beta: 0.2
preprocessing time for sampling: 0.1916179656982422
amortized time for sample size  5 is:  0.00022578239440917971
preprocessing time for sampling: 0.1899700164794922
amortized time for sample size  10 is:  0.0002271347045898437
preprocessing time for sampling: 0.1939530372619629
amortized time for sample size  15 is:  0.00022782341639200846
preprocessing time for sampling: 0.18999195098876953
amortized time for sample size  20 is:  0.000240439772605896
preprocessing time for sampling: 0.18979215621948242
amortized time for sample size  25 is:  0.00022811012268066409
preprocessing time for sampling: 0.1902790069580078
amortized time for sample size  30 is:  0.00022386805216471353
preprocessing time for sampling: 0.187208890914917
amortized time for sample size  35 is:  0.00022416734695434573
preprocessing time for sampling: 0.18865704536437988
amortized time for sample size  40 is:  0.00022436404228210448
preprocessing time for sampling: 0.1899731159210205
amortized time for sample size  45 is:  0.00022347095277574323
preprocessing time for sampling: 0.18842697143554688
amortized time for sample size  50 is:  0.00022451858520507813
preprocessing time for sampling: 0.19217205047607422
amortized time for sample size  55 is:  0.00023270377245816315
preprocessing time for sampling: 0.19266390800476074
amortized time for sample size  60 is:  0.0002323304414749146
preprocessing time for sampling: 0.18941593170166016
amortized time for sample size  65 is:  0.00022869627292339617
preprocessing time for sampling: 0.18820595741271973
amortized time for sample size  70 is:  0.00022909648077828543
preprocessing time for sampling: 0.18720722198486328
amortized time for sample size  75 is:  0.00023076632817586266
preprocessing time for sampling: 0.19017481803894043
amortized time for sample size  80 is:  0.0002325124442577362
preprocessing time for sampling: 0.1889047622680664
amortized time for sample size  85 is:  0.0002240483901079963
preprocessing time for sampling: 0.18603873252868652
amortized time for sample size  90 is:  0.00022356703546312122
preprocessing time for sampling: 0.18657517433166504
amortized time for sample size  95 is:  0.00022355689500507556
preprocessing time for sampling: 0.1869068145751953
amortized time for sample size  100 is:  0.00022854762077331543
preprocessing time for sampling: 0.1922459602355957
amortized time for sample size  105 is:  0.0002230468704586937
preprocessing time for sampling: 0.18879103660583496
amortized time for sample size  110 is:  0.0002236575863578103
preprocessing time for sampling: 0.18922901153564453
amortized time for sample size  115 is:  0.0002244930060013481
preprocessing time for sampling: 0.18936705589294434
amortized time for sample size  120 is:  0.00022381552060445151
preprocessing time for sampling: 0.18887090682983398
amortized time for sample size  125 is:  0.00022463932037353516
preprocessing time for sampling: 0.18893218040466309
amortized time for sample size  130 is:  0.00022422983096196105
preprocessing time for sampling: 0.1896369457244873
amortized time for sample size  135 is:  0.00022399930600766786
preprocessing time for sampling: 0.1886909008026123
amortized time for sample size  140 is:  0.00022394222872597832
preprocessing time for sampling: 0.18966889381408691
amortized time for sample size  145 is:  0.00022547309152011211
preprocessing time for sampling: 0.18867802619934082
amortized time for sample size  150 is:  0.00022488587697347008
preprocessing time for sampling: 0.1888282299041748
amortized time for sample size  155 is:  0.00022702387840517105
preprocessing time for sampling: 0.18913722038269043
amortized time for sample size  160 is:  0.00022562748193740844
preprocessing time for sampling: 0.1887068748474121
amortized time for sample size  165 is:  0.00022643490993615355
preprocessing time for sampling: 0.19072723388671875
amortized time for sample size  170 is:  0.0002254797430599437
preprocessing time for sampling: 0.18914294242858887
amortized time for sample size  175 is:  0.0002264283997671945
preprocessing time for sampling: 0.1891770362854004
amortized time for sample size  180 is:  0.00022578142748938668
preprocessing time for sampling: 0.18864202499389648
amortized time for sample size  185 is:  0.0002258779551531817
preprocessing time for sampling: 0.18914484977722168
amortized time for sample size  190 is:  0.00022439588998493396
preprocessing time for sampling: 0.1911008358001709
amortized time for sample size  195 is:  0.0002282965488922901
preprocessing time for sampling: 0.19341182708740234
amortized time for sample size  200 is:  0.00022896337509155276
preprocessing time for sampling: 0.19433069229125977
amortized time for sample size  205 is:  0.00022671892584823986
preprocessing time for sampling: 0.19109201431274414
amortized time for sample size  210 is:  0.00022501122383844288
preprocessing time for sampling: 0.19308686256408691
amortized time for sample size  215 is:  0.00022816358610641127
preprocessing time for sampling: 0.2132718563079834
amortized time for sample size  220 is:  0.00022507498481056908
preprocessing time for sampling: 0.18992209434509277
amortized time for sample size  225 is:  0.00022451139026217988
preprocessing time for sampling: 0.18938398361206055
amortized time for sample size  230 is:  0.0002243335661680802
preprocessing time for sampling: 0.1894516944885254
amortized time for sample size  235 is:  0.0002246988783491419
preprocessing time for sampling: 0.18889379501342773
amortized time for sample size  240 is:  0.00022422340512275694
preprocessing time for sampling: 0.18950200080871582
amortized time for sample size  245 is:  0.00022394353516247807
preprocessing time for sampling: 0.18875813484191895
amortized time for sample size  250 is:  0.00022505869865417486
*** results for plotting, beta= 0.2 

mean_list= [np.float64(0.32999999999999996), np.float64(0.5199999999999999), np.float64(0.53), np.float64(0.57), np.float64(0.5599999999999999), np.float64(0.49000000000000005), np.float64(0.5700000000000001), np.float64(0.6399999999999999), np.float64(0.51), np.float64(0.5), np.float64(0.6699999999999999), np.float64(0.69), np.float64(0.64), np.float64(0.58), np.float64(0.6), np.float64(0.71), np.float64(0.6), np.float64(0.66), np.float64(0.6799999999999999), np.float64(0.7), np.float64(0.6599999999999999), np.float64(0.7200000000000001), np.float64(0.7), np.float64(0.6799999999999999), np.float64(0.71), np.float64(0.76), np.float64(0.63), np.float64(0.6100000000000001), np.float64(0.72), np.float64(0.6900000000000001), np.float64(0.76), np.float64(0.78), np.float64(0.6), np.float64(0.72), np.float64(0.76), np.float64(0.72), np.float64(0.7800000000000001), np.float64(0.75), np.float64(0.71), np.float64(0.74), np.float64(0.6900000000000001), np.float64(0.73), np.float64(0.78), np.float64(0.74), np.float64(0.64), np.float64(0.76), np.float64(0.7), np.float64(0.7800000000000001), np.float64(0.8099999999999999), np.float64(0.7)]
std_list= [np.float64(0.12688577540449522), np.float64(0.10770329614269006), np.float64(0.14177446878757824), np.float64(0.14866068747318506), np.float64(0.22449944320643647), np.float64(0.16401219466856726), np.float64(0.14866068747318506), np.float64(0.2154065922853802), np.float64(0.1445683229480096), np.float64(0.17320508075688773), np.float64(0.12688577540449522), np.float64(0.157797338380595), np.float64(0.1562049935181331), np.float64(0.1469693845669907), np.float64(0.1341640786499874), np.float64(0.12206555615733705), np.float64(0.1341640786499874), np.float64(0.19595917942265426), np.float64(0.13999999999999999), np.float64(0.11832159566199235), np.float64(0.13564659966250536), np.float64(0.16613247725836153), np.float64(0.14832396974191325), np.float64(0.19390719429665318), np.float64(0.20223748416156684), np.float64(0.10198039027185572), np.float64(0.20024984394500786), np.float64(0.16401219466856723), np.float64(0.10770329614269011), np.float64(0.11357816691600549), np.float64(0.128062484748657), np.float64(0.0871779788708135), np.float64(0.14142135623730953), np.float64(0.11661903789690603), np.float64(0.09165151389911683), np.float64(0.18330302779823363), np.float64(0.14696938456699069), np.float64(0.12041594578792297), np.float64(0.1135781669160055), np.float64(0.14282856857085702), np.float64(0.1972308292331602), np.float64(0.14866068747318506), np.float64(0.12489995996796799), np.float64(0.128062484748657), np.float64(0.14282856857085702), np.float64(0.1356465996625054), np.float64(0.10000000000000003), np.float64(0.12489995996796797), np.float64(0.13000000000000003), np.float64(0.11832159566199235)]
beta: 0.4
preprocessing time for sampling: 0.18908333778381348
amortized time for sample size  5 is:  0.00022394657135009762
preprocessing time for sampling: 0.18627595901489258
amortized time for sample size  10 is:  0.00022348451614379882
preprocessing time for sampling: 0.1863539218902588
amortized time for sample size  15 is:  0.00022363440195719396
preprocessing time for sampling: 0.18738102912902832
amortized time for sample size  20 is:  0.00022339022159576419
preprocessing time for sampling: 0.18847990036010742
amortized time for sample size  25 is:  0.000223717212677002
preprocessing time for sampling: 0.1887218952178955
amortized time for sample size  30 is:  0.00022454452514648435
preprocessing time for sampling: 0.1884479522705078
amortized time for sample size  35 is:  0.00022323540278843467
preprocessing time for sampling: 0.18896198272705078
amortized time for sample size  40 is:  0.00022276449203491213
preprocessing time for sampling: 0.186445951461792
amortized time for sample size  45 is:  0.00022329235076904298
preprocessing time for sampling: 0.1861109733581543
amortized time for sample size  50 is:  0.00022340869903564447
preprocessing time for sampling: 0.1889021396636963
amortized time for sample size  55 is:  0.00022320487282492896
preprocessing time for sampling: 0.1890087127685547
amortized time for sample size  60 is:  0.0002234696944554646
preprocessing time for sampling: 0.18891596794128418
amortized time for sample size  65 is:  0.00022374960092397836
preprocessing time for sampling: 0.18885397911071777
amortized time for sample size  70 is:  0.00022310713359287808
preprocessing time for sampling: 0.19049596786499023
amortized time for sample size  75 is:  0.0002231161117553711
preprocessing time for sampling: 0.19180798530578613
amortized time for sample size  80 is:  0.0002237052321434021
preprocessing time for sampling: 0.18619203567504883
amortized time for sample size  85 is:  0.0002234823002534754
preprocessing time for sampling: 0.18602395057678223
amortized time for sample size  90 is:  0.00022341783841451002
preprocessing time for sampling: 0.19129180908203125
amortized time for sample size  95 is:  0.00022330530066239207
preprocessing time for sampling: 0.18877816200256348
amortized time for sample size  100 is:  0.0002236197948455811
preprocessing time for sampling: 0.18891096115112305
amortized time for sample size  105 is:  0.00022374716259184336
preprocessing time for sampling: 0.18825006484985352
amortized time for sample size  110 is:  0.00022343535856767131
preprocessing time for sampling: 0.1864619255065918
amortized time for sample size  115 is:  0.00022317529761272926
preprocessing time for sampling: 0.186506986618042
amortized time for sample size  120 is:  0.00022319378455479938
preprocessing time for sampling: 0.1884307861328125
amortized time for sample size  125 is:  0.0002235358428955078
preprocessing time for sampling: 0.1886887550354004
amortized time for sample size  130 is:  0.00022376192533052884
preprocessing time for sampling: 0.18833518028259277
amortized time for sample size  135 is:  0.00022354306115044493
preprocessing time for sampling: 0.18831515312194824
amortized time for sample size  140 is:  0.0002234741619655064
preprocessing time for sampling: 0.1862173080444336
amortized time for sample size  145 is:  0.00022353137772658776
preprocessing time for sampling: 0.18692302703857422
amortized time for sample size  150 is:  0.00022541122436523436
preprocessing time for sampling: 0.1887509822845459
amortized time for sample size  155 is:  0.00022456505990797474
preprocessing time for sampling: 0.18898582458496094
amortized time for sample size  160 is:  0.00022455254197120664
preprocessing time for sampling: 0.18964910507202148
amortized time for sample size  165 is:  0.0002244103460600882
preprocessing time for sampling: 0.18941378593444824
amortized time for sample size  170 is:  0.00022442082797779757
preprocessing time for sampling: 0.1869349479675293
amortized time for sample size  175 is:  0.00022404711587088445
preprocessing time for sampling: 0.186784029006958
amortized time for sample size  180 is:  0.00022466831737094455
preprocessing time for sampling: 0.18916988372802734
amortized time for sample size  185 is:  0.00022468838820586333
preprocessing time for sampling: 0.1943378448486328
amortized time for sample size  190 is:  0.00022467344685604698
preprocessing time for sampling: 0.18813419342041016
amortized time for sample size  195 is:  0.00022572277753781045
preprocessing time for sampling: 0.1902480125427246
amortized time for sample size  200 is:  0.00022442092895507817
preprocessing time for sampling: 0.18619799613952637
amortized time for sample size  205 is:  0.00022450877398979375
preprocessing time for sampling: 0.18607187271118164
amortized time for sample size  210 is:  0.000224193186987014
preprocessing time for sampling: 0.18833613395690918
amortized time for sample size  215 is:  0.00022487123622450713
preprocessing time for sampling: 0.18857121467590332
amortized time for sample size  220 is:  0.00022428364103490656
preprocessing time for sampling: 0.1883702278137207
amortized time for sample size  225 is:  0.00022461820178561743
preprocessing time for sampling: 0.18817591667175293
amortized time for sample size  230 is:  0.0002252381262571915
preprocessing time for sampling: 0.18629193305969238
amortized time for sample size  235 is:  0.0002251606393367686
preprocessing time for sampling: 0.18609976768493652
amortized time for sample size  240 is:  0.00022417609890302022
preprocessing time for sampling: 0.18859601020812988
amortized time for sample size  245 is:  0.00022597956170841138
preprocessing time for sampling: 0.1882622241973877
amortized time for sample size  250 is:  0.00022573473930358892
*** results for plotting, beta= 0.4 

mean_list= [np.float64(0.5499999999999999), np.float64(0.6599999999999999), np.float64(0.75), np.float64(0.86), np.float64(0.76), np.float64(0.8100000000000002), np.float64(0.85), np.float64(0.86), np.float64(0.8700000000000001), np.float64(0.9199999999999999), np.float64(0.9099999999999999), np.float64(0.9199999999999999), np.float64(0.85), np.float64(0.8200000000000001), np.float64(0.93), np.float64(0.9100000000000001), np.float64(0.9400000000000001), np.float64(0.95), np.float64(0.89), np.float64(0.8600000000000001), np.float64(0.9), np.float64(0.8700000000000001), np.float64(0.96), np.float64(0.9199999999999999), np.float64(0.93), np.float64(0.96), np.float64(0.9600000000000002), np.float64(0.9400000000000001), np.float64(0.95), np.float64(0.95), np.float64(0.96), np.float64(0.97), np.float64(0.97), np.float64(0.9700000000000001), np.float64(0.99), np.float64(0.97), np.float64(0.97), np.float64(0.97), np.float64(0.9800000000000001), np.float64(0.9700000000000001), np.float64(0.99), np.float64(0.99), np.float64(0.9800000000000001), np.float64(0.9800000000000001), np.float64(0.9700000000000001), np.float64(0.97), np.float64(0.99), np.float64(0.99), np.float64(0.9700000000000001), np.float64(0.99)]
std_list= [np.float64(0.10246950765959596), np.float64(0.10198039027185568), np.float64(0.15000000000000002), np.float64(0.128062484748657), np.float64(0.14282856857085702), np.float64(0.12206555615733705), np.float64(0.12041594578792296), np.float64(0.10198039027185571), np.float64(0.10049875621120889), np.float64(0.0748331477354788), np.float64(0.08306623862918072), np.float64(0.09797958971132714), np.float64(0.09219544457292889), np.float64(0.15362291495737218), np.float64(0.07810249675906653), np.float64(0.05385164807134503), np.float64(0.06633249580710798), np.float64(0.04999999999999999), np.float64(0.08306623862918075), np.float64(0.06633249580710798), np.float64(0.11832159566199232), np.float64(0.07810249675906655), np.float64(0.06633249580710798), np.float64(0.1077032961426901), np.float64(0.07810249675906653), np.float64(0.04898979485566355), np.float64(0.06633249580710798), np.float64(0.04898979485566354), np.float64(0.06708203932499368), np.float64(0.06708203932499367), np.float64(0.04898979485566356), np.float64(0.04582575694955839), np.float64(0.04582575694955839), np.float64(0.04582575694955839), np.float64(0.029999999999999992), np.float64(0.04582575694955839), np.float64(0.04582575694955839), np.float64(0.06403124237432847), np.float64(0.05999999999999999), np.float64(0.04582575694955839), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.039999999999999994), np.float64(0.05999999999999999), np.float64(0.04582575694955839), np.float64(0.04582575694955839), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.04582575694955839), np.float64(0.029999999999999992)]
beta: 0.6
preprocessing time for sampling: 0.18926501274108887
amortized time for sample size  5 is:  0.00022492647171020507
preprocessing time for sampling: 0.18634605407714844
amortized time for sample size  10 is:  0.0002265193462371826
preprocessing time for sampling: 0.1869509220123291
amortized time for sample size  15 is:  0.00022681236267089845
preprocessing time for sampling: 0.18635821342468262
amortized time for sample size  20 is:  0.00022535371780395508
preprocessing time for sampling: 0.1887528896331787
amortized time for sample size  25 is:  0.00022399196624755854
preprocessing time for sampling: 0.18875813484191895
amortized time for sample size  30 is:  0.00022509773572285973
preprocessing time for sampling: 0.1889021396636963
amortized time for sample size  35 is:  0.0002250888007027762
preprocessing time for sampling: 0.1904759407043457
amortized time for sample size  40 is:  0.00022573214769363407
preprocessing time for sampling: 0.18690180778503418
amortized time for sample size  45 is:  0.0002289026048448351
preprocessing time for sampling: 0.18623995780944824
amortized time for sample size  50 is:  0.00022449164390563967
preprocessing time for sampling: 0.1891031265258789
amortized time for sample size  55 is:  0.00022563405470414595
preprocessing time for sampling: 0.18932080268859863
amortized time for sample size  60 is:  0.00022384202480316167
preprocessing time for sampling: 0.1890559196472168
amortized time for sample size  65 is:  0.0002237730759840745
preprocessing time for sampling: 0.18891692161560059
amortized time for sample size  70 is:  0.0002240332535334996
preprocessing time for sampling: 0.18902206420898438
amortized time for sample size  75 is:  0.00022517391840616861
preprocessing time for sampling: 0.18932080268859863
amortized time for sample size  80 is:  0.00022647121548652647
preprocessing time for sampling: 0.1865227222442627
amortized time for sample size  85 is:  0.00022731441609999715
preprocessing time for sampling: 0.18629193305969238
amortized time for sample size  90 is:  0.0002246156268649631
preprocessing time for sampling: 0.18860912322998047
amortized time for sample size  95 is:  0.00022586739690680255
preprocessing time for sampling: 0.18873000144958496
amortized time for sample size  100 is:  0.00022404501438140872
preprocessing time for sampling: 0.18828105926513672
amortized time for sample size  105 is:  0.00022396557671683172
preprocessing time for sampling: 0.19043707847595215
amortized time for sample size  110 is:  0.00022404889626936476
preprocessing time for sampling: 0.18610692024230957
amortized time for sample size  115 is:  0.00022537457424661386
preprocessing time for sampling: 0.18680095672607422
amortized time for sample size  120 is:  0.0002241782546043396
preprocessing time for sampling: 0.18891000747680664
amortized time for sample size  125 is:  0.00022414405822753902
preprocessing time for sampling: 0.18835711479187012
amortized time for sample size  130 is:  0.0002236300064967229
preprocessing time for sampling: 0.18888211250305176
amortized time for sample size  135 is:  0.00022383774651421444
preprocessing time for sampling: 0.18842291831970215
amortized time for sample size  140 is:  0.0002243498734065465
preprocessing time for sampling: 0.18615293502807617
amortized time for sample size  145 is:  0.0002272013466933678
preprocessing time for sampling: 0.18631601333618164
amortized time for sample size  150 is:  0.00022847270965576177
preprocessing time for sampling: 0.19025206565856934
amortized time for sample size  155 is:  0.00022638376297489288
preprocessing time for sampling: 0.18904495239257812
amortized time for sample size  160 is:  0.00022751653194427496
preprocessing time for sampling: 0.18984508514404297
amortized time for sample size  165 is:  0.00022634334275216766
preprocessing time for sampling: 0.1922001838684082
amortized time for sample size  170 is:  0.00022501851530636055
preprocessing time for sampling: 0.18695282936096191
amortized time for sample size  175 is:  0.00022821423666817802
preprocessing time for sampling: 0.18645811080932617
amortized time for sample size  180 is:  0.00022599433528052438
preprocessing time for sampling: 0.19085216522216797
amortized time for sample size  185 is:  0.0002263964446815285
preprocessing time for sampling: 0.18859505653381348
amortized time for sample size  190 is:  0.00022441039587322035
preprocessing time for sampling: 0.18875598907470703
amortized time for sample size  195 is:  0.00022557064203115613
preprocessing time for sampling: 0.18898892402648926
amortized time for sample size  200 is:  0.0002266282081604004
preprocessing time for sampling: 0.18721675872802734
amortized time for sample size  205 is:  0.00022584121983225752
preprocessing time for sampling: 0.18741512298583984
amortized time for sample size  210 is:  0.00022730659303211033
preprocessing time for sampling: 0.18967509269714355
amortized time for sample size  215 is:  0.0002270654523095419
preprocessing time for sampling: 0.19267821311950684
amortized time for sample size  220 is:  0.0002279733961278742
preprocessing time for sampling: 0.19352078437805176
amortized time for sample size  225 is:  0.0002273739708794488
preprocessing time for sampling: 0.19198894500732422
amortized time for sample size  230 is:  0.0002277456677478293
preprocessing time for sampling: 0.19019484519958496
amortized time for sample size  235 is:  0.00022824947884742255
preprocessing time for sampling: 0.18797087669372559
amortized time for sample size  240 is:  0.00022823421160380044
preprocessing time for sampling: 0.1910390853881836
amortized time for sample size  245 is:  0.00022860112482187703
preprocessing time for sampling: 0.18934178352355957
amortized time for sample size  250 is:  0.00022791257858276369
*** results for plotting, beta= 0.6 

mean_list= [np.float64(0.68), np.float64(0.74), np.float64(0.89), np.float64(0.95), np.float64(0.9100000000000001), np.float64(0.9400000000000001), np.float64(0.9800000000000001), np.float64(0.9800000000000001), np.float64(0.97), np.float64(0.97), np.float64(0.99), np.float64(0.9700000000000001), np.float64(0.9800000000000001), np.float64(1.0), np.float64(1.0), np.float64(0.99), 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(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(0.99), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0)]
std_list= [np.float64(0.16613247725836153), np.float64(0.09165151389911683), np.float64(0.11357816691600547), np.float64(0.06708203932499368), np.float64(0.06999999999999999), np.float64(0.06633249580710798), np.float64(0.039999999999999994), np.float64(0.039999999999999994), np.float64(0.04582575694955839), np.float64(0.04582575694955839), np.float64(0.029999999999999992), np.float64(0.04582575694955839), np.float64(0.039999999999999994), np.float64(0.0), np.float64(0.0), np.float64(0.029999999999999992), 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(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0)]
beta: 0.8
preprocessing time for sampling: 0.18967294692993164
amortized time for sample size  5 is:  0.00022479104995727536
preprocessing time for sampling: 0.18732309341430664
amortized time for sample size  10 is:  0.00022740578651428225
preprocessing time for sampling: 0.18860077857971191
amortized time for sample size  15 is:  0.0002266573905944824
preprocessing time for sampling: 0.187424898147583
amortized time for sample size  20 is:  0.000226934552192688
preprocessing time for sampling: 0.18871188163757324
amortized time for sample size  25 is:  0.00022734327316284173
preprocessing time for sampling: 0.19020676612854004
amortized time for sample size  30 is:  0.00022636342048645023
preprocessing time for sampling: 0.1922309398651123
amortized time for sample size  35 is:  0.00022681747164045058
preprocessing time for sampling: 0.1894540786743164
amortized time for sample size  40 is:  0.00022688651084899904
preprocessing time for sampling: 0.1873319149017334
amortized time for sample size  45 is:  0.0002272008260091146
preprocessing time for sampling: 0.18646717071533203
amortized time for sample size  50 is:  0.0002267746448516846
preprocessing time for sampling: 0.19260215759277344
amortized time for sample size  55 is:  0.00022689385847611857
preprocessing time for sampling: 0.1929028034210205
amortized time for sample size  60 is:  0.00022733227411905928
preprocessing time for sampling: 0.19155097007751465
amortized time for sample size  65 is:  0.00022694019170907826
preprocessing time for sampling: 0.18622708320617676
amortized time for sample size  70 is:  0.0002272092614855085
preprocessing time for sampling: 0.192155122756958
amortized time for sample size  75 is:  0.0002268427530924479
preprocessing time for sampling: 0.1926419734954834
amortized time for sample size  80 is:  0.00022926515340805057
preprocessing time for sampling: 0.1967301368713379
amortized time for sample size  85 is:  0.00023194063411039465
preprocessing time for sampling: 0.19575715065002441
amortized time for sample size  90 is:  0.00022873679796854657
preprocessing time for sampling: 0.18862509727478027
amortized time for sample size  95 is:  0.0002273787950214587
preprocessing time for sampling: 0.1903400421142578
amortized time for sample size  100 is:  0.00022786452770233152
preprocessing time for sampling: 0.1922318935394287
amortized time for sample size  105 is:  0.00022727664311726888
preprocessing time for sampling: 0.19201016426086426
amortized time for sample size  110 is:  0.00022782338749278676
preprocessing time for sampling: 0.19234418869018555
amortized time for sample size  115 is:  0.00022771516053572943
preprocessing time for sampling: 0.19120502471923828
amortized time for sample size  120 is:  0.00022829407453536988
preprocessing time for sampling: 0.18987703323364258
amortized time for sample size  125 is:  0.00022920211791992195
preprocessing time for sampling: 0.18987011909484863
amortized time for sample size  130 is:  0.00022823502467228816
preprocessing time for sampling: 0.19200491905212402
amortized time for sample size  135 is:  0.000228179101590757
preprocessing time for sampling: 0.1907188892364502
amortized time for sample size  140 is:  0.0002283752816064017
preprocessing time for sampling: 0.18949198722839355
amortized time for sample size  145 is:  0.00022834406227901068
preprocessing time for sampling: 0.19162797927856445
amortized time for sample size  150 is:  0.00022822154362996417
preprocessing time for sampling: 0.18973493576049805
amortized time for sample size  155 is:  0.00022825610253118702
preprocessing time for sampling: 0.18752408027648926
amortized time for sample size  160 is:  0.00022809553146362307
preprocessing time for sampling: 0.19100475311279297
amortized time for sample size  165 is:  0.000228372284860322
preprocessing time for sampling: 0.19191622734069824
amortized time for sample size  170 is:  0.00022814228955437155
preprocessing time for sampling: 0.19448018074035645
amortized time for sample size  175 is:  0.00022839488983154296
preprocessing time for sampling: 0.19187307357788086
amortized time for sample size  180 is:  0.00022846480210622153
preprocessing time for sampling: 0.19010615348815918
amortized time for sample size  185 is:  0.00022826585254153692
preprocessing time for sampling: 0.18874001502990723
amortized time for sample size  190 is:  0.00022802612656041193
preprocessing time for sampling: 0.19259285926818848
amortized time for sample size  195 is:  0.00022856138914059367
preprocessing time for sampling: 0.1923069953918457
amortized time for sample size  200 is:  0.00022891315221786502
preprocessing time for sampling: 0.1921999454498291
amortized time for sample size  205 is:  0.00022788283883071525
preprocessing time for sampling: 0.19208288192749023
amortized time for sample size  210 is:  0.0002284868558247884
preprocessing time for sampling: 0.1900491714477539
amortized time for sample size  215 is:  0.00022855127689450284
preprocessing time for sampling: 0.18992114067077637
amortized time for sample size  220 is:  0.0002282115221023559
preprocessing time for sampling: 0.19206476211547852
amortized time for sample size  225 is:  0.00023006104363335503
preprocessing time for sampling: 0.19274377822875977
amortized time for sample size  230 is:  0.00022922475441642428
preprocessing time for sampling: 0.19228291511535645
amortized time for sample size  235 is:  0.00022857518906288957
preprocessing time for sampling: 0.19216632843017578
amortized time for sample size  240 is:  0.00022838617364565535
preprocessing time for sampling: 0.19033503532409668
amortized time for sample size  245 is:  0.00022769832611083986
preprocessing time for sampling: 0.19001102447509766
amortized time for sample size  250 is:  0.00022775141716003419
*** results for plotting, beta= 0.8 

mean_list= [np.float64(0.8400000000000001), np.float64(0.95), np.float64(0.95), np.float64(0.97), np.float64(0.9800000000000001), np.float64(0.99), np.float64(0.99), np.float64(1.0), np.float64(1.0), np.float64(0.99), np.float64(0.99), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), 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(0.14966629547095767), np.float64(0.06708203932499368), np.float64(0.06708203932499367), np.float64(0.04582575694955839), np.float64(0.039999999999999994), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), 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: 0.2255258560180664
amortized time for sample size  5 is:  0.00023935079574584966
preprocessing time for sampling: 0.22550010681152344
amortized time for sample size  10 is:  0.00024525856971740725
preprocessing time for sampling: 0.22680997848510742
amortized time for sample size  15 is:  0.00023966534932454427
preprocessing time for sampling: 0.22580718994140625
amortized time for sample size  20 is:  0.0002394458055496216
preprocessing time for sampling: 0.2242288589477539
amortized time for sample size  25 is:  0.0002398517608642578
preprocessing time for sampling: 0.22605419158935547
amortized time for sample size  30 is:  0.00023981730143229167
preprocessing time for sampling: 0.2256450653076172
amortized time for sample size  35 is:  0.0002398208209446498
preprocessing time for sampling: 0.22522902488708496
amortized time for sample size  40 is:  0.00024098676443099976
preprocessing time for sampling: 0.22492098808288574
amortized time for sample size  45 is:  0.00023885149425930446
preprocessing time for sampling: 0.22407197952270508
amortized time for sample size  50 is:  0.0002390259742736817
preprocessing time for sampling: 0.2243788242340088
amortized time for sample size  55 is:  0.00023858551545576613
preprocessing time for sampling: 0.2252352237701416
amortized time for sample size  60 is:  0.00023917516072591147
preprocessing time for sampling: 0.2249300479888916
amortized time for sample size  65 is:  0.0002398647895226112
preprocessing time for sampling: 0.22379493713378906
amortized time for sample size  70 is:  0.0002384297847747803
preprocessing time for sampling: 0.22476601600646973
amortized time for sample size  75 is:  0.00023850663503011067
preprocessing time for sampling: 0.22362112998962402
amortized time for sample size  80 is:  0.00023857060074806215
preprocessing time for sampling: 0.22348427772521973
amortized time for sample size  85 is:  0.00023879236333510453
preprocessing time for sampling: 0.2225031852722168
amortized time for sample size  90 is:  0.00023908742268880206
preprocessing time for sampling: 0.22490501403808594
amortized time for sample size  95 is:  0.00023835187209279913
preprocessing time for sampling: 0.22481894493103027
amortized time for sample size  100 is:  0.00023857686519622803
preprocessing time for sampling: 0.22418928146362305
amortized time for sample size  105 is:  0.00023903272265479676
preprocessing time for sampling: 0.22374701499938965
amortized time for sample size  110 is:  0.00023908821019259365
preprocessing time for sampling: 0.2234961986541748
amortized time for sample size  115 is:  0.0002387260561404021
preprocessing time for sampling: 0.22313809394836426
amortized time for sample size  120 is:  0.00023866983254750568
preprocessing time for sampling: 0.22495007514953613
amortized time for sample size  125 is:  0.00023938051223754885
preprocessing time for sampling: 0.22803473472595215
amortized time for sample size  130 is:  0.0002395588801457332
preprocessing time for sampling: 0.2246110439300537
amortized time for sample size  135 is:  0.00023972744411892362
preprocessing time for sampling: 0.22388982772827148
amortized time for sample size  140 is:  0.00023911241122654504
preprocessing time for sampling: 0.22329497337341309
amortized time for sample size  145 is:  0.0002392601144724879
preprocessing time for sampling: 0.22386384010314941
amortized time for sample size  150 is:  0.0002398307641347249
preprocessing time for sampling: 0.22985291481018066
amortized time for sample size  155 is:  0.00023892679522114415
preprocessing time for sampling: 0.2251262664794922
amortized time for sample size  160 is:  0.00023924833536148068
preprocessing time for sampling: 0.22497105598449707
amortized time for sample size  165 is:  0.00023990243853944725
preprocessing time for sampling: 0.22362709045410156
amortized time for sample size  170 is:  0.00023971107426811668
preprocessing time for sampling: 0.2237248420715332
amortized time for sample size  175 is:  0.00023972557612827845
preprocessing time for sampling: 0.22391200065612793
amortized time for sample size  180 is:  0.00024072240458594427
preprocessing time for sampling: 0.22494888305664062
amortized time for sample size  185 is:  0.00023993613268878008
preprocessing time for sampling: 0.22497892379760742
amortized time for sample size  190 is:  0.0002419526827962775
preprocessing time for sampling: 0.22442388534545898
amortized time for sample size  195 is:  0.0035582128916031284
preprocessing time for sampling: 0.22152185440063477
amortized time for sample size  200 is:  0.0002360015392303467
preprocessing time for sampling: 0.2195267677307129
amortized time for sample size  205 is:  0.00023635635143373073
preprocessing time for sampling: 0.21933984756469727
amortized time for sample size  210 is:  0.00023744155111766997
preprocessing time for sampling: 0.2230379581451416
amortized time for sample size  215 is:  0.00023754133180130358
preprocessing time for sampling: 0.2205500602722168
amortized time for sample size  220 is:  0.00024103049798445265
preprocessing time for sampling: 0.22115588188171387
amortized time for sample size  225 is:  0.00023856846491495772
preprocessing time for sampling: 0.21945667266845703
amortized time for sample size  230 is:  0.000235647263734237
preprocessing time for sampling: 0.2198951244354248
amortized time for sample size  235 is:  0.00023637357671210107
preprocessing time for sampling: 0.21964597702026367
amortized time for sample size  240 is:  0.0002369470596313477
preprocessing time for sampling: 0.22106599807739258
amortized time for sample size  245 is:  0.00023598530827736368
preprocessing time for sampling: 0.22211480140686035
amortized time for sample size  250 is:  0.00023738967895507813
*** results for plotting, beta= 1 

mean_list= [np.float64(0.93), np.float64(0.97), 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), np.float64(1.0)]
std_list= [np.float64(0.09), np.float64(0.04582575694955839), 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), np.float64(0.0)]
beta: 1.2
preprocessing time for sampling: 0.1891310214996338
amortized time for sample size  5 is:  0.00022372627258300778
preprocessing time for sampling: 0.1869499683380127
amortized time for sample size  10 is:  0.00022626566886901854
preprocessing time for sampling: 0.18633794784545898
amortized time for sample size  15 is:  0.0002239977518717448
preprocessing time for sampling: 0.18934988975524902
amortized time for sample size  20 is:  0.0002230358123779297
preprocessing time for sampling: 0.1886138916015625
amortized time for sample size  25 is:  0.00022351398468017578
preprocessing time for sampling: 0.186553955078125
amortized time for sample size  30 is:  0.00022535022099812822
preprocessing time for sampling: 0.1894831657409668
amortized time for sample size  35 is:  0.0002261503083365304
preprocessing time for sampling: 0.19310212135314941
amortized time for sample size  40 is:  0.00022497010231018068
preprocessing time for sampling: 0.1862490177154541
amortized time for sample size  45 is:  0.0002282628483242459
preprocessing time for sampling: 0.1916501522064209
amortized time for sample size  50 is:  0.00023081846237182617
preprocessing time for sampling: 0.18901610374450684
amortized time for sample size  55 is:  0.00022507819262417887
preprocessing time for sampling: 0.18674802780151367
amortized time for sample size  60 is:  0.00022637104988098143
preprocessing time for sampling: 0.19109702110290527
amortized time for sample size  65 is:  0.00022998795142540566
preprocessing time for sampling: 0.19043993949890137
amortized time for sample size  70 is:  0.00022765391213553293
preprocessing time for sampling: 0.19089889526367188
amortized time for sample size  75 is:  0.0002275464693705241
preprocessing time for sampling: 0.19010305404663086
amortized time for sample size  80 is:  0.00022773382067680357
preprocessing time for sampling: 0.1907060146331787
amortized time for sample size  85 is:  0.00022721531811882467
preprocessing time for sampling: 0.19088387489318848
amortized time for sample size  90 is:  0.00022951515515645345
preprocessing time for sampling: 0.19140410423278809
amortized time for sample size  95 is:  0.00022860484374196904
preprocessing time for sampling: 0.1876201629638672
amortized time for sample size  100 is:  0.00022914116382598878
preprocessing time for sampling: 0.1922600269317627
amortized time for sample size  105 is:  0.00022994886125837056
preprocessing time for sampling: 0.19220781326293945
amortized time for sample size  110 is:  0.0002272933613170277
preprocessing time for sampling: 0.18850111961364746
amortized time for sample size  115 is:  0.00022692319621210513
preprocessing time for sampling: 0.19109797477722168
amortized time for sample size  120 is:  0.00023109944661458333
preprocessing time for sampling: 0.1938769817352295
amortized time for sample size  125 is:  0.0002276728057861328
preprocessing time for sampling: 0.1900479793548584
amortized time for sample size  130 is:  0.0002271475791931152
preprocessing time for sampling: 0.19271230697631836
amortized time for sample size  135 is:  0.00022769797289813004
preprocessing time for sampling: 0.19306612014770508
amortized time for sample size  140 is:  0.00022997558116912839
preprocessing time for sampling: 0.19087910652160645
amortized time for sample size  145 is:  0.0002300082239611396
preprocessing time for sampling: 0.22506380081176758
amortized time for sample size  150 is:  0.00022921754519144696
preprocessing time for sampling: 0.19345784187316895
amortized time for sample size  155 is:  0.00022981729815083163
preprocessing time for sampling: 0.1900651454925537
amortized time for sample size  160 is:  0.0002281738817691803
preprocessing time for sampling: 0.19226980209350586
amortized time for sample size  165 is:  0.00022807031689268172
preprocessing time for sampling: 0.1920158863067627
amortized time for sample size  170 is:  0.00022985973077661854
preprocessing time for sampling: 0.19096803665161133
amortized time for sample size  175 is:  0.00022856232779366629
preprocessing time for sampling: 0.19249510765075684
amortized time for sample size  180 is:  0.00022923900021447078
preprocessing time for sampling: 0.1933000087738037
amortized time for sample size  185 is:  0.00023410440135646513
preprocessing time for sampling: 0.19219684600830078
amortized time for sample size  190 is:  0.00022815363030684622
preprocessing time for sampling: 0.19116997718811035
amortized time for sample size  195 is:  0.00022885188078268978
preprocessing time for sampling: 0.19527697563171387
amortized time for sample size  200 is:  0.0002301879048347473
preprocessing time for sampling: 0.19008517265319824
amortized time for sample size  205 is:  0.0002279500263493235
preprocessing time for sampling: 0.19269394874572754
amortized time for sample size  210 is:  0.00022814846038818362
preprocessing time for sampling: 0.19182705879211426
amortized time for sample size  215 is:  0.00022779448087825334
preprocessing time for sampling: 0.18976092338562012
amortized time for sample size  220 is:  0.00022810158946297385
preprocessing time for sampling: 0.19359803199768066
amortized time for sample size  225 is:  0.00022828986909654404
preprocessing time for sampling: 0.19414806365966797
amortized time for sample size  230 is:  0.00023127766277479086
preprocessing time for sampling: 0.19072771072387695
amortized time for sample size  235 is:  0.00022966580695294318
preprocessing time for sampling: 0.19249916076660156
amortized time for sample size  240 is:  0.00023024513324101763
preprocessing time for sampling: 0.19208693504333496
amortized time for sample size  245 is:  0.00022842365381669027
preprocessing time for sampling: 0.18968915939331055
amortized time for sample size  250 is:  0.00022963333129882816
*** results for plotting, beta= 1.2 

mean_list= [np.float64(0.9100000000000001), np.float64(0.99), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(0.99), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0)]
std_list= [np.float64(0.06999999999999999), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0)]
