beta: 0.2
preprocessing time for sampling: 0.293245792388916
amortized time for sample size  5 is:  0.0003110337257385254
preprocessing time for sampling: 0.2895207405090332
amortized time for sample size  10 is:  0.0003126606941223145
preprocessing time for sampling: 0.2915029525756836
amortized time for sample size  15 is:  0.0003158162434895834
preprocessing time for sampling: 0.2883331775665283
amortized time for sample size  20 is:  0.00030886805057525634
preprocessing time for sampling: 0.2861969470977783
amortized time for sample size  25 is:  0.0003097477912902832
preprocessing time for sampling: 0.29105114936828613
amortized time for sample size  30 is:  0.0003086413542429606
preprocessing time for sampling: 0.28675293922424316
amortized time for sample size  35 is:  0.0003131010872977121
preprocessing time for sampling: 0.29347896575927734
amortized time for sample size  40 is:  0.00031186056137084956
preprocessing time for sampling: 0.29012608528137207
amortized time for sample size  45 is:  0.00031071223153008356
preprocessing time for sampling: 0.28952908515930176
amortized time for sample size  50 is:  0.00031110053062438967
preprocessing time for sampling: 0.2907888889312744
amortized time for sample size  55 is:  0.00030945825576782226
preprocessing time for sampling: 0.2910771369934082
amortized time for sample size  60 is:  0.0003116816679636637
preprocessing time for sampling: 0.29230809211730957
amortized time for sample size  65 is:  0.00030986525462223935
preprocessing time for sampling: 0.2913801670074463
amortized time for sample size  70 is:  0.0003104469094957624
preprocessing time for sampling: 0.287722110748291
amortized time for sample size  75 is:  0.000311125119527181
preprocessing time for sampling: 0.2888948917388916
amortized time for sample size  80 is:  0.0003099721372127533
preprocessing time for sampling: 0.29328203201293945
amortized time for sample size  85 is:  0.00030931540096507354
preprocessing time for sampling: 0.2864842414855957
amortized time for sample size  90 is:  0.0003095831076304118
preprocessing time for sampling: 0.28637075424194336
amortized time for sample size  95 is:  0.00030867313083849453
preprocessing time for sampling: 0.2865629196166992
amortized time for sample size  100 is:  0.0003132014513015747
preprocessing time for sampling: 0.2899179458618164
amortized time for sample size  105 is:  0.00031028434208461213
preprocessing time for sampling: 0.2888970375061035
amortized time for sample size  110 is:  0.00030944004925814543
preprocessing time for sampling: 0.28891801834106445
amortized time for sample size  115 is:  0.0003106097760407821
preprocessing time for sampling: 0.2888059616088867
amortized time for sample size  120 is:  0.000309475044409434
preprocessing time for sampling: 0.2887899875640869
amortized time for sample size  125 is:  0.000311206283569336
preprocessing time for sampling: 0.29253411293029785
amortized time for sample size  130 is:  0.0003139774249150203
preprocessing time for sampling: 0.29473209381103516
amortized time for sample size  135 is:  0.0003126168780856662
preprocessing time for sampling: 0.2953979969024658
amortized time for sample size  140 is:  0.0003151946067810059
preprocessing time for sampling: 0.2897531986236572
amortized time for sample size  145 is:  0.0003130564196356411
preprocessing time for sampling: 0.29005908966064453
amortized time for sample size  150 is:  0.0003122118631998698
preprocessing time for sampling: 0.29666709899902344
amortized time for sample size  155 is:  0.0003123970647012034
preprocessing time for sampling: 0.2988560199737549
amortized time for sample size  160 is:  0.000310836836695671
preprocessing time for sampling: 0.2899179458618164
amortized time for sample size  165 is:  0.00031155090621023463
preprocessing time for sampling: 0.31282567977905273
amortized time for sample size  170 is:  0.000313112735748291
preprocessing time for sampling: 0.289247989654541
amortized time for sample size  175 is:  0.0003147790227617537
preprocessing time for sampling: 0.2907710075378418
amortized time for sample size  180 is:  0.00031394735972086585
preprocessing time for sampling: 0.2983667850494385
amortized time for sample size  185 is:  0.0003232517242431641
preprocessing time for sampling: 0.29411983489990234
amortized time for sample size  190 is:  0.0003142095490505821
preprocessing time for sampling: 0.29522013664245605
amortized time for sample size  195 is:  0.00031591460643670493
preprocessing time for sampling: 0.2929341793060303
amortized time for sample size  200 is:  0.00031460341215133666
preprocessing time for sampling: 0.290935754776001
amortized time for sample size  205 is:  0.0003135430289477837
preprocessing time for sampling: 0.2928340435028076
amortized time for sample size  210 is:  0.00031290012314206075
preprocessing time for sampling: 0.29346418380737305
amortized time for sample size  215 is:  0.00031427386749622433
preprocessing time for sampling: 0.2942330837249756
amortized time for sample size  220 is:  0.0003149503144350919
preprocessing time for sampling: 0.29209280014038086
amortized time for sample size  225 is:  0.00031441401375664605
preprocessing time for sampling: 0.29300999641418457
amortized time for sample size  230 is:  0.0003173896437105925
preprocessing time for sampling: 0.29428720474243164
amortized time for sample size  235 is:  0.00031558251888193987
preprocessing time for sampling: 0.2948338985443115
amortized time for sample size  240 is:  0.0003152638872464498
preprocessing time for sampling: 0.29183411598205566
amortized time for sample size  245 is:  0.0003152106440797144
preprocessing time for sampling: 0.290604829788208
amortized time for sample size  250 is:  0.000315689811706543
*** results for plotting, beta= 0.2 

mean_list= [np.float64(0.31), np.float64(0.44000000000000006), np.float64(0.44000000000000006), np.float64(0.4), np.float64(0.48999999999999994), np.float64(0.55), np.float64(0.55), np.float64(0.6299999999999999), np.float64(0.51), np.float64(0.6199999999999999), np.float64(0.5900000000000001), np.float64(0.6399999999999999), np.float64(0.63), np.float64(0.68), np.float64(0.63), np.float64(0.61), np.float64(0.6699999999999999), np.float64(0.6599999999999999), np.float64(0.73), np.float64(0.72), np.float64(0.67), np.float64(0.7200000000000001), np.float64(0.6199999999999999), np.float64(0.65), np.float64(0.6799999999999999), np.float64(0.68), np.float64(0.69), np.float64(0.64), np.float64(0.6599999999999999), np.float64(0.7500000000000001), np.float64(0.7100000000000001), np.float64(0.7499999999999999), np.float64(0.77), np.float64(0.6799999999999999), np.float64(0.78), np.float64(0.7), np.float64(0.8300000000000001), np.float64(0.74), np.float64(0.82), np.float64(0.7300000000000001), np.float64(0.76), np.float64(0.65), np.float64(0.8200000000000001), np.float64(0.86), np.float64(0.75), np.float64(0.72), np.float64(0.7500000000000001), np.float64(0.77), np.float64(0.74), np.float64(0.6799999999999999)]
std_list= [np.float64(0.13), np.float64(0.13564659966250536), np.float64(0.17435595774162693), np.float64(0.11832159566199231), np.float64(0.13), np.float64(0.2539685019840059), np.float64(0.20615528128088303), np.float64(0.18466185312619388), np.float64(0.09433981132056601), np.float64(0.13999999999999999), np.float64(0.1374772708486752), np.float64(0.14966629547095767), np.float64(0.13453624047073712), np.float64(0.12489995996796797), np.float64(0.1676305461424021), np.float64(0.09433981132056604), np.float64(0.09000000000000001), np.float64(0.12000000000000001), np.float64(0.10049875621120892), np.float64(0.1777638883463118), np.float64(0.15524174696260024), np.float64(0.20396078054371142), np.float64(0.18867962264113208), np.float64(0.13601470508735444), np.float64(0.16613247725836153), np.float64(0.20880613017821104), np.float64(0.17), np.float64(0.18000000000000002), np.float64(0.08), np.float64(0.15000000000000002), np.float64(0.18681541692269404), np.float64(0.13601470508735444), np.float64(0.09000000000000002), np.float64(0.09797958971132714), np.float64(0.13266499161421602), np.float64(0.17320508075688776), np.float64(0.0640312423743285), np.float64(0.12000000000000002), np.float64(0.09797958971132714), np.float64(0.15524174696260024), np.float64(0.10198039027185572), np.float64(0.15652475842498528), np.float64(0.13266499161421602), np.float64(0.12000000000000002), np.float64(0.1284523257866513), np.float64(0.06000000000000003), np.float64(0.0921954445729289), np.float64(0.11000000000000001), np.float64(0.1356465996625054), np.float64(0.18867962264113208)]
beta: 0.4
preprocessing time for sampling: 0.2940530776977539
amortized time for sample size  5 is:  0.00031291389465332024
preprocessing time for sampling: 0.2890591621398926
amortized time for sample size  10 is:  0.00031481027603149405
preprocessing time for sampling: 0.29190611839294434
amortized time for sample size  15 is:  0.0003130807876586914
preprocessing time for sampling: 0.287276029586792
amortized time for sample size  20 is:  0.00031209981441497793
preprocessing time for sampling: 0.2891578674316406
amortized time for sample size  25 is:  0.0003116985321044922
preprocessing time for sampling: 0.290330171585083
amortized time for sample size  30 is:  0.00031340106328328447
preprocessing time for sampling: 0.2922391891479492
amortized time for sample size  35 is:  0.00031465802873883927
preprocessing time for sampling: 0.29235100746154785
amortized time for sample size  40 is:  0.00031477779150009157
preprocessing time for sampling: 0.29155993461608887
amortized time for sample size  45 is:  0.00031494855880737305
preprocessing time for sampling: 0.2879331111907959
amortized time for sample size  50 is:  0.0003149110317230224
preprocessing time for sampling: 0.29300713539123535
amortized time for sample size  55 is:  0.00031689730557528406
preprocessing time for sampling: 0.29471611976623535
amortized time for sample size  60 is:  0.00033605929215749106
preprocessing time for sampling: 0.2956390380859375
amortized time for sample size  65 is:  0.0003387273274935209
preprocessing time for sampling: 0.33884119987487793
amortized time for sample size  70 is:  0.00033699655532836917
preprocessing time for sampling: 0.31043219566345215
amortized time for sample size  75 is:  0.00032364530563354485
preprocessing time for sampling: 0.2978181838989258
amortized time for sample size  80 is:  0.0003154366612434387
preprocessing time for sampling: 0.29238200187683105
amortized time for sample size  85 is:  0.00031642243441413434
preprocessing time for sampling: 0.29190611839294434
amortized time for sample size  90 is:  0.0003154277271694608
preprocessing time for sampling: 0.29431891441345215
amortized time for sample size  95 is:  0.0003153564302544844
preprocessing time for sampling: 0.2952141761779785
amortized time for sample size  100 is:  0.0003155686140060425
preprocessing time for sampling: 0.2943918704986572
amortized time for sample size  105 is:  0.00032242207300095337
preprocessing time for sampling: 0.29407787322998047
amortized time for sample size  110 is:  0.00031620723550969897
preprocessing time for sampling: 0.2913808822631836
amortized time for sample size  115 is:  0.00031856518206389053
preprocessing time for sampling: 0.29166388511657715
amortized time for sample size  120 is:  0.00032277148962020876
preprocessing time for sampling: 0.3142735958099365
amortized time for sample size  125 is:  0.00032076202392578127
preprocessing time for sampling: 0.2944908142089844
amortized time for sample size  130 is:  0.00031479507226210373
preprocessing time for sampling: 0.29470181465148926
amortized time for sample size  135 is:  0.0003163372852184155
preprocessing time for sampling: 0.29466986656188965
amortized time for sample size  140 is:  0.0003212962150573731
preprocessing time for sampling: 0.29207301139831543
amortized time for sample size  145 is:  0.000316983568257299
preprocessing time for sampling: 0.292341947555542
amortized time for sample size  150 is:  0.0003147026697794596
preprocessing time for sampling: 0.2942068576812744
amortized time for sample size  155 is:  0.00031455116887246407
preprocessing time for sampling: 0.2945690155029297
amortized time for sample size  160 is:  0.00032389707863330843
preprocessing time for sampling: 0.29494500160217285
amortized time for sample size  165 is:  0.00031913407643636066
preprocessing time for sampling: 0.29452085494995117
amortized time for sample size  170 is:  0.00031579237825730267
preprocessing time for sampling: 0.2937960624694824
amortized time for sample size  175 is:  0.00033942273003714427
preprocessing time for sampling: 0.30965709686279297
amortized time for sample size  180 is:  0.0003420199288262262
preprocessing time for sampling: 0.30608582496643066
amortized time for sample size  185 is:  0.00033704764134175064
preprocessing time for sampling: 0.30504512786865234
amortized time for sample size  190 is:  0.0003210341804905941
preprocessing time for sampling: 0.2946760654449463
amortized time for sample size  195 is:  0.0003242321014404297
preprocessing time for sampling: 0.2941780090332031
amortized time for sample size  200 is:  0.000316720724105835
preprocessing time for sampling: 0.2952282428741455
amortized time for sample size  205 is:  0.0003173462937517864
preprocessing time for sampling: 0.295180082321167
amortized time for sample size  210 is:  0.0003168842451913017
preprocessing time for sampling: 0.2941172122955322
amortized time for sample size  215 is:  0.0003217642917189487
preprocessing time for sampling: 0.30896520614624023
amortized time for sample size  220 is:  0.0003189176537773826
preprocessing time for sampling: 0.29725217819213867
amortized time for sample size  225 is:  0.0003190150472852919
preprocessing time for sampling: 0.30709004402160645
amortized time for sample size  230 is:  0.00031812576625658124
preprocessing time for sampling: 0.2954518795013428
amortized time for sample size  235 is:  0.000316933662333387
preprocessing time for sampling: 0.29430389404296875
amortized time for sample size  240 is:  0.00031727701425552366
preprocessing time for sampling: 0.29471802711486816
amortized time for sample size  245 is:  0.0003170720898375219
preprocessing time for sampling: 0.29676008224487305
amortized time for sample size  250 is:  0.0003157983779907226
*** results for plotting, beta= 0.4 

mean_list= [np.float64(0.54), np.float64(0.74), np.float64(0.7000000000000001), np.float64(0.89), np.float64(0.74), np.float64(0.8699999999999999), np.float64(0.8800000000000001), np.float64(0.8800000000000001), np.float64(0.8100000000000002), np.float64(0.8300000000000001), np.float64(0.9200000000000002), np.float64(0.9099999999999999), np.float64(0.89), np.float64(0.9099999999999999), np.float64(0.97), np.float64(0.8699999999999999), np.float64(0.9400000000000001), np.float64(0.9200000000000002), np.float64(0.9200000000000002), np.float64(0.95), np.float64(0.9200000000000002), np.float64(0.96), np.float64(0.9200000000000002), np.float64(0.95), np.float64(0.95), np.float64(0.9400000000000001), np.float64(0.95), np.float64(0.96), np.float64(0.96), np.float64(0.95), np.float64(0.97), np.float64(0.97), np.float64(0.96), np.float64(0.95), np.float64(0.99), np.float64(0.96), np.float64(0.9800000000000001), np.float64(0.97), np.float64(0.99), np.float64(1.0), np.float64(0.96), np.float64(0.9800000000000001), np.float64(0.99), np.float64(0.99), np.float64(0.99), np.float64(0.97), np.float64(0.9800000000000001), np.float64(1.0), np.float64(0.9800000000000001), np.float64(0.99)]
std_list= [np.float64(0.04898979485566356), np.float64(0.1356465996625054), np.float64(0.10000000000000002), np.float64(0.11357816691600547), np.float64(0.08000000000000003), np.float64(0.1676305461424021), np.float64(0.08717797887081345), np.float64(0.10770329614269009), np.float64(0.10440306508910552), np.float64(0.1004987562112089), np.float64(0.08717797887081345), np.float64(0.09433981132056604), np.float64(0.11357816691600547), np.float64(0.08306623862918076), np.float64(0.04582575694955839), np.float64(0.1004987562112089), np.float64(0.04898979485566355), np.float64(0.0748331477354788), np.float64(0.0748331477354788), np.float64(0.06708203932499368), np.float64(0.0748331477354788), np.float64(0.04898979485566354), np.float64(0.059999999999999984), np.float64(0.08062257748298547), np.float64(0.04999999999999999), np.float64(0.06633249580710798), np.float64(0.09219544457292887), np.float64(0.04898979485566356), np.float64(0.04898979485566355), np.float64(0.06708203932499368), np.float64(0.04582575694955839), np.float64(0.06403124237432847), np.float64(0.06633249580710798), np.float64(0.06708203932499368), np.float64(0.029999999999999992), np.float64(0.04898979485566354), np.float64(0.039999999999999994), np.float64(0.06403124237432847), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.04898979485566355), np.float64(0.039999999999999994), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.06403124237432847), np.float64(0.05999999999999999), np.float64(0.0), np.float64(0.039999999999999994), np.float64(0.029999999999999992)]
beta: 0.6
preprocessing time for sampling: 0.2942030429840088
amortized time for sample size  5 is:  0.00031449317932128905
preprocessing time for sampling: 0.29199719429016113
amortized time for sample size  10 is:  0.00031561303138732906
preprocessing time for sampling: 0.2918868064880371
amortized time for sample size  15 is:  0.0003153829574584961
preprocessing time for sampling: 0.2919468879699707
amortized time for sample size  20 is:  0.0003156003952026367
preprocessing time for sampling: 0.2941739559173584
amortized time for sample size  25 is:  0.00031499567031860346
preprocessing time for sampling: 0.2954549789428711
amortized time for sample size  30 is:  0.00031523338953653974
preprocessing time for sampling: 0.29494500160217285
amortized time for sample size  35 is:  0.00031713914871215823
preprocessing time for sampling: 0.29430103302001953
amortized time for sample size  40 is:  0.00031553882360458376
preprocessing time for sampling: 0.29225993156433105
amortized time for sample size  45 is:  0.0003161410755581326
preprocessing time for sampling: 0.29476284980773926
amortized time for sample size  50 is:  0.0003149195194244385
preprocessing time for sampling: 0.2951328754425049
amortized time for sample size  55 is:  0.0003159921819513494
preprocessing time for sampling: 0.2954709529876709
amortized time for sample size  60 is:  0.0003175363540649414
preprocessing time for sampling: 0.29781413078308105
amortized time for sample size  65 is:  0.0003199998048635629
preprocessing time for sampling: 0.29575085639953613
amortized time for sample size  70 is:  0.00031807783671787803
preprocessing time for sampling: 0.294874906539917
amortized time for sample size  75 is:  0.00031478846867879226
preprocessing time for sampling: 0.2942988872528076
amortized time for sample size  80 is:  0.00032102000713348384
preprocessing time for sampling: 0.2919490337371826
amortized time for sample size  85 is:  0.0003170880429884967
preprocessing time for sampling: 0.2922179698944092
amortized time for sample size  90 is:  0.00031754835446675615
preprocessing time for sampling: 0.2981545925140381
amortized time for sample size  95 is:  0.00031727168434544613
preprocessing time for sampling: 0.29830074310302734
amortized time for sample size  100 is:  0.00031703338623046876
preprocessing time for sampling: 0.29465794563293457
amortized time for sample size  105 is:  0.0003159293220156715
preprocessing time for sampling: 0.2950739860534668
amortized time for sample size  110 is:  0.0003152818896553733
preprocessing time for sampling: 0.2921631336212158
amortized time for sample size  115 is:  0.00031526208960491677
preprocessing time for sampling: 0.2928650379180908
amortized time for sample size  120 is:  0.000317262868086497
preprocessing time for sampling: 0.29473209381103516
amortized time for sample size  125 is:  0.000316060962677002
preprocessing time for sampling: 0.2959599494934082
amortized time for sample size  130 is:  0.000317676250751202
preprocessing time for sampling: 0.2949838638305664
amortized time for sample size  135 is:  0.00031743595335218645
preprocessing time for sampling: 0.2979588508605957
amortized time for sample size  140 is:  0.0003175184897014072
preprocessing time for sampling: 0.29401493072509766
amortized time for sample size  145 is:  0.0003156958777329017
preprocessing time for sampling: 0.2922322750091553
amortized time for sample size  150 is:  0.00031448500951131186
preprocessing time for sampling: 0.2948019504547119
amortized time for sample size  155 is:  0.00031863192589052266
preprocessing time for sampling: 0.2978999614715576
amortized time for sample size  160 is:  0.00031528063118457794
preprocessing time for sampling: 0.293424129486084
amortized time for sample size  165 is:  0.00031472901142004766
preprocessing time for sampling: 0.2970888614654541
amortized time for sample size  170 is:  0.0003145100228926714
preprocessing time for sampling: 0.2917790412902832
amortized time for sample size  175 is:  0.0003154345648629325
preprocessing time for sampling: 0.29233717918395996
amortized time for sample size  180 is:  0.0003150889343685574
preprocessing time for sampling: 0.2974278926849365
amortized time for sample size  185 is:  0.0003163183057630384
preprocessing time for sampling: 0.29752016067504883
amortized time for sample size  190 is:  0.00031574386044552457
preprocessing time for sampling: 0.2967569828033447
amortized time for sample size  195 is:  0.00031903531001164365
preprocessing time for sampling: 0.29621410369873047
amortized time for sample size  200 is:  0.00031544868946075435
preprocessing time for sampling: 0.29190802574157715
amortized time for sample size  205 is:  0.000315128058922
preprocessing time for sampling: 0.2920498847961426
amortized time for sample size  210 is:  0.0003148389430273147
preprocessing time for sampling: 0.2945437431335449
amortized time for sample size  215 is:  0.00031513189715008406
preprocessing time for sampling: 0.2948899269104004
amortized time for sample size  220 is:  0.0003148440772836858
preprocessing time for sampling: 0.29407596588134766
amortized time for sample size  225 is:  0.00031493138207329646
preprocessing time for sampling: 0.2943899631500244
amortized time for sample size  230 is:  0.0003151021211043648
preprocessing time for sampling: 0.29222989082336426
amortized time for sample size  235 is:  0.0003149041520788314
preprocessing time for sampling: 0.296004056930542
amortized time for sample size  240 is:  0.00031522641579310106
preprocessing time for sampling: 0.29402875900268555
amortized time for sample size  245 is:  0.0003150253685153261
preprocessing time for sampling: 0.29596686363220215
amortized time for sample size  250 is:  0.00031576885223388667
*** results for plotting, beta= 0.6 

mean_list= [np.float64(0.8699999999999999), np.float64(0.8400000000000001), np.float64(0.95), np.float64(0.95), np.float64(0.9099999999999999), np.float64(0.93), np.float64(0.99), np.float64(0.97), np.float64(0.97), np.float64(0.96), np.float64(0.97), np.float64(0.93), np.float64(0.97), np.float64(0.9800000000000001), np.float64(0.9800000000000001), np.float64(1.0), np.float64(0.9800000000000001), np.float64(0.99), np.float64(0.97), 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(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(0.99)]
std_list= [np.float64(0.12688577540449522), np.float64(0.12000000000000001), np.float64(0.06708203932499368), np.float64(0.06708203932499367), np.float64(0.08306623862918076), np.float64(0.06403124237432847), np.float64(0.029999999999999992), np.float64(0.04582575694955839), np.float64(0.045825756949558386), np.float64(0.09165151389911681), np.float64(0.06403124237432847), np.float64(0.06403124237432847), np.float64(0.04582575694955839), np.float64(0.039999999999999994), np.float64(0.039999999999999994), np.float64(0.0), np.float64(0.039999999999999994), np.float64(0.029999999999999992), np.float64(0.06403124237432847), 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(0.029999999999999992), 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(0.029999999999999992)]
beta: 0.8
preprocessing time for sampling: 0.3068430423736572
amortized time for sample size  5 is:  0.0003183746337890625
preprocessing time for sampling: 0.29180312156677246
amortized time for sample size  10 is:  0.0003152730464935303
preprocessing time for sampling: 0.2916121482849121
amortized time for sample size  15 is:  0.0003140513102213541
preprocessing time for sampling: 0.29168701171875
amortized time for sample size  20 is:  0.00031404221057891845
preprocessing time for sampling: 0.2970259189605713
amortized time for sample size  25 is:  0.0003143041610717774
preprocessing time for sampling: 0.2938709259033203
amortized time for sample size  30 is:  0.0003159666856129964
preprocessing time for sampling: 0.2982170581817627
amortized time for sample size  35 is:  0.00031398752757481164
preprocessing time for sampling: 0.2938551902770996
amortized time for sample size  40 is:  0.0003139789700508118
preprocessing time for sampling: 0.29403209686279297
amortized time for sample size  45 is:  0.00031417957941691076
preprocessing time for sampling: 0.29209113121032715
amortized time for sample size  50 is:  0.0003143778324127197
preprocessing time for sampling: 0.2938659191131592
amortized time for sample size  55 is:  0.00031414946642788975
preprocessing time for sampling: 0.29511117935180664
amortized time for sample size  60 is:  0.00031393945217132567
preprocessing time for sampling: 0.29804396629333496
amortized time for sample size  65 is:  0.00031950319730318514
preprocessing time for sampling: 0.2946910858154297
amortized time for sample size  70 is:  0.00031508118765694753
preprocessing time for sampling: 0.2940988540649414
amortized time for sample size  75 is:  0.0003144186019897461
preprocessing time for sampling: 0.2969939708709717
amortized time for sample size  80 is:  0.00031522458791732785
preprocessing time for sampling: 0.29462695121765137
amortized time for sample size  85 is:  0.0003158028546501608
preprocessing time for sampling: 0.2948012351989746
amortized time for sample size  90 is:  0.0003153781361050076
preprocessing time for sampling: 0.2921760082244873
amortized time for sample size  95 is:  0.00031531903618260427
preprocessing time for sampling: 0.2915639877319336
amortized time for sample size  100 is:  0.00031601791381835934
preprocessing time for sampling: 0.2949810028076172
amortized time for sample size  105 is:  0.00031533540998186386
preprocessing time for sampling: 0.2944610118865967
amortized time for sample size  110 is:  0.0003160593943162398
preprocessing time for sampling: 0.29516100883483887
amortized time for sample size  115 is:  0.0003152202108631964
preprocessing time for sampling: 0.2941579818725586
amortized time for sample size  120 is:  0.0003149684270222982
preprocessing time for sampling: 0.29190707206726074
amortized time for sample size  125 is:  0.00031566204071044925
preprocessing time for sampling: 0.2921268939971924
amortized time for sample size  130 is:  0.0003158167692331168
preprocessing time for sampling: 0.2945680618286133
amortized time for sample size  135 is:  0.0003151260835153086
preprocessing time for sampling: 0.2942068576812744
amortized time for sample size  140 is:  0.00031497664111001145
preprocessing time for sampling: 0.2947230339050293
amortized time for sample size  145 is:  0.00031460321360620954
preprocessing time for sampling: 0.29525279998779297
amortized time for sample size  150 is:  0.000314734141031901
preprocessing time for sampling: 0.2917289733886719
amortized time for sample size  155 is:  0.00031460243655789284
preprocessing time for sampling: 0.29141783714294434
amortized time for sample size  160 is:  0.00031493340432643885
preprocessing time for sampling: 0.29415297508239746
amortized time for sample size  165 is:  0.00031518983840942376
preprocessing time for sampling: 0.29372191429138184
amortized time for sample size  170 is:  0.000314642962287454
preprocessing time for sampling: 0.29836606979370117
amortized time for sample size  175 is:  0.00031486794607979906
preprocessing time for sampling: 0.29411911964416504
amortized time for sample size  180 is:  0.00031626244386037195
preprocessing time for sampling: 0.29166507720947266
amortized time for sample size  185 is:  0.00031446272618061786
preprocessing time for sampling: 0.29209303855895996
amortized time for sample size  190 is:  0.00031539410038998255
preprocessing time for sampling: 0.2951791286468506
amortized time for sample size  195 is:  0.00031513709288377023
preprocessing time for sampling: 0.29442691802978516
amortized time for sample size  200 is:  0.00031573580503463746
preprocessing time for sampling: 0.296389102935791
amortized time for sample size  205 is:  0.00031480755457064
preprocessing time for sampling: 0.2944958209991455
amortized time for sample size  210 is:  0.00031544521876743854
preprocessing time for sampling: 0.29189300537109375
amortized time for sample size  215 is:  0.0003145108001176701
preprocessing time for sampling: 0.292050838470459
amortized time for sample size  220 is:  0.00031525376710024746
preprocessing time for sampling: 0.29547619819641113
amortized time for sample size  225 is:  0.000315276919470893
preprocessing time for sampling: 0.29404592514038086
amortized time for sample size  230 is:  0.0003164581423220427
preprocessing time for sampling: 0.29424118995666504
amortized time for sample size  235 is:  0.00031533336639404303
preprocessing time for sampling: 0.29489612579345703
amortized time for sample size  240 is:  0.0003149071733156841
preprocessing time for sampling: 0.29225611686706543
amortized time for sample size  245 is:  0.0003146397434935277
preprocessing time for sampling: 0.2921640872955322
amortized time for sample size  250 is:  0.0003154344177246094
*** results for plotting, beta= 0.8 

mean_list= [np.float64(0.8099999999999999), np.float64(0.9), np.float64(0.95), np.float64(0.9800000000000001), np.float64(0.99), np.float64(0.95), 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(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), 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(0.12206555615733704), np.float64(0.06324555320336757), np.float64(0.06708203932499368), np.float64(0.039999999999999994), np.float64(0.029999999999999992), np.float64(0.06708203932499368), 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(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), 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: 0.327556848526001
amortized time for sample size  5 is:  0.0003258047103881837
preprocessing time for sampling: 0.32775092124938965
amortized time for sample size  10 is:  0.0003284163475036621
preprocessing time for sampling: 0.3278501033782959
amortized time for sample size  15 is:  0.00032544946670532224
preprocessing time for sampling: 0.3275301456451416
amortized time for sample size  20 is:  0.0003257013559341431
preprocessing time for sampling: 0.32776498794555664
amortized time for sample size  25 is:  0.00032528266906738275
preprocessing time for sampling: 0.3277111053466797
amortized time for sample size  30 is:  0.0003254543940226237
preprocessing time for sampling: 0.3278310298919678
amortized time for sample size  35 is:  0.00032643583842686236
preprocessing time for sampling: 0.33713603019714355
amortized time for sample size  40 is:  0.00032723349332809454
preprocessing time for sampling: 0.32680511474609375
amortized time for sample size  45 is:  0.00032530864079793295
preprocessing time for sampling: 0.32575106620788574
amortized time for sample size  50 is:  0.00032623667716979977
preprocessing time for sampling: 0.32722997665405273
amortized time for sample size  55 is:  0.0003260926766829057
preprocessing time for sampling: 0.3271360397338867
amortized time for sample size  60 is:  0.0003266027768452962
preprocessing time for sampling: 0.32705211639404297
amortized time for sample size  65 is:  0.000325578836294321
preprocessing time for sampling: 0.32712435722351074
amortized time for sample size  70 is:  0.000324934720993042
preprocessing time for sampling: 0.3274190425872803
amortized time for sample size  75 is:  0.0003254302978515625
preprocessing time for sampling: 0.32628297805786133
amortized time for sample size  80 is:  0.00032481381297111515
preprocessing time for sampling: 0.3263380527496338
amortized time for sample size  85 is:  0.0003244055579690372
preprocessing time for sampling: 0.326261043548584
amortized time for sample size  90 is:  0.0003246987130906847
preprocessing time for sampling: 0.3273138999938965
amortized time for sample size  95 is:  0.00032521561572426244
preprocessing time for sampling: 0.32848620414733887
amortized time for sample size  100 is:  0.000325775408744812
preprocessing time for sampling: 0.3277699947357178
amortized time for sample size  105 is:  0.000324909664335705
preprocessing time for sampling: 0.32636117935180664
amortized time for sample size  110 is:  0.0003256493481722745
preprocessing time for sampling: 0.3260979652404785
amortized time for sample size  115 is:  0.000326674627221149
preprocessing time for sampling: 0.32642388343811035
amortized time for sample size  120 is:  0.00032523242632548013
preprocessing time for sampling: 0.32709479331970215
amortized time for sample size  125 is:  0.00032532808303833006
preprocessing time for sampling: 0.32738518714904785
amortized time for sample size  130 is:  0.00032635635596055235
preprocessing time for sampling: 0.3274662494659424
amortized time for sample size  135 is:  0.0003256232296978985
preprocessing time for sampling: 0.3264040946960449
amortized time for sample size  140 is:  0.0003256675345557076
preprocessing time for sampling: 0.32666015625
amortized time for sample size  145 is:  0.0003268342511407261
preprocessing time for sampling: 0.3259861469268799
amortized time for sample size  150 is:  0.00032635771433512365
preprocessing time for sampling: 0.3340909481048584
amortized time for sample size  155 is:  0.0003253719268306609
preprocessing time for sampling: 0.32743406295776367
amortized time for sample size  160 is:  0.000325534239411354
preprocessing time for sampling: 0.3275489807128906
amortized time for sample size  165 is:  0.00032685989322084373
preprocessing time for sampling: 0.32643723487854004
amortized time for sample size  170 is:  0.0003260612768285414
preprocessing time for sampling: 0.32660889625549316
amortized time for sample size  175 is:  0.00032609331948416575
preprocessing time for sampling: 0.3263418674468994
amortized time for sample size  180 is:  0.000326408412721422
preprocessing time for sampling: 0.32784104347229004
amortized time for sample size  185 is:  0.0003258325602557208
preprocessing time for sampling: 0.32756900787353516
amortized time for sample size  190 is:  0.000326563559080425
preprocessing time for sampling: 0.3274061679840088
amortized time for sample size  195 is:  0.00032567151387532557
preprocessing time for sampling: 0.32666015625
amortized time for sample size  200 is:  0.0003258450508117676
preprocessing time for sampling: 0.32692694664001465
amortized time for sample size  205 is:  0.00032570127161537723
preprocessing time for sampling: 0.32647705078125
amortized time for sample size  210 is:  0.0003257231712341308
preprocessing time for sampling: 0.327315092086792
amortized time for sample size  215 is:  0.0003262436334476914
preprocessing time for sampling: 0.32717323303222656
amortized time for sample size  220 is:  0.00032559784975918853
preprocessing time for sampling: 0.32793092727661133
amortized time for sample size  225 is:  0.00032599184248182506
preprocessing time for sampling: 0.32624173164367676
amortized time for sample size  230 is:  0.00032654736353003464
preprocessing time for sampling: 0.326657772064209
amortized time for sample size  235 is:  0.0003269885550154017
preprocessing time for sampling: 0.32927393913269043
amortized time for sample size  240 is:  0.00032600494225819906
preprocessing time for sampling: 0.32924818992614746
amortized time for sample size  245 is:  0.039061220626441795
preprocessing time for sampling: 0.32984137535095215
amortized time for sample size  250 is:  0.00031972173690795894
*** results for plotting, beta= 1 

mean_list= [np.float64(0.85), np.float64(0.95), np.float64(0.99), np.float64(0.9800000000000001), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0)]
std_list= [np.float64(0.0806225774829855), np.float64(0.06708203932499368), np.float64(0.029999999999999992), np.float64(0.05999999999999999), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), 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: 0.2879199981689453
amortized time for sample size  5 is:  0.00030780029296875
preprocessing time for sampling: 0.2853560447692871
amortized time for sample size  10 is:  0.0003083744049072266
preprocessing time for sampling: 0.2903611660003662
amortized time for sample size  15 is:  0.0003077381451924642
preprocessing time for sampling: 0.28845810890197754
amortized time for sample size  20 is:  0.00030800390243530275
preprocessing time for sampling: 0.2920701503753662
amortized time for sample size  25 is:  0.00030811710357666017
preprocessing time for sampling: 0.2857680320739746
amortized time for sample size  30 is:  0.0003077406088511149
preprocessing time for sampling: 0.2884507179260254
amortized time for sample size  35 is:  0.00031241069521222795
preprocessing time for sampling: 0.29810404777526855
amortized time for sample size  40 is:  0.0003086535930633545
preprocessing time for sampling: 0.28641414642333984
amortized time for sample size  45 is:  0.00030841366449991863
preprocessing time for sampling: 0.2889060974121094
amortized time for sample size  50 is:  0.0003079078197479248
preprocessing time for sampling: 0.29367923736572266
amortized time for sample size  55 is:  0.0003083718906749378
preprocessing time for sampling: 0.28626012802124023
amortized time for sample size  60 is:  0.00030832473436991374
preprocessing time for sampling: 0.2892169952392578
amortized time for sample size  65 is:  0.00030971816869882434
preprocessing time for sampling: 0.2877030372619629
amortized time for sample size  70 is:  0.0003089197703770229
preprocessing time for sampling: 0.2886500358581543
amortized time for sample size  75 is:  0.00030883156458536785
preprocessing time for sampling: 0.2898519039154053
amortized time for sample size  80 is:  0.00030947184562683106
preprocessing time for sampling: 0.2864539623260498
amortized time for sample size  85 is:  0.0003086759342866785
preprocessing time for sampling: 0.2888450622558594
amortized time for sample size  90 is:  0.00030904078483581543
preprocessing time for sampling: 0.2885000705718994
amortized time for sample size  95 is:  0.10526085231178683
preprocessing time for sampling: 0.2869281768798828
amortized time for sample size  100 is:  0.00031102094650268554
preprocessing time for sampling: 0.28925228118896484
amortized time for sample size  105 is:  0.0003098040308271136
preprocessing time for sampling: 0.2901878356933594
amortized time for sample size  110 is:  0.0003093299215490168
preprocessing time for sampling: 0.2865450382232666
amortized time for sample size  115 is:  0.00030878664099651836
preprocessing time for sampling: 0.2888967990875244
amortized time for sample size  120 is:  0.00030953647692998244
preprocessing time for sampling: 0.2891411781311035
amortized time for sample size  125 is:  0.0003088644409179688
preprocessing time for sampling: 0.2862977981567383
amortized time for sample size  130 is:  0.0003096640293414776
preprocessing time for sampling: 0.28825926780700684
amortized time for sample size  135 is:  0.0003101667298210992
preprocessing time for sampling: 0.2885570526123047
amortized time for sample size  140 is:  0.00030861752373831613
preprocessing time for sampling: 0.28646206855773926
amortized time for sample size  145 is:  0.00030896209848338163
preprocessing time for sampling: 0.2936990261077881
amortized time for sample size  150 is:  0.00030854121843973804
preprocessing time for sampling: 0.28931283950805664
amortized time for sample size  155 is:  0.00030802037639002645
preprocessing time for sampling: 0.28670787811279297
amortized time for sample size  160 is:  0.06024140848219394
preprocessing time for sampling: 0.2998697757720947
amortized time for sample size  165 is:  0.0003112329858722109
preprocessing time for sampling: 0.2881600856781006
amortized time for sample size  170 is:  0.00030833708538728605
preprocessing time for sampling: 0.2861061096191406
amortized time for sample size  175 is:  0.0003099390574863979
preprocessing time for sampling: 0.294421911239624
amortized time for sample size  180 is:  0.0003087315162022909
preprocessing time for sampling: 0.2885887622833252
amortized time for sample size  185 is:  0.0003092840942176613
preprocessing time for sampling: 0.28673839569091797
amortized time for sample size  190 is:  0.00030832187752974653
preprocessing time for sampling: 0.2898402214050293
amortized time for sample size  195 is:  0.000308618704477946
preprocessing time for sampling: 0.288165807723999
amortized time for sample size  200 is:  0.045215206587314614
preprocessing time for sampling: 0.2892279624938965
amortized time for sample size  205 is:  0.0003078855654088462
preprocessing time for sampling: 0.2890589237213135
amortized time for sample size  210 is:  0.0003086095537458147
preprocessing time for sampling: 0.2889080047607422
amortized time for sample size  215 is:  0.0003092138600903888
preprocessing time for sampling: 0.28663015365600586
amortized time for sample size  220 is:  0.00030923654816367407
preprocessing time for sampling: 0.29005885124206543
amortized time for sample size  225 is:  0.0003091931449042426
preprocessing time for sampling: 0.28855109214782715
amortized time for sample size  230 is:  0.0003093891558439835
preprocessing time for sampling: 0.286283016204834
amortized time for sample size  235 is:  0.00030956398172581447
preprocessing time for sampling: 0.2889389991760254
amortized time for sample size  240 is:  0.03800615246097246
preprocessing time for sampling: 0.28876304626464844
amortized time for sample size  245 is:  0.00031098920471814214
preprocessing time for sampling: 0.2886331081390381
amortized time for sample size  250 is:  0.00030881172180175783
*** results for plotting, beta= 1.2 

mean_list= [np.float64(0.9200000000000002), 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), np.float64(1.0), np.float64(1.0), np.float64(1.0)]
std_list= [np.float64(0.0748331477354788), 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), np.float64(0.0), np.float64(0.0), np.float64(0.0)]
