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[]
[null,null,null,null,null,null,null,null,"Hubbard Decision Research\n2S410 Canterbury Ct\nGlen Ellyn, IL 60137\nwww.hubbardresearch.com"]
[]
[]
[null,null,null,null,"Table of Contents for Additional Simulation Examples"]
[]
[null,null,null,null,"1) Examples of Distributions from Chapter 9\n2) Capital investment Monte Carlo Example from Chapter 10\n3) Power Law Example from Chapter 10\n4) Correlation in Data and R Squared from Chapter 10 and 12\n5) HDR PRNG Chapter 13"]

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["Examples of Distributions (Chapter 9)"]
[null,"Hubbard Decision Research","These are the calculations for Appendix A: Selected Distributions.  There are several useful random distributions here that apply to a variety of different cybersecurity risks.  The Binary (aka Bernoulli) produces a \"1\" or \"0\" (which can be used as \"event occurred\" or \"event didn't occur\").  It applies to whether a security event such as a data breach occurred on the first place.  The other distributions are more appropriate for types of impacts that result after an event occurs - such as a system outage, a number of records compromised, the costs of legal liabilities, and so on. Yellow cells are for user inputs to define the distribution.  If you want to simply copy the formula for another sheet, use the formula in the \"Random Result\" cell.  NOTE: The formula for the triangular was wrong in the book!  The formula was incorrectly transcribed in the first place and then a last minute change before printing was incorrectly applied to such an extent that what was left was unrecognizable as anything like the triangular distribution.  The formula below, however, is correct."]
[null,"www.hubbardresearch.com"]
[null,"info@hubbardresearch.com"]
["Trial ID Slider"]
[4998]
["Triangular (CORRECTED!)"]
["Bin Size",10,null,null,null,null,"For a triangular distribution, the UB and LB represent absolute limits. There is no chance that a value could be generated outside of these bounds. In addition to the UB and LB, this distribution also has a mode that can vary to any value between the UB and LB. This is sometimes useful as a substitute for a lognormal, when you want to set absolute limits on what the values can be but you want to skew the output in a way similar to the lognormal. It is useful in any situation where you know of absolute limits but the most likely value might not be in the middle, like the normal distribution.\n \n■■When to Use: When you want control over where the most likely value is compared to the range, and when the range has absolute limits.\n■■ Examples: Number of records lost if you think the most likely number is near the top of the range and yet you have a finite number of records you know cannot be exceeded.\n■■ Mean: =(LB+Mode+UB)/3"]
["Var ID",10000]
["HDR PRNG",{"$f":"(MOD((MOD(MOD(999999999999989,MOD($A$6*9929+$B$9*9721,31907)*4177+7450581)*30119,31607)*31607+MOD(MOD(997969999999967,MOD($A$6*9857+$B$9*9949,33493)*4051+7450581)*29633,31607))*1000981,4294967296)+0.5)/4294967296","v":7.5588156119920313E-2}]
["Random Result",{"$f":"IF(B10<(B14-B12)/(B13-B12),B12+SQRT(B10)*(B14-B12),B13-SQRT(B10)*(B13-B14))","v":1.5498660059320646}]
["Lower Bound",1]
["Upper Bound",4]
["Mode",3]
[]
["Binary"]
["Bin Size",0.1,null,null,null,null,"Unlike the other distributions mentioned here, a discrete binary distribution (also known as a Bernoulli distribution) generates just two possible outcomes: success or failure. The probability of success is p and the probability of failure is q = (1 – p). For example, if success means to flip a fair coin heads‐up, the probability of success is p = .5, and the probability of failure is q = (1 – .5) = .5.\n\n■■ When to use: This is used in either/or situations—something either happens or it doesn’t.\n■■ Example: The occurrence of a data breach in a given period of time.\n■■ Mean: =P"]
["Var ID",20000]
["HDR PRNG",{"$f":"(MOD((MOD(MOD(999999999999989,MOD($A$6*9929+$B$18*9721,31907)*4177+7450581)*30119,31607)*31607+MOD(MOD(997969999999967,MOD($A$6*9857+$B$18*9949,33493)*4051+7450581)*29633,31607))*1000981,4294967296)+0.5)/4294967296","v":0.72061247320380062}]
["Random Result",{"$f":"IF(B19<B21,1,0)","v":0}]
["Probability",0.2]
["Complement",{"$f":"1-B21","v":0.8}]
[]
["Normal"]
["Bin Size",3,null,null,null,null,"A normal (or Gaussian) distribution is a bell‐shaped curve that is symmetrically distributed about the mean. Many natural phenomenon follow this distribution but in some applications it will underestimate the probability of extreme events.\n\n■■ When to Use: When there is equal probability of observing a result above or below the mean.\n■■ Examples: Test scores, travel time.\n■■ Mean: =(UB + LB)/2"]
["Var ID",30000]
["HDR PRNG",{"$f":"(MOD((MOD(MOD(999999999999989,MOD(A6*9929+B26*9721,31907)*4177+7450581)*30119,31607)*31607+MOD(MOD(997969999999967,MOD(A6*9857+ B26*9949,33493)*4051+7450581)*29633,31607))*1000981,4294967296)+0.5)/4294967296","v":0.52593696455005556}]
["Random Result",{"$f":"_xlfn.NORM.INV(B27,(B30+B29)/2,(B30-B29)/3.29)","v":1519.775136076255}]
["Lower Bound",1000]
["Upper Bound",2000]
[]
["Lognormal"]
["Bin Size",10,null,null,null,null,"The lognormal distribution is an often preferred alternative to the normal distribution when a sample can only take positive values. It also allows for the possibility of extreme values on the upper end and, therefore, may fit some phenomena better than a normal. \n\n■ When to Use: To model positive values that are primarily moderate in scope but have potential for rare extreme events.\n■ Examples: Losses incurred by a cyberattack, the cost of a project.\n■ Excel Formula: =lognorm.inv(rand(),(ln(UB) + ln(LB))/2, (ln(UB)‐ln(LB))/3.29)\n■ Mean: = ((ln(UB)+ln(LB))/2)"]
["Var ID",40000]
["HDR PRNG",{"$f":"(MOD((MOD(MOD(999999999999989,MOD(A6*9929+B34*9721,31907)*4177+7450581)*30119,31607)*31607+MOD(MOD(997969999999967,MOD(A6*9857+ B34*9949,33493)*4051+7450581)*29633,31607))*1000981,4294967296)+0.5)/4294967296","v":0.82298107037786394}]
["Random Result",{"$f":"_xlfn.LOGNORM.INV(B35,(LN(B38)+LN(B37))/2,(LN(B38)-LN(B37))/3.29)","v":351.87084323313582}]
["Lower Bound",100]
["Upper Bound",500]
[]
["Beta"]
["Bin Size",0.01,null,null,null,null,"Beta distributions are extremely versatile. They can be used to generate values between 0 and 1 but where some values are more likely than others. This result can also be used in other formulas to generate any range of values you like. They are particularly useful when modeling the frequency of an event, especially when the frequency is estimated based on random samples of a population or historical observations. In this distribution it is not quite as easy as in other distributions to determine the parameters based only on upper and lower bounds. The only solution is iteratively trying different “alpha” and “beta” values until you get the 90% CI you want. If alpha and beta are each greater than 1 and equal to each other, then it will be symmetrical, where values near .5 are the most likely and less likely further away from .5. The larger you make both alpha and beta, the narrower the distribution. If you make alpha larger than beta, the distribution will skew to the left, and if you make beta larger, it skews to the right.\n \n■■ When to Use: Any situation that can be characterized as a set of “hits” and “misses.” For each hit, increase alpha by 1. For each miss, increase beta by 1.\n■■ Examples: Frequency of an event (such as a data breach) when the frequency is less than 1 per time unit (e.g., year), the proportion of employees following a security procedure correctly."]
["Var ID",50000]
["HDR PRNG",{"$f":"(MOD((MOD(MOD(999999999999989,MOD(A6*9929+B42*9721,31907)*4177+7450581)*30119,31607)*31607+MOD(MOD(997969999999967,MOD(A6*9857+ B42*9949,33493)*4051+7450581)*29633,31607))*1000981,4294967296)+0.5)/4294967296","v":9.2320787836797535E-2}]
["Random Result",{"$f":"_xlfn.BETA.INV(B43,B45,B46)","v":9.2453108731258574E-2}]
["Alpha",3]
["Beta",10]
["5 Percentile",{"$f":"_xlfn.BETA.INV(0.05,B45,B46)","v":7.1870255542269806E-2}]
["95 Percentile",{"$f":"_xlfn.BETA.INV(0.95,B45,B46)","v":0.4381054351153113}]
[]
[]
["Power Law"]
["Bin Size",0.01,null,null,null,null,null,"The power law is a useful distribution for describing phenomena with extreme, catastrophic possibilities - even more than lognormal. The “fat tail” of the power law distribution allows us to acknowledge the common small event, while still accounting for more extreme possibilities.  In fact, sometimes this type of distribution may not always have a defined-mean because the tails goes out so far.  Be careful of producing unintended extreme results.  To keep this from producing unrealistic results, you might prefer to use the Truncated Power Law Below.  We show this distribution in a simple form which requires that you enter \"alpha\" and \"theta\" iteratively until you get the 90% Confidence Interval you want.\n\n■■ When to Use: When you want to make sure that catastrophic events, while rare, will be given nontrivial probabilities.\n■■ Examples: Phenomena like earthquakes, power outages, epidemics, and other types of “cascade failures” have this property."]
["Var ID",60000]
["HDR PRNG",{"$f":"(MOD((MOD(MOD(999999999999989,MOD(A6*9929+B53*9721,31907)*4177+7450581)*30119,31607)*31607+MOD(MOD(997969999999967,MOD(A6*9857+ B53*9949,33493)*4051+7450581)*29633,31607))*1000981,4294967296)+0.5)/4294967296","v":3.6127750063315034E-3}]
["Random Result",{"$f":"(B57/B54)^B56","v":1.6455984235363919}]
["Alpha",0.15]
["Theta (Scale)",0.1]
["Computed 5 Percentile",{"$f":"(B57/(1-0.05))^B56","v":0.71341372328442154}]
["Computed 95 Percentile",{"$f":"(B57/(1-0.95))^B56","v":1.1095694720678448}]
["Max in 10k Scenarios",{"$f":"MAX(F78:F10077)","v":3.2607597849539722}]
[]
["Truncated Power Law"]
["Bin Size",0.01,null,null,null,null,"The truncated power law distribution is simply the power law distribution, but with an upper limit that is imposed by the user. While the heavy tail of the power law distribution allows us to account for the rare catastrophic event, there may be a theoretical bound to the size of such an event. If this upper limit is not factored into the model, we may produce a misleading and unnecessarily grim forecast.  As above, you need to enter values for alpha, theta and truncated percentile until you see 5 percentile, 95 percentile, and truncated value (the upper limit) that agrees with how you want to model this quantity.\n\n■■ When to Use: The power law distribution should be truncated if an upper bound on the severity of an event is known.\n■■ Example: Losses of records may follow a power law but you know you only have a finite number of records to lose. "]
["Var ID",70000]
["HDR PRNG",{"$f":"(MOD((MOD(MOD(999999999999989,MOD(A6*9929+B64*9721,31907)*4177+7450581)*30119,31607)*31607+MOD(MOD(997969999999967,MOD(A6*9857+ B64*9949,33493)*4051+7450581)*29633,31607))*1000981,4294967296)+0.5)/4294967296","v":2.3237221990711987E-2}]
["Random Result",{"$f":"(B68/(B65*B69+1-B69))^B67","v":1.0503450091032802}]
["Alpha ",0.15]
["Theta",0.1]
["Truncated Percentile",0.95]
["Computed 5 Percentile",{"$f":"(B68/((1-0.05)*B69+1-B69))^B67","v":0.71313253792361353}]
["Computed 95 Percentile",{"$f":"(B68/((1-0.95)*B69+1-B69))^B67","v":1.003804891488109}]
["Truncated Value",{"$f":"(B68/(1-B69))^B67","v":1.1095694720678448}]
[]
["Data Table for Distributions",null,null,null,null,null,null,null,"Data Table for Distributions"]
["Below was the Excel Data Table created to produce the distributions above.  There are 10,000 scenarios, so depending on your system performance, it may have taken a while to run.  To manage speed and file size, the data table was converted back to a fixed table of values.  If you would like to convert it back to a data table that dynamically generates the values, just go to the \"Data\" panel in Excel and then choose \"What If Analysis\"/\"Data Table.\"  See Excel help for instructions on creating data tables.",null,null,null,null,null,null,null,"Below is the histogram to create the distributions above based on the simulations in the table to the left.  If you change the table to the left back to a data table, these will change dynamically (but may take a while for each run)."]
[null,"Triangular","Normal","Log-Normal","Beta","Power Law","Truncated Power Law",null,null,"Triangular","Normal","Log-Normal","Beta","Power Law","Truncated Power Law"]
[null,{"$f":"B11","v":1.5498660059320646},{"$f":"B28","v":1519.775136076255},{"$f":"B36","v":351.87084323313582},{"$f":"B44","v":9.2453108731258574E-2},{"$f":"B55","v":1.6455984235363919},{"$f":"B66","v":1.0503450091032802}]
[1,2.5625096814174526,1152.8589829990508,197.11629838331584,0.20605354247146662,0.85478470958089559,0.7417914081754784,null,"Min",{"$f":"MIN(B78:B10077)","v":1.0260371393845933},{"$f":"MIN(C78:C10077)","v":437.58304277886828},25.989133840624998,7.8378190516327217E-3,0.70795239911554442,0.70794684194997082]
[2,3.8887034152567721,1597.1361014608717,156.0689778264879,0.17069037402624723,0.71003794571370393,1.0471574926957323,null,"Max",{"$f":"MAX(B78:B10077)","v":3.9855408415300277},{"$f":"MAX(C78:C10077)","v":2983.8649019559962},1570.9005619919085,0.74558895558183103,3.2607597849539722,1.1091970123380324]
[3,2.7452336755592301,1232.5787411339961,165.9754076308314,0.11270356685831825,0.74287041236625606,0.77512727010514149,null,"Increment",{"$f":"(J79-J78)/40","v":7.3987592553635864E-2},{"$f":"(K79-K78)/40","v":63.657046479428196},{"$f":"(L79-L78)/40","v":38.622785703782085},1.8443778413254959E-2,6.3820184645960704E-2,1.0031254259701538E-2]
[4,2.8238288579396826,1273.2883627018457,375.32417438106393,0.14074295135809972,0.74598062695270229,0.92217727885379619]
[5,2.1158669839767974,1395.0156177096758,173.6345540888862,0.28885708380595942,0.82595662420095917,0.79343201504666427,null,0,{"$f":"COUNTIFS(B$78:B$10077,\"<\"&(J$78+J$80*$I82+J$80/2),B$78:B$10077,\">=\"&(J$78+J$80*$I82-J$80/2))","v":5},1,7,12,2550,496]
[6,1.6164105070332631,1151.8440560182239,254.82086602433594,9.3792480002995268E-2,0.91167996551838704,0.89288192960272161,null,1,35,5,241,77,3136,896]
[7,3.3566329012534628,900.79521875304215,148.19440307859054,0.24238852196064453,0.74215778530626897,1.0891434655291665,null,2,56,6,839,154,1765,798]
[8,3.0627864879822422,1037.7319465989949,311.2953118242753,0.23528679518184648,0.76122376611192633,0.71836597919879663,null,3,56,14,1393,252,938,715]
[9,3.6841836776501227,1186.6714120321797,329.80013705033645,0.11959835614908432,0.72513233510438457,0.74834564638451306,null,4,80,17,1598,356,547,659]
[10,3.4601715251666132,1874.2871520463282,211.89091640612338,0.19144650443826203,0.75907041122047558,0.81641330670407819,null,5,83,38,1443,463,376,570]
[11,2.5461433846270594,1404.5678174134264,296.94081946027512,0.40092705749345248,0.72323934277622148,0.71157517619797805,null,6,125,60,1207,551,228,553]
[12,3.3862521920360504,1480.8724177373388,102.82528685716551,0.16645348966313217,0.78646616546615622,0.8785915271488437,null,7,132,107,900,641,141,483]
[13,2.8536701427637867,1897.5542113762774,236.68240736403931,0.28920955194781561,1.2713598757562601,0.74727870957298737,null,8,167,177,661,667,79,416]
[14,3.297531177329196,1152.5814571614901,290.64977715545888,0.20140528435418215,1.1328874937117392,0.81133099289367472,null,9,153,215,496,687,74,392]
[15,2.9391627208344371,1358.7902392281276,187.95095886165282,0.35755698920537904,0.72618357334112682,0.84578842464965043,null,10,199,307,354,692,36,345]
[16,1.3864134714786867,1402.6914829039592,336.16416559287717,0.28412561337247255,1.0350506697629704,1.0006305916633911,null,11,213,421,247,628,31,327]
[17,2.3318551824459988,1383.0885737142369,199.55195227818277,0.27274599432642765,0.79898350329116341,0.88091183580106436,null,12,248,516,176,603,17,284]
[18,2.9900523813648041,1169.7461294878442,190.90873650747182,0.10390847843602152,0.78896019595011369,0.77742609123454998,null,13,246,616,137,575,15,269]
[19,3.6645613930599694,1382.806222046223,155.02987001345466,0.49344980029435481,0.86435429295579014,0.77266501995862447,null,14,287,719,83,526,11,254]
[20,1.6344965367682054,1577.6347017952264,133.36698753922934,0.12361999476537068,1.0085125501463816,0.86875432293607013,null,15,297,824,57,484,14,273]
[21,3.26897200775882,1303.7722772532052,122.08626007324827,0.17869528122880443,0.75917313585515001,0.75833598296972404,null,16,300,827,46,397,9,234]
[22,2.8033657443539228,1138.800293802243,553.26744176130967,0.21196728084738317,1.1900455254754592,0.79191191657320126,null,17,307,797,33,401,7,183]
[23,2.7892306272577985,1504.1635176300181,216.94601587220717,0.22410319595512274,0.71397097105454521,0.89250009082153259,null,18,327,797,22,297,3,173]
[24,2.7263970531330735,2126.6943017552003,227.17384085434188,5.4994639139400843E-2,0.78001113333931094,0.74344510769470806,null,19,353,695,14,277,6,162]
[25,2.397597735347869,829.07377702109386,276.5186341278764,0.20670466132160958,0.76619946541847128,0.73156089872357921,null,20,376,680,6,248,2,133]
[26,2.9852643028744943,1720.6838052771725,204.58603572451824,0.19072270135822694,0.83661929440642901,0.76669725700614055,null,21,373,570,10,201,6,121]
[27,3.1150182760864906,1385.8817349201533,215.45881211542823,6.5580863862377492E-2,0.93394837715570977,0.74141673766017613,null,22,407,452,11,203,0,121]
[28,2.8083263800380802,1392.3081709925239,445.99081830887565,0.22638831164625739,0.7674740932815759,0.7969832919565174,null,23,416,348,1,108,2,128]
[29,2.7928334014241587,1592.4866769671621,240.62782186088108,0.19258222616674386,0.72578851420359236,0.8104126092379198,null,24,454,272,5,125,1,100]
[30,2.1719773971785932,1589.1674858344959,108.03203781337695,0.19143080464565437,0.71197867486826349,1.0312282320945487,null,25,449,172,3,91,0,104]
[31,2.9586056057973278,1531.7530277770556,146.63737439759575,0.57035340010524904,0.7098731889901414,0.81474895902810573,null,26,461,112,3,74,2,95]
[32,3.5084815521426478,2112.4081951112271,266.62259493780499,0.30707623707726417,0.70922879150419638,0.94197075579010259,null,27,496,106,1,50,1,93]
[33,3.7343518833485727,1640.4271793891801,175.57876166322475,0.31570155547059531,0.75590640795820374,0.72473781243417423,null,28,447,53,1,54,0,96]
[34,3.4983491635053214,1241.8628719708945,213.91987944417227,0.22187605005521793,0.75974714430377355,0.71099401286187958,null,29,383,36,1,31,0,55]
[35,3.0227299015862252,1026.0848855334052,391.71730396877831,0.22637690107386121,0.75130816915047838,0.79549685554363581,null,30,376,17,2,19,0,68]
[36,1.7569330748301812,1490.7360956125601,103.0461575857919,0.21578032103673128,0.73388217490424967,0.74375935337955179,null,31,337,13,1,19,0,66]
[37,3.4630725257663126,1642.1181648965473,86.836402651721912,0.22877844176784123,0.74387073422826677,0.72178763789888722,null,32,277,6,0,6,1,56]
[38,3.5816063714309783,1726.3772592272514,580.42319273919054,0.24563673298914523,0.73382017850311065,0.79103133796946024,null,33,243,0,0,14,0,47]
[39,1.154601071686183,1855.992132998213,153.56017461965124,0.39748788014593217,0.75197495765698308,0.7175284673164789,null,34,237,1,0,3,0,48]
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[1952,3.4816718193051464,1467.3226521940883,227.39572232667669,0.27604649689980743,0.90547992692147872,0.89536146223754531]
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[1969,2.5277293544507522,1443.6278648134098,104.44388803090931,0.10211918558131146,0.89021610795591322,0.72872746492455553]
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[1975,3.3616032569582974,1621.5276776312035,167.23223570296386,9.4935975903517544E-2,0.85777031775550638,0.7445637738979104]
[1976,2.4794604327363743,1543.0410366542924,189.51396178694179,0.21851091266296319,0.7654824057478955,0.75257175025044853]
[1977,1.7810736428104263,1484.264769822943,293.67329279899161,0.38817940807454832,0.85005811114331598,1.0387297585012882]
[1978,2.7501585481544151,970.11346737676661,228.69355655655451,0.33239220549415105,0.70892133672325031,0.7512662508960315]
[1979,2.614882687541888,1196.293911379518,234.95290420805759,0.13825414973587427,0.84401588054233989,0.75015617100676035]
[1980,2.4875052225787315,1908.7895746329616,257.38876598370246,0.35732418256898568,0.75563223191308049,0.71922427440349546]
[1981,2.5902975981693466,1523.8415179950939,301.69006000134954,0.24498979019747691,0.83663541145754516,0.76149381162188967]
[1982,1.8113063351582777,1721.8662909109471,232.49263580393418,0.27599215875446725,0.74574340681201612,0.9062179985825396]
[1983,2.8715803818652388,1289.2027107653917,101.62715287836133,0.13064277213168068,0.79035790848376319,0.82709327383465625]
[1984,2.3548329842830169,868.51180877758884,116.66301264126498,0.11662027625258474,0.76890148630559985,1.0097456480999969]
[1985,3.6671722187130387,1576.0168682108406,178.87003139815008,7.8146432754362061E-2,0.76889828857662135,0.74019072894430604]
[1986,2.6991052360833221,1347.0056863061648,320.10219891425413,0.13553146108107531,1.2354068250991039,0.77942684166611986]
[1987,2.8977593419870171,1655.0665862098454,240.22690948439478,0.35576905488175026,0.73708780768798565,0.78514844374134563]
[1988,2.6309091347384035,1616.2406694104129,91.287396755830883,0.30566498786742702,0.73549041999367015,0.76892814669210685]
[1989,3.8655547032064232,1183.7895327608501,146.79652616707534,0.14711893911278856,0.74895078383337221,0.88089294768607296]
[1990,2.3730591330994661,1711.6520848715215,367.70081027129186,0.1554230209075067,0.85107996805201869,0.71417855948102615]
[1991,1.6623535969237335,912.61638939875138,312.4512581653579,0.22889580853319358,0.71285341754503517,0.78243143882801502]
[1992,3.0307469468335553,1492.5880354626913,188.98594076273559,9.9722512058646934E-2,0.96657361315933554,0.79917724403597368]
[1993,1.4251207238424679,1563.1845972615001,212.70061780897223,0.21461700589700611,0.7398145676731368,0.73175731862379745]
[1994,3.6040340536753068,1769.5769969328828,389.68484011966837,0.15852630428585693,0.81338793677199051,0.82411320271186306]
[1995,3.8334292306067033,1732.9148751677474,97.778292810145928,0.13815644786820958,0.74203104022353583,0.72379929257100073]
[1996,2.6390381940143084,1450.8879631358714,372.32283612936044,0.18291086910713206,1.1675424437575339,0.83903389318168842]
[1997,2.8346084031273215,975.88986295918039,141.08621186306112,0.14334494125951996,0.72034002282209575,0.72192395455748659]
[1998,3.5613358707515737,1119.3312299669731,235.94368501808992,0.19700214226268903,0.75156047569709206,0.80393604807631769]
[1999,3.1065516460686595,1772.868100447422,509.9322795254659,0.11490951323034915,0.75341638899918462,0.71975969565453179]
[2000,2.8295702110846586,1669.6326686410598,264.03646379171278,0.23207270094824006,0.97279091874787249,0.79147154031360278]
[2001,2.5341718300608029,1771.9859990135055,159.86145341409309,0.17295694437254019,0.91232014884270529,0.74859862974538949]
[2002,3.4177688286956549,1341.478051364197,135.30935689252649,0.24150778074443846,0.75636453813539051,0.72253618413853626]
[2003,3.5604089392548386,1466.5312938199679,84.084526585373865,0.18445576505614603,0.91867256946962805,0.71205211615563802]
[2004,2.2730099753011523,1640.0916240390352,208.08958539825281,0.33201182094775039,1.0827119273122425,0.7133022585821196]
[2005,2.9469511597952365,1467.7636386736424,105.81384826279819,0.12198914781822048,1.0028189180652776,0.81037698398844005]
[2006,2.7892830899770682,1244.3565866498136,317.8425049785003,0.38025778876764571,0.7667007917477564,0.84586955191462021]
[2007,2.2162619901953562,1701.4723135196782,161.11156598261749,0.31144280910748079,0.75196386166741136,0.73987079917025045]
[2008,2.1873540377981513,1202.072241971679,325.57260990214371,0.4175163512836213,0.87315278558072751,0.70842361088561168]
[2009,2.6107404178721185,1635.1856067742247,128.82342495405504,0.22253840549722015,0.82604810395230399,0.72043891457620524]
[2010,2.9829262324795112,1597.242685394607,282.62964308117097,2.0950093635828421E-2,0.85134260687151364,0.72670136578037237]
[2011,3.6310962423304054,1436.667285938832,331.63584571252585,0.20125860482623717,0.72021036923381843,1.0039031478102689]
[2012,3.1916948744160778,2165.0248475195949,484.24911644694254,0.19854445812201907,0.72601415963905325,0.95941425787173695]
[2013,2.1927328668788393,1700.7870086658868,445.03093393409415,0.110500568436116,0.78040690275547009,0.75108876313100337]
[2014,1.985360440365862,1737.9262009635418,467.31670630231565,0.20401993217726749,0.71092844823499901,0.71220788141116187]
[2015,2.9976432636829351,1418.1649942321512,160.9327659441268,0.29182117185284617,0.71479098004886377,0.75069147047232199]
[2016,2.6570838243855341,1463.6668125060148,161.00656989018424,0.35642455723711486,0.80258343858266701,0.84103007490908999]
[2017,2.7749954738634939,1395.0355661822161,315.59113331591743,0.16348106182343608,0.82203416335543888,0.72504906037982975]
[2018,2.6184760189475895,1354.966168048569,236.51161763051621,0.1673228788175177,0.75754625437399958,0.89346818598271205]
[2019,2.9997307983090318,1958.7176246937051,231.93038863296619,0.27936735026480419,0.76926674389931338,0.71053956087159231]
[2020,3.2759219447894115,1778.7798159803838,220.95072882579632,0.16194859979337417,0.77086998688281994,0.74209846305544336]
[2021,2.5061839656121729,1472.7116943183357,264.55684661682409,0.45896590253798586,0.75217287038228386,0.81020861271130573]
[2022,1.5886592545547509,1108.0645061287037,198.07194729431757,0.30339664669539335,0.88709095363161194,0.78821617644933117]
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["Monte Carlo Example 1 (Chapter 10)"]
["This was the example of where we computed the risk of not saving enough money from new equipment to justify the lease.  If you have read my first book How to Measure Anything, this is similar to the Chapter 9 Example, but a little simpler and with a better \"dynamic\" histogram.  This runs 10,000 random scenarios.  Try holding down the F9 key to recalcuate the scenarios.  The histogram below and right will change slightly.  This is a very simple Monte Carlo example.  "]
["The annual lease.  Savings per year must be greater to breakeven.",null,null,null,null,null,1000000]
["Maximum Production Capacity",null,null,null,null,null,1250000]
["Chance that lease will be a net gain.",null,null,null,null,null,{"$f":"AVERAGE(H16:H10015)","v":0.85240000000000005}]
["The risk that the breakeven will not be met (the new machine lease is a loss)",null,null,null,null,null,{"$f":"1-G5","v":0.14759999999999995}]
[]
[null,null,null,"Units Demanded","Savings per units"]
["Upper Bound",null,null,1750000,2.5]
["Mean",null,null,1000000,2]
["Lower Bound",null,null,250000,1.5]
["Standard Deviation",null,null,{"$f":"(D9-D11)/3.29","v":455927.05167173251},{"$f":"(E9-E11)/3.29","v":0.303951367781155}]
["PRNG ->",200001,200002]
["Scenarios",null,null,null,null,null,null,null,null,null," Histogram"]
["Scenario #","Units Demanded Random Number","Savings Per Units Random Number","Units Demanded (this incorporates the contraint that demand can't be less than zero)","Actual Production (Given capacity constraint)","Savings per units","Savings ($ per year)","Breakeven met?",null,null,"Bin ($millions)","Cumulative Frequency","Bin Frequency","Cumulative Chance That Profit<Value on Horizontal Axis"]
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[9975,0.96411002345848829,0.20691076281946152,1820901.7734093787,1250000,1.7516148697393996,1189518.5871742493,1]
[9976,0.77857589989434928,0.87765321636106819,1349874.9893840244,1250000,2.3535972968320835,1941996.6210401044,1]
[9977,0.4971294739516452,0.63535618258174509,996719.42073966609,996719.42073966609,2.105189450354493,1098283.2095045862,1]
[9978,0.80808766430709511,0.77065607265103608,1397053.5817783829,1250000,2.2252307635912127,1781538.454489016,1]
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[9981,0.83786826755385846,0.53740956482943147,1449422.9780271347,1250000,2.0285439886755801,1535679.9858444752,1]
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[9985,0.96533941233064979,0.12034477794077247,1828109.7903332105,1250000,1.6433845005348364,1054230.6256685455,1]
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[{"$f":"A10001+1","v":9987},0.48414966173004359,0.11860616074409336,981880.83676953777,{"$f":"MIN(1250000,D10002)","v":981880.83676953777},1.6407345548325134,611005.81761564338,1]
[9988,5.3715708781965077E-2,0.58859741396736354,266027.52893660206,266027.52893660206,2.0680664077673896,-449837.4038648461,0]
[9989,0.21898406150285155,0.75904492975678295,646369.79592867021,646369.79592867021,2.2137488353692207,430900.38295493461,1]
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[10000,0.41006186266895384,0.69578540360089391,896328.64165548224,896328.64165548224,2.155719442714334,{"$f":"F10015*E10015-1000000","v":932233.07987845223},1]

{"sheet":"Correlations in Data","index":3,"n_rows":222,"n_cols":5,"rows_kept":222,"cut":false,"hidden":false,"merged":[[15,0,20,1],[1,0,2,4],[4,0,4,1],[5,0,5,1],[6,2,6,4],[7,0,14,1]]}
["Examples of Correlations in Hypothetical Data and R2 (Chapter 10 and 12)"]
["For the purpose of learning about some basic statistical concepts used later with actual data, these are examples of correlations between some hypothetical \"real world\" data and predictions of the real world data based on data mined from the Internet.  The real world data in this case is based on some weekly report and it could be about economic trends, public opinion, flu diagnosis or any other data collected from government reports or weekly surveys.  The predictions could be based on Google searches on particular terms, purchases on eBay with a specific category, Tweets with certain words.  The predictions would be orgainized like the real-world data into weekly or monthly segments.  Ideally, several years of real-world data and Internet data would be compared to see what the correlation might be.  Scroll below to see examples of calculations, examples of charts, and the original hypothetical data that these are based on.  (In the next spreadsheet, we will use actual data from the Bureau of Labor Statistics and Google Searches on the word \"unemployment\")"]
[]
[null,null,"Predictions from Model 1","Predictions from Model 2","Predictions from Model 3"]
["Correlation \"R\"; This value could be anywhere from -1 to +1.  A value of zero means two data sets are uncorrelated - knowing one tells us nothing about the other.  A value of 1 means that two values move up and down in perfect harmony with each other such that if we know one we can exactly compute the other.  A correlation of -1 also allows one value to be computed exactly from another value but the two move in perfect opposition (as one goes up the other goes down).",null,-3.8336440833304314E-2,0.69422216696805084,0.90219736941488204]
["R Squared; This value is simply the square of the correlation R.  It can be intperpreted as the amount of variation in one variable that is \"explained\" by the other.   If the R squared of X to Y is .8, then 80% of the variation of Y can be explained by variations in X and 20% of the variation in Y is independent of X.",null,{"$f":"C5^2","v":1.4696826957654424E-3},{"$f":"D5^2","v":0.48194441710981623},{"$f":"E5^2","v":0.81396009337913311}]
[null,null,"Data from the Internet (Google searches on particular terms, purchases on eBay with a specific category, Tweets with certain words, etc.)"]
["XY Scatter Plots: \"Scatter plots\" give a visual representation of how data might be correlated.  Each of the three hypothetical data sets produces very different looking scatter plots and the difference in correlation is visable.  The data set with a correlation of nearly zero is to the far left and the data set with a correlation of about .9 is to the right.  In the zero correlation set, knowing the predicted value tells us nothing about the actual value.  In the example on the right, however, knowing the predicted value gives us a fairly good idea of what the actual value will be."]
[]
[]
[]
[]
[]
[]
[]
["Time Charts: Time charts show how data changes over time.  In this case, we show the real world data changing in the dark color, and the predicted values changing in the lighter grey.  In the data on the left the predicted values seem to go up and down independently of the actual data.  Like the XY scatter plot, this shows us that knowing the predicted value from this model doesn't say much about the real world data.  But the chart on the far right shows that the predicted data moves value closely with the actual data (The values are offset slightly vertically so the actual data doesn't overwrite the predicted data)."]
[]
[]
[]
[]
[]
[]
["Date of Data","\"Real World\" data (e.g., economic trends, public opinion, flu diagnosis, etc.)","Predictions from Model 1","Predictions from Model 2","Predictions from Model 3"]
["2012-01-09",-0.39388930716453585,1.4142604931427551,-3.403037691928068E-3,-0.34584486724542374]
[{"$f":"A24+7","v":"2012-01-16"},-0.45111095158232972,1.3510798705367983,-6.05362333530029E-2,-0.31365392571239448]
[{"$f":"A25+7","v":"2012-01-23"},0.33817053814246856,1.4781991210977372,0.61555441722714033,0.48883844603222049]
["2012-01-30",0.26287789711363285,1.298053589863517,0.58972126874966602,0.76127662882149605]
["2012-02-06",0.65154031835434367,1.1459273183054575,0.94883182730722027,1.087827904264286]
["2012-02-13",0.18735293819265916,1.1202539489933585,0.78382733956421691,1.111628990160773]
["2012-02-20",0.16812720299512188,1.4903432926674229,0.48579592530204796,1.534006882757815]
["2012-02-27",0.36286089485370088,1.3425726758285279,0.26081291376712612,1.5532368411005397]
["2012-03-05",0.56829361831634251,1.3297141991179613,0.48845013288335015,1.7292251190032262]
["2012-03-12",0.59840443713700453,1.3347373715702353,0.35170843131468482,1.8421497411165983]
["2012-03-19",0.63960569184589833,0.70938282298645117,0.63271297702763962,1.7310293145717575]
["2012-03-26",6.232220196375643E-2,0.47169655547945455,0.48506182492469274,1.2220235690619217]
["2012-04-02",-8.072242562496218E-2,1.2207098907406122,0.56149788350979968,1.1815123797067626]
["2012-04-09",0.10136861189508066,1.389393836409361,0.81379168760130827,1.4445219182308704]
["2012-04-16",-6.3122275477485057E-2,1.7318223877733139,0.39010693416750447,1.6586049267117644]
["2012-04-23",-0.1002758080300393,1.8673511982023914,0.49927064978327373,2.0684818296383876]
["2012-04-30",-0.1221739211816851,1.7397583781859569,0.74220652363890571,2.0522514775992846]
["2012-05-07",-0.13019608730087134,2.3538171201623528,1.0883567963745595,1.9819918584545644]
["2012-05-14",-0.58432003573846092,2.0618735453751897,1.1070694365418221,1.8578555654351294]
["2012-05-21",-1.1871881380893934,2.4008471488535337,0.69118661926250347,1.1357555287308829]
["2012-05-28",-0.85565810622225158,2.3788341274156868,0.86965882021652274,1.3852789707942712]
["2012-06-04",-1.4076260985085187,2.5105712817832369,0.52886204522111824,1.0393903204454311]
["2012-06-11",-1.3411332861994554,2.4789930654790076,0.2539683814750891,1.1594416646847785]
["2012-06-18",-1.2775505447072284,2.5964320232407028,8.0825108309421995E-2,1.0365412766587507]
["2012-06-25",-1.9290582723312701,3.1477962651910079,0.21159352066205164,0.79405053720046337]
["2012-07-02",-1.3611858122535563,3.6658594418092476,0.48060455312682004,1.1337410553405636]
["2012-07-09",-0.94391642777520812,3.7686785834383598,0.66143137235491634,1.0852198282756975]
["2012-07-16",-0.69882460053890805,2.8425136434524747,0.41929564207133618,1.3368927871943765]
["2012-07-23",-0.3738984105751087,2.6012157839157255,0.59032152148714578,1.8609764094554013]
["2012-07-30",-0.72343470160593704,2.3018491060152595,0.31014274714841483,1.8308321141494837]
["2012-08-06",-0.5987585577939829,3.1033861137995533,0.40978261346897399,2.2723821790593428]
["2012-08-13",-0.55047809142640469,3.9586388467866538,0.57795602827489723,2.1959963116637287]
["2012-08-20",-0.32839462811189674,4.2006937890431546,0.69217211787672706,2.1613549479843366]
["2012-08-27",-0.20658194685555931,4.7334706725369848,0.89823384099417902,2.0175757754695711]
["2012-09-03",-0.73215658664235561,4.7784266474699928,0.50306443025846304,1.615041044650019]
["2012-09-10",-0.53910643701937189,4.608666052240963,0.73090481711631416,1.8009487560211856]
["2012-09-17",-0.69800361669829236,4.5878510384334046,0.75598610803059663,1.5732974809008478]
["2012-09-24",-1.5293362471936083,4.4817811882073997,0.32200177445561889,0.92741560185609107]
["2012-10-01",-1.3587358452625655,4.4180819656668122,0.76326790865583238,1.2469935622723409]
["2012-10-08",-1.2527162785792001,3.6379085826061988,0.70765624098444713,0.98980523832488787]
["2012-10-15",-0.7440674254276749,3.8661948261320243,1.141543670985006,1.3786761299517845]
["2012-10-22",-1.5024935796918151,4.5418315656157873,1.3190159195136133,0.65219643672949434]
["2012-10-29",-1.6394471427949939,4.1723694421207718,1.3774967960668385,0.55143079111858706]
["2012-11-05",-1.2993229583431063,3.938831991907489,1.3429996374999802,0.99167593611723559]
["2012-11-12",-0.72488792728127094,4.1036140982010574,1.6464291332762655,1.3863416082777995]
["2012-11-19",-0.32708928793595643,4.0259617356523218,1.4588274059098567,1.5345334390447505]
["2012-11-26",-0.34962039972486975,3.2064132431584893,1.3465632586432652,1.3933741720156578]
["2012-12-03",-0.66906870851016353,3.3178080106403822,1.1929849477069361,1.0488350189463806]
["2012-12-10",-0.19151453937192897,3.1766648328776901,1.4156514039629626,1.189306535350664]
["2012-12-17",-0.51302008248331643,3.877140530042483,1.2593281383833597,0.81103265011115999]
["2012-12-24",-0.50088748946459938,4.0927982564565788,1.3908852735264183,0.91304063576014738]
["2012-12-31",-0.46746093516747389,3.8120221497335418,1.3412776170228546,0.9758352708814968]
["2013-01-07",-0.26151014569004644,3.7815709494469094,1.369345416734171,1.2563442728597884]
["2013-01-14",0.46256133801414967,3.5840717062437411,1.2890679305657662,1.8140516701485578]
["2013-01-21",1.3016319966979311,3.7457521026455929,1.677378252354409,2.5653225154442851]
["2013-01-28",1.8116285485070889,4.037888999873565,1.6775483830439133,3.0559158001291555]
["2013-02-04",1.8302718460025098,3.5989408848468192,1.6030670287919977,3.2861676822955284]
["2013-02-11",1.8367872941065386,3.5965200099762655,1.5869796838628789,3.7338127547775382]
["2013-02-18",1.1947566080801522,3.9716461218695054,1.3576992128501648,2.9006084648819543]
["2013-02-25",0.92981395681733026,3.3746011134613556,1.2889126087815377,2.9823781637422178]
["2013-03-04",0.98561633107863444,2.484508944746243,1.6403949667844737,2.9482960121068387]
["2013-03-11",0.46247755190899326,2.684013473436544,1.3418179613100996,2.4965749211286496]
["2013-03-18",0.58476112248353007,2.4295865082875885,1.3920798469788571,2.3019109831542424]
["2013-03-25",9.0024734948472851E-3,1.795950208625716,0.8642642107313947,1.7639314194091444]
["2013-04-01",0.10649401631105614,1.8493457194350704,1.0966755184433021,1.6760825726355584]
["2013-04-08",0.18433487179391406,1.9828950225193056,1.1971106487321146,1.7690111994866571]
[{"$f":"A89+7","v":"2013-04-15"},6.5548750016841684E-2,1.2069533711235922,1.4759437151919137,1.7075171340466198]
["2013-04-22",0.1456309364067459,1.1068580442984692,1.7366164245510112,1.6043880845193965]
["2013-04-29",-0.30578421805257217,1.9831086516618175,1.5731080065543444,1.2832859467410871]
["2013-05-06",-0.86706468885917998,1.9639206207036259,1.5759980446411161,0.90700812669851771]
["2013-05-13",-0.32065888445342028,1.6729104104480983,1.6078112895734462,1.5543983820989413]
["2013-05-20",6.5384785487284103E-3,1.8121503983919169,2.0443049842101124,1.8197633261129291]
["2013-05-27",0.75455580312225612,1.834713451913957,2.1848102212752698,2.4169948125345213]
["2013-06-03",0.55354010624884398,1.8584398933288573,2.220042336650252,2.385849269221159]
["2013-06-10",0.33545114701097062,2.3019053890683554,2.3508511213490597,2.2935168041495353]
["2013-06-17",0.16051650230294906,1.5582187259351499,2.5150779152249778,1.8774635902353849]
["2013-06-24",0.60511774059004575,1.5574910192722065,2.9842321567694325,2.359944209127848]
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["2015-09-21",5.0210061896612386,2.5779468890833073,4.7222800651544832,8.2718723260388352]
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[{"$f":"A218+7","v":"2015-10-05"},4.5380993377502223,1.6686166986978295,4.5632902758595657,8.2617416355683986]
[{"$f":"A219+7","v":"2015-10-12"},5.5181713923186662,2.4062065705106233,5.0278013996352273,8.7193001662720064]
[{"$f":"A220+7","v":"2015-10-19"},5.7656248238624919,2.615892546018618,5.0446420365514903,8.8391915873310776]
[{"$f":"A221+7","v":"2015-10-26"},5.5836962555960685,2.8977187275733098,5.2898925226264737,8.7522071270356463]

{"sheet":"HDR PRNG","index":4,"n_rows":20,"n_cols":9,"rows_kept":20,"cut":false,"hidden":false,"merged":[[14,2,15,9],[17,7,22,9],[1,7,4,7],[1,8,4,15],[6,4,6,15],[7,4,7,15],[8,4,8,15],[11,1,12,10]]}
["Hubbard Decision Research PRNG Chapter 12"]
["Trial ID",7,null,null,null,null,null,"Formula Text","rand = ((mod((mod(mod(999999999999989,mod(trialID*2499997+varID*1800451,7450589)*4658+7450581)*383,99991)*7440893+mod(mod(999999999999989,mod(trialID*2246527+varID*2399993,7450987)*7580+7560584)*17669,7440893))*1343,4294967296))+0.5)/2^32"]
[]
[null,"Variable ID","HDR PRNG"]
[null,1000,{"$f":"((MOD((MOD(MOD(999999999999989,MOD($B$2*2499997+B5*1800451,7450589)*4658+7450581)*383,99991)*7440893+MOD(MOD(999999999999989,MOD($B$2*2246527+B5*2399993,7450987)*7580+7560584)*17669,7440893))*1343,4294967296))+0.5)/2^32","v":0.93461240420583636},"← Copy this cell to use the PRNG in your exercises"]
[]
[null,"Dimension","1st Term","2nd Term","Description"]
[null,"Trial",2499997,2246527,"This represents a unique identifier for a given scenario in a simulation. This 8 decimal digit identifier allows for up to 100 million unique trials for each variable in a model."]
[null,"Variable",1800451,2399993,"This is a unique identifier for a variable. It would be an 8-digit variable ID allowing for up to 100 million unique variables. For example, if “Monthly Demand for Product X” and “average time spent in activity Y” were variables in a model, they would each be given unique variable IDs. Organizations may structure their Variables IDs so that related variables are in groups. For example, perhaps all marketing and sales related variables have “11” for the first two digits and all cybersecurity related variables have “73” for the first two digits, and so on. Variable IDs could be assigned on an ad hoc basis but a large organization making many models with a lot of shared variables would want to develop an internal library of assigned variable IDs similar to an accountant’s “chart of accounts.” "]
[]
[]
[null,"Sampling Error Around Dieharder Tests Results"]
[null,null,null,null,null,null,null,"Figure 1: Sampling error around Dieharder tests results. This uses a Beta Distribution to with a prior of alpha=1 and beta=1 to compute a 90% confidence interval for estimate of mean weak/fails out Dieharder test suite. The top row of brackets are estimates of WEAK result rates and the bottom row are estimates of FAIL rates."]
[]
[null,"•","This uses a Beta Distribution with a prior of alpha=1 and beta=1 to compute a 90% confidence interval for the estimate of mean weak/fail rates in the Dieharder test suite. "]
[]
[]
[null,null,null,null,null,null,null,"The top row of brackets are estimates of WEAK result rates and the bottom row are estimates of FAIL rates."]
[null,null,null,null,null,null,"•"]
[null,null," "]

{"sheet":"Validation","index":5,"n_rows":6,"n_cols":1,"rows_kept":6,"cut":false,"hidden":true,"merged":[]}
["Normal"]
["Binary"]
["Uniform"]
["Lognorm"]
["Triangular"]
["Constant"]