beta: 0.2
preprocessing time for sampling: 0.008955717086791992
amortized time for sample size  5 is:  7.891464233398438e-05
preprocessing time for sampling: 0.008891820907592773
amortized time for sample size  10 is:  7.967281341552734e-05
preprocessing time for sampling: 0.009177207946777344
amortized time for sample size  15 is:  7.80175526936849e-05
preprocessing time for sampling: 0.008895158767700195
amortized time for sample size  20 is:  7.777607440948488e-05
preprocessing time for sampling: 0.00872802734375
amortized time for sample size  25 is:  7.738513946533203e-05
preprocessing time for sampling: 0.008704900741577148
amortized time for sample size  30 is:  7.76513417561849e-05
preprocessing time for sampling: 0.009067058563232422
amortized time for sample size  35 is:  7.889522824968612e-05
preprocessing time for sampling: 0.008874177932739258
amortized time for sample size  40 is:  7.95813798904419e-05
preprocessing time for sampling: 0.008882999420166016
amortized time for sample size  45 is:  7.849401897854276e-05
preprocessing time for sampling: 0.008965730667114258
amortized time for sample size  50 is:  7.786498069763183e-05
preprocessing time for sampling: 0.009429931640625
amortized time for sample size  55 is:  7.80655254017223e-05
preprocessing time for sampling: 0.008826732635498047
amortized time for sample size  60 is:  7.883636156717937e-05
preprocessing time for sampling: 0.008795976638793945
amortized time for sample size  65 is:  7.8033263866718e-05
preprocessing time for sampling: 0.008957147598266602
amortized time for sample size  70 is:  7.772180012294225e-05
preprocessing time for sampling: 0.009052038192749023
amortized time for sample size  75 is:  7.875426610310873e-05
preprocessing time for sampling: 0.008746862411499023
amortized time for sample size  80 is:  7.812970876693725e-05
preprocessing time for sampling: 0.00900578498840332
amortized time for sample size  85 is:  7.857586355770334e-05
preprocessing time for sampling: 0.008906841278076172
amortized time for sample size  90 is:  7.814102702670627e-05
preprocessing time for sampling: 0.00875997543334961
amortized time for sample size  95 is:  7.850965700651471e-05
preprocessing time for sampling: 0.008758068084716797
amortized time for sample size  100 is:  7.73380994796753e-05
preprocessing time for sampling: 0.008728742599487305
amortized time for sample size  105 is:  7.726526260375975e-05
preprocessing time for sampling: 0.008739948272705078
amortized time for sample size  110 is:  7.727705348621715e-05
preprocessing time for sampling: 0.00874185562133789
amortized time for sample size  115 is:  7.754715629245925e-05
preprocessing time for sampling: 0.008734941482543945
amortized time for sample size  120 is:  7.719683647155763e-05
preprocessing time for sampling: 0.008713245391845703
amortized time for sample size  125 is:  7.737083435058593e-05
preprocessing time for sampling: 0.00872492790222168
amortized time for sample size  130 is:  7.732816842886118e-05
preprocessing time for sampling: 0.008726835250854492
amortized time for sample size  135 is:  7.794092319629811e-05
preprocessing time for sampling: 0.008767843246459961
amortized time for sample size  140 is:  7.762842518942696e-05
preprocessing time for sampling: 0.008774995803833008
amortized time for sample size  145 is:  7.729841100758519e-05
preprocessing time for sampling: 0.008745908737182617
amortized time for sample size  150 is:  7.73176352183024e-05
preprocessing time for sampling: 0.008741140365600586
amortized time for sample size  155 is:  7.736295269381617e-05
preprocessing time for sampling: 0.008729934692382812
amortized time for sample size  160 is:  7.763627171516419e-05
preprocessing time for sampling: 0.008725881576538086
amortized time for sample size  165 is:  7.755224632494376e-05
preprocessing time for sampling: 0.008726119995117188
amortized time for sample size  170 is:  7.730576571296244e-05
preprocessing time for sampling: 0.008731842041015625
amortized time for sample size  175 is:  7.765372140066964e-05
preprocessing time for sampling: 0.008774042129516602
amortized time for sample size  180 is:  7.79395235909356e-05
preprocessing time for sampling: 0.00886392593383789
amortized time for sample size  185 is:  7.921941860302074e-05
preprocessing time for sampling: 0.008768081665039062
amortized time for sample size  190 is:  7.768752700404117e-05
preprocessing time for sampling: 0.008733987808227539
amortized time for sample size  195 is:  7.805201946160731e-05
preprocessing time for sampling: 0.008734941482543945
amortized time for sample size  200 is:  7.850890159606933e-05
preprocessing time for sampling: 0.00881195068359375
amortized time for sample size  205 is:  7.789581577952316e-05
preprocessing time for sampling: 0.00872492790222168
amortized time for sample size  210 is:  7.898319335210891e-05
preprocessing time for sampling: 0.009016752243041992
amortized time for sample size  215 is:  7.788057105485783e-05
preprocessing time for sampling: 0.00877690315246582
amortized time for sample size  220 is:  7.788370956074107e-05
preprocessing time for sampling: 0.008804082870483398
amortized time for sample size  225 is:  7.960450914171007e-05
preprocessing time for sampling: 0.008713960647583008
amortized time for sample size  230 is:  7.752827976060949e-05
preprocessing time for sampling: 0.008726835250854492
amortized time for sample size  235 is:  7.862685589080161e-05
preprocessing time for sampling: 0.008730888366699219
amortized time for sample size  240 is:  7.868787646293638e-05
preprocessing time for sampling: 0.01697683334350586
amortized time for sample size  245 is:  7.823932414152186e-05
preprocessing time for sampling: 0.00877070426940918
amortized time for sample size  250 is:  7.812275886535645e-05
*** results for plotting, beta= 0.2 

mean_list= [np.float64(0.36), np.float64(0.45999999999999996), np.float64(0.41000000000000003), np.float64(0.45), np.float64(0.4800000000000001), np.float64(0.38), np.float64(0.5700000000000001), np.float64(0.6), np.float64(0.55), np.float64(0.63), np.float64(0.57), np.float64(0.6), np.float64(0.62), np.float64(0.64), np.float64(0.58), np.float64(0.5399999999999999), np.float64(0.55), np.float64(0.55), np.float64(0.5800000000000001), np.float64(0.5700000000000001), np.float64(0.6900000000000001), np.float64(0.5599999999999999), np.float64(0.65), np.float64(0.6100000000000001), np.float64(0.5999999999999999), np.float64(0.6900000000000001), np.float64(0.64), np.float64(0.6499999999999999), np.float64(0.59), np.float64(0.53), np.float64(0.62), np.float64(0.6399999999999999), np.float64(0.6399999999999999), np.float64(0.6799999999999999), np.float64(0.6199999999999999), np.float64(0.65), np.float64(0.5800000000000001), np.float64(0.63), np.float64(0.58), np.float64(0.6799999999999999), np.float64(0.57), np.float64(0.6700000000000002), np.float64(0.6399999999999999), np.float64(0.72), np.float64(0.5800000000000001), np.float64(0.72), np.float64(0.6699999999999999), np.float64(0.62), np.float64(0.67), np.float64(0.6699999999999999)]
std_list= [np.float64(0.13564659966250536), np.float64(0.1854723699099141), np.float64(0.16401219466856723), np.float64(0.15652475842498528), np.float64(0.12489995996796796), np.float64(0.10770329614269007), np.float64(0.16763054614240208), np.float64(0.1341640786499874), np.float64(0.13601470508735442), np.float64(0.1676305461424021), np.float64(0.11874342087037916), np.float64(0.09999999999999999), np.float64(0.059999999999999984), np.float64(0.1562049935181331), np.float64(0.17204650534085253), np.float64(0.07999999999999999), np.float64(0.13601470508735442), np.float64(0.15000000000000002), np.float64(0.12489995996796796), np.float64(0.12688577540449517), np.float64(0.157797338380595), np.float64(0.11135528725660043), np.float64(0.11180339887498948), np.float64(0.19209372712298547), np.float64(0.11832159566199232), np.float64(0.1972308292331602), np.float64(0.12000000000000002), np.float64(0.09219544457292887), np.float64(0.09433981132056601), np.float64(0.1345362404707371), np.float64(0.18867962264113208), np.float64(0.13564659966250536), np.float64(0.14966629547095767), np.float64(0.1077032961426901), np.float64(0.1077032961426901), np.float64(0.24186773244895649), np.float64(0.1661324772583615), np.float64(0.14177446878757824), np.float64(0.11661903789690597), np.float64(0.12489995996796797), np.float64(0.10049875621120888), np.float64(0.1345362404707371), np.float64(0.0916515138991168), np.float64(0.18867962264113208), np.float64(0.14), np.float64(0.14696938456699069), np.float64(0.11), np.float64(0.13999999999999999), np.float64(0.19519221295943137), np.float64(0.14866068747318506)]
beta: 0.4
preprocessing time for sampling: 0.009015083312988281
amortized time for sample size  5 is:  7.850790023803711e-05
preprocessing time for sampling: 0.008738994598388672
amortized time for sample size  10 is:  9.090781211853025e-05
preprocessing time for sampling: 0.008978843688964844
amortized time for sample size  15 is:  9.213558832804364e-05
preprocessing time for sampling: 0.008877992630004883
amortized time for sample size  20 is:  7.815051078796386e-05
preprocessing time for sampling: 0.008763313293457031
amortized time for sample size  25 is:  7.780294418334961e-05
preprocessing time for sampling: 0.00878000259399414
amortized time for sample size  30 is:  7.775473594665528e-05
preprocessing time for sampling: 0.008747100830078125
amortized time for sample size  35 is:  7.743433543613978e-05
preprocessing time for sampling: 0.008727788925170898
amortized time for sample size  40 is:  7.759296894073486e-05
preprocessing time for sampling: 0.008748054504394531
amortized time for sample size  45 is:  7.734992769029406e-05
preprocessing time for sampling: 0.008730888366699219
amortized time for sample size  50 is:  7.842502593994139e-05
preprocessing time for sampling: 0.00873708724975586
amortized time for sample size  55 is:  7.759757475419478e-05
preprocessing time for sampling: 0.008800029754638672
amortized time for sample size  60 is:  7.776304086049398e-05
preprocessing time for sampling: 0.008828878402709961
amortized time for sample size  65 is:  7.84917978140024e-05
preprocessing time for sampling: 0.00876307487487793
amortized time for sample size  70 is:  7.785541670663016e-05
preprocessing time for sampling: 0.00878000259399414
amortized time for sample size  75 is:  7.788689931233724e-05
preprocessing time for sampling: 0.008939027786254883
amortized time for sample size  80 is:  7.877895236015319e-05
preprocessing time for sampling: 0.008734941482543945
amortized time for sample size  85 is:  7.958384121165558e-05
preprocessing time for sampling: 0.008750677108764648
amortized time for sample size  90 is:  7.83695379892985e-05
preprocessing time for sampling: 0.008810758590698242
amortized time for sample size  95 is:  7.80942063582571e-05
preprocessing time for sampling: 0.008819103240966797
amortized time for sample size  100 is:  7.796378135681151e-05
preprocessing time for sampling: 0.008841276168823242
amortized time for sample size  105 is:  7.815202077229817e-05
preprocessing time for sampling: 0.008877038955688477
amortized time for sample size  110 is:  7.904601097106932e-05
preprocessing time for sampling: 0.008741140365600586
amortized time for sample size  115 is:  7.77386997057044e-05
preprocessing time for sampling: 0.008754968643188477
amortized time for sample size  120 is:  7.828046878178915e-05
preprocessing time for sampling: 0.00879526138305664
amortized time for sample size  125 is:  7.784967422485351e-05
preprocessing time for sampling: 0.008836030960083008
amortized time for sample size  130 is:  7.797679534325233e-05
preprocessing time for sampling: 0.008835077285766602
amortized time for sample size  135 is:  7.791808799461082e-05
preprocessing time for sampling: 0.008768796920776367
amortized time for sample size  140 is:  7.752518994467598e-05
preprocessing time for sampling: 0.008740901947021484
amortized time for sample size  145 is:  7.796218477446458e-05
preprocessing time for sampling: 0.009313106536865234
amortized time for sample size  150 is:  7.743959426879883e-05
preprocessing time for sampling: 0.008754253387451172
amortized time for sample size  155 is:  7.729505723522555e-05
preprocessing time for sampling: 0.008754968643188477
amortized time for sample size  160 is:  7.744750380516053e-05
preprocessing time for sampling: 0.008727788925170898
amortized time for sample size  165 is:  7.735930067120178e-05
preprocessing time for sampling: 0.00873708724975586
amortized time for sample size  170 is:  7.720212375416475e-05
preprocessing time for sampling: 0.008719921112060547
amortized time for sample size  175 is:  7.727233341761998e-05
preprocessing time for sampling: 0.008726119995117188
amortized time for sample size  180 is:  7.748283280266656e-05
preprocessing time for sampling: 0.008755922317504883
amortized time for sample size  185 is:  7.721489828986091e-05
preprocessing time for sampling: 0.008734941482543945
amortized time for sample size  190 is:  7.72388734315571e-05
preprocessing time for sampling: 0.00873112678527832
amortized time for sample size  195 is:  7.748663731110402e-05
preprocessing time for sampling: 0.008731842041015625
amortized time for sample size  200 is:  7.732607126235963e-05
preprocessing time for sampling: 0.008772850036621094
amortized time for sample size  205 is:  7.722908113060927e-05
preprocessing time for sampling: 0.008723020553588867
amortized time for sample size  210 is:  7.739169257027762e-05
preprocessing time for sampling: 0.008744239807128906
amortized time for sample size  215 is:  7.723498898883199e-05
preprocessing time for sampling: 0.008733987808227539
amortized time for sample size  220 is:  7.730735432017934e-05
preprocessing time for sampling: 0.00871586799621582
amortized time for sample size  225 is:  7.793697781032988e-05
preprocessing time for sampling: 0.009372949600219727
amortized time for sample size  230 is:  7.874756274016008e-05
preprocessing time for sampling: 0.009150028228759766
amortized time for sample size  235 is:  7.831669868306912e-05
preprocessing time for sampling: 0.008939027786254883
amortized time for sample size  240 is:  7.790979743003845e-05
preprocessing time for sampling: 0.008734941482543945
amortized time for sample size  245 is:  7.783003242648377e-05
preprocessing time for sampling: 0.008725643157958984
amortized time for sample size  250 is:  7.758541107177735e-05
*** results for plotting, beta= 0.4 

mean_list= [np.float64(0.5599999999999999), np.float64(0.61), np.float64(0.6199999999999999), np.float64(0.79), np.float64(0.76), np.float64(0.7700000000000001), np.float64(0.8), np.float64(0.8200000000000001), np.float64(0.8400000000000002), np.float64(0.7899999999999999), np.float64(0.8799999999999999), np.float64(0.8600000000000001), np.float64(0.85), np.float64(0.8700000000000001), np.float64(0.8600000000000001), np.float64(0.89), np.float64(0.93), np.float64(0.8899999999999999), np.float64(0.8899999999999999), np.float64(0.9), np.float64(0.9), np.float64(0.89), np.float64(0.8799999999999999), np.float64(0.89), np.float64(0.96), np.float64(0.97), np.float64(0.9), np.float64(0.9200000000000002), np.float64(0.9100000000000001), np.float64(0.93), np.float64(0.9600000000000002), np.float64(0.97), np.float64(0.9600000000000002), np.float64(0.9800000000000001), np.float64(0.95), np.float64(0.9800000000000001), np.float64(0.93), np.float64(0.95), np.float64(0.96), np.float64(0.9400000000000001), np.float64(0.96), np.float64(0.95), np.float64(0.97), np.float64(0.9700000000000001), np.float64(0.93), np.float64(0.95), np.float64(0.9400000000000001), np.float64(0.9700000000000001), np.float64(0.9399999999999998), np.float64(0.96)]
std_list= [np.float64(0.14282856857085696), np.float64(0.1044030650891055), np.float64(0.15362291495737218), np.float64(0.10440306508910552), np.float64(0.128062484748657), np.float64(0.12688577540449522), np.float64(0.08944271909999162), np.float64(0.1077032961426901), np.float64(0.08), np.float64(0.157797338380595), np.float64(0.11661903789690603), np.float64(0.08), np.float64(0.10246950765959599), np.float64(0.11874342087037916), np.float64(0.04898979485566355), np.float64(0.12206555615733704), np.float64(0.06403124237432847), np.float64(0.12206555615733702), np.float64(0.09433981132056604), np.float64(0.09999999999999999), np.float64(0.08944271909999159), np.float64(0.11357816691600549), np.float64(0.09797958971132713), np.float64(0.13), np.float64(0.06633249580710798), np.float64(0.045825756949558386), np.float64(0.11832159566199232), np.float64(0.059999999999999984), np.float64(0.08306623862918074), np.float64(0.06403124237432847), np.float64(0.06633249580710798), np.float64(0.06403124237432847), np.float64(0.06633249580710798), np.float64(0.039999999999999994), np.float64(0.04999999999999999), np.float64(0.039999999999999994), np.float64(0.07810249675906653), np.float64(0.08062257748298547), np.float64(0.04898979485566356), np.float64(0.07999999999999999), np.float64(0.06633249580710798), np.float64(0.06708203932499368), np.float64(0.04582575694955839), np.float64(0.06403124237432847), np.float64(0.07810249675906653), np.float64(0.04999999999999999), np.float64(0.06633249580710798), np.float64(0.04582575694955839), np.float64(0.09165151389911681), np.float64(0.04898979485566355)]
beta: 0.6
preprocessing time for sampling: 0.008745908737182617
amortized time for sample size  5 is:  7.71956443786621e-05
preprocessing time for sampling: 0.008717060089111328
amortized time for sample size  10 is:  7.715511322021484e-05
preprocessing time for sampling: 0.008723258972167969
amortized time for sample size  15 is:  7.774750391642253e-05
preprocessing time for sampling: 0.008978128433227539
amortized time for sample size  20 is:  7.763993740081788e-05
preprocessing time for sampling: 0.008734941482543945
amortized time for sample size  25 is:  7.708158493041994e-05
preprocessing time for sampling: 0.008727073669433594
amortized time for sample size  30 is:  7.707937558492025e-05
preprocessing time for sampling: 0.008732080459594727
amortized time for sample size  35 is:  7.693508693150112e-05
preprocessing time for sampling: 0.008728981018066406
amortized time for sample size  40 is:  7.714790105819702e-05
preprocessing time for sampling: 0.00874185562133789
amortized time for sample size  45 is:  7.724073198106554e-05
preprocessing time for sampling: 0.00872182846069336
amortized time for sample size  50 is:  7.75791645050049e-05
preprocessing time for sampling: 0.008727073669433594
amortized time for sample size  55 is:  7.712134447964755e-05
preprocessing time for sampling: 0.008785009384155273
amortized time for sample size  60 is:  7.78714418411255e-05
preprocessing time for sampling: 0.008908987045288086
amortized time for sample size  65 is:  7.78377239520733e-05
preprocessing time for sampling: 0.008749961853027344
amortized time for sample size  70 is:  7.737016677856444e-05
preprocessing time for sampling: 0.008740901947021484
amortized time for sample size  75 is:  7.715644836425782e-05
preprocessing time for sampling: 0.008739948272705078
amortized time for sample size  80 is:  7.708382606506346e-05
preprocessing time for sampling: 0.008747100830078125
amortized time for sample size  85 is:  7.731563904706169e-05
preprocessing time for sampling: 0.008735895156860352
amortized time for sample size  90 is:  7.699804835849338e-05
preprocessing time for sampling: 0.008726835250854492
amortized time for sample size  95 is:  7.729650798596833e-05
preprocessing time for sampling: 0.009068012237548828
amortized time for sample size  100 is:  7.74947166442871e-05
preprocessing time for sampling: 0.008790969848632812
amortized time for sample size  105 is:  7.706038157145183e-05
preprocessing time for sampling: 0.008751153945922852
amortized time for sample size  110 is:  7.713367722251199e-05
preprocessing time for sampling: 0.008744001388549805
amortized time for sample size  115 is:  7.7057465263035e-05
preprocessing time for sampling: 0.008766412734985352
amortized time for sample size  120 is:  7.711424430211384e-05
preprocessing time for sampling: 0.008740663528442383
amortized time for sample size  125 is:  7.762950897216796e-05
preprocessing time for sampling: 0.00875997543334961
amortized time for sample size  130 is:  7.751088875990647e-05
preprocessing time for sampling: 0.00873708724975586
amortized time for sample size  135 is:  7.721636030409072e-05
preprocessing time for sampling: 0.00877690315246582
amortized time for sample size  140 is:  7.802311011723108e-05
preprocessing time for sampling: 0.008814096450805664
amortized time for sample size  145 is:  7.766647996573613e-05
preprocessing time for sampling: 0.009002923965454102
amortized time for sample size  150 is:  7.734217643737792e-05
preprocessing time for sampling: 0.00874781608581543
amortized time for sample size  155 is:  7.724674286380892e-05
preprocessing time for sampling: 0.008751869201660156
amortized time for sample size  160 is:  7.826438546180726e-05
preprocessing time for sampling: 0.00872802734375
amortized time for sample size  165 is:  7.899243903882577e-05
preprocessing time for sampling: 0.009332895278930664
amortized time for sample size  170 is:  8.540627535651713e-05
preprocessing time for sampling: 0.009261131286621094
amortized time for sample size  175 is:  8.043065752301898e-05
preprocessing time for sampling: 0.009001970291137695
amortized time for sample size  180 is:  7.86052147547404e-05
preprocessing time for sampling: 0.008713960647583008
amortized time for sample size  185 is:  7.739381532411316e-05
preprocessing time for sampling: 0.008726835250854492
amortized time for sample size  190 is:  7.751980580781636e-05
preprocessing time for sampling: 0.008733034133911133
amortized time for sample size  195 is:  7.739927829840244e-05
preprocessing time for sampling: 0.00878000259399414
amortized time for sample size  200 is:  7.738603353500365e-05
preprocessing time for sampling: 0.008752107620239258
amortized time for sample size  205 is:  7.719415571631455e-05
preprocessing time for sampling: 0.008732080459594727
amortized time for sample size  210 is:  7.752201670692081e-05
preprocessing time for sampling: 0.008738994598388672
amortized time for sample size  215 is:  7.723254935685978e-05
preprocessing time for sampling: 0.008733272552490234
amortized time for sample size  220 is:  7.732772827148438e-05
preprocessing time for sampling: 0.008739233016967773
amortized time for sample size  225 is:  7.744168175591362e-05
preprocessing time for sampling: 0.008720159530639648
amortized time for sample size  230 is:  7.733535766601562e-05
preprocessing time for sampling: 0.008742809295654297
amortized time for sample size  235 is:  7.728829282395383e-05
preprocessing time for sampling: 0.008769035339355469
amortized time for sample size  240 is:  7.747981945673624e-05
preprocessing time for sampling: 0.00872492790222168
amortized time for sample size  245 is:  7.780964520512795e-05
preprocessing time for sampling: 0.008733987808227539
amortized time for sample size  250 is:  7.769780158996582e-05
*** results for plotting, beta= 0.6 

mean_list= [np.float64(0.76), np.float64(0.86), np.float64(0.78), np.float64(0.89), np.float64(0.9200000000000002), np.float64(0.9), np.float64(0.96), np.float64(0.99), np.float64(0.99), np.float64(0.97), np.float64(0.95), np.float64(0.9400000000000001), np.float64(0.9800000000000001), np.float64(0.96), np.float64(0.95), np.float64(0.99), np.float64(0.99), np.float64(0.97), np.float64(1.0), np.float64(1.0), np.float64(0.99), np.float64(0.99), np.float64(0.99), np.float64(1.0), np.float64(1.0), np.float64(0.9800000000000001), np.float64(0.99), np.float64(1.0), 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(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(0.99), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(0.99), np.float64(1.0)]
std_list= [np.float64(0.11135528725660046), np.float64(0.10198039027185571), np.float64(0.14), np.float64(0.11357816691600549), np.float64(0.07483314773547882), np.float64(0.07745966692414831), np.float64(0.04898979485566355), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.09000000000000001), np.float64(0.06708203932499368), np.float64(0.07999999999999999), np.float64(0.039999999999999994), np.float64(0.06633249580710798), np.float64(0.06708203932499367), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.04582575694955839), np.float64(0.0), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.0), np.float64(0.039999999999999994), np.float64(0.029999999999999992), np.float64(0.0), 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(0.029999999999999992), 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(0.029999999999999992), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.0)]
beta: 0.8
preprocessing time for sampling: 0.008716821670532227
amortized time for sample size  5 is:  7.781505584716797e-05
preprocessing time for sampling: 0.008805990219116211
amortized time for sample size  10 is:  7.821416854858399e-05
preprocessing time for sampling: 0.008816003799438477
amortized time for sample size  15 is:  7.790629069010417e-05
preprocessing time for sampling: 0.008783102035522461
amortized time for sample size  20 is:  7.74151086807251e-05
preprocessing time for sampling: 0.008713006973266602
amortized time for sample size  25 is:  7.70994186401367e-05
preprocessing time for sampling: 0.008752107620239258
amortized time for sample size  30 is:  7.865850130716961e-05
preprocessing time for sampling: 0.008805036544799805
amortized time for sample size  35 is:  7.78524535042899e-05
preprocessing time for sampling: 0.008790969848632812
amortized time for sample size  40 is:  7.790702581405638e-05
preprocessing time for sampling: 0.0087738037109375
amortized time for sample size  45 is:  7.784557342529296e-05
preprocessing time for sampling: 0.008785724639892578
amortized time for sample size  50 is:  7.740240097045899e-05
preprocessing time for sampling: 0.008791208267211914
amortized time for sample size  55 is:  7.742482965642754e-05
preprocessing time for sampling: 0.008835077285766602
amortized time for sample size  60 is:  8.447500069936116e-05
preprocessing time for sampling: 0.008807897567749023
amortized time for sample size  65 is:  7.769133494450496e-05
preprocessing time for sampling: 0.00878596305847168
amortized time for sample size  70 is:  7.778218814304896e-05
preprocessing time for sampling: 0.008814811706542969
amortized time for sample size  75 is:  7.787885665893555e-05
preprocessing time for sampling: 0.008722066879272461
amortized time for sample size  80 is:  7.757374644279479e-05
preprocessing time for sampling: 0.00873112678527832
amortized time for sample size  85 is:  7.738856708302218e-05
preprocessing time for sampling: 0.00875997543334961
amortized time for sample size  90 is:  7.73781140645345e-05
preprocessing time for sampling: 0.008727073669433594
amortized time for sample size  95 is:  7.738133480674343e-05
preprocessing time for sampling: 0.008728265762329102
amortized time for sample size  100 is:  7.748880386352539e-05
preprocessing time for sampling: 0.008734941482543945
amortized time for sample size  105 is:  7.899652208600727e-05
preprocessing time for sampling: 0.00890803337097168
amortized time for sample size  110 is:  7.764278758655894e-05
preprocessing time for sampling: 0.008732080459594727
amortized time for sample size  115 is:  7.922321817149289e-05
preprocessing time for sampling: 0.008756875991821289
amortized time for sample size  120 is:  7.73706833521525e-05
preprocessing time for sampling: 0.008731842041015625
amortized time for sample size  125 is:  7.755203247070312e-05
preprocessing time for sampling: 0.008994102478027344
amortized time for sample size  130 is:  7.868066200843224e-05
preprocessing time for sampling: 0.008922100067138672
amortized time for sample size  135 is:  7.85483784145779e-05
preprocessing time for sampling: 0.008898019790649414
amortized time for sample size  140 is:  7.900190353393555e-05
preprocessing time for sampling: 0.008831977844238281
amortized time for sample size  145 is:  7.74412648431186e-05
preprocessing time for sampling: 0.008738994598388672
amortized time for sample size  150 is:  7.755025227864584e-05
preprocessing time for sampling: 0.015750885009765625
amortized time for sample size  155 is:  7.823874873499714e-05
preprocessing time for sampling: 0.008771181106567383
amortized time for sample size  160 is:  7.72394984960556e-05
preprocessing time for sampling: 0.008727788925170898
amortized time for sample size  165 is:  7.734687400586677e-05
preprocessing time for sampling: 0.008756875991821289
amortized time for sample size  170 is:  7.864605679231531e-05
preprocessing time for sampling: 0.008898019790649414
amortized time for sample size  175 is:  7.828089850289481e-05
preprocessing time for sampling: 0.008739233016967773
amortized time for sample size  180 is:  7.788260777791342e-05
preprocessing time for sampling: 0.008909225463867188
amortized time for sample size  185 is:  7.786065178948479e-05
preprocessing time for sampling: 0.008730173110961914
amortized time for sample size  190 is:  7.73869188208329e-05
preprocessing time for sampling: 0.008764982223510742
amortized time for sample size  195 is:  7.737318674723307e-05
preprocessing time for sampling: 0.008744001388549805
amortized time for sample size  200 is:  7.743403911590575e-05
preprocessing time for sampling: 0.008730888366699219
amortized time for sample size  205 is:  7.731093429937595e-05
preprocessing time for sampling: 0.00872802734375
amortized time for sample size  210 is:  7.746921266828264e-05
preprocessing time for sampling: 0.008729934692382812
amortized time for sample size  215 is:  7.843672951986622e-05
preprocessing time for sampling: 0.00890493392944336
amortized time for sample size  220 is:  7.800828326832164e-05
preprocessing time for sampling: 0.008744955062866211
amortized time for sample size  225 is:  7.731841405232748e-05
preprocessing time for sampling: 0.00872802734375
amortized time for sample size  230 is:  7.794537751570992e-05
preprocessing time for sampling: 0.008750677108764648
amortized time for sample size  235 is:  7.735443115234375e-05
preprocessing time for sampling: 0.008733987808227539
amortized time for sample size  240 is:  7.744062940279643e-05
preprocessing time for sampling: 0.008723974227905273
amortized time for sample size  245 is:  7.744283092265225e-05
preprocessing time for sampling: 0.008739948272705078
amortized time for sample size  250 is:  7.818912506103517e-05
*** results for plotting, beta= 0.8 

mean_list= [np.float64(0.8400000000000001), np.float64(0.9199999999999999), np.float64(0.9099999999999999), np.float64(0.9199999999999999), np.float64(0.96), np.float64(0.95), np.float64(0.9700000000000001), np.float64(0.99), np.float64(0.99), np.float64(1.0), np.float64(0.99), np.float64(1.0), np.float64(1.0), np.float64(0.99), np.float64(1.0), np.float64(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)]
std_list= [np.float64(0.13564659966250536), np.float64(0.08717797887081348), np.float64(0.06999999999999998), np.float64(0.0748331477354788), np.float64(0.06633249580710798), np.float64(0.06708203932499368), np.float64(0.04582575694955839), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.029999999999999992), 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)]
beta: 1
preprocessing time for sampling: 0.009866952896118164
amortized time for sample size  5 is:  8.73723030090332e-05
preprocessing time for sampling: 0.010175943374633789
amortized time for sample size  10 is:  8.313369750976564e-05
preprocessing time for sampling: 0.009926080703735352
amortized time for sample size  15 is:  8.404270807902017e-05
preprocessing time for sampling: 0.009894132614135742
amortized time for sample size  20 is:  9.194517135620119e-05
preprocessing time for sampling: 0.009896993637084961
amortized time for sample size  25 is:  8.465938568115234e-05
preprocessing time for sampling: 0.009900093078613281
amortized time for sample size  30 is:  8.444666862487791e-05
preprocessing time for sampling: 0.012263774871826172
amortized time for sample size  35 is:  8.474268232073103e-05
preprocessing time for sampling: 0.010607242584228516
amortized time for sample size  40 is:  8.322203159332276e-05
preprocessing time for sampling: 0.009734869003295898
amortized time for sample size  45 is:  8.267784118652345e-05
preprocessing time for sampling: 0.009740114212036133
amortized time for sample size  50 is:  8.261399269104002e-05
preprocessing time for sampling: 0.009699106216430664
amortized time for sample size  55 is:  8.244583823464135e-05
preprocessing time for sampling: 0.009678125381469727
amortized time for sample size  60 is:  8.333555857340495e-05
preprocessing time for sampling: 0.009716033935546875
amortized time for sample size  65 is:  8.251487291776218e-05
preprocessing time for sampling: 0.00971078872680664
amortized time for sample size  70 is:  8.238005638122558e-05
preprocessing time for sampling: 0.009694099426269531
amortized time for sample size  75 is:  8.37608337402344e-05
preprocessing time for sampling: 0.009943962097167969
amortized time for sample size  80 is:  8.420324325561522e-05
preprocessing time for sampling: 0.009894847869873047
amortized time for sample size  85 is:  8.395346473245058e-05
preprocessing time for sampling: 0.009900093078613281
amortized time for sample size  90 is:  8.367143736945259e-05
preprocessing time for sampling: 0.01002812385559082
amortized time for sample size  95 is:  8.309735749897204e-05
preprocessing time for sampling: 0.009742975234985352
amortized time for sample size  100 is:  8.246343135833741e-05
preprocessing time for sampling: 0.009677886962890625
amortized time for sample size  105 is:  8.378746396019344e-05
preprocessing time for sampling: 0.009877204895019531
amortized time for sample size  110 is:  8.436428416859018e-05
preprocessing time for sampling: 0.009888172149658203
amortized time for sample size  115 is:  8.443575320036517e-05
preprocessing time for sampling: 0.009877920150756836
amortized time for sample size  120 is:  8.449159065882365e-05
preprocessing time for sampling: 0.009888887405395508
amortized time for sample size  125 is:  8.445924758911133e-05
preprocessing time for sampling: 0.009888172149658203
amortized time for sample size  130 is:  8.465286401601938e-05
preprocessing time for sampling: 0.009914875030517578
amortized time for sample size  135 is:  8.437119589911569e-05
preprocessing time for sampling: 0.00988626480102539
amortized time for sample size  140 is:  8.416106019701279e-05
preprocessing time for sampling: 0.009887933731079102
amortized time for sample size  145 is:  8.292462907988449e-05
preprocessing time for sampling: 0.009855031967163086
amortized time for sample size  150 is:  8.412575721740721e-05
preprocessing time for sampling: 0.009927988052368164
amortized time for sample size  155 is:  8.419335273004347e-05
preprocessing time for sampling: 0.009902238845825195
amortized time for sample size  160 is:  8.42277854681015e-05
preprocessing time for sampling: 0.009906291961669922
amortized time for sample size  165 is:  8.408563787286933e-05
preprocessing time for sampling: 0.009896993637084961
amortized time for sample size  170 is:  8.404632175669952e-05
preprocessing time for sampling: 0.009684085845947266
amortized time for sample size  175 is:  8.40125628880092e-05
preprocessing time for sampling: 0.009998083114624023
amortized time for sample size  180 is:  8.424886067708334e-05
preprocessing time for sampling: 0.009737968444824219
amortized time for sample size  185 is:  8.260292620272249e-05
preprocessing time for sampling: 0.009690046310424805
amortized time for sample size  190 is:  8.310783536810625e-05
preprocessing time for sampling: 0.009920120239257812
amortized time for sample size  195 is:  8.414121774526742e-05
preprocessing time for sampling: 0.009721040725708008
amortized time for sample size  200 is:  8.268895149230959e-05
preprocessing time for sampling: 0.009709835052490234
amortized time for sample size  205 is:  8.351163166325266e-05
preprocessing time for sampling: 0.009894847869873047
amortized time for sample size  210 is:  8.35249083382743e-05
preprocessing time for sampling: 0.009702920913696289
amortized time for sample size  215 is:  8.278647134470384e-05
preprocessing time for sampling: 0.009890079498291016
amortized time for sample size  220 is:  8.273292671550405e-05
preprocessing time for sampling: 0.009718894958496094
amortized time for sample size  225 is:  8.413722780015734e-05
preprocessing time for sampling: 0.009905815124511719
amortized time for sample size  230 is:  8.408772427102794e-05
preprocessing time for sampling: 0.009703874588012695
amortized time for sample size  235 is:  8.320254467903302e-05
preprocessing time for sampling: 0.009900093078613281
amortized time for sample size  240 is:  8.386590083440144e-05
preprocessing time for sampling: 0.009694099426269531
amortized time for sample size  245 is:  8.40480084321937e-05
preprocessing time for sampling: 0.009910821914672852
amortized time for sample size  250 is:  8.423973083496097e-05
*** results for plotting, beta= 1 

mean_list= [np.float64(0.8699999999999999), np.float64(0.96), np.float64(1.0), 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(0.99), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0)]
std_list= [np.float64(0.11000000000000001), np.float64(0.04898979485566355), np.float64(0.0), 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(0.029999999999999992), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0)]
beta: 1.2
preprocessing time for sampling: 0.008809089660644531
amortized time for sample size  5 is:  7.758235931396484e-05
preprocessing time for sampling: 0.008915185928344727
amortized time for sample size  10 is:  7.85703659057617e-05
preprocessing time for sampling: 0.008918046951293945
amortized time for sample size  15 is:  7.943550745646158e-05
preprocessing time for sampling: 0.00894021987915039
amortized time for sample size  20 is:  7.936644554138185e-05
preprocessing time for sampling: 0.008885860443115234
amortized time for sample size  25 is:  7.842426300048827e-05
preprocessing time for sampling: 0.008931875228881836
amortized time for sample size  30 is:  7.843343416849773e-05
preprocessing time for sampling: 0.008765935897827148
amortized time for sample size  35 is:  7.732943126133509e-05
preprocessing time for sampling: 0.008749008178710938
amortized time for sample size  40 is:  7.83931016921997e-05
preprocessing time for sampling: 0.008935928344726562
amortized time for sample size  45 is:  7.793521881103515e-05
preprocessing time for sampling: 0.008756875991821289
amortized time for sample size  50 is:  7.719464302062987e-05
preprocessing time for sampling: 0.009081125259399414
amortized time for sample size  55 is:  7.882811806418679e-05
preprocessing time for sampling: 0.008941888809204102
amortized time for sample size  60 is:  7.853690783182779e-05
preprocessing time for sampling: 0.008981943130493164
amortized time for sample size  65 is:  7.907258547269381e-05
preprocessing time for sampling: 0.008947134017944336
amortized time for sample size  70 is:  7.71876403263637e-05
preprocessing time for sampling: 0.008919715881347656
amortized time for sample size  75 is:  7.775036493937175e-05
preprocessing time for sampling: 0.008921146392822266
amortized time for sample size  80 is:  7.809898257255554e-05
preprocessing time for sampling: 0.008747100830078125
amortized time for sample size  85 is:  7.787690443151136e-05
preprocessing time for sampling: 0.008911848068237305
amortized time for sample size  90 is:  7.77897834777832e-05
preprocessing time for sampling: 0.00874781608581543
amortized time for sample size  95 is:  7.800039492155376e-05
preprocessing time for sampling: 0.008923053741455078
amortized time for sample size  100 is:  7.8409743309021e-05
preprocessing time for sampling: 0.008772134780883789
amortized time for sample size  105 is:  7.774850300380162e-05
preprocessing time for sampling: 0.008862018585205078
amortized time for sample size  110 is:  7.835663448680532e-05
preprocessing time for sampling: 0.008772134780883789
amortized time for sample size  115 is:  7.790159142535666e-05
preprocessing time for sampling: 0.008913755416870117
amortized time for sample size  120 is:  7.876729965209962e-05
preprocessing time for sampling: 0.00896000862121582
amortized time for sample size  125 is:  7.874002456665039e-05
preprocessing time for sampling: 0.008933067321777344
amortized time for sample size  130 is:  7.937288284301758e-05
preprocessing time for sampling: 0.008936166763305664
amortized time for sample size  135 is:  7.87376121238426e-05
preprocessing time for sampling: 0.00891876220703125
amortized time for sample size  140 is:  7.875841004507882e-05
preprocessing time for sampling: 0.008986711502075195
amortized time for sample size  145 is:  7.878209804666454e-05
preprocessing time for sampling: 0.008922815322875977
amortized time for sample size  150 is:  7.884966532389322e-05
preprocessing time for sampling: 0.008923053741455078
amortized time for sample size  155 is:  7.868051528930665e-05
preprocessing time for sampling: 0.008922100067138672
amortized time for sample size  160 is:  7.843279838562012e-05
preprocessing time for sampling: 0.008940935134887695
amortized time for sample size  165 is:  7.750592087254378e-05
preprocessing time for sampling: 0.0089111328125
amortized time for sample size  170 is:  7.759108262903551e-05
preprocessing time for sampling: 0.008753776550292969
amortized time for sample size  175 is:  7.873469761439733e-05
preprocessing time for sampling: 0.008948087692260742
amortized time for sample size  180 is:  7.875874307420517e-05
preprocessing time for sampling: 0.008790016174316406
amortized time for sample size  185 is:  7.876014709472656e-05
preprocessing time for sampling: 0.008783817291259766
amortized time for sample size  190 is:  7.872739591096576e-05
preprocessing time for sampling: 0.008930206298828125
amortized time for sample size  195 is:  7.882274725498299e-05
preprocessing time for sampling: 0.008916854858398438
amortized time for sample size  200 is:  7.844557762145995e-05
preprocessing time for sampling: 0.008948802947998047
amortized time for sample size  205 is:  7.859617326317764e-05
preprocessing time for sampling: 0.008971214294433594
amortized time for sample size  210 is:  7.921326728094194e-05
preprocessing time for sampling: 0.00899505615234375
amortized time for sample size  215 is:  7.868623733520506e-05
preprocessing time for sampling: 0.008781909942626953
amortized time for sample size  220 is:  7.817363739013671e-05
preprocessing time for sampling: 0.009068012237548828
amortized time for sample size  225 is:  7.91702800326877e-05
preprocessing time for sampling: 0.008996009826660156
amortized time for sample size  230 is:  7.914324428724207e-05
preprocessing time for sampling: 0.008908987045288086
amortized time for sample size  235 is:  7.865212826018637e-05
preprocessing time for sampling: 0.008937835693359375
amortized time for sample size  240 is:  7.866333921750387e-05
preprocessing time for sampling: 0.008918046951293945
amortized time for sample size  245 is:  7.919929465469048e-05
preprocessing time for sampling: 0.009734153747558594
amortized time for sample size  250 is:  7.885019302368164e-05
*** results for plotting, beta= 1.2 

mean_list= [np.float64(0.93), np.float64(0.96), 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)]
std_list= [np.float64(0.1004987562112089), np.float64(0.07999999999999999), 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)]
