beta: 0.2
preprocessing time for sampling: 0.01269388198852539
amortized time for sample size  5 is:  0.00011878442764282226
preprocessing time for sampling: 0.012611150741577148
amortized time for sample size  10 is:  0.0001193344593048096
preprocessing time for sampling: 0.012795209884643555
amortized time for sample size  15 is:  0.00011821428934733073
preprocessing time for sampling: 0.012664079666137695
amortized time for sample size  20 is:  0.00011853647232055663
preprocessing time for sampling: 0.01248311996459961
amortized time for sample size  25 is:  0.00011873264312744141
preprocessing time for sampling: 0.012481927871704102
amortized time for sample size  30 is:  0.00011848529179890947
preprocessing time for sampling: 0.012455940246582031
amortized time for sample size  35 is:  0.00011841528756277902
preprocessing time for sampling: 0.012480020523071289
amortized time for sample size  40 is:  0.00011816567182540893
preprocessing time for sampling: 0.012452840805053711
amortized time for sample size  45 is:  0.00011929379569159616
preprocessing time for sampling: 0.012479066848754883
amortized time for sample size  50 is:  0.00011892862319946287
preprocessing time for sampling: 0.012911796569824219
amortized time for sample size  55 is:  0.00011848020553588869
preprocessing time for sampling: 0.013131856918334961
amortized time for sample size  60 is:  0.00011924974123636882
preprocessing time for sampling: 0.012816905975341797
amortized time for sample size  65 is:  0.00012068513723520133
preprocessing time for sampling: 0.012773752212524414
amortized time for sample size  70 is:  0.00012209439277648926
preprocessing time for sampling: 0.012558937072753906
amortized time for sample size  75 is:  0.00011989161173502603
preprocessing time for sampling: 0.012688159942626953
amortized time for sample size  80 is:  0.00012085190415382386
preprocessing time for sampling: 0.012497186660766602
amortized time for sample size  85 is:  0.00012010692147647632
preprocessing time for sampling: 0.01248788833618164
amortized time for sample size  90 is:  0.00011926651000976561
preprocessing time for sampling: 0.012467145919799805
amortized time for sample size  95 is:  0.00011821254930998148
preprocessing time for sampling: 0.012485027313232422
amortized time for sample size  100 is:  0.00011883676052093506
preprocessing time for sampling: 0.012480020523071289
amortized time for sample size  105 is:  0.00011893980843680247
preprocessing time for sampling: 0.012490034103393555
amortized time for sample size  110 is:  0.00011893799088217994
preprocessing time for sampling: 0.012511014938354492
amortized time for sample size  115 is:  0.00011853562230649203
preprocessing time for sampling: 0.012494087219238281
amortized time for sample size  120 is:  0.00011936734120051067
preprocessing time for sampling: 0.012579202651977539
amortized time for sample size  125 is:  0.000120980224609375
preprocessing time for sampling: 0.01278996467590332
amortized time for sample size  130 is:  0.00012006042553828313
preprocessing time for sampling: 0.012497901916503906
amortized time for sample size  135 is:  0.00011974684397379556
preprocessing time for sampling: 0.012512922286987305
amortized time for sample size  140 is:  0.00011930062089647566
preprocessing time for sampling: 0.012609004974365234
amortized time for sample size  145 is:  0.00011931442392283473
preprocessing time for sampling: 0.012480020523071289
amortized time for sample size  150 is:  0.00011975943247477216
preprocessing time for sampling: 0.012553930282592773
amortized time for sample size  155 is:  0.0001190249535345262
preprocessing time for sampling: 0.01256704330444336
amortized time for sample size  160 is:  0.00011920480430126188
preprocessing time for sampling: 0.01288914680480957
amortized time for sample size  165 is:  0.00011876221859093868
preprocessing time for sampling: 0.012488126754760742
amortized time for sample size  170 is:  0.00011958841716541965
preprocessing time for sampling: 0.012506961822509766
amortized time for sample size  175 is:  0.00012006673812866211
preprocessing time for sampling: 0.012877941131591797
amortized time for sample size  180 is:  0.00012053808901045056
preprocessing time for sampling: 0.01251983642578125
amortized time for sample size  185 is:  0.0001191511025299897
preprocessing time for sampling: 0.012478113174438477
amortized time for sample size  190 is:  0.00011902929607190582
preprocessing time for sampling: 0.012497901916503906
amortized time for sample size  195 is:  0.00011885325113932293
preprocessing time for sampling: 0.012482166290283203
amortized time for sample size  200 is:  0.00011855313777923586
preprocessing time for sampling: 0.01250004768371582
amortized time for sample size  205 is:  0.00011885432499211008
preprocessing time for sampling: 0.012484073638916016
amortized time for sample size  210 is:  0.00011850399062747046
preprocessing time for sampling: 0.012530803680419922
amortized time for sample size  215 is:  0.00011898052969644235
preprocessing time for sampling: 0.012501955032348633
amortized time for sample size  220 is:  0.00011885475028644908
preprocessing time for sampling: 0.012552022933959961
amortized time for sample size  225 is:  0.00011876405080159503
preprocessing time for sampling: 0.012499809265136719
amortized time for sample size  230 is:  0.00011891620055488918
preprocessing time for sampling: 0.012485027313232422
amortized time for sample size  235 is:  0.0001197068843435734
preprocessing time for sampling: 0.012495994567871094
amortized time for sample size  240 is:  0.00011851351459821066
preprocessing time for sampling: 0.012485980987548828
amortized time for sample size  245 is:  0.00011860815359621631
preprocessing time for sampling: 0.012511968612670898
amortized time for sample size  250 is:  0.00011853664398193361
*** results for plotting, beta= 0.2 

mean_list= [np.float64(0.33), np.float64(0.45999999999999996), np.float64(0.38999999999999996), np.float64(0.4800000000000001), np.float64(0.61), np.float64(0.5), np.float64(0.5399999999999999), np.float64(0.59), np.float64(0.48), np.float64(0.55), np.float64(0.63), np.float64(0.44000000000000006), np.float64(0.6), np.float64(0.6399999999999999), np.float64(0.48), np.float64(0.5900000000000001), np.float64(0.48999999999999994), np.float64(0.63), np.float64(0.69), np.float64(0.53), np.float64(0.51), np.float64(0.68), np.float64(0.59), np.float64(0.72), np.float64(0.66), np.float64(0.6799999999999999), np.float64(0.6500000000000001), np.float64(0.58), np.float64(0.6699999999999999), np.float64(0.65), np.float64(0.67), np.float64(0.6199999999999999), np.float64(0.61), np.float64(0.53), np.float64(0.7), np.float64(0.7), np.float64(0.7500000000000001), np.float64(0.65), np.float64(0.6700000000000002), np.float64(0.7000000000000001), np.float64(0.6599999999999999), np.float64(0.6500000000000001), np.float64(0.7), np.float64(0.63), np.float64(0.67), np.float64(0.7), np.float64(0.6599999999999999), np.float64(0.7), np.float64(0.6699999999999999), np.float64(0.64)]
std_list= [np.float64(0.14866068747318506), np.float64(0.13564659966250536), np.float64(0.08306623862918075), np.float64(0.14696938456699066), np.float64(0.11357816691600545), np.float64(0.15491933384829665), np.float64(0.09165151389911677), np.float64(0.11357816691600546), np.float64(0.1777638883463118), np.float64(0.12845232578665128), np.float64(0.14866068747318506), np.float64(0.10198039027185568), np.float64(0.11832159566199231), np.float64(0.15620499351813308), np.float64(0.11661903789690602), np.float64(0.157797338380595), np.float64(0.20223748416156687), np.float64(0.1268857754044952), np.float64(0.17), np.float64(0.20518284528683195), np.float64(0.16401219466856726), np.float64(0.13999999999999999), np.float64(0.06999999999999999), np.float64(0.11661903789690603), np.float64(0.17435595774162693), np.float64(0.14), np.float64(0.1284523257866513), np.float64(0.15362291495737218), np.float64(0.11000000000000001), np.float64(0.0806225774829855), np.float64(0.14866068747318506), np.float64(0.08717797887081348), np.float64(0.1374772708486752), np.float64(0.1345362404707371), np.float64(0.1341640786499874), np.float64(0.18973665961010278), np.float64(0.12041594578792296), np.float64(0.11180339887498948), np.float64(0.21470910553583888), np.float64(0.17320508075688773), np.float64(0.14282856857085702), np.float64(0.15652475842498528), np.float64(0.1414213562373095), np.float64(0.19519221295943134), np.float64(0.11000000000000001), np.float64(0.10000000000000002), np.float64(0.128062484748657), np.float64(0.14142135623730953), np.float64(0.11), np.float64(0.18)]
beta: 0.4
preprocessing time for sampling: 0.012536048889160156
amortized time for sample size  5 is:  0.00011911439895629882
preprocessing time for sampling: 0.012515068054199219
amortized time for sample size  10 is:  0.00011838841438293456
preprocessing time for sampling: 0.012668848037719727
amortized time for sample size  15 is:  0.00011844714482625323
preprocessing time for sampling: 0.012554168701171875
amortized time for sample size  20 is:  0.00011876225471496582
preprocessing time for sampling: 0.012513160705566406
amortized time for sample size  25 is:  0.0001186293601989746
preprocessing time for sampling: 0.012531042098999023
amortized time for sample size  30 is:  0.00011844491958618165
preprocessing time for sampling: 0.012530326843261719
amortized time for sample size  35 is:  0.0001187654903956822
preprocessing time for sampling: 0.012514114379882812
amortized time for sample size  40 is:  0.00011832100152969362
preprocessing time for sampling: 0.012745857238769531
amortized time for sample size  45 is:  0.00011846081415812175
preprocessing time for sampling: 0.012518882751464844
amortized time for sample size  50 is:  0.00011860475540161132
preprocessing time for sampling: 0.012526750564575195
amortized time for sample size  55 is:  0.00011809405413540926
preprocessing time for sampling: 0.012644052505493164
amortized time for sample size  60 is:  0.00011828974882761639
preprocessing time for sampling: 0.012573957443237305
amortized time for sample size  65 is:  0.0001185296498812162
preprocessing time for sampling: 0.012536048889160156
amortized time for sample size  70 is:  0.00011874805177961077
preprocessing time for sampling: 0.012515068054199219
amortized time for sample size  75 is:  0.0001185505231221517
preprocessing time for sampling: 0.012731075286865234
amortized time for sample size  80 is:  0.00011914068460464477
preprocessing time for sampling: 0.012501955032348633
amortized time for sample size  85 is:  0.00011907392389634078
preprocessing time for sampling: 0.012686967849731445
amortized time for sample size  90 is:  0.00011907177501254612
preprocessing time for sampling: 0.012554168701171875
amortized time for sample size  95 is:  0.00011840925718608655
preprocessing time for sampling: 0.012505769729614258
amortized time for sample size  100 is:  0.00011891634464263916
preprocessing time for sampling: 0.012518882751464844
amortized time for sample size  105 is:  0.00011901260557628815
preprocessing time for sampling: 0.012502908706665039
amortized time for sample size  110 is:  0.00011850784041664819
preprocessing time for sampling: 0.012521028518676758
amortized time for sample size  115 is:  0.00011871240449988327
preprocessing time for sampling: 0.012511968612670898
amortized time for sample size  120 is:  0.00011903969446818032
preprocessing time for sampling: 0.012513160705566406
amortized time for sample size  125 is:  0.00011842731475830079
preprocessing time for sampling: 0.012696981430053711
amortized time for sample size  130 is:  0.00011922654738793007
preprocessing time for sampling: 0.012518167495727539
amortized time for sample size  135 is:  0.00011857244703504773
preprocessing time for sampling: 0.012523889541625977
amortized time for sample size  140 is:  0.00011913636752537319
preprocessing time for sampling: 0.012490987777709961
amortized time for sample size  145 is:  0.0001184554100036621
preprocessing time for sampling: 0.012552261352539062
amortized time for sample size  150 is:  0.00011896646817525227
preprocessing time for sampling: 0.012521982192993164
amortized time for sample size  155 is:  0.00011849889447612146
preprocessing time for sampling: 0.012520074844360352
amortized time for sample size  160 is:  0.00011874458193778992
preprocessing time for sampling: 0.012513875961303711
amortized time for sample size  165 is:  0.00011910906704989347
preprocessing time for sampling: 0.012511968612670898
amortized time for sample size  170 is:  0.00011899088410770191
preprocessing time for sampling: 0.012880325317382812
amortized time for sample size  175 is:  0.000119255188533238
preprocessing time for sampling: 0.012530088424682617
amortized time for sample size  180 is:  0.00014339709281921385
preprocessing time for sampling: 0.016572952270507812
amortized time for sample size  185 is:  0.00015743218241511165
preprocessing time for sampling: 0.01659083366394043
amortized time for sample size  190 is:  0.00015706368496543486
preprocessing time for sampling: 0.01657700538635254
amortized time for sample size  195 is:  0.0001570122547638722
preprocessing time for sampling: 0.016676902770996094
amortized time for sample size  200 is:  0.0001578404426574707
preprocessing time for sampling: 0.016521930694580078
amortized time for sample size  205 is:  0.00015639401645195194
preprocessing time for sampling: 0.016503095626831055
amortized time for sample size  210 is:  0.00015743838037763323
preprocessing time for sampling: 0.01653003692626953
amortized time for sample size  215 is:  0.00015799261802850766
preprocessing time for sampling: 0.017004013061523438
amortized time for sample size  220 is:  0.00015813015807758678
preprocessing time for sampling: 0.01649618148803711
amortized time for sample size  225 is:  0.0001563672383626302
preprocessing time for sampling: 0.01651597023010254
amortized time for sample size  230 is:  0.00015730375828950302
preprocessing time for sampling: 0.016530990600585938
amortized time for sample size  235 is:  0.00015692843782140855
preprocessing time for sampling: 0.01648998260498047
amortized time for sample size  240 is:  0.00015741904576619469
preprocessing time for sampling: 0.01676321029663086
amortized time for sample size  245 is:  0.00015853756301257077
preprocessing time for sampling: 0.016532182693481445
amortized time for sample size  250 is:  0.00015724207878112793
*** results for plotting, beta= 0.4 

mean_list= [np.float64(0.55), np.float64(0.6900000000000001), np.float64(0.64), np.float64(0.6699999999999999), np.float64(0.75), np.float64(0.73), np.float64(0.78), np.float64(0.89), np.float64(0.89), np.float64(0.8400000000000001), np.float64(0.9), np.float64(0.8700000000000001), np.float64(0.8700000000000001), np.float64(0.93), np.float64(0.8099999999999999), np.float64(0.9099999999999999), np.float64(0.8600000000000001), np.float64(0.8899999999999999), np.float64(0.9099999999999999), np.float64(0.9), np.float64(0.9000000000000001), np.float64(0.9600000000000002), np.float64(0.9), np.float64(0.93), np.float64(0.9200000000000002), np.float64(0.9099999999999999), np.float64(0.9099999999999999), np.float64(0.93), np.float64(0.93), np.float64(0.9800000000000001), np.float64(0.9100000000000001), np.float64(0.95), np.float64(0.96), np.float64(0.96), np.float64(0.9400000000000001), np.float64(0.95), np.float64(0.99), np.float64(0.93), np.float64(0.9800000000000001), np.float64(0.96), np.float64(0.9400000000000001), np.float64(0.9700000000000001), np.float64(0.9400000000000001), np.float64(0.9700000000000001), np.float64(0.9400000000000001), np.float64(0.95), np.float64(0.96), np.float64(0.97), np.float64(0.97), np.float64(1.0)]
std_list= [np.float64(0.1746424919657298), np.float64(0.1374772708486752), np.float64(0.128062484748657), np.float64(0.09000000000000001), np.float64(0.15000000000000002), np.float64(0.11000000000000003), np.float64(0.13266499161421602), np.float64(0.05385164807134503), np.float64(0.10440306508910552), np.float64(0.09165151389911681), np.float64(0.07745966692414831), np.float64(0.06403124237432847), np.float64(0.045825756949558386), np.float64(0.04582575694955839), np.float64(0.09433981132056607), np.float64(0.10440306508910549), np.float64(0.06633249580710798), np.float64(0.08306623862918074), np.float64(0.08306623862918072), np.float64(0.09999999999999999), np.float64(0.07745966692414831), np.float64(0.06633249580710798), np.float64(0.07745966692414831), np.float64(0.1004987562112089), np.float64(0.05999999999999999), np.float64(0.06999999999999998), np.float64(0.05385164807134503), np.float64(0.08999999999999997), np.float64(0.07810249675906653), np.float64(0.039999999999999994), np.float64(0.09433981132056601), np.float64(0.04999999999999999), np.float64(0.04898979485566355), np.float64(0.04898979485566355), np.float64(0.10198039027185571), np.float64(0.04999999999999999), np.float64(0.029999999999999992), np.float64(0.06403124237432847), np.float64(0.039999999999999994), np.float64(0.06633249580710798), np.float64(0.09165151389911681), np.float64(0.04582575694955839), np.float64(0.07999999999999999), np.float64(0.04582575694955839), np.float64(0.04898979485566355), np.float64(0.06708203932499368), np.float64(0.04898979485566356), np.float64(0.04582575694955839), np.float64(0.045825756949558386), np.float64(0.0)]
beta: 0.6
preprocessing time for sampling: 0.016575098037719727
amortized time for sample size  5 is:  0.000157437801361084
preprocessing time for sampling: 0.016759872436523438
amortized time for sample size  10 is:  0.0001566932201385498
preprocessing time for sampling: 0.016582965850830078
amortized time for sample size  15 is:  0.00015808312098185222
preprocessing time for sampling: 0.016616106033325195
amortized time for sample size  20 is:  0.0001564328670501709
preprocessing time for sampling: 0.01653599739074707
amortized time for sample size  25 is:  0.0001566349983215332
preprocessing time for sampling: 0.016604900360107422
amortized time for sample size  30 is:  0.00015813692410786946
preprocessing time for sampling: 0.016514062881469727
amortized time for sample size  35 is:  0.00015813112258911133
preprocessing time for sampling: 0.01673126220703125
amortized time for sample size  40 is:  0.0001576122045516968
preprocessing time for sampling: 0.016574859619140625
amortized time for sample size  45 is:  0.00015824815962049696
preprocessing time for sampling: 0.016489028930664062
amortized time for sample size  50 is:  0.0001571679592132568
preprocessing time for sampling: 0.016615867614746094
amortized time for sample size  55 is:  0.00015846603566950016
preprocessing time for sampling: 0.01668381690979004
amortized time for sample size  60 is:  0.00015691264470418293
preprocessing time for sampling: 0.016600847244262695
amortized time for sample size  65 is:  0.00015782664372370795
preprocessing time for sampling: 0.016498804092407227
amortized time for sample size  70 is:  0.00015733674594334195
preprocessing time for sampling: 0.016499042510986328
amortized time for sample size  75 is:  0.00015814647674560546
preprocessing time for sampling: 0.01649308204650879
amortized time for sample size  80 is:  0.00015775984525680543
preprocessing time for sampling: 0.016701221466064453
amortized time for sample size  85 is:  0.00015756169487448298
preprocessing time for sampling: 0.016719818115234375
amortized time for sample size  90 is:  0.0001573806073930528
preprocessing time for sampling: 0.016489028930664062
amortized time for sample size  95 is:  0.00015769371233488385
preprocessing time for sampling: 0.016479969024658203
amortized time for sample size  100 is:  0.00015669620037078857
preprocessing time for sampling: 0.01651787757873535
amortized time for sample size  105 is:  0.00015764052527291437
preprocessing time for sampling: 0.01687908172607422
amortized time for sample size  110 is:  0.0001580305966463956
preprocessing time for sampling: 0.016515731811523438
amortized time for sample size  115 is:  0.00015662160127059274
preprocessing time for sampling: 0.016520023345947266
amortized time for sample size  120 is:  0.0001564126213391622
preprocessing time for sampling: 0.016713857650756836
amortized time for sample size  125 is:  0.0001572592353820801
preprocessing time for sampling: 0.016709089279174805
amortized time for sample size  130 is:  0.00015813049903282755
preprocessing time for sampling: 0.016557931900024414
amortized time for sample size  135 is:  0.00015747670774106628
preprocessing time for sampling: 0.01659393310546875
amortized time for sample size  140 is:  0.00015746491295950754
preprocessing time for sampling: 0.016503095626831055
amortized time for sample size  145 is:  0.00015756131862771923
preprocessing time for sampling: 0.016571044921875
amortized time for sample size  150 is:  0.00015687150955200193
preprocessing time for sampling: 0.016571998596191406
amortized time for sample size  155 is:  0.00015920079138971143
preprocessing time for sampling: 0.016509294509887695
amortized time for sample size  160 is:  0.000156428724527359
preprocessing time for sampling: 0.01659417152404785
amortized time for sample size  165 is:  0.00015820266261245265
preprocessing time for sampling: 0.01673579216003418
amortized time for sample size  170 is:  0.0001575962094699635
preprocessing time for sampling: 0.016562938690185547
amortized time for sample size  175 is:  0.00015721804755074637
preprocessing time for sampling: 0.016522884368896484
amortized time for sample size  180 is:  0.00015655324194166397
preprocessing time for sampling: 0.01667499542236328
amortized time for sample size  185 is:  0.00015761795559444944
preprocessing time for sampling: 0.016518831253051758
amortized time for sample size  190 is:  0.00015781895737898975
preprocessing time for sampling: 0.016535043716430664
amortized time for sample size  195 is:  0.00015721907982459434
preprocessing time for sampling: 0.0167391300201416
amortized time for sample size  200 is:  0.00015829663276672364
preprocessing time for sampling: 0.016581058502197266
amortized time for sample size  205 is:  0.00015679065192618022
preprocessing time for sampling: 0.016636133193969727
amortized time for sample size  210 is:  0.00015760240100678947
preprocessing time for sampling: 0.01690983772277832
amortized time for sample size  215 is:  0.00015768981534381246
preprocessing time for sampling: 0.01671004295349121
amortized time for sample size  220 is:  0.00015704641558907247
preprocessing time for sampling: 0.016604185104370117
amortized time for sample size  225 is:  0.00015633539623684353
preprocessing time for sampling: 0.016596078872680664
amortized time for sample size  230 is:  0.00015852847306624705
preprocessing time for sampling: 0.016846179962158203
amortized time for sample size  235 is:  0.00015724468231201176
preprocessing time for sampling: 0.0165708065032959
amortized time for sample size  240 is:  0.00016092719634373982
preprocessing time for sampling: 0.01656198501586914
amortized time for sample size  245 is:  0.00015762505239369918
preprocessing time for sampling: 0.016549110412597656
amortized time for sample size  250 is:  0.0001577246379852295
*** results for plotting, beta= 0.6 

mean_list= [np.float64(0.6900000000000001), np.float64(0.8400000000000001), np.float64(0.78), np.float64(0.89), np.float64(0.9), np.float64(0.97), np.float64(0.9200000000000002), np.float64(0.9400000000000001), np.float64(0.9100000000000001), np.float64(0.9700000000000001), np.float64(0.9800000000000001), np.float64(0.96), np.float64(0.99), np.float64(0.9800000000000001), np.float64(1.0), np.float64(1.0), np.float64(0.96), np.float64(0.99), np.float64(0.9800000000000001), np.float64(0.99), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(0.99), np.float64(1.0), np.float64(0.9800000000000001), np.float64(0.99), np.float64(0.99), np.float64(1.0), np.float64(0.99), np.float64(0.99), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), 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(0.17), np.float64(0.11135528725660045), np.float64(0.14), np.float64(0.08306623862918074), np.float64(0.14832396974191325), np.float64(0.045825756949558386), np.float64(0.0748331477354788), np.float64(0.09165151389911681), np.float64(0.06999999999999999), np.float64(0.04582575694955839), np.float64(0.039999999999999994), np.float64(0.04898979485566354), np.float64(0.029999999999999992), np.float64(0.039999999999999994), np.float64(0.0), np.float64(0.0), np.float64(0.04898979485566356), np.float64(0.029999999999999992), np.float64(0.039999999999999994), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.039999999999999994), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), 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: 0.016869783401489258
amortized time for sample size  5 is:  0.0001575641632080078
preprocessing time for sampling: 0.01650404930114746
amortized time for sample size  10 is:  0.00015707278251647947
preprocessing time for sampling: 0.016641855239868164
amortized time for sample size  15 is:  0.00015873368581136068
preprocessing time for sampling: 0.01684284210205078
amortized time for sample size  20 is:  0.00015709447860717777
preprocessing time for sampling: 0.016479969024658203
amortized time for sample size  25 is:  0.00015638580322265626
preprocessing time for sampling: 0.01646113395690918
amortized time for sample size  30 is:  0.0001559590498606364
preprocessing time for sampling: 0.016484975814819336
amortized time for sample size  35 is:  0.0001559702328273228
preprocessing time for sampling: 0.016475915908813477
amortized time for sample size  40 is:  0.00015890800952911378
preprocessing time for sampling: 0.016483068466186523
amortized time for sample size  45 is:  0.00015787903467814126
preprocessing time for sampling: 0.01649188995361328
amortized time for sample size  50 is:  0.00015682516098022462
preprocessing time for sampling: 0.016531944274902344
amortized time for sample size  55 is:  0.0001569229472767223
preprocessing time for sampling: 0.01662898063659668
amortized time for sample size  60 is:  0.00015744622548421224
preprocessing time for sampling: 0.01676797866821289
amortized time for sample size  65 is:  0.00015806421866783728
preprocessing time for sampling: 0.01650714874267578
amortized time for sample size  70 is:  0.0001569311959402902
preprocessing time for sampling: 0.01649308204650879
amortized time for sample size  75 is:  0.00015804357528686523
preprocessing time for sampling: 0.01650714874267578
amortized time for sample size  80 is:  0.00015719297528266906
preprocessing time for sampling: 0.01657414436340332
amortized time for sample size  85 is:  0.0001575585814083324
preprocessing time for sampling: 0.01654195785522461
amortized time for sample size  90 is:  0.00015699389245775014
preprocessing time for sampling: 0.01667308807373047
amortized time for sample size  95 is:  0.00015721933465254935
preprocessing time for sampling: 0.016607999801635742
amortized time for sample size  100 is:  0.00015786733627319336
preprocessing time for sampling: 0.016507863998413086
amortized time for sample size  105 is:  0.0001571242922828311
preprocessing time for sampling: 0.016551971435546875
amortized time for sample size  110 is:  0.00015690560774369672
preprocessing time for sampling: 0.016724109649658203
amortized time for sample size  115 is:  0.00015751492458841075
preprocessing time for sampling: 0.01669025421142578
amortized time for sample size  120 is:  0.00015745629866917928
preprocessing time for sampling: 0.016534090042114258
amortized time for sample size  125 is:  0.00015688745498657227
preprocessing time for sampling: 0.016536951065063477
amortized time for sample size  130 is:  0.0001569952964782715
preprocessing time for sampling: 0.016638994216918945
amortized time for sample size  135 is:  0.0001572031268367061
preprocessing time for sampling: 0.016551971435546875
amortized time for sample size  140 is:  0.00015726997171129498
preprocessing time for sampling: 0.016493797302246094
amortized time for sample size  145 is:  0.0001578088299981479
preprocessing time for sampling: 0.016535043716430664
amortized time for sample size  150 is:  0.00015707944234212237
preprocessing time for sampling: 0.016538143157958984
amortized time for sample size  155 is:  0.00015715134528375443
preprocessing time for sampling: 0.01649308204650879
amortized time for sample size  160 is:  0.00015829911828041076
preprocessing time for sampling: 0.016656875610351562
amortized time for sample size  165 is:  0.00015638784928755325
preprocessing time for sampling: 0.016946077346801758
amortized time for sample size  170 is:  0.0001573906085070442
preprocessing time for sampling: 0.016629695892333984
amortized time for sample size  175 is:  0.0001567802974155971
preprocessing time for sampling: 0.016658782958984375
amortized time for sample size  180 is:  0.0001580762995613946
preprocessing time for sampling: 0.016710996627807617
amortized time for sample size  185 is:  0.00015720442179087044
preprocessing time for sampling: 0.016502857208251953
amortized time for sample size  190 is:  0.00015758877051504034
preprocessing time for sampling: 0.016853809356689453
amortized time for sample size  195 is:  0.00015801785542414736
preprocessing time for sampling: 0.01668524742126465
amortized time for sample size  200 is:  0.00015774754285812376
preprocessing time for sampling: 0.0168609619140625
amortized time for sample size  205 is:  0.00015675504033158463
preprocessing time for sampling: 0.016615867614746094
amortized time for sample size  210 is:  0.00016218478339059014
preprocessing time for sampling: 0.01650714874267578
amortized time for sample size  215 is:  0.0001566603239192519
preprocessing time for sampling: 0.016508817672729492
amortized time for sample size  220 is:  0.00015708020600405608
preprocessing time for sampling: 0.01655864715576172
amortized time for sample size  225 is:  0.0001565444204542372
preprocessing time for sampling: 0.01651287078857422
amortized time for sample size  230 is:  0.0001584672409555186
preprocessing time for sampling: 0.016664981842041016
amortized time for sample size  235 is:  0.00015717248713716548
preprocessing time for sampling: 0.016519784927368164
amortized time for sample size  240 is:  0.00015708639224370317
preprocessing time for sampling: 0.016533851623535156
amortized time for sample size  245 is:  0.00015721794050567003
preprocessing time for sampling: 0.016522884368896484
amortized time for sample size  250 is:  0.00015752440452575684
*** results for plotting, beta= 0.8 

mean_list= [np.float64(0.8800000000000001), np.float64(0.9400000000000001), np.float64(0.9099999999999999), np.float64(0.96), np.float64(0.99), np.float64(0.9800000000000001), np.float64(0.9800000000000001), np.float64(0.99), np.float64(0.99), np.float64(1.0), np.float64(0.99), np.float64(1.0), 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)]
std_list= [np.float64(0.08717797887081348), np.float64(0.04898979485566355), np.float64(0.10440306508910549), np.float64(0.04898979485566355), np.float64(0.029999999999999992), np.float64(0.039999999999999994), np.float64(0.039999999999999994), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.0), 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)]
beta: 1
preprocessing time for sampling: 0.017754077911376953
amortized time for sample size  5 is:  0.0001633610725402832
preprocessing time for sampling: 0.017755985260009766
amortized time for sample size  10 is:  0.000164376974105835
preprocessing time for sampling: 0.01774883270263672
amortized time for sample size  15 is:  0.00016457684834798178
preprocessing time for sampling: 0.017850875854492188
amortized time for sample size  20 is:  0.00016689467430114745
preprocessing time for sampling: 0.01781773567199707
amortized time for sample size  25 is:  0.0001641031265258789
preprocessing time for sampling: 0.017846107482910156
amortized time for sample size  30 is:  0.00016356762250264488
preprocessing time for sampling: 0.01797318458557129
amortized time for sample size  35 is:  0.0001644904272896903
preprocessing time for sampling: 0.0179140567779541
amortized time for sample size  40 is:  0.00016432303190231325
preprocessing time for sampling: 0.017870187759399414
amortized time for sample size  45 is:  0.00016387547387017144
preprocessing time for sampling: 0.01789999008178711
amortized time for sample size  50 is:  0.0001639291286468506
preprocessing time for sampling: 0.018374919891357422
amortized time for sample size  55 is:  0.00016537037762728605
preprocessing time for sampling: 0.017724990844726562
amortized time for sample size  60 is:  0.00016394718488057448
preprocessing time for sampling: 0.01774001121520996
amortized time for sample size  65 is:  0.00016451648565439078
preprocessing time for sampling: 0.017978191375732422
amortized time for sample size  70 is:  0.0001648099422454834
preprocessing time for sampling: 0.017745256423950195
amortized time for sample size  75 is:  0.00016500225067138678
preprocessing time for sampling: 0.017783641815185547
amortized time for sample size  80 is:  0.00016443786025047299
preprocessing time for sampling: 0.01789116859436035
amortized time for sample size  85 is:  0.00016564531887278838
preprocessing time for sampling: 0.018105745315551758
amortized time for sample size  90 is:  0.00016448789172702366
preprocessing time for sampling: 0.017747879028320312
amortized time for sample size  95 is:  0.00016342424091539884
preprocessing time for sampling: 0.017915725708007812
amortized time for sample size  100 is:  0.0001654989719390869
preprocessing time for sampling: 0.018031835556030273
amortized time for sample size  105 is:  0.00016512012481689452
preprocessing time for sampling: 0.01781296730041504
amortized time for sample size  110 is:  0.0001644539833068847
preprocessing time for sampling: 0.017759084701538086
amortized time for sample size  115 is:  0.0001639085645261018
preprocessing time for sampling: 0.0177919864654541
amortized time for sample size  120 is:  0.00016486807664235434
preprocessing time for sampling: 0.017947912216186523
amortized time for sample size  125 is:  0.00016456047058105466
preprocessing time for sampling: 0.018219947814941406
amortized time for sample size  130 is:  0.0001648407349219689
preprocessing time for sampling: 0.017783164978027344
amortized time for sample size  135 is:  0.00016436184777153865
preprocessing time for sampling: 0.017785072326660156
amortized time for sample size  140 is:  0.00016429632050650464
preprocessing time for sampling: 0.01788330078125
amortized time for sample size  145 is:  0.000164800972774111
preprocessing time for sampling: 0.017819881439208984
amortized time for sample size  150 is:  0.00016429222424825033
preprocessing time for sampling: 0.01801919937133789
amortized time for sample size  155 is:  0.00016368055343627929
preprocessing time for sampling: 0.017831802368164062
amortized time for sample size  160 is:  0.0001644805520772934
preprocessing time for sampling: 0.017853975296020508
amortized time for sample size  165 is:  0.00016430736310554271
preprocessing time for sampling: 0.017763853073120117
amortized time for sample size  170 is:  0.00016391247861525596
preprocessing time for sampling: 0.017811059951782227
amortized time for sample size  175 is:  0.00016402988433837892
preprocessing time for sampling: 0.017987966537475586
amortized time for sample size  180 is:  0.00016448975933922662
preprocessing time for sampling: 0.017796039581298828
amortized time for sample size  185 is:  0.00016463260392884953
preprocessing time for sampling: 0.01791691780090332
amortized time for sample size  190 is:  0.00016483286807411596
preprocessing time for sampling: 0.018291234970092773
amortized time for sample size  195 is:  0.0001649232644301194
preprocessing time for sampling: 0.017913818359375
amortized time for sample size  200 is:  0.00016578316688537593
preprocessing time for sampling: 0.01786184310913086
amortized time for sample size  205 is:  0.00016507484854721445
preprocessing time for sampling: 0.018131017684936523
amortized time for sample size  210 is:  0.00016472604161217098
preprocessing time for sampling: 0.018208026885986328
amortized time for sample size  215 is:  0.0001679183937782465
preprocessing time for sampling: 0.01804804801940918
amortized time for sample size  220 is:  0.0001640503623268821
preprocessing time for sampling: 0.01799297332763672
amortized time for sample size  225 is:  0.0001640925937228733
preprocessing time for sampling: 0.017885923385620117
amortized time for sample size  230 is:  0.00016400750823642897
preprocessing time for sampling: 0.017795801162719727
amortized time for sample size  235 is:  0.0001635032410317279
preprocessing time for sampling: 0.017771005630493164
amortized time for sample size  240 is:  0.00016333695252736407
preprocessing time for sampling: 0.01776909828186035
amortized time for sample size  245 is:  0.00016315105010052114
preprocessing time for sampling: 0.01784801483154297
amortized time for sample size  250 is:  0.00016305981636047365
*** results for plotting, beta= 1 

mean_list= [np.float64(0.8800000000000001), np.float64(0.9200000000000002), np.float64(0.97), np.float64(1.0), np.float64(1.0), np.float64(0.99), np.float64(0.99), np.float64(1.0), np.float64(0.99), np.float64(1.0), np.float64(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(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), 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(0.05999999999999999), np.float64(0.0748331477354788), np.float64(0.04582575694955839), np.float64(0.0), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.0), 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(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), 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: 0.016534805297851562
amortized time for sample size  5 is:  0.00015575408935546877
preprocessing time for sampling: 0.01648712158203125
amortized time for sample size  10 is:  0.0001558270454406738
preprocessing time for sampling: 0.016512155532836914
amortized time for sample size  15 is:  0.00015546258290608726
preprocessing time for sampling: 0.016505002975463867
amortized time for sample size  20 is:  0.00015579748153686523
preprocessing time for sampling: 0.016500234603881836
amortized time for sample size  25 is:  0.00015590076446533201
preprocessing time for sampling: 0.01651597023010254
amortized time for sample size  30 is:  0.0001557941436767578
preprocessing time for sampling: 0.016538143157958984
amortized time for sample size  35 is:  0.00015571723665509904
preprocessing time for sampling: 0.016510009765625
amortized time for sample size  40 is:  0.00015573120117187502
preprocessing time for sampling: 0.016508817672729492
amortized time for sample size  45 is:  0.00015583806567721895
preprocessing time for sampling: 0.016520023345947266
amortized time for sample size  50 is:  0.00015574097633361814
preprocessing time for sampling: 0.016868114471435547
amortized time for sample size  55 is:  0.0001584676829251376
preprocessing time for sampling: 0.016665220260620117
amortized time for sample size  60 is:  0.00015865468978881837
preprocessing time for sampling: 0.016756057739257812
amortized time for sample size  65 is:  0.00015759750512930063
preprocessing time for sampling: 0.016646862030029297
amortized time for sample size  70 is:  0.00015751307351248605
preprocessing time for sampling: 0.016885042190551758
amortized time for sample size  75 is:  0.00015782082875569661
preprocessing time for sampling: 0.016777992248535156
amortized time for sample size  80 is:  0.0001577046513557434
preprocessing time for sampling: 0.016680002212524414
amortized time for sample size  85 is:  0.00015903416801901424
preprocessing time for sampling: 0.016686201095581055
amortized time for sample size  90 is:  0.00015850014156765406
preprocessing time for sampling: 0.016698122024536133
amortized time for sample size  95 is:  0.0001567899051465486
preprocessing time for sampling: 0.016571044921875
amortized time for sample size  100 is:  0.00015714366436004638
preprocessing time for sampling: 0.01666092872619629
amortized time for sample size  105 is:  0.00015728936876569476
preprocessing time for sampling: 0.016862869262695312
amortized time for sample size  110 is:  0.00015827933224764736
preprocessing time for sampling: 0.01668095588684082
amortized time for sample size  115 is:  0.00016206162908802862
preprocessing time for sampling: 0.01667475700378418
amortized time for sample size  120 is:  0.00015597198406855264
preprocessing time for sampling: 0.016499996185302734
amortized time for sample size  125 is:  0.00015587945938110354
preprocessing time for sampling: 0.016532182693481445
amortized time for sample size  130 is:  0.00015564951529869667
preprocessing time for sampling: 0.016495943069458008
amortized time for sample size  135 is:  0.00015632428063286675
preprocessing time for sampling: 0.01654815673828125
amortized time for sample size  140 is:  0.00015624981267111642
preprocessing time for sampling: 0.016524791717529297
amortized time for sample size  145 is:  0.00015595559416146115
preprocessing time for sampling: 0.016547203063964844
amortized time for sample size  150 is:  0.00015633260409037272
preprocessing time for sampling: 0.01651620864868164
amortized time for sample size  155 is:  0.00016021320896763953
preprocessing time for sampling: 0.016648054122924805
amortized time for sample size  160 is:  0.00015783141553401945
preprocessing time for sampling: 0.01653313636779785
amortized time for sample size  165 is:  0.00015769312598488548
preprocessing time for sampling: 0.01666712760925293
amortized time for sample size  170 is:  0.0001574237907634062
preprocessing time for sampling: 0.016635894775390625
amortized time for sample size  175 is:  0.00015913088662283762
preprocessing time for sampling: 0.016624927520751953
amortized time for sample size  180 is:  0.00015735220909118648
preprocessing time for sampling: 0.016657114028930664
amortized time for sample size  185 is:  0.00015770552609417892
preprocessing time for sampling: 0.016643285751342773
amortized time for sample size  190 is:  0.00015763309127406072
preprocessing time for sampling: 0.016784191131591797
amortized time for sample size  195 is:  0.0001574439635643592
preprocessing time for sampling: 0.0165407657623291
amortized time for sample size  200 is:  0.00015766844749450683
preprocessing time for sampling: 0.016591787338256836
amortized time for sample size  205 is:  0.0001582696030779583
preprocessing time for sampling: 0.016591787338256836
amortized time for sample size  210 is:  0.00015805104800633023
preprocessing time for sampling: 0.016687870025634766
amortized time for sample size  215 is:  0.00015733479344567588
preprocessing time for sampling: 0.016656875610351562
amortized time for sample size  220 is:  0.00015857182849537244
preprocessing time for sampling: 0.016709089279174805
amortized time for sample size  225 is:  0.00015938595665825734
preprocessing time for sampling: 0.016756057739257812
amortized time for sample size  230 is:  0.00015850699466207755
preprocessing time for sampling: 0.0167539119720459
amortized time for sample size  235 is:  0.00015821874902603475
preprocessing time for sampling: 0.016665935516357422
amortized time for sample size  240 is:  0.00015821316838264464
preprocessing time for sampling: 0.016593217849731445
amortized time for sample size  245 is:  0.0001582603357276138
preprocessing time for sampling: 0.01672077178955078
amortized time for sample size  250 is:  0.00015873680114746093
*** results for plotting, beta= 1.2 

mean_list= [np.float64(0.9099999999999999), np.float64(0.96), np.float64(0.97), 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)]
std_list= [np.float64(0.10440306508910549), np.float64(0.06633249580710798), np.float64(0.04582575694955839), 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)]
