beta: 0.2
preprocessing time for sampling: 1.067866325378418
amortized time for sample size  5 is:  0.0007497019767761232
preprocessing time for sampling: 1.063486099243164
amortized time for sample size  10 is:  0.0007456274032592774
preprocessing time for sampling: 1.0618090629577637
amortized time for sample size  15 is:  0.0007332417170206704
preprocessing time for sampling: 1.0607330799102783
amortized time for sample size  20 is:  0.0007308337688446044
preprocessing time for sampling: 1.0628001689910889
amortized time for sample size  25 is:  0.0007373410224914551
preprocessing time for sampling: 1.056792974472046
amortized time for sample size  30 is:  0.0007348399162292482
preprocessing time for sampling: 1.064526081085205
amortized time for sample size  35 is:  0.0007294352395193916
preprocessing time for sampling: 1.0584521293640137
amortized time for sample size  40 is:  0.0007244356274604798
preprocessing time for sampling: 1.055290937423706
amortized time for sample size  45 is:  0.0007221453454759385
preprocessing time for sampling: 1.0562188625335693
amortized time for sample size  50 is:  0.0007228183269500732
preprocessing time for sampling: 1.0635409355163574
amortized time for sample size  55 is:  0.0007204287268898703
preprocessing time for sampling: 1.054534912109375
amortized time for sample size  60 is:  0.0007492116292317708
preprocessing time for sampling: 1.0578069686889648
amortized time for sample size  65 is:  0.0007486675335810733
preprocessing time for sampling: 1.0608859062194824
amortized time for sample size  70 is:  0.0007409024238586426
preprocessing time for sampling: 1.0533571243286133
amortized time for sample size  75 is:  0.0007432459513346354
preprocessing time for sampling: 1.0592539310455322
amortized time for sample size  80 is:  0.000723201870918274
preprocessing time for sampling: 1.0601060390472412
amortized time for sample size  85 is:  0.0007227729348575366
preprocessing time for sampling: 1.0605840682983398
amortized time for sample size  90 is:  0.0007234514554341634
preprocessing time for sampling: 1.0562798976898193
amortized time for sample size  95 is:  0.0007213738090113591
preprocessing time for sampling: 1.055859088897705
amortized time for sample size  100 is:  0.0007213754892349243
preprocessing time for sampling: 1.0561590194702148
amortized time for sample size  105 is:  0.0007213162240527923
preprocessing time for sampling: 1.054992914199829
amortized time for sample size  110 is:  0.0007209651470184328
preprocessing time for sampling: 1.0653791427612305
amortized time for sample size  115 is:  0.0007214024377905804
preprocessing time for sampling: 1.055469036102295
amortized time for sample size  120 is:  0.0007201782862345378
preprocessing time for sampling: 1.0597507953643799
amortized time for sample size  125 is:  0.0007290899658203124
preprocessing time for sampling: 1.0593862533569336
amortized time for sample size  130 is:  0.0007317347343151384
preprocessing time for sampling: 1.0560052394866943
amortized time for sample size  135 is:  0.0007295413193879302
preprocessing time for sampling: 1.0554702281951904
amortized time for sample size  140 is:  0.0007282096658434187
preprocessing time for sampling: 1.0623469352722168
amortized time for sample size  145 is:  0.0007255678012453276
preprocessing time for sampling: 1.0613288879394531
amortized time for sample size  150 is:  0.0007439237594604492
preprocessing time for sampling: 1.0542521476745605
amortized time for sample size  155 is:  0.000737345157131072
preprocessing time for sampling: 1.0596647262573242
amortized time for sample size  160 is:  0.0007344774007797242
preprocessing time for sampling: 1.0600957870483398
amortized time for sample size  165 is:  0.0007333598281397964
preprocessing time for sampling: 1.0695161819458008
amortized time for sample size  170 is:  0.0007352457467247459
preprocessing time for sampling: 1.068345069885254
amortized time for sample size  175 is:  0.0007340208189828055
preprocessing time for sampling: 1.0789291858673096
amortized time for sample size  180 is:  0.0007348296907212999
preprocessing time for sampling: 1.0844500064849854
amortized time for sample size  185 is:  0.0007361418620960133
preprocessing time for sampling: 1.0798518657684326
amortized time for sample size  190 is:  0.0007412671289945905
preprocessing time for sampling: 1.1047029495239258
amortized time for sample size  195 is:  0.0007445521476941229
preprocessing time for sampling: 1.0916709899902344
amortized time for sample size  200 is:  0.0007459009051322937
preprocessing time for sampling: 1.0855560302734375
amortized time for sample size  205 is:  0.0007389128964121748
preprocessing time for sampling: 1.0886931419372559
amortized time for sample size  210 is:  0.0007436618577866327
preprocessing time for sampling: 1.0765178203582764
amortized time for sample size  215 is:  0.0007401640027068382
preprocessing time for sampling: 1.0921688079833984
amortized time for sample size  220 is:  0.000758950872854753
preprocessing time for sampling: 1.0770916938781738
amortized time for sample size  225 is:  0.0007411376423305934
preprocessing time for sampling: 1.091521978378296
amortized time for sample size  230 is:  0.0007407334265501601
preprocessing time for sampling: 1.090364933013916
amortized time for sample size  235 is:  0.0007409104793629747
preprocessing time for sampling: 1.0781002044677734
amortized time for sample size  240 is:  0.0007702346642812094
preprocessing time for sampling: 1.153285026550293
amortized time for sample size  245 is:  0.0007494995058799278
preprocessing time for sampling: 1.108994960784912
amortized time for sample size  250 is:  0.0007742141437530517
*** results for plotting, beta= 0.2 

mean_list= [np.float64(0.29000000000000004), np.float64(0.43), np.float64(0.52), np.float64(0.61), np.float64(0.57), np.float64(0.51), np.float64(0.53), np.float64(0.6499999999999999), np.float64(0.55), np.float64(0.61), np.float64(0.5900000000000001), np.float64(0.6200000000000001), np.float64(0.5700000000000001), np.float64(0.6799999999999999), np.float64(0.6499999999999999), np.float64(0.6900000000000001), np.float64(0.7), np.float64(0.7299999999999999), np.float64(0.7), np.float64(0.69), np.float64(0.72), np.float64(0.58), np.float64(0.69), np.float64(0.73), np.float64(0.6300000000000001), np.float64(0.64), np.float64(0.7499999999999999), np.float64(0.69), np.float64(0.6799999999999999), np.float64(0.72), np.float64(0.74), np.float64(0.7699999999999999), np.float64(0.6900000000000001), np.float64(0.76), np.float64(0.78), np.float64(0.74), np.float64(0.7300000000000001), np.float64(0.72), np.float64(0.8), np.float64(0.71), np.float64(0.7100000000000001), np.float64(0.73), np.float64(0.77), np.float64(0.74), np.float64(0.79), np.float64(0.78), np.float64(0.6900000000000001), np.float64(0.76), np.float64(0.8), np.float64(0.8099999999999999)]
std_list= [np.float64(0.16401219466856723), np.float64(0.10999999999999999), np.float64(0.15362291495737215), np.float64(0.11357816691600546), np.float64(0.1345362404707371), np.float64(0.157797338380595), np.float64(0.14866068747318506), np.float64(0.1118033988749895), np.float64(0.09219544457292886), np.float64(0.157797338380595), np.float64(0.16401219466856726), np.float64(0.17204650534085256), np.float64(0.1345362404707371), np.float64(0.08717797887081348), np.float64(0.1118033988749895), np.float64(0.10440306508910553), np.float64(0.14142135623730953), np.float64(0.09000000000000002), np.float64(0.11832159566199235), np.float64(0.12206555615733704), np.float64(0.14), np.float64(0.18867962264113208), np.float64(0.15132745950421556), np.float64(0.11000000000000001), np.float64(0.14866068747318506), np.float64(0.15620499351813308), np.float64(0.16881943016134132), np.float64(0.12206555615733704), np.float64(0.17204650534085256), np.float64(0.13266499161421602), np.float64(0.12000000000000002), np.float64(0.09000000000000002), np.float64(0.15132745950421558), np.float64(0.14282856857085702), np.float64(0.10770329614269011), np.float64(0.2009975124224178), np.float64(0.12688577540449522), np.float64(0.15362291495737218), np.float64(0.07745966692414837), np.float64(0.13000000000000003), np.float64(0.157797338380595), np.float64(0.11000000000000003), np.float64(0.16155494421403513), np.float64(0.1356465996625054), np.float64(0.13000000000000003), np.float64(0.18867962264113208), np.float64(0.13747727084867523), np.float64(0.1356465996625054), np.float64(0.11832159566199234), np.float64(0.13000000000000003)]
beta: 0.4
preprocessing time for sampling: 1.1417858600616455
amortized time for sample size  5 is:  0.0007499098777770997
preprocessing time for sampling: 1.1261849403381348
amortized time for sample size  10 is:  0.0007342867851257324
preprocessing time for sampling: 1.1096069812774658
amortized time for sample size  15 is:  0.0007614170710245768
preprocessing time for sampling: 1.0961921215057373
amortized time for sample size  20 is:  0.0007611471414566041
preprocessing time for sampling: 1.1571719646453857
amortized time for sample size  25 is:  0.0007219167709350585
preprocessing time for sampling: 1.0890769958496094
amortized time for sample size  30 is:  0.0007216536204020181
preprocessing time for sampling: 1.0937449932098389
amortized time for sample size  35 is:  0.0007240681648254397
preprocessing time for sampling: 1.110107183456421
amortized time for sample size  40 is:  0.0007214064002037049
preprocessing time for sampling: 1.0892541408538818
amortized time for sample size  45 is:  0.0007249001397026909
preprocessing time for sampling: 1.0767741203308105
amortized time for sample size  50 is:  0.0007223893165588379
preprocessing time for sampling: 1.0818190574645996
amortized time for sample size  55 is:  0.0007266633727333764
preprocessing time for sampling: 1.0744798183441162
amortized time for sample size  60 is:  0.000718239148457845
preprocessing time for sampling: 1.0944690704345703
amortized time for sample size  65 is:  0.0007329187393188478
preprocessing time for sampling: 1.0751700401306152
amortized time for sample size  70 is:  0.00073191693850926
preprocessing time for sampling: 1.0888760089874268
amortized time for sample size  75 is:  0.0007296912511189777
preprocessing time for sampling: 1.0749666690826416
amortized time for sample size  80 is:  0.000736881285905838
preprocessing time for sampling: 1.0764169692993164
amortized time for sample size  85 is:  0.0007330997410942526
preprocessing time for sampling: 1.0772559642791748
amortized time for sample size  90 is:  0.0007345647811889649
preprocessing time for sampling: 1.0839569568634033
amortized time for sample size  95 is:  0.0007435499241477565
preprocessing time for sampling: 1.0824036598205566
amortized time for sample size  100 is:  0.0007354055166244509
preprocessing time for sampling: 1.0792529582977295
amortized time for sample size  105 is:  0.0007347119649251302
preprocessing time for sampling: 1.0748019218444824
amortized time for sample size  110 is:  0.0007348838285966354
preprocessing time for sampling: 1.077087163925171
amortized time for sample size  115 is:  0.0007429207511570143
preprocessing time for sampling: 1.082519769668579
amortized time for sample size  120 is:  0.0007409063776334125
preprocessing time for sampling: 1.0735528469085693
amortized time for sample size  125 is:  0.000732818088531494
preprocessing time for sampling: 1.0740079879760742
amortized time for sample size  130 is:  0.0007473105100484996
preprocessing time for sampling: 1.0989611148834229
amortized time for sample size  135 is:  0.0007344753653914841
preprocessing time for sampling: 1.0718331336975098
amortized time for sample size  140 is:  0.0007404707329613821
preprocessing time for sampling: 1.0740020275115967
amortized time for sample size  145 is:  0.0007331142261110503
preprocessing time for sampling: 1.0795278549194336
amortized time for sample size  150 is:  0.000736411698659261
preprocessing time for sampling: 1.068526268005371
amortized time for sample size  155 is:  0.0007423828801801126
preprocessing time for sampling: 1.070167064666748
amortized time for sample size  160 is:  0.0007345622777938843
preprocessing time for sampling: 1.0570309162139893
amortized time for sample size  165 is:  0.0007426968776818478
preprocessing time for sampling: 1.094101905822754
amortized time for sample size  170 is:  0.000733355956919053
preprocessing time for sampling: 1.0548880100250244
amortized time for sample size  175 is:  0.0007337377820696149
preprocessing time for sampling: 1.0808420181274414
amortized time for sample size  180 is:  0.0007330262660980226
preprocessing time for sampling: 1.0587859153747559
amortized time for sample size  185 is:  0.0007335233946104306
preprocessing time for sampling: 1.055413007736206
amortized time for sample size  190 is:  0.0007365458388077586
preprocessing time for sampling: 1.0654189586639404
amortized time for sample size  195 is:  0.0007352919211754433
preprocessing time for sampling: 1.0548229217529297
amortized time for sample size  200 is:  0.00073039710521698
preprocessing time for sampling: 1.054792881011963
amortized time for sample size  205 is:  0.0007324021502238949
preprocessing time for sampling: 1.0632619857788086
amortized time for sample size  210 is:  0.0007345536663418724
preprocessing time for sampling: 1.0607879161834717
amortized time for sample size  215 is:  0.0007309903433156569
preprocessing time for sampling: 1.0584099292755127
amortized time for sample size  220 is:  0.0007265328060496938
preprocessing time for sampling: 1.0543701648712158
amortized time for sample size  225 is:  0.0007321938726637099
preprocessing time for sampling: 1.0706188678741455
amortized time for sample size  230 is:  0.0007357641924982485
preprocessing time for sampling: 1.0761430263519287
amortized time for sample size  235 is:  0.0007400282393110559
preprocessing time for sampling: 1.0732779502868652
amortized time for sample size  240 is:  0.0007376774251461028
preprocessing time for sampling: 1.0735621452331543
amortized time for sample size  245 is:  0.0007389959705119231
preprocessing time for sampling: 1.0749900341033936
amortized time for sample size  250 is:  0.0007409079551696778
*** results for plotting, beta= 0.4 

mean_list= [np.float64(0.6), np.float64(0.62), np.float64(0.72), np.float64(0.8099999999999999), np.float64(0.9), np.float64(0.75), np.float64(0.8400000000000001), np.float64(0.8400000000000001), np.float64(0.9), np.float64(0.8800000000000001), np.float64(0.89), np.float64(0.9400000000000001), np.float64(0.8700000000000001), np.float64(0.8800000000000001), np.float64(0.9), np.float64(0.8899999999999999), np.float64(0.96), np.float64(0.9400000000000001), np.float64(0.9400000000000001), np.float64(0.93), np.float64(0.96), np.float64(0.95), np.float64(0.95), np.float64(0.89), np.float64(0.95), np.float64(0.96), np.float64(0.9700000000000001), np.float64(0.96), np.float64(0.9800000000000001), np.float64(0.9700000000000001), np.float64(0.9800000000000001), np.float64(0.9200000000000002), np.float64(1.0), np.float64(0.99), np.float64(0.97), np.float64(0.96), np.float64(0.95), np.float64(0.9700000000000001), np.float64(1.0), np.float64(0.9800000000000001), np.float64(0.9800000000000001), np.float64(0.96), np.float64(0.9700000000000001), np.float64(1.0), np.float64(0.9800000000000001), np.float64(1.0), np.float64(0.99), np.float64(0.99), np.float64(0.97), np.float64(0.99)]
std_list= [np.float64(0.14832396974191323), np.float64(0.1661324772583615), np.float64(0.1077032961426901), np.float64(0.13000000000000003), np.float64(0.1264911064067352), np.float64(0.13601470508735444), np.float64(0.09165151389911681), np.float64(0.08), np.float64(0.0894427190999916), np.float64(0.11661903789690603), np.float64(0.08306623862918076), np.float64(0.07999999999999999), np.float64(0.07810249675906655), np.float64(0.1777638883463118), np.float64(0.09999999999999999), np.float64(0.09433981132056604), np.float64(0.06633249580710798), np.float64(0.07999999999999999), np.float64(0.06633249580710798), np.float64(0.06403124237432847), np.float64(0.04898979485566355), np.float64(0.04999999999999999), np.float64(0.06708203932499368), np.float64(0.08306623862918075), np.float64(0.06708203932499368), np.float64(0.04898979485566355), np.float64(0.04582575694955839), np.float64(0.04898979485566356), np.float64(0.039999999999999994), np.float64(0.04582575694955839), np.float64(0.039999999999999994), np.float64(0.0748331477354788), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.04582575694955839), np.float64(0.06633249580710798), np.float64(0.10246950765959598), np.float64(0.04582575694955839), np.float64(0.0), np.float64(0.05999999999999999), np.float64(0.039999999999999994), np.float64(0.04898979485566356), np.float64(0.04582575694955839), np.float64(0.0), np.float64(0.039999999999999994), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.045825756949558386), np.float64(0.029999999999999992)]
beta: 0.6
preprocessing time for sampling: 1.0768449306488037
amortized time for sample size  5 is:  0.0007076072692871093
preprocessing time for sampling: 1.0767369270324707
amortized time for sample size  10 is:  0.0007079026699066165
preprocessing time for sampling: 1.0837111473083496
amortized time for sample size  15 is:  0.0007075745264689127
preprocessing time for sampling: 1.0750787258148193
amortized time for sample size  20 is:  0.0007245669364929198
preprocessing time for sampling: 1.0756897926330566
amortized time for sample size  25 is:  0.0007075718879699708
preprocessing time for sampling: 1.074497938156128
amortized time for sample size  30 is:  0.0007061189015706381
preprocessing time for sampling: 1.0729620456695557
amortized time for sample size  35 is:  0.0007057207652500698
preprocessing time for sampling: 1.0744130611419678
amortized time for sample size  40 is:  0.0007057606577873229
preprocessing time for sampling: 1.0787363052368164
amortized time for sample size  45 is:  0.0007084533903333875
preprocessing time for sampling: 1.0750939846038818
amortized time for sample size  50 is:  0.0007362639904022215
preprocessing time for sampling: 1.0752980709075928
amortized time for sample size  55 is:  0.0007250492356040259
preprocessing time for sampling: 1.080503225326538
amortized time for sample size  60 is:  0.0007281577984491986
preprocessing time for sampling: 1.076293706893921
amortized time for sample size  65 is:  0.0007462009283212515
preprocessing time for sampling: 1.0793848037719727
amortized time for sample size  70 is:  0.000732184750693185
preprocessing time for sampling: 1.075721263885498
amortized time for sample size  75 is:  0.0007330211639404296
preprocessing time for sampling: 1.0754969120025635
amortized time for sample size  80 is:  0.0007351915538311005
preprocessing time for sampling: 1.073843002319336
amortized time for sample size  85 is:  0.0007408527486464556
preprocessing time for sampling: 1.072688102722168
amortized time for sample size  90 is:  0.000736680958006117
preprocessing time for sampling: 1.0760083198547363
amortized time for sample size  95 is:  0.0007340826486286363
preprocessing time for sampling: 1.0820863246917725
amortized time for sample size  100 is:  0.0007340019702911377
preprocessing time for sampling: 1.078273057937622
amortized time for sample size  105 is:  0.0007327036176409038
preprocessing time for sampling: 1.0749990940093994
amortized time for sample size  110 is:  0.0007449247837066652
preprocessing time for sampling: 1.0791068077087402
amortized time for sample size  115 is:  0.0007363690293353537
preprocessing time for sampling: 1.0764820575714111
amortized time for sample size  120 is:  0.046595587352911645
preprocessing time for sampling: 1.0663249492645264
amortized time for sample size  125 is:  0.0007355688476562501
preprocessing time for sampling: 1.0749850273132324
amortized time for sample size  130 is:  0.0007215876946082482
preprocessing time for sampling: 1.0503919124603271
amortized time for sample size  135 is:  0.0007266805260269729
preprocessing time for sampling: 1.058394193649292
amortized time for sample size  140 is:  0.0007207868099212647
preprocessing time for sampling: 1.055588722229004
amortized time for sample size  145 is:  0.0007216439904837772
preprocessing time for sampling: 1.0611038208007812
amortized time for sample size  150 is:  0.0007199999809265137
preprocessing time for sampling: 1.0636098384857178
amortized time for sample size  155 is:  0.0007207215678307319
preprocessing time for sampling: 1.0672698020935059
amortized time for sample size  160 is:  0.0007214145213365555
preprocessing time for sampling: 1.0556299686431885
amortized time for sample size  165 is:  0.0007282652854919433
preprocessing time for sampling: 1.0592849254608154
amortized time for sample size  170 is:  0.0007214267674614402
preprocessing time for sampling: 1.054849624633789
amortized time for sample size  175 is:  0.0007222983087812151
preprocessing time for sampling: 1.0589799880981445
amortized time for sample size  180 is:  0.0007256485356224907
preprocessing time for sampling: 1.0663690567016602
amortized time for sample size  185 is:  0.0007202948364051613
preprocessing time for sampling: 1.0587687492370605
amortized time for sample size  190 is:  0.0007259565529070401
preprocessing time for sampling: 1.0593647956848145
amortized time for sample size  195 is:  0.0007337300960834209
preprocessing time for sampling: 1.0556788444519043
amortized time for sample size  200 is:  0.0007221367835998534
preprocessing time for sampling: 1.0603151321411133
amortized time for sample size  205 is:  0.0007322512138180616
preprocessing time for sampling: 1.0540671348571777
amortized time for sample size  210 is:  0.0007304450784410748
preprocessing time for sampling: 1.0604579448699951
amortized time for sample size  215 is:  0.0007349727763686069
preprocessing time for sampling: 1.0567779541015625
amortized time for sample size  220 is:  0.0007274534702301024
preprocessing time for sampling: 1.05967116355896
amortized time for sample size  225 is:  0.0007353289816114639
preprocessing time for sampling: 1.0731379985809326
amortized time for sample size  230 is:  0.0007331822747769562
preprocessing time for sampling: 1.0742108821868896
amortized time for sample size  235 is:  0.0007338862013309559
preprocessing time for sampling: 1.0725939273834229
amortized time for sample size  240 is:  0.0007339001794656118
preprocessing time for sampling: 1.0737659931182861
amortized time for sample size  245 is:  0.0007355841130626445
preprocessing time for sampling: 1.0634679794311523
amortized time for sample size  250 is:  0.0007394007587432862
*** results for plotting, beta= 0.6 

mean_list= [np.float64(0.7100000000000001), np.float64(0.85), np.float64(0.9000000000000001), np.float64(0.9400000000000001), np.float64(0.9), np.float64(0.9400000000000001), np.float64(0.97), np.float64(0.93), np.float64(0.93), np.float64(0.97), np.float64(0.97), np.float64(0.95), np.float64(0.99), np.float64(0.97), np.float64(1.0), np.float64(0.99), 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(0.99), 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)]
std_list= [np.float64(0.09433981132056607), np.float64(0.0806225774829855), np.float64(0.0894427190999916), np.float64(0.04898979485566355), np.float64(0.07745966692414835), np.float64(0.06633249580710798), np.float64(0.04582575694955839), np.float64(0.06403124237432847), np.float64(0.07810249675906653), np.float64(0.04582575694955839), np.float64(0.045825756949558386), np.float64(0.06708203932499368), np.float64(0.029999999999999992), np.float64(0.06403124237432847), np.float64(0.0), np.float64(0.029999999999999992), 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(0.029999999999999992), 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)]
beta: 0.8
preprocessing time for sampling: 1.075289249420166
amortized time for sample size  5 is:  0.0007075648307800293
preprocessing time for sampling: 1.0715689659118652
amortized time for sample size  10 is:  0.0007084598541259765
preprocessing time for sampling: 1.076949119567871
amortized time for sample size  15 is:  0.0007078604698181151
preprocessing time for sampling: 1.079068899154663
amortized time for sample size  20 is:  0.0007077747583389282
preprocessing time for sampling: 1.07124924659729
amortized time for sample size  25 is:  0.0007242017745971679
preprocessing time for sampling: 1.0664219856262207
amortized time for sample size  30 is:  0.0007065970102945962
preprocessing time for sampling: 1.0651137828826904
amortized time for sample size  35 is:  0.000707038266318185
preprocessing time for sampling: 1.071516990661621
amortized time for sample size  40 is:  0.0007127718329429626
preprocessing time for sampling: 1.0822746753692627
amortized time for sample size  45 is:  0.0007125426398383247
preprocessing time for sampling: 1.0769779682159424
amortized time for sample size  50 is:  0.000722555160522461
preprocessing time for sampling: 1.0719828605651855
amortized time for sample size  55 is:  0.0007222168228842997
preprocessing time for sampling: 1.0698802471160889
amortized time for sample size  60 is:  0.0007129058837890626
preprocessing time for sampling: 1.0717990398406982
amortized time for sample size  65 is:  0.0007412987122168909
preprocessing time for sampling: 1.0749092102050781
amortized time for sample size  70 is:  0.0007327723503112792
preprocessing time for sampling: 1.0722811222076416
amortized time for sample size  75 is:  0.0007308483441670735
preprocessing time for sampling: 1.079777717590332
amortized time for sample size  80 is:  0.0007418904304504395
preprocessing time for sampling: 1.0767250061035156
amortized time for sample size  85 is:  0.0007311822105856504
preprocessing time for sampling: 1.0819520950317383
amortized time for sample size  90 is:  0.000743686596552531
preprocessing time for sampling: 1.0831332206726074
amortized time for sample size  95 is:  0.0007384631006341232
preprocessing time for sampling: 1.0871610641479492
amortized time for sample size  100 is:  0.0007419650316238403
preprocessing time for sampling: 1.0744249820709229
amortized time for sample size  105 is:  0.0007361655916486467
preprocessing time for sampling: 1.0815448760986328
amortized time for sample size  110 is:  0.0007417148460041393
preprocessing time for sampling: 1.0790069103240967
amortized time for sample size  115 is:  0.0007459905665853752
preprocessing time for sampling: 1.082118034362793
amortized time for sample size  120 is:  0.0007515298326810201
preprocessing time for sampling: 1.0841608047485352
amortized time for sample size  125 is:  0.0007406511878967284
preprocessing time for sampling: 1.0811021327972412
amortized time for sample size  130 is:  0.0007424586186042199
preprocessing time for sampling: 1.0828509330749512
amortized time for sample size  135 is:  0.0007390558631331833
preprocessing time for sampling: 1.0827229022979736
amortized time for sample size  140 is:  0.0007411578382764544
preprocessing time for sampling: 1.0752849578857422
amortized time for sample size  145 is:  0.0007471105805758774
preprocessing time for sampling: 1.076153039932251
amortized time for sample size  150 is:  0.0007359107653299967
preprocessing time for sampling: 1.0800278186798096
amortized time for sample size  155 is:  0.0007371931845141997
preprocessing time for sampling: 1.0801990032196045
amortized time for sample size  160 is:  0.0007376222759485244
preprocessing time for sampling: 1.083211898803711
amortized time for sample size  165 is:  0.0007325017235495828
preprocessing time for sampling: 1.0774006843566895
amortized time for sample size  170 is:  0.0007335214334375719
preprocessing time for sampling: 1.0767040252685547
amortized time for sample size  175 is:  0.0007345770290919712
preprocessing time for sampling: 1.0778648853302002
amortized time for sample size  180 is:  0.0007339156601164076
preprocessing time for sampling: 1.076416015625
amortized time for sample size  185 is:  0.0007340861140070735
preprocessing time for sampling: 1.075253963470459
amortized time for sample size  190 is:  0.0007337232388948139
preprocessing time for sampling: 1.0823378562927246
amortized time for sample size  195 is:  0.000736214246505346
preprocessing time for sampling: 1.0780210494995117
amortized time for sample size  200 is:  0.0007338333487510681
preprocessing time for sampling: 1.0745508670806885
amortized time for sample size  205 is:  0.0007366485246797888
preprocessing time for sampling: 1.0792508125305176
amortized time for sample size  210 is:  0.0007343816076006207
preprocessing time for sampling: 1.0888299942016602
amortized time for sample size  215 is:  0.0007343402685121049
preprocessing time for sampling: 1.0745038986206055
amortized time for sample size  220 is:  0.0007341471260244195
preprocessing time for sampling: 1.081857681274414
amortized time for sample size  225 is:  0.0007333991156684029
preprocessing time for sampling: 1.0761449337005615
amortized time for sample size  230 is:  0.000736573716868525
preprocessing time for sampling: 1.0796737670898438
amortized time for sample size  235 is:  0.0007373191042149321
preprocessing time for sampling: 1.0757460594177246
amortized time for sample size  240 is:  0.0007329526543617249
preprocessing time for sampling: 1.0755839347839355
amortized time for sample size  245 is:  0.0007344162123543877
preprocessing time for sampling: 1.0781598091125488
amortized time for sample size  250 is:  0.0007398803329467774
*** results for plotting, beta= 0.8 

mean_list= [np.float64(0.8200000000000001), np.float64(0.9200000000000002), np.float64(0.96), np.float64(0.95), np.float64(0.9800000000000001), np.float64(0.99), np.float64(0.99), np.float64(0.9800000000000001), 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(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(0.11661903789690603), np.float64(0.0748331477354788), np.float64(0.06633249580710798), np.float64(0.08062257748298547), np.float64(0.039999999999999994), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.039999999999999994), 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(0.029999999999999992), 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
preprocessing time for sampling: 1.2766571044921875
amortized time for sample size  5 is:  0.0007269401550292969
preprocessing time for sampling: 1.2766189575195312
amortized time for sample size  10 is:  0.0007324094772338867
preprocessing time for sampling: 1.2736880779266357
amortized time for sample size  15 is:  0.0007257339159647625
preprocessing time for sampling: 1.2702281475067139
amortized time for sample size  20 is:  0.0007227123975753784
preprocessing time for sampling: 1.2681879997253418
amortized time for sample size  25 is:  0.0007240766525268555
preprocessing time for sampling: 1.2704980373382568
amortized time for sample size  30 is:  0.0007365663051605224
preprocessing time for sampling: 1.2650649547576904
amortized time for sample size  35 is:  0.0007222376550946917
preprocessing time for sampling: 1.2662501335144043
amortized time for sample size  40 is:  0.0007238093614578248
preprocessing time for sampling: 1.2658650875091553
amortized time for sample size  45 is:  0.0007361531787448458
preprocessing time for sampling: 1.2619740962982178
amortized time for sample size  50 is:  0.0007392261028289794
preprocessing time for sampling: 1.2758409976959229
amortized time for sample size  55 is:  0.0007426922971552069
preprocessing time for sampling: 1.2724049091339111
amortized time for sample size  60 is:  0.0007445028225580852
preprocessing time for sampling: 1.262188196182251
amortized time for sample size  65 is:  0.0007488688689011794
preprocessing time for sampling: 1.2647480964660645
amortized time for sample size  70 is:  0.0007498409407479423
preprocessing time for sampling: 1.2643799781799316
amortized time for sample size  75 is:  0.0007642406781514485
preprocessing time for sampling: 1.2692899703979492
amortized time for sample size  80 is:  0.0007496320903301239
preprocessing time for sampling: 1.2652699947357178
amortized time for sample size  85 is:  0.0007485094350927015
preprocessing time for sampling: 1.2729730606079102
amortized time for sample size  90 is:  0.0007522989643944635
preprocessing time for sampling: 1.2658376693725586
amortized time for sample size  95 is:  0.0007498119504828201
preprocessing time for sampling: 1.265758991241455
amortized time for sample size  100 is:  0.0007507889509201052
preprocessing time for sampling: 1.2661941051483154
amortized time for sample size  105 is:  0.0007501077879042853
preprocessing time for sampling: 1.2633600234985352
amortized time for sample size  110 is:  0.0007494430325248025
preprocessing time for sampling: 1.2751929759979248
amortized time for sample size  115 is:  0.0007513894412828531
preprocessing time for sampling: 1.269925832748413
amortized time for sample size  120 is:  0.0007537512977917987
preprocessing time for sampling: 1.2677950859069824
amortized time for sample size  125 is:  0.0007506915092468264
preprocessing time for sampling: 1.2665488719940186
amortized time for sample size  130 is:  0.0007531343240004322
preprocessing time for sampling: 1.2658977508544922
amortized time for sample size  135 is:  0.00075797141039813
preprocessing time for sampling: 1.2707955837249756
amortized time for sample size  140 is:  0.0007586205005645754
preprocessing time for sampling: 1.2727899551391602
amortized time for sample size  145 is:  0.0007495003239861847
preprocessing time for sampling: 1.2671458721160889
amortized time for sample size  150 is:  0.0007512407302856446
preprocessing time for sampling: 1.2664597034454346
amortized time for sample size  155 is:  0.0007513874730756206
preprocessing time for sampling: 1.264775037765503
amortized time for sample size  160 is:  0.0007505230903625488
preprocessing time for sampling: 1.2669010162353516
amortized time for sample size  165 is:  0.0007491634975780141
preprocessing time for sampling: 1.261448860168457
amortized time for sample size  170 is:  0.0007513690135058235
preprocessing time for sampling: 1.2728791236877441
amortized time for sample size  175 is:  0.0007561557769775392
preprocessing time for sampling: 1.2689940929412842
amortized time for sample size  180 is:  0.0007502334647708468
preprocessing time for sampling: 1.2668359279632568
amortized time for sample size  185 is:  0.000750602000468486
preprocessing time for sampling: 1.2718532085418701
amortized time for sample size  190 is:  0.0007546530020864385
preprocessing time for sampling: 1.267383098602295
amortized time for sample size  195 is:  0.0007595169116289186
preprocessing time for sampling: 1.2659599781036377
amortized time for sample size  200 is:  0.0007584652543067932
preprocessing time for sampling: 1.2701499462127686
amortized time for sample size  205 is:  0.0007990918508390101
preprocessing time for sampling: 1.3196289539337158
amortized time for sample size  210 is:  0.0007858149097079323
preprocessing time for sampling: 1.2898008823394775
amortized time for sample size  215 is:  0.0007825159915657932
preprocessing time for sampling: 1.2652151584625244
amortized time for sample size  220 is:  0.000749505801634355
preprocessing time for sampling: 1.266679048538208
amortized time for sample size  225 is:  0.0007599247508578831
preprocessing time for sampling: 1.2779209613800049
amortized time for sample size  230 is:  0.0007503214193427046
preprocessing time for sampling: 1.2645628452301025
amortized time for sample size  235 is:  0.0007487704906057803
preprocessing time for sampling: 1.2644381523132324
amortized time for sample size  240 is:  0.0007667252719402312
preprocessing time for sampling: 1.2682528495788574
amortized time for sample size  245 is:  0.0007572666868871572
preprocessing time for sampling: 1.3094427585601807
amortized time for sample size  250 is:  0.0007630135536193848
*** results for plotting, beta= 1 

mean_list= [np.float64(0.93), np.float64(0.9099999999999999), np.float64(0.9800000000000001), np.float64(0.9800000000000001), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0)]
std_list= [np.float64(0.06403124237432847), np.float64(0.08306623862918076), np.float64(0.039999999999999994), np.float64(0.039999999999999994), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0)]
beta: 1.2
preprocessing time for sampling: 1.0736348628997803
amortized time for sample size  5 is:  0.0007309460639953612
preprocessing time for sampling: 1.0834801197052002
amortized time for sample size  10 is:  0.0007398903369903563
preprocessing time for sampling: 1.0774641036987305
amortized time for sample size  15 is:  0.0007690801620483398
preprocessing time for sampling: 1.099877119064331
amortized time for sample size  20 is:  0.0007513598203659057
preprocessing time for sampling: 1.0740201473236084
amortized time for sample size  25 is:  0.0007472304344177247
preprocessing time for sampling: 1.085270881652832
amortized time for sample size  30 is:  0.0007553105354309081
preprocessing time for sampling: 1.0794827938079834
amortized time for sample size  35 is:  0.0007442013195582797
preprocessing time for sampling: 1.0813112258911133
amortized time for sample size  40 is:  0.0007411071062088013
preprocessing time for sampling: 1.0812101364135742
amortized time for sample size  45 is:  0.0007403961817423505
preprocessing time for sampling: 1.0781440734863281
amortized time for sample size  50 is:  0.0007481988430023193
preprocessing time for sampling: 1.0757250785827637
amortized time for sample size  55 is:  0.0007389648177407003
preprocessing time for sampling: 1.0936458110809326
amortized time for sample size  60 is:  0.0007533074617385864
preprocessing time for sampling: 1.0836870670318604
amortized time for sample size  65 is:  0.0007534003991347092
preprocessing time for sampling: 1.0870180130004883
amortized time for sample size  70 is:  0.0007406578745160785
preprocessing time for sampling: 1.0722072124481201
amortized time for sample size  75 is:  0.0007397191047668457
preprocessing time for sampling: 1.1056559085845947
amortized time for sample size  80 is:  0.0007623165547847747
preprocessing time for sampling: 1.0791599750518799
amortized time for sample size  85 is:  0.0007462665894452263
preprocessing time for sampling: 1.0794591903686523
amortized time for sample size  90 is:  0.0007471530967288548
preprocessing time for sampling: 1.1286661624908447
amortized time for sample size  95 is:  0.0007456836951406379
preprocessing time for sampling: 1.0783281326293945
amortized time for sample size  100 is:  0.0007379182815551757
preprocessing time for sampling: 1.0810470581054688
amortized time for sample size  105 is:  0.0007394387154352097
preprocessing time for sampling: 1.0710132122039795
amortized time for sample size  110 is:  0.0007398455359719018
preprocessing time for sampling: 1.0768511295318604
amortized time for sample size  115 is:  0.0007427925856217095
preprocessing time for sampling: 1.0890240669250488
amortized time for sample size  120 is:  0.0007484259605407715
preprocessing time for sampling: 1.0899782180786133
amortized time for sample size  125 is:  0.0007483412361145019
preprocessing time for sampling: 1.0759518146514893
amortized time for sample size  130 is:  0.0007517411525432881
preprocessing time for sampling: 1.081104040145874
amortized time for sample size  135 is:  0.0007477133715594257
preprocessing time for sampling: 1.1436779499053955
amortized time for sample size  140 is:  0.0007423571007592334
preprocessing time for sampling: 1.0759122371673584
amortized time for sample size  145 is:  0.0007416133880615236
preprocessing time for sampling: 1.0754399299621582
amortized time for sample size  150 is:  0.0007517554759979248
preprocessing time for sampling: 1.0839250087738037
amortized time for sample size  155 is:  0.00074345064163208
preprocessing time for sampling: 1.082247018814087
amortized time for sample size  160 is:  0.0007452601343393325
preprocessing time for sampling: 1.0881268978118896
amortized time for sample size  165 is:  0.0007459306138934512
preprocessing time for sampling: 1.076815128326416
amortized time for sample size  170 is:  0.000742476084653069
preprocessing time for sampling: 1.0855591297149658
amortized time for sample size  175 is:  0.0007371866907392229
preprocessing time for sampling: 1.0736818313598633
amortized time for sample size  180 is:  0.0007400740385055545
preprocessing time for sampling: 1.0974321365356445
amortized time for sample size  185 is:  0.0007412921286918022
preprocessing time for sampling: 1.085906982421875
amortized time for sample size  190 is:  0.0007415161258295962
preprocessing time for sampling: 1.0778708457946777
amortized time for sample size  195 is:  0.0007542773882548015
preprocessing time for sampling: 1.0829408168792725
amortized time for sample size  200 is:  0.0007413348436355589
preprocessing time for sampling: 1.1153528690338135
amortized time for sample size  205 is:  0.0007451306319818265
preprocessing time for sampling: 1.0805130004882812
amortized time for sample size  210 is:  0.0007475609325227284
preprocessing time for sampling: 1.0817747116088867
amortized time for sample size  215 is:  0.0007445504277251487
preprocessing time for sampling: 1.0780048370361328
amortized time for sample size  220 is:  0.0007428458278829403
preprocessing time for sampling: 1.0789878368377686
amortized time for sample size  225 is:  0.000743567975362142
preprocessing time for sampling: 1.0803611278533936
amortized time for sample size  230 is:  0.000747077402861222
preprocessing time for sampling: 1.0764920711517334
amortized time for sample size  235 is:  0.000744707503217332
preprocessing time for sampling: 1.093034029006958
amortized time for sample size  240 is:  0.0007467616001764933
preprocessing time for sampling: 1.0907390117645264
amortized time for sample size  245 is:  0.0007496813170763911
preprocessing time for sampling: 1.0802853107452393
amortized time for sample size  250 is:  0.0007485112380981446
*** results for plotting, beta= 1.2 

mean_list= [np.float64(0.9400000000000001), np.float64(0.97), np.float64(1.0), np.float64(0.99), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0)]
std_list= [np.float64(0.06633249580710798), np.float64(0.045825756949558386), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0)]
