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{"sheet":"Cover and Checklist","index":0,"n_rows":16,"n_cols":14,"rows_kept":16,"cut":false,"hidden":false,"merged":[[15,5,15,6],[4,6,8,10],[1,12,1,16],[12,5,12,6],[13,5,13,6],[14,5,14,6]]}
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[null,null,null,null,null,null,null,null,null,null,null,null,"Skills checklist"]
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[null,null,null,null,null,null,null,null,null,null,null,null,null,"Reviewing basic concepts"]
[null,null,null,null,null,null,"Creating Simulations in Excel: Intermediate",null,null,null,null,null,null,"Modeling additional distributions"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Applying the HDR PRNG to create a time series"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Building a risk register"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Using more advanced data table techniques"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Computing information value for your decision"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Quantifying risk tolerance"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Markov example"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,"Examples of more advanced models"]
[null,null,null,null,null,"Hubbard Decision Research"]
[null,null,null,null,null,"2S410 Canterbury Ct"]
[null,null,null,null,null,"Glen Ellyn, IL 60137"]
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{"sheet":"Deterministic Cash Flow","index":1,"n_rows":16,"n_cols":7,"rows_kept":16,"cut":false,"hidden":false,"merged":[[15,1,16,1],[15,2,16,2]]}
["Deterministic Cash Flow Example"]
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[null,"Input Variables",null,"Point Est."]
[null,"Percent reduction in labor cost",null,0.03]
[null,"Current total labor cost",null,75000000]
[null,"Initial development costs (2020)",null,5000000]
[null,"Cost of money",null,9.5000000000000001E-2]
[]
[null,"Cash Flow"]
[null,null,2020,2021,2022,2023,2024]
[null,"Total costs",{"$f":"D6","v":5000000}]
[null,"Total benefits",null,{"$f":"$D5*$D4","v":2250000},{"$f":"$D5*$D4","v":2250000},{"$f":"$D5*$D4","v":2250000},{"$f":"$D5*$D4","v":2250000}]
[null,"Net benefit",{"$f":"C12-C11","v":-5000000},{"$f":"D12-D11","v":2250000},{"$f":"E12-E11","v":2250000},{"$f":"F12-F11","v":2250000},{"$f":"G12-G11","v":2250000}]
[]
[null,"Results"]
[null,"Net Present Value",{"$f":"NPV(D7, C13:G13)","v":2018340.2034300801}]

{"sheet":"Probabalistic Cash Flow HDR","index":2,"n_rows":505,"n_cols":21,"rows_kept":505,"cut":false,"hidden":false,"merged":[[16,1,17,1],[16,2,17,2],[0,10,0,11],[0,13,0,15],[1,2,1,3],[1,10,2,11],[1,13,2,15],[2,2,2,5]]}
["Probabalistic Cash Flow Example",null,null,null,null,null,null,null,null,null,"Data Table",null,null,"Histogram"]
["Trial ID: ",1,"Insert scroll bar.",null,null,null,null,null,null,null,"Build a data table with 500 scenarios.",null,null,"Enter the logic for a histogram below."]
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[null,"Initial development costs (2020)",null,4125207.0654882118,3000000,8000000,3,{"$f":" ((MOD((MOD(MOD(999999999999989,MOD($B$2*2499997+G7*1800451,7450589)*4658+7450581)*383,99991)*7440893+MOD(MOD(999999999999989,MOD($B$2*2246527+G7*2399993,7450987)*7580+7560584)*17669,7440893))*1343,4294967296))+0.5)/2^32","v":0.22504141309764236},null,null,2,-3396093.306531088,null,{"$f":"N6+1000000","v":-8000000},0,{"$f":"O7-O6","v":0},null,null,null,"Insert histogram here."]
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[null,"Cash Flow",null,null,null,null,null,null,null,null,5,2371661.2201658995,null,-5000000,2E-3,2E-3]
[null,null,2020,2021,2022,2023,2024,null,null,null,6,-1652466.392929123,null,-4000000,0.03,2.7999999999999997E-2]
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[null,"Net benefit",{"$f":"C13-C12","v":-4125207.0654882118},{"$f":"D13-D12","v":1033586.193146474},{"$f":"E13-E12","v":1033586.193146474},{"$f":"F13-F12","v":1033586.193146474},{"$f":"G13-G12","v":1033586.193146474},null,null,null,9,10948827.843154831,null,-1000000,0.188,6.6000000000000003E-2]
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[null,"Results",null,null,null,null,null,null,null,null,11,4928917.0960270716,null,1000000,0.37,9.7999999999999976E-2,null,null,null,"Average NPV",{"$f":"AVERAGE(L6:L505)","v":2562769.0729460958}]
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[]
["Trial ID",1]
[]
["Modeling additional distributions"]
["Variable","Simulated value","Lower bound","Mode or P","Upper bound","Variable ID","PRNG","Shape","Shape notes"]
["Percent reduction in labor cost",null,0.05,0.1,0.3,1,null,null,"Won't be outside our range. Our best guess is 10%."]
["Current total labor cost",null,10000000,null,20000000,2,null,null,"Could be outside our range about 10% of the time. We think the middle of the range is most likely and the actual value is just as likely to be above the mean as below."]
["Change in labor cost",null,-0.05,null,0.1,3,null,null,"Could be outside our range about 10% of the time. We think the middle of the range is most likely and the actual value is just as likely to be above the mean as below."]
["Initial development costs (2020)",null,3000000,null,10000000,4,null,null,"Won't be 0 or negative, but could be outside our range about 10% of the time."]
["Cost of money",null,0.03,null,0.05,5,null,null,"Could be outside our range about 10% of the time. We think the middle of the range is most likely and the actual value is just as likely to be above the mean as below."]
["Project cancellation",null,null,0.1,null,6,null,null,"Only two possible outcomes."]
[]
["Applying the HDR PRNG to create a time series"]
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["Benefits"]
["Current labor cost"]
["PRNG (for labor)"]
["Change in labor cost (changes yearly)"]
["Forecasted labor cost (2021-2025)"]
["Reduction in labor cost"]
["Labor savings"]
["Net benefit"]
[]
["Building a Risk Register"]
[null,null,null,null,"Variable IDs -->",1000,null,2000]
["Risk #","Risk name","Annual likelihood","Impact per event",null,"Likelihood rand","Simulated number of events","Impact rand","Simulated loss per event (lognormal distribution)","Expected Loss","Total simulated loss"]
[null,null,null,"Lower Bound","Upper Bound"]
[1,"Risk 1",0.12,5000,50000,null,null,null,null,{"$f":"IFERROR(EXP(((LN(E31)+LN(D31))/2)+((LN(E31)-LN(D31))/3.28971)^2/2)*-LN(1-C31), 0)","v":2582.2412470389536},{"$f":"I31*G31","v":0}]
[2,"Risk 2",0.4,1000,30000,null,null,null,null,{"$f":"IFERROR(EXP(((LN(E32)+LN(D32))/2)+((LN(E32)-LN(D32))/3.28971)^2/2)*-LN(1-C32), 0)","v":4774.7216784821549},{"$f":"I32*G32","v":0}]
[3,"Risk 3",0.05,75000,150000,null,null,null,null,5562.5911739355661,{"$f":"I33*G33","v":0}]
[]
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[]
["Using more advanced data table techniques"]
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["NPV"]
["Percent reduction in labor cost"]
["Current total labor cost"]
["Change in labor cost"]
["Initial development costs (2020)"]
["Cost of money"]
["Project cancellation"]
[]
["Computing information value for your decision"]
["Average NPV",{"$f":"IFERROR(AVERAGE(C55:ALN55), \"\")","v":""},"Cost of being wrong",{"$f":"IFERROR(IF(B65=\"Approve\", AVERAGEIF(C55:ALN55, \"<0\"), AVERAGEIF(C55:ALN55, \">0\")), \"\")","v":""}]
["Default Decision",{"$f":"IF(B64=\"\", \"\", IF(B64>0, \"Approve\", \"Deny\"))","v":""},"Chance of being wrong",{"$f":"IF(B65=\"\", \"\", IF(B65=\"Approve\", COUNTIF(C55:ALN55, \"<0\"), COUNTIF(C55:ALN55, \">0\"))/1000)","v":""}]
["Expected Opportunity Loss",{"$f":"IFERROR(ABS(D64*D65), \"\")","v":""}]
[]
[null,"Avg NPV, given X in bottom 10%","Avg NPV, given X in top 10%"]
["Percent reduction in labor cost",{"$f":"IFERROR(AVERAGEIFS($C$55:$ALN$55, $C56:$ALN56, \"<\"&PERCENTILE($C56:$ALN56, 0.1)), \"\")","v":""},{"$f":"IFERROR(AVERAGEIFS($C$55:$ALN$55, $C56:$ALN56, \">\"&PERCENTILE($C56:$ALN56, 0.9)), \"\")","v":""}]
["Current total labor cost",{"$f":"IFERROR(AVERAGEIFS($C$55:$ALN$55, $C57:$ALN57, \"<\"&PERCENTILE($C57:$ALN57, 0.1)), \"\")","v":""},{"$f":"IFERROR(AVERAGEIFS($C$55:$ALN$55, $C57:$ALN57, \">\"&PERCENTILE($C57:$ALN57, 0.9)), \"\")","v":""}]
["Change in labor cost",{"$f":"IFERROR(AVERAGEIFS($C$55:$ALN$55, $C58:$ALN58, \"<\"&PERCENTILE($C58:$ALN58, 0.1)), \"\")","v":""},{"$f":"IFERROR(AVERAGEIFS($C$55:$ALN$55, $C58:$ALN58, \">\"&PERCENTILE($C58:$ALN58, 0.9)), \"\")","v":""}]
["Initial development costs (2020)",{"$f":"IFERROR(AVERAGEIFS($C$55:$ALN$55, $C59:$ALN59, \"<\"&PERCENTILE($C59:$ALN59, 0.1)), \"\")","v":""},{"$f":"IFERROR(AVERAGEIFS($C$55:$ALN$55, $C59:$ALN59, \">\"&PERCENTILE($C59:$ALN59, 0.9)), \"\")","v":""}]
["Cost of money",{"$f":"IFERROR(AVERAGEIFS($C$55:$ALN$55, $C60:$ALN60, \"<\"&PERCENTILE($C60:$ALN60, 0.1)), \"\")","v":""},{"$f":"IFERROR(AVERAGEIFS($C$55:$ALN$55, $C60:$ALN60, \">\"&PERCENTILE($C60:$ALN60, 0.9)), \"\")","v":""}]
["Project cancellation",{"$f":"IFERROR(AVERAGEIFS($C$55:$ALN$55, $C61:$ALN61, \"=0\"), \"\")","v":""},{"$f":"IFERROR(AVERAGEIFS($C$55:$ALN$55, $C61:$ALN61, \"=1\"), \"\")","v":""}]

{"sheet":"Distributions","index":4,"n_rows":47,"n_cols":14,"rows_kept":47,"cut":false,"hidden":false,"merged":[[10,10,11,10],[4,0,4,7],[9,0,9,7],[14,0,14,7],[19,0,19,7],[29,0,29,7],[41,13,42,13],[44,0,44,10],[24,0,24,7],[34,0,34,8],[39,0,39,9]]}
["Selected Distributions"]
["Trial ID",1]
[]
["Uniform"]
["One of the simplest  distributions you can use is the uniform distribution. There is no chance of a value being above the maximum or below the minimum, and every value between the min and max are equally likely.\n\n■ When to use: When you know the minimum and maximum values, but any value in between is equally likely.\n■ Examples: The proportion of people that would buy a product, number of employees that do some activity.\n■ Mean = (min + max)/2\n■ Simulated value = rand * (max - min) + min"]
["Simulated Value","Minimum",null,"Maximum","Variable ID","HDR PRNG"]
[{"$f":"F7*(D7-B7)+B7","v":0.19655135844368488},0,null,1,1,{"$f":" ((MOD((MOD(MOD(999999999999989,MOD($B$2*2499997+E7*1800451,7450589)*4658+7450581)*383,99991)*7440893+MOD(MOD(999999999999989,MOD($B$2*2246527+E7*2399993,7450987)*7580+7560584)*17669,7440893))*1343,4294967296))+0.5)/2^32","v":0.19655135844368488}]
[]
["Triangular"]
["For a triangular distribution, the UB and LB represent absolute limits. There is no chance that a value could be generated outside of these bounds. In addition to the UB and LB, this distribution also has a mode that can vary to any value between the UB and LB. This is sometimes useful as a substitute for a lognormal, when you want to set absolute limits on what the values can be but you want to skew the output in a way similar to the lognormal. It is useful in any situation where you know of absolute limits but the most likely value might not be in the middle, like the normal distribution.\n \n■When to Use: When you want control over where the most likely value is compared to the range, and when the range has absolute limits.\n■ Examples: Number of records lost if you think the most likely number is near the top of the range and yet you have a finite number of records you know cannot be exceeded.\n■ Mean: =(min+mode+max)/3\n■ Simulated value = IF(rand<(mode-min)/(max-min), 1, 0) * (min + SQRT(rand*(max-min)*(mode-min))) + IF(rand>= (mode-min)/(max-min), 1, 0) * (max - SQRT((1-rand) * (max - min) * (max - mode)))"]
["Simulated Value","Minimum","Mode","Maximum","Variable ID","HDR PRNG",null,null,null,null,"Introduced in Basic Simulations Course"]
[{"$f":"IF(F12<(C12-B12)/(D12-B12), 1, 0) * (B12 + SQRT(F12*(D12-B12)*(C12-B12))) + IF(F12>= (C12-B12)/(D12-B12), 1, 0) * (D12 - SQRT((1-F12) * (D12 - B12) * (D12 - C12)))","v":1.0809191826859248},1,1,4,2,{"$f":" ((MOD((MOD(MOD(999999999999989,MOD($B$2*2499997+E12*1800451,7450589)*4658+7450581)*383,99991)*7440893+MOD(MOD(999999999999989,MOD($B$2*2246527+E12*2399993,7450987)*7580+7560584)*17669,7440893))*1343,4294967296))+0.5)/2^32","v":5.3218575776554644E-2}]
[]
["Binary"]
["Unlike the other distributions mentioned here, a discrete binary distribution (also known as a Bernoulli distribution) generates just two possible outcomes: success or failure. The probability of success is p and the probability of failure is q = (1 – p). For example, if success means to flip a fair coin heads‐up, the probability of success is p = .5, and the probability of failure is q = (1 – .5) = .5.\n\n■ When to use: This is used in either/or situations—something either happens or it doesn’t.\n■ Example: The occurrence of a data breach in a given period of time.\n■ Mean: =P\n■ Simulated value = if(rand<probability, 1, 0)"]
["Simulated Value",null,"Probability",null,"Variable ID","HDR PRNG"]
[{"$f":"IF(F17<C17,1,0)","v":1},null,0.3,null,3,{"$f":" ((MOD((MOD(MOD(999999999999989,MOD($B$2*2499997+E17*1800451,7450589)*4658+7450581)*383,99991)*7440893+MOD(MOD(999999999999989,MOD($B$2*2246527+E17*2399993,7450987)*7580+7560584)*17669,7440893))*1343,4294967296))+0.5)/2^32","v":0.22504141309764236}]
[]
["Normal"]
["A normal (or Gaussian) distribution is a bell‐shaped curve that is symmetrically distributed about the mean. Many natural phenomenon follow this distribution but in some applications it will underestimate the probability of extreme events.\n\n■ When to Use: When there is equal probability of observing a result above or below the mean.\n■ Examples: Test scores, travel time.\n■ Mean: =(UB + LB)/2"]
["Simulated Value","Lower Bound",null,"Upper Bound","Variable ID","HDR PRNG"]
[{"$f":"_xlfn.NORM.INV(F22, (D22+B22)/2, (D22-B22)/3.29)","v":1871.8829079269308},1000,null,2000,4,{"$f":"((MOD((MOD(MOD(999999999999989,MOD($B$2*2499997+E22*1800451,7450589)*4658+7450581)*383,99991)*7440893+MOD(MOD(999999999999989,MOD($B$2*2246527+E22*2399993,7450987)*7580+7560584)*17669,7440893))*1343,4294967296))+0.5)/2^32","v":0.88942856027279049}]
[]
["Lognormal"]
["The lognormal distribution is an often preferred alternative to the normal distribution when a sample can only take positive values. It also allows for the possibility of extreme values on the upper end and, therefore, may fit some phenomena better than a normal. \n\n■ When to Use: To model positive values that are primarily moderate in scope but have potential for rare extreme events.\n■ Examples: Losses incurred by a cyberattack, the cost of a project.\n■ Excel Formula: =lognorm.inv(rand(),(ln(UB) + ln(LB))/2, (ln(UB)‐ln(LB))/3.29)\n■ Mean: = ((ln(UB)+ln(LB))/2)"]
["Simulated Value","Lower Bound",null,"Upper Bound","Variable ID","HDR PRNG"]
[{"$f":"_xlfn.LOGNORM.INV(F27, (LN(D27)+LN(B27))/2, (LN(D27)-LN(B27))/3.29)","v":1715.4485982655624},1000,null,2000,5,{"$f":"((MOD((MOD(MOD(999999999999989,MOD($B$2*2499997+E27*1800451,7450589)*4658+7450581)*383,99991)*7440893+MOD(MOD(999999999999989,MOD($B$2*2246527+E27*2399993,7450987)*7580+7560584)*17669,7440893))*1343,4294967296))+0.5)/2^32","v":0.82031012407969683}]
[]
["Poisson/Binomial"]
["The poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in some period of time if these events occur with a constant mean rate and independently of the time since the last event. For example, if the likelihood of some event ocurring at least once in a year is 40%, then the poisson distribution tells us the probability of that event occuring two, three, four, etc., times. Note that the events must be independent, meaning that the probability of the second event in a year is not affected by when the first event occurs. Excel does not have a \"POISSON.INV()\", so we approximate it using an inverse binomial distribution with a large number of trials.\n\n■ When to Use: To model the number of times an event occurs in a given time period when the mean frequency is known or estimated. \n■ Examples: Number of cybersecurity events in a year, number of project cancellations over 10 years.\n■ Excel Formula: =binom.inv(1000000, -ln(1-P)/1000000, rand())\n■ Mean: = -ln(1-P)"]
["Simulated Value",null,"Probability",null,"Variable ID","HDR PRNG"]
[{"$f":"_xlfn.BINOM.INV(1000000, -LN(1-C32)/1000000, F32)","v":1},null,0.4,null,5,{"$f":"((MOD((MOD(MOD(999999999999989,MOD($B$2*2499997+E32*1800451,7450589)*4658+7450581)*383,99991)*7440893+MOD(MOD(999999999999989,MOD($B$2*2246527+E32*2399993,7450987)*7580+7560584)*17669,7440893))*1343,4294967296))+0.5)/2^32","v":0.82031012407969683}]
[]
["Beta"]
["Beta distributions are extremely versatile. They can be used to generate values between 0 and 1 but where some values are more likely than others. This result can also be used in other formulas to generate any range of values you like. They are particularly useful when modeling the frequency of an event, especially when the frequency is estimated based on random samples of a population or historical observations. In this distribution it is not quite as easy as in other distributions to determine the parameters based only on upper and lower bounds. The only solution is iteratively trying different “alpha” and “beta” values until you get the 90% CI you want. If alpha and beta are each greater than 1 and equal to each other, then it will be symmetrical, where values near .5 are the most likely and less likely further away from .5. The larger you make both alpha and beta, the narrower the distribution. If you make alpha larger than beta, the distribution will skew to the left, and if you make beta larger, it skews to the right.\n \n■ When to Use: Any situation that can be characterized as a set of “hits” and “misses.” For each hit, increase alpha by 1. For each miss, increase beta by 1.\n■ Examples: Frequency of an event (such as a data breach) when the frequency is less than 1 per time unit (e.g., year), the proportion of employees following a security procedure correctly."]
["Simulated Value","Alpha","Beta","Computed 5th Percentile","Computed 95th Percentile","Variable ID","HDR PRNG"]
[{"$f":"_xlfn.BETA.INV(G37, B37, C37)","v":0.43512507845970921},4,3,{"$f":"_xlfn.BETA.INV(0.05, B37, C37)","v":0.27133837251975251},{"$f":"_xlfn.BETA.INV(0.95, B37, C37)","v":0.84683888202477686},6,{"$f":"((MOD((MOD(MOD(999999999999989,MOD($B$2*2499997+F37*1800451,7450589)*4658+7450581)*383,99991)*7440893+MOD(MOD(999999999999989,MOD($B$2*2246527+F37*2399993,7450987)*7580+7560584)*17669,7440893))*1343,4294967296))+0.5)/2^32","v":0.23122715030331165}]
[]
["Power Law"]
["The power law is a useful distribution for describing phenomena with extreme, catastrophic possibilities - even more than lognormal. The “fat tail” of the power law distribution allows us to acknowledge the common small event, while still accounting for more extreme possibilities.  In fact, sometimes this type of distribution may not always have a defined-mean because the tails goes out so far.  Be careful of producing unintended extreme results.  To keep this from producing unrealistic results, you might prefer to use the Truncated Power Law Below.  We show this distribution in a simple form which requires that you enter \"alpha\" and \"theta\" iteratively until you get the 90% Confidence Interval you want.\n\n■ When to Use: When you want to make sure that catastrophic events, while rare, will be given nontrivial probabilities.\n■ Examples: Phenomena like earthquakes, power outages, epidemics, and other types of “cascade failures” have this property."]
["Simulated Value","Alpha","Theta (scale)","Computed 5th Percentile","Computed 95th Percentile","Computed 99.99th Percentile","Variable ID","HDR PRNG"]
[{"$f":"(C42/H42)^B42","v":1.6976456697103071},0.5,0.5,{"$f":"(C42/(1-0.05))^B42","v":0.7254762501100116},{"$f":"(C42/(1-0.95))^B42","v":3.1622776601683777},{"$f":"(C42/(1-0.9999))^B42","v":70.710678118658649},7,{"$f":"((MOD((MOD(MOD(999999999999989,MOD($B$2*2499997+G42*1800451,7450589)*4658+7450581)*383,99991)*7440893+MOD(MOD(999999999999989,MOD($B$2*2246527+G42*2399993,7450987)*7580+7560584)*17669,7440893))*1343,4294967296))+0.5)/2^32","v":0.17349058215040714},null,null,null,null,null,"Aspirational"]
[]
["Truncated Power Law"]
["The truncated power law distribution is simply the power law distribution, but with an upper limit that is imposed by the user. While the heavy tail of the power law distribution allows us to account for the rare catastrophic event, there may be a theoretical bound to the size of such an event. If this upper limit is not factored into the model, we may produce a misleading and unnecessarily grim forecast.  As above, you need to enter values for alpha, theta and truncated percentile until you see 5 percentile, 95 percentile, and truncated value (the upper limit) that agrees with how you want to model this quantity.\n\n■ When to Use: The power law distribution should be truncated if an upper bound on the severity of an event is known.\n■ Example: Losses of records may follow a power law but you know you only have a finite number of records to lose. "]
["Simulated Value","Alpha","Theta (scale)","Truncated Percentile","Computed 5th Percentile","Computed 95th Percentile","Truncated Value","Variable ID","HDR PRNG"]
[{"$f":"(C47/(I47*D47+1-D47))^B47","v":2.0230547962396055},0.5,4,0.95,{"$f":"(C47/((1-0.05)*D47+1-D47))^B47","v":2.0492620783142401},{"$f":"(C47/((1-0.95)*D47+1-D47))^B47","v":6.405126152203481},{"$f":"(C47/(1-D47))^B47","v":8.9442719099991557},8,{"$f":"((MOD((MOD(MOD(999999999999989,MOD($B$2*2499997+H47*1800451,7450589)*4658+7450581)*383,99991)*7440893+MOD(MOD(999999999999989,MOD($B$2*2246527+H47*2399993,7450987)*7580+7560584)*17669,7440893))*1343,4294967296))+0.5)/2^32","v":0.97614505945239216}]

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["Hubbard Decision Research PRNG"]
["Trial ID",724,null,null,null,null,null,"Formula Text","rand = ((mod((mod(mod(999999999999989,mod(trialID*2499997+varID*1800451+ID3*2000371+ID4*1796777+ID5*2299603,7450589)*4658+7450581)*383,99991)*7440893+mod(mod(999999999999989,mod(trialID*2246527+varID*2399993+ID3*2100869+ID4*1918303+ID5*1624729,7450987)*7580+7560584)*17669,7440893))*1343,4294967296))+0.5)/2^32"]
[]
[null,"ID5","ID4","ID3","Variable ID","HDR PRNG"]
[null,1000,2100869,1918303,212,{"$f":" ((MOD((MOD(MOD(999999999999989,MOD($B$2*2499997+E5*1800451+D5*2000371+C5*1796777+B5*2299603,7450589)*4658+7450581)*383,99991)*7440893+MOD(MOD(999999999999989,MOD($B$2*2246527+E5*2399993+D5*2100869+C5*1918303+B5*1624729,7450987)*7580+7560584)*17669,7440893))*1343,4294967296))+0.5)/2^32","v":9.6274989773519337E-2}]
[null,null,2100869,1918303,212,{"$f":" ((MOD((MOD(MOD(999999999999989,MOD($B$2*2499997+E6*1800451+D6*2000371+C6*1796777,7450589)*4658+7450581)*383,99991)*7440893+MOD(MOD(999999999999989,MOD($B$2*2246527+E6*2399993+D6*2100869+C6*1918303,7450987)*7580+7560584)*17669,7440893))*1343,4294967296))+0.5)/2^32","v":0.61775720363948494}]
[null,null,null,1918303,212,{"$f":" ((MOD((MOD(MOD(999999999999989,MOD($B$2*2499997+E7*1800451+D7*2000371,7450589)*4658+7450581)*383,99991)*7440893+MOD(MOD(999999999999989,MOD($B$2*2246527+E7*2399993+D7*2100869,7450987)*7580+7560584)*17669,7440893))*1343,4294967296))+0.5)/2^32","v":0.84156044514384121}]
[null,null,null,null,212,{"$f":" ((MOD((MOD(MOD(999999999999989,MOD($B$2*2499997+E8*1800451,7450589)*4658+7450581)*383,99991)*7440893+MOD(MOD(999999999999989,MOD($B$2*2246527+E8*2399993,7450987)*7580+7560584)*17669,7440893))*1343,4294967296))+0.5)/2^32","v":0.29207670956384391}]
[]
[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,"Entity",2000371,2100869,"This identifies an organization or some other category of users. A corporation or government agency may be assigned a unique 8 decimal digit Entity ID. Since this provides for 100 million potential entities, that should be enough for every business, not for profit and government agency that wants one on the planet. This is useful if there are models using random variables from many organizations do not have variables that produce the same random sequences. For example, many banks may use variables defined by the FDIC for “stress testing” to ensure banks are financially stable even during times of economic stress. The bank would want to ensure that internally defined variables with the same Variable ID are not correlated to the shared variables. The FDIC would supply the variable ID along with the Entity ID of the FDIC so that every bank using those variables produces the same sequence while avoiding duplicating the sequence of internally defined variables. A default Entity ID of 0 can be used by anyone as long as sharing variables would not be an issue."]
[null,"Time",1796777,1918303,"This identifies a particular time unit for a given variable/trial/entity combination. This allows one scenario for a given variable to contain an entire unique time series. A 7digit time series ID would allow for time series containing 115 days of seconds, 19 years of minutes, or 27,397 years of days. This is an optional dimension. Variables that do not represent a time series use the default Time ID of 0."]
[null,"Agent",2299603,1624729,"This provides a fifth optional dimension for the counter-based PRNG. One possible use is as an identify for agents in agent-based modeling. If this ID is not used, the default value is 0. "]
[]
[]
[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," "]

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["Quantifying Risk Tolerance"]
[]
["Loss Exceedance Tolerance",null,null,null,null,null,null,null,null,null,null,"Constant Absolute Risk Aversion"]
[null,"Loss Threshold","Acceptable Probability for Loss Exceeded",null,null,null,null,null,null,null,null,null,"X",null,"Award","Probability","Utility","Certain Monetary Equivalent"]
[null,100000,0.8,null,null,null,null,null,null,null,null,null,850000,null,1500000,0.25,{"$f":"1-EXP(-O5/M5)","v":0.8287628570552118},{"$f":"-M5*LN(1-Q5*P5)","v":197346.69593373491}]
[null,1000000,0.2]
[null,5000000,0.05,null,null,null,null,null,null,null,null,null,null,"Flip a coin…"]
[null,10000000,0.01]
[]
[null,"Example Histogram for Loss Exceedance Curve"]
[null,"Loss","Prob. of Inherent Loss or Greater"]
[null,1E-4,0.75800000000000001]
[null,500000.0001,0.57299999999999995]
[null,1000000.0001000001,0.51300000000000001,null,null,null,null,null,null,null,null,null,null,"Win $X",null,"Lose $X/2"]
[null,1070000.0001070001,0.502]
[null,1144900.0001144903,0.48899999999999999]
[null,1225043.0001225048,0.47599999999999998]
[null,1310796.0101310802,0.47]
[null,1402551.730840256,0.46300000000000002]
[null,1500730.351999074,0.45100000000000001]
[null,1605781.4766390093,0.441]
[null,1718186.1800037401,0.43]
[null,1838459.2126040021,0.42299999999999999]
[null,1967151.3574862822,0.40899999999999997]
[null,2104851.952510322,0.4]
[null,2252191.5891860449,0.38500000000000001]
[null,2409845.0004290682,0.374]
[null,2578534.1504591033,0.35099999999999998]
[null,2759031.5409912406,0.33100000000000002]
[null,2952163.7488606279,0.307]
[null,3158815.2112808721,0.28799999999999998]
[null,3379932.2760705333,0.26800000000000002]
[null,3616527.5353954709,0.246]
[null,3869684.4628731543,0.218]
[null,4140562.3752742754,0.20699999999999999]
[null,4430401.7415434746,0.193]
[null,4740529.8634515181,0.17799999999999999]
[null,5072366.9538931251,0.16700000000000001]
[null,5427432.6406656438,0.152]
[null,5807352.9255122393,0.13400000000000001]
[null,6213867.6302980967,0.11]
[null,6648838.3644189639,0.10299999999999999]
[null,7114257.0499282917,8.4000000000000005E-2]
[null,7612255.0434232727,7.0999999999999994E-2]
[null,8145112.8964629024,6.0999999999999999E-2]
[null,8715270.7992153056,5.1999999999999998E-2]
[null,9325339.7551603783,4.4999999999999998E-2]
[null,9978113.5380216055,4.1000000000000002E-2]
[null,10676581.485683119,3.5999999999999997E-2]
[null,11423942.189680938,2.5999999999999999E-2]
[null,12223618.142958604,2.1000000000000001E-2]
[null,13079271.412965707,0.02]
[null,13994820.411873307,1.9E-2]
[null,14974457.840704439,1.4E-2]
[null,16022669.889553752,0.01]
[null,17144256.781822514,0.01]
[null,18344354.756550092,8.0000000000000002E-3]
[null,19628459.589508601,8.0000000000000002E-3]
[null,21002451.760774203,7.0000000000000001E-3]
[null,22472623.384028398,6.0000000000000001E-3]
[null,24045707.020910386,6.0000000000000001E-3]
[null,25728906.512374114,6.0000000000000001E-3]
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[null,29457025.066017125,4.0000000000000001E-3]
[null,31519016.820638325,3.0000000000000001E-3]
[null,33725347.99808301,2E-3]

{"sheet":"2D Data Table","index":7,"n_rows":2005,"n_cols":33,"rows_kept":2005,"cut":false,"hidden":false,"merged":[[21,1,21,2],[22,1,22,2],[23,1,23,2],[15,1,15,2],[16,1,16,2],[17,1,17,2],[18,1,18,2],[19,1,19,2],[9,1,9,2],[12,1,12,2],[13,1,13,2],[14,1,14,2],[20,1,20,2],[4,1,4,2],[5,1,5,2],[6,1,6,2],[7,1,7,2],[8,1,8,2],[1,22,2,23],[1,24,2,25],[0,11,0,15],[0,17,0,19],[3,1,3,2],[1,2,1,3],[2,2,2,6],[1,11,2,15],[1,18,2,19],[1,20,2,21]]}
["Detailed Probabalistic Cash Flow Example from Workspace",null,null,null,null,null,null,null,null,null,null,"Data Table",null,null,null,null,null,"Histogram"]
["Trial ID: ",30,"Insert scroll bar.",null,null,null,null,null,null,null,null,"Build a 2D data table with 2000 rows (Trial ID) and 4 columns (Percent reduction). Make the column values 10%, 12%, 14%, and 16%. Trial IDs have already been entered for you.",null,null,null,null,null,null,"Percent reduction = 10%",null,"Percent reduction = 12%",null,"Percent reduction = 14%",null,"Percent reduction = 16%"]
[]
[null,"Variable",null,"Simulated value","Lower bound","Mode or P","Upper bound","Variable ID","HDR PRNG",null,null,null,null,null,null,null,null,"Bin","Cumulative","Frequency","Cumulative","Frequency","Cumulative","Frequency","Cumulative","Frequency"]
[null,"Percent reduction in labor cost",null,{"$f":"IF(I5<(F5-E5)/(G5-E5), 1, 0) * (E5 + SQRT(I5*(G5-E5)*(F5-E5))) + IF(I5>= (F5-E5)/(G5-E5), 1, 0) * (G5 - SQRT((1-I5) * (G5 - E5) * (G5 - F5)))","v":6.0468328142406907E-2},0.05,0.1,0.3,1,{"$f":" ((MOD((MOD(MOD(999999999999989,MOD($B$2*2499997+H5*1800451,7450589)*4658+7450581)*383,99991)*7440893+MOD(MOD(999999999999989,MOD($B$2*2246527+H5*2399993,7450987)*7580+7560584)*17669,7440893))*1343,4294967296))+0.5)/2^32","v":8.7668715277686715E-3},null,null,null,null,null,null,null,null,-16000000,{"$f":"COUNTIF($M$6:$M$2005, \"<\"&$R5)","v":0},{"$f":"S5/2000","v":0},{"$f":"COUNTIF($N$6:$N$2005, \"<\"&$R5)","v":0},{"$f":"U5/2000","v":0},{"$f":"COUNTIF($O$6:$O$2005, \"<\"&$R5)","v":0},{"$f":"W5/2000","v":0},{"$f":"COUNTIF($P$6:$P$2005, \"<\"&$R5)","v":0},{"$f":"Y5/2000","v":0}]
[null,"Current total labor cost",null,{"$f":"_xlfn.NORM.INV(I6, (G6+E6)/2, (G6-E6)/3.29)","v":17831555.392926883},10000000,null,20000000,2,{"$f":" ((MOD((MOD(MOD(999999999999989,MOD($B$2*2499997+H6*1800451,7450589)*4658+7450581)*383,99991)*7440893+MOD(MOD(999999999999989,MOD($B$2*2246527+H6*2399993,7450987)*7580+7560584)*17669,7440893))*1343,4294967296))+0.5)/2^32","v":0.82422363420482725},null,null,1,null,null,null,null,null,{"$f":"R5+1500000","v":-14500000},0,{"$f":"(S6-S5)/2000","v":0},0,{"$f":"(U6-U5)/2000","v":0},0,{"$f":"(W6-W5)/2000","v":0},0,{"$f":"(Y6-Y5)/2000","v":0}]
[null,"Change in labor cost",null,{"$f":"_xlfn.NORM.INV(I7, (G7+E7)/2, (G7-E7)/3.29)","v":2.710981809016938E-2},-0.02,null,0.05,3,0.71537671040277928,null,null,2,null,null,null,null,null,{"$f":"R6+1500000","v":-13000000},0,{"$f":"(S7-S6)/2000","v":0},0,{"$f":"(U7-U6)/2000","v":0},0,0,0,{"$f":"(Y7-Y6)/2000","v":0},null,null,null,"Insert histogram here."]
[null,"Initial development costs (2020)",null,{"$f":"_xlfn.LOGNORM.INV(I8, (LN(G8)+LN(E8))/2, (LN(G8)-LN(E8))/3.29)","v":4682327.0510774329},3000000,null,10000000,4,0.33414928789716214,null,null,3,null,null,null,null,null,-11500000,0,0,0,{"$f":"(U8-U7)/2000","v":0},0,0,0,{"$f":"(Y8-Y7)/2000","v":0}]
[null,"Cost of money",null,{"$f":"_xlfn.NORM.INV(I9, (G9+E9)/2, (G9-E9)/3.29)","v":5.1404424414155346E-2},0.03,null,0.05,5,{"$f":" ((MOD((MOD(MOD(999999999999989,MOD($B$2*2499997+H9*1800451,7450589)*4658+7450581)*383,99991)*7440893+MOD(MOD(999999999999989,MOD($B$2*2246527+H9*2399993,7450987)*7580+7560584)*17669,7440893))*1343,4294967296))+0.5)/2^32","v":0.96967426978517324},null,null,4,null,null,null,null,null,-10000000,0,0,0,{"$f":"(U9-U8)/2000","v":0},0,0,0,{"$f":"(Y9-Y8)/2000","v":0}]
[null,"Project cancellation",null,{"$f":"IF(I10<F10,1,0)","v":1},null,0.1,null,6,8.8138123392127454E-2,null,null,5,null,null,null,null,null,-8500000,0,0,0,{"$f":"(U10-U9)/2000","v":0},0,0,0,{"$f":"(Y10-Y9)/2000","v":0}]
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[null,"Cash Flow",null,null,null,null,null,null,null,null,null,7,null,null,null,null,null,-5500000,0,0,0,{"$f":"(U12-U11)/2000","v":0},0,0,0,{"$f":"(Y12-Y11)/2000","v":0}]
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[null,"Costs",null,null,null,null,null,null,null,null,null,9,null,null,null,null,null,-2500000,0,0,0,{"$f":"(U14-U13)/2000","v":0},0,{"$f":"(W14-W13)/2000","v":0},0,{"$f":"(Y14-Y13)/2000","v":0}]
[null,"Initial dev costs",null,{"$f":"D8","v":4682327.0510774329},null,null,null,null,null,null,null,10,null,null,null,null,null,-1000000,0,0,0,{"$f":"(U15-U14)/2000","v":0},0,0,0,{"$f":"(Y15-Y14)/2000","v":0}]
[null,"Cancelled?",null,{"$f":"D10","v":1},null,null,null,null,null,null,null,11,null,null,null,null,null,500000,0,0,0,{"$f":"(U16-U15)/2000","v":0},0,0,0,{"$f":"(Y16-Y15)/2000","v":0},null,null,"Percent reduction",0.1,0.12,0.14000000000000001,0.16]
[null,"Benefits",null,null,null,null,null,null,null,null,null,12,null,null,null,null,null,2000000,0,0,0,{"$f":"(U17-U16)/2000","v":0},0,0,0,{"$f":"(Y17-Y16)/2000","v":0},null,null,"Average NPV",{"$f":"IFERROR(AVERAGE(M6:M2005), \"\")","v":""},{"$f":"IFERROR(AVERAGE(N6:N2005), \"\")","v":""},"",""]
[null,"Current labor cost",null,{"$f":"D6","v":17831555.392926883},null,null,null,null,null,null,null,13,null,null,null,null,null,3500000,0,0,0,{"$f":"(U18-U17)/2000","v":0},0,0,0,{"$f":"(Y18-Y17)/2000","v":0},null,null,"P(NPV<0)",{"$f":"COUNTIF(M6:M2005, \"<0\")/2000","v":0},{"$f":"COUNTIF(N6:N2005, \"<0\")/2000","v":0},0,{"$f":"COUNTIF(P6:P2005, \"<0\")/2000","v":0}]
[null,"PRNG (for labor)",null,{"$f":" ((MOD((MOD(MOD(999999999999989,MOD($B$2*2499997+$H8*1800451+D13*2000371,7450589)*4658+7450581)*383,99991)*7440893+MOD(MOD(999999999999989,MOD($B$2*2246527+$H8*2399993+D13*2100869,7450987)*7580+7560584)*17669,7440893))*1343,4294967296))+0.5)/2^32","v":0.68510927341412753},{"$f":" ((MOD((MOD(MOD(999999999999989,MOD($B$2*2499997+$H8*1800451+E13*2000371,7450589)*4658+7450581)*383,99991)*7440893+MOD(MOD(999999999999989,MOD($B$2*2246527+$H8*2399993+E13*2100869,7450987)*7580+7560584)*17669,7440893))*1343,4294967296))+0.5)/2^32","v":0.84089960425626487},0.5523971013026312,{"$f":" ((MOD((MOD(MOD(999999999999989,MOD($B$2*2499997+$H8*1800451+G13*2000371,7450589)*4658+7450581)*383,99991)*7440893+MOD(MOD(999999999999989,MOD($B$2*2246527+$H8*2399993+G13*2100869,7450987)*7580+7560584)*17669,7440893))*1343,4294967296))+0.5)/2^32","v":0.22273952385876328},0.96871240891050547,null,null,null,14,null,null,null,null,null,5000000,0,0,0,{"$f":"(U19-U18)/2000","v":0},0,0,0,{"$f":"(Y19-Y18)/2000","v":0}]
[null,"Change in labor cost (changes yearly)",null,{"$f":"_xlfn.NORM.INV(D19, ($G$7+$E$7)/2, ($G$7-$E$7)/3.29)","v":2.5256052746580028E-2},{"$f":"_xlfn.NORM.INV(E19, ($G$7+$E$7)/2, ($G$7-$E$7)/3.29)","v":3.6237490160158328E-2},1.7802552337377344E-2,-1.2334841601433725E-3,5.462123465759533E-2,null,null,null,15,null,null,null,null,null,6500000,0,0,0,{"$f":"(U20-U19)/2000","v":0},0,0,0,{"$f":"(Y20-Y19)/2000","v":0}]
[null,"Forecasted labor cost (2021-2025)",null,{"$f":"D18*(1+D20)","v":18281910.096484207},{"$f":"D21*(1+E20)","v":18944400.633714452},{"$f":"E21*(1+F20)","v":19281659.317496397},19257875.696146984,20309764.64355303,null,null,null,16,null,null,null,null,null,8000000,0,0,0,{"$f":"(U21-U20)/2000","v":0},0,0,0,{"$f":"(Y21-Y20)/2000","v":0}]
[null,"Reduction in labor cost",null,null,{"$f":"$D5","v":6.0468328142406907E-2},{"$f":"$D5","v":6.0468328142406907E-2},6.0468328142406907E-2,6.0468328142406907E-2,null,null,null,17,null,null,null,null,null,9500000,0,0,0,{"$f":"(U22-U21)/2000","v":0},0,0,0,{"$f":"(Y22-Y21)/2000","v":0}]
[null,"Labor savings",null,null,{"$f":"E21*E22","v":1145536.2339806668},{"$f":"F21*F22","v":1165929.7027404697},{"$f":"G21*G22","v":1164491.5469202986},1228097.5129614184,null,null,null,18,null,null,null,null,null,11000000,0,0,0,{"$f":"(U23-U22)/2000","v":0},0,0,0,{"$f":"(Y23-Y22)/2000","v":0}]
[null,"Net benefit",null,{"$f":"D23-D15","v":-4682327.0510774329},{"$f":"IF($D16, 0, E23-E15)","v":0},{"$f":"IF($D16, 0, F23-F15)","v":0},0,0,null,null,null,19,null,null,null,null,null,12500000,0,0,0,{"$f":"(U24-U23)/2000","v":0},0,0,0,{"$f":"(Y24-Y23)/2000","v":0}]
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[null,"Results",null,null,null,null,null,null,null,null,null,21]
[null,"Net Present Value",{"$f":"NPV(D9, D24:H24)","v":-4453402.4608907606},null,null,null,null,null,null,null,null,22]
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[null,null,null,null,null,null,null,null,null,null,null,1930]
[null,null,null,null,null,null,null,null,null,null,null,1931]
[null,null,null,null,null,null,null,null,null,null,null,1932]
[null,null,null,null,null,null,null,null,null,null,null,1933]
[null,null,null,null,null,null,null,null,null,null,null,1934]
[null,null,null,null,null,null,null,null,null,null,null,1935]
[null,null,null,null,null,null,null,null,null,null,null,1936]
[null,null,null,null,null,null,null,null,null,null,null,1937]
[null,null,null,null,null,null,null,null,null,null,null,1938]
[null,null,null,null,null,null,null,null,null,null,null,1939]
[null,null,null,null,null,null,null,null,null,null,null,1940]
[null,null,null,null,null,null,null,null,null,null,null,1941]
[null,null,null,null,null,null,null,null,null,null,null,1942]
[null,null,null,null,null,null,null,null,null,null,null,1943]
[null,null,null,null,null,null,null,null,null,null,null,1944]
[null,null,null,null,null,null,null,null,null,null,null,1945]
[null,null,null,null,null,null,null,null,null,null,null,1946]
[null,null,null,null,null,null,null,null,null,null,null,1947]
[null,null,null,null,null,null,null,null,null,null,null,1948]
[null,null,null,null,null,null,null,null,null,null,null,1949]
[null,null,null,null,null,null,null,null,null,null,null,1950]
[null,null,null,null,null,null,null,null,null,null,null,1951]
[null,null,null,null,null,null,null,null,null,null,null,1952]
[null,null,null,null,null,null,null,null,null,null,null,1953]
[null,null,null,null,null,null,null,null,null,null,null,1954]
[null,null,null,null,null,null,null,null,null,null,null,1955]
[null,null,null,null,null,null,null,null,null,null,null,1956]
[null,null,null,null,null,null,null,null,null,null,null,1957]
[null,null,null,null,null,null,null,null,null,null,null,1958]
[null,null,null,null,null,null,null,null,null,null,null,1959]
[null,null,null,null,null,null,null,null,null,null,null,1960]
[null,null,null,null,null,null,null,null,null,null,null,1961]
[null,null,null,null,null,null,null,null,null,null,null,1962]
[null,null,null,null,null,null,null,null,null,null,null,1963]
[null,null,null,null,null,null,null,null,null,null,null,1964]
[null,null,null,null,null,null,null,null,null,null,null,1965]
[null,null,null,null,null,null,null,null,null,null,null,1966]
[null,null,null,null,null,null,null,null,null,null,null,1967]
[null,null,null,null,null,null,null,null,null,null,null,1968]
[null,null,null,null,null,null,null,null,null,null,null,1969]
[null,null,null,null,null,null,null,null,null,null,null,1970]
[null,null,null,null,null,null,null,null,null,null,null,1971]
[null,null,null,null,null,null,null,null,null,null,null,1972]
[null,null,null,null,null,null,null,null,null,null,null,1973]
[null,null,null,null,null,null,null,null,null,null,null,1974]
[null,null,null,null,null,null,null,null,null,null,null,1975]
[null,null,null,null,null,null,null,null,null,null,null,1976]
[null,null,null,null,null,null,null,null,null,null,null,1977]
[null,null,null,null,null,null,null,null,null,null,null,1978]
[null,null,null,null,null,null,null,null,null,null,null,1979]
[null,null,null,null,null,null,null,null,null,null,null,1980]
[null,null,null,null,null,null,null,null,null,null,null,1981]
[null,null,null,null,null,null,null,null,null,null,null,1982]
[null,null,null,null,null,null,null,null,null,null,null,1983]
[null,null,null,null,null,null,null,null,null,null,null,1984]
[null,null,null,null,null,null,null,null,null,null,null,1985]
[null,null,null,null,null,null,null,null,null,null,null,1986]
[null,null,null,null,null,null,null,null,null,null,null,1987]
[null,null,null,null,null,null,null,null,null,null,null,1988]
[null,null,null,null,null,null,null,null,null,null,null,1989]
[null,null,null,null,null,null,null,null,null,null,null,1990]
[null,null,null,null,null,null,null,null,null,null,null,1991]
[null,null,null,null,null,null,null,null,null,null,null,1992]
[null,null,null,null,null,null,null,null,null,null,null,1993]
[null,null,null,null,null,null,null,null,null,null,null,1994]
[null,null,null,null,null,null,null,null,null,null,null,1995]
[null,null,null,null,null,null,null,null,null,null,null,1996]
[null,null,null,null,null,null,null,null,null,null,null,1997]
[null,null,null,null,null,null,null,null,null,null,null,1998]
[null,null,null,null,null,null,null,null,null,null,null,1999]
[null,null,null,null,null,null,null,null,null,null,null,2000]

{"sheet":"MarkovSimulation","index":8,"n_rows":54,"n_cols":14,"rows_kept":54,"cut":false,"hidden":false,"merged":[[19,0,20,7],[0,0,0,14],[11,0,11,7],[12,0,12,1],[12,2,12,7],[18,0,18,7],[11,10,11,13],[12,10,13,10],[12,11,13,11],[12,12,13,12],[2,0,9,13]]}
["HTMA 3ed Chapter 6: Air-To-Air Combat Markov Simulation Example"]
["Trial ID",5234]
["This is an example of a Markov chain used to simulate aerial combat between two fighter planes, A and B.  Combat is divided into rounds and in each round, either plane can be on the other's tail, they can be disengaged, or one of the planes can win.  A given plane can shoot down another only if it is on the other plane's tail.  The combat ends when one plane shoots down the other.  The \"State Probabilities\" table shows the chance that in a given state of the \"system\" (i.e., in this case, the aerial combat) will occur given a previous state.  When one fighter is on the other's tail, the most likely outcome in the next time increment is that the same state will persist and the same fighter will still be on the other's tail.  There is also a chance that the other fighter could disengage, that the tailing fighter becomes the tailed fighter, or that the tailed fighter is shot down.  Note that there is no chance of a fighter that is being tailed to shoot down the tailing fighter unless it first manages to reverse postions and tail the other fighter.  In the probabilities initially set for this combat simulation, Fighter A has an advantage.  Fighter A is slightly more likely to get on B's tail and stay there and when it is on B's tail, A is slightly more likely to shoot B down."]
[]
[]
[]
[]
[]
[]
[]
[]
["State Probabilities",null,null,null,null,null,null,null,null,null,"Simulation"]
[null,null,"State on Round N+1",null,null,null,null,null,null,null,"State Code","State Description","Round"]
["State on Round N","State Code","A on tail","B on tail","Disengaged","A victory","B victory","Sum Check",null,null,null,null,null,"HDR PRNG"]
["A on tail",1,0.6,0.1,0.15,0.15,0,{"$f":"SUM(C15:G15)","v":1},null,"Initial State=>",1,{"$f":"CHOOSE(K15,C$26,D$26,E$26,F$26,G$26)","v":"A on tail"},1,{"$f":" ((MOD((MOD(MOD(999999999999989,MOD($B$2*2499997+M15*1800451,7450589)*4658+7450581)*383,99991)*7440893+MOD(MOD(999999999999989,MOD($B$2*2246527+M15*2399993,7450987)*7580+7560584)*17669,7440893))*1343,4294967296))+0.5)/2^32","v":0.32695659424643964}]
["B on tail",2,0.1,0.5,0.3,0,0.1,{"$f":"SUM(C16:G16)","v":0.99999999999999989},null,null,{"$f":"IF(K15>3,\"\",HLOOKUP(N15,OFFSET($C$22,K15-1,0):$G$25,4-K15+1))","v":1},{"$f":"IF(K15>3,\"\",CHOOSE(K16,C$26,D$26,E$26,F$26,G$26))","v":"A on tail"},2,{"$f":" ((MOD((MOD(MOD(999999999999989,MOD($B$2*2499997+M16*1800451,7450589)*4658+7450581)*383,99991)*7440893+MOD(MOD(999999999999989,MOD($B$2*2246527+M16*2399993,7450987)*7580+7560584)*17669,7440893))*1343,4294967296))+0.5)/2^32","v":5.0273898523300886E-4}]
["Disengaged",3,0.55000000000000004,0.45,0,0,0,1,null,null,{"$f":"IF(K16>3,\"\",HLOOKUP(N16,OFFSET($C$22,K16-1,0):$G$25,4-K16+1))","v":1},{"$f":"IF(K16>3,\"\",CHOOSE(K17,C$26,D$26,E$26,F$26,G$26))","v":"A on tail"},3,0.66620063001755625]
[null,null,null,null,null,null,null,null,null,null,{"$f":"IF(K17>3,\"\",HLOOKUP(N17,OFFSET($C$22,K17-1,0):$G$25,4-K17+1))","v":2},"B on tail",4,0.5824252589372918]
["Cumulative Probability-Lookup Table",null,null,null,null,null,null,null,null,null,{"$f":"IF(K18>3,\"\",HLOOKUP(N18,OFFSET($C$22,K18-1,0):$G$25,4-K18+1))","v":2},"B on tail",5,0.81229893153067678]
["This table uses cumulative probabilities of the states in the table above so that the states can be found with the Excel hlookup function",null,null,null,null,null,null,null,null,null,{"$f":"IF(K19>3,\"\",HLOOKUP(N19,OFFSET($C$22,K19-1,0):$G$25,4-K19+1))","v":3},"Disengaged",6,0.14761167706456035]
[null,null,null,null,null,null,null,null,null,null,{"$f":"IF(K20>3,\"\",HLOOKUP(N20,OFFSET($C$22,K20-1,0):$G$25,4-K20+1))","v":1},"A on tail",7,0.12604688049759716]
[{"$f":"A15","v":"A on tail"},null,0,{"$f":"SUM($C15:C15)","v":0.6},{"$f":"SUM($C15:D15)","v":0.7},{"$f":"SUM($C15:E15)","v":0.85},{"$f":"SUM($C15:F15)","v":1},null,null,null,{"$f":"IF(K21>3,\"\",HLOOKUP(N21,OFFSET($C$22,K21-1,0):$G$25,4-K21+1))","v":1},"A on tail",8,0.80195554892998189]
[{"$f":"A16","v":"B on tail"},null,0,{"$f":"SUM($C16:C16)","v":0.1},{"$f":"SUM($C16:D16)","v":0.6},{"$f":"SUM($C16:E16)","v":0.89999999999999991},{"$f":"SUM($C16:F16)","v":0.89999999999999991},null,null,null,{"$f":"IF(K22>3,\"\",HLOOKUP(N22,OFFSET($C$22,K22-1,0):$G$25,4-K22+1))","v":3},"Disengaged",9,0.94867510756012052]
[{"$f":"A17","v":"Disengaged"},null,0,{"$f":"SUM($C17:C17)","v":0.55000000000000004},{"$f":"SUM($C17:D17)","v":1},{"$f":"SUM($C17:E17)","v":1},{"$f":"SUM($C17:F17)","v":1},null,null,null,{"$f":"IF(K23>3,\"\",HLOOKUP(N23,OFFSET($C$22,K23-1,0):$G$25,4-K23+1))","v":2},"B on tail",10,0.28580176329705864]
["State Code",null,1,2,3,4,5,null,null,null,{"$f":"IF(K24>3,\"\",HLOOKUP(N24,OFFSET($C$22,K24-1,0):$G$25,4-K24+1))","v":2},"B on tail",11,0.88656197895761579]
["State Description",null,"A on tail","B on tail","Disengaged","A victory!","B victory!",null,null,null,{"$f":"IF(K25>3,\"\",HLOOKUP(N25,OFFSET($C$22,K25-1,0):$G$25,4-K25+1))","v":3},"Disengaged",12,2.8989615733735263E-2]
[null,null,null,null,null,null,null,null,null,null,{"$f":"IF(K26>3,\"\",HLOOKUP(N26,OFFSET($C$22,K26-1,0):$G$25,4-K26+1))","v":1},"A on tail",13,3.1553187989629805E-2]
[null,null,null,null,null,null,null,null,null,null,{"$f":"IF(K27>3,\"\",HLOOKUP(N27,OFFSET($C$22,K27-1,0):$G$25,4-K27+1))","v":1},"A on tail",14,0.84476675896439701]
[null,null,null,null,null,null,null,null,null,null,{"$f":"IF(K28>3,\"\",HLOOKUP(N28,OFFSET($C$22,K28-1,0):$G$25,4-K28+1))","v":3},"Disengaged",15,0.88356871402356774]
[null,null,null,null,null,null,null,null,null,null,{"$f":"IF(K29>3,\"\",HLOOKUP(N29,OFFSET($C$22,K29-1,0):$G$25,4-K29+1))","v":2},"B on tail",16,0.95401036262046546]
[null,null,null,null,null,null,null,null,null,null,{"$f":"IF(K30>3,\"\",HLOOKUP(N30,OFFSET($C$22,K30-1,0):$G$25,4-K30+1))","v":5},"B victory!",17,0.9659031123155728]
[null,null,null,null,null,null,null,null,null,null,{"$f":"IF(K31>3,\"\",HLOOKUP(N31,OFFSET($C$22,K31-1,0):$G$25,4-K31+1))","v":""},"",18,0.5772144888760522]
[null,null,null,null,null,null,null,null,null,null,{"$f":"IF(K32>3,\"\",HLOOKUP(N32,OFFSET($C$22,K32-1,0):$G$25,4-K32+1))","v":""},"",19,0.27046088862698525]
[null,null,null,null,null,null,null,null,null,null,{"$f":"IF(K33>3,\"\",HLOOKUP(N33,OFFSET($C$22,K33-1,0):$G$25,4-K33+1))","v":""},"",20,0.36564539663959295]
[null,null,null,null,null,null,null,null,null,null,{"$f":"IF(K34>3,\"\",HLOOKUP(N34,OFFSET($C$22,K34-1,0):$G$25,4-K34+1))","v":""},"",21,0.94493064109701663]
[null,null,null,null,null,null,null,null,null,null,{"$f":"IF(K35>3,\"\",HLOOKUP(N35,OFFSET($C$22,K35-1,0):$G$25,4-K35+1))","v":""},"",22,0.96827055409085006]
[null,null,null,null,null,null,null,null,null,null,{"$f":"IF(K36>3,\"\",HLOOKUP(N36,OFFSET($C$22,K36-1,0):$G$25,4-K36+1))","v":""},"",23,0.98888477275613695]
[null,null,null,null,null,null,null,null,null,null,{"$f":"IF(K37>3,\"\",HLOOKUP(N37,OFFSET($C$22,K37-1,0):$G$25,4-K37+1))","v":""},"",24,8.5249908152036369E-2]
[null,null,null,null,null,null,null,null,null,null,{"$f":"IF(K38>3,\"\",HLOOKUP(N38,OFFSET($C$22,K38-1,0):$G$25,4-K38+1))","v":""},"",25,0.23480975616257638]
[null,null,null,null,null,null,null,null,null,null,{"$f":"IF(K39>3,\"\",HLOOKUP(N39,OFFSET($C$22,K39-1,0):$G$25,4-K39+1))","v":""},"",26,0.18160330469254404]
[null,null,null,null,null,null,null,null,null,null,{"$f":"IF(K40>3,\"\",HLOOKUP(N40,OFFSET($C$22,K40-1,0):$G$25,4-K40+1))","v":""},"",27,0.92935826268512756]
[null,null,null,null,null,null,null,null,null,null,{"$f":"IF(K41>3,\"\",HLOOKUP(N41,OFFSET($C$22,K41-1,0):$G$25,4-K41+1))","v":""},"",28,2.6012172573246062E-2]
[null,null,null,null,null,null,null,null,null,null,{"$f":"IF(K42>3,\"\",HLOOKUP(N42,OFFSET($C$22,K42-1,0):$G$25,4-K42+1))","v":""},"",29,0.53167785832192749]
[null,null,null,null,null,null,null,null,null,null,{"$f":"IF(K43>3,\"\",HLOOKUP(N43,OFFSET($C$22,K43-1,0):$G$25,4-K43+1))","v":""},"",30,0.86035402968991548]
[null,null,null,null,null,null,null,null,null,null,{"$f":"IF(K44>3,\"\",HLOOKUP(N44,OFFSET($C$22,K44-1,0):$G$25,4-K44+1))","v":""},"",31,0.33479570772033185]
[null,null,null,null,null,null,null,null,null,null,{"$f":"IF(K45>3,\"\",HLOOKUP(N45,OFFSET($C$22,K45-1,0):$G$25,4-K45+1))","v":""},"",32,0.36261843692045659]
[null,null,null,null,null,null,null,null,null,null,{"$f":"IF(K46>3,\"\",HLOOKUP(N46,OFFSET($C$22,K46-1,0):$G$25,4-K46+1))","v":""},"",33,0.89853601192589849]
[null,null,null,null,null,null,null,null,null,null,{"$f":"IF(K47>3,\"\",HLOOKUP(N47,OFFSET($C$22,K47-1,0):$G$25,4-K47+1))","v":""},"",34,0.4512684642104432]
[null,null,null,null,null,null,null,null,null,null,{"$f":"IF(K48>3,\"\",HLOOKUP(N48,OFFSET($C$22,K48-1,0):$G$25,4-K48+1))","v":""},"",35,0.21881947608198971]
[null,null,null,null,null,null,null,null,null,null,{"$f":"IF(K49>3,\"\",HLOOKUP(N49,OFFSET($C$22,K49-1,0):$G$25,4-K49+1))","v":""},"",36,0.61312230594921857]
[null,null,null,null,null,null,null,null,null,null,{"$f":"IF(K50>3,\"\",HLOOKUP(N50,OFFSET($C$22,K50-1,0):$G$25,4-K50+1))","v":""},"",37,0.70111891941633075]
[null,null,null,null,null,null,null,null,null,null,{"$f":"IF(K51>3,\"\",HLOOKUP(N51,OFFSET($C$22,K51-1,0):$G$25,4-K51+1))","v":""},"",38,0.85391798720229417]
[null,null,null,null,null,null,null,null,null,null,{"$f":"IF(K52>3,\"\",HLOOKUP(N52,OFFSET($C$22,K52-1,0):$G$25,4-K52+1))","v":""},"",39,0.51300135033670813]
[null,null,null,null,null,null,null,null,null,null,{"$f":"IF(K53>3,\"\",HLOOKUP(N53,OFFSET($C$22,K53-1,0):$G$25,4-K53+1))","v":""},"",40,0.27066265244502574]

{"sheet":"Contact","index":9,"n_rows":35,"n_cols":4,"rows_kept":35,"cut":false,"hidden":false,"merged":[[20,1,21,10],[34,2,35,9],[1,1,2,10]]}
[]
[null,"What's Next?"]
[]
[]
[]
[null,null,"Keep an eye on our newsletter for the Advanced Simulations in Excel launch date."]
[]
[null,null,"Topics covered will include things like:"]
[null,null,null,"Applying more advanced methods for risk tolerance"]
[null,null,null,"Building more advanced simulations, like Markov and agent based models"]
[null,null,null,"Computing more advanced information values "]
[null,null,null,"Using distributions based on observed data"]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"Contact"]
[]
[]
[]
[null,null,"Doug Hubbard"]
[null,null,"dwhubbard@hubbardresearch.com"]
[null,null,"630 858 2788"]
[]
[null,null,"Jon Murphy"]
[null,null,"jmurphy@hubbardresearch.com"]
[null,null,"704 773 3464"]
[]
[null,null,"Visit www.hubbardresearch.com for more information on training and consulting."]
[]
[null,null,"Visit www.howtomeasureanything.com for information about Doug's books and accompanying free downloads."]