Guide To Exploring Data Guide To Analyzing Data
NotesRegression and Survival AnalysisTyler MooreComputer Science & Engineering Department, SMU, Dallas, TXLecture 15–16Guide to exploring dataNotesType of DataExplorationRByExone way t-test, Wilcoxon test6.3–prop.test3.16.2anova, Permutation2-way t, Wilcoxon test, Perm.106.4χ2 test3.2–3.50.00.40.8ecdf(br logbreach)Fn(x)Statistics 0 2 4 6 80x2468log(#records breached)04008001 numerical variableCARDHACK1 categorical variable# categories 2PHYSSTAT1 categorical, 1 numerical# categories 2246 TRUEBreach type FALSE8 0log(#records breached)–BSF EDU0Organization Type2468log(#records BSOBSREDUGOVMEDNGO2 categorical variables2 / 71Guide to analyzing dataNotesAfter visual exploration and any descriptive statistics, you maywant to investigate relationships between variables morecloselyIn particular, you can investigate how one or more explanatory(aka independent) variables influences response (akadependent) variablesStatistical MethodResponse VariableExplanatory VariableOdds ratiosLinear regressionLogistic regressionSurvival analysisBinary (case/control)NumericalBinaryTime to eventCategorical variables (1 at a time)One or more variables (numerical or categorical)One or more variables (numerical or categorical)One or more variables (numerical or categorical)3 / 71Linear regressionNotesSuppose the values of a numerical variable Y depend on thevalues of another variable X .Y c0 c1 X If that dependence is linear then we can use linear regressionto estimate the best-fit values of the constants c0 and c1 thatminimize the error values for all the values yi Y .For more info see “R by Example” Ch. 7.1–7.34 / 71
NotesWhy?5 / 71NotesNotesNotes
Dataset for linear regression exampleNotesSuppose you hypothesize that the popularity of a CMSplatform influences the number of exploits made availableWe can use linear regression to test for such a bloggerconcrete5contaodatalife enginediscuzdrupal3.50.10.21.51.37.210113812Code: http://lyle.smu.edu/ tylerm/courses/econsec/code/exregress.RData: http://lyle.smu.edu/ tylerm/courses/econsec/data/eims.csv9 / 71Scatter plotNotes400marExp numExploits600800 200 0 01000000020000000300000004000000050000000marExp numServersplot(y marExp numExploits,x marExp numServers)10 / 71Scatter plot (log-transformed)500 1000Notes 100 50 10marExp numExploits 5 1 100000 50000020000001000000050000000marExp numServersplot(y marExp numExploits,x marExp numServers,log ’xy’)11 / 71Linear regressionNotes reg - lm(lgExploits lgServers, data marExp2) summary(reg)Call:lm(formula lgExploits lgServers, data marExp2)Residuals:Min1Q Median-2.9692 -1.0655 -0.60133Q0.5555Max5.4554Coefficients:Estimate Std. Error t value Pr( t )(Intercept) -9.40673.1924 -2.947 0.006280 **lgServers0.63040.16813.750 0.000784 ***--Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.11Residual standard error: 2.091 on 29 degrees of freedomMultiple R-squared: 0.3266, Adjusted R-squared: 0.3034F-statistic: 14.07 on 1 and 29 DF, p-value: 0.000784212 / 71
Best-fit linear regression10Notes joomla6phpnuke xoops vbulletin mybb4lg(# exploits available per CMS)8 wordpress blogger discuztypo3 cms made simplevivvo drupalsharepoint2 engineez publish datalife php link directoryspipdotnetnuke 0 typepadepiserversupesite ip.boarducozprestashopmediawiki18202224lg(# Servers per CMS)plot(y marExp2 lgExploits, x marExp2 lgServers,xlab "lg(# Servers per CMS)",ylab "lg(# exploits available per CMS)",)text(x marExp2 lgServers, y marExp2 lgExploits - 0.3,lab marExp2 generatorType)abline(reg coef)13 / 71Illicit online pharmaciesNotesWhat do illicit online pharmacies have to do with phishing?Both make use of a similar criminal supply chain12345Traffic: hijack web search results (or send email spam)Host: compromise a high-ranking server to redirect topharmacyHook: affiliate programs let criminals set up websitefront-ends to sell drugsMonetize: sell drugs ordered by consumersCash out: no need to hire mules, just take credit cards!For more: http://lyle.smu.edu/ tylerm/usenix11.pdf14 / 71Case-control study: search-redirection attacksNotesPopulation:pharma searchresultsCase: Searchredirection attackExposed:.EDU TLDsNot Exposed:Other TLDsPresentPastControl: NoredirectionExposed:.EDU TLDsNot Exposed:Other TLDs15 / 71Case-control study: search-redirection attacksNotesR code: http://lyle.smu.edu/ tylerm/courses/econsec/code/pharmaOdds.RData 32011-11-032011-11-032011-11-032011-11-03Search BingBingbingBingBingSearch seoverdoseoverdosePos. hoo.com/question/index?qid x?qid l-20- mg-of-ambien- wers.yahoo.com/question/index?qid g.meambiendosage.netRedirects? other.NET16 / 71
Guide to analyzing dataNotesAfter visual exploration and any descriptive statistics, you maywant to investigate relationships between variables morecloselyIn particular, you can investigate how one or more explanatory(aka independent) variables influences response (akadependent) variablesStatistical MethodResponse VariableExplanatory VariableOdds ratiosLinear regressionLogistic regressionSurvival analysisBinary (case/control)NumericalBinaryTime to eventCategorical variables (1 at a time)One or more variables (numerical or categorical)One or more variables (numerical or categorical)One or more variables (numerical or categorical)17 / 71Odds ratios for case-control studyNotes library(epitools) pr.tldodds -oddsratio(pr tld,pr redirects,verbose T) pr.tldodds measureodds ratio with 95% C.I.Predictor estimatelowerupper.COM 1.0000000NANA.EDU 5.8390966 5.5363269 6.1591917.GOV 0.4311855 0.3064817 0.5882604.NET 0.5946029 0.5568593 0.6342355.ORG 2.8811488 2.7971838 2.9674615other 1.3437113 1.2809207 1.409066918 / 71Odds ratios for case-control studyNotes pr.tldodds p.valuetwo-sidedPredictormidp.exact.COMNA.EDU 0.000000000000000.GOV 0.000000009212499.NET 0.000000000000000.ORG 0.000000000000000other MNA.EDU 00000000000000000000.GOV 36342908442020416260.NET 00000000000003109266.ORG 00000000000000000000other OMNA.EDU 000000000000.GOV 959159977734.NET 000000017562.ORG 000000000000other 347442976835 19 / 71A word on odds ratiosNotesDefining oddsSuppose we have an event with two possible outcomes:success (S)and failure (S̄)The probability of each occurring happens with ps andpS̄ 1 ps .psThe odds of the event are given by 1 psDefining odds ratiosSuppose now there are two events A and B, both of which canoccur (with probabilities pA and pB ).odd’s ratio odds(A)odds(B) pA1 pApB1 pB pA (1 pB )(1 pA ) pB20 / 71
Odds ratio exampleNotesAdapted htmSuppose that 7 of 10 male applicants to engineering schoolare admitted, compared to 4 of 10 female applicantspmale acc. 0.7, pmale rej. 1 0.7 0.3pfemale acc. 0.4, pfemale rej. 1 0.4 0.6podds(male acc.) 0.70.3 2.33podds(female acc.) 0.40.6 0.6672.33OR 0.667 3.5Hence, we can say that the odds of a male applicant beingadmitted are 3.5 times stronger than for a female applicant.21 / 71Back to the case-control study: how to interpret the oddsratios?Notes library(epitools) pr.tldodds -oddsratio(pr tld,pr redirects,verbose T) pr.tldodds measureodds ratio with 95% C.I.Predictor estimatelowerupper.COM 1.0000000NANA.EDU 5.8390966 5.5363269 6.1591917.GOV 0.4311855 0.3064817 0.5882604.NET 0.5946029 0.5568593 0.6342355.ORG 2.8811488 2.7971838 2.9674615other 1.3437113 1.2809207 1.409066922 / 71Guide to analyzing dataNotesAfter visual exploration and any descriptive statistics, you maywant to investigate relationships between variables morecloselyIn particular, you can investigate how one or more explanatory(aka independent) variables influences response (akadependent) variablesStatistical MethodResponse VariableExplanatory VariableOdds ratiosLinear regressionLogistic regressionSurvival analysisBinary (case/control)NumericalBinaryTime to eventCategorical variables (1 at a time)One or more variables (numerical or categorical)One or more variables (numerical or categorical)One or more variables (numerical or categorical)23 / 71Logistic regressionNotesSuppose we wanted to examine how a numerical variable(e.g., position in search results) affects a binary responsevariable (e.g., whether the URL redirects or not)We can’t use the odds ratios from case-control studiesbecause that requires a categorical variableSuppose that we’d also like to examine how both position insearch results and TLD affect whether a URL redirectsFor these cases, we need a logistic regressionlogp c0 c1 x1 c2 x2 1 pSo for the example above considering position and TLD:logpredir c0 c1 Position1 c2 TLD2 1 predir24 / 71
Logistic regression in actionNotesCode: http://lyle.smu.edu/ tylerm/courses/econsec/code/pharmaLogit.R pr.logit - glm(redirects tld, data pr, family binomial(link "logit")) summary(pr.logit)Call:glm(formula redirects tld, family binomial(link "logit"),data pr)Deviance Residuals:Min1QMedian-1.1476 -0.5442 -0.54423Q-0.5442Max2.3438Coefficients:Estimate Std. Error z value(Intercept) -1.8351650.008626 -212.75 tld.EDU1.7645950.02715964.97 165 -15.68 tld.ORG1.0581950.01507970.18 tldother0.2953900.02432312.14 --Signif. codes: 0 *** 0.001 ** 0.01 * 0.05Pr( z 02. 0.1******************125 / 71(Dispersion parameter for binomial family taken to be 1)Null regressiondeviance: 165287on 175794(ctd.)degrees of freedomLogisticin actionResidual deviance: 156797AIC: 156809on 175789Notesdegrees of freedomNumber of Fisher Scoring iterations: 4 NagelkerkeR2(pr.logit)(Dispersion parameter for binomial family taken to be 1) N[1] 175795Null deviance: 165287Residual deviance: 156797 R2AIC:156809[1] 0.07736148on 175794on 175789degrees of freedomdegrees of freedomNumber of Fisher Scoring iterations: 4 NagelkerkeR2(pr.logit) N[1] 175795 R2[1] 0.0773614826 / 71Obtaining the odds ratiosNotesRecall the logistic regression equationp c0 c1 x1 c2 x2 log1 pExponentiate coefficients to get interpretable odds ratios ORG-1.83516541.7645946 -0.8451420 -0.51999591.0581945 #get odds ratios for the coefficients plus 95% CI exp(cbind(OR coef(pr.logit), confint(pr.logit)))Waiting for profiling to be done.OR2.5 %97.5 %(Intercept) 0.1595871 0.1569062 0.1623025tld.EDU5.8392049 5.5364431 6.1584001tld.GOV0.4294964 0.3053796 0.5858515tld.NET0.5945230 0.5568118 0.6341472tld.ORG2.8811645 2.7972246 2.9675454tldother1.3436501 1.2808599 1.4090019tldother0.295389827 / 71Logistic regression #2: TLD and search result positionNotes pr.logit2 - glm(redirects tld resultPosition, data pr, family binomial(link "logit")) summary(pr.logit2)Call:glm(formula redirects tld resultPosition, family binomial(link "logit"),data pr)Deviance Residuals:Min1QMedian-1.2680 -0.5968 -0.53553Q-0.4757Max2.4268Coefficients:Estimate Std. Error z valuePr( z )(Intercept)-2.140120.01497 -142.920 0.0000000000000002tld.EDU1.773550.0272665.072 0000402tld.NET-0.531210.03321 -15.993 0.0000000000000002tld.ORG1.051850.0151269.587 0.0000000000000002tldother0.300330.0243712.322 0.0000000000000002resultPosition 0.018030.0007025.762 0.0000000000000002--Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.11(Dispersion parameter for binomial family taken to be 1)*********************28 / 71
Logistic regression #2: TLD and search result positionNotes exp(cbind(OR coef(pr.logit2), confint(pr.logit2)))Waiting for profiling to be done.NagelkerkeR2(pr.logit2) #compute pseudo R 2 on logistic regressionOR2.5 %(Intercept)0.1176407 0.1142316tld.EDU5.8917404 5.5852012tld.GOV0.4314497 0.3067092tld.NET0.5878939 0.5505610tld.ORG2.8629455 2.7793345tldother1.3503082 1.2870831resultPosition 1.0181977 1.0168021 NagelkerkeR2(pr.logit2) #compute N[1] 17579597.5 612261.0195962pseudo R 2 on logistic regression R2[1] 0.0832934129 / 71Logistic regression #3: TLD, position, search engineNotes pr.logit3 - glm(redirects tld resultPosition searchEngine, data pr, family binomial(link "logit")) summary(pr.logit3)Call:glm(formula redirects tld resultPosition searchEngine,family binomial(link "logit"), data pr)Deviance Residuals:Min1QMedian-1.3270 -0.6539 -0.48123Q-0.3956Max2.5988Coefficients:Estimate Std. Error z value(Intercept)-2.5813149 0.0172986 -149.221tld.EDU1.5001887 0.027777654.007tld.GOV-0.8537354 0.1666852-5.122tld.NET-0.4290936 0.0335099 -12.805tld.ORG0.9098682 0.015435858.945tldother0.3191095 0.024674612.933resultPosition0.0185985 0.000708126.265searchEnginegoogle 0.8310798 0.013737560.497--Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1Pr( z ) 0.0000000000000002 *** 0.0000000000000002 ***0.000000303 *** 0.0000000000000002 *** 0.0000000000000002 *** 0.0000000000000002 *** 0.0000000000000002 *** 0.0000000000000002 ***1(Dispersion parameter for binomial family taken to be 1)30 / 71Null deviance: 165287Residual deviance: 152322AIC: 152338on 175794on 175787degrees of freedomdegrees of freedomLogistic regression #3: TLD, position, search engineNotesNumber of Fisher Scoring iterations: 5 exp(cbind(OR coef(pr.logit3), confint(pr.logit3)))Waiting for profiling to be done.OR2.5 %97.5 %(Intercept)0.07567444 0.0731465 0.07827858tld.EDU4.48253465 4.2449618 4.73330372tld.GOV0.42582135 0.3022669 0.58201442tld.NET0.65109897 0.6094052 0.69495871tld.ORG2.48399513 2.4099342 2.56025578tldother1.37590197 1.3107099 1.44382462resultPosition1.01877252 1.0173601 1.02018796searchEnginegoogle 2.29579645 2.2348606 2.35850810 NagelkerkeR2(pr.logit3) #compute pseudo R 2 on logistic regression N[1] 175795 R2[1] 0.116654631 / 71Guide to analyzing dataNotesAfter visual exploration and any descriptive statistics, you maywant to investigate relationships between variables morecloselyIn particular, you can investigate how one or more explanatory(aka independent) variables influences response (akadependent) variablesStatistical MethodResponse VariableExplanatory VariableOdds ratiosLinear regressionLogistic regressionSurvival analysisBinary (case/control)NumericalBinaryTime to eventCategorical variables (1 at a time)One or more variables (numerical or categorical)One or more variables (numerical or categorical)One or more variables (numerical or categorical)32 / 71
Survival ectionreportedremovedtime33 / 71Censored data happens a lotNotesReal-world situationsLife-expectancyCriminal recidivism ratesCybercrime applicationsMeasuring time to remove X (where X malware, phishing,scam website, . . . )Measuring time to compromiseMeasuring time to re-infectionBest resource I found on survival analysis in urvival-analysis.pdf34 / 71Survival analysis (package survival in R)NotesKey challenge: estimating probability of survival when somedata points survive at the end of the measurementSolution: use the Kaplan-Meier estimator to computeprobabilities that account for samples still alive (survfit in R)Common question: Are survival functions split overcategorical variables statistically differentUse the log-rank test (survdiff in R)Analagous to χ2 testCox-proportional hazard model (coxph in R) is a moresophisticated way to see how multiple variables affect thehazard rateHazard function h(t): expected number of failures during thetime period t35 / 71Pharmacy redirection duration by TLDNotes1.0Survival function for search results (TLD)0.20.4S(t)0.60.8all95% CI.COM.ORG.EDU.NETother050100150200t days source infection remains in search results36 / 71
Pharmacy redirection duration by PageRankNotes1.0Survival function for search results (PageRank)0.20.4S(t)0.60.8all95% CIPR 70 PR 7PR 0050100150200t days source infection remains in search results37 / 71Statistics disentangle effect of TLD, PageRank on durationNotesCox-proportional hazard modelh(t) exp(α PageRankx1 TLDx2 )PageRank.edu.net.orgother 71.11.11.4Std. Err.)0.00940.0840.0810.0520.053Significancep 0.001p 0.001p 0.001log-rank test: Q 159.6, p 0.00138 / 71Phishing website recompromiseNotesFull paper: http://lyle.smu.edu/ tylerm/cs81.pdfWhat constitutes recompromise?If one attacker loads two phishing websites on the same servera few hours apart, we classify it as one compromiseIf the phishing pages are placed into different directories, it ismore likely two distinct compromisesFor simplicity, we define website recompromise as distinctattacks on the same host occurring 7 days apart83% of phishing websites with recompromises 7 days apartare placed in different directories on the server39 / 71The WebalizerNotesWeb page usage statistics aresometimes set up by default in aworld-readable stateWe automatically checked allsites reported to our feeds for theWebalizer package, revealing over2 486 sites from June2007–March 20081 320 (53%) recorded searchterms obtained from ‘Referrer’header in the HTTP requestUsing these logs, we candetermine whether a host used forphishing had been discoveredusing targeted search40 / 71
Types of evil searchNotesVulnerability searches: phpizabi v0.848b c1 hfp1(unrestricted file upload vuln.), inurl: com juser (arbitraryPHP execution vuln.)Compromise searches: allintitle:welcome paypalShell searches: intitle: ’’index of’’ r57.php,c99shell drwxrwxSearch typeAny evil searchVulnerability searchCompromise searchShell searchWebsites2041265647Phrases45620699151Visits1 20758226536041 / 71One phishing website compromised using evil searchNotes42 / 71One phishing website compromised using evil searchNotes1: 2007-11-30 10:31:33 phishing URL reported: b.co.uk/lloyds tsb/logon.ibc.html2: 2007-11-30no evil search term0 hits3: 2007-12-01no evil search term0 hits4: 2007-12-02phpizabi v0.415b r31 hit5: 2007-12-03phpizabi v0.415b r31 hit6: 2007-12-04 21:14:06 phishing URL reported: ine banking/index.html7: 2007-12-04phpizabi v0.415b r31 hit43 / 71Let’s work with the dataNotesR code: http://lyle.smu.edu/ tylerm/courses/econsec/code/surviveEvil2.RData format:TLD 1st Compromise 2nd Compromise # days Censored Evil ETRUETRUETRUETRUETRUETRUE44 / 71
Step 1: Create a survival objectNotes#Remember the definition of censored# 0 has not been recompromised# 1 has been recompromised head(webzlt)dom startdateenddate lt censored hasevil tld1 com 2008-01-28 2008-03-31 630TRUE com2 com 2007-11-23 2008-03-31 1290TRUE com3 IP 2008-01-16 2008-03-31 750TRUE IP4 com 2008-01-16 2008-03-31 750TRUE com5 com 2007-10-28 2007-11-0681TRUE com6 com 2008-01-20 2008-03-31 710TRUE com S.all -Surv(time webzlt lt,event webzlt censor,type ’right’)45 / 71Working with survival objectsNotes1Empirically estimate survival probability overallSupply survfit with a constant right-hand side formulaE.g.:surv.all -survfit(S.all 1)2Empirically estimate survival probability compared to singlecategorical variableSupply survfit with a constant categorical variable inright-hand side of formulaE.g.:survfit(S.all webzlt hasevil)3Regression with survival probability as response variableSupply survfit with a constant categorical variable inright-hand side of formulaE.g.:coxph( S.all webzlt hasevil, method "breslow")46 / 71#1: Empirically estimate survival probability overallNotes1.00.90.80.70.60.50.4S(t): probability website has not been recompromised within t daysSurvival function for phishing websites050100150t days before recompromiseS.all -Surv(time webzlt lt,event webzlt censor,type ’right’)surv.all -survfit(S.all 1)plot(surv.all,xlab ’t days before recompromise’,ylab ’S(t): probability website has not been recompromised within t days’,ylim c(0.4,1), main ’Survival function for phishing websites’,lwd 1.5)47 / 71#2: Emp. estimate survival prob. for 1 cat. var.Notes1.0Survival function for phishing websites0.70.40.50.6S(t)0.80.9has evil termsno evil terms050100150t days before recompromiseS.all -Surv(time webzlt lt,event webzlt censor,type ’right’)surv.evil -survfit(S.all webzlt hasevil)plot(surv.evil,xlab ’t days before recompromise’,ylab ’S(t)’,ylim c(0.4,1), lwd 1.5,col c(’blue’,’red’),main ’Survival function for phishing websites’)legend("topright",legend c("has evil terms","no evil terms"),col c("red","blue"),lty 1)48 / 71
#2: Emp. estimate survival prob. for 1 cat. var.NotesIs the difference between survival probabilities acrosscategories statistically significant? survdiff(S.all webzlt hasevil)Call:survdiff(formula S.all webzlt hasevil)N Observed Expected (O-E) 2/E (O-E) 2/Vwebzlt hasevil FALSE 746140156.71.7913.4webzlt hasevil TRUE 1214124.311.5513.4Chisq 13.4on 1 degrees of freedom, p 0.00024949 / 71#3: Regression with survival prob. as response variableNotesS.all -Surv(time webzlt lt,event webzlt censor,type ’right’)evil.ph - coxph( S.all webzlt hasevil, method "breslow")summary(evil.ph) summary(evil.ph)Call:coxph(formula Surv(webzlt lt, webzlt censor) webzlt hasevil,method "breslow")n 867, number of events 181coef exp(coef) se(coef)z Pr( z )webzlt hasevilTRUE 0.63931.89510.1778 3.595 0.000325 ***--Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.11webzlt hasevilTRUEexp(coef) exp(-coef) lower .95 upper .951.8950.52771.3372.685Concordance 0.539 (se 0.013 )Rsquare 0.013(max possible 0.932 )Likelihood ratio test 11.43 on 1 df,Wald test 12.92 on 1 df,Score (logrank) test 13.37 on 1 df,p 0.0007219p 0.0003246p 0.00025650 / 71One more survival example: Bitcoin currency exchangesNotesBitcoin is a digital crypto-currencyDecentralization is a key feature of Bitcoin’s designYet an extensive ecosystem of 3rd-party intermediaries nowsupports Bitcoin transactions: currency exchanges, escrowservices, online wallets, mining pools, investment services, . . .Most risk Bitcoin holders face stems from interacting withthese intermediaries, who act as de facto central authoritiesWe focus on risk posed by failures of currency exchangesR code: http://lyle.smu.edu/ tylerm/data/bitcoin/bitcoinExScript.R51 / 71Notes
NotesNotesNotesNotes
NotesData collection methodologyNotesData sources123Daily transaction volume data on 40 exchanges converting into33 currencies from bitcoincharts.comChecked for closure, mention of security breaches and whetherinvestors were repaid on Bitcoin Wiki and forumsTo assess impact of pressure from financial regulators, weidentified each exchange’s country of incorporation and used aWorld Bank index on compliance with anti-money launderingregulationsKey measure: exchange lifetimeTime difference between first and last observed tradeWe deem an exchange closed if no transactions are observed atleast 2 weeks before data collection finished58 / 71Some initial summary statisticsNotes40 Bitcoin currency exchanges opened since 201018 have subsequently closed (45% failure rate)Median lifetime is 381 days45% of closed exchanges did not reimburse customers9 exchanges were breached (5 closed)59 / 7118 closed Bitcoin currency exchangesNotesExchangeOriginDates BitCoins.comBitchange.plBrasil Bitcoin MarketAqoinGlobal Bitcoin ExchangeBitcoin2CashTradeHillWorld Bitcoin ExchangeRuxumbtctreebtcex.comIMCEX.comCrypto X NRUSCAUPL4/10 – 6/114/11 – 8/118/11 – 9/116/11 – 10/116/11 – 10/118/11 – 10/119/11 – 11/119/11 – 11/119/11 – 1/124/11 - 1/126/11 - 2/128/11 – 2/126/11 – 4/125/12 – 7/129/10 – 7/127/11 – 10/1211/11 – 11/124/11 – 12/12Daily 727.934.334.325.734.329.227.711.925.721.760 / 71
22 open Bitcoin currency exchangesNotesExchangeOriginDates ActiveDaily vol.bitNZICBIT Stock ExchangeWeExchangeVircurexbtc-e.comMercado BitcoinCanadian Virtual Bitcoin CentralMt. GoxBitcurexKapitonbitstampInterSangoBitfloorCamp BXThe Rock Trading SESLUKUSUSUSUSSG9/11 – pres.3/12 – pres.10/11 – pres.12/11 – pres.8/11 – pres.7/11 – pres.6/11 – pres.6/11 – pres.5/12 – pres.4/11 – pres.8/11 – pres.1/11 – pres.7/10 – pres.7/12 – pres.4/12 – pres.9/11 – pres.7/11 – pres.5/12 – pres.7/11 – pres.6/11 – pres.7/12 – pres.1/13 – 721.727.035.335.334.334.334.334.333.761 / 71What factors affect whether an exchange closes?NotesWe hypothesize three variables affect survival time for aBitcoin exchange123Average daily transaction volume (positive)Experiencing security breach (negative)AML/CFT compliance (negative)Since lifetimes are censored, we construct a Cox proportionalhazards
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