beta: 0.2
preprocessing time for sampling: 0.035027265548706055
amortized time for sample size  5 is:  9.595537185668946e-05
preprocessing time for sampling: 0.034845829010009766
amortized time for sample size  10 is:  9.71670150756836e-05
preprocessing time for sampling: 0.035096168518066406
amortized time for sample size  15 is:  9.64056650797526e-05
preprocessing time for sampling: 0.03525400161743164
amortized time for sample size  20 is:  9.734451770782471e-05
preprocessing time for sampling: 0.034828901290893555
amortized time for sample size  25 is:  9.647789001464842e-05
preprocessing time for sampling: 0.03492617607116699
amortized time for sample size  30 is:  9.632221857706705e-05
preprocessing time for sampling: 0.034960031509399414
amortized time for sample size  35 is:  9.655918393816266e-05
preprocessing time for sampling: 0.03510236740112305
amortized time for sample size  40 is:  9.678751230239868e-05
preprocessing time for sampling: 0.03503680229187012
amortized time for sample size  45 is:  9.631156921386721e-05
preprocessing time for sampling: 0.03481411933898926
amortized time for sample size  50 is:  9.59641456604004e-05
preprocessing time for sampling: 0.03474783897399902
amortized time for sample size  55 is:  9.530990773981267e-05
preprocessing time for sampling: 0.03747916221618652
amortized time for sample size  60 is:  9.493537743886313e-05
preprocessing time for sampling: 0.034399986267089844
amortized time for sample size  65 is:  9.534351642315203e-05
preprocessing time for sampling: 0.03478407859802246
amortized time for sample size  70 is:  9.5336880002703e-05
preprocessing time for sampling: 0.03485727310180664
amortized time for sample size  75 is:  9.61184819539388e-05
preprocessing time for sampling: 0.03498125076293945
amortized time for sample size  80 is:  9.649208188056945e-05
preprocessing time for sampling: 0.03511500358581543
amortized time for sample size  85 is:  9.589276594274183e-05
preprocessing time for sampling: 0.03511691093444824
amortized time for sample size  90 is:  9.62661902109782e-05
preprocessing time for sampling: 0.03499197959899902
amortized time for sample size  95 is:  9.640043660214072e-05
preprocessing time for sampling: 0.03580212593078613
amortized time for sample size  100 is:  9.601078033447267e-05
preprocessing time for sampling: 0.03480386734008789
amortized time for sample size  105 is:  9.61152712504069e-05
preprocessing time for sampling: 0.03493928909301758
amortized time for sample size  110 is:  9.56157771023837e-05
preprocessing time for sampling: 0.034800052642822266
amortized time for sample size  115 is:  9.55737362737241e-05
preprocessing time for sampling: 0.0349268913269043
amortized time for sample size  120 is:  9.628798564275105e-05
preprocessing time for sampling: 0.034913063049316406
amortized time for sample size  125 is:  9.576362609863283e-05
preprocessing time for sampling: 0.03480386734008789
amortized time for sample size  130 is:  9.752735724815954e-05
preprocessing time for sampling: 0.03490304946899414
amortized time for sample size  135 is:  9.562038492273401e-05
preprocessing time for sampling: 0.03477621078491211
amortized time for sample size  140 is:  9.572991303035192e-05
preprocessing time for sampling: 0.03477191925048828
amortized time for sample size  145 is:  9.560708341927363e-05
preprocessing time for sampling: 0.03475475311279297
amortized time for sample size  150 is:  9.543150266011557e-05
preprocessing time for sampling: 0.03473806381225586
amortized time for sample size  155 is:  9.541503844722624e-05
preprocessing time for sampling: 0.034826040267944336
amortized time for sample size  160 is:  9.576535224914553e-05
preprocessing time for sampling: 0.03480100631713867
amortized time for sample size  165 is:  9.583152424205433e-05
preprocessing time for sampling: 0.03478097915649414
amortized time for sample size  170 is:  9.561519061817841e-05
preprocessing time for sampling: 0.034780025482177734
amortized time for sample size  175 is:  9.604157039097376e-05
preprocessing time for sampling: 0.034783124923706055
amortized time for sample size  180 is:  9.520906872219509e-05
preprocessing time for sampling: 0.03531289100646973
amortized time for sample size  185 is:  9.550072695757894e-05
preprocessing time for sampling: 0.03482317924499512
amortized time for sample size  190 is:  9.510494533338044e-05
preprocessing time for sampling: 0.034787654876708984
amortized time for sample size  195 is:  9.520975748697918e-05
preprocessing time for sampling: 0.03491711616516113
amortized time for sample size  200 is:  9.515050649642943e-05
preprocessing time for sampling: 0.03493475914001465
amortized time for sample size  205 is:  9.518594276614308e-05
preprocessing time for sampling: 0.03483891487121582
amortized time for sample size  210 is:  9.540661176045736e-05
preprocessing time for sampling: 0.03479599952697754
amortized time for sample size  215 is:  9.630361823148506e-05
preprocessing time for sampling: 0.034874916076660156
amortized time for sample size  220 is:  9.549401023171164e-05
preprocessing time for sampling: 0.03485608100891113
amortized time for sample size  225 is:  9.561897913614909e-05
preprocessing time for sampling: 0.03478884696960449
amortized time for sample size  230 is:  9.51665277066438e-05
preprocessing time for sampling: 0.034774065017700195
amortized time for sample size  235 is:  9.531750577561399e-05
preprocessing time for sampling: 0.034715890884399414
amortized time for sample size  240 is:  9.519049525260928e-05
preprocessing time for sampling: 0.03479409217834473
amortized time for sample size  245 is:  9.520424628744322e-05
preprocessing time for sampling: 0.03471088409423828
amortized time for sample size  250 is:  9.516791343688966e-05
*** results for plotting, beta= 0.2 

mean_list= [np.float64(0.38000000000000006), np.float64(0.44000000000000006), np.float64(0.4600000000000001), np.float64(0.51), np.float64(0.48999999999999994), np.float64(0.45), np.float64(0.5399999999999999), np.float64(0.43), np.float64(0.55), np.float64(0.7), np.float64(0.65), np.float64(0.5700000000000001), np.float64(0.6199999999999999), np.float64(0.65), np.float64(0.5599999999999999), np.float64(0.61), np.float64(0.64), np.float64(0.6399999999999999), np.float64(0.5999999999999999), np.float64(0.6300000000000001), np.float64(0.6100000000000001), np.float64(0.67), np.float64(0.61), np.float64(0.6300000000000001), np.float64(0.7), np.float64(0.74), np.float64(0.6699999999999999), np.float64(0.5800000000000001), np.float64(0.6200000000000001), np.float64(0.73), np.float64(0.6900000000000001), np.float64(0.74), np.float64(0.6900000000000001), np.float64(0.5999999999999999), np.float64(0.6200000000000001), np.float64(0.69), np.float64(0.71), np.float64(0.71), np.float64(0.69), np.float64(0.65), np.float64(0.6199999999999999), np.float64(0.66), np.float64(0.64), np.float64(0.73), np.float64(0.7300000000000001), np.float64(0.72), np.float64(0.69), np.float64(0.7300000000000001), np.float64(0.7), np.float64(0.77)]
std_list= [np.float64(0.24), np.float64(0.16852299546352717), np.float64(0.17999999999999997), np.float64(0.06999999999999999), np.float64(0.157797338380595), np.float64(0.24596747752497683), np.float64(0.142828568570857), np.float64(0.1268857754044952), np.float64(0.20615528128088303), np.float64(0.10954451150103325), np.float64(0.1118033988749895), np.float64(0.14866068747318506), np.float64(0.1536229149573722), np.float64(0.12041594578792296), np.float64(0.142828568570857), np.float64(0.11357816691600546), np.float64(0.17435595774162696), np.float64(0.1562049935181331), np.float64(0.14832396974191325), np.float64(0.14177446878757827), np.float64(0.09433981132056604), np.float64(0.15524174696260024), np.float64(0.15132745950421558), np.float64(0.17916472867168917), np.float64(0.10000000000000003), np.float64(0.06633249580710804), np.float64(0.1004987562112089), np.float64(0.17204650534085256), np.float64(0.18330302779823363), np.float64(0.09000000000000002), np.float64(0.157797338380595), np.float64(0.14282856857085702), np.float64(0.17), np.float64(0.07745966692414831), np.float64(0.18867962264113208), np.float64(0.12206555615733704), np.float64(0.09433981132056607), np.float64(0.13747727084867523), np.float64(0.08306623862918076), np.float64(0.1746424919657298), np.float64(0.16), np.float64(0.17435595774162696), np.float64(0.1356465996625054), np.float64(0.11000000000000003), np.float64(0.17349351572897473), np.float64(0.16), np.float64(0.09433981132056606), np.float64(0.1846618531261939), np.float64(0.14832396974191325), np.float64(0.16155494421403513)]
beta: 0.4
preprocessing time for sampling: 0.03488516807556152
amortized time for sample size  5 is:  9.492111206054689e-05
preprocessing time for sampling: 0.03479599952697754
amortized time for sample size  10 is:  9.489870071411131e-05
preprocessing time for sampling: 0.03477787971496582
amortized time for sample size  15 is:  9.511073430379231e-05
preprocessing time for sampling: 0.034774065017700195
amortized time for sample size  20 is:  9.517085552215575e-05
preprocessing time for sampling: 0.03476977348327637
amortized time for sample size  25 is:  9.511518478393556e-05
preprocessing time for sampling: 0.03481030464172363
amortized time for sample size  30 is:  9.505716959635417e-05
preprocessing time for sampling: 0.03482222557067871
amortized time for sample size  35 is:  9.507581165858678e-05
preprocessing time for sampling: 0.03477311134338379
amortized time for sample size  40 is:  9.508293867111207e-05
preprocessing time for sampling: 0.03476405143737793
amortized time for sample size  45 is:  9.520467122395832e-05
preprocessing time for sampling: 0.03476405143737793
amortized time for sample size  50 is:  9.522833824157715e-05
preprocessing time for sampling: 0.0347440242767334
amortized time for sample size  55 is:  9.533825787630947e-05
preprocessing time for sampling: 0.0348658561706543
amortized time for sample size  60 is:  9.493672847747802e-05
preprocessing time for sampling: 0.034372806549072266
amortized time for sample size  65 is:  9.48960230900691e-05
preprocessing time for sampling: 0.03476595878601074
amortized time for sample size  70 is:  9.505517142159598e-05
preprocessing time for sampling: 0.03475689888000488
amortized time for sample size  75 is:  9.507694244384766e-05
preprocessing time for sampling: 0.034744977951049805
amortized time for sample size  80 is:  9.519401192665102e-05
preprocessing time for sampling: 0.03484797477722168
amortized time for sample size  85 is:  9.532782610724955e-05
preprocessing time for sampling: 0.03480982780456543
amortized time for sample size  90 is:  9.494659635755752e-05
preprocessing time for sampling: 0.0347590446472168
amortized time for sample size  95 is:  9.500332882529808e-05
preprocessing time for sampling: 0.03478503227233887
amortized time for sample size  100 is:  9.633138179779055e-05
preprocessing time for sampling: 0.03476095199584961
amortized time for sample size  105 is:  9.542749041602724e-05
preprocessing time for sampling: 0.03483915328979492
amortized time for sample size  110 is:  9.501589428294788e-05
preprocessing time for sampling: 0.03488612174987793
amortized time for sample size  115 is:  9.5012789187224e-05
preprocessing time for sampling: 0.03490900993347168
amortized time for sample size  120 is:  9.515655040740968e-05
preprocessing time for sampling: 0.0347599983215332
amortized time for sample size  125 is:  9.51185417175293e-05
preprocessing time for sampling: 0.034790992736816406
amortized time for sample size  130 is:  9.512743583092323e-05
preprocessing time for sampling: 0.03474879264831543
amortized time for sample size  135 is:  9.530720887360747e-05
preprocessing time for sampling: 0.034729957580566406
amortized time for sample size  140 is:  9.713082654135568e-05
preprocessing time for sampling: 0.03481483459472656
amortized time for sample size  145 is:  9.577900787879678e-05
preprocessing time for sampling: 0.03484702110290527
amortized time for sample size  150 is:  9.54498767852783e-05
preprocessing time for sampling: 0.03478407859802246
amortized time for sample size  155 is:  9.509309645622008e-05
preprocessing time for sampling: 0.03476309776306152
amortized time for sample size  160 is:  9.521074593067167e-05
preprocessing time for sampling: 0.03475689888000488
amortized time for sample size  165 is:  9.51851497996937e-05
preprocessing time for sampling: 0.03483867645263672
amortized time for sample size  170 is:  9.512270198148843e-05
preprocessing time for sampling: 0.03475809097290039
amortized time for sample size  175 is:  9.520504815237864e-05
preprocessing time for sampling: 0.034803152084350586
amortized time for sample size  180 is:  9.516555733150904e-05
preprocessing time for sampling: 0.034802913665771484
amortized time for sample size  185 is:  9.546483529580608e-05
preprocessing time for sampling: 0.03480815887451172
amortized time for sample size  190 is:  9.529955763565865e-05
preprocessing time for sampling: 0.03492283821105957
amortized time for sample size  195 is:  9.523183871538211e-05
preprocessing time for sampling: 0.03473186492919922
amortized time for sample size  200 is:  9.531315565109252e-05
preprocessing time for sampling: 0.04114103317260742
amortized time for sample size  205 is:  9.512411675802091e-05
preprocessing time for sampling: 0.03485894203186035
amortized time for sample size  210 is:  9.5444917678833e-05
preprocessing time for sampling: 0.035117149353027344
amortized time for sample size  215 is:  9.610105115313863e-05
preprocessing time for sampling: 0.03486180305480957
amortized time for sample size  220 is:  9.598553180694578e-05
preprocessing time for sampling: 0.03489398956298828
amortized time for sample size  225 is:  9.572473102145726e-05
preprocessing time for sampling: 0.03493785858154297
amortized time for sample size  230 is:  9.484070280323857e-05
preprocessing time for sampling: 0.034826040267944336
amortized time for sample size  235 is:  9.483623504638673e-05
preprocessing time for sampling: 0.034776926040649414
amortized time for sample size  240 is:  9.482151269912722e-05
preprocessing time for sampling: 0.034822940826416016
amortized time for sample size  245 is:  9.48754719325474e-05
preprocessing time for sampling: 0.0348358154296875
amortized time for sample size  250 is:  9.49137306213379e-05
*** results for plotting, beta= 0.4 

mean_list= [np.float64(0.51), np.float64(0.6199999999999999), np.float64(0.82), np.float64(0.76), np.float64(0.78), np.float64(0.7999999999999999), np.float64(0.8800000000000001), np.float64(0.85), np.float64(0.8400000000000001), np.float64(0.9000000000000001), np.float64(0.82), np.float64(0.86), np.float64(0.89), np.float64(0.9199999999999999), np.float64(0.8800000000000001), np.float64(0.9400000000000001), np.float64(0.9400000000000001), np.float64(0.9), np.float64(0.97), np.float64(0.93), np.float64(0.89), np.float64(0.9000000000000001), np.float64(0.96), np.float64(0.9200000000000002), np.float64(0.9600000000000002), np.float64(0.9400000000000001), np.float64(0.9), np.float64(0.9600000000000002), np.float64(0.9), np.float64(0.9700000000000001), np.float64(0.95), np.float64(0.9400000000000001), np.float64(0.96), np.float64(0.9400000000000001), np.float64(0.9700000000000001), np.float64(0.9800000000000001), np.float64(0.93), np.float64(1.0), np.float64(0.95), np.float64(0.9199999999999999), np.float64(0.9800000000000001), np.float64(0.9800000000000001), np.float64(0.95), np.float64(0.9800000000000001), np.float64(0.99), np.float64(0.99), np.float64(0.96), np.float64(0.9800000000000001), np.float64(0.9700000000000001), np.float64(0.9800000000000001)]
std_list= [np.float64(0.17), np.float64(0.19390719429665318), np.float64(0.07483314773547885), np.float64(0.14966629547095767), np.float64(0.07483314773547886), np.float64(0.10954451150103323), np.float64(0.059999999999999984), np.float64(0.0806225774829855), np.float64(0.12000000000000001), np.float64(0.07745966692414831), np.float64(0.1077032961426901), np.float64(0.10198039027185571), np.float64(0.11357816691600547), np.float64(0.09797958971132713), np.float64(0.09797958971132711), np.float64(0.07999999999999999), np.float64(0.07999999999999999), np.float64(0.08944271909999159), np.float64(0.04582575694955839), np.float64(0.06403124237432847), np.float64(0.05385164807134503), np.float64(0.07745966692414831), np.float64(0.04898979485566356), np.float64(0.0748331477354788), np.float64(0.06633249580710798), np.float64(0.04898979485566356), np.float64(0.11832159566199232), np.float64(0.06633249580710798), np.float64(0.07745966692414831), np.float64(0.04582575694955839), np.float64(0.06708203932499367), np.float64(0.04898979485566356), np.float64(0.06633249580710798), np.float64(0.06633249580710798), np.float64(0.06403124237432847), np.float64(0.039999999999999994), np.float64(0.045825756949558386), np.float64(0.0), np.float64(0.06708203932499368), np.float64(0.09797958971132713), np.float64(0.039999999999999994), np.float64(0.039999999999999994), np.float64(0.08062257748298547), np.float64(0.039999999999999994), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.06633249580710798), np.float64(0.039999999999999994), np.float64(0.04582575694955839), np.float64(0.039999999999999994)]
beta: 0.6
preprocessing time for sampling: 0.03491687774658203
amortized time for sample size  5 is:  9.481573104858398e-05
preprocessing time for sampling: 0.03483295440673828
amortized time for sample size  10 is:  9.462213516235352e-05
preprocessing time for sampling: 0.03486824035644531
amortized time for sample size  15 is:  9.478410085042317e-05
preprocessing time for sampling: 0.034783363342285156
amortized time for sample size  20 is:  9.452104568481446e-05
preprocessing time for sampling: 0.034813880920410156
amortized time for sample size  25 is:  9.454135894775389e-05
preprocessing time for sampling: 0.034850120544433594
amortized time for sample size  30 is:  9.446144104003907e-05
preprocessing time for sampling: 0.03478407859802246
amortized time for sample size  35 is:  9.450204031808036e-05
preprocessing time for sampling: 0.03484678268432617
amortized time for sample size  40 is:  9.432673454284668e-05
preprocessing time for sampling: 0.03483319282531738
amortized time for sample size  45 is:  9.443971845838759e-05
preprocessing time for sampling: 0.0347750186920166
amortized time for sample size  50 is:  9.467058181762695e-05
preprocessing time for sampling: 0.03480219841003418
amortized time for sample size  55 is:  9.465456008911133e-05
preprocessing time for sampling: 0.03467702865600586
amortized time for sample size  60 is:  9.59602197011312e-05
preprocessing time for sampling: 0.03443598747253418
amortized time for sample size  65 is:  9.481235650869519e-05
preprocessing time for sampling: 0.03482317924499512
amortized time for sample size  70 is:  9.463105882917131e-05
preprocessing time for sampling: 0.03483009338378906
amortized time for sample size  75 is:  9.470361073811849e-05
preprocessing time for sampling: 0.03481006622314453
amortized time for sample size  80 is:  9.467443823814393e-05
preprocessing time for sampling: 0.03484201431274414
amortized time for sample size  85 is:  9.469873764935662e-05
preprocessing time for sampling: 0.0348358154296875
amortized time for sample size  90 is:  9.476425912645126e-05
preprocessing time for sampling: 0.03482699394226074
amortized time for sample size  95 is:  9.476310328433389e-05
preprocessing time for sampling: 0.03489327430725098
amortized time for sample size  100 is:  9.483261108398439e-05
preprocessing time for sampling: 0.03481698036193848
amortized time for sample size  105 is:  9.483800615583148e-05
preprocessing time for sampling: 0.03484916687011719
amortized time for sample size  110 is:  9.47974595156583e-05
preprocessing time for sampling: 0.03490090370178223
amortized time for sample size  115 is:  9.499668038409692e-05
preprocessing time for sampling: 0.03489995002746582
amortized time for sample size  120 is:  9.496543804804483e-05
preprocessing time for sampling: 0.03481602668762207
amortized time for sample size  125 is:  9.484264373779297e-05
preprocessing time for sampling: 0.03481483459472656
amortized time for sample size  130 is:  9.496505443866437e-05
preprocessing time for sampling: 0.03479886054992676
amortized time for sample size  135 is:  9.484434127807617e-05
preprocessing time for sampling: 0.03481793403625488
amortized time for sample size  140 is:  9.466150828770229e-05
preprocessing time for sampling: 0.03487062454223633
amortized time for sample size  145 is:  9.475999042905609e-05
preprocessing time for sampling: 0.034800052642822266
amortized time for sample size  150 is:  9.479106267293295e-05
preprocessing time for sampling: 0.034810781478881836
amortized time for sample size  155 is:  9.47947809773107e-05
preprocessing time for sampling: 0.03481912612915039
amortized time for sample size  160 is:  9.46066081523895e-05
preprocessing time for sampling: 0.0348668098449707
amortized time for sample size  165 is:  9.471160715276545e-05
preprocessing time for sampling: 0.03485393524169922
amortized time for sample size  170 is:  9.481944757349349e-05
preprocessing time for sampling: 0.03479194641113281
amortized time for sample size  175 is:  9.472555433000835e-05
preprocessing time for sampling: 0.03480410575866699
amortized time for sample size  180 is:  9.488969379001194e-05
preprocessing time for sampling: 0.03482317924499512
amortized time for sample size  185 is:  9.49446575061695e-05
preprocessing time for sampling: 0.03490614891052246
amortized time for sample size  190 is:  9.504645749142294e-05
preprocessing time for sampling: 0.03485417366027832
amortized time for sample size  195 is:  9.494676345433943e-05
preprocessing time for sampling: 0.03483915328979492
amortized time for sample size  200 is:  9.674992561340333e-05
preprocessing time for sampling: 0.034777164459228516
amortized time for sample size  205 is:  9.539259933843844e-05
preprocessing time for sampling: 0.03481316566467285
amortized time for sample size  210 is:  9.549222673688614e-05
preprocessing time for sampling: 0.03476905822753906
amortized time for sample size  215 is:  9.541145590848701e-05
preprocessing time for sampling: 0.03479194641113281
amortized time for sample size  220 is:  9.550738334655761e-05
preprocessing time for sampling: 0.034922122955322266
amortized time for sample size  225 is:  9.52545271979438e-05
preprocessing time for sampling: 0.03481602668762207
amortized time for sample size  230 is:  9.5498686251433e-05
preprocessing time for sampling: 0.034806251525878906
amortized time for sample size  235 is:  9.524908471614756e-05
preprocessing time for sampling: 0.0348050594329834
amortized time for sample size  240 is:  9.521758556365969e-05
preprocessing time for sampling: 0.03487896919250488
amortized time for sample size  245 is:  9.565801036601162e-05
preprocessing time for sampling: 0.03484010696411133
amortized time for sample size  250 is:  9.494892120361328e-05
*** results for plotting, beta= 0.6 

mean_list= [np.float64(0.75), np.float64(0.86), np.float64(0.9000000000000001), np.float64(0.82), np.float64(0.9200000000000002), np.float64(0.9200000000000002), np.float64(0.95), np.float64(0.93), np.float64(0.9800000000000001), np.float64(0.9400000000000001), np.float64(0.9099999999999999), np.float64(0.99), np.float64(0.95), np.float64(0.9800000000000001), np.float64(0.9800000000000001), np.float64(1.0), np.float64(0.9800000000000001), np.float64(0.99), np.float64(1.0), np.float64(0.9800000000000001), np.float64(0.9800000000000001), np.float64(0.99), np.float64(0.99), np.float64(0.99), np.float64(1.0), 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(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), 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(0.08062257748298553), np.float64(0.11135528725660045), np.float64(0.06324555320336757), np.float64(0.14), np.float64(0.0748331477354788), np.float64(0.0748331477354788), np.float64(0.04999999999999999), np.float64(0.06403124237432847), np.float64(0.039999999999999994), np.float64(0.06633249580710798), np.float64(0.09433981132056604), np.float64(0.029999999999999992), np.float64(0.08062257748298547), np.float64(0.039999999999999994), np.float64(0.039999999999999994), np.float64(0.0), np.float64(0.039999999999999994), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.039999999999999994), np.float64(0.039999999999999994), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.0), 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(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), 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: 0.034816741943359375
amortized time for sample size  5 is:  9.482574462890625e-05
preprocessing time for sampling: 0.03482198715209961
amortized time for sample size  10 is:  9.480285644531247e-05
preprocessing time for sampling: 0.03490400314331055
amortized time for sample size  15 is:  9.496704737345378e-05
preprocessing time for sampling: 0.0348360538482666
amortized time for sample size  20 is:  9.478580951690676e-05
preprocessing time for sampling: 0.0348508358001709
amortized time for sample size  25 is:  9.470930099487306e-05
preprocessing time for sampling: 0.03481888771057129
amortized time for sample size  30 is:  9.468523661295572e-05
preprocessing time for sampling: 0.03487992286682129
amortized time for sample size  35 is:  9.464032309395926e-05
preprocessing time for sampling: 0.03482794761657715
amortized time for sample size  40 is:  9.4815194606781e-05
preprocessing time for sampling: 0.03489804267883301
amortized time for sample size  45 is:  9.477901458740234e-05
preprocessing time for sampling: 0.03482794761657715
amortized time for sample size  50 is:  9.479861259460449e-05
preprocessing time for sampling: 0.034829139709472656
amortized time for sample size  55 is:  9.464025497436525e-05
preprocessing time for sampling: 0.034712791442871094
amortized time for sample size  60 is:  9.476820627848306e-05
preprocessing time for sampling: 0.03445792198181152
amortized time for sample size  65 is:  9.478070185734676e-05
preprocessing time for sampling: 0.034822940826416016
amortized time for sample size  70 is:  9.465193748474122e-05
preprocessing time for sampling: 0.03479290008544922
amortized time for sample size  75 is:  9.462823867797855e-05
preprocessing time for sampling: 0.03484797477722168
amortized time for sample size  80 is:  9.478902816772461e-05
preprocessing time for sampling: 0.0348050594329834
amortized time for sample size  85 is:  9.482978372012867e-05
preprocessing time for sampling: 0.03482389450073242
amortized time for sample size  90 is:  9.467845492892795e-05
preprocessing time for sampling: 0.034883975982666016
amortized time for sample size  95 is:  9.473389073422081e-05
preprocessing time for sampling: 0.03481888771057129
amortized time for sample size  100 is:  9.477496147155761e-05
preprocessing time for sampling: 0.03484392166137695
amortized time for sample size  105 is:  9.476850146339054e-05
preprocessing time for sampling: 0.034793853759765625
amortized time for sample size  110 is:  9.47426665912975e-05
preprocessing time for sampling: 0.03480815887451172
amortized time for sample size  115 is:  9.465426984040633e-05
preprocessing time for sampling: 0.03481912612915039
amortized time for sample size  120 is:  9.479029973347982e-05
preprocessing time for sampling: 0.034826040267944336
amortized time for sample size  125 is:  9.471031188964843e-05
preprocessing time for sampling: 0.034822940826416016
amortized time for sample size  130 is:  9.472333467923677e-05
preprocessing time for sampling: 0.03480982780456543
amortized time for sample size  135 is:  9.469781098542391e-05
preprocessing time for sampling: 0.034889936447143555
amortized time for sample size  140 is:  9.480105127607075e-05
preprocessing time for sampling: 0.034803152084350586
amortized time for sample size  145 is:  9.485026063590217e-05
preprocessing time for sampling: 0.03481006622314453
amortized time for sample size  150 is:  9.492843945821127e-05
preprocessing time for sampling: 0.034806013107299805
amortized time for sample size  155 is:  9.474542064051477e-05
preprocessing time for sampling: 0.034845829010009766
amortized time for sample size  160 is:  9.479929506778719e-05
preprocessing time for sampling: 0.034828901290893555
amortized time for sample size  165 is:  9.481456063010475e-05
preprocessing time for sampling: 0.03484010696411133
amortized time for sample size  170 is:  9.471817577586455e-05
preprocessing time for sampling: 0.03479909896850586
amortized time for sample size  175 is:  9.677374703543526e-05
preprocessing time for sampling: 0.034897804260253906
amortized time for sample size  180 is:  9.517323970794676e-05
preprocessing time for sampling: 0.03488302230834961
amortized time for sample size  185 is:  9.519848952422272e-05
preprocessing time for sampling: 0.034867286682128906
amortized time for sample size  190 is:  9.520080215052556e-05
preprocessing time for sampling: 0.034832000732421875
amortized time for sample size  195 is:  9.615937257424378e-05
preprocessing time for sampling: 0.03532004356384277
amortized time for sample size  200 is:  9.51529264450073e-05
preprocessing time for sampling: 0.03479290008544922
amortized time for sample size  205 is:  9.509322701430904e-05
preprocessing time for sampling: 0.03516101837158203
amortized time for sample size  210 is:  9.51656727563767e-05
preprocessing time for sampling: 0.034780263900756836
amortized time for sample size  215 is:  9.556782522866892e-05
preprocessing time for sampling: 0.034889936447143555
amortized time for sample size  220 is:  9.563143686814742e-05
preprocessing time for sampling: 0.034845829010009766
amortized time for sample size  225 is:  9.533192316691082e-05
preprocessing time for sampling: 0.03482198715209961
amortized time for sample size  230 is:  9.511683298193892e-05
preprocessing time for sampling: 0.034945011138916016
amortized time for sample size  235 is:  9.510054486863156e-05
preprocessing time for sampling: 0.03486514091491699
amortized time for sample size  240 is:  9.484802683194477e-05
preprocessing time for sampling: 0.03487205505371094
amortized time for sample size  245 is:  9.543532741313078e-05
preprocessing time for sampling: 0.03484392166137695
amortized time for sample size  250 is:  9.501709938049316e-05
*** results for plotting, beta= 0.8 

mean_list= [np.float64(0.7800000000000001), np.float64(0.89), np.float64(0.97), np.float64(0.9400000000000001), np.float64(0.9800000000000001), np.float64(0.97), np.float64(0.9800000000000001), np.float64(0.99), np.float64(1.0), np.float64(0.9800000000000001), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(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)]
std_list= [np.float64(0.12489995996796797), np.float64(0.11357816691600549), np.float64(0.04582575694955839), np.float64(0.07999999999999999), np.float64(0.039999999999999994), np.float64(0.045825756949558386), np.float64(0.039999999999999994), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.039999999999999994), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.029999999999999992), 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)]
beta: 1
preprocessing time for sampling: 0.04054999351501465
amortized time for sample size  5 is:  0.0001029067039489746
preprocessing time for sampling: 0.0405118465423584
amortized time for sample size  10 is:  0.00010321211814880372
preprocessing time for sampling: 0.04056501388549805
amortized time for sample size  15 is:  0.00010275236765543621
preprocessing time for sampling: 0.04042315483093262
amortized time for sample size  20 is:  0.000102933406829834
preprocessing time for sampling: 0.04040884971618652
amortized time for sample size  25 is:  0.00010338010787963866
preprocessing time for sampling: 0.04058504104614258
amortized time for sample size  30 is:  0.00010335350036621095
preprocessing time for sampling: 0.04057192802429199
amortized time for sample size  35 is:  0.00010320547648838588
preprocessing time for sampling: 0.04045701026916504
amortized time for sample size  40 is:  0.00010330343246459962
preprocessing time for sampling: 0.04056406021118164
amortized time for sample size  45 is:  0.00010327508714463976
preprocessing time for sampling: 0.04051709175109863
amortized time for sample size  50 is:  0.0001032670021057129
preprocessing time for sampling: 0.040283203125
amortized time for sample size  55 is:  0.00010306960886174981
preprocessing time for sampling: 0.040342092514038086
amortized time for sample size  60 is:  0.00010312449932098389
preprocessing time for sampling: 0.0404210090637207
amortized time for sample size  65 is:  0.00010302231861994816
preprocessing time for sampling: 0.04025912284851074
amortized time for sample size  70 is:  0.00010350421496800012
preprocessing time for sampling: 0.04065299034118652
amortized time for sample size  75 is:  0.00010322233835856119
preprocessing time for sampling: 0.04054403305053711
amortized time for sample size  80 is:  0.00010273957252502444
preprocessing time for sampling: 0.04031991958618164
amortized time for sample size  85 is:  0.00010273406084846046
preprocessing time for sampling: 0.04049205780029297
amortized time for sample size  90 is:  0.00010291428036159939
preprocessing time for sampling: 0.04053521156311035
amortized time for sample size  95 is:  0.0001029006807427657
preprocessing time for sampling: 0.04033017158508301
amortized time for sample size  100 is:  0.0001028157949447632
preprocessing time for sampling: 0.04047989845275879
amortized time for sample size  105 is:  0.0001030583381652832
preprocessing time for sampling: 0.04062080383300781
amortized time for sample size  110 is:  0.00010315153815529565
preprocessing time for sampling: 0.04028177261352539
amortized time for sample size  115 is:  0.00010297082818072776
preprocessing time for sampling: 0.04047703742980957
amortized time for sample size  120 is:  0.00010306090116500853
preprocessing time for sampling: 0.04047703742980957
amortized time for sample size  125 is:  0.00010295467376708984
preprocessing time for sampling: 0.040283918380737305
amortized time for sample size  130 is:  0.00010310836938711312
preprocessing time for sampling: 0.04051089286804199
amortized time for sample size  135 is:  0.00010293831648649991
preprocessing time for sampling: 0.040487051010131836
amortized time for sample size  140 is:  0.00010636600426265172
preprocessing time for sampling: 0.040255069732666016
amortized time for sample size  145 is:  0.00010290223154528388
preprocessing time for sampling: 0.04049825668334961
amortized time for sample size  150 is:  0.00010296707153320311
preprocessing time for sampling: 0.04047203063964844
amortized time for sample size  155 is:  0.00010285918943343623
preprocessing time for sampling: 0.04024195671081543
amortized time for sample size  160 is:  0.00010294042527675629
preprocessing time for sampling: 0.04051995277404785
amortized time for sample size  165 is:  0.00010276110967000324
preprocessing time for sampling: 0.040522098541259766
amortized time for sample size  170 is:  0.00010315418243408205
preprocessing time for sampling: 0.04032111167907715
amortized time for sample size  175 is:  0.00010296505519321987
preprocessing time for sampling: 0.04046511650085449
amortized time for sample size  180 is:  0.00010291273064083522
preprocessing time for sampling: 0.04047083854675293
amortized time for sample size  185 is:  0.00010301240714820656
preprocessing time for sampling: 0.04030585289001465
amortized time for sample size  190 is:  0.00010306784981175472
preprocessing time for sampling: 0.040488243103027344
amortized time for sample size  195 is:  0.00010296288514748601
preprocessing time for sampling: 0.04040694236755371
amortized time for sample size  200 is:  0.00010281759500503537
preprocessing time for sampling: 0.04027700424194336
amortized time for sample size  205 is:  0.00010302102856519746
preprocessing time for sampling: 0.04050397872924805
amortized time for sample size  210 is:  0.00010391058240618022
preprocessing time for sampling: 0.040544986724853516
amortized time for sample size  215 is:  0.00010303554978481558
preprocessing time for sampling: 0.040266990661621094
amortized time for sample size  220 is:  0.00010322811386801977
preprocessing time for sampling: 0.04047107696533203
amortized time for sample size  225 is:  0.0001030229886372884
preprocessing time for sampling: 0.04047417640686035
amortized time for sample size  230 is:  0.00010316526371499767
preprocessing time for sampling: 0.040268659591674805
amortized time for sample size  235 is:  0.00010307345491774542
preprocessing time for sampling: 0.04048299789428711
amortized time for sample size  240 is:  0.00010314713915189108
preprocessing time for sampling: 0.04043912887573242
amortized time for sample size  245 is:  0.00010316648288648956
preprocessing time for sampling: 0.04030013084411621
amortized time for sample size  250 is:  0.00010311681747436524
*** results for plotting, beta= 1 

mean_list= [np.float64(0.89), np.float64(0.93), np.float64(0.97), np.float64(0.9400000000000001), 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), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), 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(0.1044030650891055), np.float64(0.07810249675906653), np.float64(0.045825756949558386), np.float64(0.06633249580710798), 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), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), 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: 0.034850120544433594
amortized time for sample size  5 is:  9.496545791625977e-05
preprocessing time for sampling: 0.03481698036193848
amortized time for sample size  10 is:  9.488821029663086e-05
preprocessing time for sampling: 0.03486514091491699
amortized time for sample size  15 is:  9.494098027547202e-05
preprocessing time for sampling: 0.034829139709472656
amortized time for sample size  20 is:  9.504759311676025e-05
preprocessing time for sampling: 0.03448605537414551
amortized time for sample size  25 is:  9.531536102294922e-05
preprocessing time for sampling: 0.034513235092163086
amortized time for sample size  30 is:  9.497372309366864e-05
preprocessing time for sampling: 0.03481793403625488
amortized time for sample size  35 is:  9.497138432094029e-05
preprocessing time for sampling: 0.0348207950592041
amortized time for sample size  40 is:  9.496206045150756e-05
preprocessing time for sampling: 0.034774065017700195
amortized time for sample size  45 is:  9.480396906534828e-05
preprocessing time for sampling: 0.03481721878051758
amortized time for sample size  50 is:  9.484343528747559e-05
preprocessing time for sampling: 0.034447669982910156
amortized time for sample size  55 is:  9.513174403797498e-05
preprocessing time for sampling: 0.040534019470214844
amortized time for sample size  60 is:  9.452581405639646e-05
preprocessing time for sampling: 0.034475088119506836
amortized time for sample size  65 is:  9.551701178917517e-05
preprocessing time for sampling: 0.034811973571777344
amortized time for sample size  70 is:  9.47435242789132e-05
preprocessing time for sampling: 0.034853219985961914
amortized time for sample size  75 is:  9.476734797159832e-05
preprocessing time for sampling: 0.03483390808105469
amortized time for sample size  80 is:  9.508118033409119e-05
preprocessing time for sampling: 0.03448128700256348
amortized time for sample size  85 is:  9.515434152939745e-05
preprocessing time for sampling: 0.03449106216430664
amortized time for sample size  90 is:  9.497751129998101e-05
preprocessing time for sampling: 0.03486299514770508
amortized time for sample size  95 is:  9.487490904958623e-05
preprocessing time for sampling: 0.034807682037353516
amortized time for sample size  100 is:  9.558129310607907e-05
preprocessing time for sampling: 0.03481602668762207
amortized time for sample size  105 is:  9.530289967854818e-05
preprocessing time for sampling: 0.03487372398376465
amortized time for sample size  110 is:  9.532000801780008e-05
preprocessing time for sampling: 0.034520626068115234
amortized time for sample size  115 is:  9.497059946474822e-05
preprocessing time for sampling: 0.03451418876647949
amortized time for sample size  120 is:  9.493241707483928e-05
preprocessing time for sampling: 0.034851789474487305
amortized time for sample size  125 is:  9.482603073120117e-05
preprocessing time for sampling: 0.03483009338378906
amortized time for sample size  130 is:  9.508835352384127e-05
preprocessing time for sampling: 0.034816741943359375
amortized time for sample size  135 is:  9.477461708916556e-05
preprocessing time for sampling: 0.034802913665771484
amortized time for sample size  140 is:  9.48643684387207e-05
preprocessing time for sampling: 0.034525156021118164
amortized time for sample size  145 is:  9.521305149999158e-05
preprocessing time for sampling: 0.0344851016998291
amortized time for sample size  150 is:  9.491734504699709e-05
preprocessing time for sampling: 0.03485584259033203
amortized time for sample size  155 is:  9.483315867762412e-05
preprocessing time for sampling: 0.03479313850402832
amortized time for sample size  160 is:  9.514275193214416e-05
preprocessing time for sampling: 0.03482699394226074
amortized time for sample size  165 is:  9.50007727651885e-05
preprocessing time for sampling: 0.03481602668762207
amortized time for sample size  170 is:  9.490397397209617e-05
preprocessing time for sampling: 0.034552812576293945
amortized time for sample size  175 is:  9.509432656424383e-05
preprocessing time for sampling: 0.034487009048461914
amortized time for sample size  180 is:  9.499828020731609e-05
preprocessing time for sampling: 0.034809112548828125
amortized time for sample size  185 is:  9.49623520309861e-05
preprocessing time for sampling: 0.03481292724609375
amortized time for sample size  190 is:  9.959164418672262e-05
preprocessing time for sampling: 0.03531503677368164
amortized time for sample size  195 is:  9.833026543641704e-05
preprocessing time for sampling: 0.0354456901550293
amortized time for sample size  200 is:  9.682096242904663e-05
preprocessing time for sampling: 0.03457212448120117
amortized time for sample size  205 is:  9.721593159001045e-05
preprocessing time for sampling: 0.03467917442321777
amortized time for sample size  210 is:  9.567052977425713e-05
preprocessing time for sampling: 0.03512287139892578
amortized time for sample size  215 is:  9.551151408705602e-05
preprocessing time for sampling: 0.03482818603515625
amortized time for sample size  220 is:  9.53916094519875e-05
preprocessing time for sampling: 0.03497505187988281
amortized time for sample size  225 is:  9.550431569417318e-05
preprocessing time for sampling: 0.03492569923400879
amortized time for sample size  230 is:  9.557154904241147e-05
preprocessing time for sampling: 0.03461503982543945
amortized time for sample size  235 is:  9.539434757638488e-05
preprocessing time for sampling: 0.034452199935913086
amortized time for sample size  240 is:  9.607611099878946e-05
preprocessing time for sampling: 0.035012006759643555
amortized time for sample size  245 is:  9.54698543159329e-05
preprocessing time for sampling: 0.03483295440673828
amortized time for sample size  250 is:  9.501020431518557e-05
*** results for plotting, beta= 1.2 

mean_list= [np.float64(0.9800000000000001), 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(0.039999999999999994), 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)]
