beta: 0.2
preprocessing time for sampling: 1.487358808517456
amortized time for sample size  5 is:  0.0008495488166809081
preprocessing time for sampling: 1.4890940189361572
amortized time for sample size  10 is:  0.0008645482063293458
preprocessing time for sampling: 1.4916930198669434
amortized time for sample size  15 is:  0.0008565753300984701
preprocessing time for sampling: 1.478013277053833
amortized time for sample size  20 is:  0.0008394527435302736
preprocessing time for sampling: 1.4865660667419434
amortized time for sample size  25 is:  0.0008426968574523926
preprocessing time for sampling: 1.4882879257202148
amortized time for sample size  30 is:  0.0008323814074198406
preprocessing time for sampling: 1.488680124282837
amortized time for sample size  35 is:  0.0008545836039951869
preprocessing time for sampling: 1.4787960052490234
amortized time for sample size  40 is:  0.000835653007030487
preprocessing time for sampling: 1.4788649082183838
amortized time for sample size  45 is:  0.0008297929233974881
preprocessing time for sampling: 1.4770607948303223
amortized time for sample size  50 is:  0.0008279232501983642
preprocessing time for sampling: 1.4851949214935303
amortized time for sample size  55 is:  0.0008375880067998713
preprocessing time for sampling: 1.4786930084228516
amortized time for sample size  60 is:  0.0008391958475112916
preprocessing time for sampling: 1.488050937652588
amortized time for sample size  65 is:  0.00082786985544058
preprocessing time for sampling: 1.4819798469543457
amortized time for sample size  70 is:  0.0008271970748901366
preprocessing time for sampling: 1.4876821041107178
amortized time for sample size  75 is:  0.0008490678469340007
preprocessing time for sampling: 1.5241971015930176
amortized time for sample size  80 is:  0.0008670479357242584
preprocessing time for sampling: 1.545922040939331
amortized time for sample size  85 is:  0.0008575469185324276
preprocessing time for sampling: 1.482133150100708
amortized time for sample size  90 is:  0.0008483012252383762
preprocessing time for sampling: 1.4982903003692627
amortized time for sample size  95 is:  0.0008370459707159743
preprocessing time for sampling: 1.4907071590423584
amortized time for sample size  100 is:  0.0008423554420471192
preprocessing time for sampling: 1.500920057296753
amortized time for sample size  105 is:  0.0008467696053641182
preprocessing time for sampling: 1.518380880355835
amortized time for sample size  110 is:  0.0008452462283047764
preprocessing time for sampling: 1.4895679950714111
amortized time for sample size  115 is:  0.0008405400566432787
preprocessing time for sampling: 1.4826600551605225
amortized time for sample size  120 is:  0.0008389327327410381
preprocessing time for sampling: 1.4931418895721436
amortized time for sample size  125 is:  0.0008403765487670897
preprocessing time for sampling: 1.4949560165405273
amortized time for sample size  130 is:  0.0008431380895467903
preprocessing time for sampling: 1.495063066482544
amortized time for sample size  135 is:  0.0008395750434310349
preprocessing time for sampling: 1.4859240055084229
amortized time for sample size  140 is:  0.0008438005958284651
preprocessing time for sampling: 1.4972810745239258
amortized time for sample size  145 is:  0.000843738128399027
preprocessing time for sampling: 1.492926836013794
amortized time for sample size  150 is:  0.0008510357538859051
preprocessing time for sampling: 1.5215659141540527
amortized time for sample size  155 is:  0.000857606780144476
preprocessing time for sampling: 1.499479055404663
amortized time for sample size  160 is:  0.00084318807721138
preprocessing time for sampling: 1.4832630157470703
amortized time for sample size  165 is:  0.0008359980149702593
preprocessing time for sampling: 1.492307186126709
amortized time for sample size  170 is:  0.000840661511701696
preprocessing time for sampling: 1.4879488945007324
amortized time for sample size  175 is:  0.0008372434207371306
preprocessing time for sampling: 1.4907431602478027
amortized time for sample size  180 is:  0.0008390512466430662
preprocessing time for sampling: 1.483910083770752
amortized time for sample size  185 is:  0.0008332922394211228
preprocessing time for sampling: 1.4820928573608398
amortized time for sample size  190 is:  0.0008305024724257619
preprocessing time for sampling: 1.4903171062469482
amortized time for sample size  195 is:  0.0008350800367502064
preprocessing time for sampling: 1.4845309257507324
amortized time for sample size  200 is:  0.0008365194916725159
preprocessing time for sampling: 1.484635829925537
amortized time for sample size  205 is:  0.0008333223738321445
preprocessing time for sampling: 1.4841279983520508
amortized time for sample size  210 is:  0.0008370302745274134
preprocessing time for sampling: 1.4813079833984375
amortized time for sample size  215 is:  0.0008669725018878316
preprocessing time for sampling: 1.490004062652588
amortized time for sample size  220 is:  0.0008383512822064487
preprocessing time for sampling: 1.492460012435913
amortized time for sample size  225 is:  0.0008410837491353352
preprocessing time for sampling: 1.4893310070037842
amortized time for sample size  230 is:  0.0008392438266588292
preprocessing time for sampling: 1.4856159687042236
amortized time for sample size  235 is:  0.0008348265810215728
preprocessing time for sampling: 1.479518175125122
amortized time for sample size  240 is:  0.0008333804011344912
preprocessing time for sampling: 1.4795489311218262
amortized time for sample size  245 is:  0.0008355023520333427
preprocessing time for sampling: 1.485541820526123
amortized time for sample size  250 is:  0.0008356251239776614
*** results for plotting, beta= 0.2 

mean_list= [np.float64(0.29000000000000004), np.float64(0.49000000000000005), np.float64(0.48999999999999994), np.float64(0.59), np.float64(0.6199999999999999), np.float64(0.62), np.float64(0.54), np.float64(0.6399999999999999), np.float64(0.6799999999999999), np.float64(0.6599999999999999), np.float64(0.5700000000000001), np.float64(0.57), np.float64(0.5599999999999999), np.float64(0.69), np.float64(0.7), np.float64(0.7), np.float64(0.7), np.float64(0.6399999999999999), np.float64(0.72), np.float64(0.7), np.float64(0.7300000000000001), np.float64(0.7), np.float64(0.72), np.float64(0.7), np.float64(0.78), np.float64(0.6799999999999999), np.float64(0.69), np.float64(0.7699999999999999), np.float64(0.77), np.float64(0.71), np.float64(0.74), np.float64(0.76), np.float64(0.73), np.float64(0.76), np.float64(0.76), np.float64(0.74), np.float64(0.7200000000000001), np.float64(0.72), np.float64(0.78), np.float64(0.6900000000000001), np.float64(0.79), np.float64(0.75), np.float64(0.73), np.float64(0.75), np.float64(0.6799999999999999), np.float64(0.8), np.float64(0.77), np.float64(0.82), np.float64(0.76), np.float64(0.8099999999999999)]
std_list= [np.float64(0.12206555615733704), np.float64(0.16999999999999998), np.float64(0.19209372712298547), np.float64(0.15132745950421556), np.float64(0.09797958971132709), np.float64(0.198997487421324), np.float64(0.13564659966250536), np.float64(0.10198039027185571), np.float64(0.10770329614269009), np.float64(0.2009975124224178), np.float64(0.08999999999999998), np.float64(0.1004987562112089), np.float64(0.142828568570857), np.float64(0.10440306508910552), np.float64(0.15491933384829668), np.float64(0.2), np.float64(0.1341640786499874), np.float64(0.1562049935181331), np.float64(0.10770329614269011), np.float64(0.11832159566199232), np.float64(0.11000000000000003), np.float64(0.10000000000000003), np.float64(0.08717797887081351), np.float64(0.1264911064067352), np.float64(0.198997487421324), np.float64(0.1661324772583615), np.float64(0.13747727084867523), np.float64(0.14177446878757827), np.float64(0.12688577540449522), np.float64(0.12206555615733705), np.float64(0.11135528725660046), np.float64(0.12000000000000002), np.float64(0.11000000000000003), np.float64(0.128062484748657), np.float64(0.1356465996625054), np.float64(0.08000000000000003), np.float64(0.1777638883463118), np.float64(0.13999999999999999), np.float64(0.0871779788708135), np.float64(0.10440306508910553), np.float64(0.08306623862918076), np.float64(0.16278820596099708), np.float64(0.15524174696260024), np.float64(0.13601470508735444), np.float64(0.13266499161421602), np.float64(0.10000000000000003), np.float64(0.1004987562112089), np.float64(0.13999999999999999), np.float64(0.11135528725660046), np.float64(0.08306623862918078)]
beta: 0.4
preprocessing time for sampling: 1.4929420948028564
amortized time for sample size  5 is:  0.0008470911979675293
preprocessing time for sampling: 1.4828517436981201
amortized time for sample size  10 is:  0.0008463468551635743
preprocessing time for sampling: 1.479231834411621
amortized time for sample size  15 is:  0.0008366978963216145
preprocessing time for sampling: 1.4699270725250244
amortized time for sample size  20 is:  0.0008288353681564331
preprocessing time for sampling: 1.485116958618164
amortized time for sample size  25 is:  0.0008446654319763183
preprocessing time for sampling: 1.488480806350708
amortized time for sample size  30 is:  0.0008462414741516114
preprocessing time for sampling: 1.4935779571533203
amortized time for sample size  35 is:  0.0008282715252467564
preprocessing time for sampling: 1.4836089611053467
amortized time for sample size  40 is:  0.0008481374979019165
preprocessing time for sampling: 1.4761989116668701
amortized time for sample size  45 is:  0.0008303163846333822
preprocessing time for sampling: 1.4746918678283691
amortized time for sample size  50 is:  0.0008435731410980225
preprocessing time for sampling: 1.483557939529419
amortized time for sample size  55 is:  0.0008288875493136318
preprocessing time for sampling: 1.4862217903137207
amortized time for sample size  60 is:  0.000834068497021993
preprocessing time for sampling: 1.5508060455322266
amortized time for sample size  65 is:  0.0008350616968595063
preprocessing time for sampling: 1.497020959854126
amortized time for sample size  70 is:  0.0008419945240020754
preprocessing time for sampling: 1.486694097518921
amortized time for sample size  75 is:  0.0008342867215474448
preprocessing time for sampling: 1.5318231582641602
amortized time for sample size  80 is:  0.0008383287787437439
preprocessing time for sampling: 1.492408037185669
amortized time for sample size  85 is:  0.0008416889415067784
preprocessing time for sampling: 1.499197244644165
amortized time for sample size  90 is:  0.0008279313511318631
preprocessing time for sampling: 1.4920220375061035
amortized time for sample size  95 is:  0.0008411632588035182
preprocessing time for sampling: 1.48563814163208
amortized time for sample size  100 is:  0.0008413622140884398
preprocessing time for sampling: 1.5643179416656494
amortized time for sample size  105 is:  0.0008433444386436826
preprocessing time for sampling: 1.4876501560211182
amortized time for sample size  110 is:  0.000833384188738736
preprocessing time for sampling: 1.4865679740905762
amortized time for sample size  115 is:  0.0008391463860221532
preprocessing time for sampling: 1.500972032546997
amortized time for sample size  120 is:  0.0008418074846267701
preprocessing time for sampling: 1.4869649410247803
amortized time for sample size  125 is:  0.0008494486236572266
preprocessing time for sampling: 1.5169458389282227
amortized time for sample size  130 is:  0.000848910093307495
preprocessing time for sampling: 1.4880990982055664
amortized time for sample size  135 is:  0.0008439929397017868
preprocessing time for sampling: 1.5238392353057861
amortized time for sample size  140 is:  0.0008403603519712174
preprocessing time for sampling: 1.5053188800811768
amortized time for sample size  145 is:  0.0008422200268712538
preprocessing time for sampling: 1.495793104171753
amortized time for sample size  150 is:  0.0008412696679433187
preprocessing time for sampling: 1.4850492477416992
amortized time for sample size  155 is:  0.000837051929966096
preprocessing time for sampling: 1.496293067932129
amortized time for sample size  160 is:  0.0008351863324642181
preprocessing time for sampling: 1.4932069778442383
amortized time for sample size  165 is:  0.0008367771957859847
preprocessing time for sampling: 1.4816341400146484
amortized time for sample size  170 is:  0.0008357365271624397
preprocessing time for sampling: 1.483288049697876
amortized time for sample size  175 is:  0.0008467271668570382
preprocessing time for sampling: 1.5197529792785645
amortized time for sample size  180 is:  0.0008353258106443616
preprocessing time for sampling: 1.4916222095489502
amortized time for sample size  185 is:  0.0008479164097760175
preprocessing time for sampling: 1.4893701076507568
amortized time for sample size  190 is:  0.0008409146509672466
preprocessing time for sampling: 1.4785089492797852
amortized time for sample size  195 is:  0.0008424760622855942
preprocessing time for sampling: 1.4912667274475098
amortized time for sample size  200 is:  0.0008405103325843812
preprocessing time for sampling: 1.4841041564941406
amortized time for sample size  205 is:  0.0008401940973793586
preprocessing time for sampling: 1.4881258010864258
amortized time for sample size  210 is:  0.0008341155165717717
preprocessing time for sampling: 1.481748104095459
amortized time for sample size  215 is:  0.0008340006539987965
preprocessing time for sampling: 1.4838848114013672
amortized time for sample size  220 is:  0.0008391956632787531
preprocessing time for sampling: 1.4838809967041016
amortized time for sample size  225 is:  0.0008392585966322158
preprocessing time for sampling: 1.4789340496063232
amortized time for sample size  230 is:  0.0008343311289082403
preprocessing time for sampling: 1.4875459671020508
amortized time for sample size  235 is:  0.0008267568223019865
preprocessing time for sampling: 1.4802329540252686
amortized time for sample size  240 is:  0.0008275497257709502
preprocessing time for sampling: 1.4745969772338867
amortized time for sample size  245 is:  0.0008401005414067482
preprocessing time for sampling: 1.46002197265625
amortized time for sample size  250 is:  0.0008328988838195801
*** results for plotting, beta= 0.4 

mean_list= [np.float64(0.47000000000000003), np.float64(0.69), np.float64(0.78), np.float64(0.8500000000000002), np.float64(0.8600000000000001), np.float64(0.79), np.float64(0.8099999999999999), np.float64(0.9299999999999999), np.float64(0.8400000000000001), np.float64(0.9), np.float64(0.8800000000000001), np.float64(0.9), np.float64(0.9099999999999999), np.float64(0.8899999999999999), np.float64(0.9400000000000001), np.float64(0.95), np.float64(0.9099999999999999), np.float64(0.9200000000000002), np.float64(0.9700000000000001), np.float64(0.96), np.float64(0.95), np.float64(0.96), np.float64(0.99), np.float64(0.93), np.float64(0.9800000000000001), np.float64(0.96), np.float64(0.9800000000000001), np.float64(0.9400000000000001), np.float64(0.97), np.float64(0.95), np.float64(0.96), np.float64(0.9800000000000001), np.float64(0.95), np.float64(0.99), np.float64(0.99), np.float64(0.96), np.float64(0.9800000000000001), np.float64(1.0), np.float64(0.9800000000000001), np.float64(0.99), np.float64(1.0), np.float64(0.99), np.float64(0.9800000000000001), np.float64(0.99), np.float64(0.9700000000000001), np.float64(0.99), np.float64(0.99), np.float64(0.99), np.float64(0.99), np.float64(0.9800000000000001)]
std_list= [np.float64(0.1345362404707371), np.float64(0.17), np.float64(0.12489995996796799), np.float64(0.0921954445729289), np.float64(0.11135528725660043), np.float64(0.10440306508910552), np.float64(0.13000000000000003), np.float64(0.1004987562112089), np.float64(0.06633249580710801), np.float64(0.1264911064067352), np.float64(0.07483314773547885), np.float64(0.07745966692414831), np.float64(0.09433981132056604), np.float64(0.07000000000000002), np.float64(0.06633249580710798), np.float64(0.04999999999999999), np.float64(0.06999999999999998), np.float64(0.0748331477354788), np.float64(0.04582575694955839), np.float64(0.06633249580710798), np.float64(0.04999999999999999), np.float64(0.09165151389911681), np.float64(0.029999999999999992), np.float64(0.06403124237432847), np.float64(0.039999999999999994), np.float64(0.06633249580710798), np.float64(0.039999999999999994), np.float64(0.06633249580710798), np.float64(0.04582575694955839), np.float64(0.04999999999999999), np.float64(0.04898979485566356), np.float64(0.039999999999999994), np.float64(0.04999999999999999), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.06633249580710798), np.float64(0.039999999999999994), np.float64(0.0), np.float64(0.039999999999999994), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.039999999999999994), np.float64(0.029999999999999992), np.float64(0.06403124237432847), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.039999999999999994)]
beta: 0.6
preprocessing time for sampling: 1.4834280014038086
amortized time for sample size  5 is:  0.0008637084960937501
preprocessing time for sampling: 1.4786171913146973
amortized time for sample size  10 is:  0.0008407144546508789
preprocessing time for sampling: 1.473951816558838
amortized time for sample size  15 is:  0.0008264757792154948
preprocessing time for sampling: 1.4672629833221436
amortized time for sample size  20 is:  0.000840136408805847
preprocessing time for sampling: 1.4817390441894531
amortized time for sample size  25 is:  0.0008347023963928223
preprocessing time for sampling: 1.497128963470459
amortized time for sample size  30 is:  0.0008354166348775228
preprocessing time for sampling: 1.476957082748413
amortized time for sample size  35 is:  0.0008465854099818638
preprocessing time for sampling: 1.4817771911621094
amortized time for sample size  40 is:  0.0008382233381271363
preprocessing time for sampling: 1.4998621940612793
amortized time for sample size  45 is:  0.0008418102264404298
preprocessing time for sampling: 1.4629318714141846
amortized time for sample size  50 is:  0.0008266713142395019
preprocessing time for sampling: 1.4607107639312744
amortized time for sample size  55 is:  0.0008269045569679954
preprocessing time for sampling: 1.4733779430389404
amortized time for sample size  60 is:  0.0008406776189804077
preprocessing time for sampling: 1.4707908630371094
amortized time for sample size  65 is:  0.0008363724855276254
preprocessing time for sampling: 1.4817121028900146
amortized time for sample size  70 is:  0.0008347243581499372
preprocessing time for sampling: 1.482327938079834
amortized time for sample size  75 is:  0.0008354397773742674
preprocessing time for sampling: 1.4863197803497314
amortized time for sample size  80 is:  0.0008371419310569766
preprocessing time for sampling: 1.4773330688476562
amortized time for sample size  85 is:  0.0008294014650232652
preprocessing time for sampling: 1.457780122756958
amortized time for sample size  90 is:  0.0008280733691321477
preprocessing time for sampling: 1.4540088176727295
amortized time for sample size  95 is:  0.0008266848012020712
preprocessing time for sampling: 1.4608657360076904
amortized time for sample size  100 is:  0.0008355621099472045
preprocessing time for sampling: 1.4819741249084473
amortized time for sample size  105 is:  0.0008549023809887114
preprocessing time for sampling: 1.4826130867004395
amortized time for sample size  110 is:  0.0008611538843675092
preprocessing time for sampling: 1.5138731002807617
amortized time for sample size  115 is:  0.0008346165366794754
preprocessing time for sampling: 1.47853684425354
amortized time for sample size  120 is:  0.0008402498364448547
preprocessing time for sampling: 1.4826698303222656
amortized time for sample size  125 is:  0.0008523222732543948
preprocessing time for sampling: 1.5391418933868408
amortized time for sample size  130 is:  0.0008517995247474084
preprocessing time for sampling: 1.5183331966400146
amortized time for sample size  135 is:  0.000860218118738245
preprocessing time for sampling: 1.483926773071289
amortized time for sample size  140 is:  0.0008382920707975117
preprocessing time for sampling: 1.4812662601470947
amortized time for sample size  145 is:  0.0008290098453390187
preprocessing time for sampling: 1.483867883682251
amortized time for sample size  150 is:  0.0008360625425974529
preprocessing time for sampling: 1.4802749156951904
amortized time for sample size  155 is:  0.0008281236310159008
preprocessing time for sampling: 1.4935171604156494
amortized time for sample size  160 is:  0.000833813801407814
preprocessing time for sampling: 1.4877591133117676
amortized time for sample size  165 is:  0.0008344981887123801
preprocessing time for sampling: 1.4813899993896484
amortized time for sample size  170 is:  0.0008289475861717671
preprocessing time for sampling: 1.4819409847259521
amortized time for sample size  175 is:  0.0008302950859069825
preprocessing time for sampling: 1.4816551208496094
amortized time for sample size  180 is:  0.0008330965042114258
preprocessing time for sampling: 1.4882590770721436
amortized time for sample size  185 is:  0.000835460869041649
preprocessing time for sampling: 1.4803340435028076
amortized time for sample size  190 is:  0.0008361474589297646
preprocessing time for sampling: 1.4883031845092773
amortized time for sample size  195 is:  0.0008340025803981685
preprocessing time for sampling: 1.481719970703125
amortized time for sample size  200 is:  0.000832478642463684
preprocessing time for sampling: 1.4838080406188965
amortized time for sample size  205 is:  0.000834725484615419
preprocessing time for sampling: 1.479396104812622
amortized time for sample size  210 is:  0.0008319745858510336
preprocessing time for sampling: 1.4881620407104492
amortized time for sample size  215 is:  0.0008297836835994276
preprocessing time for sampling: 1.4831490516662598
amortized time for sample size  220 is:  0.0008408675952391189
preprocessing time for sampling: 1.4804489612579346
amortized time for sample size  225 is:  0.0008291964954800075
preprocessing time for sampling: 1.487454891204834
amortized time for sample size  230 is:  0.0008297864354175071
preprocessing time for sampling: 1.480841875076294
amortized time for sample size  235 is:  0.0008273487395428596
preprocessing time for sampling: 1.487476110458374
amortized time for sample size  240 is:  0.0008305645883083343
preprocessing time for sampling: 1.4880478382110596
amortized time for sample size  245 is:  0.0008336438548808195
preprocessing time for sampling: 1.4995169639587402
amortized time for sample size  250 is:  0.0008312458705902099
*** results for plotting, beta= 0.6 

mean_list= [np.float64(0.7500000000000001), np.float64(0.7699999999999999), np.float64(0.9100000000000001), np.float64(0.8800000000000001), np.float64(0.97), np.float64(0.9200000000000002), np.float64(0.9399999999999998), np.float64(0.9400000000000001), np.float64(0.99), np.float64(0.96), np.float64(0.9400000000000001), np.float64(0.97), np.float64(0.99), np.float64(0.99), np.float64(0.99), np.float64(0.99), np.float64(1.0), np.float64(1.0), np.float64(0.99), np.float64(0.99), np.float64(1.0), np.float64(0.99), np.float64(1.0), np.float64(0.99), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(0.99), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(0.99), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0)]
std_list= [np.float64(0.08062257748298553), np.float64(0.11000000000000003), np.float64(0.08306623862918074), np.float64(0.14696938456699069), np.float64(0.045825756949558386), np.float64(0.059999999999999984), np.float64(0.09165151389911681), np.float64(0.06633249580710798), np.float64(0.029999999999999992), np.float64(0.06633249580710798), np.float64(0.04898979485566356), np.float64(0.04582575694955839), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0)]
beta: 0.8
preprocessing time for sampling: 1.4776828289031982
amortized time for sample size  5 is:  0.0008310232162475587
preprocessing time for sampling: 1.4808204174041748
amortized time for sample size  10 is:  0.0008340606689453124
preprocessing time for sampling: 1.4821197986602783
amortized time for sample size  15 is:  0.0008461232185363771
preprocessing time for sampling: 1.4880669116973877
amortized time for sample size  20 is:  0.0008310332298278808
preprocessing time for sampling: 1.4808671474456787
amortized time for sample size  25 is:  0.0008371874809265139
preprocessing time for sampling: 1.4819140434265137
amortized time for sample size  30 is:  0.0008379409313201905
preprocessing time for sampling: 1.4806239604949951
amortized time for sample size  35 is:  0.0008279412133353096
preprocessing time for sampling: 1.4905710220336914
amortized time for sample size  40 is:  0.0008287457823753355
preprocessing time for sampling: 1.4832000732421875
amortized time for sample size  45 is:  0.0008263580534193249
preprocessing time for sampling: 1.4891889095306396
amortized time for sample size  50 is:  0.0008252574443817137
preprocessing time for sampling: 1.482992172241211
amortized time for sample size  55 is:  0.0008324583660472523
preprocessing time for sampling: 1.4819848537445068
amortized time for sample size  60 is:  0.0008329201936721802
preprocessing time for sampling: 1.482734203338623
amortized time for sample size  65 is:  0.0008457579245934122
preprocessing time for sampling: 1.483299970626831
amortized time for sample size  70 is:  0.0008255110808781216
preprocessing time for sampling: 1.486051082611084
amortized time for sample size  75 is:  0.000824650287628174
preprocessing time for sampling: 1.5069019794464111
amortized time for sample size  80 is:  0.0008437719345092772
preprocessing time for sampling: 1.4935791492462158
amortized time for sample size  85 is:  0.000831922082340016
preprocessing time for sampling: 1.4813599586486816
amortized time for sample size  90 is:  0.0008301870822906495
preprocessing time for sampling: 1.4798011779785156
amortized time for sample size  95 is:  0.000830971918608013
preprocessing time for sampling: 1.483368158340454
amortized time for sample size  100 is:  0.0008321670532226561
preprocessing time for sampling: 1.4827980995178223
amortized time for sample size  105 is:  0.0008264724186488559
preprocessing time for sampling: 1.4896221160888672
amortized time for sample size  110 is:  0.000832986376502297
preprocessing time for sampling: 1.4861340522766113
amortized time for sample size  115 is:  0.000831285932789678
preprocessing time for sampling: 1.48256516456604
amortized time for sample size  120 is:  0.0008286676605542502
preprocessing time for sampling: 1.4810872077941895
amortized time for sample size  125 is:  0.0008344686317443849
preprocessing time for sampling: 1.488696813583374
amortized time for sample size  130 is:  0.0008276726282559909
preprocessing time for sampling: 1.4816458225250244
amortized time for sample size  135 is:  0.0008289989365471735
preprocessing time for sampling: 1.4927000999450684
amortized time for sample size  140 is:  0.0008335858753749302
preprocessing time for sampling: 1.4811341762542725
amortized time for sample size  145 is:  0.0008271378648692164
preprocessing time for sampling: 1.4738538265228271
amortized time for sample size  150 is:  0.0008314783255259197
preprocessing time for sampling: 1.4733190536499023
amortized time for sample size  155 is:  0.0008340646989883915
preprocessing time for sampling: 1.4707329273223877
amortized time for sample size  160 is:  0.0008279978185892107
preprocessing time for sampling: 1.4648370742797852
amortized time for sample size  165 is:  0.0008283969994747277
preprocessing time for sampling: 1.4558162689208984
amortized time for sample size  170 is:  0.0008237817147198846
preprocessing time for sampling: 1.4595441818237305
amortized time for sample size  175 is:  0.0008235149383544922
preprocessing time for sampling: 1.4655258655548096
amortized time for sample size  180 is:  0.0008203253083758884
preprocessing time for sampling: 1.4565999507904053
amortized time for sample size  185 is:  0.0008204177521370554
preprocessing time for sampling: 1.458855390548706
amortized time for sample size  190 is:  0.0008163976041894211
preprocessing time for sampling: 1.464526891708374
amortized time for sample size  195 is:  0.0008132419586181642
preprocessing time for sampling: 1.4526288509368896
amortized time for sample size  200 is:  0.0008154701828956604
preprocessing time for sampling: 1.454169750213623
amortized time for sample size  205 is:  0.0008191841055707234
preprocessing time for sampling: 1.472149133682251
amortized time for sample size  210 is:  0.0008335534050351098
preprocessing time for sampling: 1.4796128273010254
amortized time for sample size  215 is:  0.0008247383361638978
preprocessing time for sampling: 1.4788877964019775
amortized time for sample size  220 is:  0.0008376594998619776
preprocessing time for sampling: 1.48502516746521
amortized time for sample size  225 is:  0.0008274751557244195
preprocessing time for sampling: 1.4998929500579834
amortized time for sample size  230 is:  0.0008270119169484015
preprocessing time for sampling: 1.4781787395477295
amortized time for sample size  235 is:  0.0008318359293836231
preprocessing time for sampling: 1.480616807937622
amortized time for sample size  240 is:  0.0008314495384693148
preprocessing time for sampling: 1.4852993488311768
amortized time for sample size  245 is:  0.0008308982946434798
preprocessing time for sampling: 907.3101561069489
amortized time for sample size  250 is:  0.0008214409255981448
*** results for plotting, beta= 0.8 

mean_list= [np.float64(0.86), np.float64(0.9099999999999999), np.float64(0.97), np.float64(0.9800000000000001), np.float64(0.96), np.float64(0.9800000000000001), np.float64(0.99), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(0.99), np.float64(0.99), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0)]
std_list= [np.float64(0.09165151389911681), np.float64(0.06999999999999998), np.float64(0.045825756949558386), np.float64(0.039999999999999994), np.float64(0.04898979485566355), np.float64(0.039999999999999994), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0)]
beta: 1
preprocessing time for sampling: 1.6322910785675049
amortized time for sample size  5 is:  0.0008284621238708496
preprocessing time for sampling: 1.633997917175293
amortized time for sample size  10 is:  0.0008271415233612061
preprocessing time for sampling: 1.6314589977264404
amortized time for sample size  15 is:  0.0008298010826110841
preprocessing time for sampling: 1.6279230117797852
amortized time for sample size  20 is:  0.0008273252248764038
preprocessing time for sampling: 1.6285760402679443
amortized time for sample size  25 is:  0.0008269907951354982
preprocessing time for sampling: 1.6338489055633545
amortized time for sample size  30 is:  0.0008269009590148924
preprocessing time for sampling: 1.6272351741790771
amortized time for sample size  35 is:  0.000826413767678397
preprocessing time for sampling: 404.1634030342102
amortized time for sample size  40 is:  0.0008491728901863098
preprocessing time for sampling: 1.6305809020996094
amortized time for sample size  45 is:  0.0008312487602233887
preprocessing time for sampling: 1.6338770389556885
amortized time for sample size  50 is:  0.0008308453559875488
preprocessing time for sampling: 1.626720905303955
amortized time for sample size  55 is:  0.0008283553990450773
preprocessing time for sampling: 1.6352629661560059
amortized time for sample size  60 is:  0.0008298545281092327
preprocessing time for sampling: 1.6301839351654053
amortized time for sample size  65 is:  0.0008254387928889347
preprocessing time for sampling: 1.62925386428833
amortized time for sample size  70 is:  0.0008383164405822755
preprocessing time for sampling: 1.6291048526763916
amortized time for sample size  75 is:  0.011880211098988848
preprocessing time for sampling: 1.6400549411773682
amortized time for sample size  80 is:  0.0008432993292808534
preprocessing time for sampling: 1.6425971984863281
amortized time for sample size  85 is:  0.0008419942575342516
preprocessing time for sampling: 1.6757919788360596
amortized time for sample size  90 is:  0.0008590496116214332
preprocessing time for sampling: 1.638293981552124
amortized time for sample size  95 is:  0.0008389956072757119
preprocessing time for sampling: 1.628981113433838
amortized time for sample size  100 is:  0.0008299750328063966
preprocessing time for sampling: 1.6333701610565186
amortized time for sample size  105 is:  0.000841555459158761
preprocessing time for sampling: 1.7067139148712158
amortized time for sample size  110 is:  0.0008464997681704435
preprocessing time for sampling: 1.6447179317474365
amortized time for sample size  115 is:  0.0008421003092890199
preprocessing time for sampling: 1.6347007751464844
amortized time for sample size  120 is:  0.0008315644264221192
preprocessing time for sampling: 1.6321990489959717
amortized time for sample size  125 is:  0.0008345533752441407
preprocessing time for sampling: 1.660346269607544
amortized time for sample size  130 is:  0.0008336462057553806
preprocessing time for sampling: 1.640953779220581
amortized time for sample size  135 is:  0.0008377642808137117
preprocessing time for sampling: 1.642009973526001
amortized time for sample size  140 is:  0.000842449801308768
preprocessing time for sampling: 1.6442630290985107
amortized time for sample size  145 is:  0.0008384914233766753
preprocessing time for sampling: 1.6683588027954102
amortized time for sample size  150 is:  0.0008417194048563638
preprocessing time for sampling: 1.6424970626831055
amortized time for sample size  155 is:  0.0008397578424023043
preprocessing time for sampling: 1.6469578742980957
amortized time for sample size  160 is:  0.0008331165015697479
preprocessing time for sampling: 1.6314728260040283
amortized time for sample size  165 is:  0.0008374190763993697
preprocessing time for sampling: 1.6423051357269287
amortized time for sample size  170 is:  0.0008440528056200815
preprocessing time for sampling: 1.6480467319488525
amortized time for sample size  175 is:  0.0008468863759722028
preprocessing time for sampling: 1.6683170795440674
amortized time for sample size  180 is:  0.0008418651156955293
preprocessing time for sampling: 1.6416370868682861
amortized time for sample size  185 is:  0.0008513591869457348
preprocessing time for sampling: 1.6404757499694824
amortized time for sample size  190 is:  0.0008454820231387489
preprocessing time for sampling: 1.6428720951080322
amortized time for sample size  195 is:  0.0008418572865999663
preprocessing time for sampling: 1.6670191287994385
amortized time for sample size  200 is:  0.000844974946975708
preprocessing time for sampling: 1.6590378284454346
amortized time for sample size  205 is:  0.0008428371592265804
preprocessing time for sampling: 1.6471669673919678
amortized time for sample size  210 is:  0.0008492230574289959
preprocessing time for sampling: 1.6461410522460938
amortized time for sample size  215 is:  0.0008460656210433605
preprocessing time for sampling: 1.645157814025879
amortized time for sample size  220 is:  0.0008442543311552568
preprocessing time for sampling: 1.6687848567962646
amortized time for sample size  225 is:  0.0008524622069464787
preprocessing time for sampling: 1.6722490787506104
amortized time for sample size  230 is:  0.000853700544523156
preprocessing time for sampling: 1.6712980270385742
amortized time for sample size  235 is:  0.0008556150476983253
preprocessing time for sampling: 1.7092349529266357
amortized time for sample size  240 is:  0.0008530390361944834
preprocessing time for sampling: 1.675447940826416
amortized time for sample size  245 is:  0.0008517210240266762
preprocessing time for sampling: 1.6861040592193604
amortized time for sample size  250 is:  0.0008505862903594969
*** results for plotting, beta= 1 

mean_list= [np.float64(0.89), np.float64(0.9200000000000002), np.float64(0.9800000000000001), np.float64(1.0), np.float64(1.0), np.float64(0.99), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0)]
std_list= [np.float64(0.09433981132056604), np.float64(0.059999999999999984), np.float64(0.039999999999999994), np.float64(0.0), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0)]
beta: 1.2
preprocessing time for sampling: 1.4804620742797852
amortized time for sample size  5 is:  0.0008262567520141603
preprocessing time for sampling: 1.4858081340789795
amortized time for sample size  10 is:  0.0008403172492980958
preprocessing time for sampling: 1.4794409275054932
amortized time for sample size  15 is:  0.0008322828610738118
preprocessing time for sampling: 1.4831209182739258
amortized time for sample size  20 is:  0.0008317050933837892
preprocessing time for sampling: 1.4912467002868652
amortized time for sample size  25 is:  0.0008385774612426757
preprocessing time for sampling: 1.484065055847168
amortized time for sample size  30 is:  0.0008361895084381105
preprocessing time for sampling: 1.4929311275482178
amortized time for sample size  35 is:  0.0008391901424952918
preprocessing time for sampling: 1.4924559593200684
amortized time for sample size  40 is:  0.0008524568080902099
preprocessing time for sampling: 1.4893379211425781
amortized time for sample size  45 is:  0.0008433247142367892
preprocessing time for sampling: 1.4943079948425293
amortized time for sample size  50 is:  0.0008382855415344239
preprocessing time for sampling: 1.4891698360443115
amortized time for sample size  55 is:  0.0008457534529946066
preprocessing time for sampling: 1.4842851161956787
amortized time for sample size  60 is:  0.0008385783036549885
preprocessing time for sampling: 1.494175910949707
amortized time for sample size  65 is:  0.000836578919337346
preprocessing time for sampling: 1.4738109111785889
amortized time for sample size  70 is:  0.0008308145659310476
preprocessing time for sampling: 1.5021209716796875
amortized time for sample size  75 is:  0.0008389254252115885
preprocessing time for sampling: 1.501706838607788
amortized time for sample size  80 is:  0.0008255816400051118
preprocessing time for sampling: 1.4827451705932617
amortized time for sample size  85 is:  0.0008360467798569623
preprocessing time for sampling: 1.506507158279419
amortized time for sample size  90 is:  0.000837851153479682
preprocessing time for sampling: 1.4999721050262451
amortized time for sample size  95 is:  0.0008320457558882864
preprocessing time for sampling: 1.4935531616210938
amortized time for sample size  100 is:  0.0008362584352493286
preprocessing time for sampling: 1.499568223953247
amortized time for sample size  105 is:  0.0008384509767804828
preprocessing time for sampling: 1.4915850162506104
amortized time for sample size  110 is:  0.0008392501094124534
preprocessing time for sampling: 1.4989702701568604
amortized time for sample size  115 is:  0.0008449385269828463
preprocessing time for sampling: 1.5140888690948486
amortized time for sample size  120 is:  0.0008438936670621235
preprocessing time for sampling: 1.4893929958343506
amortized time for sample size  125 is:  0.0008267808914184571
preprocessing time for sampling: 1.4865429401397705
amortized time for sample size  130 is:  0.0008295624072735125
preprocessing time for sampling: 1.4788827896118164
amortized time for sample size  135 is:  0.0008275544555098924
preprocessing time for sampling: 1.500641107559204
amortized time for sample size  140 is:  0.0008314559119088311
preprocessing time for sampling: 1.4931137561798096
amortized time for sample size  145 is:  0.000832831333423483
preprocessing time for sampling: 1.4962241649627686
amortized time for sample size  150 is:  0.0008417668501536052
preprocessing time for sampling: 1.4986319541931152
amortized time for sample size  155 is:  0.0008358210748241792
preprocessing time for sampling: 1.5056979656219482
amortized time for sample size  160 is:  0.0008430165946483613
preprocessing time for sampling: 1.4916150569915771
amortized time for sample size  165 is:  0.0008363697456591058
preprocessing time for sampling: 1.4847562313079834
amortized time for sample size  170 is:  0.0008394519301021801
preprocessing time for sampling: 1.4891071319580078
amortized time for sample size  175 is:  0.0008411836079188756
preprocessing time for sampling: 1.4977118968963623
amortized time for sample size  180 is:  0.0008358788490295409
preprocessing time for sampling: 1.4979298114776611
amortized time for sample size  185 is:  0.0008378445779955067
preprocessing time for sampling: 1.5016279220581055
amortized time for sample size  190 is:  0.0008348102820547004
preprocessing time for sampling: 1.4878368377685547
amortized time for sample size  195 is:  0.0008422374114012108
preprocessing time for sampling: 1.487151861190796
amortized time for sample size  200 is:  0.0008356242060661315
preprocessing time for sampling: 1.4836132526397705
amortized time for sample size  205 is:  0.000835785958825088
preprocessing time for sampling: 1.4900939464569092
amortized time for sample size  210 is:  0.0008311766442798432
preprocessing time for sampling: 1.4998230934143066
amortized time for sample size  215 is:  0.0008367604433104052
preprocessing time for sampling: 1.4937269687652588
amortized time for sample size  220 is:  0.0008338235833428123
preprocessing time for sampling: 1.485361099243164
amortized time for sample size  225 is:  0.000832463052537706
preprocessing time for sampling: 1.4822421073913574
amortized time for sample size  230 is:  0.0008293818909188974
preprocessing time for sampling: 1.4833641052246094
amortized time for sample size  235 is:  0.0008321860901852871
preprocessing time for sampling: 1.4894790649414062
amortized time for sample size  240 is:  0.0008299966355164847
preprocessing time for sampling: 1.4834959506988525
amortized time for sample size  245 is:  0.0008344609494111976
preprocessing time for sampling: 1.4846200942993164
amortized time for sample size  250 is:  0.0008357202339172365
*** results for plotting, beta= 1.2 

mean_list= [np.float64(0.96), np.float64(0.9800000000000001), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(0.99), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0)]
std_list= [np.float64(0.06633249580710798), np.float64(0.039999999999999994), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0)]
