beta: 0.2
preprocessing time for sampling: 0.012716054916381836
amortized time for sample size  5 is:  0.00011946773529052733
preprocessing time for sampling: 0.012626171112060547
amortized time for sample size  10 is:  0.00012018346786499024
preprocessing time for sampling: 0.013363838195800781
amortized time for sample size  15 is:  0.00012016423543294272
preprocessing time for sampling: 0.012662887573242188
amortized time for sample size  20 is:  0.00011839783191680908
preprocessing time for sampling: 0.012578964233398438
amortized time for sample size  25 is:  0.00011857738494873048
preprocessing time for sampling: 0.012458086013793945
amortized time for sample size  30 is:  0.00011864256858825682
preprocessing time for sampling: 0.012459039688110352
amortized time for sample size  35 is:  0.0001191308157784598
preprocessing time for sampling: 0.012681961059570312
amortized time for sample size  40 is:  0.00012128460407257081
preprocessing time for sampling: 0.012716054916381836
amortized time for sample size  45 is:  0.00012019830279880101
preprocessing time for sampling: 0.012537002563476562
amortized time for sample size  50 is:  0.00011854944229125978
preprocessing time for sampling: 0.012518882751464844
amortized time for sample size  55 is:  0.00011855918710882011
preprocessing time for sampling: 0.012572050094604492
amortized time for sample size  60 is:  0.00011941230297088623
preprocessing time for sampling: 0.012700080871582031
amortized time for sample size  65 is:  0.00012083038916954627
preprocessing time for sampling: 0.012588977813720703
amortized time for sample size  70 is:  0.00011969889913286482
preprocessing time for sampling: 0.012515783309936523
amortized time for sample size  75 is:  0.00011833260854085285
preprocessing time for sampling: 0.012505769729614258
amortized time for sample size  80 is:  0.00012060227990150453
preprocessing time for sampling: 0.01332402229309082
amortized time for sample size  85 is:  0.00012290531046250288
preprocessing time for sampling: 0.012559890747070312
amortized time for sample size  90 is:  0.00011863417095608183
preprocessing time for sampling: 0.012461185455322266
amortized time for sample size  95 is:  0.00011845172078985916
preprocessing time for sampling: 0.012494087219238281
amortized time for sample size  100 is:  0.00011871356964111329
preprocessing time for sampling: 0.012719869613647461
amortized time for sample size  105 is:  0.00012028324036371142
preprocessing time for sampling: 0.012591123580932617
amortized time for sample size  110 is:  0.00012000981244173918
preprocessing time for sampling: 0.012517929077148438
amortized time for sample size  115 is:  0.00012019285948380179
preprocessing time for sampling: 0.01256704330444336
amortized time for sample size  120 is:  0.00011897683143615722
preprocessing time for sampling: 0.012482166290283203
amortized time for sample size  125 is:  0.00012081193923950193
preprocessing time for sampling: 0.012895822525024414
amortized time for sample size  130 is:  0.0001199813072498028
preprocessing time for sampling: 0.012696027755737305
amortized time for sample size  135 is:  0.0001213669070491084
preprocessing time for sampling: 0.012558221817016602
amortized time for sample size  140 is:  0.00011985378605978827
preprocessing time for sampling: 0.013041973114013672
amortized time for sample size  145 is:  0.00011955608170607992
preprocessing time for sampling: 0.012497901916503906
amortized time for sample size  150 is:  0.00011830946604410806
preprocessing time for sampling: 0.012476921081542969
amortized time for sample size  155 is:  0.00011982462483067667
preprocessing time for sampling: 0.012598991394042969
amortized time for sample size  160 is:  0.00012282758951187133
preprocessing time for sampling: 0.012610673904418945
amortized time for sample size  165 is:  0.00011932753071640473
preprocessing time for sampling: 0.01252603530883789
amortized time for sample size  170 is:  0.00011858464689815745
preprocessing time for sampling: 0.012502193450927734
amortized time for sample size  175 is:  0.00011852035522460938
preprocessing time for sampling: 0.012485265731811523
amortized time for sample size  180 is:  0.0001185777054892646
preprocessing time for sampling: 0.01248478889465332
amortized time for sample size  185 is:  0.00011858963321995092
preprocessing time for sampling: 0.012488126754760742
amortized time for sample size  190 is:  0.00011961983379564788
preprocessing time for sampling: 0.013176202774047852
amortized time for sample size  195 is:  0.00012067546599950544
preprocessing time for sampling: 0.012814044952392578
amortized time for sample size  200 is:  0.00012029352188110354
preprocessing time for sampling: 0.012849092483520508
amortized time for sample size  205 is:  0.00012059614134997857
preprocessing time for sampling: 0.012711048126220703
amortized time for sample size  210 is:  0.00012001512164161317
preprocessing time for sampling: 0.013169050216674805
amortized time for sample size  215 is:  0.00012208671348039495
preprocessing time for sampling: 0.013236045837402344
amortized time for sample size  220 is:  0.00011964621327140115
preprocessing time for sampling: 0.012891292572021484
amortized time for sample size  225 is:  0.00012171129650539822
preprocessing time for sampling: 0.012513160705566406
amortized time for sample size  230 is:  0.000118790864944458
preprocessing time for sampling: 0.012489080429077148
amortized time for sample size  235 is:  0.00011948149254981509
preprocessing time for sampling: 0.012557029724121094
amortized time for sample size  240 is:  0.00011921458443005879
preprocessing time for sampling: 0.012483835220336914
amortized time for sample size  245 is:  0.00011917674784757655
preprocessing time for sampling: 0.012979984283447266
amortized time for sample size  250 is:  0.00011851869583129882
*** results for plotting, beta= 0.2 

mean_list= [np.float64(0.39), np.float64(0.5299999999999999), np.float64(0.38), np.float64(0.48), np.float64(0.5), np.float64(0.37), np.float64(0.49000000000000005), np.float64(0.5800000000000001), np.float64(0.5800000000000001), np.float64(0.5200000000000001), np.float64(0.5599999999999999), np.float64(0.6100000000000001), np.float64(0.56), np.float64(0.72), np.float64(0.6), np.float64(0.71), np.float64(0.62), np.float64(0.59), np.float64(0.6300000000000001), np.float64(0.6300000000000001), np.float64(0.66), np.float64(0.67), np.float64(0.5900000000000001), np.float64(0.61), np.float64(0.58), np.float64(0.6300000000000001), np.float64(0.56), np.float64(0.62), np.float64(0.64), np.float64(0.55), np.float64(0.62), np.float64(0.65), np.float64(0.67), np.float64(0.6100000000000001), np.float64(0.58), np.float64(0.73), np.float64(0.59), np.float64(0.6099999999999999), np.float64(0.68), np.float64(0.6299999999999999), np.float64(0.6699999999999999), np.float64(0.6900000000000001), np.float64(0.6900000000000001), np.float64(0.52), np.float64(0.73), np.float64(0.6), np.float64(0.5900000000000001), np.float64(0.72), np.float64(0.61), np.float64(0.6699999999999999)]
std_list= [np.float64(0.1044030650891055), np.float64(0.14866068747318506), np.float64(0.17204650534085256), np.float64(0.132664991614216), np.float64(0.12649110640673517), np.float64(0.20024984394500786), np.float64(0.18138357147217055), np.float64(0.13999999999999999), np.float64(0.1661324772583615), np.float64(0.1661324772583615), np.float64(0.1562049935181331), np.float64(0.13), np.float64(0.19595917942265423), np.float64(0.1777638883463118), np.float64(0.10954451150103323), np.float64(0.1135781669160055), np.float64(0.116619037896906), np.float64(0.16401219466856723), np.float64(0.10999999999999999), np.float64(0.1268857754044952), np.float64(0.18000000000000002), np.float64(0.21000000000000002), np.float64(0.1374772708486752), np.float64(0.18138357147217055), np.float64(0.208806130178211), np.float64(0.16155494421403513), np.float64(0.1356465996625054), np.float64(0.16), np.float64(0.12000000000000001), np.float64(0.2109502310972899), np.float64(0.116619037896906), np.float64(0.15652475842498528), np.float64(0.14177446878757824), np.float64(0.11357816691600547), np.float64(0.20396078054371142), np.float64(0.07810249675906658), np.float64(0.20223748416156687), np.float64(0.09433981132056604), np.float64(0.18330302779823363), np.float64(0.09), np.float64(0.0640312423743285), np.float64(0.09433981132056607), np.float64(0.09433981132056607), np.float64(0.14696938456699069), np.float64(0.15524174696260024), np.float64(0.14832396974191325), np.float64(0.19209372712298547), np.float64(0.12489995996796799), np.float64(0.14456832294800961), np.float64(0.11000000000000001)]
beta: 0.4
preprocessing time for sampling: 0.012514829635620117
amortized time for sample size  5 is:  0.0001186823844909668
preprocessing time for sampling: 0.012508153915405273
amortized time for sample size  10 is:  0.00011835098266601562
preprocessing time for sampling: 0.012495756149291992
amortized time for sample size  15 is:  0.00011835670471191407
preprocessing time for sampling: 0.01250004768371582
amortized time for sample size  20 is:  0.00011870968341827394
preprocessing time for sampling: 0.012518882751464844
amortized time for sample size  25 is:  0.00011864271163940429
preprocessing time for sampling: 0.012517929077148438
amortized time for sample size  30 is:  0.00011832650502522787
preprocessing time for sampling: 0.012515068054199219
amortized time for sample size  35 is:  0.00011853143147059849
preprocessing time for sampling: 0.012737035751342773
amortized time for sample size  40 is:  0.0001204742193222046
preprocessing time for sampling: 0.012604236602783203
amortized time for sample size  45 is:  0.00012063042322794596
preprocessing time for sampling: 0.012513875961303711
amortized time for sample size  50 is:  0.0001184420108795166
preprocessing time for sampling: 0.01251673698425293
amortized time for sample size  55 is:  0.00011873778429898349
preprocessing time for sampling: 0.012600898742675781
amortized time for sample size  60 is:  0.00011887848377227783
preprocessing time for sampling: 0.012700796127319336
amortized time for sample size  65 is:  0.0001197348741384653
preprocessing time for sampling: 0.012602090835571289
amortized time for sample size  70 is:  0.0001193505014692034
preprocessing time for sampling: 0.012888908386230469
amortized time for sample size  75 is:  0.0001205193519592285
preprocessing time for sampling: 0.012575149536132812
amortized time for sample size  80 is:  0.00012169194221496582
preprocessing time for sampling: 0.01258707046508789
amortized time for sample size  85 is:  0.00011914572996251722
preprocessing time for sampling: 0.012510061264038086
amortized time for sample size  90 is:  0.00011962244245741103
preprocessing time for sampling: 0.012514829635620117
amortized time for sample size  95 is:  0.00012044505069130347
preprocessing time for sampling: 0.012872934341430664
amortized time for sample size  100 is:  0.00011900000572204592
preprocessing time for sampling: 0.012839078903198242
amortized time for sample size  105 is:  0.00011968499138241723
preprocessing time for sampling: 0.012584924697875977
amortized time for sample size  110 is:  0.00011944283138621936
preprocessing time for sampling: 0.012557744979858398
amortized time for sample size  115 is:  0.00012099771914274798
preprocessing time for sampling: 0.013165950775146484
amortized time for sample size  120 is:  0.00012063324451446531
preprocessing time for sampling: 0.012712240219116211
amortized time for sample size  125 is:  0.00012080707550048829
preprocessing time for sampling: 0.012500286102294922
amortized time for sample size  130 is:  0.00011951314485990085
preprocessing time for sampling: 0.01283884048461914
amortized time for sample size  135 is:  0.0001228181167885109
preprocessing time for sampling: 0.013192176818847656
amortized time for sample size  140 is:  0.00012172807965959821
preprocessing time for sampling: 0.012497186660766602
amortized time for sample size  145 is:  0.00011976075994557348
preprocessing time for sampling: 0.012848138809204102
amortized time for sample size  150 is:  0.00012003064155578614
preprocessing time for sampling: 0.012525796890258789
amortized time for sample size  155 is:  0.00011908877280450635
preprocessing time for sampling: 0.012532234191894531
amortized time for sample size  160 is:  0.00012140677869319915
preprocessing time for sampling: 0.012639999389648438
amortized time for sample size  165 is:  0.00011927994814786043
preprocessing time for sampling: 0.012586116790771484
amortized time for sample size  170 is:  0.00011951609218821806
preprocessing time for sampling: 0.012533903121948242
amortized time for sample size  175 is:  0.00011926578794206891
preprocessing time for sampling: 0.012628316879272461
amortized time for sample size  180 is:  0.00012166052394443089
preprocessing time for sampling: 0.012637853622436523
amortized time for sample size  185 is:  0.00011917994473431563
preprocessing time for sampling: 0.012655019760131836
amortized time for sample size  190 is:  0.00012145353618421053
preprocessing time for sampling: 0.012607812881469727
amortized time for sample size  195 is:  0.00011913761725792516
preprocessing time for sampling: 0.012533903121948242
amortized time for sample size  200 is:  0.00011936205625534057
preprocessing time for sampling: 0.012651920318603516
amortized time for sample size  205 is:  0.00011975327933706887
preprocessing time for sampling: 0.01265406608581543
amortized time for sample size  210 is:  0.00012078773407709031
preprocessing time for sampling: 0.012605905532836914
amortized time for sample size  215 is:  0.00011926475791044014
preprocessing time for sampling: 0.013221025466918945
amortized time for sample size  220 is:  0.0001191451441157948
preprocessing time for sampling: 0.012800931930541992
amortized time for sample size  225 is:  0.00012145505481296117
preprocessing time for sampling: 0.012762308120727539
amortized time for sample size  230 is:  0.00012114742527837339
preprocessing time for sampling: 0.01264500617980957
amortized time for sample size  235 is:  0.00011961639688370076
preprocessing time for sampling: 0.012804269790649414
amortized time for sample size  240 is:  0.00012096818288167317
preprocessing time for sampling: 0.01277017593383789
amortized time for sample size  245 is:  0.00012046572626853475
preprocessing time for sampling: 0.012572050094604492
amortized time for sample size  250 is:  0.00011885598182678224
*** results for plotting, beta= 0.4 

mean_list= [np.float64(0.61), np.float64(0.5599999999999999), np.float64(0.78), np.float64(0.75), np.float64(0.78), np.float64(0.6599999999999999), np.float64(0.8800000000000001), np.float64(0.73), np.float64(0.75), np.float64(0.8099999999999999), np.float64(0.8700000000000001), np.float64(0.8400000000000001), np.float64(0.9400000000000001), np.float64(0.89), np.float64(0.8300000000000001), np.float64(0.7899999999999999), np.float64(0.9400000000000001), np.float64(0.86), np.float64(0.93), np.float64(0.9200000000000002), np.float64(0.89), np.float64(0.93), np.float64(0.96), np.float64(0.9099999999999998), np.float64(0.9700000000000001), np.float64(0.8700000000000001), np.float64(0.9099999999999999), np.float64(0.93), np.float64(0.96), np.float64(0.96), np.float64(0.96), np.float64(0.8800000000000001), np.float64(0.97), np.float64(0.95), np.float64(0.9400000000000001), np.float64(0.93), np.float64(0.95), np.float64(0.96), np.float64(0.97), np.float64(0.97), np.float64(0.9099999999999999), np.float64(0.9100000000000001), np.float64(0.9400000000000001), np.float64(0.93), np.float64(0.96), np.float64(0.9400000000000001), np.float64(0.97), np.float64(0.9800000000000001), np.float64(0.96), np.float64(0.97)]
std_list= [np.float64(0.13), np.float64(0.15620499351813305), np.float64(0.11661903789690603), np.float64(0.12041594578792297), np.float64(0.12489995996796799), np.float64(0.14966629547095767), np.float64(0.11661903789690602), np.float64(0.12688577540449522), np.float64(0.1284523257866513), np.float64(0.13747727084867523), np.float64(0.11000000000000001), np.float64(0.10198039027185571), np.float64(0.07999999999999999), np.float64(0.09433981132056604), np.float64(0.11000000000000001), np.float64(0.09433981132056607), np.float64(0.06633249580710798), np.float64(0.17435595774162693), np.float64(0.06403124237432847), np.float64(0.059999999999999984), np.float64(0.09433981132056604), np.float64(0.1004987562112089), np.float64(0.06633249580710798), np.float64(0.11357816691600549), np.float64(0.04582575694955839), np.float64(0.07810249675906653), np.float64(0.1044030650891055), np.float64(0.06403124237432847), np.float64(0.04898979485566354), np.float64(0.06633249580710798), np.float64(0.04898979485566355), np.float64(0.09797958971132714), np.float64(0.04582575694955839), np.float64(0.04999999999999999), np.float64(0.06633249580710798), np.float64(0.1004987562112089), np.float64(0.04999999999999999), np.float64(0.04898979485566355), np.float64(0.045825756949558386), np.float64(0.04582575694955839), np.float64(0.11357816691600549), np.float64(0.1044030650891055), np.float64(0.06633249580710798), np.float64(0.07810249675906653), np.float64(0.04898979485566356), np.float64(0.09165151389911678), np.float64(0.06403124237432847), np.float64(0.039999999999999994), np.float64(0.04898979485566355), np.float64(0.04582575694955839)]
beta: 0.6
preprocessing time for sampling: 0.012664079666137695
amortized time for sample size  5 is:  0.00012082481384277341
preprocessing time for sampling: 0.012620210647583008
amortized time for sample size  10 is:  0.00012019133567810059
preprocessing time for sampling: 0.012705087661743164
amortized time for sample size  15 is:  0.00012093989054361978
preprocessing time for sampling: 0.012861013412475586
amortized time for sample size  20 is:  0.00012468087673187257
preprocessing time for sampling: 0.012968301773071289
amortized time for sample size  25 is:  0.00012159099578857422
preprocessing time for sampling: 0.013014078140258789
amortized time for sample size  30 is:  0.00011914761861165365
preprocessing time for sampling: 0.012563943862915039
amortized time for sample size  35 is:  0.0001187889916556222
preprocessing time for sampling: 0.012891292572021484
amortized time for sample size  40 is:  0.0001218317747116089
preprocessing time for sampling: 0.012789011001586914
amortized time for sample size  45 is:  0.0001206449932522244
preprocessing time for sampling: 0.012886762619018555
amortized time for sample size  50 is:  0.00011997275352478026
preprocessing time for sampling: 0.012875080108642578
amortized time for sample size  55 is:  0.00012262790853326974
preprocessing time for sampling: 0.01272130012512207
amortized time for sample size  60 is:  0.00011943892637888589
preprocessing time for sampling: 0.012849807739257812
amortized time for sample size  65 is:  0.00011949704243586615
preprocessing time for sampling: 0.01258707046508789
amortized time for sample size  70 is:  0.00011962171963282993
preprocessing time for sampling: 0.012746095657348633
amortized time for sample size  75 is:  0.00012333129247029623
preprocessing time for sampling: 0.012798070907592773
amortized time for sample size  80 is:  0.00011948361992835997
preprocessing time for sampling: 0.012614011764526367
amortized time for sample size  85 is:  0.00012147008671480065
preprocessing time for sampling: 0.01281118392944336
amortized time for sample size  90 is:  0.00012111473083496094
preprocessing time for sampling: 0.012539148330688477
amortized time for sample size  95 is:  0.00011972756134836299
preprocessing time for sampling: 0.022032976150512695
amortized time for sample size  100 is:  0.00012042121887207031
preprocessing time for sampling: 0.012613058090209961
amortized time for sample size  105 is:  0.00012202946345011393
preprocessing time for sampling: 0.012664794921875
amortized time for sample size  110 is:  0.00012144433368336071
preprocessing time for sampling: 0.012794971466064453
amortized time for sample size  115 is:  0.0001204501442287279
preprocessing time for sampling: 0.012549161911010742
amortized time for sample size  120 is:  0.00012072972456614176
preprocessing time for sampling: 0.012683868408203125
amortized time for sample size  125 is:  0.00011983631134033205
preprocessing time for sampling: 0.01258707046508789
amortized time for sample size  130 is:  0.00011918539267319899
preprocessing time for sampling: 0.012609004974365234
amortized time for sample size  135 is:  0.0001189265251159668
preprocessing time for sampling: 0.012551307678222656
amortized time for sample size  140 is:  0.00012190209116254534
preprocessing time for sampling: 0.012758970260620117
amortized time for sample size  145 is:  0.00012126736805356781
preprocessing time for sampling: 0.012586832046508789
amortized time for sample size  150 is:  0.00011988677978515623
preprocessing time for sampling: 0.01264810562133789
amortized time for sample size  155 is:  0.00012109837993498773
preprocessing time for sampling: 0.012756109237670898
amortized time for sample size  160 is:  0.00012010283768177033
preprocessing time for sampling: 0.012611150741577148
amortized time for sample size  165 is:  0.0001204883980028557
preprocessing time for sampling: 0.012514829635620117
amortized time for sample size  170 is:  0.0001194796141456155
preprocessing time for sampling: 0.012786865234375
amortized time for sample size  175 is:  0.00012157971518380299
preprocessing time for sampling: 0.01346898078918457
amortized time for sample size  180 is:  0.00012096500396728516
preprocessing time for sampling: 0.012521982192993164
amortized time for sample size  185 is:  0.00012112043999336862
preprocessing time for sampling: 0.012830257415771484
amortized time for sample size  190 is:  0.00012029329099153215
preprocessing time for sampling: 0.01289987564086914
amortized time for sample size  195 is:  0.00012113556495079628
preprocessing time for sampling: 0.012628793716430664
amortized time for sample size  200 is:  0.00012136956453323362
preprocessing time for sampling: 0.0126800537109375
amortized time for sample size  205 is:  0.00012085625020469107
preprocessing time for sampling: 0.01265716552734375
amortized time for sample size  210 is:  0.00012026460965474447
preprocessing time for sampling: 0.012769937515258789
amortized time for sample size  215 is:  0.0001209754278493482
preprocessing time for sampling: 0.012887239456176758
amortized time for sample size  220 is:  0.00012167132984508169
preprocessing time for sampling: 0.012813806533813477
amortized time for sample size  225 is:  0.0001225932863023546
preprocessing time for sampling: 0.012837886810302734
amortized time for sample size  230 is:  0.00012057942929475203
preprocessing time for sampling: 0.012804031372070312
amortized time for sample size  235 is:  0.00012132342318271072
preprocessing time for sampling: 0.01264500617980957
amortized time for sample size  240 is:  0.00012133623162905377
preprocessing time for sampling: 0.01282191276550293
amortized time for sample size  245 is:  0.00011989600317818777
preprocessing time for sampling: 0.012666940689086914
amortized time for sample size  250 is:  0.00012098498344421386
*** results for plotting, beta= 0.6 

mean_list= [np.float64(0.7), np.float64(0.86), np.float64(0.8700000000000001), np.float64(0.89), np.float64(0.9000000000000001), np.float64(0.9), np.float64(0.95), np.float64(0.9700000000000001), np.float64(0.95), np.float64(0.9400000000000001), np.float64(0.99), np.float64(0.9400000000000001), np.float64(0.96), np.float64(0.99), np.float64(0.9099999999999999), np.float64(1.0), np.float64(0.9800000000000001), np.float64(0.99), np.float64(1.0), np.float64(0.96), np.float64(0.99), np.float64(0.99), np.float64(0.99), np.float64(1.0), np.float64(0.9800000000000001), np.float64(0.99), np.float64(0.9800000000000001), np.float64(0.9800000000000001), np.float64(0.99), np.float64(1.0), np.float64(0.9800000000000001), 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(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)]
std_list= [np.float64(0.1341640786499874), np.float64(0.09165151389911681), np.float64(0.07810249675906653), np.float64(0.05385164807134503), np.float64(0.11832159566199234), np.float64(0.08944271909999157), np.float64(0.06708203932499367), np.float64(0.06403124237432847), np.float64(0.04999999999999999), np.float64(0.06633249580710798), np.float64(0.029999999999999992), np.float64(0.07999999999999999), np.float64(0.04898979485566355), np.float64(0.029999999999999992), np.float64(0.06999999999999999), np.float64(0.0), np.float64(0.039999999999999994), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.04898979485566355), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.05999999999999999), np.float64(0.029999999999999992), np.float64(0.039999999999999994), np.float64(0.039999999999999994), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.039999999999999994), 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(0.029999999999999992), 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)]
beta: 0.8
preprocessing time for sampling: 0.012747049331665039
amortized time for sample size  5 is:  0.00012074851989746091
preprocessing time for sampling: 0.0127410888671875
amortized time for sample size  10 is:  0.0001206068992614746
preprocessing time for sampling: 0.012745857238769531
amortized time for sample size  15 is:  0.00011991357803344727
preprocessing time for sampling: 0.01250910758972168
amortized time for sample size  20 is:  0.00012064647674560547
preprocessing time for sampling: 0.012997150421142578
amortized time for sample size  25 is:  0.00012079668045043946
preprocessing time for sampling: 0.012744903564453125
amortized time for sample size  30 is:  0.00012044946352640787
preprocessing time for sampling: 0.01275491714477539
amortized time for sample size  35 is:  0.00012037311281476702
preprocessing time for sampling: 0.012750864028930664
amortized time for sample size  40 is:  0.00012025433778762818
preprocessing time for sampling: 0.012733936309814453
amortized time for sample size  45 is:  0.00012092150582207573
preprocessing time for sampling: 0.012729167938232422
amortized time for sample size  50 is:  0.0001202821731567383
preprocessing time for sampling: 0.012725353240966797
amortized time for sample size  55 is:  0.00012048703973943536
preprocessing time for sampling: 0.012814760208129883
amortized time for sample size  60 is:  0.00012061083316802979
preprocessing time for sampling: 0.0128021240234375
amortized time for sample size  65 is:  0.00012043553132277268
preprocessing time for sampling: 0.012737035751342773
amortized time for sample size  70 is:  0.00012057440621512277
preprocessing time for sampling: 0.012627363204956055
amortized time for sample size  75 is:  0.00012262468338012695
preprocessing time for sampling: 0.012809991836547852
amortized time for sample size  80 is:  0.00012032049894332887
preprocessing time for sampling: 0.012827157974243164
amortized time for sample size  85 is:  0.00012058558183557848
preprocessing time for sampling: 0.012705087661743164
amortized time for sample size  90 is:  0.00011978981229994033
preprocessing time for sampling: 0.012478113174438477
amortized time for sample size  95 is:  0.00012037036293431334
preprocessing time for sampling: 0.012897014617919922
amortized time for sample size  100 is:  0.00012067854404449463
preprocessing time for sampling: 0.01254892349243164
amortized time for sample size  105 is:  0.00012147814886910573
preprocessing time for sampling: 0.012630224227905273
amortized time for sample size  110 is:  0.00012058084661310368
preprocessing time for sampling: 0.01284480094909668
amortized time for sample size  115 is:  0.0001251414962436842
preprocessing time for sampling: 0.012723922729492188
amortized time for sample size  120 is:  0.00012072964509328209
preprocessing time for sampling: 0.012761831283569336
amortized time for sample size  125 is:  0.00012040952682495118
preprocessing time for sampling: 0.012740850448608398
amortized time for sample size  130 is:  0.00012055167785057652
preprocessing time for sampling: 0.012803077697753906
amortized time for sample size  135 is:  0.00012109918947573058
preprocessing time for sampling: 0.01273488998413086
amortized time for sample size  140 is:  0.00012030727522713797
preprocessing time for sampling: 0.012761116027832031
amortized time for sample size  145 is:  0.00012104904240575328
preprocessing time for sampling: 0.012757062911987305
amortized time for sample size  150 is:  0.00012038555145263672
preprocessing time for sampling: 0.012861967086791992
amortized time for sample size  155 is:  0.00012203058119743103
preprocessing time for sampling: 0.012753963470458984
amortized time for sample size  160 is:  0.00012263223528861998
preprocessing time for sampling: 0.012575387954711914
amortized time for sample size  165 is:  0.00012110418261903705
preprocessing time for sampling: 0.012750864028930664
amortized time for sample size  170 is:  0.00012131974276374368
preprocessing time for sampling: 0.012853145599365234
amortized time for sample size  175 is:  0.00012052691323416574
preprocessing time for sampling: 0.012812137603759766
amortized time for sample size  180 is:  0.00012071874406602648
preprocessing time for sampling: 0.012764930725097656
amortized time for sample size  185 is:  0.00012121504706305426
preprocessing time for sampling: 0.012798309326171875
amortized time for sample size  190 is:  0.00012065528568468595
preprocessing time for sampling: 0.012781143188476562
amortized time for sample size  195 is:  0.00012135023948473808
preprocessing time for sampling: 0.013128995895385742
amortized time for sample size  200 is:  0.0001208279848098755
preprocessing time for sampling: 0.012784004211425781
amortized time for sample size  205 is:  0.00012128492680991569
preprocessing time for sampling: 0.01328897476196289
amortized time for sample size  210 is:  0.00012208033743358796
preprocessing time for sampling: 0.01276087760925293
amortized time for sample size  215 is:  0.0001223272722820903
preprocessing time for sampling: 0.013038158416748047
amortized time for sample size  220 is:  0.0001210956790230491
preprocessing time for sampling: 0.012777090072631836
amortized time for sample size  225 is:  0.00012241599824693467
preprocessing time for sampling: 0.013113021850585938
amortized time for sample size  230 is:  0.0001208198588827382
preprocessing time for sampling: 0.012871026992797852
amortized time for sample size  235 is:  0.00012090519641308074
preprocessing time for sampling: 0.01282191276550293
amortized time for sample size  240 is:  0.00012090042233467104
preprocessing time for sampling: 0.012816905975341797
amortized time for sample size  245 is:  0.00012095258673843074
preprocessing time for sampling: 0.012820005416870117
amortized time for sample size  250 is:  0.00012147828102111815
*** results for plotting, beta= 0.8 

mean_list= [np.float64(0.79), np.float64(0.9099999999999999), np.float64(0.93), np.float64(0.99), np.float64(0.9700000000000001), np.float64(0.99), np.float64(0.99), np.float64(0.9800000000000001), np.float64(0.9800000000000001), np.float64(1.0), 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(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(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)]
std_list= [np.float64(0.10440306508910552), np.float64(0.08306623862918076), np.float64(0.06403124237432847), np.float64(0.029999999999999992), np.float64(0.06403124237432847), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.039999999999999994), np.float64(0.039999999999999994), np.float64(0.0), 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(0.0), 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(0.029999999999999992), 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)]
beta: 1
preprocessing time for sampling: 0.013833045959472656
amortized time for sample size  5 is:  0.0001270051002502441
preprocessing time for sampling: 0.013840198516845703
amortized time for sample size  10 is:  0.0001269102096557617
preprocessing time for sampling: 0.013685941696166992
amortized time for sample size  15 is:  0.00012774419784545896
preprocessing time for sampling: 0.01363992691040039
amortized time for sample size  20 is:  0.0001263364553451538
preprocessing time for sampling: 0.013734102249145508
amortized time for sample size  25 is:  0.00012664165496826174
preprocessing time for sampling: 0.013809919357299805
amortized time for sample size  30 is:  0.0001262675921122233
preprocessing time for sampling: 0.013869762420654297
amortized time for sample size  35 is:  0.00012681075504847937
preprocessing time for sampling: 0.013753175735473633
amortized time for sample size  40 is:  0.0001262543797492981
preprocessing time for sampling: 0.013725996017456055
amortized time for sample size  45 is:  0.00012784624099731448
preprocessing time for sampling: 0.013740062713623047
amortized time for sample size  50 is:  0.00012721753120422362
preprocessing time for sampling: 0.013829708099365234
amortized time for sample size  55 is:  0.00012668943405151368
preprocessing time for sampling: 0.014168977737426758
amortized time for sample size  60 is:  0.00012724852561950685
preprocessing time for sampling: 0.013820171356201172
amortized time for sample size  65 is:  0.0001274888698871319
preprocessing time for sampling: 0.013824939727783203
amortized time for sample size  70 is:  0.00012719719750540597
preprocessing time for sampling: 0.013872861862182617
amortized time for sample size  75 is:  0.0001268697738647461
preprocessing time for sampling: 0.01377725601196289
amortized time for sample size  80 is:  0.0001260412335395813
preprocessing time for sampling: 0.013708114624023438
amortized time for sample size  85 is:  0.00012601959004121668
preprocessing time for sampling: 0.013923168182373047
amortized time for sample size  90 is:  0.0001271544032626682
preprocessing time for sampling: 0.01378488540649414
amortized time for sample size  95 is:  0.00012647337662546258
preprocessing time for sampling: 0.013791084289550781
amortized time for sample size  100 is:  0.00012670214176177975
preprocessing time for sampling: 0.014080047607421875
amortized time for sample size  105 is:  0.0001287203062148321
preprocessing time for sampling: 0.01370382308959961
amortized time for sample size  110 is:  0.00012770206278020686
preprocessing time for sampling: 0.013701200485229492
amortized time for sample size  115 is:  0.00012806537876958434
preprocessing time for sampling: 0.013916015625
amortized time for sample size  120 is:  0.00012711705764134726
preprocessing time for sampling: 0.013864994049072266
amortized time for sample size  125 is:  0.00012660339355468752
preprocessing time for sampling: 0.014024972915649414
amortized time for sample size  130 is:  0.00012764268655043382
preprocessing time for sampling: 0.014137029647827148
amortized time for sample size  135 is:  0.00012725174868548358
preprocessing time for sampling: 0.013931989669799805
amortized time for sample size  140 is:  0.00012775170803070067
preprocessing time for sampling: 0.013788938522338867
amortized time for sample size  145 is:  0.00012747901061485554
preprocessing time for sampling: 0.013861894607543945
amortized time for sample size  150 is:  0.00012686713536580403
preprocessing time for sampling: 0.013782024383544922
amortized time for sample size  155 is:  0.00012764197011147776
preprocessing time for sampling: 0.014122247695922852
amortized time for sample size  160 is:  0.0001286811828613281
preprocessing time for sampling: 0.013823986053466797
amortized time for sample size  165 is:  0.00012757166949185458
preprocessing time for sampling: 0.013820886611938477
amortized time for sample size  170 is:  0.00012849353341495286
preprocessing time for sampling: 0.013862133026123047
amortized time for sample size  175 is:  0.0001284104210989816
preprocessing time for sampling: 0.013815164566040039
amortized time for sample size  180 is:  0.00012934120496114094
preprocessing time for sampling: 0.014162778854370117
amortized time for sample size  185 is:  0.00012758976704365497
preprocessing time for sampling: 0.013842105865478516
amortized time for sample size  190 is:  0.00012682377664666427
preprocessing time for sampling: 0.013830900192260742
amortized time for sample size  195 is:  0.0001269098673111353
preprocessing time for sampling: 0.013648033142089844
amortized time for sample size  200 is:  0.00012795029878616334
preprocessing time for sampling: 0.013900995254516602
amortized time for sample size  205 is:  0.00012756747734255907
preprocessing time for sampling: 0.01385188102722168
amortized time for sample size  210 is:  0.00012844025521051316
preprocessing time for sampling: 0.013782024383544922
amortized time for sample size  215 is:  0.0001263610595880553
preprocessing time for sampling: 0.013876914978027344
amortized time for sample size  220 is:  0.00012700008262287485
preprocessing time for sampling: 0.01384282112121582
amortized time for sample size  225 is:  0.00012666163974338107
preprocessing time for sampling: 0.013839006423950195
amortized time for sample size  230 is:  0.0001263358385666557
preprocessing time for sampling: 0.013821840286254883
amortized time for sample size  235 is:  0.00012634774471851108
preprocessing time for sampling: 0.013795137405395508
amortized time for sample size  240 is:  0.00012662341197331746
preprocessing time for sampling: 0.013756990432739258
amortized time for sample size  245 is:  0.00012625896687410318
preprocessing time for sampling: 0.015548944473266602
amortized time for sample size  250 is:  0.00012717414855957032
*** results for plotting, beta= 1 

mean_list= [np.float64(0.8800000000000001), np.float64(0.9400000000000001), np.float64(0.9800000000000001), np.float64(0.99), np.float64(1.0), np.float64(0.9800000000000001), np.float64(0.9800000000000001), 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(0.06633249580710798), np.float64(0.039999999999999994), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.039999999999999994), np.float64(0.039999999999999994), 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: 0.012974739074707031
amortized time for sample size  5 is:  0.0001232738494873047
preprocessing time for sampling: 0.012948989868164062
amortized time for sample size  10 is:  0.00012114644050598145
preprocessing time for sampling: 0.012897014617919922
amortized time for sample size  15 is:  0.0001226240793863932
preprocessing time for sampling: 0.013283729553222656
amortized time for sample size  20 is:  0.00012252402305603028
preprocessing time for sampling: 0.01295614242553711
amortized time for sample size  25 is:  0.00012327594757080077
preprocessing time for sampling: 0.012859821319580078
amortized time for sample size  30 is:  0.0001212321917215983
preprocessing time for sampling: 0.01278996467590332
amortized time for sample size  35 is:  0.00012076255253383091
preprocessing time for sampling: 0.012948036193847656
amortized time for sample size  40 is:  0.00012125968933105469
preprocessing time for sampling: 0.012792110443115234
amortized time for sample size  45 is:  0.00012244266933865016
preprocessing time for sampling: 0.012778997421264648
amortized time for sample size  50 is:  0.00012069301605224607
preprocessing time for sampling: 0.012791156768798828
amortized time for sample size  55 is:  0.00012087093700062146
preprocessing time for sampling: 0.013157129287719727
amortized time for sample size  60 is:  0.0001230309009552002
preprocessing time for sampling: 0.012861013412475586
amortized time for sample size  65 is:  0.00012168693542480466
preprocessing time for sampling: 0.012660980224609375
amortized time for sample size  70 is:  0.00012138983181544714
preprocessing time for sampling: 0.012887239456176758
amortized time for sample size  75 is:  0.00012314554850260414
preprocessing time for sampling: 0.012815713882446289
amortized time for sample size  80 is:  0.00012132808566093444
preprocessing time for sampling: 0.012805938720703125
amortized time for sample size  85 is:  0.00012239686180563536
preprocessing time for sampling: 0.012807130813598633
amortized time for sample size  90 is:  0.0001228066815270318
preprocessing time for sampling: 0.012804746627807617
amortized time for sample size  95 is:  0.00012113711708470397
preprocessing time for sampling: 0.012778043746948242
amortized time for sample size  100 is:  0.00012202022075653077
preprocessing time for sampling: 0.012892007827758789
amortized time for sample size  105 is:  0.00012103823253086638
preprocessing time for sampling: 0.0128326416015625
amortized time for sample size  110 is:  0.00012392954392866654
preprocessing time for sampling: 0.012797832489013672
amortized time for sample size  115 is:  0.00012079456578130307
preprocessing time for sampling: 0.01281118392944336
amortized time for sample size  120 is:  0.0001209903558095296
preprocessing time for sampling: 0.012762069702148438
amortized time for sample size  125 is:  0.0001208626937866211
preprocessing time for sampling: 0.012777328491210938
amortized time for sample size  130 is:  0.00012137983395503116
preprocessing time for sampling: 0.012786149978637695
amortized time for sample size  135 is:  0.0001206417966772009
preprocessing time for sampling: 0.01279902458190918
amortized time for sample size  140 is:  0.00012133576188768658
preprocessing time for sampling: 0.01277613639831543
amortized time for sample size  145 is:  0.00012119406667248958
preprocessing time for sampling: 0.012768030166625977
amortized time for sample size  150 is:  0.00012079512278238934
preprocessing time for sampling: 0.012755870819091797
amortized time for sample size  155 is:  0.00012177105872861801
preprocessing time for sampling: 0.012762784957885742
amortized time for sample size  160 is:  0.00012185452878475188
preprocessing time for sampling: 0.012803077697753906
amortized time for sample size  165 is:  0.00012072847828720555
preprocessing time for sampling: 0.012772798538208008
amortized time for sample size  170 is:  0.00012072361216825596
preprocessing time for sampling: 0.012738943099975586
amortized time for sample size  175 is:  0.00012033335821969169
preprocessing time for sampling: 0.012756824493408203
amortized time for sample size  180 is:  0.00012095673878987632
preprocessing time for sampling: 0.012883901596069336
amortized time for sample size  185 is:  0.00012149741198565508
preprocessing time for sampling: 0.012786865234375
amortized time for sample size  190 is:  0.00012058795125860917
preprocessing time for sampling: 0.012801885604858398
amortized time for sample size  195 is:  0.00012117230586516551
preprocessing time for sampling: 0.01274871826171875
amortized time for sample size  200 is:  0.00012114725112915038
preprocessing time for sampling: 0.013813018798828125
amortized time for sample size  205 is:  0.00012096869073263027
preprocessing time for sampling: 0.012809991836547852
amortized time for sample size  210 is:  0.00012108260109311058
preprocessing time for sampling: 0.012761831283569336
amortized time for sample size  215 is:  0.00012124367647392805
preprocessing time for sampling: 0.01277017593383789
amortized time for sample size  220 is:  0.00012163926254619254
preprocessing time for sampling: 0.012845993041992188
amortized time for sample size  225 is:  0.00012140008078681097
preprocessing time for sampling: 0.013417959213256836
amortized time for sample size  230 is:  0.00012125789600869883
preprocessing time for sampling: 0.012740135192871094
amortized time for sample size  235 is:  0.00012173900198429188
preprocessing time for sampling: 0.012816190719604492
amortized time for sample size  240 is:  0.0001220116714636485
preprocessing time for sampling: 0.012788057327270508
amortized time for sample size  245 is:  0.00012141486576625281
preprocessing time for sampling: 0.012742042541503906
amortized time for sample size  250 is:  0.00012142663955688477
*** results for plotting, beta= 1.2 

mean_list= [np.float64(0.9200000000000002), np.float64(0.99), np.float64(0.9400000000000001), np.float64(0.9800000000000001), 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(0.08717797887081348), np.float64(0.029999999999999992), np.float64(0.06633249580710798), np.float64(0.039999999999999994), 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)]
