Market Segmentation Based on Risk of Misinforming Reduction

Transcription

1 Issues n Informng Scence and Informaton Technology Volume 9, 2012 Maret Segmentaton Based on Rs of Msnformng Reducton Dmtar Chrstozov Amercan Unversty n Bulgara, Blagoevgrad, Bulgara dgc@aubg.bg Stefana Chuova Vctora Unversty of Wellngton, Wellngton, New Zealand stefana@vuw.ac.nz Plamen Mateev Sofa Unversty St. Klment Ohrds, Sofa, Bulgara pmat@fm.un-sofa.bg Abstract Provdng the approprate nformaton n the rght format to the rght group of potental customers of a partcular product s the natural obectve n maret segmentaton. Ths paper explores measures for quantfyng the rs of msnformng and ther usage for maret studes, leadng to an approach for dentfyng maret clusters. The proposed segmentaton s based on the cost of the addtonal nformaton a partcular customer needs for the revson of hs/her purchase decson, so that hs/her ntally wrong purchase decson s approprately corrected. The rs for wrong purchase decson s two-fold to buy somethng that s not perfectly sutable or not to buy somethng, whch s really sutable. Addtonal, adustng nformaton may reduce these rss. The cost of ths addtonal nformaton s calculated n a way to mnmze the cost for adustng decson regardng the buyer s tass over all possble nformng scenaros. Further, the cost for addtonal nformaton s used to defne the dstance between clents. Ths dstance serves to dentfy maret segments,.e., clusters of clents wth smlar nformaton needs. Key words: rs of msnformng, optmzaton problem, maret segmentaton Introducton In warranty studes we model and analyze two types of rss, the rs of malfunctonng of a product quantfed by ts relablty, and the rs of msunderstandng the features and qualtes of a product whle decdng whether to buy Materal publshed as part of ths publcaton, ether on-lne or n prnt, s copyrghted by the Informng Scence Insttute. Permsson to mae dgtal or paper copy of part or all of these wors for personal or classroom use s granted wthout fee provded that the copes are not made or dstrbuted for proft or commercal advantage AND that copes 1) bear ths notce n full and 2) gve the full ctaton on the frst page. It s permssble to abstract these wors so long as credt s gven. To copy n all other cases or to republsh or to post on a server or to redstrbute to lsts requres specfc permsson and payment of a fee. Contact Publsher@InformngScence.org to request redstrbuton permsson. t. The later rs s caused by the nformaton asymmetry, whch s a natural property of any communcaton process, see Chrstozov, Chuova, Mateev (2009a), we call t rs of msnformng. Due to the strong mpact of the nformaton asymmetry on the marets and specfcally on the completon n the maretplace, studes related to nformaton asymmetry attracted the attenton of

2 Maret Segmentaton several research teams. Muhopadhyay, Yue and Zhu (2011) studed the mpact of nformaton asymmetry on maret completon. Aan, Ata and Larvere (2011) studed outsourcng and the assocated contractng problem under nformaton asymmetry. Knll, Mnnc and Neadmalayer (2011) examned whether t s ratonal for analysts to post based estmates and how nformaton asymmetry and analyst experence factor nto the decson amng to mnmze forecastng error. Informaton provded by the Seller nforms dfferent clents dfferently, because of the dfferent nformaton asymmetry. Some are nformed correctly regardng all propertes of the product, but the same nformaton may mslead others. Maret segmentaton allows sellers to approach dfferent categores of potental buyers dfferently, so that they can address them wth advertsng messages, or messages wth the product descrpton, n the most approprate and benefcal way. In ths paper we propose an approach for segmentaton of the populaton of potental customers based on how they understand the seller s message and the level of needed addtonal adustng nformaton for reducng ther rs of mang a wrong purchase decson,.e., the rs of msnformng. It s natural to use the quanttatve measures of the rs of msnformng for maret segmentaton. The earler studes addressed manly the warranty aspect of proposed measures for quantfyng the rs of msnformng (see Chrstozov, Chuova, Mateev 2009b). The current study, nfluenced also by the deas behnd maxmzng the nformaton gan measure (see for example Han, Kamber, Pe (2011), Chapter 8), s addresses mprovement of communcaton process. The dea s that maxmzaton of nformaton gan mnmze the rs of msnformng. In ths study we defne a dstance between customers of a gven product based on the nformaton needed to mnmze the rs of msnformng and the seller s losses caused by ths msnformng. Nowadays, the maret segmentaton s based on the nformaton needs of the targeted group, so ablty to mae a conscous and realstc purchase decson s crtcal. A wrong purchase decson has a negatve effect on the customer, and can lead to a sgnfcant losses ncurred by the seller. These losses could be of two types based on a mssed sale or due to creatng an unsatsfed customer. If the product s covered by a warranty of msnformng, an unsatsfed customer could cause drect fnancal losses by mang a legtmate warranty clam. Ths concept was ntroduced n Chrstozov, Chuova, Mateev (2006) where postve and negatve wrong purchase decsons were dentfed,.e., the postve wrong purchase decson wll generate a legtmate warranty clam, whereas the negatve wrong purchase decson wll lead to a mssed sale. Both rss are caused by the msunderstandng or msnterpretaton of the message provded by the seller to the customers. A natural queston amng to address ths msunderstandng s: what must be the content of the addtonal message provded by seller to the customer so that hs/her understandng about the real propertes of the product s approprately adusted. Also, what s the seller s cost for provdng such a message. It s clear that a partcular customer must be provded wth specfc addtonal nformaton, whch reflects hs/her specfc product needs (see Chrstozov, Chuova, Mateev (2006)). Also, n Chrstozov, Chuova, Mateev (2006), was ntroduced a parameter, whch reflects the mnmal product requrements of the th buyer for hs/her th tas. It s obvous that f a gven customer needs to solve multple tass wth the product, the message to adust hs/her decson must address the needs and mnmal requrements for every specfc tas. In other words, for a gven customer, the seller has to provde addtonal message addressng every tas, and n ths way the cost of ths addtonal message s composed by the costs for adustng the message for every dstnct tas. In ths way a customer can be dentfed by a vector of costs for the message that wll adust hs/her understandng regardng the product. Two customers, who need the same or smlar adustng message, can be consdered as belongng to one and the same maret nche. Therefore, the addtonal nformaton needed to ensure a correct purchase decson can be used to n q 254

3 Chrstozov, Chuova, & Mateev defne a dstance between customers, and further to use ths dstance for clusterng the customers populaton or for maret segmentaton. The paper s organzed as follows. The next secton ntroduces the problem s bacground by descrbng notatons and model components, whch are used further n the paper and provdes useful references. In the followng secton we formulate an optmsaton problem so that the Informaton Adustng Cost s ntroduced. The thrd secton s dedcated to the defnton of dstance between customers as a functon of the Informaton Adustng Cost for dfferent categores of tass. The last secton provdes a dscusson on how to use the dstance to structure the maret by dstngushng clusters of clents wth smlar nformaton needs. A summary of presented models and deas and future research drectons are gven n the concluson. Bacground The maret s represented by the populaton of potental buyers of a partcular product D. Let us denote ths populaton by B = {b }, =1, 2,, n, where b represents the th buyer. A buyer b s consdered a member of the maret, because he/she has a set of tass that needs to be solved for wth product D. Let us also assume that A = {a }, = 1, 2,,, s the set of tass that b needs to solve for wth product D. Moreover, two addtonal parameters, degree of acceptance q and needs n, characterse the relaton of b to hs/her tass n A. The degree of acceptance of the product D, q, s a measure of the buyer s udgment regardng the mnmal qualty the product D has to have n order to be sutable for the buyer b to solve the tas a. It s descrbed n terms of qualty of the product and ts value can be normalzed to be wthn [0, 1] (see Chrstozov, Chuova, Mateev, 2008), where zero refers to the case where every product s acceptable and one means that only the top qualty products could be satsfactory to the buyer. Here we assume that q s nown and normalzed. Furthermore, we assume that every ndvdual tas a of buyer b belongs to a class of tass A and that A U A s the set of all categores of tass, whch are common for many, not necessarly 1 all, buyers n B. We assume that every b has tass from each of the classes A, but for some of these tass hs/her need n s zero. The product D s produced n a way to allow solvng the tass from A. It has the potental or capablty to solve tas from a gven class wth probablty p. In the case that a buyer needs to solve for a tas that s not among the tass the product D s desgned for, correspondng p = 0. The need of the b to solve for a tas from category A s n, where 0 n 1. If n = 0, then b does not need to solve for any tas from A, whereas, f n =1, b defntely needs to solve for a tas from A. In case of n = 0, then q =0,.e., f b does not need to solve for a tas from A, then any product s acceptable for hm/her. The value of n s completely subectve and could be estmated usng customers surveys. The seller advertses the product D by sendng a message to B descrbng the propertes of D. Based on ths message b assesses the probablty pˆ pa ˆ( ) that the product D s sutable to solve for hs/her tas a. Followng ths assessment, b maes hs/her purchase decson based on the comparson between { p ˆ } and {q } over all tass from hs/her set A, the values of p and p ˆ may dffer sgnfcantly. There are sx cases, descrbed n Chrstozov, Chuova, Mateev (2006), addressng the rss r assocated wth such a purchase decson: 1. p ˆ p q - the product s not sutable to solve for tas a, the buyer s estmaton of the sutablty of the product s optmstc,.e., p p ˆ, and below the degree of acceptance, thus the decson s negatve and correct and r =0; 255

4 Maret Segmentaton p q p - the product s not sutable to solve for tas a, the buyer s estmaton of 2. ˆ the sutablty of the product s optmstc and above the threshold of acceptance, thus the decson s postve and wrong, and r =1; 3. q p pˆ - the product s sutable to solve for tas a, the buyer s estmaton of the sutablty of the product s optmstc and above the threshold of acceptance, thus the decson s postve and correct, and r =0; 4. pˆ p q - the product s not sutable to solve for tas a, the buyer s estmaton of the sutablty of the product s pessmstc,.e., p ˆ s less than p, and below the threshold of acceptance, thus the decson s agan negatve and correct, and r =0; 5. pˆ q p - the product s sutable to solve for tas a, the buyer s estmaton of the sutablty of the product s pessmstc and below the threshold of acceptance, thus the decson s negatve and wrong, and r =1; 6. q pˆ p - the product s sutable to solve for tas a, the buyer s estmaton of the sutablty of the product s pessmstc and above the threshold of acceptance, thus the decson s postve and correct, and r =0. The two wrong decsons relate to the two categores of rss for the seller: case 2 ( p q pˆ ) corresponds to mssed sales and mssed proft; and case 5 ( pˆ q p ) corresponds to the potental dssatsfacton of the buyer. If the product s covered by a msnformng warranty contract (see Chrstozov, Chuova Mateev, 2009a), the second rs could result n drect fnancal losses due to customer s mang a legal warranty clam. These rss could be non-zero only f q s between p and pˆ. It s natural to expect that the seller s am s to reduce both of these rss. To do that the seller has to develop nformaton polcy (advertse or dstrbute addtonal messages) to address buyers specfc nformaton needs so that the gap between p and pˆ s reduced. Ths wll reduce the rs for experencng ether of the two types of losses. Ths requres dentfyng the clusters of buyers wth smlar understandng of the orgnal message and need of smlar addtonal nformaton to adust ther purchase decson. In our modellng, onwards, we assume that provdng such addtonal nformaton comes wth certan cost to the seller. Optmzaton Problem: Mnmzng Informaton Adustng Cost In what follows we am to formulate an optmsaton problem related to the rs of msnformng, so that the related costs are mnmzed. We ntroduce an approprate cost measure and study the case of lmted resources. As mentoned above, there are two types of rss: p ˆ q p- the product s not sutable to solve for tas a, the buyer s estmaton of the sutablty of the product s optmstc and above the threshold of acceptance, thus the decson s postve and wrong, and r =1. Ths stuaton creates an opportunty for a warranty clam. The buyer wll realse that the product s not sutable to address hs/her expectatons regardng tas a and would be prompted to mae a warranty clam aganst the product. It could create a number of 256

5 Chrstozov, Chuova, & Mateev dssatsfed customers and affect the overall maret reputaton of the seller. Denote ths type of rs by r wc. pˆ q p - the product s sutable to solve for tas a, the buyer s estmaton of the sutablty of the product s pessmstc and below the threshold of acceptance, thus the decson s negatve and wrong, and r =1. Ths stuaton creates an opportunty for a mssed sale, whch leads to a reduced proft for the seller. Denote ths type of rs by r ms. It s easy to notce that the rs of msnformng s non-zero only f q (mn ( p, p ˆ ), max ( p, p ˆ )),.e., q s between p and. Let the preference of the seller n mnmsng these pˆ two types of rss (r ms, r wc ) s gven by (τ, 1- τ), where 0 τ 1. Therefore, the obectve functon of the optmsaton problem related to the b could be formulated as follows: mn Z = τ R ms + (1- τ) R wc, ms ms wc wc where R r and 1 R r 1. Onwards, we wll assume that the rss (r ms, r wc ) are zero whenever p ˆ q por pˆ q p,.e., the rs s zero f the acceptance level q s equal to the probablty pˆ problem. Assume that q and p are nown whereas. Next, let us dscuss the possble constrants for ths optmzaton P s uncertan,.e., t s a random varable ˆ wth nown probablty dstrbuton. We assume that P has a standard beta dstrbuton wth parameters (α, β ),.e., P ˆ ˆ : Beta(, ) and the reported (observed) value p s the mode of ˆ ths dstrbuton. For more on the standard beta dstrbuton wth parameters (α, β ), ncludng the probablty densty functon, mean value and varance, see Appendx II. Therefore for the a tas of b, the trple ( pˆ, q, p ) represents the level of nformng nduced by the sellers message regardng the features of product D. Assume that for b t s true that (r ms, r wc ) (0, 0). The seller could provde an addtonal nformaton to the buyer, so that the buyer s rss (r ms, r wc ) = (0, 0). For provdng ths addtonal nformaton the seller wll ncur certan cost, but wll beneft from the reducton of the rs of msnformng of b wth respect of tas a. Assume that the effect of the nformaton n the addtonal message s measured by the shft of the ntal ~ Beta(, ) to Beta( ~, ), whch preserves the varance of the ntal dstrbuton and assures that the mode of the new beta dstrbuton Beta ~ ~, ) s equal to q,.e., assures that the ( correspondng rs of msnformng becomes zero. How bad the ntal message was (measured by Beta(, ), Fgure1) s estmated by the followng cost : the absolute value of the dfference between the mean values of the ntal beta dstrbuton µ and the mean value ~ of the beta dstrbuton nduced, see Fgure 2, by the new message, normalsed by the common standard devaton of these two dstrbutons. 257

6 Maret Segmentaton Fgure 1: Intal Beta Dstrbuton Fgure 2. Intal and nduced Beta dstrbutons We are almost ready to formulate the optmzaton problem amng to dentfy the best new message for b, gven lmted seller s resources. The last component n the formulaton of the optmzaton problem wll address the entre set of tass of b, not only one of hs/her tass a, as t was n the context above. Let, 0 1, = 1,, be the mportance, from seller s vewpont, n addressng wth the new message the msnformng related to the th tas of the b. Due to maretng or compettve reasons the seller may have preferences n nvestng hs/her resources towards a specfc subset of tass. In the formulaton of the optmzaton problem, the parameters are assumed to be nown. Therefore, we are ready to consder the followng problem: mn Z = τ R ms + (1- τ) R wc, ~ subect to: v C 1 ms where ms wc wc R r, and C s a nown constant, whch represents the lmted R 1 r 1 resources of the seller. What type of soluton for ths optmzaton problem are we loong for? What s the meanng of ~ ths soluton? We need to dentfy a transformaton form Beta(, ) to Beta ~, ), so that the obectve functon Z s mnmzed and the cost constrant s satsfed. Let us also denote the cost of transformaton for a gven tas as ~ c v. (1) Next, usng an example, we llustrate the deas presented n ths secton. ( 258

7 Chrstozov, Chuova, & Mateev An Example Let us assume that the set of tass of the th buyer conssts of sx tass: A = {a 1, a 2,, a 6 }, such that pˆ 1 q1 p 1, pˆ 4 q4 p 4 and p3 q ˆ 3 p3. In addton, t s nown that q = 0.6, q 3 = 0.55, q 4 = 0.65; and let p1 0.7, p 0.3, p 0.8. Also t s nown that the ntal beta 3 4 dstrbutons are as follows: : Beta(5, 25 ), : Beta( 23,7) and : Beta(3,12), whch Pˆ1 Pˆ3 leads to the followng values for p , p ˆ and pˆ For the ˆ1 remanng three tass (r ms, r wc ) = (0, 0), = 2,5,6. Therefore we have Pˆ4 1. Next, assumng partcular values for the model parameters such as: v 1 0.2, v3 0.4, v , 0.7, C 1.5, we wll llustrate the process of solvng the optmzaton problem formulated n the prevous secton: mn Z = 0.7 R ms + 0.3R wc, subect to: v 1,3,4 ~ 3 2 r r r ms ms wc What does ths partcular set of model parameters reveal? The value of α = 0.7 suggests that the seller s man concern s to mnmse the losses due to mssed sales,.e., the seller places hgher prorty on reducng the rs of the mssed sales compared to the rs of recevng a warranty clam. Moreover, the values of, show that the seller places the hghest mportance n elmnatng the msnformng related to tas a 4, whereas he s least concern wth the rs assocated wth tas a 1. The value C=1.5 represents the upper bound of the resource (or the cost ) the seller s allowed or wllng to nvest n the new message amng to reduce the rs of msnformng. Next we present the soluton of the problem. ms For tas a 1 t s gven that pˆ 1 q1 p ,.e., the rs r 1 =1 s for wrong negatve decson. We need to fnd a transformaton, preservng the standard devaton, of the ntal Beta(5, 25) wth mode equal to pˆ to a new Beta(, ) wth mode equal to q Usng the popular software MATHE- MATICA (see we were able to wrte a scrpt that searches for ths type of transformaton. For tas a 1 the new beta dstrbuton wth the requred propertes s Beta( , ) and the cost of ths transformaton s c v ~ wc For tas a 3 t s gven that p ˆ 3 q3 p ,.e., the rs r 3 =1 s for wrong postve decson. We need to fnd a transformaton, preservng the standard devaton, of the ntal Beta(23,7) wth mode equal to pˆ to a new Beta(, ) wth mode equal to q Agan usng the MATHEMATICA scrpt, we were able to determne that for a 3 the new beta dstrbuton wth the requred propertes s Beta( , ) and the cost of ths transformaton s 259

8 Maret Segmentaton c ~ v At last, for tas a 4 t s gven that pˆ 4 q4 p ,.e., the ms rs r 4 =1 s for wrong negatve decson. We need to fnd a transformaton, preservng the standard devaton, of the ntal Beta(3,12) wth mode equal to pˆ to a new Beta(, ) wth mode equal to q Agan usng the MATHEMATICA scrpt, we were able to determne that for a 4 the new beta dstrbuton wth the requred propertes s Beta( , ) and the cost of ths transformaton s c ~ v We have evaluated the costs of the transformatons related to each of the tass of nterest. Next, we consder all possble transformatons scenaros and select the best one that satsfes the resource constrant and leads to the smallest value of the obectve functon. We present our fndngs n Table 1. # scenaro # transform Tas 1 Tas 3 Tas 4 Cost of the Constrants Scenaro Satsfed? 1 3 yes yes yes No 2 2 yes yes no No 3 2 yes no yes No 4 2 no yes yes No 5 1 no no yes No 6 1 no yes no Yes 7 1 yes no no Yes Table 1. Cost of all nformng scenaros From Table 1 t s easy to conclude that only the last two scenaros satsfy the constrants of the optmzaton problem. Next, we have to mae a decson whch of these two scenaros to use as a bases n formng our new message. Let us compute the value of the obectve functon over each of these scenaros. We have for scenaro 6, Z 6 = 0.7 x x 0 = 1.4, whereas for scenaro 7, Z 7 = 0.7 x x 1 = 1. Thus, the mnmum value of the obectve functon s reached over scenaro 7, and therefore the new message should be desgned so that t targets tas 1 of the th buyer. Defnton of Dstance based on Informaton Adustng In the prevous secton we outlned an approach for computng the optmal cost for composng an adustng message for a sngle ndependent potental buyer. For mnmzng the overall cost, t s mportant to dentfy groups of buyers, whch can be targeted smultaneously wth one and the same adustng message. Ths s a typcal cluster analyss tas where the essental part s to defne 260

9 Chrstozov, Chuova, & Mateev dstance between any two obects dst( b, b 1 2 buyers B). ), belongng to the studed populaton (the set of all Let us assume that the rss of wrong purchase decson for buyer b wth respect of hs/her set of tass are r(b )={r 1, r 2,..., r }, whch s a bnary vector, composed only by zeros and ones. The buyer needs addtonal nformaton, whch has to address the propertes of the product D, whch are essental for the descrpton of the performance of the product D regardng tass wth rs of wrong purchase decson equal to one. The ntal message nformed correctly the buyer regardng the propertes of the product relevant to the tass wth rs of wrong purchase decson equal to zero. In other words, the addtonal, adustng nformaton should address the nformaton needs of buyer b, so that the rs of wrong decson s reduced,.e., t has to address only the propertes of product D that have mpact on ts performance related to solvng tass wth non-zero rs. The adustng message has to address the buyers dfferent nformaton needs and t s worth to dentfy maret segments based on the buyers needs of addtonal nformaton. To dentfy dfferent clusters of buyers, we need to defne a dstance between buyers accordng to ther needs of adustng nformaton. Next, we propose two possble defntons for the dstance between two buyers: Tas-based dstance the message addresses product s propertes relevant only to the rsy tass. These vectors {r 1, r 2,..., r }, =1,...,n hold asymmetrc bnary values. The dstance can be defned by countng dfferences (see for example Han, Kamber, Pe (2011), secton 2.4.3, page 70). Cost-based dstance n composng the adustng message the cost of the adustng message s taen nto account. Ths measure uses vectors {c 1, c 2,, c }, whch ncludes contnuous values. The costs of the transformaton needed to convert non-zero rss tass nto zero rs tass are calculated accordng to the formulae (1) n the prevous secton. The Mnows dstance dst( b, b ) between buyers and based on the correspondng cost (see Han, Kamber, 1 b 2 1 b 2 Pe (2011), secton 2.4.4, page 72) s gven by the formulae h h dst b, b ) c c (. If n the above formulae h = 1, we have Manhattan dstance, and f h = 2 Eucldean dstance. Moreover, when h we get, the so called, Chebyshev s dstance. It s defned as follows: h 1 h h 2 dst( b, b ) lm( c c ) max c c. So, any of the above dstances could be used to dentfy clusters of buyers. As follow up from the example n the prevous secton, t seems that the Chebyshev s dstance s the smplest and reflects well our deas n optmzng the effect of the adustng message under gven cost constrant. The cost-based dstance wll dentfy buyers wth small maxmal cost dstance over all tass. These buyers could be grouped together n a cluster that could be targeted by one and the same approprately desgned adustng message. These clusters wll form the segmentaton of the maret based on the rs of msnformng. 261

10 Maret Segmentaton Concluson In ths paper we presented an approach to structure the maret by segmentaton based on nformaton needed by customers to mae accurate rs-free purchase decson. Provdng the necessary nformaton n a correct format to the targeted group of customers s the natural obectve of maret segmentatons. The proposed segmentaton ams to reduce the rs of msnformng leadng to two categores of losses losses due to mssed sales/purchases and losses due to customer dssatsfacton. These rss may have monetary mplcatons for both partes - the sellers as well as the buyers. Two approaches to defne dstance between potental buyers, based on the process of adustng the message on the propertes of the product, are presented. The frst addresses only the content of the message for dfferent groups of buyers. The second one s based on mnmzng the cost of the adustng message. Ether of these approaches can be used for further clusterng of the maret. There are several aspects of the proposed model that need addtonal extenson and clarfcaton, such as: 1. Develop a procedure to dentfy whether the observed rss represent outlers and are not worthy to addtonal nvestment n fne-tunng the message. 2. How and what nformaton to collect n order to evaluate these rss? a. It s obvous that t s much easer to obtan nformaton regardng the rs caused by users dssatsfacton. If the product s covered by warranty of msnformng ths nformaton wll be recorded n the correspondng warranty database. b. It s much more dffcult to collect nformaton regardng the rs of mssed sales. To collect ths nformaton the seller has to nvest n provdng specal survellance or careful recordng, surveyng and analyss of all purchase nqures. 3. How to assess the rs related to the changes n the needs of a partcular buyer on the use of the product and some of the partcular product features? In our follow up studes we wll mae an attempt to address all or part of the lsted above extensons of the proposed model. References Aan, M., Ata, B., & Larvere, M. A. (2011). Asymmetrc nformaton and economes of scale n servce contractng. Manufacturng and Servce Operatons Management, 13(1), Brayn, F. J. M. (2005). Multvarate statstcal methods - A prmer (3rd ed). Chapman and Hall. Chrstozov, D., Chuova, S., & Mateev, P. (2006). A measure of rs caused by nformaton asymmetry n e-commerce. Journal of Issues n Informng Scence and Informaton Technology, 3, Chrstozov, D., Chuova, S., & Mateev, P. (2008). Warranty and the rs of msnformng: evaluaton of the degree of acceptance. Journal of Issues n Informng Scence and Informaton Technology, 5, Chrstozov, D., Chuova, S., & Mateev, P. (2009a). On two types of warrantes: Warranty of malfunctonng and warranty of msnformng. Asa-Pacfc Journal on Operaton research, 26(3), Chrstozov, D., Chuova, S., & Mateev P. (2009b). Chapter 11: Informng processes, rss, evaluaton of the rs of msnformng. In T. G. Gll & E. Cohen (Eds.), Foundatons of Informng Scence (pp ). Santa Rosa, CA: Informng Scence Press. Han, J., Kamber, M., & Pe, J. (2011). Data mnng: Concepts and technques. Morgan Kaufmann. 262

11 Chrstozov, Chuova, & Mateev Knll, A., Mnnc, K., & Neadmalayer, A. (2011). Experence, nformaton asymmetry, and ratonal forecast bas. Revew of Quanttatve Fnance and Accountng, Muhopadhyay, S. K., Yue, X., & Zhu, X. (2011). A Stacelberg model of prcng of complementary goods under nformaton asymmetry. Internatonal Journal of Producton Economcs, 134(2), Owen, C. B., (2008). Parameter estmaton for the beta dstrbuton. MSc thess, Brgham Young Unversty, Utah, USA Appendx 1. Notatons and defntons, (see Chrstozov, Chuova, Mateev (2011) Notaton D B = {b }, =1, 2,, n A = {a }, = 1, 2,, A the product buyers Defnton tass, whch b needs to solve by usng the product n set of tass of all buyers A 1 A *, 1,2,..., categores of tass n the need of b to solve hs/her tas a. 0 n 1 q p = p(a * ) pˆ pa ˆ( ) r degree of acceptance. The mnmal qualty, whch the product must possess to meet the customer b expectatons regardng hs/her tas a. threshold. probablty that the product wll solve problems from category A *. Or the level to whch the product D may satsfy the buyers needs regardng the tass from ths category. subectve assessment of the buyer b regardng the probablty (level of satsfacton) that the product wll be sutable for solvng hs/her tas a. ndcator of the decson correctness r =0 f the decson s correct; r =1 means wrong decson. Appendx II. Standard beta dstrbuton wth parameters (α, β) The Beta dstrbuton s a contnuous probablty dstrbuton defned on [0,1]. For more detals on the standard beta dstrbuton see Owen C. B., (2008). The probablty densty functon (pdf) of 1 1 x (1 x) ths dstrbuton s defned by f p ( x) for x n [0,1], where B(, ) 263

12 Maret Segmentaton 1 1 (, ) x (1 x) dx B. The mean value of ˆ P: Beta(, ) s equal to, ts mode s gven by pˆ and the varance by. ( 2 ) 2 ( ) ( 1) Moreover, t s well nown that the pdf s unmodal and strongly sewed to the rght f α >1, β > 1 and. If we eep α fxed and ncrease the value of β t maes the densty more pced. The dstrbuton gets less sewed and the mode approaches 0.5 as α and β approach each other. The dstrbuton s symmetrc around 0.5 f. If 1 then the beta dstrbuton becomes the well nown unform dstrbuton over [0, 1]. In the case of left sewed pdf, f we eep β fxed and ncrease the value of α t maes the densty more pced. The pdf s rght sewed f the values of α and β were swtched. If P s Beta(α, β ), then Q=1-P s Beta( β, α ). Beta dstrbuton s very flexble because t s two postve shape parameters α and β are frequently used to estmate an unnown proporton parameter p, whch s between 0 and 1. Increasng the parameter α s equvalent to evdence of postve behavour, because the mean value and mode are movng to rght. The opposte case ncreasng parameter β leads to decreasng the mean value and mode, whch corresponds to negatve behavour. In both cases the varance s decreasng. So, the two parameters of the beta dstrbuton may be used to weght all pros and cons regardng the values of the proporton parameter p. In the table below the mean value, mode and standard devaton are shown for some combnatons of the parameters α and β. β α mean mode stdev mean mode stdev mean mode stdev mean mode stdev mean mode stdev mean mode stdev mean mode stdev 264

13 Chrstozov, Chuova, & Mateev Bographes Dmtar Chrstozov s a Professor of Computer Scence at the Amercan Unversty n Bulgara, Blagoevgrad 2700, Bulgara snce 1993, e- mal: dgc@aubg.bg. He has more than 30 years of experence n areas as computer scence, qualty management and nformaton systems. He graduated Mathematcs from Sofa Unversty St. Klment Ohrds n He completed hs PhD thess Computer Aded Evaluaton of Machne Relablty n In 2009 he completes hs D.Sc. thess on Quanttatve Measures of Informng Qualty. In ICTT Informa ( ) Dr. Chrstozov was nvolved n establshng the natonal nformaton networ for technology transfer and conducted research n the areas of technologes assessment, ntegral qualty measures and nformaton systems for qualty management. In these areas he was recognzed as one of the leadng experts n Bulgara. Professor Chrstozov has more than 80 publcatons as separate volume, ournal papers and papers n refereed proceedngs. He s a foundng member of Informng Scence Insttute and char of Bulgaran Informng Scence Socety; and foundng member of the Bulgaran Statstcal Socety. Dr. Stefana Chuova s an Assocate Professor n Operatons Research at the School of Mathematcs, Statstcs and Operaton Research, Vctora Unversty of Wellngton, Prvate Bag 600, Wellngton, New Zealand, e-mal: schuova@msor.vuw.ac.nz. She has a PhD and MSc n Mathematcs (concentraton n Probablty and Statstcs) and BSc n Mathematcs from Unversty of Sofa, Sofa, Bulgara. Her research nterests are n appled stochastc models, warranty analyss, relablty and queung. She has more than 80 publcatons and has presented papers at natonal and nternatonal conferences. Dr. Plamen Mateev s Assocate Professor n Faculty of Mathematcs and Informatcs, Sofa Unversty "St.Klment Ohrds", Department "Probablty, Operaton Research, Statstcs", Bulgara, 1164 Sofa, 5, J.Boucher str., e-mal: pmat@fm.un-sofa.bg. Hs MSc n Mathematcal Statstcs s from Sofa Unversty and hs PhD s from Moscow State Unversty. The research nterests are n communcaton theory, appled statstcs, statstcal software and applcatons. More than 70 papers are publshed n scentfc ournals and proceedngs of scentfc conferences. He was the Char of Bulgaran Statstcal Socety and member of ENBIS and Bulgaran Informng Scence Socety. 265