Assessing the Discriminatory Power of Credit Scores


 Anne Wilcox
 2 years ago
 Views:
Transcription
1 Aeing the Dicriminatory Power of Credit Score Holger Kraft 1, Gerald Kroiandt 1, Marlene Müller 1,2 1 Fraunhofer Intitut für Techno und Wirtchaftmathematik (ITWM) GottliebDaimlerStr. 49, Kaierlautern, Germany 2 HumboldtUniverität zu Berlin, Intitut für Statitik & Ökonometrie Spandauer Str. 1, Berlin, Germany Augut 15, 2002 We dicu how to ae the performance for credit core under the aumption that for credit data only a part of the default and nondefault i oberved. The paper introduce a criterion that i baed on the difference of the core ditribution under default and nondefault. We how how to etimate bound for thi criterion, the Gini coefficient and the accuracy ratio. Keyword: credit rating, credit core, dicriminatory power, ample election, Gini coefficient, accuracy ratio JEL Claification: G21
2 1 Introduction A bank which want to decide whether a credit applicant will get a credit or not ha to ae if the applicant will be able to redeem the credit. Among other criteria, the bank require an etimate of the probability that the applicant will default prior to the maturity of the credit. At thi tep, a rating of the applicant i a valuable deciion upport. The idea of a rating ytem i to identify criteria which eparate the good from the bad creditor, a for example liquidity ratio or ratio concerning the capital tructure of a firm. In a more formal ene a rating correpond to a gue of the default probability of the credit. Obviouly, the quetion arie how a bank can identify a ufficient number of elective criteria and, epecially, what electivity and dicriminatory power mean in thi context. In the following ection we try to make a firt tep to a rigorou treatment of thi ubject which i rarely addreed in literature. Apart from the theoretical attractivene thi iue i of highly practical importance. Thi i due to the fact that the Bael Committee on Banking Superviion i working on a New Capital Accord (Bael II) where default rik adjuted capital requirement hall be etablihed. In thi context rating and the deign of rating play an important role. Clearly, the committee want the bank to identify factor which have an ability to differentiate rik [and] have predictive and dicriminatory power (Banking Committee on Banking Superviion, 2001, p. 50). Unfortunately, they do not give any formal definition of predictive or dicriminatory power. The paper i organized a follow: In Section 2 we dicu how to meaure dicriminatory power of a core (a numerical value that reflect the rating of a credit applicant). We introduce a criterion that i baed on the difference between the ditribution of the core conditioned on default or nondefault and i imple to compute. Section 3 dicue the conequence of the typical cenoring in credit data due to the fact that not all credit applicant are accepted. Thi implie that we do have default or nondefault information only for a retricted et of applicant. To keep thing imple we firt dicu dicriminatory power uing a parametric etting. In Section 4 we conider the nonparametric cae and how how to find lower and upper bound for the propoed criterion. Finally, Section 5 extend our approach to lower and upper bound for the Gini coefficient and the accuracy ratio (AR). 2 Dicriminatory Power of a Score Let u tart with the following claification problem: Conider random variable X 1,..., X p and a group indicator Y {0, 1}. A core S (ued to rate applicant 1
3 for a loan) i an aggregation of the variable X 1,..., X p into a ingle number. Hence, we can conider any real valued function S(X 1,..., X p ) to be a core. For the ake of brevity we will ue S to denote the random variable S(X 1,..., X p ). In the following we will only tudy the relation between S and Y. There exit a variety of criteria to ae the quality of a core. A reaonable core function for credit rating hould aign higher core value to credit applicant who have higher probabilitie of default (PD). Therefore the capability to eparate the two group of obervation correponding to Y = 1 (default) and Y = 0 (nondefault) i a baic feature of a credit core function. A meaure for the dicriminatory power can conequently be ued a a performance meaure for a credit core. A traightforward approach to ae dicriminatory power i the comparion of the conditional ditribution of S given default or nondefault. We will firt focu on the difference of thee two conditional ditribution. The methodology that i derived here can however be ued for other meaure of performance a well. Overlapping of Normal Denitie f0, f Figure 1: Overlapping area U for two normal denitie In the cae of a normal ditribution the conditional denitie of S given Y = j, j = 0, 1 are eay to viualize and to compute. Denote f 0, f 1 the probability denitie of S Y = 0 and S Y = 1, further F 0, F 1 their cumulative ditribution function. Conider firt the pecial cae that f 0 and f 1 have exactly one point of interection, cf. Figure 1. (A condition for thi property will be given in a moment.) Let be the horizontal coordinate of thi interection. Auming a normal ditribution mean that both denitie f 0 and f 1 are determined by their expectation µ 0, µ 1 and tandard deviation σ 0, σ 1. We uppoe (w.l.o.g.) in the 2
4 following that µ 1 > µ 0. Then the region of overlapping U for the two denitie can be calculated a U = F 1 () + 1 F 0 (). (1) If in the normal cae both tandard deviation are identical (σ 0 = σ 1 ), there i exactly one point of interection which i given by = µ 0 + µ 1 2 For different tandard deviation (σ 0 σ 1 ), there may be one or two point of interection (a in quadratic dicriminance analyi) and the horizontal coordinate are determined by f 0 () = f 1 () i.e. a olution of the quadratic equation 2 (σ 2 1 σ 2 0) + 2(µ 1 σ 2 0 µ 0 σ 2 1) + µ 2 0σ 2 1 µ 2 1σ σ 2 1 log(σ 0 ) σ 2 0 log(σ 1 ) = 0. The definition of U can be eaily generalized to the nonparametric cae when no ditributional aumption for S i made: U = min{f 0 (), f 1 ()} d. (2) Thi definition allow any number of interection point of f 0 and f 1. Alternatively, auming a monotone relationhip between the core S and the default probability, a variant of the definition can be given by. U = min {F 1 () + 1 F 0 ()}. (3) Thi definition i baed on the idea that only one optimal interection point hould exit in thi cae. A for the normal cae, we aume that f 1 i right of f 0. An analogou definition could be formulated for a monotone decreaing relationhip. It i obviou that for denitie f 0, f 1 on completely different upport (perfect eparation) the region of overlapping U i zero. If both denitie are identical (no eparation) then U equal one. In all other cae U will take on value between 0 and 1. An indicator of dicriminatory power i now given by T = 1 U. (4) A U, the dicriminatory power indicator T take on value in the interval [0, 1]. In practice we have obervation S (i) for the core and Y (i) for the group (default and nondefault in credit coring). Under the aumption of a normal ditribution U (and hence T ) can be computed uing the empirical moment µ 0, µ 1, σ 0, and σ 1. Under more general aumption on the ditribution, U and T can be computed for example by nonparametric etimate of the denitie (hitogram, kernel denity etimator). In the monotone cae it i ufficient to have nonparametric 3
5 etimate of the cumulative ditribution function F 0, F 1. Thoe etimate can be eaily found by the empirical ditribution function i F j () = I(S(i), Y (i) = j) i I(Y, j = 0, 1. (5) (i) = j) We remark that the ditribution of T i related to the KolmogorovSmirnov tet tatitic, which check the hypothei F 0 = F 1. Hence, thi tet can be applied to find out if the core influence the PD at all. 3 Credit Scoring & Unobervable Area Conider now a ample of n credit applicant, for which a et of variable i given (e.g. age of the applicant, amount and duration of the loan, income etc.). A above we aume that a real valued core S i calculated from thee variable at time t = 0 and the default (Y = 1) or nondefault (Y = 1) i oberved at time t = 1. The particular problem of credit coring i that we oberve default and nondefault only for a ubample of applicant. In more detail, thi mean that the bank compute core for N applicant but only n of them (n < N) are accepted for a loan. Hence, default and nondefault obervation are preelected by a condition, which we denote by A. Thi type of ample preelection i uually decribed a cenoring or ample election. The problem of ample election ha been mainly tudied in the (econometric) literature with a focu on the etimating regreion coefficient and PD. Greene (1998) for example ue a Heckman twotep procedure (ee Heckman, 1979) for etimating probit and count data model for credit data. Gourieroux and Jaiak (2001, Ch. 7) conider maximumlikelihood probit and a Bayeian approach wherea a rather general approach i introduced by Horowitz and Manki (1998). We conider the problem of etimating dicriminatory power in the cenored cae under very general ditributional aumption. Thi will lead to upper and lower bound for the performance criteria rather than claical point etimate. To illutrate the effect of cenoring (or ample election) for etimating U and T aume again that both denitie f 0, f 1 have exactly one interection point. Aume alo that the cenoring condition i A = {S c}, (6) where c i a threhold uch that no credit applicant are accepted for a loan when their core S i larger than c. Figure 2 how thi modified ituation in comparion to Figure 1. The ditribution right to the black line (here c = 2) 4
6 Overlapping for Credit f0, f Figure 2: Truncated overlapping area for credit data cannot be oberved but need in fact to be conidered for a correct aement of the performance of the core. Denote S = (S A) und Ỹ = (Y A) the oberved part of the core and the group variable. Hence, we have only obervation for S j = ( S Ỹ = j), j = 0, 1 while we are intereted in S j = (S Y = j). Under the aumption (6), the relation between S j and S j i given by P ( S j ) = P ( S, Ỹ = j) P (Ỹ = j) = P (S, Y = j) = P (S c, Y = j) P (S, Y = j A) P (Y = j A) if c. Since P (S j ) = P (S Y = j) = P (S, Y = j)/p (Y = j) it follow that P ( S j ) = P (S j ) P (Y = j) P (S c, Y = j) = P (S j ) P (S j c), which how F j () = F j() F j (c). (7) Here F j denote the cumulative ditribution function of S j. Under the aumption that S j ha a continuou ditribution, (7) reult in an equivalent recaling of the denitie by F j (c). Thee denitie and their region of overlapping Ũ for 5
7 Overlapping of Truncated Denitie f0, f Figure 3: Oberved overlapping area Ũ the normal cae are hown in Figure 3. Note the difference to Figure 2 on the vertical cale, ince f j () f j (). We will now examine the difference between Ũ and U, the region of overlapping for the cenored (oberved) and the noncenored (partially unoberved) ample. In the following we will conider the monotone verion of the overlapping region: U = min {F 1 () + 1 F 0 ()}. Computing the overlapping region Ũ in the ame way and uing (7), would hence give { Ũ = min F1 () + 1 F } { F1 () 0 () = min F 1 (c) + 1 F } 0(). (8) F 0 (c) Thi how that the naive calculation of the overlapping from incompletely oberved data i uually different (biaed) from the objective overlapping region U. The difference in Ũ and U (or T and T ) can be coniderably important a a mall Monte Carlo imulation how. We have imulated 100 data et, each of N = 500 obervation. The core S (i) are generated only once and come from a normal ditribution with expectation 3 and variance The imulated PD are obtained from a Logit model, i.e. p() = exp( ) and the Y (i) are Bernoulli random variable with probability parameter p(s (i) ). The threhold i choen a c = 0.5, thi give here n =
8 Dicriminatory Power T T Figure 4: Boxplot for T (upper) and T (lower) Figure 4 how boxplot for the realized ditribution of the etimated T = 1 Ũ (lower boxplot) and T = 1 U (upper boxplot). The graphic how that in our imulated example T i typically maller than T. In particular, both mean and median of the 100 etimated T are a large a the upper quartile of the etimated T. A cloer inpection of the data how that in 95 cae T < T and in 5 cae T > T. So uing T at the place of T can milead in aeing the performance of the core in both direction (over and underetimation). Under the aumption that the type of the ditribution of S j are known a correction for Ũ can be eaily calculated. Let u outline thi for the example of normal ditribution: Here the moment of S j, j = 0, 1, can be calculated (Greene, 1993, Theorem 22.2) by E(S j S j c) = µ j + σ j λ(α j ), (9) V ar(s j S j c) = σ 2 j [1 λ(α j ){λ(α j ) α j }], (10) with µ j and σ j denoting the moment of the unconditional ditribution, α j = c µ j and λ(α) = φ(α) σ j Φ(α) denoting the invere Mill ratio. The expectation µ j = E(S j ) and variance σ 2 j = V ar(s j ) can hence be calculated from the credit data uing the empirical moment of S j and by olving the ytem of equation (9) (10). Etimate of f j and F j are then obtained by plugging µ j, σ j into the denity and cumulative ditribution function of the normal ditribution. 7
9 We remark that thi idea can be generalized to any monotone tranformation of the normal ditribution. For example, many variable ued for credit coring have a kewed ditribution. Thi typically tranfer to core which are linearly weighted um of thee variable. The lognormal ditribution, which can model uch a kewed core, ha a direct relation to the normal ditribution: Aume S j i lognormal with parameter µ j, σ j, then for the logcore Since the logarithm i monotone log(s j ) N(µ j, σ 2 j ). (11) F j () = P (S j ) = P (log(s j ) log()). (12) The computation for lognormal core i therefore completely determined by the normal cae. An even wider cla of ditribution i covered by uing any monotone ditribution a e.g a Box Cox tranformation. A correction of Ũ i alo poible if the cenoring i determined by another core function S, i.e. A = {S c}. (13) Thi i a more realitic aumption ince in practice S can be conidered a the core function from a previou credit rating ytem. If the credit rating ytem i redeigned, the performance of the new core function S need to be aeed. Under the very retrictive aumption of a joint normal ditribution of S j and S j with moment µ j, σ j, µ j, σ j and correlation ρ j it i known that E(S j S j < c) = µ j + ρ j σ j λ(α j ), (14) V ar(s j S j < c) = (σ j ) 2 [1 ρ 2 jλ(α j ){λ(α j ) α j }], (15) ee e.g. Greene (1993, Theorem 22.4). Here α j = c µ j σ j and λ denote the invere Mill ratio a before. In addition we have ( x µ F j j (x) = Φ 2, c µ ) { ( )} 1 j c µj, ρ σj j Φ. (16) σ j σ j The moment of S j could be etimated from equation analogou to (9) (10). With thee etimate for µ j, σ j, the ytem of equation (14) (16) could be ued to find etimate of the unconditional moment µ j, σ j and ρ j. Thi technique could again be generalized to monotone tranformation a the logarithm or the BoxCox tranformation. However, apart from the retrictive ditributional aumption thi approach require that obervation for both core function S and S given A = {S c} are available. 8
10 4 Inequalitie for the Nonparametric Cae A we have een in Section 3, the computation of U from S j require pecific aumption on the ditribution of S j and their relation to the cenoring condition A. In the cae of completely unknown ditribution there i no poibility to etimate thee ditribution beyond A. Thi i a relevant problem when a bank redeign it credit rating ytem, ince data on rejected applicant are normally not available. A poible remedy to thi problem i the calculation of upper and lower bound for the dicriminatory power T. The general aumption throughout thi ection i that we know the percentage of rejected loan, i.e. the full number of credit applicant. Denote thi number of all credit (accepted or rejected) by N. Under the aumption that the percentage of both rejected applicant and default are mall, relatively narrow bound can be found for T. We want to tre that N typically doe not contain applicant who are rejected without being rated. Recall that the computation of U require the cumulative ditribution function F j () of S j = (S Y = j). However, we only oberve F j (), the cumulative ditribution function of Sj = (S Y = j, A). Therefore we conider now the relation between F j () and F j () in thi general cae. We have hence F j () = P (S Y = j) = P (S, A Y = j) + P (S, A Y = j) = P (S A, Y = j)p (A Y = j) + P (S, A Y = j), F j () = F j () P (A Y = j) + P (S, A Y = j) (17) where A denote the complement of A. We find an upper bound for F j () by uing that {S } A A in the econd term of (17), i.e. F j () F j ()P (A Y = j) + P (A Y = j) = 1 P (A Y = j){1 F j ()}. (18) A lower bound for F j () i given by omitting the econd term of (17) completely, uch that F j () F j ()P (A Y = j). (19) Both inequalitie (18) and (19) involve P (A Y = j) which can not be directly etimated, ince the ditribution of Y in A i unknown. However, we can decribe the range of P (A Y = j). We tart with a firt approximation. Let u introduce the notation α j = P (A Y = j), 9
11 uch that (18) and (19) can be written a α j Fj () F j () 1 α j + α j Fj (). (20) From P (Y = j) = P (A, Y = j) + P (A, Y = j) we conclude that P (A, Y = j) P (Y = j) P (A, Y = j) + P (A). (21) Thu from α j = P (A Y = j) = P (Y = j A)P (A) P (Y = j) = P (Ỹ = j)p (A) P (Y = j) it follow that α j α j 1, where α j = P (Ỹ = j)p (A). (22) P (Ỹ = j)p (A) + P (A) Equation (20) together with (22) yield α 1 F 1 () + α 0{1 F 0 ()} F 1 () + 1 F 0 () 2 α 1 {1 F 1 ()} α 0 F 0 (). (23) A a conequence we obtain upper and lower bound for the dicriminatory power indicator T = 1 U = 1 min{f 1 () + 1 F 0 ()} which are given by [ 1 min 2 α1 {1 F 1 ()} α F ] 0 0 () [ T 1 min α F 1 1 () + α 0{1 F ] 0 ()}. (24) We want to tre that in the pecial cae where all credit applicant are accepted we have A = Ω and α 0 = α 1 = 1. A a conequence (24) reduce to T = 1 min {F 1 () + 1 F 0 ()}, which i exactly the definition introduced in Section 2. More ophiticated bound for F 1 () + 1 F 0 () can be obtained a follow. We ue the additional abbreviation β j = P (A, Y = j), p j = P (Y = j), uch that α j = β j p j. 10
12 Conider the lower bound firt. From (18) and (19) we have F 1 () + 1 F 0 () α 1 F1 () + α 0 {1 F 0 ()} = β 1 1 p 0 F1 () + β 0 p 0 {1 F 0 ()} (25) In the lat term every probability can be etimated from the oberved data except for p 0. Hence, for given the lat term ha to be minimized with repect to p 0. For thi minimization one ha to conider the three cae β 1 F1 () = β 0 {1 F 0 ()}, β 1 F1 () > β 0 {1 F 0 ()}, and β 1 F1 () < β 0 {1 F 0 ()}, which all lead to the ame reult: β 0 if γ < β 0, p 0 = β 0 + P (A) if γ > β 0 + P (A), (26) γ, otherwie, and γ = β 0 {1 F 0 ()} β 0 {1 F 0 ()} + β 1 F1 (). (27) The upper and lower threhold in (26) are conequence of the bound in (21). To derive an upper bound of F 1 () + 1 F 0 () we conclude from (18) and (19) F 1 () + 1 F 0 () 2 α 1 {1 F 1 ()} α 0 F0 () = 2 β 1 1 p 0 {1 F 1 ()} β 0 p 0 F0 (). (28) Maximization of the lat term with repect to p 0 lead to a imilar reult a before: β 0 if δ < β 0, p 0 = β 0 + P (A) if δ > β 0 + P (A), (29) δ, otherwie, and δ = Combining the reult we obtain β 0 F0 () + β 0 F0 () β 1 {1 F 1 ()}. (30) β 1 1 p 0 F 1 () + β 0 {1 p F 0 ()} 0 F 1 () + 1 F 0 () 2 β 1 {1 1 p F 1 ()} β 0 0 p 0 F 0 () (31) 11
13 and a in (24) 1 min [ 2 β 1 1 p 0 {1 F 1 ()} β 0 T 1 min [ β1 1 p 0 p 0 ] F 0 () F 1 () + β ] 0 {1 p F 0 ()} 0. (32) All quantitie in the inequalitie (24) and (32) can be etimated. For the oberved core under default and nondefault we have their empirical ditribution function a in (5). To etimate αj, β j, p 0 and p 0 we conider the probabilitie of the event {Ỹ = j}, A and A which can be etimated by their oberved relative frequencie P (Ỹ = j) = n j n, P (A) = n N, P (A) = N n N. (33) Here n 0 denote the number of oberved nondefault (Y (i) = 0) and n 1 the number of oberved default (Y (i) = 1). A before we ue n for the ample ize of the oberved credit (i.e. n = n 0 + n 1 ), and N for the number of all the credit. Thi give the etimate α j = n j n j + N n, βj = n j N. (34) Etimate for p 0 and p 0 can be found by plugging β j, P (A) and F j () into (27) and (30). A before we ue a Monte Carlo imulation to illutrate the effect of thee etimated bound. The contruction of the imulated data et i a above with one modification: We ue core S (i) with a variance of Thi yield a value of n = 491 for the ample ize of the obervable core. We find T > T in 91 cae and T < T in 9 cae. Figure 5 how etimate for T (thick olid line), T (thin olid line) and the etimated upper and lower bound according to (32) for all 100 imulated data et (orted by the etimated T ). The bound according to (24) are wider but of very imilar ize, uch that we omit them here. Recall that in practice the etimation of T could not have been carried out, thi i only poible here for imulated data. The imulation how in particular, that in the mentioned 9 cae T a a replacement of T would have led to a too large value for the dicriminatory power of the core. The upper and lower bound however (which cover both T and T ) indicate a correctly pecified range for T. We remark that the lower bound in Figure 5 eem to be quite far away from both T and T. Thi i a conequence of the fact that thi bound doe not require 12
14 Dicriminatory Power T and Bound T Figure 5: Etimated T (thick olid), T (olid) and bound (dahed) any information about the tructure of the cenoring condition A. Thi bound could be coniderably improved if additional information a e.g. A = {S c} i ued. 5 Gini coefficient and Accuracy Ratio An alternative and frequently ued meaure for the performance of a core i the accuracy ratio AR which i baed on the Lorenz curve and it Gini coefficient. In the cae of cenored data, the accuracy ratio computed from the oberved part of the data i biaed a well. A for T we can etimate bound for the AR if the ditribution of the core i unknown. Let u firt introduce the relevant term. The Lorenz curve viualize core by mean of comparing the ditribution of S 1 and S. Figure 6 how the principle of the Lorenz curve. On the horizontal and vertical cale, the percentage of applicant are orted from high to low core. The Lorenz curve i alo known a election curve. Variant of the Lorenz curve are the receiver operating characteritic (ROC) curve (Hand and Henley, 1997) and the performance curve (Gourieroux and Jaiak, 2001, Ch. 4). 13
15 To operate with cumulative ditribution function denote the negative core by V = S. The Lorenz curve of S i then defined by the coordinate {L 1 (v), L 2 (v)} = {P (V < v), P (V < v Y = 1)}, v (, ). Since P (V < v) = 1 F ( v), thi i equivalent to {L 1 (), L 2 ()} = {1 F (), 1 F 1 ()}, (, ). A etimate of the Lorenz curve can be computed by mean of the empirical cumulative ditribution function F and F 1. 1 F( Y=1) 100% optimal curve Lorenz curve Percentage of Default Percentage of Applicant (ordered from bad to good) 100% 1 F() Figure 6: Lorenz curve for Credit Scoring Recall that core hould aign higher core value to credit applicant with higher PD. Such a credit core i obviouly good if all vertical coordinate of the Lorenz curve are large. The bet (optimal) Lorenz curve correpond to a core that exactly eparate default and nondefault. Thi optimal curve reache the vertical 100% at a horizontal percentage of P (Y = 1), the probability of default. A random aignment of credit applicant to core value correpond to a Lorenz curve identical to the diagonal. Lorenz curve can alo be ued to compare different core function. Better core are more cloe to the optimal Lorenz curve. A quantitative meaure for 14
16 the performance of a core i baed on the area between the Lorenz curve and the diagonal. The Gini coefficient G denote twice thi area, i.e. G = {1 F 1 (H(z))} dz 1 = F 1 (H(z)) dz (35) where H i the invere of 1 F. In practice the latter integral i etimated by numeric integration of F 1 over the range of F. To compare different core, their accuracy ratio AR are defined by relating the Gini coefficient of each core to the Gini coefficient of the optimal Lorenz curve. The accuracy ratio i hence defined a AR = G G opt = G P (Y = 0). In the cenored cae we would compute G and ÃR intead of G and AR. Note that a for T and T the Gini coefficient and accuracy ratio are biaed. We will now how how to obtain upper and lower bound for G and AR in thi cenored cae, i.e. if obervation for A are not available. A before let S 1, S denote the oberved core and F 1, F their cumulative ditribution function. We ue (18) and (19) for F 1 and derive imilar inequalitie for F uing the ame idea we ued for F j. Conider firt F () = P (S, A) P (A) P (S ) P (A) = F () P (A). Alo we have Together thi give F () = F () P (A) + P ( S A) P (A) = F () P (A) + P ({ S } A) F () P (A) + P (A) = 1 P (A) {1 F ()}. F () P (A) F () 1 P (A) {1 F ()}. (36) Uing thi together with (20) for F 1, we find lower bound [ { L 1(), L 2()} = P (A) {1 F } { (), α1 1 F }] 1 () and upper bound { L 1(), L 2()} = { 1 P (A) F } (), 1 α 1 F 1 () 15
17 Accuracy Ratio AR and Bound T Figure 7: Etimated AR (thick olid), ÃR (olid) and bound (dahed) for the Lorenz curve. In practice we ue the etimate α 1, Section 4 and i F () = I(S(i) ). n F 1 (), P (A) from The upper and lower bound for the Lorenz curve obviouly lead to upper and lower bound Ĝ and Ĝ for the Gini coefficient ince integration preerve monotonicity. For the accuracy ratio AR we need the additional etimate for P (Y = 0). A we dicued before, a point etimate of P (Y = 0) i not available. However (21) motivate upper and lower etimate n 0 N P (Y = 0) N n 1 N. Hence, bound for the etimated accuracy ratio can be found from N N n 1 Ĝ ÂR N n 0 Ĝ. (37) A we have een for T, in the pecial cae that all credit applicant are accepted, it hold A = Ω and α 0 = α 1 = 1. Hence, the upper and lower bound for the 16
18 Lorenz curve a well for Gini coefficient and accuracy ratio coincide with their repective value in thi fully oberved cae. A an illutration, we ue the data from the Monte Carlo imulation in Section 4. Figure 7 how the etimated AR (thick olid line) and ÃR (thin olid line) a well a the etimated upper and lower bound according for all 100 imulated data et (orted by the etimated AR). We find ÂR > ÃR in 97 cae and ÂR < ÃR in 3 cae. A for T we can conclude that uing ÃR a a replacement of AR would have led to too large or mall value for the dicriminatory power of the core, wherea the upper and lower bound indicate a correctly pecified range for ÂR. We alo remark that the reulting plot in Figure 7 i very imilar to that for T in Figure 5. Reference Banking Committee on Banking Superviion (2001). Accord, Bank for International Settlement. The New Bael Capital Gourieroux, C. and Jaiak, J. (2001). Financial Econometric: Problem, Model, and Method, Princeton Univerity Pre. Greene, W. H. (1993). Econometric Analyi, 2 edn, Prentice Hall. Greene, W. H. (1998). Sample election in creditcoring model, Japan an the World Economy 10: Hand, D. J. and Henley, W. E. (1997). Statitical claification method in conumer credit coring: a review, Journal of the Royal Statitical Society, Serie A 160: Heckman, J. (1979). Sample election bia a a pecification error, Econometrica 47: Horowitz, J. L. and Manki, C. F. (1998). Cenoring of outcome and regreor due to urvey nonrepone: Identification and etimation uing weight and imputation, Journal of Econometric 84:
Redesigning Ratings: Assessing the Discriminatory Power of Credit Scores under Censoring
Redeigning Rating: Aeing the Dicriminatory Power of Credit Score under Cenoring Holger Kraft, Gerald Kroiandt, Marlene Müller Fraunhofer Intitut für Techno und Wirtchaftmathematik (ITWM) Thi verion: June
More informationUnit 11 Using Linear Regression to Describe Relationships
Unit 11 Uing Linear Regreion to Decribe Relationhip Objective: To obtain and interpret the lope and intercept of the leat quare line for predicting a quantitative repone variable from a quantitative explanatory
More informationQueueing systems with scheduled arrivals, i.e., appointment systems, are typical for frontal service systems,
MANAGEMENT SCIENCE Vol. 54, No. 3, March 28, pp. 565 572 in 25199 ein 1526551 8 543 565 inform doi 1.1287/mnc.17.82 28 INFORMS Scheduling Arrival to Queue: A SingleServer Model with NoShow INFORMS
More informationA technical guide to 2014 key stage 2 to key stage 4 value added measures
A technical guide to 2014 key tage 2 to key tage 4 value added meaure CONTENTS Introduction: PAGE NO. What i value added? 2 Change to value added methodology in 2014 4 Interpretation: Interpreting chool
More informationThus far. Inferences When Comparing Two Means. Testing differences between two means or proportions
Inference When Comparing Two Mean Dr. Tom Ilvento FREC 48 Thu far We have made an inference from a ingle ample mean and proportion to a population, uing The ample mean (or proportion) The ample tandard
More informationA Note on Profit Maximization and Monotonicity for Inbound Call Centers
OPERATIONS RESEARCH Vol. 59, No. 5, September October 2011, pp. 1304 1308 in 0030364X ein 15265463 11 5905 1304 http://dx.doi.org/10.1287/opre.1110.0990 2011 INFORMS TECHNICAL NOTE INFORMS hold copyright
More informationOptical Illusion. Sara Bolouki, Roger Grosse, Honglak Lee, Andrew Ng
Optical Illuion Sara Bolouki, Roger Groe, Honglak Lee, Andrew Ng. Introduction The goal of thi proect i to explain ome of the illuory phenomena uing pare coding and whitening model. Intead of the pare
More informationA note on profit maximization and monotonicity for inbound call centers
A note on profit maximization and monotonicity for inbound call center Ger Koole & Aue Pot Department of Mathematic, Vrije Univeriteit Amterdam, The Netherland 23rd December 2005 Abtract We conider an
More informationQueueing Models for Multiclass Call Centers with RealTime Anticipated Delays
Queueing Model for Multicla Call Center with RealTime Anticipated Delay Oualid Jouini Yve Dallery Zeynep Akşin Ecole Centrale Pari Koç Univerity Laboratoire Génie Indutriel College of Adminitrative Science
More informationTtest for dependent Samples. Difference Scores. The t Test for Dependent Samples. The t Test for Dependent Samples. s D
The t Tet for ependent Sample Ttet for dependent Sample (ak.a., Paired ample ttet, Correlated Group eign, Within Subject eign, Repeated Meaure,.. RepeatedMeaure eign When you have two et of core from
More informationDISTRIBUTED DATA PARALLEL TECHNIQUES FOR CONTENTMATCHING INTRUSION DETECTION SYSTEMS. G. Chapman J. Cleese E. Idle
DISTRIBUTED DATA PARALLEL TECHNIQUES FOR CONTENTMATCHING INTRUSION DETECTION SYSTEMS G. Chapman J. Cleee E. Idle ABSTRACT Content matching i a neceary component of any ignaturebaed network Intruion Detection
More informationG*Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences
Behavior Reearch Method 007, 39 (), 759 G*Power 3: A flexible tatitical power analyi program for the ocial, behavioral, and biomedical cience FRAZ FAUL ChritianAlbrechtUniverität Kiel, Kiel, Germany
More informationRisk Management for a Global Supply Chain Planning under Uncertainty: Models and Algorithms
Rik Management for a Global Supply Chain Planning under Uncertainty: Model and Algorithm Fengqi You 1, John M. Waick 2, Ignacio E. Gromann 1* 1 Dept. of Chemical Engineering, Carnegie Mellon Univerity,
More informationIndependent Samples T test
Independent Sample T tet With previou tet, we were intereted in comparing a ingle ample with a population With mot reearch, you do not have knowledge about the population  you don t know the population
More informationSector Concentration in Loan Portfolios and Economic Capital. Abstract
Sector Concentration in Loan Portfolio and Economic Capital Klau Düllmann and Nancy Machelein 2 Thi verion: September 2006 Abtract The purpoe of thi paper i to meaure the potential impact of buineector
More informationDISTRIBUTED DATA PARALLEL TECHNIQUES FOR CONTENTMATCHING INTRUSION DETECTION SYSTEMS
DISTRIBUTED DATA PARALLEL TECHNIQUES FOR CONTENTMATCHING INTRUSION DETECTION SYSTEMS Chritopher V. Kopek Department of Computer Science Wake Foret Univerity WintonSalem, NC, 2709 Email: kopekcv@gmail.com
More informationTIME SERIES ANALYSIS AND TRENDS BY USING SPSS PROGRAMME
TIME SERIES ANALYSIS AND TRENDS BY USING SPSS PROGRAMME RADMILA KOCURKOVÁ Sileian Univerity in Opava School of Buine Adminitration in Karviná Department of Mathematical Method in Economic Czech Republic
More informationPartial optimal labeling search for a NPhard subclass of (max,+) problems
Partial optimal labeling earch for a NPhard ubcla of (max,+) problem Ivan Kovtun International Reearch and Training Center of Information Technologie and Sytem, Kiev, Uraine, ovtun@image.iev.ua Dreden
More informationTwo Dimensional FEM Simulation of Ultrasonic Wave Propagation in Isotropic Solid Media using COMSOL
Excerpt from the Proceeding of the COMSO Conference 0 India Two Dimenional FEM Simulation of Ultraonic Wave Propagation in Iotropic Solid Media uing COMSO Bikah Ghoe *, Krihnan Balaubramaniam *, C V Krihnamurthy
More informationMixed Method of Model Reduction for Uncertain Systems
SERBIAN JOURNAL OF ELECTRICAL ENGINEERING Vol 4 No June Mixed Method of Model Reduction for Uncertain Sytem N Selvaganean Abtract: A mixed method for reducing a higher order uncertain ytem to a table reduced
More informationUnobserved Heterogeneity and Risk in Wage Variance: Does Schooling Provide Earnings Insurance?
TI 011045/3 Tinbergen Intitute Dicuion Paper Unoberved Heterogeneity and Rik in Wage Variance: Doe Schooling Provide Earning Inurance? Jacopo Mazza Han van Ophem Joop Hartog * Univerity of Amterdam; *
More informationIntroduction to the article Degrees of Freedom.
Introduction to the article Degree of Freedom. The article by Walker, H. W. Degree of Freedom. Journal of Educational Pychology. 3(4) (940) 5369, wa trancribed from the original by Chri Olen, George Wahington
More information2. METHOD DATA COLLECTION
Key to learning in pecific ubject area of engineering education an example from electrical engineering AnnaKarin Cartenen,, and Jonte Bernhard, School of Engineering, Jönköping Univerity, S Jönköping,
More informationReview of Multiple Regression Richard Williams, University of Notre Dame, http://www3.nd.edu/~rwilliam/ Last revised January 13, 2015
Review of Multiple Regreion Richard William, Univerity of Notre Dame, http://www3.nd.edu/~rwilliam/ Lat revied January 13, 015 Aumption about prior nowledge. Thi handout attempt to ummarize and yntheize
More information1 Introduction. Reza Shokri* Privacy Games: Optimal UserCentric Data Obfuscation
Proceeding on Privacy Enhancing Technologie 2015; 2015 (2):1 17 Reza Shokri* Privacy Game: Optimal UerCentric Data Obfucation Abtract: Conider uer who hare their data (e.g., location) with an untruted
More informationPOSSIBILITIES OF INDIVIDUAL CLAIM RESERVE RISK MODELING
POSSIBILITIES OF INDIVIDUAL CLAIM RESERVE RISK MODELING Pavel Zimmermann * 1. Introduction A ignificant increae in demand for inurance and financial rik quantification ha occurred recently due to the fact
More informationSocially Optimal Pricing of Cloud Computing Resources
Socially Optimal Pricing of Cloud Computing Reource Ihai Menache Microoft Reearch New England Cambridge, MA 02142 timena@microoft.com Auman Ozdaglar Laboratory for Information and Deciion Sytem Maachuett
More informationProject Management Basics
Project Management Baic A Guide to undertanding the baic component of effective project management and the key to ucce 1 Content 1.0 Who hould read thi Guide... 3 1.1 Overview... 3 1.2 Project Management
More informationNETWORK TRAFFIC ENGINEERING WITH VARIED LEVELS OF PROTECTION IN THE NEXT GENERATION INTERNET
Chapter 1 NETWORK TRAFFIC ENGINEERING WITH VARIED LEVELS OF PROTECTION IN THE NEXT GENERATION INTERNET S. Srivatava Univerity of Miouri Kana City, USA hekhar@conrel.ice.umkc.edu S. R. Thirumalaetty now
More informationProgress 8 measure in 2016, 2017, and 2018. Guide for maintained secondary schools, academies and free schools
Progre 8 meaure in 2016, 2017, and 2018 Guide for maintained econdary chool, academie and free chool July 2016 Content Table of figure 4 Summary 5 A ummary of Attainment 8 and Progre 8 5 Expiry or review
More informationMSc Financial Economics: International Finance. Bubbles in the Foreign Exchange Market. Anne Sibert. Revised Spring 2013. Contents
MSc Financial Economic: International Finance Bubble in the Foreign Exchange Market Anne Sibert Revied Spring 203 Content Introduction................................................. 2 The Mone Market.............................................
More informationA Resolution Approach to a Hierarchical Multiobjective Routing Model for MPLS Networks
A Reolution Approach to a Hierarchical Multiobjective Routing Model for MPLS Networ Joé Craveirinha a,c, Rita GirãoSilva a,c, João Clímaco b,c, Lúcia Martin a,c a b c DEECFCTUC FEUC INESCCoimbra International
More informationMorningstar Fixed Income Style Box TM Methodology
Morningtar Fixed Income Style Box TM Methodology Morningtar Methodology Paper Augut 3, 00 00 Morningtar, Inc. All right reerved. The information in thi document i the property of Morningtar, Inc. Reproduction
More informationExposure Metering Relating Subject Lighting to Film Exposure
Expoure Metering Relating Subject Lighting to Film Expoure By Jeff Conrad A photographic expoure meter meaure ubject lighting and indicate camera etting that nominally reult in the bet expoure of the film.
More informationMECH 2110  Statics & Dynamics
Chapter D Problem 3 Solution 1/7/8 1:8 PM MECH 11  Static & Dynamic Chapter D Problem 3 Solution Page 7, Engineering Mechanic  Dynamic, 4th Edition, Meriam and Kraige Given: Particle moving along a traight
More information6. Friction, Experiment and Theory
6. Friction, Experiment and Theory The lab thi wee invetigate the rictional orce and the phyical interpretation o the coeicient o riction. We will mae ue o the concept o the orce o gravity, the normal
More information1) Assume that the sample is an SRS. The problem state that the subjects were randomly selected.
12.1 Homework for t Hypothei Tet 1) Below are the etimate of the daily intake of calcium in milligram for 38 randomly elected women between the age of 18 and 24 year who agreed to participate in a tudy
More informationTRADING rules are widely used in financial market as
Complex Stock Trading Strategy Baed on Particle Swarm Optimization Fei Wang, Philip L.H. Yu and David W. Cheung Abtract Trading rule have been utilized in the tock market to make profit for more than a
More informationCHARACTERISTICS OF WAITING LINE MODELS THE INDICATORS OF THE CUSTOMER FLOW MANAGEMENT SYSTEMS EFFICIENCY
Annale Univeritati Apuleni Serie Oeconomica, 2(2), 200 CHARACTERISTICS OF WAITING LINE MODELS THE INDICATORS OF THE CUSTOMER FLOW MANAGEMENT SYSTEMS EFFICIENCY Sidonia Otilia Cernea Mihaela Jaradat 2 Mohammad
More informationReport 46681b 30.10.2010. Measurement report. Sylomer  field test
Report 46681b Meaurement report Sylomer  field tet Report 46681b 2(16) Contet 1 Introduction... 3 1.1 Cutomer... 3 1.2 The ite and purpoe of the meaurement... 3 2 Meaurement... 6 2.1 Attenuation of
More informationControl of Wireless Networks with Flow Level Dynamics under Constant Time Scheduling
Control of Wirele Network with Flow Level Dynamic under Contant Time Scheduling Long Le and Ravi R. Mazumdar Department of Electrical and Computer Engineering Univerity of Waterloo,Waterloo, ON, Canada
More informationSolutions to Sample Problems for Test 3
22 Differential Equation Intructor: Petronela Radu November 8 25 Solution to Sample Problem for Tet 3 For each of the linear ytem below find an interval in which the general olution i defined (a) x = x
More informationProfitability of Loyalty Programs in the Presence of Uncertainty in Customers Valuations
Proceeding of the 0 Indutrial Engineering Reearch Conference T. Doolen and E. Van Aken, ed. Profitability of Loyalty Program in the Preence of Uncertainty in Cutomer Valuation Amir Gandomi and Saeed Zolfaghari
More informationAN OVERVIEW ON CLUSTERING METHODS
IOSR Journal Engineering AN OVERVIEW ON CLUSTERING METHODS T. Soni Madhulatha Aociate Preor, Alluri Intitute Management Science, Warangal. ABSTRACT Clutering i a common technique for tatitical data analyi,
More informationAvailability of WDM Multi Ring Networks
Paper Availability of WDM Multi Ring Network Ivan Rado and Katarina Rado H d.o.o. Motar, Motar, Bonia and Herzegovina Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, Univerity
More informationProgress 8 and Attainment 8 measure in 2016, 2017, and 2018. Guide for maintained secondary schools, academies and free schools
Progre 8 and Attainment 8 meaure in 2016, 2017, and 2018 Guide for maintained econdary chool, academie and free chool September 2016 Content Table of figure 4 Summary 5 A ummary of Attainment 8 and Progre
More informationSupport Vector Machine Based Electricity Price Forecasting For Electricity Markets utilising Projected Assessment of System Adequacy Data.
The Sixth International Power Engineering Conference (IPEC23, 2729 November 23, Singapore Support Vector Machine Baed Electricity Price Forecating For Electricity Maret utiliing Projected Aement of Sytem
More informationv = x t = x 2 x 1 t 2 t 1 The average speed of the particle is absolute value of the average velocity and is given Distance travelled t
Chapter 2 Motion in One Dimenion 2.1 The Important Stuff 2.1.1 Poition, Time and Diplacement We begin our tudy of motion by conidering object which are very mall in comparion to the ize of their movement
More informationSCM integration: organiational, managerial and technological iue M. Caridi 1 and A. Sianei 2 Dipartimento di Economia e Produzione, Politecnico di Milano, Italy Email: maria.caridi@polimi.it Itituto
More informationLinear energypreserving integrators for Poisson systems
BIT manucript No. (will be inerted by the editor Linear energypreerving integrator for Poion ytem David Cohen Ernt Hairer Received: date / Accepted: date Abtract For Hamiltonian ytem with noncanonical
More informationEXPERIMENT 11 CONSOLIDATION TEST
119 EXPERIMENT 11 CONSOLIDATION TEST Purpoe: Thi tet i performed to determine the magnitude and rate of volume decreae that a laterally confined oil pecimen undergoe when ubjected to different vertical
More informationScheduling of Jobs and Maintenance Activities on Parallel Machines
Scheduling of Job and Maintenance Activitie on Parallel Machine ChungYee Lee* Department of Indutrial Engineering Texa A&M Univerity College Station, TX 778433131 cylee@ac.tamu.edu ZhiLong Chen** Department
More informationAdaptive Window Size Image Denoising Based on Intersection of Confidence Intervals (ICI) Rule
Journal of Mathematical Imaging and Viion 16: 223±235, 2002 # 2002 Kluwer Academic Publiher. Manufactured in The Netherland. Adaptive Window Size Image Denoiing Baed on Interection of Confidence Interval
More informationA model for the relationship between tropical precipitation and column water vapor
Click Here for Full Article GEOPHYSICAL RESEARCH LETTERS, VOL. 36, L16804, doi:10.1029/2009gl039667, 2009 A model for the relationhip between tropical precipitation and column water vapor Caroline J. Muller,
More informationTHE IMPACT OF MULTIFACTORIAL GENETIC DISORDERS ON CRITICAL ILLNESS INSURANCE: A SIMULATION STUDY BASED ON UK BIOBANK ABSTRACT KEYWORDS
THE IMPACT OF MULTIFACTORIAL GENETIC DISORDERS ON CRITICAL ILLNESS INSURANCE: A SIMULATION STUDY BASED ON UK BIOBANK BY ANGUS MACDONALD, DELME PRITCHARD AND PRADIP TAPADAR ABSTRACT The UK Biobank project
More informationProceedings of Power Tech 2007, July 15, Lausanne
Second Order Stochatic Dominance Portfolio Optimization for an Electric Energy Company M.P. Cheong, Student Member, IEEE, G. B. Sheble, Fellow, IEEE, D. Berleant, Senior Member, IEEE and C.C. Teoh, Student
More informationSENSING IMAGES. School of Remote Sensing and Information Engineering, Wuhan University, 129# Luoyu Road, Wuhan, China,ych@whu.edu.
International Archive of the Photogrammetry, Remote Sening and Spatial Information Science, Volume X/W, 3 8th International Sympoium on Spatial Data Quality, 3 May  June 3, Hong Kong COUD DETECTION METHOD
More informationRiskSharing within Families: Evidence from the Health and Retirement Study
RikSharing within Familie: Evidence from the Health and Retirement Study Ş. Nuray Akın and Okana Leukhina December 14, 2014 We report trong empirical upport for the preence of elfinteretbaed rik haring
More informationA New Optimum Jitter Protection for Conversational VoIP
Proc. Int. Conf. Wirele Commun., Signal Proceing (Nanjing, China), 5 pp., Nov. 2009 A New Optimum Jitter Protection for Converational VoIP Qipeng Gong, Peter Kabal Electrical & Computer Engineering, McGill
More informationBidding for Representative Allocations for Display Advertising
Bidding for Repreentative Allocation for Diplay Advertiing Arpita Ghoh, Preton McAfee, Kihore Papineni, and Sergei Vailvitkii Yahoo! Reearch. {arpita, mcafee, kpapi, ergei}@yahooinc.com Abtract. Diplay
More informationREDUCTION OF TOTAL SUPPLY CHAIN CYCLE TIME IN INTERNAL BUSINESS PROCESS OF REAMER USING DOE AND TAGUCHI METHODOLOGY. Abstract. 1.
International Journal of Advanced Technology & Engineering Reearch (IJATER) REDUCTION OF TOTAL SUPPLY CHAIN CYCLE TIME IN INTERNAL BUSINESS PROCESS OF REAMER USING DOE AND Abtract TAGUCHI METHODOLOGY Mr.
More informationName: SID: Instructions
CS168 Fall 2014 Homework 1 Aigned: Wedneday, 10 September 2014 Due: Monday, 22 September 2014 Name: SID: Dicuion Section (Day/Time): Intruction  Submit thi homework uing Pandagrader/GradeScope(http://www.gradecope.com/
More informationTurbulent Mixing and Chemical Reaction in Stirred Tanks
Turbulent Mixing and Chemical Reaction in Stirred Tank André Bakker Julian B. Faano Blend time and chemical product ditribution in turbulent agitated veel can be predicted with the aid of Computational
More informationPerformance of a BrowserBased JavaScript Bandwidth Test
Performance of a BrowerBaed JavaScript Bandwidth Tet David A. Cohen II May 7, 2013 CP SC 491/H495 Abtract An exiting browerbaed bandwidth tet written in JavaScript wa modified for the purpoe of further
More informationStochasticity in Transcriptional Regulation: Origins, Consequences, and Mathematical Representations
36 Biophyical Journal Volume 8 December 200 36 336 Stochaticity in Trancriptional Regulation: Origin, Conequence, and Mathematical Repreentation Thoma B. Kepler* and Timothy C. Elton *Santa Fe Intitute,
More informationChapter 32. OPTICAL IMAGES 32.1 Mirrors
Chapter 32 OPTICAL IMAGES 32.1 Mirror The point P i called the image or the virtual image of P (light doe not emanate from it) The leftright reveral in the mirror i alo called the depth inverion (the
More informationGrowth and Sustainability of Managed Security Services Networks: An Economic Perspective
Growth and Sutainability of Managed Security Service etwork: An Economic Perpective Alok Gupta Dmitry Zhdanov Department of Information and Deciion Science Univerity of Minneota Minneapoli, M 55455 (agupta,
More informationOriginal Article: TOWARDS FLUID DYNAMICS EQUATIONS
Peer Reviewed, Open Acce, Free Online Journal Publihed monthly : ISSN: 88X Iue 4(5); April 15 Original Article: TOWARDS FLUID DYNAMICS EQUATIONS Citation Zaytev M.L., Akkerman V.B., Toward Fluid Dynamic
More informationHUMAN CAPITAL AND THE FUTURE OF TRANSITION ECONOMIES * Michael Spagat Royal Holloway, University of London, CEPR and Davidson Institute.
HUMAN CAPITAL AND THE FUTURE OF TRANSITION ECONOMIES * By Michael Spagat Royal Holloway, Univerity of London, CEPR and Davidon Intitute Abtract Tranition economie have an initial condition of high human
More informationMultiObjective Optimization for Sponsored Search
MultiObjective Optimization for Sponored Search Yilei Wang 1,*, Bingzheng Wei 2, Jun Yan 2, Zheng Chen 2, Qiao Du 2,3 1 Yuanpei College Peking Univerity Beijing, China, 100871 (+86)15120078719 wangyileipku@gmail.com
More informationTeaching RankBased Tests by Emphasizing Structural Similarities to Corresponding Parametric Tests
Journal of Statitic Education, Volume 8, Number (00) Teaching RankBaed Tet by Emphaizing Structural Similaritie to Correponding Parametric Tet ewayne R. erryberry Sue B. Schou Idaho State Univerity W.
More informationFEDERATION OF ARAB SCIENTIFIC RESEARCH COUNCILS
Aignment Report RP/98983/5/0./03 Etablihment of cientific and technological information ervice for economic and ocial development FOR INTERNAL UE NOT FOR GENERAL DITRIBUTION FEDERATION OF ARAB CIENTIFIC
More informationCASE STUDY BRIDGE. www.futureprocessing.com
CASE STUDY BRIDGE TABLE OF CONTENTS #1 ABOUT THE CLIENT 3 #2 ABOUT THE PROJECT 4 #3 OUR ROLE 5 #4 RESULT OF OUR COLLABORATION 67 #5 THE BUSINESS PROBLEM THAT WE SOLVED 8 #6 CHALLENGES 9 #7 VISUAL IDENTIFICATION
More informationAuction Theory. Jonathan Levin. October 2004
Auction Theory Jonathan Levin October 2004 Our next topic i auction. Our objective will be to cover a few of the main idea and highlight. Auction theory can be approached from different angle from the
More informationMBA 570x Homework 1 Due 9/24/2014 Solution
MA 570x Homework 1 Due 9/24/2014 olution Individual work: 1. Quetion related to Chapter 11, T Why do you think i a fund of fund market for hedge fund, but not for mutual fund? Anwer: Invetor can inexpenively
More informationSenior Thesis. Horse Play. Optimal Wagers and the Kelly Criterion. Author: Courtney Kempton. Supervisor: Professor Jim Morrow
Senior Thei Hore Play Optimal Wager and the Kelly Criterion Author: Courtney Kempton Supervior: Profeor Jim Morrow June 7, 20 Introduction The fundamental problem in gambling i to find betting opportunitie
More informationEvaluating Teaching in Higher Education. September 2008. Bruce A. Weinberg The Ohio State University *, IZA, and NBER weinberg.27@osu.
Evaluating Teaching in Higher Education September 2008 Bruce A. Weinberg The Ohio State Univerity *, IZA, and NBER weinberg.27@ou.edu Belton M. Fleiher The Ohio State Univerity * and IZA fleiher.1@ou.edu
More informationEstimating V s(30) (or NEHRP Site Classes) from Shallow Velocity Models (Depths 30 m)
Bulletin of the Seimological Society of America, Vol. 94, No. 2, pp. 591 597, April 4 Etimating V () (or NEHRP Site Clae) from Shallow Velocity Model (Depth m) by David M. Boore Abtract The average velocity
More informationA Spam Message Filtering Method: focus on run time
, pp.2933 http://dx.doi.org/10.14257/atl.2014.76.08 A Spam Meage Filtering Method: focu on run time SinEon Kim 1, JungTae Jo 2, SangHyun Choi 3 1 Department of Information Security Management 2 Department
More informationUsing Graph Analysis to Study Networks of Adaptive Agent
Uing Graph Analyi to Study Network of Adaptive Agent Sherief Abdallah Britih Univerity in Dubai, United Arab Emirate Univerity of Edinburgh, United Kingdom hario@ieee.org ABSTRACT Experimental analyi of
More informationJanuary 21, 2015. Abstract
T S U I I E P : T R M C S J. R January 21, 2015 Abtract Thi paper evaluate the trategic behavior of a monopolit to influence environmental policy, either with taxe or with tandard, comparing two alternative
More informationDMA Departamento de Matemática e Aplicações Universidade do Minho
Univeridade do Minho DMA Departamento de Matemática e Aplicaçõe Univeridade do Minho Campu de Gualtar 4757 Braga Portugal www.math.uminho.pt Univeridade do Minho Ecola de Ciência Departamento de Matemática
More informationUnusual Option Market Activity and the Terrorist Attacks of September 11, 2001*
Allen M. Potehman Univerity of Illinoi at UrbanaChampaign Unuual Option Market Activity and the Terrorit Attack of September 11, 2001* I. Introduction In the aftermath of the terrorit attack on the World
More informationTowards ControlRelevant Forecasting in Supply Chain Management
25 American Control Conference June 81, 25. Portland, OR, USA WeA7.1 Toward ControlRelevant Forecating in Supply Chain Management Jay D. Schwartz, Daniel E. Rivera 1, and Karl G. Kempf Control Sytem
More informationDUE to the small size and low cost of a sensor node, a
1992 IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 14, NO. 10, OCTOBER 2015 A Networ Coding Baed Energy Efficient Data Bacup in SurvivabilityHeterogeneou Senor Networ Jie Tian, Tan Yan, and Guiling Wang
More informationResearch Article An (s, S) Production Inventory Controlled SelfService Queuing System
Probability and Statitic Volume 5, Article ID 558, 8 page http://dxdoiorg/55/5/558 Reearch Article An (, S) Production Inventory Controlled SelfService Queuing Sytem Anoop N Nair and M J Jacob Department
More informationTax Evasion and SelfEmployment in a HighTax Country: Evidence from Sweden
Tax Evaion and SelfEmployment in a HighTax Country: Evidence from Sweden by Per Engtröm * and Bertil Holmlund ** Thi verion: May 17, 2006 Abtract Selfemployed individual have arguably greater opportunitie
More informationMassachusetts Institute of Technology Department of Electrical Engineering and Computer Science
aachuett Intitute of Technology Department of Electrical Engineering and Computer Science 6.685 Electric achinery Cla Note 10: Induction achine Control and Simulation c 2003 Jame L. Kirtley Jr. 1 Introduction
More informationUtilityBased Flow Control for Sequential Imagery over Wireless Networks
UtilityBaed Flow Control for Sequential Imagery over Wirele Networ Tomer Kihoni, Sara Callaway, and Mar Byer Abtract Wirele enor networ provide a unique et of characteritic that mae them uitable for building
More informationMobile Network Configuration for Largescale Multimedia Delivery on a Single WLAN
Mobile Network Configuration for Largecale Multimedia Delivery on a Single WLAN Huigwang Je, Dongwoo Kwon, Hyeonwoo Kim, and Hongtaek Ju Dept. of Computer Engineering Keimyung Univerity Daegu, Republic
More informationAnalysis of Mesostructure Unit Cells Comprised of Octettruss Structures
Analyi of Meotructure Unit Cell Compried of Octettru Structure Scott R. Johnton *, Marque Reed *, Hongqing V. Wang, and David W. Roen * * The George W. Woodruff School of Mechanical Engineering, Georgia
More informationSolution of the Heat Equation for transient conduction by LaPlace Transform
Solution of the Heat Equation for tranient conduction by LaPlace Tranform Thi notebook ha been written in Mathematica by Mark J. McCready Profeor and Chair of Chemical Engineering Univerity of Notre Dame
More informationClusterAware Cache for Network Attached Storage *
CluterAware Cache for Network Attached Storage * Bin Cai, Changheng Xie, and Qiang Cao National Storage Sytem Laboratory, Department of Computer Science, Huazhong Univerity of Science and Technology,
More informationOUTPUT STREAM OF BINDING NEURON WITH DELAYED FEEDBACK
binding neuron, biological and medical cybernetic, interpike interval ditribution, complex ytem, cognition and ytem Alexander VIDYBIDA OUTPUT STREAM OF BINDING NEURON WITH DELAYED FEEDBACK A binding neuron
More informationA Duality Model of TCP and Queue Management Algorithms
A Duality Model of TCP and Queue Management Algorithm Steven H. Low CS and EE Department California Intitute of Technology Paadena, CA 95 low@caltech.edu May 4, Abtract We propoe a duality model of endtoend
More informationThe Arms Race on American Roads: The Effect of SUV s and Pickup Trucks on Traffic Safety
The Arm Race on American Road: The Effect of SUV and Pickup Truck on Traffic Safety Michelle J. White Univerity of California, San Diego, and NBER Abtract Driver have been running an arm race on American
More information1. Introduction. C. Camisullis 1, V. Giard 2, G. MendyBilek 3
Proceeding of the 3 rd International Conference on Information Sytem, Logitic and Supply Chain Creating value through green upply chain ILS 2010 Caablanca (Morocco), April 1416 The right information to
More informationINFORMATION Technology (IT) infrastructure management
IEEE TRANSACTIONS ON CLOUD COMPUTING, VOL. 2, NO. 1, MAY 214 1 BuineDriven Longterm Capacity Planning for SaaS Application David Candeia, Ricardo Araújo Santo and Raquel Lope Abtract Capacity Planning
More informationGrowth and Sustainability of Managed Security Services Networks: An Economic Perspective
Growth and Sutainability of Managed Security Service etwork: An Economic Perpective Alok Gupta Dmitry Zhdanov Department of Information and Deciion Science Univerity of Minneota Minneapoli, M 55455 (agupta,
More informationMorningstar FixedIncome Style Box TM Methodology
Morningtar FixedIncome Style Box TM Methodology Morningtar Methodology Paper April 30, 01 01 Morningtar, Inc. All right reerved. The information in thi document i the property of Morningtar, Inc. Reproduction
More information