beta: 0.2
preprocessing time for sampling: 0.23494887351989746
amortized time for sample size  5 is:  0.0002575974464416504
preprocessing time for sampling: 0.22898316383361816
amortized time for sample size  10 is:  0.00025766921043395995
preprocessing time for sampling: 0.22882699966430664
amortized time for sample size  15 is:  0.000256166140238444
preprocessing time for sampling: 0.2294151782989502
amortized time for sample size  20 is:  0.00025648987293243406
preprocessing time for sampling: 0.22634601593017578
amortized time for sample size  25 is:  0.00025520124435424803
preprocessing time for sampling: 0.23235106468200684
amortized time for sample size  30 is:  0.00026012754440307614
preprocessing time for sampling: 0.23091602325439453
amortized time for sample size  35 is:  0.0002568725858415876
preprocessing time for sampling: 0.24216794967651367
amortized time for sample size  40 is:  0.00025626611709594725
preprocessing time for sampling: 0.23000192642211914
amortized time for sample size  45 is:  0.00025654141108194983
preprocessing time for sampling: 0.23054003715515137
amortized time for sample size  50 is:  0.0002574124813079834
preprocessing time for sampling: 0.23275423049926758
amortized time for sample size  55 is:  0.0002569061626087535
preprocessing time for sampling: 0.22835206985473633
amortized time for sample size  60 is:  0.0002575238545735677
preprocessing time for sampling: 0.23034906387329102
amortized time for sample size  65 is:  0.00026046998684222885
preprocessing time for sampling: 0.23551583290100098
amortized time for sample size  70 is:  0.00025971412658691405
preprocessing time for sampling: 0.23990511894226074
amortized time for sample size  75 is:  0.00026540552775065104
preprocessing time for sampling: 0.22915101051330566
amortized time for sample size  80 is:  0.0002562069594860077
preprocessing time for sampling: 0.22960710525512695
amortized time for sample size  85 is:  0.0002563934045679429
preprocessing time for sampling: 0.22584986686706543
amortized time for sample size  90 is:  0.00025631292661031086
preprocessing time for sampling: 0.22631335258483887
amortized time for sample size  95 is:  0.00025620134253250926
preprocessing time for sampling: 0.22616887092590332
amortized time for sample size  100 is:  0.0002572093486785889
preprocessing time for sampling: 0.22979116439819336
amortized time for sample size  105 is:  0.00025656398137410477
preprocessing time for sampling: 0.23197603225708008
amortized time for sample size  110 is:  0.0002579709616574374
preprocessing time for sampling: 0.23370695114135742
amortized time for sample size  115 is:  0.000260415097941523
preprocessing time for sampling: 0.2306690216064453
amortized time for sample size  120 is:  0.0002577672004699707
preprocessing time for sampling: 0.23070311546325684
amortized time for sample size  125 is:  0.0002598758697509766
preprocessing time for sampling: 0.22910213470458984
amortized time for sample size  130 is:  0.00025848909524770885
preprocessing time for sampling: 0.22905182838439941
amortized time for sample size  135 is:  0.0002581456325672291
preprocessing time for sampling: 0.27826690673828125
amortized time for sample size  140 is:  0.00025853943824768067
preprocessing time for sampling: 0.2293088436126709
amortized time for sample size  145 is:  0.00025861442500147325
preprocessing time for sampling: 0.23300981521606445
amortized time for sample size  150 is:  0.00025938223203023276
preprocessing time for sampling: 0.22972893714904785
amortized time for sample size  155 is:  0.00026050642997987807
preprocessing time for sampling: 0.2308647632598877
amortized time for sample size  160 is:  0.0002585644274950027
preprocessing time for sampling: 0.2335820198059082
amortized time for sample size  165 is:  0.0002615655985745517
preprocessing time for sampling: 0.23592281341552734
amortized time for sample size  170 is:  0.0002598259028266458
preprocessing time for sampling: 0.2333238124847412
amortized time for sample size  175 is:  0.0002612609590802874
preprocessing time for sampling: 0.23937201499938965
amortized time for sample size  180 is:  0.00026181374655829534
preprocessing time for sampling: 0.23430228233337402
amortized time for sample size  185 is:  0.00026253317497872017
preprocessing time for sampling: 0.23732686042785645
amortized time for sample size  190 is:  0.00026275721349214255
preprocessing time for sampling: 0.23245596885681152
amortized time for sample size  195 is:  0.00026394425905667824
preprocessing time for sampling: 0.23431611061096191
amortized time for sample size  200 is:  0.00026196372509002685
preprocessing time for sampling: 0.23128414154052734
amortized time for sample size  205 is:  0.0002619790100469822
preprocessing time for sampling: 0.23468279838562012
amortized time for sample size  210 is:  0.0002620984599703834
preprocessing time for sampling: 0.23613309860229492
amortized time for sample size  215 is:  0.00026152259250019873
preprocessing time for sampling: 0.2463397979736328
amortized time for sample size  220 is:  0.00026211736418984156
preprocessing time for sampling: 0.23436522483825684
amortized time for sample size  225 is:  0.0002621684180365668
preprocessing time for sampling: 0.23609089851379395
amortized time for sample size  230 is:  0.0002623371766961139
preprocessing time for sampling: 0.2337338924407959
amortized time for sample size  235 is:  0.00026185640375664897
preprocessing time for sampling: 0.233367919921875
amortized time for sample size  240 is:  0.000262674460808436
preprocessing time for sampling: 0.234144926071167
amortized time for sample size  245 is:  0.00026152952349915796
preprocessing time for sampling: 0.2338411808013916
amortized time for sample size  250 is:  0.0002625277233123779
*** results for plotting, beta= 0.2 

mean_list= [np.float64(0.33999999999999997), np.float64(0.49000000000000005), np.float64(0.5), np.float64(0.54), np.float64(0.53), np.float64(0.6), np.float64(0.69), np.float64(0.5799999999999998), np.float64(0.5599999999999999), np.float64(0.5599999999999999), np.float64(0.6399999999999999), np.float64(0.7100000000000001), np.float64(0.71), np.float64(0.65), np.float64(0.6599999999999999), np.float64(0.64), np.float64(0.71), np.float64(0.58), np.float64(0.66), np.float64(0.6799999999999999), np.float64(0.6700000000000002), np.float64(0.65), np.float64(0.7), np.float64(0.6900000000000001), np.float64(0.73), np.float64(0.73), np.float64(0.6399999999999999), np.float64(0.6300000000000001), np.float64(0.7), np.float64(0.8099999999999999), np.float64(0.69), np.float64(0.71), np.float64(0.74), np.float64(0.71), np.float64(0.72), np.float64(0.76), np.float64(0.69), np.float64(0.63), np.float64(0.7300000000000001), np.float64(0.64), np.float64(0.76), np.float64(0.73), np.float64(0.7), np.float64(0.73), np.float64(0.74), np.float64(0.72), np.float64(0.72), np.float64(0.75), np.float64(0.73), np.float64(0.73)]
std_list= [np.float64(0.09165151389911681), np.float64(0.15132745950421553), np.float64(0.08944271909999157), np.float64(0.1624807680927192), np.float64(0.14866068747318506), np.float64(0.15491933384829668), np.float64(0.16401219466856726), np.float64(0.14696938456699069), np.float64(0.1854723699099141), np.float64(0.142828568570857), np.float64(0.13564659966250536), np.float64(0.1135781669160055), np.float64(0.17), np.float64(0.191049731745428), np.float64(0.11135528725660043), np.float64(0.14282856857085702), np.float64(0.12206555615733705), np.float64(0.14696938456699069), np.float64(0.10198039027185571), np.float64(0.14), np.float64(0.1676305461424021), np.float64(0.12041594578792295), np.float64(0.20493901531919198), np.float64(0.15132745950421558), np.float64(0.1951922129594314), np.float64(0.14177446878757827), np.float64(0.14282856857085702), np.float64(0.1268857754044952), np.float64(0.10000000000000003), np.float64(0.15132745950421558), np.float64(0.15132745950421556), np.float64(0.12206555615733704), np.float64(0.1356465996625054), np.float64(0.08306623862918078), np.float64(0.15362291495737218), np.float64(0.09165151389911684), np.float64(0.13000000000000003), np.float64(0.14866068747318506), np.float64(0.11874342087037919), np.float64(0.128062484748657), np.float64(0.16852299546352717), np.float64(0.10049875621120893), np.float64(0.16733200530681513), np.float64(0.13453624047073712), np.float64(0.18000000000000002), np.float64(0.11661903789690603), np.float64(0.0871779788708135), np.float64(0.11180339887498951), np.float64(0.16155494421403513), np.float64(0.15524174696260024)]
beta: 0.4
preprocessing time for sampling: 0.23469901084899902
amortized time for sample size  5 is:  0.00026101160049438475
preprocessing time for sampling: 0.23194479942321777
amortized time for sample size  10 is:  0.0002609210014343262
preprocessing time for sampling: 0.2321019172668457
amortized time for sample size  15 is:  0.00026145855585734047
preprocessing time for sampling: 0.23213815689086914
amortized time for sample size  20 is:  0.00026136553287506103
preprocessing time for sampling: 0.23453402519226074
amortized time for sample size  25 is:  0.00026300382614135746
preprocessing time for sampling: 0.2768068313598633
amortized time for sample size  30 is:  0.0002636396884918213
preprocessing time for sampling: 0.23331570625305176
amortized time for sample size  35 is:  0.00026068142482212607
preprocessing time for sampling: 0.2335050106048584
amortized time for sample size  40 is:  0.0002607433795928955
preprocessing time for sampling: 0.23128390312194824
amortized time for sample size  45 is:  0.0002651188108656142
preprocessing time for sampling: 0.23093914985656738
amortized time for sample size  50 is:  0.00026045246124267583
preprocessing time for sampling: 0.23308181762695312
amortized time for sample size  55 is:  0.00026042881878939544
preprocessing time for sampling: 0.23319101333618164
amortized time for sample size  60 is:  0.000261454701423645
preprocessing time for sampling: 0.23390793800354004
amortized time for sample size  65 is:  0.000259855893942026
preprocessing time for sampling: 0.23297500610351562
amortized time for sample size  70 is:  0.00026054883003234867
preprocessing time for sampling: 0.23365092277526855
amortized time for sample size  75 is:  0.00026064847310384114
preprocessing time for sampling: 0.2367846965789795
amortized time for sample size  80 is:  0.00026159402728080747
preprocessing time for sampling: 0.23263192176818848
amortized time for sample size  85 is:  0.00026185164732091563
preprocessing time for sampling: 0.23126602172851562
amortized time for sample size  90 is:  0.00026119229528639054
preprocessing time for sampling: 0.23429083824157715
amortized time for sample size  95 is:  0.0002610256295455129
preprocessing time for sampling: 0.2341597080230713
amortized time for sample size  100 is:  0.00026152131557464597
preprocessing time for sampling: 0.2335679531097412
amortized time for sample size  105 is:  0.00026586523510160903
preprocessing time for sampling: 0.24136590957641602
amortized time for sample size  110 is:  0.0002691290812058882
preprocessing time for sampling: 0.2436826229095459
amortized time for sample size  115 is:  0.0002663984091385551
preprocessing time for sampling: 0.2323458194732666
amortized time for sample size  120 is:  0.0002634602387746175
preprocessing time for sampling: 0.2349257469177246
amortized time for sample size  125 is:  0.0002710448455810547
preprocessing time for sampling: 0.23384308815002441
amortized time for sample size  130 is:  0.0002628045448890099
preprocessing time for sampling: 0.23352384567260742
amortized time for sample size  135 is:  0.00026194480613425924
preprocessing time for sampling: 0.23481202125549316
amortized time for sample size  140 is:  0.00026597227369035993
preprocessing time for sampling: 0.23058700561523438
amortized time for sample size  145 is:  0.00026266196678424703
preprocessing time for sampling: 0.2310938835144043
amortized time for sample size  150 is:  0.0002610287030537923
preprocessing time for sampling: 0.23321104049682617
amortized time for sample size  155 is:  0.00026094468947379814
preprocessing time for sampling: 0.2334918975830078
amortized time for sample size  160 is:  0.0002614423185586929
preprocessing time for sampling: 0.23296809196472168
amortized time for sample size  165 is:  0.00026180804859508166
preprocessing time for sampling: 0.2331550121307373
amortized time for sample size  170 is:  0.0002623384840348187
preprocessing time for sampling: 0.2312641143798828
amortized time for sample size  175 is:  0.0002609574590410505
preprocessing time for sampling: 0.23066115379333496
amortized time for sample size  180 is:  0.0002624389727910359
preprocessing time for sampling: 0.23407411575317383
amortized time for sample size  185 is:  0.00026097988437961896
preprocessing time for sampling: 0.23932099342346191
amortized time for sample size  190 is:  0.00026273131370544437
preprocessing time for sampling: 0.23433971405029297
amortized time for sample size  195 is:  0.0002623026065337352
preprocessing time for sampling: 0.23351812362670898
amortized time for sample size  200 is:  0.0002610358715057373
preprocessing time for sampling: 0.23166108131408691
amortized time for sample size  205 is:  0.00026170151408125714
preprocessing time for sampling: 0.23198723793029785
amortized time for sample size  210 is:  0.0002628166789100284
preprocessing time for sampling: 0.2338118553161621
amortized time for sample size  215 is:  0.0002619155063185581
preprocessing time for sampling: 0.2345118522644043
amortized time for sample size  220 is:  0.0002626356753436002
preprocessing time for sampling: 0.23532962799072266
amortized time for sample size  225 is:  0.00026305676566229925
preprocessing time for sampling: 0.23480892181396484
amortized time for sample size  230 is:  0.00026345287198605743
preprocessing time for sampling: 0.23078703880310059
amortized time for sample size  235 is:  0.00026214249590609937
preprocessing time for sampling: 0.23332500457763672
amortized time for sample size  240 is:  0.00026347331206003825
preprocessing time for sampling: 0.23439693450927734
amortized time for sample size  245 is:  0.000263908678171586
preprocessing time for sampling: 0.2353370189666748
amortized time for sample size  250 is:  0.0002627705001831055
*** results for plotting, beta= 0.4 

mean_list= [np.float64(0.5200000000000001), np.float64(0.72), np.float64(0.79), np.float64(0.8500000000000002), np.float64(0.8200000000000001), np.float64(0.7899999999999999), np.float64(0.8600000000000001), np.float64(0.8699999999999999), np.float64(0.8799999999999999), np.float64(0.89), np.float64(0.8600000000000001), np.float64(0.86), np.float64(0.9000000000000001), np.float64(0.89), np.float64(0.9000000000000001), np.float64(0.93), np.float64(0.93), np.float64(0.9), np.float64(0.96), np.float64(0.9400000000000001), np.float64(0.9200000000000002), np.float64(0.9700000000000001), np.float64(0.9400000000000001), np.float64(0.95), np.float64(0.96), np.float64(0.96), np.float64(0.93), np.float64(0.9099999999999999), np.float64(0.9800000000000001), np.float64(0.9800000000000001), np.float64(0.93), np.float64(0.9700000000000001), np.float64(0.9400000000000001), np.float64(0.95), np.float64(1.0), np.float64(0.97), np.float64(0.9800000000000001), np.float64(0.9700000000000001), np.float64(1.0), np.float64(0.97), np.float64(1.0), np.float64(0.95), np.float64(0.99), np.float64(0.9800000000000001), np.float64(0.9800000000000001), np.float64(0.9800000000000001), np.float64(0.96), np.float64(0.99), np.float64(0.99), np.float64(0.95)]
std_list= [np.float64(0.23579652245103191), np.float64(0.11661903789690603), np.float64(0.12206555615733704), np.float64(0.10246950765959599), np.float64(0.07483314773547885), np.float64(0.10440306508910553), np.float64(0.04898979485566355), np.float64(0.14866068747318506), np.float64(0.08717797887081348), np.float64(0.10440306508910552), np.float64(0.10198039027185568), np.float64(0.11135528725660047), np.float64(0.07745966692414831), np.float64(0.11357816691600549), np.float64(0.07745966692414831), np.float64(0.06403124237432847), np.float64(0.06403124237432847), np.float64(0.11832159566199232), np.float64(0.09165151389911681), np.float64(0.06633249580710798), np.float64(0.09797958971132713), np.float64(0.04582575694955839), np.float64(0.07999999999999997), np.float64(0.04999999999999999), np.float64(0.04898979485566355), np.float64(0.04898979485566355), np.float64(0.1004987562112089), np.float64(0.08306623862918072), np.float64(0.039999999999999994), np.float64(0.039999999999999994), np.float64(0.07810249675906653), np.float64(0.04582575694955839), np.float64(0.06633249580710798), np.float64(0.06708203932499368), np.float64(0.0), np.float64(0.045825756949558386), np.float64(0.039999999999999994), np.float64(0.04582575694955839), np.float64(0.0), np.float64(0.04582575694955839), np.float64(0.0), np.float64(0.04999999999999999), np.float64(0.029999999999999992), np.float64(0.039999999999999994), np.float64(0.039999999999999994), np.float64(0.039999999999999994), np.float64(0.04898979485566355), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.049999999999999996)]
beta: 0.6
preprocessing time for sampling: 0.23959612846374512
amortized time for sample size  5 is:  0.0002639594078063965
preprocessing time for sampling: 0.23507213592529297
amortized time for sample size  10 is:  0.000263556718826294
preprocessing time for sampling: 0.23310327529907227
amortized time for sample size  15 is:  0.0002629569371541341
preprocessing time for sampling: 0.2332611083984375
amortized time for sample size  20 is:  0.0002625153064727783
preprocessing time for sampling: 0.235260009765625
amortized time for sample size  25 is:  0.0002623398780822754
preprocessing time for sampling: 0.23505210876464844
amortized time for sample size  30 is:  0.0002798934777577718
preprocessing time for sampling: 0.23509907722473145
amortized time for sample size  35 is:  0.0002656655992780413
preprocessing time for sampling: 0.23517203330993652
amortized time for sample size  40 is:  0.00026511770486831664
preprocessing time for sampling: 0.23356199264526367
amortized time for sample size  45 is:  0.0002631836467319065
preprocessing time for sampling: 0.2336108684539795
amortized time for sample size  50 is:  0.00026418194770812985
preprocessing time for sampling: 0.2359778881072998
amortized time for sample size  55 is:  0.00026349098032171076
preprocessing time for sampling: 0.23372507095336914
amortized time for sample size  60 is:  0.00026393115520477293
preprocessing time for sampling: 0.23556804656982422
amortized time for sample size  65 is:  0.0002625760298508864
preprocessing time for sampling: 0.23322319984436035
amortized time for sample size  70 is:  0.0002628772599356515
preprocessing time for sampling: 0.2348480224609375
amortized time for sample size  75 is:  0.00026327053705851237
preprocessing time for sampling: 0.23595809936523438
amortized time for sample size  80 is:  0.00026349633932113646
preprocessing time for sampling: 0.23302316665649414
amortized time for sample size  85 is:  0.00026373038572423597
preprocessing time for sampling: 0.2314767837524414
amortized time for sample size  90 is:  0.0002644008265601264
preprocessing time for sampling: 0.23639893531799316
amortized time for sample size  95 is:  0.0002636873596592953
preprocessing time for sampling: 0.23482966423034668
amortized time for sample size  100 is:  0.0002654107570648193
preprocessing time for sampling: 0.23389601707458496
amortized time for sample size  105 is:  0.000265792483375186
preprocessing time for sampling: 0.23337316513061523
amortized time for sample size  110 is:  0.00026338200135664504
preprocessing time for sampling: 0.23146390914916992
amortized time for sample size  115 is:  0.00026310976691867996
preprocessing time for sampling: 0.23098015785217285
amortized time for sample size  120 is:  0.00026328653097152705
preprocessing time for sampling: 0.2347719669342041
amortized time for sample size  125 is:  0.0002632467842102051
preprocessing time for sampling: 0.23454499244689941
amortized time for sample size  130 is:  0.00026202566807086657
preprocessing time for sampling: 0.23450613021850586
amortized time for sample size  135 is:  0.0002665193345811632
preprocessing time for sampling: 0.2337489128112793
amortized time for sample size  140 is:  0.0002626501662390573
preprocessing time for sampling: 0.2319929599761963
amortized time for sample size  145 is:  0.00026237523966822127
preprocessing time for sampling: 0.23178505897521973
amortized time for sample size  150 is:  0.00026160980860392253
preprocessing time for sampling: 0.23856806755065918
amortized time for sample size  155 is:  0.0002630154548152801
preprocessing time for sampling: 0.23368501663208008
amortized time for sample size  160 is:  0.00026349401473999023
preprocessing time for sampling: 0.23534893989562988
amortized time for sample size  165 is:  0.0002624701875628847
preprocessing time for sampling: 0.23800182342529297
amortized time for sample size  170 is:  0.0002634913079878863
preprocessing time for sampling: 0.2321453094482422
amortized time for sample size  175 is:  0.00026283508028302865
preprocessing time for sampling: 0.2327110767364502
amortized time for sample size  180 is:  0.00026271523369683164
preprocessing time for sampling: 0.2361159324645996
amortized time for sample size  185 is:  0.00026194269592697553
preprocessing time for sampling: 0.23478198051452637
amortized time for sample size  190 is:  0.00026273229247645327
preprocessing time for sampling: 0.23713898658752441
amortized time for sample size  195 is:  0.0002630661573165502
preprocessing time for sampling: 0.2354581356048584
amortized time for sample size  200 is:  0.00026335635185241696
preprocessing time for sampling: 0.23317790031433105
amortized time for sample size  205 is:  0.00026381877573525037
preprocessing time for sampling: 0.23323488235473633
amortized time for sample size  210 is:  0.00026347981180463524
preprocessing time for sampling: 0.23627901077270508
amortized time for sample size  215 is:  0.0002630537166151889
preprocessing time for sampling: 0.23548126220703125
amortized time for sample size  220 is:  0.00026440057971260765
preprocessing time for sampling: 0.23395085334777832
amortized time for sample size  225 is:  0.0002658639907836914
preprocessing time for sampling: 0.23325610160827637
amortized time for sample size  230 is:  0.0002633106915847114
preprocessing time for sampling: 0.23406314849853516
amortized time for sample size  235 is:  0.0002633354308757376
preprocessing time for sampling: 0.232496976852417
amortized time for sample size  240 is:  0.0002629418969154358
preprocessing time for sampling: 0.2353811264038086
amortized time for sample size  245 is:  0.00026328061551463846
preprocessing time for sampling: 0.23646330833435059
amortized time for sample size  250 is:  0.00026347043991088866
*** results for plotting, beta= 0.6 

mean_list= [np.float64(0.74), np.float64(0.85), np.float64(0.85), np.float64(0.8700000000000001), np.float64(0.9099999999999999), np.float64(0.97), np.float64(0.93), np.float64(0.95), np.float64(0.97), np.float64(0.9400000000000001), np.float64(0.9800000000000001), np.float64(0.9700000000000001), np.float64(0.9800000000000001), np.float64(0.9700000000000001), np.float64(1.0), np.float64(1.0), np.float64(0.97), np.float64(1.0), np.float64(0.99), np.float64(0.99), np.float64(0.99), np.float64(0.99), np.float64(1.0), np.float64(1.0), np.float64(0.9800000000000001), 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)]
std_list= [np.float64(0.16852299546352717), np.float64(0.15), np.float64(0.1284523257866513), np.float64(0.07810249675906655), np.float64(0.06999999999999999), np.float64(0.06403124237432847), np.float64(0.07810249675906653), np.float64(0.06708203932499368), np.float64(0.045825756949558386), np.float64(0.04898979485566356), np.float64(0.039999999999999994), np.float64(0.06403124237432847), np.float64(0.039999999999999994), np.float64(0.04582575694955839), np.float64(0.0), np.float64(0.0), np.float64(0.06403124237432847), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.0), np.float64(0.039999999999999994), 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)]
beta: 0.8
preprocessing time for sampling: 0.2358100414276123
amortized time for sample size  5 is:  0.00026223087310791015
preprocessing time for sampling: 0.23225712776184082
amortized time for sample size  10 is:  0.0002628705501556397
preprocessing time for sampling: 0.23305416107177734
amortized time for sample size  15 is:  0.00026196114222208655
preprocessing time for sampling: 0.23299098014831543
amortized time for sample size  20 is:  0.0002621278762817383
preprocessing time for sampling: 0.2340259552001953
amortized time for sample size  25 is:  0.0002661970138549805
preprocessing time for sampling: 0.23963499069213867
amortized time for sample size  30 is:  0.0002628926436106364
preprocessing time for sampling: 0.2351682186126709
amortized time for sample size  35 is:  0.000262223516191755
preprocessing time for sampling: 0.2372570037841797
amortized time for sample size  40 is:  0.00026235437393188477
preprocessing time for sampling: 0.23311090469360352
amortized time for sample size  45 is:  0.00026250473658243816
preprocessing time for sampling: 0.23200106620788574
amortized time for sample size  50 is:  0.0002658018112182617
preprocessing time for sampling: 0.23598408699035645
amortized time for sample size  55 is:  0.0002605106613852761
preprocessing time for sampling: 0.23548507690429688
amortized time for sample size  60 is:  0.00026344295342763265
preprocessing time for sampling: 0.23952102661132812
amortized time for sample size  65 is:  0.00026359172967764044
preprocessing time for sampling: 0.23773407936096191
amortized time for sample size  70 is:  0.0002637792655399867
preprocessing time for sampling: 0.2386789321899414
amortized time for sample size  75 is:  0.00027109988530476885
preprocessing time for sampling: 0.2347419261932373
amortized time for sample size  80 is:  0.0002653946280479431
preprocessing time for sampling: 0.23569583892822266
amortized time for sample size  85 is:  0.0002617662093218635
preprocessing time for sampling: 0.2333528995513916
amortized time for sample size  90 is:  0.0002622127268049452
preprocessing time for sampling: 0.23238706588745117
amortized time for sample size  95 is:  0.0002627416911878084
preprocessing time for sampling: 0.2306969165802002
amortized time for sample size  100 is:  0.00026290152072906497
preprocessing time for sampling: 0.23608016967773438
amortized time for sample size  105 is:  0.0002634072076706659
preprocessing time for sampling: 0.23526406288146973
amortized time for sample size  110 is:  0.0002626717524095016
preprocessing time for sampling: 0.23580598831176758
amortized time for sample size  115 is:  0.00026218151009601095
preprocessing time for sampling: 0.23314785957336426
amortized time for sample size  120 is:  0.00026132633288701373
preprocessing time for sampling: 0.23317193984985352
amortized time for sample size  125 is:  0.0002639534568786621
preprocessing time for sampling: 0.23491382598876953
amortized time for sample size  130 is:  0.0002628870377173791
preprocessing time for sampling: 0.2354140281677246
amortized time for sample size  135 is:  0.00026206671750103985
preprocessing time for sampling: 0.2347099781036377
amortized time for sample size  140 is:  0.00026411429473331997
preprocessing time for sampling: 0.2360248565673828
amortized time for sample size  145 is:  0.0002624442330722151
preprocessing time for sampling: 0.23294305801391602
amortized time for sample size  150 is:  0.0002622867266337077
preprocessing time for sampling: 0.23169302940368652
amortized time for sample size  155 is:  0.0002628911848991148
preprocessing time for sampling: 0.23069119453430176
amortized time for sample size  160 is:  0.00026329669356346127
preprocessing time for sampling: 0.23395204544067383
amortized time for sample size  165 is:  0.0002637292110558712
preprocessing time for sampling: 0.2359619140625
amortized time for sample size  170 is:  0.00026457183501299686
preprocessing time for sampling: 0.23894906044006348
amortized time for sample size  175 is:  0.00026258542197091244
preprocessing time for sampling: 0.23341798782348633
amortized time for sample size  180 is:  0.00026625921991136334
preprocessing time for sampling: 0.232741117477417
amortized time for sample size  185 is:  0.00026310247988314237
preprocessing time for sampling: 0.23379921913146973
amortized time for sample size  190 is:  0.00026343044481779397
preprocessing time for sampling: 0.23568105697631836
amortized time for sample size  195 is:  0.0002625672633831318
preprocessing time for sampling: 0.24001479148864746
amortized time for sample size  200 is:  0.0002641374707221985
preprocessing time for sampling: 0.23657798767089844
amortized time for sample size  205 is:  0.00026340883534129074
preprocessing time for sampling: 0.2367410659790039
amortized time for sample size  210 is:  0.00026362986791701547
preprocessing time for sampling: 0.2312178611755371
amortized time for sample size  215 is:  0.00026443857370420944
preprocessing time for sampling: 0.23221111297607422
amortized time for sample size  220 is:  0.00026351249217987057
preprocessing time for sampling: 0.2350001335144043
amortized time for sample size  225 is:  0.0002638046052720812
preprocessing time for sampling: 0.23395609855651855
amortized time for sample size  230 is:  0.0002625146119490914
preprocessing time for sampling: 0.2354729175567627
amortized time for sample size  235 is:  0.000263300155071502
preprocessing time for sampling: 0.23474717140197754
amortized time for sample size  240 is:  0.00026295953989028927
preprocessing time for sampling: 0.2332618236541748
amortized time for sample size  245 is:  0.00026279614896190405
preprocessing time for sampling: 0.23240017890930176
amortized time for sample size  250 is:  0.0002636568927764892
*** results for plotting, beta= 0.8 

mean_list= [np.float64(0.8400000000000001), np.float64(0.9099999999999999), np.float64(0.9400000000000001), np.float64(0.99), np.float64(0.96), np.float64(1.0), np.float64(0.99), np.float64(0.97), 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(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)]
std_list= [np.float64(0.13564659966250536), np.float64(0.09433981132056604), np.float64(0.06633249580710798), np.float64(0.029999999999999992), np.float64(0.04898979485566355), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.06403124237432847), 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(0.029999999999999992), 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)]
beta: 1
preprocessing time for sampling: 0.26889586448669434
amortized time for sample size  5 is:  0.00027412700653076176
preprocessing time for sampling: 0.2706260681152344
amortized time for sample size  10 is:  0.000273897647857666
preprocessing time for sampling: 0.26945996284484863
amortized time for sample size  15 is:  0.00027364857991536457
preprocessing time for sampling: 0.2682650089263916
amortized time for sample size  20 is:  0.0002790619134902954
preprocessing time for sampling: 0.26867008209228516
amortized time for sample size  25 is:  0.0002731124877929688
preprocessing time for sampling: 0.2676839828491211
amortized time for sample size  30 is:  0.00027308313051859536
preprocessing time for sampling: 0.2697310447692871
amortized time for sample size  35 is:  0.0002764265877859933
preprocessing time for sampling: 0.2717769145965576
amortized time for sample size  40 is:  0.0002741168737411499
preprocessing time for sampling: 0.26692628860473633
amortized time for sample size  45 is:  0.0002714769575330946
preprocessing time for sampling: 0.2652761936187744
amortized time for sample size  50 is:  0.0002722611904144287
preprocessing time for sampling: 0.2670929431915283
amortized time for sample size  55 is:  0.0002756767706437544
preprocessing time for sampling: 0.26751184463500977
amortized time for sample size  60 is:  0.0002736948728561401
preprocessing time for sampling: 0.2687549591064453
amortized time for sample size  65 is:  0.0002738604912391076
preprocessing time for sampling: 0.2680978775024414
amortized time for sample size  70 is:  0.0002734955719539097
preprocessing time for sampling: 0.2727351188659668
amortized time for sample size  75 is:  0.00027331549326578775
preprocessing time for sampling: 0.2669188976287842
amortized time for sample size  80 is:  0.00027353379130363466
preprocessing time for sampling: 0.2668468952178955
amortized time for sample size  85 is:  0.00027365959391874425
preprocessing time for sampling: 0.26662611961364746
amortized time for sample size  90 is:  0.0002728212674458822
preprocessing time for sampling: 0.26848506927490234
amortized time for sample size  95 is:  0.0002735478501570852
preprocessing time for sampling: 0.2665531635284424
amortized time for sample size  100 is:  0.000273325514793396
preprocessing time for sampling: 0.26862597465515137
amortized time for sample size  105 is:  0.0002769837379455566
preprocessing time for sampling: 0.26523900032043457
amortized time for sample size  110 is:  0.0002719721360640092
preprocessing time for sampling: 0.2650299072265625
amortized time for sample size  115 is:  0.00027391578840172813
preprocessing time for sampling: 0.26515698432922363
amortized time for sample size  120 is:  0.0002732852697372436
preprocessing time for sampling: 0.26929736137390137
amortized time for sample size  125 is:  0.00027223880767822265
preprocessing time for sampling: 0.26601123809814453
amortized time for sample size  130 is:  0.0002722236559941219
preprocessing time for sampling: 0.2659578323364258
amortized time for sample size  135 is:  0.00027317345583880386
preprocessing time for sampling: 0.26581716537475586
amortized time for sample size  140 is:  0.0002737034218651908
preprocessing time for sampling: 0.26680517196655273
amortized time for sample size  145 is:  0.00027400025005998275
preprocessing time for sampling: 0.26705098152160645
amortized time for sample size  150 is:  0.00027669488588968915
preprocessing time for sampling: 0.27253127098083496
amortized time for sample size  155 is:  0.00027440140324254186
preprocessing time for sampling: 0.26743102073669434
amortized time for sample size  160 is:  0.0002766165733337403
preprocessing time for sampling: 0.2662012577056885
amortized time for sample size  165 is:  0.00027208076823841446
preprocessing time for sampling: 0.26523804664611816
amortized time for sample size  170 is:  0.0002721457200891831
preprocessing time for sampling: 0.26530003547668457
amortized time for sample size  175 is:  0.00027187347412109373
preprocessing time for sampling: 0.26462697982788086
amortized time for sample size  180 is:  0.00027223408222198486
preprocessing time for sampling: 0.2655668258666992
amortized time for sample size  185 is:  0.0002775411992459684
preprocessing time for sampling: 0.2806820869445801
amortized time for sample size  190 is:  0.00027649541905051784
preprocessing time for sampling: 0.2821509838104248
amortized time for sample size  195 is:  0.0002776857400551821
preprocessing time for sampling: 0.2669651508331299
amortized time for sample size  200 is:  0.0002717992186546325
preprocessing time for sampling: 0.26468610763549805
amortized time for sample size  205 is:  0.0002730079743920303
preprocessing time for sampling: 0.26462411880493164
amortized time for sample size  210 is:  0.00027214816638401583
preprocessing time for sampling: 0.26575493812561035
amortized time for sample size  215 is:  0.00027223847633184393
preprocessing time for sampling: 0.26602697372436523
amortized time for sample size  220 is:  0.0002719910795038397
preprocessing time for sampling: 0.26593494415283203
amortized time for sample size  225 is:  0.000272752030690511
preprocessing time for sampling: 0.2648429870605469
amortized time for sample size  230 is:  0.00027510295743527613
preprocessing time for sampling: 0.26671886444091797
amortized time for sample size  235 is:  0.00027753284129690615
preprocessing time for sampling: 0.2730867862701416
amortized time for sample size  240 is:  0.0002782536049683888
preprocessing time for sampling: 0.2656698226928711
amortized time for sample size  245 is:  0.00027452801684944
preprocessing time for sampling: 0.26969099044799805
amortized time for sample size  250 is:  0.00027382688522338864
*** results for plotting, beta= 1 

mean_list= [np.float64(0.8899999999999999), np.float64(0.9800000000000001), np.float64(0.99), np.float64(1.0), np.float64(0.99), 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), np.float64(1.0)]
std_list= [np.float64(0.06999999999999999), np.float64(0.039999999999999994), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.029999999999999992), 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), np.float64(0.0)]
beta: 1.2
preprocessing time for sampling: 0.23665904998779297
amortized time for sample size  5 is:  0.0002615666389465332
preprocessing time for sampling: 0.23228073120117188
amortized time for sample size  10 is:  0.0002615296840667725
preprocessing time for sampling: 0.23242497444152832
amortized time for sample size  15 is:  0.00026137828826904296
preprocessing time for sampling: 0.23406314849853516
amortized time for sample size  20 is:  0.00026116895675659175
preprocessing time for sampling: 0.23432493209838867
amortized time for sample size  25 is:  0.00026069250106811525
preprocessing time for sampling: 0.23174214363098145
amortized time for sample size  30 is:  0.0002609138488769531
preprocessing time for sampling: 0.23381304740905762
amortized time for sample size  35 is:  0.0002611051286969866
preprocessing time for sampling: 0.2410888671875
amortized time for sample size  40 is:  0.00027716857194900514
preprocessing time for sampling: 0.2302258014678955
amortized time for sample size  45 is:  0.0002602861192491319
preprocessing time for sampling: 0.2336430549621582
amortized time for sample size  50 is:  0.00026049199104309086
preprocessing time for sampling: 0.23443007469177246
amortized time for sample size  55 is:  0.0002615458315069025
preprocessing time for sampling: 0.23044514656066895
amortized time for sample size  60 is:  0.0002615333795547485
preprocessing time for sampling: 0.2338418960571289
amortized time for sample size  65 is:  0.00026326498618492716
preprocessing time for sampling: 0.23139214515686035
amortized time for sample size  70 is:  0.00026190073149544855
preprocessing time for sampling: 0.2352609634399414
amortized time for sample size  75 is:  0.00027009477615356445
preprocessing time for sampling: 0.2335188388824463
amortized time for sample size  80 is:  0.00026471948623657223
preprocessing time for sampling: 0.23140501976013184
amortized time for sample size  85 is:  0.0002627078785615809
preprocessing time for sampling: 0.23409605026245117
amortized time for sample size  90 is:  0.00027238925298055013
preprocessing time for sampling: 0.23447299003601074
amortized time for sample size  95 is:  0.00026153777775011567
preprocessing time for sampling: 0.23074007034301758
amortized time for sample size  100 is:  0.0002618295669555664
preprocessing time for sampling: 0.23342418670654297
amortized time for sample size  105 is:  0.00026348372868129186
preprocessing time for sampling: 0.23304295539855957
amortized time for sample size  110 is:  0.00026615331389687283
preprocessing time for sampling: 0.23154401779174805
amortized time for sample size  115 is:  0.0002689931496329929
preprocessing time for sampling: 0.23740005493164062
amortized time for sample size  120 is:  0.00026740374167760213
preprocessing time for sampling: 0.25213170051574707
amortized time for sample size  125 is:  0.00026533365249633786
preprocessing time for sampling: 0.2318110466003418
amortized time for sample size  130 is:  0.000262110159947322
preprocessing time for sampling: 0.2332019805908203
amortized time for sample size  135 is:  0.0002611685858832466
preprocessing time for sampling: 0.23254609107971191
amortized time for sample size  140 is:  0.0002606710025242397
preprocessing time for sampling: 0.23064899444580078
amortized time for sample size  145 is:  0.0002607877172272781
preprocessing time for sampling: 0.23894095420837402
amortized time for sample size  150 is:  0.00026165316899617516
preprocessing time for sampling: 0.23288893699645996
amortized time for sample size  155 is:  0.00026141837335401965
preprocessing time for sampling: 0.2323160171508789
amortized time for sample size  160 is:  0.0002619128674268723
preprocessing time for sampling: 0.23261094093322754
amortized time for sample size  165 is:  0.0002629901134606563
preprocessing time for sampling: 0.23379802703857422
amortized time for sample size  170 is:  0.00026164827627294204
preprocessing time for sampling: 0.23160099983215332
amortized time for sample size  175 is:  0.00026312701361519945
preprocessing time for sampling: 0.2362062931060791
amortized time for sample size  180 is:  0.00026302370760175923
preprocessing time for sampling: 0.23378777503967285
amortized time for sample size  185 is:  0.00026261061591071054
preprocessing time for sampling: 0.23107099533081055
amortized time for sample size  190 is:  0.0002638505258058247
preprocessing time for sampling: 0.23455500602722168
amortized time for sample size  195 is:  0.000265574051783635
preprocessing time for sampling: 0.2330460548400879
amortized time for sample size  200 is:  0.0002604336857795715
preprocessing time for sampling: 0.23107671737670898
amortized time for sample size  205 is:  0.000261870372586134
preprocessing time for sampling: 0.23123908042907715
amortized time for sample size  210 is:  0.000264601400920323
preprocessing time for sampling: 0.23024368286132812
amortized time for sample size  215 is:  0.00026291412530943405
preprocessing time for sampling: 0.2303009033203125
amortized time for sample size  220 is:  0.0002616207708011974
preprocessing time for sampling: 0.23933005332946777
amortized time for sample size  225 is:  0.00026288602617051865
preprocessing time for sampling: 0.23482918739318848
amortized time for sample size  230 is:  0.00026047674469325855
preprocessing time for sampling: 0.2273108959197998
amortized time for sample size  235 is:  0.0002605484394316977
preprocessing time for sampling: 0.23257684707641602
amortized time for sample size  240 is:  0.00026097047328948976
preprocessing time for sampling: 0.23073196411132812
amortized time for sample size  245 is:  0.00026066980556565893
preprocessing time for sampling: 0.23070812225341797
amortized time for sample size  250 is:  0.0002612863540649414
*** results for plotting, beta= 1.2 

mean_list= [np.float64(0.9200000000000002), 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), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0)]
std_list= [np.float64(0.0748331477354788), 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), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0)]
