beta: 0.2
preprocessing time for sampling: 0.07938504219055176
amortized time for sample size  5 is:  0.00022603654861450201
preprocessing time for sampling: 0.07906007766723633
amortized time for sample size  10 is:  0.00022567343711853027
preprocessing time for sampling: 0.07930397987365723
amortized time for sample size  15 is:  0.00022671858469645184
preprocessing time for sampling: 0.08022618293762207
amortized time for sample size  20 is:  0.00022702419757843017
preprocessing time for sampling: 0.07903575897216797
amortized time for sample size  25 is:  0.00022689056396484376
preprocessing time for sampling: 0.08012819290161133
amortized time for sample size  30 is:  0.0002301341692606608
preprocessing time for sampling: 0.08134293556213379
amortized time for sample size  35 is:  0.00022859689167567656
preprocessing time for sampling: 0.08008599281311035
amortized time for sample size  40 is:  0.00022651505470275878
preprocessing time for sampling: 0.08034300804138184
amortized time for sample size  45 is:  0.00022761201858520507
preprocessing time for sampling: 0.07925105094909668
amortized time for sample size  50 is:  0.0002256383419036865
preprocessing time for sampling: 0.0790090560913086
amortized time for sample size  55 is:  0.0002251453399658203
preprocessing time for sampling: 0.07909774780273438
amortized time for sample size  60 is:  0.00022495055198669436
preprocessing time for sampling: 0.0784299373626709
amortized time for sample size  65 is:  0.00022746995779184196
preprocessing time for sampling: 0.08115696907043457
amortized time for sample size  70 is:  0.00022820820127214701
preprocessing time for sampling: 0.07950496673583984
amortized time for sample size  75 is:  0.00023159688313802084
preprocessing time for sampling: 0.08125185966491699
amortized time for sample size  80 is:  0.00022883850336074833
preprocessing time for sampling: 0.07986903190612793
amortized time for sample size  85 is:  0.00022939250048469094
preprocessing time for sampling: 0.08076024055480957
amortized time for sample size  90 is:  0.0002265938917795817
preprocessing time for sampling: 0.07959818840026855
amortized time for sample size  95 is:  0.0002273360051606831
preprocessing time for sampling: 0.08041024208068848
amortized time for sample size  100 is:  0.0002295698642730713
preprocessing time for sampling: 0.07925772666931152
amortized time for sample size  105 is:  0.00022552467527843653
preprocessing time for sampling: 0.07970523834228516
amortized time for sample size  110 is:  0.00022552800178527832
preprocessing time for sampling: 0.07935905456542969
amortized time for sample size  115 is:  0.00022657591363658074
preprocessing time for sampling: 0.07907700538635254
amortized time for sample size  120 is:  0.00022570325930913293
preprocessing time for sampling: 0.0789029598236084
amortized time for sample size  125 is:  0.0002253974342346191
preprocessing time for sampling: 0.08038926124572754
amortized time for sample size  130 is:  0.0002251562888805683
preprocessing time for sampling: 0.07907724380493164
amortized time for sample size  135 is:  0.00022495746612548833
preprocessing time for sampling: 0.08057093620300293
amortized time for sample size  140 is:  0.00022498195511954172
preprocessing time for sampling: 0.07927203178405762
amortized time for sample size  145 is:  0.00022593042768281082
preprocessing time for sampling: 0.07914209365844727
amortized time for sample size  150 is:  0.0002250895818074544
preprocessing time for sampling: 0.07927775382995605
amortized time for sample size  155 is:  0.0002256461112729965
preprocessing time for sampling: 0.07918500900268555
amortized time for sample size  160 is:  0.00022521220147609706
preprocessing time for sampling: 0.07935905456542969
amortized time for sample size  165 is:  0.0002249751813483961
preprocessing time for sampling: 0.07921791076660156
amortized time for sample size  170 is:  0.00022507894740385166
preprocessing time for sampling: 0.07903409004211426
amortized time for sample size  175 is:  0.00022510390962873186
preprocessing time for sampling: 0.07904410362243652
amortized time for sample size  180 is:  0.0002253044578764174
preprocessing time for sampling: 0.0790560245513916
amortized time for sample size  185 is:  0.0002255214356087349
preprocessing time for sampling: 0.07923603057861328
amortized time for sample size  190 is:  0.00022552500273052012
preprocessing time for sampling: 0.07900881767272949
amortized time for sample size  195 is:  0.0002253152040334848
preprocessing time for sampling: 0.07901597023010254
amortized time for sample size  200 is:  0.00022525302171707155
preprocessing time for sampling: 0.07902002334594727
amortized time for sample size  205 is:  0.0002248737404986126
preprocessing time for sampling: 0.07901597023010254
amortized time for sample size  210 is:  0.00022579790297008693
preprocessing time for sampling: 0.07908892631530762
amortized time for sample size  215 is:  0.0002257987732111021
preprocessing time for sampling: 0.07940077781677246
amortized time for sample size  220 is:  0.00022519731521606446
preprocessing time for sampling: 0.07921910285949707
amortized time for sample size  225 is:  0.00022537161509195963
preprocessing time for sampling: 0.0790557861328125
amortized time for sample size  230 is:  0.00022542522264563518
preprocessing time for sampling: 0.07907795906066895
amortized time for sample size  235 is:  0.0002254122977561139
preprocessing time for sampling: 0.07940363883972168
amortized time for sample size  240 is:  0.00022591858108838395
preprocessing time for sampling: 0.07935523986816406
amortized time for sample size  245 is:  0.00022676231423202824
preprocessing time for sampling: 0.07939505577087402
amortized time for sample size  250 is:  0.0056292842483520525
*** results for plotting, beta= 0.2 

mean_list= [np.float64(0.39), np.float64(0.4699999999999999), np.float64(0.4600000000000001), np.float64(0.4600000000000001), np.float64(0.54), np.float64(0.54), np.float64(0.54), np.float64(0.52), np.float64(0.5800000000000001), np.float64(0.63), np.float64(0.51), np.float64(0.44000000000000006), np.float64(0.54), np.float64(0.6), np.float64(0.59), np.float64(0.57), np.float64(0.6499999999999999), np.float64(0.6799999999999999), np.float64(0.59), np.float64(0.67), np.float64(0.63), np.float64(0.67), np.float64(0.6799999999999999), np.float64(0.6799999999999999), np.float64(0.6399999999999999), np.float64(0.67), np.float64(0.7100000000000001), np.float64(0.74), np.float64(0.6599999999999999), np.float64(0.7), np.float64(0.76), np.float64(0.76), np.float64(0.7100000000000001), np.float64(0.6599999999999999), np.float64(0.65), np.float64(0.7300000000000001), np.float64(0.69), np.float64(0.69), np.float64(0.68), np.float64(0.73), np.float64(0.63), np.float64(0.69), np.float64(0.74), np.float64(0.6799999999999999), np.float64(0.7700000000000001), np.float64(0.75), np.float64(0.8099999999999999), np.float64(0.7500000000000001), np.float64(0.6900000000000001), np.float64(0.7)]
std_list= [np.float64(0.12206555615733702), np.float64(0.2368543856465402), np.float64(0.1624807680927192), np.float64(0.13564659966250536), np.float64(0.10198039027185571), np.float64(0.12806248474865695), np.float64(0.11135528725660042), np.float64(0.1833030277982336), np.float64(0.16613247725836147), np.float64(0.10999999999999999), np.float64(0.1445683229480096), np.float64(0.15620499351813308), np.float64(0.14966629547095764), np.float64(0.1341640786499874), np.float64(0.12206555615733704), np.float64(0.13453624047073712), np.float64(0.15000000000000002), np.float64(0.11661903789690603), np.float64(0.13747727084867523), np.float64(0.11874342087037917), np.float64(0.20024984394500786), np.float64(0.16155494421403513), np.float64(0.11661903789690603), np.float64(0.13266499161421602), np.float64(0.17435595774162693), np.float64(0.09000000000000001), np.float64(0.15132745950421558), np.float64(0.10198039027185572), np.float64(0.1854723699099141), np.float64(0.10000000000000003), np.float64(0.14282856857085702), np.float64(0.12000000000000002), np.float64(0.13747727084867523), np.float64(0.12000000000000001), np.float64(0.16278820596099708), np.float64(0.19000000000000003), np.float64(0.16401219466856726), np.float64(0.12206555615733704), np.float64(0.1469693845669907), np.float64(0.10049875621120892), np.float64(0.1615549442140351), np.float64(0.17578395831246946), np.float64(0.18), np.float64(0.17204650534085256), np.float64(0.1676305461424021), np.float64(0.12041594578792297), np.float64(0.10440306508910552), np.float64(0.1746424919657298), np.float64(0.11357816691600549), np.float64(0.14832396974191325)]
beta: 0.4
preprocessing time for sampling: 0.079315185546875
amortized time for sample size  5 is:  0.00022616291046142576
preprocessing time for sampling: 0.07974886894226074
amortized time for sample size  10 is:  0.00022520923614501959
preprocessing time for sampling: 0.07894611358642578
amortized time for sample size  15 is:  0.00022498512268066408
preprocessing time for sampling: 0.0790860652923584
amortized time for sample size  20 is:  0.00022513401508331295
preprocessing time for sampling: 0.07971978187561035
amortized time for sample size  25 is:  0.00022530288696289064
preprocessing time for sampling: 0.07912778854370117
amortized time for sample size  30 is:  0.00022596979141235353
preprocessing time for sampling: 0.07973623275756836
amortized time for sample size  35 is:  0.00022534063884190148
preprocessing time for sampling: 0.07941699028015137
amortized time for sample size  40 is:  0.00022622424364089969
preprocessing time for sampling: 0.07908987998962402
amortized time for sample size  45 is:  0.00022576379776000972
preprocessing time for sampling: 0.0794219970703125
amortized time for sample size  50 is:  0.00022672834396362306
preprocessing time for sampling: 0.07962179183959961
amortized time for sample size  55 is:  0.0002284753539345481
preprocessing time for sampling: 0.0807809829711914
amortized time for sample size  60 is:  0.00023522933324178063
preprocessing time for sampling: 0.08035778999328613
amortized time for sample size  65 is:  0.00022793505741999703
preprocessing time for sampling: 0.07919001579284668
amortized time for sample size  70 is:  0.00022515566008431573
preprocessing time for sampling: 0.07909083366394043
amortized time for sample size  75 is:  0.00022543334960937501
preprocessing time for sampling: 0.07922792434692383
amortized time for sample size  80 is:  0.0002252914011478424
preprocessing time for sampling: 0.07907915115356445
amortized time for sample size  85 is:  0.00022713122648351333
preprocessing time for sampling: 0.07963418960571289
amortized time for sample size  90 is:  0.0002268422444661459
preprocessing time for sampling: 0.07951593399047852
amortized time for sample size  95 is:  0.00022842976921483093
preprocessing time for sampling: 0.07978606224060059
amortized time for sample size  100 is:  0.00023609294891357424
preprocessing time for sampling: 0.07964110374450684
amortized time for sample size  105 is:  0.00022677469253540043
preprocessing time for sampling: 0.07914900779724121
amortized time for sample size  110 is:  0.0002253297675739635
preprocessing time for sampling: 0.07903909683227539
amortized time for sample size  115 is:  0.0002269016348797342
preprocessing time for sampling: 0.07907819747924805
amortized time for sample size  120 is:  0.00022514444589614868
preprocessing time for sampling: 0.07910823822021484
amortized time for sample size  125 is:  0.00022539909362792972
preprocessing time for sampling: 0.07908129692077637
amortized time for sample size  130 is:  0.0002276197580190806
preprocessing time for sampling: 0.0791177749633789
amortized time for sample size  135 is:  0.00022569836510552297
preprocessing time for sampling: 0.08030200004577637
amortized time for sample size  140 is:  0.00022611098630087714
preprocessing time for sampling: 0.07909297943115234
amortized time for sample size  145 is:  0.00022816292992953595
preprocessing time for sampling: 0.07917523384094238
amortized time for sample size  150 is:  0.0002264552116394043
preprocessing time for sampling: 0.08057093620300293
amortized time for sample size  155 is:  0.0002260781872657037
preprocessing time for sampling: 0.07930397987365723
amortized time for sample size  160 is:  0.00022514529526233674
preprocessing time for sampling: 0.07908916473388672
amortized time for sample size  165 is:  0.0002253032164140181
preprocessing time for sampling: 0.07913899421691895
amortized time for sample size  170 is:  0.00022567896281971647
preprocessing time for sampling: 0.07930898666381836
amortized time for sample size  175 is:  0.00022530711037772045
preprocessing time for sampling: 0.07914304733276367
amortized time for sample size  180 is:  0.00023269861274295386
preprocessing time for sampling: 0.079193115234375
amortized time for sample size  185 is:  0.00022641112353350665
preprocessing time for sampling: 0.08109593391418457
amortized time for sample size  190 is:  0.00022946008883024512
preprocessing time for sampling: 0.0827639102935791
amortized time for sample size  195 is:  0.00023105466060149363
preprocessing time for sampling: 0.08062195777893066
amortized time for sample size  200 is:  0.00023090400695800783
preprocessing time for sampling: 0.09139204025268555
amortized time for sample size  205 is:  0.0002302342507897354
preprocessing time for sampling: 0.09209203720092773
amortized time for sample size  210 is:  0.00022942174048650826
preprocessing time for sampling: 0.07978606224060059
amortized time for sample size  215 is:  0.00022954466176587483
preprocessing time for sampling: 0.08051419258117676
amortized time for sample size  220 is:  0.00022954718633131545
preprocessing time for sampling: 0.0803670883178711
amortized time for sample size  225 is:  0.0002269492361280653
preprocessing time for sampling: 0.08030295372009277
amortized time for sample size  230 is:  0.00022779151667719306
preprocessing time for sampling: 0.08011889457702637
amortized time for sample size  235 is:  0.000227332703610684
preprocessing time for sampling: 0.07995796203613281
amortized time for sample size  240 is:  0.00022812122106552122
preprocessing time for sampling: 0.08040595054626465
amortized time for sample size  245 is:  0.0002281567709786551
preprocessing time for sampling: 0.08091282844543457
amortized time for sample size  250 is:  0.00022820782661437986
*** results for plotting, beta= 0.4 

mean_list= [np.float64(0.51), np.float64(0.72), np.float64(0.76), np.float64(0.74), np.float64(0.8200000000000001), np.float64(0.82), np.float64(0.82), np.float64(0.8099999999999999), np.float64(0.8000000000000002), np.float64(0.8700000000000001), np.float64(0.8800000000000001), np.float64(0.86), np.float64(0.89), np.float64(0.9099999999999999), np.float64(0.9400000000000001), np.float64(0.89), np.float64(0.9199999999999999), np.float64(0.96), np.float64(0.86), np.float64(0.9200000000000002), np.float64(0.9200000000000002), np.float64(0.9200000000000002), np.float64(0.9200000000000002), np.float64(0.93), np.float64(0.9800000000000001), np.float64(0.96), np.float64(0.9199999999999999), np.float64(0.9200000000000002), np.float64(0.93), np.float64(0.9400000000000001), np.float64(0.95), np.float64(0.93), np.float64(0.95), np.float64(0.9800000000000001), np.float64(0.9400000000000001), np.float64(0.99), np.float64(0.96), np.float64(0.9), np.float64(0.95), np.float64(0.97), np.float64(0.99), np.float64(0.99), np.float64(0.99), np.float64(0.95), np.float64(0.9700000000000001), np.float64(0.9800000000000001), np.float64(0.9800000000000001), np.float64(0.99), np.float64(0.9700000000000001), np.float64(0.97)]
std_list= [np.float64(0.12206555615733701), np.float64(0.16), np.float64(0.09165151389911684), np.float64(0.08000000000000003), np.float64(0.09797958971132714), np.float64(0.0871779788708135), np.float64(0.11661903789690603), np.float64(0.12206555615733705), np.float64(0.10000000000000003), np.float64(0.09), np.float64(0.1077032961426901), np.float64(0.128062484748657), np.float64(0.13747727084867523), np.float64(0.05385164807134503), np.float64(0.06633249580710798), np.float64(0.12206555615733702), np.float64(0.1077032961426901), np.float64(0.04898979485566355), np.float64(0.12), np.float64(0.0748331477354788), np.float64(0.059999999999999984), np.float64(0.11661903789690603), np.float64(0.08717797887081345), np.float64(0.07810249675906653), np.float64(0.039999999999999994), np.float64(0.06633249580710798), np.float64(0.0748331477354788), np.float64(0.059999999999999984), np.float64(0.09), np.float64(0.06633249580710798), np.float64(0.08062257748298547), np.float64(0.07810249675906653), np.float64(0.06708203932499368), np.float64(0.039999999999999994), np.float64(0.09165151389911681), np.float64(0.029999999999999992), np.float64(0.06633249580710798), np.float64(0.07745966692414831), np.float64(0.06708203932499368), np.float64(0.06403124237432847), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.08062257748298547), np.float64(0.04582575694955839), np.float64(0.039999999999999994), np.float64(0.039999999999999994), np.float64(0.029999999999999992), np.float64(0.04582575694955839), np.float64(0.045825756949558386)]
beta: 0.6
preprocessing time for sampling: 0.07927322387695312
amortized time for sample size  5 is:  0.00022581052780151368
preprocessing time for sampling: 0.08015990257263184
amortized time for sample size  10 is:  0.00022616291046142578
preprocessing time for sampling: 0.08024191856384277
amortized time for sample size  15 is:  0.00023082431157430018
preprocessing time for sampling: 0.08018016815185547
amortized time for sample size  20 is:  0.00022713434696197506
preprocessing time for sampling: 0.08002710342407227
amortized time for sample size  25 is:  0.00022645225524902342
preprocessing time for sampling: 0.07992291450500488
amortized time for sample size  30 is:  0.00022953518231709803
preprocessing time for sampling: 0.07996368408203125
amortized time for sample size  35 is:  0.00022641536167689733
preprocessing time for sampling: 0.07954812049865723
amortized time for sample size  40 is:  0.00022848898172378538
preprocessing time for sampling: 0.08102989196777344
amortized time for sample size  45 is:  0.0002264928287929959
preprocessing time for sampling: 0.07940912246704102
amortized time for sample size  50 is:  0.00022782011032104494
preprocessing time for sampling: 0.07989716529846191
amortized time for sample size  55 is:  0.00022761522639881476
preprocessing time for sampling: 0.07968020439147949
amortized time for sample size  60 is:  0.00022767436504364012
preprocessing time for sampling: 0.08014631271362305
amortized time for sample size  65 is:  0.0002261279913095327
preprocessing time for sampling: 0.07929182052612305
amortized time for sample size  70 is:  0.00022879351888384136
preprocessing time for sampling: 0.07976293563842773
amortized time for sample size  75 is:  0.00022742249170939127
preprocessing time for sampling: 0.08000802993774414
amortized time for sample size  80 is:  0.00022678136825561525
preprocessing time for sampling: 0.07991576194763184
amortized time for sample size  85 is:  0.00022712463491103232
preprocessing time for sampling: 0.08033919334411621
amortized time for sample size  90 is:  0.0002268439133961995
preprocessing time for sampling: 0.0799398422241211
amortized time for sample size  95 is:  0.00022811967448184363
preprocessing time for sampling: 0.07990694046020508
amortized time for sample size  100 is:  0.00022669198513031
preprocessing time for sampling: 0.0799710750579834
amortized time for sample size  105 is:  0.00022719351450602214
preprocessing time for sampling: 0.07924509048461914
amortized time for sample size  110 is:  0.0002299775860526345
preprocessing time for sampling: 0.07938313484191895
amortized time for sample size  115 is:  0.0002273571594901707
preprocessing time for sampling: 0.07939291000366211
amortized time for sample size  120 is:  0.00022761183977127074
preprocessing time for sampling: 0.0805971622467041
amortized time for sample size  125 is:  0.00022733074188232422
preprocessing time for sampling: 0.07993388175964355
amortized time for sample size  130 is:  0.00022761704371525692
preprocessing time for sampling: 0.07967185974121094
amortized time for sample size  135 is:  0.00022681870283903897
preprocessing time for sampling: 0.0804448127746582
amortized time for sample size  140 is:  0.00022767782211303707
preprocessing time for sampling: 0.07953810691833496
amortized time for sample size  145 is:  0.00022795081960743876
preprocessing time for sampling: 0.07989692687988281
amortized time for sample size  150 is:  0.00022802915573120114
preprocessing time for sampling: 0.08115506172180176
amortized time for sample size  155 is:  0.00022821830934093845
preprocessing time for sampling: 0.07986307144165039
amortized time for sample size  160 is:  0.00022749674320220948
preprocessing time for sampling: 0.08004927635192871
amortized time for sample size  165 is:  0.00022762237895618785
preprocessing time for sampling: 0.08042120933532715
amortized time for sample size  170 is:  0.00022708090613870061
preprocessing time for sampling: 0.08047103881835938
amortized time for sample size  175 is:  0.00022735887254987444
preprocessing time for sampling: 0.0794367790222168
amortized time for sample size  180 is:  0.00022717910342746311
preprocessing time for sampling: 0.07941913604736328
amortized time for sample size  185 is:  0.00022748694548735743
preprocessing time for sampling: 0.07995080947875977
amortized time for sample size  190 is:  0.0002298148807726408
preprocessing time for sampling: 0.0801079273223877
amortized time for sample size  195 is:  0.00022786730986375077
preprocessing time for sampling: 0.0794379711151123
amortized time for sample size  200 is:  0.00022865939140319827
preprocessing time for sampling: 0.0798788070678711
amortized time for sample size  205 is:  0.00022750693995778157
preprocessing time for sampling: 0.07988500595092773
amortized time for sample size  210 is:  0.00022735701288495748
preprocessing time for sampling: 0.07924413681030273
amortized time for sample size  215 is:  0.00022743363713109216
preprocessing time for sampling: 0.07962703704833984
amortized time for sample size  220 is:  0.00022805557467720723
preprocessing time for sampling: 0.08015894889831543
amortized time for sample size  225 is:  0.00022757769690619575
preprocessing time for sampling: 0.08022022247314453
amortized time for sample size  230 is:  0.00022776537356169327
preprocessing time for sampling: 0.0792989730834961
amortized time for sample size  235 is:  0.00022789484389284818
preprocessing time for sampling: 0.07946276664733887
amortized time for sample size  240 is:  0.00022761407494544986
preprocessing time for sampling: 0.07988500595092773
amortized time for sample size  245 is:  0.00022790043694632391
preprocessing time for sampling: 0.08010125160217285
amortized time for sample size  250 is:  0.0002278615760803223
*** results for plotting, beta= 0.6 

mean_list= [np.float64(0.76), np.float64(0.8800000000000001), np.float64(0.9200000000000002), np.float64(0.8300000000000001), np.float64(0.9), np.float64(0.9200000000000002), np.float64(0.95), np.float64(0.9199999999999999), np.float64(0.9700000000000001), np.float64(0.99), np.float64(0.99), np.float64(0.96), np.float64(0.9800000000000001), np.float64(0.9400000000000001), np.float64(0.99), np.float64(0.9700000000000001), np.float64(0.9800000000000001), np.float64(0.99), np.float64(0.9800000000000001), np.float64(0.99), np.float64(0.99), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(0.99), np.float64(1.0), np.float64(0.99), np.float64(0.99), 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(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(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)]
std_list= [np.float64(0.14282856857085702), np.float64(0.09797958971132713), np.float64(0.09797958971132713), np.float64(0.09000000000000002), np.float64(0.07745966692414831), np.float64(0.059999999999999984), np.float64(0.04999999999999999), np.float64(0.08717797887081345), np.float64(0.06403124237432847), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.06633249580710798), np.float64(0.039999999999999994), np.float64(0.06633249580710798), np.float64(0.029999999999999992), np.float64(0.04582575694955839), np.float64(0.039999999999999994), np.float64(0.029999999999999992), np.float64(0.039999999999999994), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.029999999999999992), 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(0.029999999999999992), 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(0.029999999999999992), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0)]
beta: 0.8
preprocessing time for sampling: 0.08005881309509277
amortized time for sample size  5 is:  0.00022573804855346682
preprocessing time for sampling: 0.07982206344604492
amortized time for sample size  10 is:  0.00022595262527465827
preprocessing time for sampling: 0.07940387725830078
amortized time for sample size  15 is:  0.00022671429316202798
preprocessing time for sampling: 0.09067296981811523
amortized time for sample size  20 is:  0.00022720658779144286
preprocessing time for sampling: 0.07954096794128418
amortized time for sample size  25 is:  0.00022663745880126954
preprocessing time for sampling: 0.08075904846191406
amortized time for sample size  30 is:  0.00022610537211100262
preprocessing time for sampling: 0.07981014251708984
amortized time for sample size  35 is:  0.00022883830751691542
preprocessing time for sampling: 0.0793311595916748
amortized time for sample size  40 is:  0.0002261914610862732
preprocessing time for sampling: 0.07974982261657715
amortized time for sample size  45 is:  0.0002284022437201606
preprocessing time for sampling: 0.08021402359008789
amortized time for sample size  50 is:  0.00022657322883605952
preprocessing time for sampling: 0.0799570083618164
amortized time for sample size  55 is:  0.00022756208073009145
preprocessing time for sampling: 0.08002996444702148
amortized time for sample size  60 is:  0.00022725244363149005
preprocessing time for sampling: 0.07891201972961426
amortized time for sample size  65 is:  0.00022664833068847655
preprocessing time for sampling: 0.0801846981048584
amortized time for sample size  70 is:  0.00022726430211748391
preprocessing time for sampling: 0.07977795600891113
amortized time for sample size  75 is:  0.00022720139821370445
preprocessing time for sampling: 0.08060908317565918
amortized time for sample size  80 is:  0.00022768858075141902
preprocessing time for sampling: 0.08067893981933594
amortized time for sample size  85 is:  0.00022711972629322727
preprocessing time for sampling: 0.08062529563903809
amortized time for sample size  90 is:  0.00022788095474243167
preprocessing time for sampling: 0.07972097396850586
amortized time for sample size  95 is:  0.0002271306640223453
preprocessing time for sampling: 0.0804758071899414
amortized time for sample size  100 is:  0.0002278666973114014
preprocessing time for sampling: 0.07962703704833984
amortized time for sample size  105 is:  0.00022760818118140814
preprocessing time for sampling: 0.08013010025024414
amortized time for sample size  110 is:  0.00022809208523143419
preprocessing time for sampling: 0.07957673072814941
amortized time for sample size  115 is:  0.00022771914108939788
preprocessing time for sampling: 0.07942700386047363
amortized time for sample size  120 is:  0.0002273962100346883
preprocessing time for sampling: 0.08007001876831055
amortized time for sample size  125 is:  0.00022771099090576174
preprocessing time for sampling: 0.07936620712280273
amortized time for sample size  130 is:  0.0002265679286076472
preprocessing time for sampling: 0.07938313484191895
amortized time for sample size  135 is:  0.00022746094950923214
preprocessing time for sampling: 0.0799412727355957
amortized time for sample size  140 is:  0.00022712423120226183
preprocessing time for sampling: 0.07969808578491211
amortized time for sample size  145 is:  0.00022803873851381503
preprocessing time for sampling: 0.07976388931274414
amortized time for sample size  150 is:  0.00022724808057149253
preprocessing time for sampling: 0.0889749526977539
amortized time for sample size  155 is:  0.0002266486383253528
preprocessing time for sampling: 0.08011698722839355
amortized time for sample size  160 is:  0.00022770613431930543
preprocessing time for sampling: 0.0798180103302002
amortized time for sample size  165 is:  0.0002270925406253699
preprocessing time for sampling: 0.07934999465942383
amortized time for sample size  170 is:  0.00022733672927407659
preprocessing time for sampling: 0.08012008666992188
amortized time for sample size  175 is:  0.0002274541446140834
preprocessing time for sampling: 0.07988834381103516
amortized time for sample size  180 is:  0.00022751584317949085
preprocessing time for sampling: 0.0794382095336914
amortized time for sample size  185 is:  0.00022752385526090058
preprocessing time for sampling: 0.08045315742492676
amortized time for sample size  190 is:  0.00022706945318924757
preprocessing time for sampling: 0.07998204231262207
amortized time for sample size  195 is:  0.00022760646771161983
preprocessing time for sampling: 0.07997989654541016
amortized time for sample size  200 is:  0.00022709088325500486
preprocessing time for sampling: 0.08021688461303711
amortized time for sample size  205 is:  0.0002271793295697468
preprocessing time for sampling: 0.08870577812194824
amortized time for sample size  210 is:  0.0002270934468223935
preprocessing time for sampling: 0.08079695701599121
amortized time for sample size  215 is:  0.00022732514004374655
preprocessing time for sampling: 0.07950806617736816
amortized time for sample size  220 is:  0.0002271841439333829
preprocessing time for sampling: 0.0807638168334961
amortized time for sample size  225 is:  0.00022690553665161137
preprocessing time for sampling: 0.08041882514953613
amortized time for sample size  230 is:  0.00022730833551158077
preprocessing time for sampling: 0.0801849365234375
amortized time for sample size  235 is:  0.00022783845536252282
preprocessing time for sampling: 0.07998204231262207
amortized time for sample size  240 is:  0.00022707071900367738
preprocessing time for sampling: 0.08026981353759766
amortized time for sample size  245 is:  0.00022743926729474752
preprocessing time for sampling: 0.08066797256469727
amortized time for sample size  250 is:  0.00022734630584716795
*** results for plotting, beta= 0.8 

mean_list= [np.float64(0.8), np.float64(0.93), np.float64(0.97), np.float64(1.0), np.float64(0.99), np.float64(0.99), np.float64(0.9800000000000001), np.float64(0.9700000000000001), np.float64(0.9800000000000001), 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)]
std_list= [np.float64(0.07745966692414837), np.float64(0.09), np.float64(0.04582575694955839), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.039999999999999994), np.float64(0.04582575694955839), np.float64(0.039999999999999994), 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)]
beta: 1
preprocessing time for sampling: 0.08724308013916016
amortized time for sample size  5 is:  0.00023707866668701172
preprocessing time for sampling: 0.08715295791625977
amortized time for sample size  10 is:  0.00023665547370910648
preprocessing time for sampling: 0.0874168872833252
amortized time for sample size  15 is:  0.0002369027137756348
preprocessing time for sampling: 0.0883641242980957
amortized time for sample size  20 is:  0.00023672366142272948
preprocessing time for sampling: 0.08751726150512695
amortized time for sample size  25 is:  0.0002401707649230957
preprocessing time for sampling: 0.08683013916015625
amortized time for sample size  30 is:  0.00023643787701924644
preprocessing time for sampling: 0.08705377578735352
amortized time for sample size  35 is:  0.00023902756827218192
preprocessing time for sampling: 0.08751106262207031
amortized time for sample size  40 is:  0.00023683577775955204
preprocessing time for sampling: 0.08759117126464844
amortized time for sample size  45 is:  0.0002387728691101074
preprocessing time for sampling: 0.0880899429321289
amortized time for sample size  50 is:  0.0002371450901031494
preprocessing time for sampling: 0.0867919921875
amortized time for sample size  55 is:  0.00023883247375488284
preprocessing time for sampling: 0.08817625045776367
amortized time for sample size  60 is:  0.0002383331855138143
preprocessing time for sampling: 0.08726024627685547
amortized time for sample size  65 is:  0.0002385624005244328
preprocessing time for sampling: 0.08790993690490723
amortized time for sample size  70 is:  0.0002381642886570522
preprocessing time for sampling: 0.08883285522460938
amortized time for sample size  75 is:  0.0002373316446940104
preprocessing time for sampling: 0.08744192123413086
amortized time for sample size  80 is:  0.00024020081758499145
preprocessing time for sampling: 0.0877530574798584
amortized time for sample size  85 is:  0.00024098197151632868
preprocessing time for sampling: 0.0880131721496582
amortized time for sample size  90 is:  0.00023871236377292213
preprocessing time for sampling: 0.08740615844726562
amortized time for sample size  95 is:  0.00023827698356226865
preprocessing time for sampling: 0.08691716194152832
amortized time for sample size  100 is:  0.00023795685768127441
preprocessing time for sampling: 0.08739399909973145
amortized time for sample size  105 is:  0.0002401034264337449
preprocessing time for sampling: 0.08730006217956543
amortized time for sample size  110 is:  0.00023846730318936437
preprocessing time for sampling: 0.08749794960021973
amortized time for sample size  115 is:  0.00023935993858005685
preprocessing time for sampling: 0.08825397491455078
amortized time for sample size  120 is:  0.00023867072661717733
preprocessing time for sampling: 0.08727288246154785
amortized time for sample size  125 is:  0.00023792356491088865
preprocessing time for sampling: 0.08719897270202637
amortized time for sample size  130 is:  0.00023896571306081919
preprocessing time for sampling: 0.08826708793640137
amortized time for sample size  135 is:  0.00023934210671318907
preprocessing time for sampling: 0.08803820610046387
amortized time for sample size  140 is:  0.00023817278657640726
preprocessing time for sampling: 0.0879817008972168
amortized time for sample size  145 is:  0.00023921335154566275
preprocessing time for sampling: 0.08727383613586426
amortized time for sample size  150 is:  0.00023839880625406903
preprocessing time for sampling: 0.08796191215515137
amortized time for sample size  155 is:  0.000237567009464387
preprocessing time for sampling: 0.08816385269165039
amortized time for sample size  160 is:  0.00023843105137348174
preprocessing time for sampling: 0.08735799789428711
amortized time for sample size  165 is:  0.0002385109121149237
preprocessing time for sampling: 0.08700990676879883
amortized time for sample size  170 is:  0.00023825850206262922
preprocessing time for sampling: 0.08718299865722656
amortized time for sample size  175 is:  0.00023794153758457725
preprocessing time for sampling: 0.08720707893371582
amortized time for sample size  180 is:  0.0002384603553348117
preprocessing time for sampling: 0.09631490707397461
amortized time for sample size  185 is:  0.0002378849596590609
preprocessing time for sampling: 0.08688211441040039
amortized time for sample size  190 is:  0.00023802113533020024
preprocessing time for sampling: 0.08713221549987793
amortized time for sample size  195 is:  0.0002383202772874099
preprocessing time for sampling: 0.08768892288208008
amortized time for sample size  200 is:  0.0002384817361831665
preprocessing time for sampling: 0.08743596076965332
amortized time for sample size  205 is:  0.00023757033231781751
preprocessing time for sampling: 0.08702206611633301
amortized time for sample size  210 is:  0.00023790860176086423
preprocessing time for sampling: 0.08736705780029297
amortized time for sample size  215 is:  0.0002376870998116427
preprocessing time for sampling: 0.08685612678527832
amortized time for sample size  220 is:  0.00023819876800883896
preprocessing time for sampling: 0.08778691291809082
amortized time for sample size  225 is:  0.000237938838534885
preprocessing time for sampling: 0.0876779556274414
amortized time for sample size  230 is:  0.00023873718925144366
preprocessing time for sampling: 0.08815479278564453
amortized time for sample size  235 is:  0.00023796535045542618
preprocessing time for sampling: 0.0879669189453125
amortized time for sample size  240 is:  0.00023748133579889932
preprocessing time for sampling: 0.08693194389343262
amortized time for sample size  245 is:  0.00023773649760654988
preprocessing time for sampling: 0.08748817443847656
amortized time for sample size  250 is:  0.0002375035858154297
*** results for plotting, beta= 1 

mean_list= [np.float64(0.8799999999999999), np.float64(0.96), np.float64(0.97), np.float64(0.9700000000000001), 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), np.float64(1.0)]
std_list= [np.float64(0.09797958971132713), np.float64(0.04898979485566355), np.float64(0.06403124237432847), np.float64(0.06403124237432847), 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), np.float64(0.0)]
beta: 1.2
preprocessing time for sampling: 0.07983207702636719
amortized time for sample size  5 is:  0.00022622346878051758
preprocessing time for sampling: 0.08027911186218262
amortized time for sample size  10 is:  0.00022612714767456055
preprocessing time for sampling: 0.07961201667785645
amortized time for sample size  15 is:  0.0002263649304707845
preprocessing time for sampling: 0.08041906356811523
amortized time for sample size  20 is:  0.0002312530279159546
preprocessing time for sampling: 0.07964205741882324
amortized time for sample size  25 is:  0.00022674608230590818
preprocessing time for sampling: 0.08051896095275879
amortized time for sample size  30 is:  0.00022634998957316076
preprocessing time for sampling: 0.07952213287353516
amortized time for sample size  35 is:  0.0002285720961434501
preprocessing time for sampling: 0.07940030097961426
amortized time for sample size  40 is:  0.00022660261392593384
preprocessing time for sampling: 0.0795888900756836
amortized time for sample size  45 is:  0.00022778092490302195
preprocessing time for sampling: 0.08000993728637695
amortized time for sample size  50 is:  0.00022639904022216797
preprocessing time for sampling: 0.07927227020263672
amortized time for sample size  55 is:  0.00022810619527643378
preprocessing time for sampling: 0.0872340202331543
amortized time for sample size  60 is:  0.00022709862391153971
preprocessing time for sampling: 0.07985401153564453
amortized time for sample size  65 is:  0.0002267989011911246
preprocessing time for sampling: 0.07992291450500488
amortized time for sample size  70 is:  0.00022765418461390908
preprocessing time for sampling: 0.07961297035217285
amortized time for sample size  75 is:  0.00022754208246866868
preprocessing time for sampling: 0.0807499885559082
amortized time for sample size  80 is:  0.0002278302907943726
preprocessing time for sampling: 0.07910823822021484
amortized time for sample size  85 is:  0.0002276890137616325
preprocessing time for sampling: 0.07945513725280762
amortized time for sample size  90 is:  0.00022807550430297856
preprocessing time for sampling: 0.08024191856384277
amortized time for sample size  95 is:  0.00022765493392944337
preprocessing time for sampling: 0.08002209663391113
amortized time for sample size  100 is:  0.0002276514530181885
preprocessing time for sampling: 0.07997393608093262
amortized time for sample size  105 is:  0.00022759859902518134
preprocessing time for sampling: 0.0797879695892334
amortized time for sample size  110 is:  0.00022960339892994275
preprocessing time for sampling: 0.0801537036895752
amortized time for sample size  115 is:  0.00022790910886681597
preprocessing time for sampling: 0.07990908622741699
amortized time for sample size  120 is:  0.00022736169894536335
preprocessing time for sampling: 0.08018994331359863
amortized time for sample size  125 is:  0.00022744243621826172
preprocessing time for sampling: 0.08025288581848145
amortized time for sample size  130 is:  0.00022705173492431637
preprocessing time for sampling: 0.08768606185913086
amortized time for sample size  135 is:  0.0002269672994260435
preprocessing time for sampling: 0.07994604110717773
amortized time for sample size  140 is:  0.00022755978788648333
preprocessing time for sampling: 0.07943606376647949
amortized time for sample size  145 is:  0.00022857429241311962
preprocessing time for sampling: 0.08034396171569824
amortized time for sample size  150 is:  0.00022744781176249187
preprocessing time for sampling: 0.08008599281311035
amortized time for sample size  155 is:  0.00022776517560405118
preprocessing time for sampling: 0.08017301559448242
amortized time for sample size  160 is:  0.00022802343964576727
preprocessing time for sampling: 0.07931208610534668
amortized time for sample size  165 is:  0.00022720539208614463
preprocessing time for sampling: 0.08062410354614258
amortized time for sample size  170 is:  0.00022770295423619888
preprocessing time for sampling: 0.08027219772338867
amortized time for sample size  175 is:  0.00022851743698120114
preprocessing time for sampling: 0.07945489883422852
amortized time for sample size  180 is:  0.00022774585088094077
preprocessing time for sampling: 0.08003592491149902
amortized time for sample size  185 is:  0.00022795192615405934
preprocessing time for sampling: 0.07968831062316895
amortized time for sample size  190 is:  0.00022767676805195058
preprocessing time for sampling: 0.0799720287322998
amortized time for sample size  195 is:  0.00022781590926341518
preprocessing time for sampling: 0.0804128646850586
amortized time for sample size  200 is:  0.00022779741287231445
preprocessing time for sampling: 0.07956814765930176
amortized time for sample size  205 is:  0.00022806829359473254
preprocessing time for sampling: 0.07892584800720215
amortized time for sample size  210 is:  0.00022827870505196703
preprocessing time for sampling: 0.0810251235961914
amortized time for sample size  215 is:  0.00022781058244926986
preprocessing time for sampling: 0.07986211776733398
amortized time for sample size  220 is:  0.00022770189155231824
preprocessing time for sampling: 0.08678770065307617
amortized time for sample size  225 is:  0.00022735313839382596
preprocessing time for sampling: 0.0797889232635498
amortized time for sample size  230 is:  0.00022784607306770656
preprocessing time for sampling: 0.07957983016967773
amortized time for sample size  235 is:  0.00022828972593266913
preprocessing time for sampling: 0.07909703254699707
amortized time for sample size  240 is:  0.00022789476315180463
preprocessing time for sampling: 0.08344697952270508
amortized time for sample size  245 is:  0.00022718747781247508
preprocessing time for sampling: 0.08606410026550293
amortized time for sample size  250 is:  0.00022739797592163084
*** results for plotting, beta= 1.2 

mean_list= [np.float64(0.9400000000000001), np.float64(0.97), 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), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0)]
std_list= [np.float64(0.04898979485566355), np.float64(0.04582575694955839), 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), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0)]
