beta: 0.2
preprocessing time for sampling: 8.912726163864136
amortized time for sample size  5 is:  0.0038542094230651857
preprocessing time for sampling: 9.00094223022461
amortized time for sample size  10 is:  0.0038667931556701667
preprocessing time for sampling: 8.927219152450562
amortized time for sample size  15 is:  0.0038441805839538575
preprocessing time for sampling: 8.944107055664062
amortized time for sample size  20 is:  0.003895045161247253
preprocessing time for sampling: 8.879570007324219
amortized time for sample size  25 is:  0.0038250397682189946
preprocessing time for sampling: 8.878825902938843
amortized time for sample size  30 is:  0.0038945338726043698
preprocessing time for sampling: 8.859776973724365
amortized time for sample size  35 is:  0.003862508501325335
preprocessing time for sampling: 8.867703676223755
amortized time for sample size  40 is:  0.00382222843170166
preprocessing time for sampling: 8.972410678863525
amortized time for sample size  45 is:  0.0037975689570109057
preprocessing time for sampling: 8.9721839427948
amortized time for sample size  50 is:  0.0037876319885253905
preprocessing time for sampling: 8.846370935440063
amortized time for sample size  55 is:  0.003843122222206809
preprocessing time for sampling: 8.917618989944458
amortized time for sample size  60 is:  0.003772095163663229
preprocessing time for sampling: 8.985489845275879
amortized time for sample size  65 is:  0.0037977656217721796
preprocessing time for sampling: 8.801263809204102
amortized time for sample size  70 is:  0.003795878376279559
preprocessing time for sampling: 8.88092303276062
amortized time for sample size  75 is:  0.003807345517476399
preprocessing time for sampling: 8.854058980941772
amortized time for sample size  80 is:  0.00379198008775711
preprocessing time for sampling: 8.79379677772522
amortized time for sample size  85 is:  0.0037606640423045444
preprocessing time for sampling: 8.824735879898071
amortized time for sample size  90 is:  0.003797244734234281
preprocessing time for sampling: 8.924006938934326
amortized time for sample size  95 is:  0.00375062894821167
preprocessing time for sampling: 8.819976091384888
amortized time for sample size  100 is:  0.0036250243425369256
preprocessing time for sampling: 8.800064086914062
amortized time for sample size  105 is:  0.0037554632822672522
preprocessing time for sampling: 8.881278991699219
amortized time for sample size  110 is:  0.0037381325635043065
preprocessing time for sampling: 8.877402067184448
amortized time for sample size  115 is:  0.0037530950670656947
preprocessing time for sampling: 8.778913021087646
amortized time for sample size  120 is:  0.0037279282410939535
preprocessing time for sampling: 8.816169023513794
amortized time for sample size  125 is:  0.0037486148834228513
preprocessing time for sampling: 8.821643114089966
amortized time for sample size  130 is:  0.003728572075183575
preprocessing time for sampling: 8.802243947982788
amortized time for sample size  135 is:  0.003753474712371826
preprocessing time for sampling: 8.836706161499023
amortized time for sample size  140 is:  0.0036869903121675767
preprocessing time for sampling: 8.781238079071045
amortized time for sample size  145 is:  0.003780843833397175
preprocessing time for sampling: 8.88539981842041
amortized time for sample size  150 is:  0.0034096819718678795
preprocessing time for sampling: 6.767395734786987
amortized time for sample size  155 is:  0.0029316218437687035
preprocessing time for sampling: 6.755759000778198
amortized time for sample size  160 is:  0.002903036996722222
preprocessing time for sampling: 6.772150039672852
amortized time for sample size  165 is:  0.0029505252549142554
preprocessing time for sampling: 6.761090993881226
amortized time for sample size  170 is:  0.002953516904045554
preprocessing time for sampling: 6.780264139175415
amortized time for sample size  175 is:  0.0028168511935642787
preprocessing time for sampling: 6.795218229293823
amortized time for sample size  180 is:  0.0028548927042219368
preprocessing time for sampling: 6.755728006362915
amortized time for sample size  185 is:  0.002815420318294216
preprocessing time for sampling: 6.767006874084473
amortized time for sample size  190 is:  0.002825953759645161
preprocessing time for sampling: 6.753929853439331
amortized time for sample size  195 is:  0.0028265038025684845
preprocessing time for sampling: 6.79456901550293
amortized time for sample size  200 is:  0.0028654767394065855
preprocessing time for sampling: 6.773529052734375
amortized time for sample size  205 is:  0.0028330733601639917
preprocessing time for sampling: 6.8055808544158936
amortized time for sample size  210 is:  0.002843719823019845
preprocessing time for sampling: 6.7847161293029785
amortized time for sample size  215 is:  0.002852020607438199
preprocessing time for sampling: 6.799337863922119
amortized time for sample size  220 is:  0.002839009328321977
preprocessing time for sampling: 6.783375024795532
amortized time for sample size  225 is:  0.04655095674726699
preprocessing time for sampling: 6.677764892578125
amortized time for sample size  230 is:  0.01926538541006005
preprocessing time for sampling: 6.718855857849121
amortized time for sample size  235 is:  0.08507392146739555
preprocessing time for sampling: 6.729442119598389
amortized time for sample size  240 is:  0.046447958767414095
preprocessing time for sampling: 6.665058851242065
amortized time for sample size  245 is:  0.0028067191085036918
preprocessing time for sampling: 910.4107310771942
amortized time for sample size  250 is:  0.0027512810516357416
*** results for plotting, beta= 0.2 

mean_list= [np.float64(0.34), np.float64(0.45999999999999996), np.float64(0.5199999999999999), np.float64(0.5700000000000001), np.float64(0.55), np.float64(0.6), np.float64(0.52), np.float64(0.6599999999999999), np.float64(0.75), np.float64(0.6499999999999999), np.float64(0.6399999999999999), np.float64(0.76), np.float64(0.63), np.float64(0.5900000000000001), np.float64(0.65), np.float64(0.78), np.float64(0.6799999999999999), np.float64(0.7799999999999999), np.float64(0.73), np.float64(0.73), np.float64(0.64), np.float64(0.72), np.float64(0.74), np.float64(0.79), np.float64(0.7), np.float64(0.74), np.float64(0.74), np.float64(0.77), np.float64(0.78), np.float64(0.8300000000000001), np.float64(0.6599999999999999), np.float64(0.78), np.float64(0.6799999999999999), np.float64(0.74), np.float64(0.8099999999999999), np.float64(0.76), np.float64(0.76), np.float64(0.86), np.float64(0.7500000000000001), np.float64(0.7700000000000001), np.float64(0.75), np.float64(0.8), np.float64(0.72), np.float64(0.8400000000000001), np.float64(0.79), np.float64(0.79), np.float64(0.78), np.float64(0.78), np.float64(0.8099999999999999), np.float64(0.8300000000000001)]
std_list= [np.float64(0.14282856857085702), np.float64(0.13564659966250536), np.float64(0.132664991614216), np.float64(0.21000000000000002), np.float64(0.08062257748298547), np.float64(0.16733200530681513), np.float64(0.13266499161421597), np.float64(0.12806248474865697), np.float64(0.18027756377319948), np.float64(0.12041594578792296), np.float64(0.11135528725660045), np.float64(0.12000000000000002), np.float64(0.10049875621120889), np.float64(0.18681541692269404), np.float64(0.15000000000000002), np.float64(0.15362291495737218), np.float64(0.07483314773547882), np.float64(0.124899959967968), np.float64(0.16155494421403513), np.float64(0.10049875621120892), np.float64(0.17435595774162696), np.float64(0.11661903789690603), np.float64(0.16248076809271922), np.float64(0.13747727084867523), np.float64(0.07745966692414837), np.float64(0.16852299546352717), np.float64(0.06633249580710804), np.float64(0.10049875621120892), np.float64(0.14), np.float64(0.11000000000000001), np.float64(0.08), np.float64(0.17204650534085256), np.float64(0.12489995996796797), np.float64(0.10198039027185572), np.float64(0.14456832294800961), np.float64(0.1356465996625054), np.float64(0.11135528725660046), np.float64(0.10198039027185571), np.float64(0.1746424919657298), np.float64(0.10049875621120893), np.float64(0.10246950765959602), np.float64(0.1341640786499874), np.float64(0.14), np.float64(0.1562049935181331), np.float64(0.10440306508910553), np.float64(0.07000000000000003), np.float64(0.12489995996796799), np.float64(0.09797958971132716), np.float64(0.12206555615733704), np.float64(0.15524174696260024)]
beta: 0.4
preprocessing time for sampling: 6.662532091140747
amortized time for sample size  5 is:  0.0029337563514709466
preprocessing time for sampling: 6.634883880615234
amortized time for sample size  10 is:  0.002947113990783692
preprocessing time for sampling: 6.658957004547119
amortized time for sample size  15 is:  0.002930407842000326
preprocessing time for sampling: 6.661581039428711
amortized time for sample size  20 is:  0.002905556082725526
preprocessing time for sampling: 6.6475489139556885
amortized time for sample size  25 is:  0.003001584529876709
preprocessing time for sampling: 6.663434982299805
amortized time for sample size  30 is:  0.0029814237753550206
preprocessing time for sampling: 6.669374942779541
amortized time for sample size  35 is:  0.0029408482142857144
preprocessing time for sampling: 6.64942193031311
amortized time for sample size  40 is:  0.00290874171257019
preprocessing time for sampling: 6.655106067657471
amortized time for sample size  45 is:  0.00287815809249878
preprocessing time for sampling: 6.6503870487213135
amortized time for sample size  50 is:  0.00283620924949646
preprocessing time for sampling: 6.667203903198242
amortized time for sample size  55 is:  0.17971229033036662
preprocessing time for sampling: 6.678859710693359
amortized time for sample size  60 is:  0.002842452843983968
preprocessing time for sampling: 6.689826965332031
amortized time for sample size  65 is:  0.14750096211066613
preprocessing time for sampling: 6.668977975845337
amortized time for sample size  70 is:  0.002808267457144601
preprocessing time for sampling: 941.7503790855408
amortized time for sample size  75 is:  0.002816833686828613
preprocessing time for sampling: 6.611516952514648
amortized time for sample size  80 is:  0.0027922636866569523
preprocessing time for sampling: 6.665201187133789
amortized time for sample size  85 is:  0.002797344600453096
preprocessing time for sampling: 6.772039890289307
amortized time for sample size  90 is:  0.0029003864129384356
preprocessing time for sampling: 6.67438006401062
amortized time for sample size  95 is:  0.10179984679975007
preprocessing time for sampling: 6.663109064102173
amortized time for sample size  100 is:  0.0027986504554748533
preprocessing time for sampling: 917.1014168262482
amortized time for sample size  105 is:  0.0027989502634320935
preprocessing time for sampling: 6.665631055831909
amortized time for sample size  110 is:  0.09026707863807676
preprocessing time for sampling: 6.664880990982056
amortized time for sample size  115 is:  0.002827582939811374
preprocessing time for sampling: 6.592055082321167
amortized time for sample size  120 is:  0.0814984812140465
preprocessing time for sampling: 6.672889232635498
amortized time for sample size  125 is:  0.002785068988800049
preprocessing time for sampling: 6.6656718254089355
amortized time for sample size  130 is:  0.04705228174649753
preprocessing time for sampling: 6.683224678039551
amortized time for sample size  135 is:  0.06988862235457809
preprocessing time for sampling: 6.6670379638671875
amortized time for sample size  140 is:  0.0688737439598356
preprocessing time for sampling: 6.682291030883789
amortized time for sample size  145 is:  0.07546074452893486
preprocessing time for sampling: 6.844250202178955
amortized time for sample size  150 is:  0.002781654691696167
preprocessing time for sampling: 983.4622437953949
amortized time for sample size  155 is:  0.0027859873617849047
preprocessing time for sampling: 6.705634117126465
amortized time for sample size  160 is:  0.0515656621903181
preprocessing time for sampling: 8.882716178894043
amortized time for sample size  165 is:  0.0036940982125022196
preprocessing time for sampling: 9.160855054855347
amortized time for sample size  170 is:  0.0037285805029027607
preprocessing time for sampling: 8.962341070175171
amortized time for sample size  175 is:  0.0036797764914376398
preprocessing time for sampling: 8.780903100967407
amortized time for sample size  180 is:  0.00369298627641466
preprocessing time for sampling: 8.817594051361084
amortized time for sample size  185 is:  0.003689727628553236
preprocessing time for sampling: 8.832439184188843
amortized time for sample size  190 is:  0.0036793009230965067
preprocessing time for sampling: 8.832625150680542
amortized time for sample size  195 is:  0.003688136883271046
preprocessing time for sampling: 8.808841943740845
amortized time for sample size  200 is:  0.0036780466318130493
preprocessing time for sampling: 8.804801940917969
amortized time for sample size  205 is:  0.003708460482155404
preprocessing time for sampling: 8.822912693023682
amortized time for sample size  210 is:  0.0037125949291955855
preprocessing time for sampling: 8.856950998306274
amortized time for sample size  215 is:  0.0037026730914448574
preprocessing time for sampling: 8.823272228240967
amortized time for sample size  220 is:  0.003693201910365711
preprocessing time for sampling: 8.818770170211792
amortized time for sample size  225 is:  0.003645436912112766
preprocessing time for sampling: 8.826589107513428
amortized time for sample size  230 is:  0.003701989826948746
preprocessing time for sampling: 8.831094980239868
amortized time for sample size  235 is:  0.003663185555884178
preprocessing time for sampling: 8.875813961029053
amortized time for sample size  240 is:  0.0036792901158332826
preprocessing time for sampling: 8.803513765335083
amortized time for sample size  245 is:  0.003673200042880312
preprocessing time for sampling: 8.876146793365479
amortized time for sample size  250 is:  0.0036694776153564455
*** results for plotting, beta= 0.4 

mean_list= [np.float64(0.61), np.float64(0.6900000000000001), np.float64(0.7500000000000001), np.float64(0.7700000000000001), np.float64(0.9), np.float64(0.89), np.float64(0.9200000000000002), np.float64(0.8600000000000001), np.float64(0.8900000000000002), np.float64(0.9400000000000001), np.float64(0.9200000000000002), np.float64(0.9200000000000002), np.float64(0.9), np.float64(0.9200000000000002), np.float64(0.95), np.float64(0.96), np.float64(0.9700000000000001), np.float64(0.95), np.float64(0.9100000000000001), np.float64(0.9400000000000001), np.float64(0.95), np.float64(0.9400000000000001), np.float64(0.96), np.float64(0.95), np.float64(0.9199999999999999), np.float64(0.97), np.float64(0.99), np.float64(0.95), np.float64(0.9800000000000001), np.float64(1.0), np.float64(0.96), np.float64(0.9800000000000001), np.float64(0.96), np.float64(1.0), np.float64(0.9800000000000001), np.float64(0.97), np.float64(0.99), np.float64(0.9800000000000001), np.float64(0.99), np.float64(0.99), np.float64(0.9800000000000001), np.float64(1.0), np.float64(0.99), np.float64(0.9800000000000001), np.float64(0.9700000000000001), np.float64(1.0), np.float64(1.0), np.float64(0.97), np.float64(0.99), np.float64(0.97)]
std_list= [np.float64(0.12206555615733701), np.float64(0.10440306508910552), np.float64(0.1746424919657298), np.float64(0.07810249675906657), np.float64(0.09999999999999999), np.float64(0.09433981132056604), np.float64(0.09797958971132713), np.float64(0.07999999999999999), np.float64(0.09433981132056601), np.float64(0.06633249580710798), np.float64(0.0748331477354788), np.float64(0.09797958971132713), np.float64(0.08944271909999157), np.float64(0.08717797887081345), np.float64(0.06708203932499368), np.float64(0.06633249580710798), np.float64(0.04582575694955839), np.float64(0.06708203932499368), np.float64(0.05385164807134503), np.float64(0.06633249580710798), np.float64(0.06708203932499368), np.float64(0.07999999999999999), np.float64(0.04898979485566355), np.float64(0.04999999999999999), np.float64(0.08717797887081345), np.float64(0.04582575694955839), np.float64(0.029999999999999992), np.float64(0.06708203932499368), np.float64(0.039999999999999994), np.float64(0.0), np.float64(0.06633249580710798), np.float64(0.039999999999999994), np.float64(0.06633249580710798), np.float64(0.0), np.float64(0.039999999999999994), np.float64(0.04582575694955839), np.float64(0.029999999999999992), np.float64(0.039999999999999994), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.05999999999999999), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.039999999999999994), np.float64(0.04582575694955839), np.float64(0.0), np.float64(0.0), np.float64(0.045825756949558386), np.float64(0.029999999999999992), np.float64(0.04582575694955839)]
beta: 0.6
preprocessing time for sampling: 8.834748029708862
amortized time for sample size  5 is:  0.003993401050567626
preprocessing time for sampling: 8.838325023651123
amortized time for sample size  10 is:  0.003955235958099365
preprocessing time for sampling: 8.84717082977295
amortized time for sample size  15 is:  0.003916314919789632
preprocessing time for sampling: 8.864528179168701
amortized time for sample size  20 is:  0.0039025208950042734
preprocessing time for sampling: 8.841772079467773
amortized time for sample size  25 is:  0.0038746917724609376
preprocessing time for sampling: 8.820215225219727
amortized time for sample size  30 is:  0.003946823914845784
preprocessing time for sampling: 8.849992275238037
amortized time for sample size  35 is:  0.0038643950053623742
preprocessing time for sampling: 9.000494003295898
amortized time for sample size  40 is:  0.0039772363305091854
preprocessing time for sampling: 9.048346042633057
amortized time for sample size  45 is:  0.003935508675045438
preprocessing time for sampling: 8.859235048294067
amortized time for sample size  50 is:  0.003868586587905884
preprocessing time for sampling: 8.888916969299316
amortized time for sample size  55 is:  0.003720003778284246
preprocessing time for sampling: 8.877557039260864
amortized time for sample size  60 is:  0.003703754862149556
preprocessing time for sampling: 8.76111102104187
amortized time for sample size  65 is:  0.0036997737150925854
preprocessing time for sampling: 8.889952898025513
amortized time for sample size  70 is:  0.003711254324231829
preprocessing time for sampling: 8.79917311668396
amortized time for sample size  75 is:  0.003712716484069824
preprocessing time for sampling: 8.76905870437622
amortized time for sample size  80 is:  0.0036601871550083166
preprocessing time for sampling: 8.789332866668701
amortized time for sample size  85 is:  0.0037291412914500525
preprocessing time for sampling: 8.79385495185852
amortized time for sample size  90 is:  0.0036613748868306478
preprocessing time for sampling: 8.79955005645752
amortized time for sample size  95 is:  0.003665471277738872
preprocessing time for sampling: 8.81415605545044
amortized time for sample size  100 is:  0.0036535557031631472
preprocessing time for sampling: 8.98917818069458
amortized time for sample size  105 is:  0.0036649065698896137
preprocessing time for sampling: 8.814720153808594
amortized time for sample size  110 is:  0.003692175865173339
preprocessing time for sampling: 8.907451152801514
amortized time for sample size  115 is:  0.0036869481542836074
preprocessing time for sampling: 8.836690902709961
amortized time for sample size  120 is:  0.003650433580080667
preprocessing time for sampling: 8.806437969207764
amortized time for sample size  125 is:  0.0036638206291198737
preprocessing time for sampling: 8.887498140335083
amortized time for sample size  130 is:  0.003746405069644635
preprocessing time for sampling: 8.814503908157349
amortized time for sample size  135 is:  0.0036516505170751503
preprocessing time for sampling: 8.548827171325684
amortized time for sample size  140 is:  0.003658085261072431
preprocessing time for sampling: 8.828622817993164
amortized time for sample size  145 is:  0.0037285559588465193
preprocessing time for sampling: 8.762838125228882
amortized time for sample size  150 is:  0.0036626673698425295
preprocessing time for sampling: 8.83824110031128
amortized time for sample size  155 is:  0.00366570823423324
preprocessing time for sampling: 8.756556749343872
amortized time for sample size  160 is:  0.003700939819216728
preprocessing time for sampling: 8.838332891464233
amortized time for sample size  165 is:  0.0037050140120766374
preprocessing time for sampling: 8.789192914962769
amortized time for sample size  170 is:  0.0037103475402383247
preprocessing time for sampling: 8.99776291847229
amortized time for sample size  175 is:  0.003680440616607666
preprocessing time for sampling: 8.990122079849243
amortized time for sample size  180 is:  0.00371729142136044
preprocessing time for sampling: 8.879789113998413
amortized time for sample size  185 is:  0.0036547465453276766
preprocessing time for sampling: 8.886279344558716
amortized time for sample size  190 is:  0.003669380740115517
preprocessing time for sampling: 8.79046106338501
amortized time for sample size  195 is:  0.0036861329323206187
preprocessing time for sampling: 8.838661909103394
amortized time for sample size  200 is:  0.003689454567432403
preprocessing time for sampling: 8.799211025238037
amortized time for sample size  205 is:  0.003658474201109352
preprocessing time for sampling: 8.79951786994934
amortized time for sample size  210 is:  0.003644869690849668
preprocessing time for sampling: 8.793662071228027
amortized time for sample size  215 is:  0.003675649321356485
preprocessing time for sampling: 8.876175165176392
amortized time for sample size  220 is:  0.003655681306665594
preprocessing time for sampling: 8.82630705833435
amortized time for sample size  225 is:  0.003660246584150527
preprocessing time for sampling: 8.758686065673828
amortized time for sample size  230 is:  0.003659570186034494
preprocessing time for sampling: 8.79477334022522
amortized time for sample size  235 is:  0.0036481485975549573
preprocessing time for sampling: 8.861606121063232
amortized time for sample size  240 is:  0.0036475592056910196
preprocessing time for sampling: 8.829240083694458
amortized time for sample size  245 is:  0.0036788865400820365
preprocessing time for sampling: 8.830312967300415
amortized time for sample size  250 is:  0.0036928062534332274
*** results for plotting, beta= 0.6 

mean_list= [np.float64(0.71), np.float64(0.8700000000000001), np.float64(0.9100000000000001), np.float64(0.8700000000000001), np.float64(0.95), np.float64(0.9400000000000001), np.float64(0.95), np.float64(0.9800000000000001), np.float64(0.9), np.float64(0.99), np.float64(0.99), np.float64(0.95), np.float64(0.9800000000000001), np.float64(0.99), np.float64(1.0), np.float64(0.9700000000000001), np.float64(1.0), np.float64(0.99), np.float64(0.9800000000000001), np.float64(0.99), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), 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(0.09433981132056606), np.float64(0.07810249675906655), np.float64(0.08306623862918074), np.float64(0.09), np.float64(0.09219544457292889), np.float64(0.10198039027185571), np.float64(0.04999999999999999), np.float64(0.039999999999999994), np.float64(0.06324555320336757), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.09219544457292889), np.float64(0.039999999999999994), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.04582575694955839), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.039999999999999994), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), 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: 8.79391098022461
amortized time for sample size  5 is:  0.0038715496063232422
preprocessing time for sampling: 8.84997296333313
amortized time for sample size  10 is:  0.003930182933807373
preprocessing time for sampling: 8.900883913040161
amortized time for sample size  15 is:  0.003856026490529378
preprocessing time for sampling: 8.857193946838379
amortized time for sample size  20 is:  0.003865994453430176
preprocessing time for sampling: 8.866831064224243
amortized time for sample size  25 is:  0.003883396244049072
preprocessing time for sampling: 8.839499950408936
amortized time for sample size  30 is:  0.003966012795766194
preprocessing time for sampling: 8.871628999710083
amortized time for sample size  35 is:  0.003870076588221959
preprocessing time for sampling: 8.792504072189331
amortized time for sample size  40 is:  0.0037822530865669257
preprocessing time for sampling: 8.84180998802185
amortized time for sample size  45 is:  0.003740435971154107
preprocessing time for sampling: 8.97891092300415
amortized time for sample size  50 is:  0.0036506786823272707
preprocessing time for sampling: 8.78744101524353
amortized time for sample size  55 is:  0.003646533705971458
preprocessing time for sampling: 8.771247863769531
amortized time for sample size  60 is:  0.0036848206520080566
preprocessing time for sampling: 8.919925928115845
amortized time for sample size  65 is:  0.003713258193089412
preprocessing time for sampling: 8.80991005897522
amortized time for sample size  70 is:  0.003665677377155849
preprocessing time for sampling: 8.825886964797974
amortized time for sample size  75 is:  0.0036934428215026852
preprocessing time for sampling: 9.017951965332031
amortized time for sample size  80 is:  0.003714754372835159
preprocessing time for sampling: 8.74740719795227
amortized time for sample size  85 is:  0.0037052649610182812
preprocessing time for sampling: 8.829694271087646
amortized time for sample size  90 is:  0.0036661191781361896
preprocessing time for sampling: 8.810830116271973
amortized time for sample size  95 is:  0.0037109311003434026
preprocessing time for sampling: 8.868004322052002
amortized time for sample size  100 is:  0.00367650945186615
preprocessing time for sampling: 8.888490915298462
amortized time for sample size  105 is:  0.0036677328291393457
preprocessing time for sampling: 8.833070039749146
amortized time for sample size  110 is:  0.0036775297468358823
preprocessing time for sampling: 8.858697175979614
amortized time for sample size  115 is:  0.0036779123181882112
preprocessing time for sampling: 8.792771100997925
amortized time for sample size  120 is:  0.003667860686779022
preprocessing time for sampling: 8.822150945663452
amortized time for sample size  125 is:  0.003667557239532471
preprocessing time for sampling: 8.78984808921814
amortized time for sample size  130 is:  0.0036268105506896964
preprocessing time for sampling: 8.842809915542603
amortized time for sample size  135 is:  0.003649269704465513
preprocessing time for sampling: 8.827329874038696
amortized time for sample size  140 is:  0.0036576492105211537
preprocessing time for sampling: 8.82335114479065
amortized time for sample size  145 is:  0.0036727462143733586
preprocessing time for sampling: 9.033470869064331
amortized time for sample size  150 is:  0.003678779649734497
preprocessing time for sampling: 8.800258874893188
amortized time for sample size  155 is:  0.0036727546876476652
preprocessing time for sampling: 8.839266777038574
amortized time for sample size  160 is:  0.003670851320028305
preprocessing time for sampling: 9.01815676689148
amortized time for sample size  165 is:  0.003714990702542392
preprocessing time for sampling: 8.87825894355774
amortized time for sample size  170 is:  0.00367591789189507
preprocessing time for sampling: 8.890032291412354
amortized time for sample size  175 is:  0.003711618832179478
preprocessing time for sampling: 8.854291915893555
amortized time for sample size  180 is:  0.003740097853872511
preprocessing time for sampling: 8.78850769996643
amortized time for sample size  185 is:  0.0036211654431111103
preprocessing time for sampling: 8.806362867355347
amortized time for sample size  190 is:  0.007602397843411094
preprocessing time for sampling: 8.839868068695068
amortized time for sample size  195 is:  0.003659783326662504
preprocessing time for sampling: 8.852396965026855
amortized time for sample size  200 is:  0.0036925506353378294
preprocessing time for sampling: 8.883779048919678
amortized time for sample size  205 is:  0.003645041965856785
preprocessing time for sampling: 8.948491096496582
amortized time for sample size  210 is:  0.003729995511827015
preprocessing time for sampling: 8.81978178024292
amortized time for sample size  215 is:  0.0036368952462839522
preprocessing time for sampling: 8.854315042495728
amortized time for sample size  220 is:  0.0036542700637470587
preprocessing time for sampling: 8.783565759658813
amortized time for sample size  225 is:  0.0036944868193732367
preprocessing time for sampling: 9.057964086532593
amortized time for sample size  230 is:  0.003626714042995286
preprocessing time for sampling: 8.83083200454712
amortized time for sample size  235 is:  0.003648340367256327
preprocessing time for sampling: 8.837002992630005
amortized time for sample size  240 is:  0.0036875659724076586
preprocessing time for sampling: 8.831151723861694
amortized time for sample size  245 is:  0.0036828524433836648
preprocessing time for sampling: 8.816293001174927
amortized time for sample size  250 is:  0.0036729500389099125
*** results for plotting, beta= 0.8 

mean_list= [np.float64(0.8500000000000002), np.float64(0.89), np.float64(0.96), np.float64(0.95), np.float64(1.0), np.float64(1.0), np.float64(0.9800000000000001), np.float64(1.0), np.float64(0.99), np.float64(0.99), np.float64(1.0), np.float64(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)]
std_list= [np.float64(0.06708203932499368), np.float64(0.05385164807134503), np.float64(0.04898979485566355), np.float64(0.06708203932499368), np.float64(0.0), np.float64(0.0), np.float64(0.039999999999999994), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.029999999999999992), 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)]
beta: 1
preprocessing time for sampling: 10.044339895248413
amortized time for sample size  5 is:  0.00392698335647583
preprocessing time for sampling: 10.042375087738037
amortized time for sample size  10 is:  0.003935445308685302
preprocessing time for sampling: 10.031944036483765
amortized time for sample size  15 is:  0.0038398427963256838
preprocessing time for sampling: 9.961024045944214
amortized time for sample size  20 is:  0.003871476411819458
preprocessing time for sampling: 10.064686059951782
amortized time for sample size  25 is:  0.003901461601257324
preprocessing time for sampling: 10.036258697509766
amortized time for sample size  30 is:  0.003931446472803753
preprocessing time for sampling: 10.026782989501953
amortized time for sample size  35 is:  0.0038973394121442524
preprocessing time for sampling: 10.229531049728394
amortized time for sample size  40 is:  0.0038250412344932555
preprocessing time for sampling: 9.952919006347656
amortized time for sample size  45 is:  0.003806731383005779
preprocessing time for sampling: 10.067793846130371
amortized time for sample size  50 is:  0.003801639747619629
preprocessing time for sampling: 10.099300146102905
amortized time for sample size  55 is:  0.003712652163072065
preprocessing time for sampling: 10.233029842376709
amortized time for sample size  60 is:  0.0037158491214116414
preprocessing time for sampling: 10.037659168243408
amortized time for sample size  65 is:  0.0037896355849045965
preprocessing time for sampling: 10.04892897605896
amortized time for sample size  70 is:  0.003693682364055089
preprocessing time for sampling: 10.035376787185669
amortized time for sample size  75 is:  0.003686583868662516
preprocessing time for sampling: 10.02367877960205
amortized time for sample size  80 is:  0.003710429012775421
preprocessing time for sampling: 10.137507915496826
amortized time for sample size  85 is:  0.0036645848891314337
preprocessing time for sampling: 10.012073993682861
amortized time for sample size  90 is:  0.0037148664792378745
preprocessing time for sampling: 10.049582958221436
amortized time for sample size  95 is:  0.003707842826843261
preprocessing time for sampling: 10.022353887557983
amortized time for sample size  100 is:  0.003696286273002624
preprocessing time for sampling: 10.11753511428833
amortized time for sample size  105 is:  0.0036899278277442576
preprocessing time for sampling: 10.184494972229004
amortized time for sample size  110 is:  0.0037328683896498244
preprocessing time for sampling: 10.072178840637207
amortized time for sample size  115 is:  0.0037037841548090396
preprocessing time for sampling: 9.998326778411865
amortized time for sample size  120 is:  0.0036977410316467287
preprocessing time for sampling: 10.08207893371582
amortized time for sample size  125 is:  0.003692479190826416
preprocessing time for sampling: 10.192131280899048
amortized time for sample size  130 is:  0.0036813467099116397
preprocessing time for sampling: 9.987518072128296
amortized time for sample size  135 is:  0.0036836068895128044
preprocessing time for sampling: 10.001253128051758
amortized time for sample size  140 is:  0.00377843063218253
preprocessing time for sampling: 10.193530082702637
amortized time for sample size  145 is:  0.003634355018878805
preprocessing time for sampling: 9.973749160766602
amortized time for sample size  150 is:  0.003656302452087402
preprocessing time for sampling: 9.993155002593994
amortized time for sample size  155 is:  0.04998952605647425
preprocessing time for sampling: 10.044422149658203
amortized time for sample size  160 is:  0.0036822337359189994
preprocessing time for sampling: 9.997995138168335
amortized time for sample size  165 is:  0.0036456575538172864
preprocessing time for sampling: 10.004388809204102
amortized time for sample size  170 is:  0.03731266599542954
preprocessing time for sampling: 10.008530855178833
amortized time for sample size  175 is:  0.0037024116243634907
preprocessing time for sampling: 10.162742853164673
amortized time for sample size  180 is:  0.0037112238804499304
preprocessing time for sampling: 10.067251920700073
amortized time for sample size  185 is:  0.0037302094021359005
preprocessing time for sampling: 10.085243225097656
amortized time for sample size  190 is:  0.0037137969669542815
preprocessing time for sampling: 10.008718967437744
amortized time for sample size  195 is:  0.0036619651011931586
preprocessing time for sampling: 10.031741857528687
amortized time for sample size  200 is:  0.0037341734528541564
preprocessing time for sampling: 9.988041877746582
amortized time for sample size  205 is:  0.0036894339817326242
preprocessing time for sampling: 10.055756092071533
amortized time for sample size  210 is:  0.0036780662990751715
preprocessing time for sampling: 10.041323184967041
amortized time for sample size  215 is:  0.003687297211136928
preprocessing time for sampling: 10.04729413986206
amortized time for sample size  220 is:  0.003756252841515975
preprocessing time for sampling: 10.168298959732056
amortized time for sample size  225 is:  0.0037220658090379504
preprocessing time for sampling: 10.04081106185913
amortized time for sample size  230 is:  0.0037354623856751816
preprocessing time for sampling: 10.066619873046875
amortized time for sample size  235 is:  0.003694978054533613
preprocessing time for sampling: 10.086071252822876
amortized time for sample size  240 is:  0.0036803693075974785
preprocessing time for sampling: 10.016540050506592
amortized time for sample size  245 is:  0.0036646016081985167
preprocessing time for sampling: 10.015970230102539
amortized time for sample size  250 is:  0.0037330881690979005
*** results for plotting, beta= 1 

mean_list= [np.float64(0.89), np.float64(0.97), np.float64(0.99), np.float64(0.9800000000000001), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0)]
std_list= [np.float64(0.08306623862918074), np.float64(0.06403124237432847), np.float64(0.029999999999999992), np.float64(0.039999999999999994), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0)]
beta: 1.2
preprocessing time for sampling: 8.93530011177063
amortized time for sample size  5 is:  0.004154399394989013
preprocessing time for sampling: 8.921107769012451
amortized time for sample size  10 is:  0.003915790796279907
preprocessing time for sampling: 8.945546865463257
amortized time for sample size  15 is:  0.0038250637054443354
preprocessing time for sampling: 8.94682788848877
amortized time for sample size  20 is:  0.0038776286840438846
preprocessing time for sampling: 8.899147987365723
amortized time for sample size  25 is:  0.003859447765350342
preprocessing time for sampling: 8.820420980453491
amortized time for sample size  30 is:  0.0038297136624654126
preprocessing time for sampling: 8.7990882396698
amortized time for sample size  35 is:  0.0038555876868111745
preprocessing time for sampling: 8.889610052108765
amortized time for sample size  40 is:  0.0038062958717346197
preprocessing time for sampling: 8.816350936889648
amortized time for sample size  45 is:  0.0038441104888916017
preprocessing time for sampling: 8.878974199295044
amortized time for sample size  50 is:  0.0037763732433319097
preprocessing time for sampling: 8.763890266418457
amortized time for sample size  55 is:  0.0037006338292902164
preprocessing time for sampling: 8.858138084411621
amortized time for sample size  60 is:  0.0037053475777308136
preprocessing time for sampling: 8.932136297225952
amortized time for sample size  65 is:  0.0036868707216702974
preprocessing time for sampling: 8.820243120193481
amortized time for sample size  70 is:  0.003676328182220459
preprocessing time for sampling: 8.816310167312622
amortized time for sample size  75 is:  0.0036522207578023273
preprocessing time for sampling: 8.876030921936035
amortized time for sample size  80 is:  0.0037174653708934783
preprocessing time for sampling: 8.811686754226685
amortized time for sample size  85 is:  0.0036631492726943073
preprocessing time for sampling: 8.866700887680054
amortized time for sample size  90 is:  0.0036316891511281326
preprocessing time for sampling: 8.816641092300415
amortized time for sample size  95 is:  0.0036487271660252617
preprocessing time for sampling: 8.82439112663269
amortized time for sample size  100 is:  0.0036458534240722653
preprocessing time for sampling: 8.812132120132446
amortized time for sample size  105 is:  0.00366603151957194
preprocessing time for sampling: 8.857617855072021
amortized time for sample size  110 is:  0.003704401774839922
preprocessing time for sampling: 8.842005968093872
amortized time for sample size  115 is:  0.003669018289317255
preprocessing time for sampling: 8.913190126419067
amortized time for sample size  120 is:  0.0036995549201965334
preprocessing time for sampling: 8.782362699508667
amortized time for sample size  125 is:  0.0036402430725097656
preprocessing time for sampling: 8.80470085144043
amortized time for sample size  130 is:  0.0036490119603964
preprocessing time for sampling: 8.812924861907959
amortized time for sample size  135 is:  0.0036631345748901374
preprocessing time for sampling: 8.862557888031006
amortized time for sample size  140 is:  0.0036553723130907326
preprocessing time for sampling: 8.776134252548218
amortized time for sample size  145 is:  0.003720698849908237
preprocessing time for sampling: 8.870200157165527
amortized time for sample size  150 is:  0.0036948683579762776
preprocessing time for sampling: 8.841213941574097
amortized time for sample size  155 is:  0.0036368693228690852
preprocessing time for sampling: 8.823038816452026
amortized time for sample size  160 is:  0.0036513947993516917
preprocessing time for sampling: 8.901094913482666
amortized time for sample size  165 is:  0.0036400287368080837
preprocessing time for sampling: 8.864266872406006
amortized time for sample size  170 is:  0.0036496872481177837
preprocessing time for sampling: 8.818887948989868
amortized time for sample size  175 is:  0.003638019589015416
preprocessing time for sampling: 8.793084144592285
amortized time for sample size  180 is:  0.003643408629629347
preprocessing time for sampling: 8.806816101074219
amortized time for sample size  185 is:  0.0036367670265403957
preprocessing time for sampling: 8.84446382522583
amortized time for sample size  190 is:  0.0036413234535016513
preprocessing time for sampling: 8.821386098861694
amortized time for sample size  195 is:  0.00367012627919515
preprocessing time for sampling: 8.876344203948975
amortized time for sample size  200 is:  0.003731751441955566
preprocessing time for sampling: 8.857464075088501
amortized time for sample size  205 is:  0.0037131256475681214
preprocessing time for sampling: 8.887749195098877
amortized time for sample size  210 is:  0.0036646270411355157
preprocessing time for sampling: 8.893537998199463
amortized time for sample size  215 is:  0.003665344138478124
preprocessing time for sampling: 8.801153898239136
amortized time for sample size  220 is:  0.0036738690029491077
preprocessing time for sampling: 8.916268825531006
amortized time for sample size  225 is:  0.0036657007005479604
preprocessing time for sampling: 8.840551376342773
amortized time for sample size  230 is:  0.0036599833861641257
preprocessing time for sampling: 8.812232255935669
amortized time for sample size  235 is:  0.0036797277065033613
preprocessing time for sampling: 8.832535982131958
amortized time for sample size  240 is:  0.0036517390906810753
preprocessing time for sampling: 8.795353889465332
amortized time for sample size  245 is:  0.0036090568717645146
preprocessing time for sampling: 8.804738998413086
amortized time for sample size  250 is:  0.022626256999969483
*** results for plotting, beta= 1.2 

mean_list= [np.float64(0.9199999999999999), 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(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), 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(0.059999999999999984), 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(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0)]
