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{"sheet":"Sheet2","index":0,"n_rows":3531,"n_cols":30,"rows_kept":3531,"cut":false,"hidden":false,"merged":[[0,20,0,22]]}
["Shifted Exponential CDF",null,"Using the inverse CDF sampling method",null,"theta",null,"Random Number","Random Draw","Observations",null,"From Jaynes",null,null,null,null,null,null,null,null,null,"Bootstrap Samples",null,null,"Bootstrap Sample Means","Overall Mean",null,null,"SE(theta)"]
["F(X) = 1-exp(-lambda*(x-theta)), x>=theta",null,"F(X) = 1-exp(theta-x)",null,10,null,{"$f":"RAND()","v":0.14104284907376297},{"$f":"$E$2-LN(1-G2)","v":10.152036240749347},{"$f":"COUNTA(G:G)-1","v":3530},null,"Observe: {10, 12, 15}, calculate frequentist 95% CI for theta",null,null,null,null,"Also consider bootstrapping {10, 12, 15}",null,null,null,1,{"$f":"INDEX(sample,ROWS(sample)*RAND()+1,COLUMNS(sample)*RAND()+1)","v":15},12,10,{"$f":"AVERAGE(U2:W2)-1","v":11.333333333333334},{"$f":"AVERAGE(X:X)","v":11.444999999999993},{"$f":"(X2-$Y$2)^2","v":1.246944444444279E-2},{"$f":"SUM(Z:Z)","v":279.83944444444415},{"$f":"(AA2/(AD6-1))^0.5","v":1.1858450000073504},null,"alpha"]
["0 otherwise",null,null,null,null,null,{"$f":"RAND()","v":0.91366454735321734},{"$f":"$E$2-LN(1-G3)","v":12.449514958219776},null,null,"low","up","Standard Deviation","Standard Error",null,null,"Original Sample",null,null,2,10,12,10,{"$f":"AVERAGE(U3:W3)-1","v":9.6666666666666661},null,{"$f":"(X3-$Y$2)^2","v":3.1624694444444224},null,null,null,0.05]
[null,null,"rand = 1-exp(theta-x)",null,null,null,{"$f":"RAND()","v":0.3869192619329207},{"$f":"$E$2-LN(1-G4)","v":10.489258641984668},null,null,10.199999999999999,12.2,{"$f":"(1/I2)^0.5","v":1.6831105696898524E-2},{"$f":"M4/I2^0.5","v":2.8328611898016995E-4},null,null,10,null,null,3,10,15,12,11.333333333333334,null,1.246944444444279E-2]
["lambda = 1 in our problem",null,null,null,null,null,0.33874657535007813,10.413618116768337,null,null,null,null,null,null,null,null,12,null,null,4,10,12,12,10.333333333333334,null,1.2358027777777614,null,null,null,"Number of bootstrap samples"]
[null,null,"theta - ln(1-rand)  = x",null,null,null,9.0400318382909295E-2,10.094750686571059,null,null,"But…",null,"width",null,null,null,15,null,null,5,15,10,15,12.333333333333334,null,0.78913611111112425,null,null,null,{"$f":"COUNTA(T:T)","v":200}]
["F(X) = 1-exp(theta-x)",null,null,null,null,null,0.18636686154631421,10.206245704431135,null,null,"Bayesian 95% credible region",null,{"$f":"L4-K4","v":2},null,null,null,null,null,null,6,15,10,15,12.333333333333334,null,0.78913611111112425]
[null,null,"Idea:",null,null,null,0.24963911559440988,10.28720100897392,null,null,"low","up",null,null,null,null,null,null,null,7,15,10,12,11.333333333333334,null,1.246944444444279E-2]
["rand = 1-exp(theta-x)",null,"generate random numbers in (0,1)",null,null,null,0.47804804302558079,10.650179731782584,null,null,9,10,null,null,null,null,null,null,null,8,15,10,15,12.333333333333334,null,0.78913611111112425]
["theta - ln(1-rand)  = x",null,"for each one, solve for x",null,null,null,0.68634485548349089,11.15946116248077,null,null,null,null,null,null,null,null,null,null,null,9,10,15,10,10.666666666666666,null,0.60580277777776803]
[null,null,null,null,null,null,0.39388324617800807,10.500682648397374,null,null,"Is this evidence that the frequentist CI is flawed?",null,null,null,null,null,null,null,null,10,12,12,15,12,null,0.3080250000000076]
[null,null,null,null,null,null,0.36710164181888072,10.457445441324769,null,null,"I do not believe so.",null,null,null,null,null,null,null,null,11,12,15,12,12,null,0.3080250000000076]
[null,null,null,null,null,null,2.3326946530378811E-2,10.023603326271825,null,null,null,null,null,null,null,null,null,null,null,12,15,10,15,12.333333333333334,null,0.78913611111112425]
[null,null,null,null,null,null,0.10792093225282717,10.114200509358339,null,null,"First, it is a small sample size situation. I do not believe any interval is great.",null,null,null,null,null,null,null,null,13,15,15,15,14,null,6.528025000000035]
[null,null,null,null,null,null,0.91596362887288019,12.476505584243204,null,null,"Second, the example disallows the frequentist to use ANY other frequentist method.",null,null,null,null,null,null,null,null,14,10,10,12,9.6666666666666661,null,3.1624694444444224]
[null,null,null,null,null,null,0.56438267074726844,10.830991106224433,null,null,"Not only that, it disallows the frequentist to use scientific knowledge that theta < min(X_i)",null,null,null,null,null,null,null,null,15,10,10,15,10.666666666666666,null,0.60580277777776803]
[null,null,null,null,null,null,0.23315634811055819,10.265472342084257,null,null,null,null,null,null,null,null,null,null,null,16,10,15,10,10.666666666666666,null,0.60580277777776803]
[null,null,null,null,null,null,0.80409458594019345,11.630123317558981,null,null,"Consider some other possibilities:",null,null,null,null,null,null,null,null,17,15,12,10,11.333333333333334,null,1.246944444444279E-2]
[null,null,null,null,null,null,0.28475575838937883,10.335131197960774,null,null,null,null,null,null,null,null,null,null,null,18,10,10,15,10.666666666666666,null,0.60580277777776803]
[null,null,null,null,null,null,6.5821024246593085E-2,10.06808723624829,null,null,"95% CI for theta, for large n","<--- Collapses to 10",null,null,null,null,null,null,null,19,15,12,10,11.333333333333334,null,1.246944444444279E-2]
[null,null,null,null,null,null,0.83710214893055157,11.814631955177243,null,null,"low","up","mean","Standard Deviation","Standard Error",null,null,null,null,20,15,15,12,13,null,2.4180250000000214]
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[null,null,null,null,null,null,0.94816830455762324,12.959753435712665,null,null,null,null,null,null,null,null,null,null,null,22,12,10,15,11.333333333333334,null,1.246944444444279E-2]
[null,null,null,null,null,null,0.94817523378787283,12.959887131772694,null,null,null,null,null,null,null,null,null,null,null,23,15,10,12,11.333333333333334,null,1.246944444444279E-2]
[null,null,null,null,null,null,0.73743862228425328,11.337270404412553,null,null,null,null,null,"And corresponding versions with up=10, keep interval same width",null,null,null,null,null,24,12,10,15,11.333333333333334,null,1.246944444444279E-2]
[null,null,null,null,null,null,0.7644985089683165,11.44603803420098,null,null,"95% confidence interval using Order Statistics",null,null,null,null,null,null,null,null,25,15,15,15,{"$f":"AVERAGE(U26:W26)-1","v":14},null,6.528025000000035]
[null,null,null,null,null,null,0.87915510940102193,12.113247451592965,null,null,"low","up","width","low","up",null,null,null,null,26,12,15,10,11.333333333333334,null,1.246944444444279E-2]
[null,null,null,null,null,null,0.12043499473130803,10.128327805917102,null,null,{"$f":"_xlfn.PERCENTILE.EXC(H:H,0.025)","v":10.026571343267824},{"$f":"_xlfn.PERCENTILE.EXC(H:H,0.975)","v":13.785828765533985},{"$f":"L28-K28","v":3.7592574222661614},{"$f":"O28-M28","v":6.2407425777338386},10,null,null,null,null,27,10,12,10,9.6666666666666661,null,3.1624694444444224]
[null,null,null,null,null,null,0.72126973451834642,11.27751075519237,null,null,null,null,null,null,null,null,null,null,null,28,15,10,10,10.666666666666666,null,0.60580277777776803]
[null,null,null,null,null,null,0.64184895685407595,11.02680047333085,null,null,null,null,null,null,null,null,null,null,null,29,15,15,15,14,null,6.528025000000035]
[null,null,null,null,null,null,0.22168293830941621,10.250621303516633,null,null,"Using min as upper, keep interval same width as original 95% CI?",null,null,null,null,null,null,null,null,30,10,10,10,9,null,5.9780249999999668]
[null,null,null,null,null,null,7.7098911661945269E-2,10.080233213452384,null,null,"low","up",null,null,null,null,null,null,null,31,10,12,12,10.333333333333334,null,1.2358027777777614]
[null,null,null,null,null,null,0.52237128602212712,10.738921597316757,null,null,{"$f":"L33-M7","v":8},{"$f":"10","v":10},null,null,null,null,null,null,null,32,15,12,10,11.333333333333334,null,1.246944444444279E-2]
[null,null,null,null,null,null,0.87467951666458088,12.076880956095664,null,null,null,null,null,null,null,null,null,null,null,33,15,12,12,12,null,0.3080250000000076]
[null,null,null,null,null,null,0.95302824970461997,13.058208915524684,null,null,null,null,null,null,null,null,null,null,null,34,12,12,15,12,null,0.3080250000000076]
[null,null,null,null,null,null,0.58383353735482924,10.876669948170417,null,null,"Basic Bootstrap 95% CI",null,null,null,null,null,null,null,null,35,10,15,10,10.666666666666666,null,0.60580277777776803]
[null,null,null,null,null,null,0.19047951025807941,10.211313194582655,null,null,"low","up","width","low","up",null,null,null,null,36,12,10,15,11.333333333333334,null,1.246944444444279E-2]
[null,null,null,null,null,null,0.31095535879279412,10.372449218765158,null,null,{"$f":"(2*$E$2)-SMALL(X2:X201,$AD$6*(1-$AD$3))","v":6},{"$f":"(2*$E$2)-SMALL(X2:X201,$AD$6*$AD$3)","v":10.333333333333334},{"$f":"L38-K38","v":4.3333333333333339},{"$f":"O38-M38","v":5.6666666666666661},10,null,null,null,null,37,12,15,15,13,null,2.4180250000000214]
[null,null,null,null,null,null,9.535698758171629E-2,10.100214874518842,null,null,null,null,null,null,null,null,null,null,null,38,15,10,10,10.666666666666666,null,0.60580277777776803]
[null,null,null,null,null,null,0.89102984631082283,12.216681253613707,null,null,null,null,null,null,null,null,null,null,null,39,15,15,15,14,null,6.528025000000035]
[null,null,null,null,null,null,0.89271617238850021,12.232277361939929,null,null,"Percentile Bootstrap 95% CI",null,null,null,null,null,null,null,null,40,10,10,15,10.666666666666666,null,0.60580277777776803]
[null,null,null,null,null,null,0.41986024148497259,10.544486241511638,null,null,"low","up","width","low","up",null,null,null,null,41,{"$f":"INDEX(sample,ROWS(sample)*RAND()+1,COLUMNS(sample)*RAND()+1)","v":12},15,10,11.333333333333334,null,1.246944444444279E-2]
[null,null,null,null,null,null,3.5024811041226345E-2,10.035652888897234,null,null,{"$f":"SMALL(X2:X201,$AD$6*$AD$3)","v":9.6666666666666661},{"$f":"SMALL(X2:X201,$AD$6*(1-$AD$3))","v":14},{"$f":"L43-K43","v":4.3333333333333339},{"$f":"O43-M43","v":5.6666666666666661},10,null,null,null,null,42,15,12,12,12,null,0.3080250000000076]
[null,null,null,null,null,null,0.19486493225232471,10.216745229616118,null,null,null,null,null,null,null,null,null,null,null,43,15,15,12,13,null,2.4180250000000214]
[null,null,null,null,null,null,0.77246785114905081,11.480463736944417,null,null,null,null,null,null,null,null,null,null,null,44,12,15,15,13,null,2.4180250000000214]
[null,null,null,null,null,null,0.46024118765328259,10.616632883001246,null,null,"Bootstrap 95% CI, using SE(theta)",null,null,null,null,null,null,null,null,45,10,10,10,9,null,5.9780249999999668]
[null,null,null,null,null,null,0.8609234447699835,11.972730740411967,null,null,"low","up","width","low","up",null,null,null,null,46,10,12,10,9.6666666666666661,null,3.1624694444444224]
[null,null,null,null,null,null,0.20343680738235637,10.227448814903857,null,null,{"$f":"$Y$2-1.96*$AB$2","v":9.1207437999855863},{"$f":"$Y$2+1.96*$AB$2","v":13.7692562000144},{"$f":"L48-K48","v":4.6485124000288138},{"$f":"O48-M48","v":5.3514875999711862},10,null,null,null,null,47,15,15,12,13,null,2.4180250000000214]
[null,null,null,null,null,null,2.0855237343476274E-2,10.021075779500958,null,null,null,null,null,null,null,null,null,null,null,48,10,10,12,9.6666666666666661,null,3.1624694444444224]
[null,null,null,null,null,null,0.91927397545996825,12.516694270686758,null,null,null,null,null,null,null,null,null,null,null,49,10,15,12,11.333333333333334,null,1.246944444444279E-2]
[null,null,null,null,null,null,0.32278425835311952,10.389765383797101,null,null,null,null,null,null,null,null,null,null,null,50,10,15,12,11.333333333333334,null,1.246944444444279E-2]
[null,null,null,null,null,null,0.46595136920698199,10.627268375267679,null,null,null,null,null,null,null,null,null,null,null,51,15,10,12,11.333333333333334,null,1.246944444444279E-2]
[null,null,null,null,null,null,0.24362043684989065,10.279211961137527,null,null,null,null,null,null,null,null,null,null,null,52,12,10,10,9.6666666666666661,null,3.1624694444444224]
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[null,null,null,null,null,null,0.82798132639977973,11.760152240618561,null,null,null,null,null,null,null,null,null,null,null,54,12,15,12,12,null,0.3080250000000076]
[null,null,null,null,null,null,1.5677258306828756E-2,10.01580144618111,null,null,null,null,null,null,null,null,null,null,null,55,10,15,12,11.333333333333334,null,1.246944444444279E-2]
[null,null,null,null,null,null,0.36953721670292827,10.461301152603923,null,null,null,null,null,null,null,null,null,null,null,56,10,15,10,10.666666666666666,null,0.60580277777776803]
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[null,null,null,null,null,null,{"$f":"RAND()","v":6.1258410559924648E-2},{"$f":"$E$2-LN(1-G68)","v":10.06321503526209},null,null,null,null,null,null,null,null,null,null,null,67,15,15,12,13,null,2.4180250000000214]
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[null,null,null,null,null,null,1.0774952436546692E-2,10.010833422624865,null,null,null,null,null,null,null,null,null,null,null,73,15,15,15,14,null,6.528025000000035]
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