOVA (analysis of variance)

Lesson 15 ANOVA (analysis of variance) Outlie Variability -betwee group variability -withi group variability -total variability -F-ratio Computatio -sums of squares (betwee/withi/total -degrees of freedom (betwee/withi/total -mea square (betwee/withi

More information

Introducing Your New Wells Fargo Trust and Investment Statement. Your Account Information Simply Stated.

Introducing Your New Wells Fargo Trust and Investment Statement. Your Account Information Simply Stated. Itroducig Your New Wells Fargo Trust ad Ivestmet Statemet. Your Accout Iformatio Simply Stated. We are pleased to itroduce your ew easy-to-read statemet. It provides a overview of your accout ad a complete

More information

Modified Line Search Method for Global Optimization

Modified Line Search Method for Global Optimization Modified Lie Search Method for Global Optimizatio Cria Grosa ad Ajith Abraham Ceter of Excellece for Quatifiable Quality of Service Norwegia Uiversity of Sciece ad Techology Trodheim, Norway {cria, ajith}@q2s.tu.o

More information

PROCEEDINGS OF THE YEREVAN STATE UNIVERSITY AN ALTERNATIVE MODEL FOR BONUS-MALUS SYSTEM

PROCEEDINGS OF THE YEREVAN STATE UNIVERSITY AN ALTERNATIVE MODEL FOR BONUS-MALUS SYSTEM PROCEEDINGS OF THE YEREVAN STATE UNIVERSITY Physical ad Mathematical Scieces 2015, 1, p. 15 19 M a t h e m a t i c s AN ALTERNATIVE MODEL FOR BONUS-MALUS SYSTEM A. G. GULYAN Chair of Actuarial Mathematics

More information

SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES

SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES SECTION 1.5 : SUMMATION NOTATION + WORK WITH SEQUENCES Read Sectio 1.5 (pages 5 9) Overview I Sectio 1.5 we lear to work with summatio otatio ad formulas. We will also itroduce a brief overview of sequeces,

More information

Trading rule extraction in stock market using the rough set approach

Trading rule extraction in stock market using the rough set approach Tradig rule extractio i stock market usig the rough set approach Kyoug-jae Kim *, Ji-youg Huh * ad Igoo Ha Abstract I this paper, we propose the rough set approach to extract tradig rules able to discrimiate

More information

Vladimir N. Burkov, Dmitri A. Novikov MODELS AND METHODS OF MULTIPROJECTS MANAGEMENT

Vladimir N. Burkov, Dmitri A. Novikov MODELS AND METHODS OF MULTIPROJECTS MANAGEMENT Keywords: project maagemet, resource allocatio, etwork plaig Vladimir N Burkov, Dmitri A Novikov MODELS AND METHODS OF MULTIPROJECTS MANAGEMENT The paper deals with the problems of resource allocatio betwee

More information

*The most important feature of MRP as compared with ordinary inventory control analysis is its time phasing feature.

*The most important feature of MRP as compared with ordinary inventory control analysis is its time phasing feature. Itegrated Productio ad Ivetory Cotrol System MRP ad MRP II Framework of Maufacturig System Ivetory cotrol, productio schedulig, capacity plaig ad fiacial ad busiess decisios i a productio system are iterrelated.

More information

CCH CRM Books Online Software Fee Protection Consultancy Advice Lines CPD Books Online Software Fee Protection Consultancy Advice Lines CPD

CCH CRM Books Online Software Fee Protection Consultancy Advice Lines CPD Books Online Software Fee Protection Consultancy Advice Lines CPD Books Olie Software Fee Fee Protectio Cosultacy Advice Advice Lies Lies CPD CPD facig today s challeges As a accoutacy practice, maagig relatioships with our cliets has to be at the heart of everythig

More information

Domain 1: Designing a SQL Server Instance and a Database Solution

Domain 1: Designing a SQL Server Instance and a Database Solution Maual SQL Server 2008 Desig, Optimize ad Maitai (70-450) 1-800-418-6789 Domai 1: Desigig a SQL Server Istace ad a Database Solutio Desigig for CPU, Memory ad Storage Capacity Requiremets Whe desigig a

More information

LECTURE 13: Cross-validation

LECTURE 13: Cross-validation LECTURE 3: Cross-validatio Resampli methods Cross Validatio Bootstrap Bias ad variace estimatio with the Bootstrap Three-way data partitioi Itroductio to Patter Aalysis Ricardo Gutierrez-Osua Texas A&M

More information

Hypothesis testing. Null and alternative hypotheses

Hypothesis testing. Null and alternative hypotheses Hypothesis testig Aother importat use of samplig distributios is to test hypotheses about populatio parameters, e.g. mea, proportio, regressio coefficiets, etc. For example, it is possible to stipulate

More information

How To Extract From Data From A College Course

How To Extract From Data From A College Course (IJACSA Iteratioal Joural of Advaced Computer Sciece ad Applicatios, Vol., No. 6, 0 Miig Educatioal Data to Aalyze Studets Performace Briesh Kumar Baradwa Research Scholor, Sighaiya Uiversity, Raastha,

More information

Evaluating Model for B2C E- commerce Enterprise Development Based on DEA

Evaluating Model for B2C E- commerce Enterprise Development Based on DEA , pp.180-184 http://dx.doi.org/10.14257/astl.2014.53.39 Evaluatig Model for B2C E- commerce Eterprise Developmet Based o DEA Weli Geg, Jig Ta Computer ad iformatio egieerig Istitute, Harbi Uiversity of

More information

How To Solve The Homewor Problem Beautifully

How To Solve The Homewor Problem Beautifully Egieerig 33 eautiful Homewor et 3 of 7 Kuszmar roblem.5.5 large departmet store sells sport shirts i three sizes small, medium, ad large, three patters plaid, prit, ad stripe, ad two sleeve legths log

More information

ODBC. Getting Started With Sage Timberline Office ODBC

ODBC. Getting Started With Sage Timberline Office ODBC ODBC Gettig Started With Sage Timberlie Office ODBC NOTICE This documet ad the Sage Timberlie Office software may be used oly i accordace with the accompayig Sage Timberlie Office Ed User Licese Agreemet.

More information

The following example will help us understand The Sampling Distribution of the Mean. C1 C2 C3 C4 C5 50 miles 84 miles 38 miles 120 miles 48 miles

The following example will help us understand The Sampling Distribution of the Mean. C1 C2 C3 C4 C5 50 miles 84 miles 38 miles 120 miles 48 miles The followig eample will help us uderstad The Samplig Distributio of the Mea Review: The populatio is the etire collectio of all idividuals or objects of iterest The sample is the portio of the populatio

More information

Determining the sample size

Determining the sample size Determiig the sample size Oe of the most commo questios ay statisticia gets asked is How large a sample size do I eed? Researchers are ofte surprised to fid out that the aswer depeds o a umber of factors

More information

Hypergeometric Distributions

Hypergeometric Distributions 7.4 Hypergeometric Distributios Whe choosig the startig lie-up for a game, a coach obviously has to choose a differet player for each positio. Similarly, whe a uio elects delegates for a covetio or you

More information

Generalization Dynamics in LMS Trained Linear Networks

Generalization Dynamics in LMS Trained Linear Networks Geeralizatio Dyamics i LMS Traied Liear Networks Yves Chauvi Psychology Departmet Staford Uiversity Staford, CA 94305 Abstract For a simple liear case, a mathematical aalysis of the traiig ad geeralizatio

More information

A probabilistic proof of a binomial identity

A probabilistic proof of a binomial identity A probabilistic proof of a biomial idetity Joatho Peterso Abstract We give a elemetary probabilistic proof of a biomial idetity. The proof is obtaied by computig the probability of a certai evet i two

More information

Asymptotic Growth of Functions

Asymptotic Growth of Functions CMPS Itroductio to Aalysis of Algorithms Fall 3 Asymptotic Growth of Fuctios We itroduce several types of asymptotic otatio which are used to compare the performace ad efficiecy of algorithms As we ll

More information

Data Mining Techniques in Fraud Detection

Data Mining Techniques in Fraud Detection Data Mining Techniques in Fraud Detection Rekha Bhowmik University of Texas at Dallas [email protected] ABSTRACT The paper presents application of data mining techniques to fraud analysis. We

More information

Week 3 Conditional probabilities, Bayes formula, WEEK 3 page 1 Expected value of a random variable

Week 3 Conditional probabilities, Bayes formula, WEEK 3 page 1 Expected value of a random variable Week 3 Coditioal probabilities, Bayes formula, WEEK 3 page 1 Expected value of a radom variable We recall our discussio of 5 card poker hads. Example 13 : a) What is the probability of evet A that a 5

More information

1 Computing the Standard Deviation of Sample Means

1 Computing the Standard Deviation of Sample Means Computig the Stadard Deviatio of Sample Meas Quality cotrol charts are based o sample meas ot o idividual values withi a sample. A sample is a group of items, which are cosidered all together for our aalysis.

More information

Lecture 2: Karger s Min Cut Algorithm

Lecture 2: Karger s Min Cut Algorithm priceto uiv. F 3 cos 5: Advaced Algorithm Desig Lecture : Karger s Mi Cut Algorithm Lecturer: Sajeev Arora Scribe:Sajeev Today s topic is simple but gorgeous: Karger s mi cut algorithm ad its extesio.

More information

Chatpun Khamyat Department of Industrial Engineering, Kasetsart University, Bangkok, Thailand [email protected]

Chatpun Khamyat Department of Industrial Engineering, Kasetsart University, Bangkok, Thailand ocpky@hotmail.com SOLVING THE OIL DELIVERY TRUCKS ROUTING PROBLEM WITH MODIFY MULTI-TRAVELING SALESMAN PROBLEM APPROACH CASE STUDY: THE SME'S OIL LOGISTIC COMPANY IN BANGKOK THAILAND Chatpu Khamyat Departmet of Idustrial

More information

Center, Spread, and Shape in Inference: Claims, Caveats, and Insights

Center, Spread, and Shape in Inference: Claims, Caveats, and Insights Ceter, Spread, ad Shape i Iferece: Claims, Caveats, ad Isights Dr. Nacy Pfeig (Uiversity of Pittsburgh) AMATYC November 2008 Prelimiary Activities 1. I would like to produce a iterval estimate for the

More information

Engineering Data Management

Engineering Data Management BaaERP 5.0c Maufacturig Egieerig Data Maagemet Module Procedure UP128A US Documetiformatio Documet Documet code : UP128A US Documet group : User Documetatio Documet title : Egieerig Data Maagemet Applicatio/Package

More information

Reliability Analysis in HPC clusters

Reliability Analysis in HPC clusters Reliability Aalysis i HPC clusters Narasimha Raju, Gottumukkala, Yuda Liu, Chokchai Box Leagsuksu 1, Raja Nassar, Stephe Scott 2 College of Egieerig & Sciece, Louisiaa ech Uiversity Oak Ridge Natioal Lab

More information

Automatic Tuning for FOREX Trading System Using Fuzzy Time Series

Automatic Tuning for FOREX Trading System Using Fuzzy Time Series utomatic Tuig for FOREX Tradig System Usig Fuzzy Time Series Kraimo Maeesilp ad Pitihate Soorasa bstract Efficiecy of the automatic currecy tradig system is time depedet due to usig fixed parameters which

More information

Chapter 7 Methods of Finding Estimators

Chapter 7 Methods of Finding Estimators Chapter 7 for BST 695: Special Topics i Statistical Theory. Kui Zhag, 011 Chapter 7 Methods of Fidig Estimators Sectio 7.1 Itroductio Defiitio 7.1.1 A poit estimator is ay fuctio W( X) W( X1, X,, X ) of

More information

Detecting Voice Mail Fraud. Detecting Voice Mail Fraud - 1

Detecting Voice Mail Fraud. Detecting Voice Mail Fraud - 1 Detectig Voice Mail Fraud Detectig Voice Mail Fraud - 1 Issue 2 Detectig Voice Mail Fraud Detectig Voice Mail Fraud Several reportig mechaisms ca assist you i determiig voice mail fraud. Call Detail Recordig

More information

Pre-Suit Collection Strategies

Pre-Suit Collection Strategies Pre-Suit Collectio Strategies Writte by Charles PT Phoeix How to Decide Whether to Pursue Collectio Calculatig the Value of Collectio As with ay busiess litigatio, all factors associated with the process

More information

The Impact of Feature Selection on Web Spam Detection

The Impact of Feature Selection on Web Spam Detection I.J. Itelliget Systems ad Applicatios, 2012, 9, 61-67 Published Olie August 2012 i MECS (http://www.mecs-press.org/) DOI: 10.5815/ijisa.2012.09.08 The Impact of Feature Selectio o Web Spam Detectio Jaber

More information

Non-life insurance mathematics. Nils F. Haavardsson, University of Oslo and DNB Skadeforsikring

Non-life insurance mathematics. Nils F. Haavardsson, University of Oslo and DNB Skadeforsikring No-life isurace mathematics Nils F. Haavardsso, Uiversity of Oslo ad DNB Skadeforsikrig Mai issues so far Why does isurace work? How is risk premium defied ad why is it importat? How ca claim frequecy

More information

facing today s challenges As an accountancy practice, managing relationships with our clients has to be at the heart of everything we do.

facing today s challenges As an accountancy practice, managing relationships with our clients has to be at the heart of everything we do. CCH CRM cliet relatios facig today s challeges As a accoutacy practice, maagig relatioships with our cliets has to be at the heart of everythig we do. That s why our CRM system ca t be a bolt-o extra it

More information

Lesson 17 Pearson s Correlation Coefficient

Lesson 17 Pearson s Correlation Coefficient Outlie Measures of Relatioships Pearso s Correlatio Coefficiet (r) -types of data -scatter plots -measure of directio -measure of stregth Computatio -covariatio of X ad Y -uique variatio i X ad Y -measurig

More information

Output Analysis (2, Chapters 10 &11 Law)

Output Analysis (2, Chapters 10 &11 Law) B. Maddah ENMG 6 Simulatio 05/0/07 Output Aalysis (, Chapters 10 &11 Law) Comparig alterative system cofiguratio Sice the output of a simulatio is radom, the comparig differet systems via simulatio should

More information

MTO-MTS Production Systems in Supply Chains

MTO-MTS Production Systems in Supply Chains NSF GRANT #0092854 NSF PROGRAM NAME: MES/OR MTO-MTS Productio Systems i Supply Chais Philip M. Kamisky Uiversity of Califoria, Berkeley Our Kaya Uiversity of Califoria, Berkeley Abstract: Icreasig cost

More information

Chapter XIV: Fundamentals of Probability and Statistics *

Chapter XIV: Fundamentals of Probability and Statistics * Objectives Chapter XIV: Fudametals o Probability ad Statistics * Preset udametal cocepts o probability ad statistics Review measures o cetral tedecy ad dispersio Aalyze methods ad applicatios o descriptive

More information

How to read A Mutual Fund shareholder report

How to read A Mutual Fund shareholder report Ivestor BulletI How to read A Mutual Fud shareholder report The SEC s Office of Ivestor Educatio ad Advocacy is issuig this Ivestor Bulleti to educate idividual ivestors about mutual fud shareholder reports.

More information

Your organization has a Class B IP address of 166.144.0.0 Before you implement subnetting, the Network ID and Host ID are divided as follows:

Your organization has a Class B IP address of 166.144.0.0 Before you implement subnetting, the Network ID and Host ID are divided as follows: Subettig Subettig is used to subdivide a sigle class of etwork i to multiple smaller etworks. Example: Your orgaizatio has a Class B IP address of 166.144.0.0 Before you implemet subettig, the Network

More information

Statistical inference: example 1. Inferential Statistics

Statistical inference: example 1. Inferential Statistics Statistical iferece: example 1 Iferetial Statistics POPULATION SAMPLE A clothig store chai regularly buys from a supplier large quatities of a certai piece of clothig. Each item ca be classified either

More information

summary of cover CONTRACT WORKS INSURANCE

summary of cover CONTRACT WORKS INSURANCE 1 SUMMARY OF COVER CONTRACT WORKS summary of cover CONTRACT WORKS INSURANCE This documet details the cover we ca provide for our commercial or church policyholders whe udertakig buildig or reovatio works.

More information

Properties of MLE: consistency, asymptotic normality. Fisher information.

Properties of MLE: consistency, asymptotic normality. Fisher information. Lecture 3 Properties of MLE: cosistecy, asymptotic ormality. Fisher iformatio. I this sectio we will try to uderstad why MLEs are good. Let us recall two facts from probability that we be used ofte throughout

More information

Systems Design Project: Indoor Location of Wireless Devices

Systems Design Project: Indoor Location of Wireless Devices Systems Desig Project: Idoor Locatio of Wireless Devices Prepared By: Bria Murphy Seior Systems Sciece ad Egieerig Washigto Uiversity i St. Louis Phoe: (805) 698-5295 Email: [email protected] Supervised

More information

.04. This means $1000 is multiplied by 1.02 five times, once for each of the remaining sixmonth

.04. This means $1000 is multiplied by 1.02 five times, once for each of the remaining sixmonth Questio 1: What is a ordiary auity? Let s look at a ordiary auity that is certai ad simple. By this, we mea a auity over a fixed term whose paymet period matches the iterest coversio period. Additioally,

More information

Plug-in martingales for testing exchangeability on-line

Plug-in martingales for testing exchangeability on-line Plug-i martigales for testig exchageability o-lie Valetia Fedorova, Alex Gammerma, Ilia Nouretdiov, ad Vladimir Vovk Computer Learig Research Cetre Royal Holloway, Uiversity of Lodo, UK {valetia,ilia,alex,vovk}@cs.rhul.ac.uk

More information

Soving Recurrence Relations

Soving Recurrence Relations Sovig Recurrece Relatios Part 1. Homogeeous liear 2d degree relatios with costat coefficiets. Cosider the recurrece relatio ( ) T () + at ( 1) + bt ( 2) = 0 This is called a homogeeous liear 2d degree

More information

Study on the application of the software phase-locked loop in tracking and filtering of pulse signal

Study on the application of the software phase-locked loop in tracking and filtering of pulse signal Advaced Sciece ad Techology Letters, pp.31-35 http://dx.doi.org/10.14257/astl.2014.78.06 Study o the applicatio of the software phase-locked loop i trackig ad filterig of pulse sigal Sog Wei Xia 1 (College

More information

Clustering Algorithm Analysis of Web Users with Dissimilarity and SOM Neural Networks

Clustering Algorithm Analysis of Web Users with Dissimilarity and SOM Neural Networks JONAL OF SOFTWARE, VOL. 7, NO., NOVEMBER 533 Clusterig Algorithm Aalysis of Web Users with Dissimilarity ad SOM Neal Networks Xiao Qiag School of Ecoomics ad maagemet, Lazhou Jiaotog Uiversity, Lazhou;

More information

Chapter 6: Variance, the law of large numbers and the Monte-Carlo method

Chapter 6: Variance, the law of large numbers and the Monte-Carlo method Chapter 6: Variace, the law of large umbers ad the Mote-Carlo method Expected value, variace, ad Chebyshev iequality. If X is a radom variable recall that the expected value of X, E[X] is the average value

More information

DAME - Microsoft Excel add-in for solving multicriteria decision problems with scenarios Radomir Perzina 1, Jaroslav Ramik 2

DAME - Microsoft Excel add-in for solving multicriteria decision problems with scenarios Radomir Perzina 1, Jaroslav Ramik 2 Itroductio DAME - Microsoft Excel add-i for solvig multicriteria decisio problems with scearios Radomir Perzia, Jaroslav Ramik 2 Abstract. The mai goal of every ecoomic aget is to make a good decisio,

More information

ANALYTICS. Insights that drive your business

ANALYTICS. Insights that drive your business ANALYTICS Isights that drive your busiess Eterprises are trasformig their busiesses by supplemetig their databases with real ad up-to-date customer data. Aalytics, as a catalyst, refies raw data ad aligs

More information

1 Correlation and Regression Analysis

1 Correlation and Regression Analysis 1 Correlatio ad Regressio Aalysis I this sectio we will be ivestigatig the relatioship betwee two cotiuous variable, such as height ad weight, the cocetratio of a ijected drug ad heart rate, or the cosumptio

More information

The analysis of the Cournot oligopoly model considering the subjective motive in the strategy selection

The analysis of the Cournot oligopoly model considering the subjective motive in the strategy selection The aalysis of the Courot oligopoly model cosiderig the subjective motive i the strategy selectio Shigehito Furuyama Teruhisa Nakai Departmet of Systems Maagemet Egieerig Faculty of Egieerig Kasai Uiversity

More information

A Mathematical Perspective on Gambling

A Mathematical Perspective on Gambling A Mathematical Perspective o Gamblig Molly Maxwell Abstract. This paper presets some basic topics i probability ad statistics, icludig sample spaces, probabilistic evets, expectatios, the biomial ad ormal

More information

Incremental calculation of weighted mean and variance

Incremental calculation of weighted mean and variance Icremetal calculatio of weighted mea ad variace Toy Fich [email protected] [email protected] Uiversity of Cambridge Computig Service February 009 Abstract I these otes I eplai how to derive formulae for umerically

More information

ADAPTIVE NETWORKS SAFETY CONTROL ON FUZZY LOGIC

ADAPTIVE NETWORKS SAFETY CONTROL ON FUZZY LOGIC 8 th Iteratioal Coferece o DEVELOPMENT AND APPLICATION SYSTEMS S u c e a v a, R o m a i a, M a y 25 27, 2 6 ADAPTIVE NETWORKS SAFETY CONTROL ON FUZZY LOGIC Vadim MUKHIN 1, Elea PAVLENKO 2 Natioal Techical

More information

5 Boolean Decision Trees (February 11)

5 Boolean Decision Trees (February 11) 5 Boolea Decisio Trees (February 11) 5.1 Graph Coectivity Suppose we are give a udirected graph G, represeted as a boolea adjacecy matrix = (a ij ), where a ij = 1 if ad oly if vertices i ad j are coected

More information

JJMIE Jordan Journal of Mechanical and Industrial Engineering

JJMIE Jordan Journal of Mechanical and Industrial Engineering JJMIE Jorda Joural of Mechaical ad Idustrial Egieerig Volume 5, Number 5, Oct. 2011 ISSN 1995-6665 Pages 439-446 Modelig Stock Market Exchage Prices Usig Artificial Neural Network: A Study of Amma Stock

More information

5.4 Amortization. Question 1: How do you find the present value of an annuity? Question 2: How is a loan amortized?

5.4 Amortization. Question 1: How do you find the present value of an annuity? Question 2: How is a loan amortized? 5.4 Amortizatio Questio 1: How do you fid the preset value of a auity? Questio 2: How is a loa amortized? Questio 3: How do you make a amortizatio table? Oe of the most commo fiacial istrumets a perso

More information

CHAPTER 3 DIGITAL CODING OF SIGNALS

CHAPTER 3 DIGITAL CODING OF SIGNALS CHAPTER 3 DIGITAL CODING OF SIGNALS Computers are ofte used to automate the recordig of measuremets. The trasducers ad sigal coditioig circuits produce a voltage sigal that is proportioal to a quatity

More information

Research Article Sign Data Derivative Recovery

Research Article Sign Data Derivative Recovery Iteratioal Scholarly Research Network ISRN Applied Mathematics Volume 0, Article ID 63070, 7 pages doi:0.540/0/63070 Research Article Sig Data Derivative Recovery L. M. Housto, G. A. Glass, ad A. D. Dymikov

More information

Spam Detection. A Bayesian approach to filtering spam

Spam Detection. A Bayesian approach to filtering spam Spam Detectio A Bayesia approach to filterig spam Kual Mehrotra Shailedra Watave Abstract The ever icreasig meace of spam is brigig dow productivity. More tha 70% of the email messages are spam, ad it

More information

SEQUENCES AND SERIES

SEQUENCES AND SERIES Chapter 9 SEQUENCES AND SERIES Natural umbers are the product of huma spirit. DEDEKIND 9.1 Itroductio I mathematics, the word, sequece is used i much the same way as it is i ordiary Eglish. Whe we say

More information

Chapter 5 Unit 1. IET 350 Engineering Economics. Learning Objectives Chapter 5. Learning Objectives Unit 1. Annual Amount and Gradient Functions

Chapter 5 Unit 1. IET 350 Engineering Economics. Learning Objectives Chapter 5. Learning Objectives Unit 1. Annual Amount and Gradient Functions Chapter 5 Uit Aual Amout ad Gradiet Fuctios IET 350 Egieerig Ecoomics Learig Objectives Chapter 5 Upo completio of this chapter you should uderstad: Calculatig future values from aual amouts. Calculatig

More information

Research Method (I) --Knowledge on Sampling (Simple Random Sampling)

Research Method (I) --Knowledge on Sampling (Simple Random Sampling) Research Method (I) --Kowledge o Samplig (Simple Radom Samplig) 1. Itroductio to samplig 1.1 Defiitio of samplig Samplig ca be defied as selectig part of the elemets i a populatio. It results i the fact

More information

CS103A Handout 23 Winter 2002 February 22, 2002 Solving Recurrence Relations

CS103A Handout 23 Winter 2002 February 22, 2002 Solving Recurrence Relations CS3A Hadout 3 Witer 00 February, 00 Solvig Recurrece Relatios Itroductio A wide variety of recurrece problems occur i models. Some of these recurrece relatios ca be solved usig iteratio or some other ad

More information

Data Analysis and Statistical Behaviors of Stock Market Fluctuations

Data Analysis and Statistical Behaviors of Stock Market Fluctuations 44 JOURNAL OF COMPUTERS, VOL. 3, NO. 0, OCTOBER 2008 Data Aalysis ad Statistical Behaviors of Stock Market Fluctuatios Ju Wag Departmet of Mathematics, Beijig Jiaotog Uiversity, Beijig 00044, Chia Email:

More information

Chair for Network Architectures and Services Institute of Informatics TU München Prof. Carle. Network Security. Chapter 2 Basics

Chair for Network Architectures and Services Institute of Informatics TU München Prof. Carle. Network Security. Chapter 2 Basics Chair for Network Architectures ad Services Istitute of Iformatics TU Müche Prof. Carle Network Security Chapter 2 Basics 2.4 Radom Number Geeratio for Cryptographic Protocols Motivatio It is crucial to

More information

University of California, Los Angeles Department of Statistics. Distributions related to the normal distribution

University of California, Los Angeles Department of Statistics. Distributions related to the normal distribution Uiversity of Califoria, Los Ageles Departmet of Statistics Statistics 100B Istructor: Nicolas Christou Three importat distributios: Distributios related to the ormal distributio Chi-square (χ ) distributio.

More information

Project Deliverables. CS 361, Lecture 28. Outline. Project Deliverables. Administrative. Project Comments

Project Deliverables. CS 361, Lecture 28. Outline. Project Deliverables. Administrative. Project Comments Project Deliverables CS 361, Lecture 28 Jared Saia Uiversity of New Mexico Each Group should tur i oe group project cosistig of: About 6-12 pages of text (ca be loger with appedix) 6-12 figures (please

More information

Institute of Actuaries of India Subject CT1 Financial Mathematics

Institute of Actuaries of India Subject CT1 Financial Mathematics Istitute of Actuaries of Idia Subject CT1 Fiacial Mathematics For 2014 Examiatios Subject CT1 Fiacial Mathematics Core Techical Aim The aim of the Fiacial Mathematics subject is to provide a groudig i

More information

Entropy of bi-capacities

Entropy of bi-capacities Etropy of bi-capacities Iva Kojadiovic LINA CNRS FRE 2729 Site école polytechique de l uiv. de Nates Rue Christia Pauc 44306 Nates, Frace [email protected] Jea-Luc Marichal Applied Mathematics

More information

AN INTELLIGENT MODEL FOR SALES AND INVENTORY MANAGEMENT

AN INTELLIGENT MODEL FOR SALES AND INVENTORY MANAGEMENT AN INTELLIGENT MODEL FOR SALES AND INVENTORY MANAGEMENT SYLVANUS O. ANIGBOGU, Ph.D. Associate Professor of Computer Sciece Departmet of Computer Sciece, Namdi Azikiwe Uiversity, Awka, Aambra State, 420001,

More information

Forecasting. Forecasting Application. Practical Forecasting. Chapter 7 OVERVIEW KEY CONCEPTS. Chapter 7. Chapter 7

Forecasting. Forecasting Application. Practical Forecasting. Chapter 7 OVERVIEW KEY CONCEPTS. Chapter 7. Chapter 7 Forecastig Chapter 7 Chapter 7 OVERVIEW Forecastig Applicatios Qualitative Aalysis Tred Aalysis ad Projectio Busiess Cycle Expoetial Smoothig Ecoometric Forecastig Judgig Forecast Reliability Choosig the

More information

FM4 CREDIT AND BORROWING

FM4 CREDIT AND BORROWING FM4 CREDIT AND BORROWING Whe you purchase big ticket items such as cars, boats, televisios ad the like, retailers ad fiacial istitutios have various terms ad coditios that are implemeted for the cosumer

More information

A Fuzzy Model of Software Project Effort Estimation

A Fuzzy Model of Software Project Effort Estimation TJFS: Turkish Joural of Fuzzy Systems (eissn: 309 90) A Official Joural of Turkish Fuzzy Systems Associatio Vol.4, No.2, pp. 68-76, 203 A Fuzzy Model of Software Project Effort Estimatio Oumout Chouseioglou

More information

Baan Service Master Data Management

Baan Service Master Data Management Baa Service Master Data Maagemet Module Procedure UP069A US Documetiformatio Documet Documet code : UP069A US Documet group : User Documetatio Documet title : Master Data Maagemet Applicatio/Package :

More information

5: Introduction to Estimation

5: Introduction to Estimation 5: Itroductio to Estimatio Cotets Acroyms ad symbols... 1 Statistical iferece... Estimatig µ with cofidece... 3 Samplig distributio of the mea... 3 Cofidece Iterval for μ whe σ is kow before had... 4 Sample

More information

BENEFIT-COST ANALYSIS Financial and Economic Appraisal using Spreadsheets

BENEFIT-COST ANALYSIS Financial and Economic Appraisal using Spreadsheets BENEIT-CST ANALYSIS iacial ad Ecoomic Appraisal usig Spreadsheets Ch. 2: Ivestmet Appraisal - Priciples Harry Campbell & Richard Brow School of Ecoomics The Uiversity of Queeslad Review of basic cocepts

More information

Effective Hybrid Intrusion Detection System: A Layered Approach

Effective Hybrid Intrusion Detection System: A Layered Approach I. J. Computer Network ad Iformatio Security, 2015, 3, 35-41 Published Olie February 2015 i MECS (http://www.mecs-press.org/) DOI: 10.5815/ijcis.2015.03.05 Effective Hybrid Itrusio Detectio System: A Layered

More information