beta: 0.2
preprocessing time for sampling: 1.2494399547576904
amortized time for sample size  5 is:  0.0007601819038391115
preprocessing time for sampling: 1.2427220344543457
amortized time for sample size  10 is:  0.0007772059440612791
preprocessing time for sampling: 1.2364587783813477
amortized time for sample size  15 is:  0.000761994202931722
preprocessing time for sampling: 1.2341320514678955
amortized time for sample size  20 is:  0.0007693126201629638
preprocessing time for sampling: 1.2467999458312988
amortized time for sample size  25 is:  0.0007605284690856934
preprocessing time for sampling: 1.2302520275115967
amortized time for sample size  30 is:  0.0007617437839508057
preprocessing time for sampling: 1.256187915802002
amortized time for sample size  35 is:  0.000757293905530657
preprocessing time for sampling: 1.2366728782653809
amortized time for sample size  40 is:  0.0007632901668548583
preprocessing time for sampling: 1.2591638565063477
amortized time for sample size  45 is:  0.0007603962156507704
preprocessing time for sampling: 1.2165577411651611
amortized time for sample size  50 is:  0.0007594284057617187
preprocessing time for sampling: 1.2277991771697998
amortized time for sample size  55 is:  0.0007535185813903808
preprocessing time for sampling: 1.2331829071044922
amortized time for sample size  60 is:  0.0007564938465754192
preprocessing time for sampling: 1.222038984298706
amortized time for sample size  65 is:  0.0007625661996694711
preprocessing time for sampling: 1.2532200813293457
amortized time for sample size  70 is:  0.0007644292286464148
preprocessing time for sampling: 1.2300736904144287
amortized time for sample size  75 is:  0.0007728286107381184
preprocessing time for sampling: 1.2209389209747314
amortized time for sample size  80 is:  0.0007553350925445557
preprocessing time for sampling: 1.2248690128326416
amortized time for sample size  85 is:  0.0007526369655833525
preprocessing time for sampling: 1.2185547351837158
amortized time for sample size  90 is:  0.0007679827743106417
preprocessing time for sampling: 1.2179319858551025
amortized time for sample size  95 is:  0.0007583537101745607
preprocessing time for sampling: 1.2199170589447021
amortized time for sample size  100 is:  0.0007654857397079468
preprocessing time for sampling: 1.2236087322235107
amortized time for sample size  105 is:  0.0007581103188650948
preprocessing time for sampling: 1.2185869216918945
amortized time for sample size  110 is:  0.0007618907581676137
preprocessing time for sampling: 1.2272489070892334
amortized time for sample size  115 is:  0.0007605345352836277
preprocessing time for sampling: 1.220362901687622
amortized time for sample size  120 is:  0.0007564106186230977
preprocessing time for sampling: 1.218346357345581
amortized time for sample size  125 is:  0.0007567754173278809
preprocessing time for sampling: 1.228950023651123
amortized time for sample size  130 is:  0.0007680247380183291
preprocessing time for sampling: 1.2500038146972656
amortized time for sample size  135 is:  0.0007793790322762949
preprocessing time for sampling: 1.2454009056091309
amortized time for sample size  140 is:  0.0007861823695046562
preprocessing time for sampling: 1.245905876159668
amortized time for sample size  145 is:  0.0007838705654801993
preprocessing time for sampling: 1.2499868869781494
amortized time for sample size  150 is:  0.0007727755069732666
preprocessing time for sampling: 1.2410547733306885
amortized time for sample size  155 is:  0.0007738068949791694
preprocessing time for sampling: 1.237123727798462
amortized time for sample size  160 is:  0.0007738656252622603
preprocessing time for sampling: 1.242541790008545
amortized time for sample size  165 is:  0.0007759188016255699
preprocessing time for sampling: 1.2636349201202393
amortized time for sample size  170 is:  0.0007772677084978889
preprocessing time for sampling: 1.2481930255889893
amortized time for sample size  175 is:  0.000768343939099993
preprocessing time for sampling: 1.2559449672698975
amortized time for sample size  180 is:  0.0007823258638381958
preprocessing time for sampling: 1.243940830230713
amortized time for sample size  185 is:  0.0007772991335069813
preprocessing time for sampling: 1.2544269561767578
amortized time for sample size  190 is:  0.0007816451097789563
preprocessing time for sampling: 1.3009939193725586
amortized time for sample size  195 is:  0.0007802923275874212
preprocessing time for sampling: 1.2645318508148193
amortized time for sample size  200 is:  0.0007873040199279786
preprocessing time for sampling: 1.2586569786071777
amortized time for sample size  205 is:  0.0007763058848497344
preprocessing time for sampling: 1.252418041229248
amortized time for sample size  210 is:  0.0007788021223885673
preprocessing time for sampling: 1.2406048774719238
amortized time for sample size  215 is:  0.0007764902336652887
preprocessing time for sampling: 1.255190134048462
amortized time for sample size  220 is:  0.0007817513292486017
preprocessing time for sampling: 1.2633631229400635
amortized time for sample size  225 is:  0.0007941096517774794
preprocessing time for sampling: 1.2848119735717773
amortized time for sample size  230 is:  0.0007801503616830575
preprocessing time for sampling: 1.2484760284423828
amortized time for sample size  235 is:  0.0007902318670394571
preprocessing time for sampling: 1.2503077983856201
amortized time for sample size  240 is:  0.0007718207140763603
preprocessing time for sampling: 1.2762091159820557
amortized time for sample size  245 is:  0.0007837053123785526
preprocessing time for sampling: 1.2505290508270264
amortized time for sample size  250 is:  0.0007808580398559571
*** results for plotting, beta= 0.2 

mean_list= [np.float64(0.31000000000000005), np.float64(0.39999999999999997), np.float64(0.5700000000000001), np.float64(0.6), np.float64(0.6199999999999999), np.float64(0.5700000000000001), np.float64(0.57), np.float64(0.71), np.float64(0.6299999999999999), np.float64(0.72), np.float64(0.62), np.float64(0.5700000000000001), np.float64(0.6700000000000002), np.float64(0.66), np.float64(0.7), np.float64(0.6399999999999999), np.float64(0.76), np.float64(0.6500000000000001), np.float64(0.6500000000000001), np.float64(0.61), np.float64(0.6100000000000001), np.float64(0.73), np.float64(0.76), np.float64(0.6599999999999999), np.float64(0.69), np.float64(0.72), np.float64(0.78), np.float64(0.67), np.float64(0.79), np.float64(0.6900000000000001), np.float64(0.73), np.float64(0.74), np.float64(0.75), np.float64(0.71), np.float64(0.73), np.float64(0.8300000000000001), np.float64(0.6799999999999999), np.float64(0.7), np.float64(0.8700000000000001), np.float64(0.75), np.float64(0.8400000000000001), np.float64(0.73), np.float64(0.7499999999999999), np.float64(0.78), np.float64(0.77), np.float64(0.7899999999999999), np.float64(0.74), np.float64(0.85), np.float64(0.7899999999999999), np.float64(0.7200000000000001)]
std_list= [np.float64(0.12206555615733702), np.float64(0.2), np.float64(0.20024984394500786), np.float64(0.1095445115010332), np.float64(0.116619037896906), np.float64(0.10999999999999997), np.float64(0.10049875621120888), np.float64(0.10440306508910553), np.float64(0.19000000000000003), np.float64(0.13266499161421605), np.float64(0.25219040425836986), np.float64(0.14177446878757824), np.float64(0.14866068747318506), np.float64(0.128062484748657), np.float64(0.1341640786499874), np.float64(0.11135528725660043), np.float64(0.09165151389911684), np.float64(0.15), np.float64(0.16278820596099708), np.float64(0.12206555615733702), np.float64(0.20712315177207977), np.float64(0.12688577540449522), np.float64(0.1562049935181331), np.float64(0.17435595774162693), np.float64(0.18138357147217055), np.float64(0.18330302779823363), np.float64(0.14), np.float64(0.15524174696260024), np.float64(0.08306623862918076), np.float64(0.13), np.float64(0.1187434208703792), np.float64(0.09165151389911684), np.float64(0.0921954445729289), np.float64(0.17578395831246946), np.float64(0.1676305461424021), np.float64(0.09), np.float64(0.14), np.float64(0.14142135623730953), np.float64(0.07810249675906653), np.float64(0.16278820596099708), np.float64(0.12000000000000001), np.float64(0.1846618531261939), np.float64(0.13601470508735444), np.float64(0.14), np.float64(0.09000000000000001), np.float64(0.11357816691600549), np.float64(0.128062484748657), np.float64(0.12041594578792296), np.float64(0.16401219466856726), np.float64(0.14)]
beta: 0.4
preprocessing time for sampling: 1.2650690078735352
amortized time for sample size  5 is:  0.0007692632675170897
preprocessing time for sampling: 1.2721412181854248
amortized time for sample size  10 is:  0.0007603282928466796
preprocessing time for sampling: 1.2563860416412354
amortized time for sample size  15 is:  0.0008011339505513508
preprocessing time for sampling: 1.2648160457611084
amortized time for sample size  20 is:  0.0007659239768981935
preprocessing time for sampling: 1.3119800090789795
amortized time for sample size  25 is:  0.0007664677619934082
preprocessing time for sampling: 1.266263723373413
amortized time for sample size  30 is:  0.0007738191286722818
preprocessing time for sampling: 1.2742133140563965
amortized time for sample size  35 is:  0.0007455692972455706
preprocessing time for sampling: 1.2530951499938965
amortized time for sample size  40 is:  0.0007502538561820984
preprocessing time for sampling: 1.2604401111602783
amortized time for sample size  45 is:  0.0007418468793233235
preprocessing time for sampling: 1.2487571239471436
amortized time for sample size  50 is:  0.0007755217075347902
preprocessing time for sampling: 1.2457432746887207
amortized time for sample size  55 is:  0.0007836380004882811
preprocessing time for sampling: 1.2596609592437744
amortized time for sample size  60 is:  0.000783653696378072
preprocessing time for sampling: 1.2669696807861328
amortized time for sample size  65 is:  0.000801547013796293
preprocessing time for sampling: 1.3056211471557617
amortized time for sample size  70 is:  0.0007840803691319057
preprocessing time for sampling: 1.2559678554534912
amortized time for sample size  75 is:  0.0007774795214335124
preprocessing time for sampling: 1.257322072982788
amortized time for sample size  80 is:  0.0007961876392364502
preprocessing time for sampling: 1.2533352375030518
amortized time for sample size  85 is:  0.0007673960293040557
preprocessing time for sampling: 1.2494959831237793
amortized time for sample size  90 is:  0.0007841114468044703
preprocessing time for sampling: 1.267463207244873
amortized time for sample size  95 is:  0.0007859949563678941
preprocessing time for sampling: 1.254584789276123
amortized time for sample size  100 is:  0.0007833754301071165
preprocessing time for sampling: 1.2435111999511719
amortized time for sample size  105 is:  0.0007810633977254232
preprocessing time for sampling: 1.2686829566955566
amortized time for sample size  110 is:  0.0008065351789647881
preprocessing time for sampling: 1.25468111038208
amortized time for sample size  115 is:  0.0007833915793377419
preprocessing time for sampling: 1.2744140625
amortized time for sample size  120 is:  0.0007884166836738585
preprocessing time for sampling: 1.2552590370178223
amortized time for sample size  125 is:  0.0007841812705993652
preprocessing time for sampling: 1.2528760433197021
amortized time for sample size  130 is:  0.0007867966248438908
preprocessing time for sampling: 1.252148151397705
amortized time for sample size  135 is:  0.0007785790584705493
preprocessing time for sampling: 1.251969814300537
amortized time for sample size  140 is:  0.0007845830747059412
preprocessing time for sampling: 1.2530808448791504
amortized time for sample size  145 is:  0.000784175001341721
preprocessing time for sampling: 1.273723840713501
amortized time for sample size  150 is:  0.0007752736568450926
preprocessing time for sampling: 1.2474257946014404
amortized time for sample size  155 is:  0.0007812522149855091
preprocessing time for sampling: 1.2552220821380615
amortized time for sample size  160 is:  0.0007810293436050417
preprocessing time for sampling: 1.2462050914764404
amortized time for sample size  165 is:  0.0007853859843629781
preprocessing time for sampling: 1.2466990947723389
amortized time for sample size  170 is:  0.0007847502371844123
preprocessing time for sampling: 1.2516210079193115
amortized time for sample size  175 is:  0.0007735802786690848
preprocessing time for sampling: 1.2483210563659668
amortized time for sample size  180 is:  0.0007802057266235352
preprocessing time for sampling: 1.2435808181762695
amortized time for sample size  185 is:  0.0007801275253295899
preprocessing time for sampling: 1.2426040172576904
amortized time for sample size  190 is:  0.0007753974763970628
preprocessing time for sampling: 1.2457032203674316
amortized time for sample size  195 is:  0.0007756511981670672
preprocessing time for sampling: 1.2519161701202393
amortized time for sample size  200 is:  0.0007797134757041932
preprocessing time for sampling: 1.2412312030792236
amortized time for sample size  205 is:  0.0007801068352489936
preprocessing time for sampling: 1.2379488945007324
amortized time for sample size  210 is:  0.0007723708947499594
preprocessing time for sampling: 1.2222957611083984
amortized time for sample size  215 is:  0.0007740078415981559
preprocessing time for sampling: 1.2397058010101318
amortized time for sample size  220 is:  0.0007759339484301479
preprocessing time for sampling: 1.2371859550476074
amortized time for sample size  225 is:  0.0007855368508232965
preprocessing time for sampling: 1.2267329692840576
amortized time for sample size  230 is:  0.0007776112349137014
preprocessing time for sampling: 1.2506239414215088
amortized time for sample size  235 is:  0.0007854196162933998
preprocessing time for sampling: 1.259552001953125
amortized time for sample size  240 is:  0.0007840404113133749
preprocessing time for sampling: 1.251720905303955
amortized time for sample size  245 is:  0.0007780033617603536
preprocessing time for sampling: 1.2217791080474854
amortized time for sample size  250 is:  0.0007760418701171877
*** results for plotting, beta= 0.4 

mean_list= [np.float64(0.62), np.float64(0.73), np.float64(0.79), np.float64(0.8300000000000001), np.float64(0.74), np.float64(0.78), np.float64(0.9099999999999999), np.float64(0.8800000000000001), np.float64(0.89), np.float64(0.95), np.float64(0.8699999999999999), np.float64(0.89), np.float64(0.93), np.float64(0.8800000000000001), np.float64(0.96), np.float64(0.9400000000000001), np.float64(0.9200000000000002), np.float64(0.9100000000000001), np.float64(0.96), np.float64(0.95), np.float64(0.95), np.float64(0.9700000000000001), np.float64(0.9400000000000001), np.float64(0.9800000000000001), np.float64(0.95), np.float64(0.97), np.float64(0.9), np.float64(0.93), np.float64(0.97), np.float64(0.9800000000000001), np.float64(0.9800000000000001), np.float64(0.9400000000000001), np.float64(0.99), np.float64(0.96), np.float64(0.9800000000000001), np.float64(0.9800000000000001), np.float64(0.95), np.float64(0.99), np.float64(0.9700000000000001), np.float64(1.0), np.float64(0.99), np.float64(0.9700000000000001), np.float64(1.0), np.float64(0.99), np.float64(0.9800000000000001), np.float64(0.99), np.float64(0.99), np.float64(0.99), np.float64(0.9800000000000001), np.float64(0.9800000000000001)]
std_list= [np.float64(0.132664991614216), np.float64(0.1187434208703792), np.float64(0.13000000000000003), np.float64(0.10049875621120892), np.float64(0.11135528725660047), np.float64(0.12489995996796799), np.float64(0.1044030650891055), np.float64(0.09797958971132714), np.float64(0.08306623862918076), np.float64(0.09219544457292889), np.float64(0.13453624047073712), np.float64(0.09433981132056604), np.float64(0.1004987562112089), np.float64(0.08717797887081348), np.float64(0.04898979485566356), np.float64(0.07999999999999999), np.float64(0.0748331477354788), np.float64(0.08306623862918074), np.float64(0.06633249580710798), np.float64(0.06708203932499368), np.float64(0.09219544457292889), np.float64(0.04582575694955839), np.float64(0.09165151389911681), np.float64(0.039999999999999994), np.float64(0.06708203932499367), np.float64(0.04582575694955839), np.float64(0.09999999999999999), np.float64(0.045825756949558386), np.float64(0.04582575694955839), np.float64(0.039999999999999994), np.float64(0.05999999999999999), np.float64(0.04898979485566355), np.float64(0.029999999999999992), np.float64(0.04898979485566355), np.float64(0.05999999999999999), np.float64(0.039999999999999994), np.float64(0.06708203932499368), np.float64(0.029999999999999992), np.float64(0.04582575694955839), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.04582575694955839), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.039999999999999994), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.039999999999999994), np.float64(0.039999999999999994)]
beta: 0.6
preprocessing time for sampling: 1.2287061214447021
amortized time for sample size  5 is:  0.0007568883895874023
preprocessing time for sampling: 1.2284960746765137
amortized time for sample size  10 is:  0.0007536871433258056
preprocessing time for sampling: 1.2452480792999268
amortized time for sample size  15 is:  0.0007572315533955893
preprocessing time for sampling: 1.2194738388061523
amortized time for sample size  20 is:  0.0007391930818557741
preprocessing time for sampling: 1.2393300533294678
amortized time for sample size  25 is:  0.0007442808151245119
preprocessing time for sampling: 1.24015474319458
amortized time for sample size  30 is:  0.0007428993384043379
preprocessing time for sampling: 1.2217538356781006
amortized time for sample size  35 is:  0.0007572904995509556
preprocessing time for sampling: 1.2323598861694336
amortized time for sample size  40 is:  0.0007635657191276551
preprocessing time for sampling: 1.2442269325256348
amortized time for sample size  45 is:  0.0007548794746398927
preprocessing time for sampling: 1.2319679260253906
amortized time for sample size  50 is:  0.0007649025917053224
preprocessing time for sampling: 1.229173183441162
amortized time for sample size  55 is:  0.0007637857957319783
preprocessing time for sampling: 1.2198128700256348
amortized time for sample size  60 is:  0.0007569308678309121
preprocessing time for sampling: 1.23301100730896
amortized time for sample size  65 is:  0.0007764487266540528
preprocessing time for sampling: 1.2321982383728027
amortized time for sample size  70 is:  0.0007663747583116804
preprocessing time for sampling: 1.2361841201782227
amortized time for sample size  75 is:  0.0007727151870727538
preprocessing time for sampling: 1.219918966293335
amortized time for sample size  80 is:  0.0008138273358345032
preprocessing time for sampling: 1.6181278228759766
amortized time for sample size  85 is:  0.0007834892553441664
preprocessing time for sampling: 1.240001916885376
amortized time for sample size  90 is:  0.000765996774037679
preprocessing time for sampling: 1.2192819118499756
amortized time for sample size  95 is:  0.0007652561539097835
preprocessing time for sampling: 1.2483577728271484
amortized time for sample size  100 is:  0.0007787182092666627
preprocessing time for sampling: 1.2439570426940918
amortized time for sample size  105 is:  0.0007771428653172084
preprocessing time for sampling: 1.2452890872955322
amortized time for sample size  110 is:  0.0007695169015364214
preprocessing time for sampling: 1.238081932067871
amortized time for sample size  115 is:  0.0007727276553278385
preprocessing time for sampling: 1.2406389713287354
amortized time for sample size  120 is:  0.000778935154279073
preprocessing time for sampling: 1.2488558292388916
amortized time for sample size  125 is:  0.0007699816894531251
preprocessing time for sampling: 1.2442879676818848
amortized time for sample size  130 is:  0.000768371141873873
preprocessing time for sampling: 1.2392630577087402
amortized time for sample size  135 is:  0.0007679449010778358
preprocessing time for sampling: 1.245128870010376
amortized time for sample size  140 is:  0.0007719592026301793
preprocessing time for sampling: 1.241610050201416
amortized time for sample size  145 is:  0.0007678232686272984
preprocessing time for sampling: 1.24467134475708
amortized time for sample size  150 is:  0.0007701414585113525
preprocessing time for sampling: 1.2392451763153076
amortized time for sample size  155 is:  0.000769103650123842
preprocessing time for sampling: 1.2623589038848877
amortized time for sample size  160 is:  0.0007833819836378098
preprocessing time for sampling: 1.2768430709838867
amortized time for sample size  165 is:  0.0007887233387340197
preprocessing time for sampling: 1.2502720355987549
amortized time for sample size  170 is:  0.0007859895509832048
preprocessing time for sampling: 1.2624521255493164
amortized time for sample size  175 is:  0.0007905756677900041
preprocessing time for sampling: 1.2625627517700195
amortized time for sample size  180 is:  0.0007803197304407755
preprocessing time for sampling: 1.2774629592895508
amortized time for sample size  185 is:  0.0007831754555573334
preprocessing time for sampling: 1.2486493587493896
amortized time for sample size  190 is:  0.0007688447299756502
preprocessing time for sampling: 1.2451660633087158
amortized time for sample size  195 is:  0.0007806849112877479
preprocessing time for sampling: 1.2775251865386963
amortized time for sample size  200 is:  0.0007742319941520693
preprocessing time for sampling: 1.2575809955596924
amortized time for sample size  205 is:  0.0007858917538712665
preprocessing time for sampling: 1.2996540069580078
amortized time for sample size  210 is:  0.0007797900154477074
preprocessing time for sampling: 1.2689902782440186
amortized time for sample size  215 is:  0.0007773125005322832
preprocessing time for sampling: 1.2585740089416504
amortized time for sample size  220 is:  0.0007802357565272937
preprocessing time for sampling: 1.249769926071167
amortized time for sample size  225 is:  0.0007785776562160915
preprocessing time for sampling: 1.2606821060180664
amortized time for sample size  230 is:  0.0007803344000940737
preprocessing time for sampling: 1.2534699440002441
amortized time for sample size  235 is:  0.0007787718975797611
preprocessing time for sampling: 1.2654330730438232
amortized time for sample size  240 is:  0.0007770511806011202
preprocessing time for sampling: 1.2706427574157715
amortized time for sample size  245 is:  0.000779024299310178
preprocessing time for sampling: 1.2481639385223389
amortized time for sample size  250 is:  0.0007816138172149657
*** results for plotting, beta= 0.6 

mean_list= [np.float64(0.78), np.float64(0.78), np.float64(0.9400000000000001), np.float64(0.93), np.float64(0.9400000000000001), np.float64(0.96), np.float64(0.96), np.float64(0.9400000000000001), np.float64(0.96), np.float64(0.99), np.float64(0.9800000000000001), np.float64(1.0), np.float64(1.0), np.float64(0.99), np.float64(0.9800000000000001), np.float64(0.99), np.float64(0.99), np.float64(1.0), np.float64(0.99), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(0.99), np.float64(0.99), np.float64(0.99), 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(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)]
std_list= [np.float64(0.11661903789690603), np.float64(0.07483314773547886), np.float64(0.06633249580710798), np.float64(0.07810249675906653), np.float64(0.07999999999999999), np.float64(0.04898979485566356), np.float64(0.04898979485566354), np.float64(0.07999999999999999), np.float64(0.04898979485566355), np.float64(0.029999999999999992), np.float64(0.039999999999999994), np.float64(0.0), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.039999999999999994), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.029999999999999992), 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(0.029999999999999992), 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)]
beta: 0.8
preprocessing time for sampling: 1.2693169116973877
amortized time for sample size  5 is:  0.0007908678054809569
preprocessing time for sampling: 1.2532720565795898
amortized time for sample size  10 is:  0.0007932322025299074
preprocessing time for sampling: 1.2536077499389648
amortized time for sample size  15 is:  0.0007819439570109049
preprocessing time for sampling: 1.2590031623840332
amortized time for sample size  20 is:  0.0008026007413864136
preprocessing time for sampling: 1.2492759227752686
amortized time for sample size  25 is:  0.0007787906646728514
preprocessing time for sampling: 1.2477259635925293
amortized time for sample size  30 is:  0.000780802090962728
preprocessing time for sampling: 1.2449958324432373
amortized time for sample size  35 is:  0.0007711465699332101
preprocessing time for sampling: 1.2462410926818848
amortized time for sample size  40 is:  0.0007851336598396299
preprocessing time for sampling: 1.249479055404663
amortized time for sample size  45 is:  0.0008059224022759332
preprocessing time for sampling: 1.2554419040679932
amortized time for sample size  50 is:  0.000786996603012085
preprocessing time for sampling: 1.2482240200042725
amortized time for sample size  55 is:  0.0007779051173817028
preprocessing time for sampling: 1.2487702369689941
amortized time for sample size  60 is:  0.0007669280370076496
preprocessing time for sampling: 1.2508399486541748
amortized time for sample size  65 is:  0.0007772168746361367
preprocessing time for sampling: 1.300978183746338
amortized time for sample size  70 is:  0.0007751238005501883
preprocessing time for sampling: 1.2423369884490967
amortized time for sample size  75 is:  0.0007773971239725749
preprocessing time for sampling: 1.2540180683135986
amortized time for sample size  80 is:  0.0007706842720508576
preprocessing time for sampling: 1.2464582920074463
amortized time for sample size  85 is:  0.0007743267452015595
preprocessing time for sampling: 1.244502067565918
amortized time for sample size  90 is:  0.0007793406380547417
preprocessing time for sampling: 1.2472970485687256
amortized time for sample size  95 is:  0.000778028086612099
preprocessing time for sampling: 1.261605978012085
amortized time for sample size  100 is:  0.0007855183839797974
preprocessing time for sampling: 1.2459509372711182
amortized time for sample size  105 is:  0.000775773184640067
preprocessing time for sampling: 1.2488791942596436
amortized time for sample size  110 is:  0.0007747776074842973
preprocessing time for sampling: 1.247974157333374
amortized time for sample size  115 is:  0.0007828391323918882
preprocessing time for sampling: 1.2495501041412354
amortized time for sample size  120 is:  0.0007819747726122537
preprocessing time for sampling: 1.2560131549835205
amortized time for sample size  125 is:  0.0007803040122985839
preprocessing time for sampling: 1.2430601119995117
amortized time for sample size  130 is:  0.0007684191557077262
preprocessing time for sampling: 1.248600959777832
amortized time for sample size  135 is:  0.0007822914476747866
preprocessing time for sampling: 1.2488899230957031
amortized time for sample size  140 is:  0.0007773295300347465
preprocessing time for sampling: 1.2869350910186768
amortized time for sample size  145 is:  0.0007759398920782683
preprocessing time for sampling: 1.2482500076293945
amortized time for sample size  150 is:  0.0007787513097127278
preprocessing time for sampling: 1.2438108921051025
amortized time for sample size  155 is:  0.0007760433227785173
preprocessing time for sampling: 1.2436330318450928
amortized time for sample size  160 is:  0.0007730524092912674
preprocessing time for sampling: 1.2456440925598145
amortized time for sample size  165 is:  0.0007706752112417508
preprocessing time for sampling: 1.2535440921783447
amortized time for sample size  170 is:  0.0007732647867763743
preprocessing time for sampling: 1.2203619480133057
amortized time for sample size  175 is:  0.0007686350277491978
preprocessing time for sampling: 1.2204971313476562
amortized time for sample size  180 is:  0.0007668980624940661
preprocessing time for sampling: 1.2268340587615967
amortized time for sample size  185 is:  0.000759947261294803
preprocessing time for sampling: 1.2329869270324707
amortized time for sample size  190 is:  0.0007685430300863165
preprocessing time for sampling: 1.2498559951782227
amortized time for sample size  195 is:  0.000786116294371776
preprocessing time for sampling: 1.2348501682281494
amortized time for sample size  200 is:  0.0007723788857460021
preprocessing time for sampling: 1.2306149005889893
amortized time for sample size  205 is:  0.000767330320870004
preprocessing time for sampling: 1.232456922531128
amortized time for sample size  210 is:  0.0007612659477052234
preprocessing time for sampling: 1.2204499244689941
amortized time for sample size  215 is:  0.0007653212214625159
preprocessing time for sampling: 1.2147669792175293
amortized time for sample size  220 is:  0.0007712576497684824
preprocessing time for sampling: 1.2322759628295898
amortized time for sample size  225 is:  0.0007671294954087998
preprocessing time for sampling: 1.2352509498596191
amortized time for sample size  230 is:  0.0007714618807253631
preprocessing time for sampling: 1.2522180080413818
amortized time for sample size  235 is:  0.0007693409311010483
preprocessing time for sampling: 1.2609457969665527
amortized time for sample size  240 is:  0.0007693600555260977
preprocessing time for sampling: 1.2423958778381348
amortized time for sample size  245 is:  0.000766056557090915
preprocessing time for sampling: 1.2499909400939941
amortized time for sample size  250 is:  0.0007692192649841309
*** results for plotting, beta= 0.8 

mean_list= [np.float64(0.8400000000000001), np.float64(0.95), np.float64(0.95), np.float64(0.96), np.float64(1.0), np.float64(0.9800000000000001), 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(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)]
std_list= [np.float64(0.11135528725660045), np.float64(0.04999999999999999), np.float64(0.049999999999999996), np.float64(0.04898979485566355), np.float64(0.0), np.float64(0.039999999999999994), 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(0.029999999999999992), 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)]
beta: 1
preprocessing time for sampling: 1.4422760009765625
amortized time for sample size  5 is:  0.00075645112991333
preprocessing time for sampling: 1.4279837608337402
amortized time for sample size  10 is:  0.0007733085155487062
preprocessing time for sampling: 1.419342041015625
amortized time for sample size  15 is:  0.0007639501889546714
preprocessing time for sampling: 1.433290958404541
amortized time for sample size  20 is:  0.0007569550275802612
preprocessing time for sampling: 1.4191479682922363
amortized time for sample size  25 is:  0.0007569127082824706
preprocessing time for sampling: 1.4248631000518799
amortized time for sample size  30 is:  0.0007571909427642823
preprocessing time for sampling: 1.4182307720184326
amortized time for sample size  35 is:  0.0007722916603088378
preprocessing time for sampling: 1.421177625656128
amortized time for sample size  40 is:  0.0007772520780563354
preprocessing time for sampling: 1.4205260276794434
amortized time for sample size  45 is:  0.0007911409801907008
preprocessing time for sampling: 1.4314079284667969
amortized time for sample size  50 is:  0.0007888283252716065
preprocessing time for sampling: 1.4199488162994385
amortized time for sample size  55 is:  0.0007899006496776234
preprocessing time for sampling: 1.4248149394989014
amortized time for sample size  60 is:  0.0007826699415842692
preprocessing time for sampling: 1.423755168914795
amortized time for sample size  65 is:  0.0007896495232215295
preprocessing time for sampling: 1.4241762161254883
amortized time for sample size  70 is:  0.0008015453815460206
preprocessing time for sampling: 1.4276947975158691
amortized time for sample size  75 is:  0.0007890240987141925
preprocessing time for sampling: 1.4288318157196045
amortized time for sample size  80 is:  0.0007978774309158326
preprocessing time for sampling: 1.4194939136505127
amortized time for sample size  85 is:  0.0007962305125068216
preprocessing time for sampling: 1.4393651485443115
amortized time for sample size  90 is:  0.0007917465898725723
preprocessing time for sampling: 1.4247286319732666
amortized time for sample size  95 is:  0.0007927157502425346
preprocessing time for sampling: 1.4404799938201904
amortized time for sample size  100 is:  0.0008021011114120483
preprocessing time for sampling: 1.419053077697754
amortized time for sample size  105 is:  0.0007877554439363027
preprocessing time for sampling: 1.428056240081787
amortized time for sample size  110 is:  0.0007979230880737304
preprocessing time for sampling: 1.4379918575286865
amortized time for sample size  115 is:  0.0007956885669542394
preprocessing time for sampling: 1.43522310256958
amortized time for sample size  120 is:  0.0007980229059855144
preprocessing time for sampling: 1.4227008819580078
amortized time for sample size  125 is:  0.000793226089477539
preprocessing time for sampling: 1.4553263187408447
amortized time for sample size  130 is:  0.000782290898836576
preprocessing time for sampling: 1.4204108715057373
amortized time for sample size  135 is:  0.0008177731655262134
preprocessing time for sampling: 1.480677843093872
amortized time for sample size  140 is:  0.0007897811787469046
preprocessing time for sampling: 1.4183151721954346
amortized time for sample size  145 is:  0.0007930844898881584
preprocessing time for sampling: 1.4266078472137451
amortized time for sample size  150 is:  0.0007946694215138753
preprocessing time for sampling: 1.4232587814331055
amortized time for sample size  155 is:  0.0007920330109134798
preprocessing time for sampling: 1.4200992584228516
amortized time for sample size  160 is:  0.0007909951210021974
preprocessing time for sampling: 1.4500081539154053
amortized time for sample size  165 is:  0.00080358599171494
preprocessing time for sampling: 1.4483063220977783
amortized time for sample size  170 is:  0.0007967971773708566
preprocessing time for sampling: 1.4297049045562744
amortized time for sample size  175 is:  0.000783268097468785
preprocessing time for sampling: 1.4236929416656494
amortized time for sample size  180 is:  0.0007932016717063055
preprocessing time for sampling: 1.4213058948516846
amortized time for sample size  185 is:  0.0007841589257523821
preprocessing time for sampling: 1.4235751628875732
amortized time for sample size  190 is:  0.0007941623236003676
preprocessing time for sampling: 1.4182929992675781
amortized time for sample size  195 is:  0.0007831285305512258
preprocessing time for sampling: 1.427340030670166
amortized time for sample size  200 is:  0.000783164119720459
preprocessing time for sampling: 1.422105073928833
amortized time for sample size  205 is:  0.0007826803719125142
preprocessing time for sampling: 1.4174418449401855
amortized time for sample size  210 is:  0.00078844039780753
preprocessing time for sampling: 1.4183969497680664
amortized time for sample size  215 is:  0.0007859342708144078
preprocessing time for sampling: 1.420017957687378
amortized time for sample size  220 is:  0.0007875510670922019
preprocessing time for sampling: 1.4044520854949951
amortized time for sample size  225 is:  0.0007897116555107964
preprocessing time for sampling: 1.402777910232544
amortized time for sample size  230 is:  0.0007819901030996574
preprocessing time for sampling: 1.4027256965637207
amortized time for sample size  235 is:  0.0007845442548711248
preprocessing time for sampling: 1.399703025817871
amortized time for sample size  240 is:  0.000785266836484273
preprocessing time for sampling: 1.42122483253479
amortized time for sample size  245 is:  0.0007844274676575952
preprocessing time for sampling: 1.4088852405548096
amortized time for sample size  250 is:  0.0007964402961730957
*** results for plotting, beta= 1 

mean_list= [np.float64(0.9), np.float64(0.97), np.float64(0.96), np.float64(0.9800000000000001), np.float64(1.0), np.float64(0.99), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(0.99), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0)]
std_list= [np.float64(0.1), np.float64(0.04582575694955839), np.float64(0.04898979485566355), np.float64(0.039999999999999994), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0)]
beta: 1.2
preprocessing time for sampling: 1.2948660850524902
amortized time for sample size  5 is:  0.0007708239555358887
preprocessing time for sampling: 1.283066987991333
amortized time for sample size  10 is:  0.0008226439952850343
preprocessing time for sampling: 1.2506461143493652
amortized time for sample size  15 is:  0.0007771848042805988
preprocessing time for sampling: 1.2358331680297852
amortized time for sample size  20 is:  0.0007994221448898316
preprocessing time for sampling: 1.257944107055664
amortized time for sample size  25 is:  0.0008020437240600587
preprocessing time for sampling: 1.239673137664795
amortized time for sample size  30 is:  0.0007786836624145509
preprocessing time for sampling: 1.2426278591156006
amortized time for sample size  35 is:  0.0007777620724269323
preprocessing time for sampling: 1.2373921871185303
amortized time for sample size  40 is:  0.0007765717506408692
preprocessing time for sampling: 1.256598949432373
amortized time for sample size  45 is:  0.00082668579949273
preprocessing time for sampling: 1.274435043334961
amortized time for sample size  50 is:  0.0007752258300781249
preprocessing time for sampling: 1.2381460666656494
amortized time for sample size  55 is:  0.0007722908366810193
preprocessing time for sampling: 1.2326111793518066
amortized time for sample size  60 is:  0.0007676684459050496
preprocessing time for sampling: 1.2311270236968994
amortized time for sample size  65 is:  0.0007676810484666091
preprocessing time for sampling: 1.226463794708252
amortized time for sample size  70 is:  0.0007665061269487655
preprocessing time for sampling: 1.251046895980835
amortized time for sample size  75 is:  0.0007754287719726563
preprocessing time for sampling: 1.2197299003601074
amortized time for sample size  80 is:  0.0007583027780056001
preprocessing time for sampling: 1.2338378429412842
amortized time for sample size  85 is:  0.0007641503390143901
preprocessing time for sampling: 1.2177553176879883
amortized time for sample size  90 is:  0.0007635390758514404
preprocessing time for sampling: 1.2613701820373535
amortized time for sample size  95 is:  0.0007555141699941535
preprocessing time for sampling: 1.2195181846618652
amortized time for sample size  100 is:  0.000764849305152893
preprocessing time for sampling: 1.2376208305358887
amortized time for sample size  105 is:  0.0007657262257167272
preprocessing time for sampling: 1.2371139526367188
amortized time for sample size  110 is:  0.0007685498974540016
preprocessing time for sampling: 1.217832088470459
amortized time for sample size  115 is:  0.0007727089342863664
preprocessing time for sampling: 1.245779037475586
amortized time for sample size  120 is:  0.0007792457342147826
preprocessing time for sampling: 1.2508411407470703
amortized time for sample size  125 is:  0.0007819231796264649
preprocessing time for sampling: 1.2476069927215576
amortized time for sample size  130 is:  0.0007786227006178636
preprocessing time for sampling: 1.2510662078857422
amortized time for sample size  135 is:  0.0007725276593808774
preprocessing time for sampling: 1.2548682689666748
amortized time for sample size  140 is:  0.0007770330905914307
preprocessing time for sampling: 1.2620108127593994
amortized time for sample size  145 is:  0.0007982828206029431
preprocessing time for sampling: 1.2511229515075684
amortized time for sample size  150 is:  0.0007699622472127278
preprocessing time for sampling: 1.2586610317230225
amortized time for sample size  155 is:  0.0007741739519180789
preprocessing time for sampling: 1.2509889602661133
amortized time for sample size  160 is:  0.0007810203582048417
preprocessing time for sampling: 1.2440319061279297
amortized time for sample size  165 is:  0.000789329890048865
preprocessing time for sampling: 1.2596158981323242
amortized time for sample size  170 is:  0.0007802371417774876
preprocessing time for sampling: 1.2515778541564941
amortized time for sample size  175 is:  0.0007735793249947682
preprocessing time for sampling: 1.2608442306518555
amortized time for sample size  180 is:  0.0007803713215721976
preprocessing time for sampling: 1.2481648921966553
amortized time for sample size  185 is:  0.0007668916341420765
preprocessing time for sampling: 1.242318868637085
amortized time for sample size  190 is:  0.0007788159721776059
preprocessing time for sampling: 1.3208909034729004
amortized time for sample size  195 is:  0.0008273230088062775
preprocessing time for sampling: 1.2769811153411865
amortized time for sample size  200 is:  0.0007797043561935425
preprocessing time for sampling: 1.310290813446045
amortized time for sample size  205 is:  0.0008237232929322776
preprocessing time for sampling: 1.310487985610962
amortized time for sample size  210 is:  0.0007890696298508418
preprocessing time for sampling: 1.2761430740356445
amortized time for sample size  215 is:  0.0007803319664888605
preprocessing time for sampling: 1.2711272239685059
amortized time for sample size  220 is:  0.0007811575152657249
preprocessing time for sampling: 1.256972074508667
amortized time for sample size  225 is:  0.0007990987989637588
preprocessing time for sampling: 1.2671470642089844
amortized time for sample size  230 is:  0.0007803963992906652
preprocessing time for sampling: 1.2538700103759766
amortized time for sample size  235 is:  0.0007788374981981644
preprocessing time for sampling: 1.2582218647003174
amortized time for sample size  240 is:  0.0007818656663099924
preprocessing time for sampling: 1.261979103088379
amortized time for sample size  245 is:  0.0007758495077794912
preprocessing time for sampling: 1.2439370155334473
amortized time for sample size  250 is:  0.0007698857307434082
*** results for plotting, beta= 1.2 

mean_list= [np.float64(0.96), np.float64(0.9800000000000001), 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(0.06633249580710798), np.float64(0.039999999999999994), np.float64(0.029999999999999992), np.float64(0.039999999999999994), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0)]
