beta: 0.2
preprocessing time for sampling: 7.5308520793914795
amortized time for sample size  5 is:  0.0028637957572937005
preprocessing time for sampling: 7.498304843902588
amortized time for sample size  10 is:  0.002880444288253784
preprocessing time for sampling: 7.592510938644409
amortized time for sample size  15 is:  0.002858723799387613
preprocessing time for sampling: 7.44242525100708
amortized time for sample size  20 is:  0.0030444184541702276
preprocessing time for sampling: 7.502922058105469
amortized time for sample size  25 is:  0.0028906078338623046
preprocessing time for sampling: 7.491206884384155
amortized time for sample size  30 is:  0.002924704551696778
preprocessing time for sampling: 7.640294075012207
amortized time for sample size  35 is:  0.0029851483617510115
preprocessing time for sampling: 7.5281360149383545
amortized time for sample size  40 is:  0.002986937165260315
preprocessing time for sampling: 7.5347301959991455
amortized time for sample size  45 is:  0.0029416028658548993
preprocessing time for sampling: 7.3863420486450195
amortized time for sample size  50 is:  0.0028880217552185055
preprocessing time for sampling: 7.508855104446411
amortized time for sample size  55 is:  0.002932613286105069
preprocessing time for sampling: 7.525116920471191
amortized time for sample size  60 is:  0.0029459640582402548
preprocessing time for sampling: 7.5450780391693115
amortized time for sample size  65 is:  0.002961788874406081
preprocessing time for sampling: 7.481070041656494
amortized time for sample size  70 is:  0.0029566979408264167
preprocessing time for sampling: 7.500830888748169
amortized time for sample size  75 is:  0.002968783060709635
preprocessing time for sampling: 7.46620512008667
amortized time for sample size  80 is:  0.0029839122593402862
preprocessing time for sampling: 7.543694019317627
amortized time for sample size  85 is:  0.0029713413294623877
preprocessing time for sampling: 7.554765224456787
amortized time for sample size  90 is:  0.0030261277622646767
preprocessing time for sampling: 7.585980176925659
amortized time for sample size  95 is:  0.0030749599557173875
preprocessing time for sampling: 7.634993076324463
amortized time for sample size  100 is:  0.0029387553453445437
preprocessing time for sampling: 7.62874698638916
amortized time for sample size  105 is:  0.0030041910807291666
preprocessing time for sampling: 7.711322784423828
amortized time for sample size  110 is:  0.0029588673981753265
preprocessing time for sampling: 7.565212249755859
amortized time for sample size  115 is:  0.002991085259810738
preprocessing time for sampling: 7.574828147888184
amortized time for sample size  120 is:  0.00295091305176417
preprocessing time for sampling: 7.535368919372559
amortized time for sample size  125 is:  0.002957438373565674
preprocessing time for sampling: 7.537409067153931
amortized time for sample size  130 is:  0.0029830986169668344
preprocessing time for sampling: 7.55401611328125
amortized time for sample size  135 is:  0.003006292908279984
preprocessing time for sampling: 7.535496234893799
amortized time for sample size  140 is:  0.002979233145713806
preprocessing time for sampling: 7.5097739696502686
amortized time for sample size  145 is:  0.002979152219048861
preprocessing time for sampling: 7.573546886444092
amortized time for sample size  150 is:  0.0030099850654602056
preprocessing time for sampling: 7.495074987411499
amortized time for sample size  155 is:  0.0029615837374041155
preprocessing time for sampling: 7.495357036590576
amortized time for sample size  160 is:  0.003009948819875717
preprocessing time for sampling: 7.54728102684021
amortized time for sample size  165 is:  0.0029453444625392095
preprocessing time for sampling: 7.495710134506226
amortized time for sample size  170 is:  0.002986205353456385
preprocessing time for sampling: 7.496524810791016
amortized time for sample size  175 is:  0.0029587402343750004
preprocessing time for sampling: 7.472716808319092
amortized time for sample size  180 is:  0.002929580887158712
preprocessing time for sampling: 7.421838045120239
amortized time for sample size  185 is:  0.0028424116340843414
preprocessing time for sampling: 7.455044984817505
amortized time for sample size  190 is:  0.0029320723759500606
preprocessing time for sampling: 7.537428855895996
amortized time for sample size  195 is:  0.0029769149560194747
preprocessing time for sampling: 7.582355976104736
amortized time for sample size  200 is:  0.002981662404537201
preprocessing time for sampling: 7.61126971244812
amortized time for sample size  205 is:  0.002983786001438048
preprocessing time for sampling: 7.545609951019287
amortized time for sample size  210 is:  0.0029545150030226936
preprocessing time for sampling: 7.553191900253296
amortized time for sample size  215 is:  0.002971257708793462
preprocessing time for sampling: 7.683592081069946
amortized time for sample size  220 is:  0.0030089921734549785
preprocessing time for sampling: 7.54243803024292
amortized time for sample size  225 is:  0.0029584322293599434
preprocessing time for sampling: 7.510571002960205
amortized time for sample size  230 is:  0.002954077938328619
preprocessing time for sampling: 7.528322696685791
amortized time for sample size  235 is:  0.002938325354393492
preprocessing time for sampling: 7.633222818374634
amortized time for sample size  240 is:  0.002964496572812398
preprocessing time for sampling: 7.570321798324585
amortized time for sample size  245 is:  0.002928999920280613
preprocessing time for sampling: 7.524515867233276
amortized time for sample size  250 is:  0.0029467400264739986
*** results for plotting, beta= 0.2 

mean_list= [np.float64(0.27999999999999997), np.float64(0.43999999999999995), np.float64(0.45999999999999996), np.float64(0.5199999999999999), np.float64(0.6299999999999999), np.float64(0.5599999999999999), np.float64(0.5599999999999999), np.float64(0.6199999999999999), np.float64(0.6499999999999999), np.float64(0.65), np.float64(0.6399999999999999), np.float64(0.69), np.float64(0.5999999999999999), np.float64(0.59), np.float64(0.5900000000000001), np.float64(0.72), np.float64(0.7200000000000001), np.float64(0.6799999999999999), np.float64(0.7), np.float64(0.6900000000000001), np.float64(0.75), np.float64(0.7900000000000001), np.float64(0.61), np.float64(0.73), np.float64(0.6900000000000001), np.float64(0.78), np.float64(0.71), np.float64(0.7899999999999999), np.float64(0.71), np.float64(0.8099999999999999), np.float64(0.6599999999999999), np.float64(0.74), np.float64(0.7700000000000001), np.float64(0.76), np.float64(0.78), np.float64(0.8), np.float64(0.75), np.float64(0.8200000000000001), np.float64(0.8), np.float64(0.77), np.float64(0.76), np.float64(0.8099999999999999), np.float64(0.76), np.float64(0.7900000000000001), np.float64(0.77), np.float64(0.79), np.float64(0.77), np.float64(0.8099999999999999), np.float64(0.8), np.float64(0.8099999999999999)]
std_list= [np.float64(0.07483314773547883), np.float64(0.13564659966250536), np.float64(0.18), np.float64(0.09797958971132711), np.float64(0.11), np.float64(0.11135528725660042), np.float64(0.12806248474865695), np.float64(0.11661903789690603), np.float64(0.16881943016134132), np.float64(0.16278820596099708), np.float64(0.18), np.float64(0.1135781669160055), np.float64(0.1341640786499874), np.float64(0.15132745950421556), np.float64(0.18138357147217055), np.float64(0.1777638883463118), np.float64(0.09797958971132716), np.float64(0.08717797887081348), np.float64(0.1341640786499874), np.float64(0.16999999999999998), np.float64(0.10246950765959602), np.float64(0.1445683229480096), np.float64(0.14456832294800961), np.float64(0.13453624047073712), np.float64(0.14456832294800961), np.float64(0.1469693845669907), np.float64(0.08306623862918078), np.float64(0.09433981132056607), np.float64(0.13747727084867523), np.float64(0.08306623862918076), np.float64(0.1356465996625054), np.float64(0.128062484748657), np.float64(0.13453624047073712), np.float64(0.1356465996625054), np.float64(0.14), np.float64(0.1264911064067352), np.float64(0.15652475842498528), np.float64(0.10770329614269009), np.float64(0.11832159566199235), np.float64(0.20024984394500786), np.float64(0.128062484748657), np.float64(0.10440306508910552), np.float64(0.11135528725660046), np.float64(0.14456832294800961), np.float64(0.17916472867168917), np.float64(0.13000000000000003), np.float64(0.06403124237432853), np.float64(0.09433981132056607), np.float64(0.14832396974191328), np.float64(0.13000000000000003)]
beta: 0.4
preprocessing time for sampling: 7.643402099609375
amortized time for sample size  5 is:  0.003026834964752197
preprocessing time for sampling: 7.612066030502319
amortized time for sample size  10 is:  0.0029416627883911126
preprocessing time for sampling: 7.5989298820495605
amortized time for sample size  15 is:  0.0029864377975463863
preprocessing time for sampling: 7.569982290267944
amortized time for sample size  20 is:  0.002976134061813355
preprocessing time for sampling: 7.621526002883911
amortized time for sample size  25 is:  0.0030037394523620598
preprocessing time for sampling: 7.527665138244629
amortized time for sample size  30 is:  0.002954747200012207
preprocessing time for sampling: 8.017937898635864
amortized time for sample size  35 is:  0.0029604093006678988
preprocessing time for sampling: 7.461318016052246
amortized time for sample size  40 is:  0.003009610116481781
preprocessing time for sampling: 7.449427366256714
amortized time for sample size  45 is:  0.002879312409294976
preprocessing time for sampling: 7.430016040802002
amortized time for sample size  50 is:  0.002933301019668579
preprocessing time for sampling: 7.389039754867554
amortized time for sample size  55 is:  0.0029193977009166366
preprocessing time for sampling: 7.404709100723267
amortized time for sample size  60 is:  0.002883287072181701
preprocessing time for sampling: 7.421701908111572
amortized time for sample size  65 is:  0.002878316769233116
preprocessing time for sampling: 7.3756632804870605
amortized time for sample size  70 is:  0.002890740530831473
preprocessing time for sampling: 7.38137412071228
amortized time for sample size  75 is:  0.0028411500930786136
preprocessing time for sampling: 7.414953231811523
amortized time for sample size  80 is:  0.0028994898796081553
preprocessing time for sampling: 7.495434045791626
amortized time for sample size  85 is:  0.0029288654327392577
preprocessing time for sampling: 7.4959681034088135
amortized time for sample size  90 is:  0.0029295128186543782
preprocessing time for sampling: 7.526138782501221
amortized time for sample size  95 is:  0.002955726623535157
preprocessing time for sampling: 7.613370895385742
amortized time for sample size  100 is:  0.0030138634204864502
preprocessing time for sampling: 7.578175067901611
amortized time for sample size  105 is:  0.0029649289449055994
preprocessing time for sampling: 7.547506093978882
amortized time for sample size  110 is:  0.0029208297729492187
preprocessing time for sampling: 7.525938987731934
amortized time for sample size  115 is:  0.002955450161643651
preprocessing time for sampling: 7.74075174331665
amortized time for sample size  120 is:  0.0030015221039454147
preprocessing time for sampling: 7.537891864776611
amortized time for sample size  125 is:  0.002980792407989502
preprocessing time for sampling: 7.56927490234375
amortized time for sample size  130 is:  0.00298694713299091
preprocessing time for sampling: 7.556636810302734
amortized time for sample size  135 is:  0.0030179841959917988
preprocessing time for sampling: 7.567043781280518
amortized time for sample size  140 is:  0.003004829542977469
preprocessing time for sampling: 7.667781114578247
amortized time for sample size  145 is:  0.003062060882305277
preprocessing time for sampling: 7.559876918792725
amortized time for sample size  150 is:  0.002969730027516683
preprocessing time for sampling: 7.493186950683594
amortized time for sample size  155 is:  0.002968564479581772
preprocessing time for sampling: 7.484384059906006
amortized time for sample size  160 is:  0.0029584917724132533
preprocessing time for sampling: 7.541628837585449
amortized time for sample size  165 is:  0.0029754057942014754
preprocessing time for sampling: 7.490132093429565
amortized time for sample size  170 is:  0.002944282910403084
preprocessing time for sampling: 7.504489898681641
amortized time for sample size  175 is:  0.0029631746019635878
preprocessing time for sampling: 7.546923875808716
amortized time for sample size  180 is:  0.0029220698806974627
preprocessing time for sampling: 7.519255876541138
amortized time for sample size  185 is:  0.0029586631800677323
preprocessing time for sampling: 7.5295939445495605
amortized time for sample size  190 is:  0.003007239529961034
preprocessing time for sampling: 7.494830131530762
amortized time for sample size  195 is:  0.002933883422460311
preprocessing time for sampling: 7.504363059997559
amortized time for sample size  200 is:  0.0029307070016860964
preprocessing time for sampling: 7.414086818695068
amortized time for sample size  205 is:  0.002867907186833823
preprocessing time for sampling: 7.416197776794434
amortized time for sample size  210 is:  0.002845977056594122
preprocessing time for sampling: 7.477618217468262
amortized time for sample size  215 is:  0.002974593362142873
preprocessing time for sampling: 7.504309892654419
amortized time for sample size  220 is:  0.002912845806642012
preprocessing time for sampling: 7.506381034851074
amortized time for sample size  225 is:  0.0028968832015991213
preprocessing time for sampling: 7.540542840957642
amortized time for sample size  230 is:  0.0028808711715366535
preprocessing time for sampling: 7.548931121826172
amortized time for sample size  235 is:  0.0029407574065188147
preprocessing time for sampling: 7.5082738399505615
amortized time for sample size  240 is:  0.0029520810842514032
preprocessing time for sampling: 7.539142847061157
amortized time for sample size  245 is:  0.0029146215964336785
preprocessing time for sampling: 7.453067064285278
amortized time for sample size  250 is:  0.0029420453262329095
*** results for plotting, beta= 0.4 

mean_list= [np.float64(0.5199999999999999), np.float64(0.62), np.float64(0.76), np.float64(0.8699999999999999), np.float64(0.8299999999999998), np.float64(0.82), np.float64(0.8300000000000001), np.float64(0.9), np.float64(0.9199999999999999), np.float64(0.93), np.float64(0.9200000000000002), np.float64(0.9199999999999999), np.float64(0.95), np.float64(0.96), np.float64(0.9100000000000001), np.float64(0.9400000000000001), np.float64(0.9), np.float64(0.95), np.float64(0.9099999999999999), np.float64(0.96), np.float64(0.9800000000000001), np.float64(0.9800000000000001), np.float64(0.93), np.float64(0.99), np.float64(0.9700000000000001), np.float64(0.9800000000000001), np.float64(0.9800000000000001), np.float64(0.99), np.float64(0.97), np.float64(0.9800000000000001), np.float64(0.97), np.float64(1.0), np.float64(1.0), np.float64(0.99), np.float64(0.9400000000000001), np.float64(0.99), np.float64(1.0), np.float64(1.0), np.float64(0.96), np.float64(0.99), np.float64(0.99), np.float64(0.9800000000000001), np.float64(0.99), np.float64(0.99), np.float64(0.97), np.float64(1.0), np.float64(0.99), np.float64(1.0), np.float64(1.0), np.float64(0.9800000000000001)]
std_list= [np.float64(0.132664991614216), np.float64(0.1777638883463118), np.float64(0.10198039027185572), np.float64(0.08999999999999998), np.float64(0.1187434208703792), np.float64(0.1077032961426901), np.float64(0.16763054614240208), np.float64(0.11832159566199232), np.float64(0.09797958971132713), np.float64(0.1004987562112089), np.float64(0.059999999999999984), np.float64(0.09797958971132713), np.float64(0.04999999999999999), np.float64(0.04898979485566355), np.float64(0.08306623862918076), np.float64(0.09165151389911681), np.float64(0.09999999999999999), np.float64(0.04999999999999999), np.float64(0.06999999999999999), np.float64(0.04898979485566355), np.float64(0.039999999999999994), np.float64(0.039999999999999994), np.float64(0.07810249675906653), np.float64(0.029999999999999992), np.float64(0.04582575694955839), np.float64(0.039999999999999994), np.float64(0.039999999999999994), np.float64(0.029999999999999992), np.float64(0.06403124237432847), np.float64(0.039999999999999994), np.float64(0.04582575694955839), np.float64(0.0), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.07999999999999999), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.0), np.float64(0.06633249580710798), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.039999999999999994), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.04582575694955839), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.0), np.float64(0.039999999999999994)]
beta: 0.6
preprocessing time for sampling: 7.431806802749634
amortized time for sample size  5 is:  0.002871172428131104
preprocessing time for sampling: 7.405786991119385
amortized time for sample size  10 is:  0.002961280822753907
preprocessing time for sampling: 7.402770042419434
amortized time for sample size  15 is:  0.002875618616739909
preprocessing time for sampling: 7.403560161590576
amortized time for sample size  20 is:  0.002908982276916504
preprocessing time for sampling: 7.432807922363281
amortized time for sample size  25 is:  0.003015232849121094
preprocessing time for sampling: 7.41904616355896
amortized time for sample size  30 is:  0.0028255430062611897
preprocessing time for sampling: 7.394784212112427
amortized time for sample size  35 is:  0.002829349109104701
preprocessing time for sampling: 7.364610195159912
amortized time for sample size  40 is:  0.002946888446807861
preprocessing time for sampling: 7.400604248046875
amortized time for sample size  45 is:  0.0028321726057264542
preprocessing time for sampling: 7.391075849533081
amortized time for sample size  50 is:  0.002868301630020141
preprocessing time for sampling: 7.427857875823975
amortized time for sample size  55 is:  0.0028649272918701172
preprocessing time for sampling: 7.398353338241577
amortized time for sample size  60 is:  0.002952564517656962
preprocessing time for sampling: 7.470468997955322
amortized time for sample size  65 is:  0.14831941648629995
preprocessing time for sampling: 7.380096912384033
amortized time for sample size  70 is:  0.002874253749847412
preprocessing time for sampling: 7.383013963699341
amortized time for sample size  75 is:  0.12685513207117718
preprocessing time for sampling: 7.396730184555054
amortized time for sample size  80 is:  0.0028047751486301427
preprocessing time for sampling: 7.394447088241577
amortized time for sample size  85 is:  0.11800799866283641
preprocessing time for sampling: 7.379894018173218
amortized time for sample size  90 is:  0.002863670852449205
preprocessing time for sampling: 7.391026973724365
amortized time for sample size  95 is:  0.006244603508397156
preprocessing time for sampling: 7.407081842422485
amortized time for sample size  100 is:  0.0027993947505950928
preprocessing time for sampling: 7.39786696434021
amortized time for sample size  105 is:  0.0028906200726826984
preprocessing time for sampling: 7.439563035964966
amortized time for sample size  110 is:  0.0028854218179529367
preprocessing time for sampling: 7.540060997009277
amortized time for sample size  115 is:  0.002902466587398364
preprocessing time for sampling: 7.4356467723846436
amortized time for sample size  120 is:  0.0028801974058151247
preprocessing time for sampling: 7.462179183959961
amortized time for sample size  125 is:  0.002878421897888184
preprocessing time for sampling: 7.462287902832031
amortized time for sample size  130 is:  0.0029449980809138376
preprocessing time for sampling: 7.538480758666992
amortized time for sample size  135 is:  0.00293004920747545
preprocessing time for sampling: 7.499744176864624
amortized time for sample size  140 is:  0.0029318686894008097
preprocessing time for sampling: 7.4545488357543945
amortized time for sample size  145 is:  0.0029170657190783268
preprocessing time for sampling: 7.639411926269531
amortized time for sample size  150 is:  0.002955366675059
preprocessing time for sampling: 7.526665925979614
amortized time for sample size  155 is:  0.002961567786432081
preprocessing time for sampling: 7.515285968780518
amortized time for sample size  160 is:  0.0029293076843023304
preprocessing time for sampling: 7.555300951004028
amortized time for sample size  165 is:  0.0029313175317012903
preprocessing time for sampling: 7.613060235977173
amortized time for sample size  170 is:  0.0029717616894665887
preprocessing time for sampling: 7.535564184188843
amortized time for sample size  175 is:  0.0029090801102774483
preprocessing time for sampling: 7.6631128787994385
amortized time for sample size  180 is:  0.0029413046042124436
preprocessing time for sampling: 7.585047245025635
amortized time for sample size  185 is:  0.0029387238476727457
preprocessing time for sampling: 7.5554039478302
amortized time for sample size  190 is:  0.002918446365155672
preprocessing time for sampling: 7.597175121307373
amortized time for sample size  195 is:  0.002947424974196996
preprocessing time for sampling: 7.542234182357788
amortized time for sample size  200 is:  0.002931132280826568
preprocessing time for sampling: 7.624395132064819
amortized time for sample size  205 is:  0.0029105304624976185
preprocessing time for sampling: 7.458626985549927
amortized time for sample size  210 is:  0.002887502329690115
preprocessing time for sampling: 7.5142340660095215
amortized time for sample size  215 is:  0.002948123521583024
preprocessing time for sampling: 7.497320175170898
amortized time for sample size  220 is:  0.00290340349890969
preprocessing time for sampling: 7.502994775772095
amortized time for sample size  225 is:  0.0029191980255974664
preprocessing time for sampling: 7.572795867919922
amortized time for sample size  230 is:  0.0028730210946953812
preprocessing time for sampling: 7.408543109893799
amortized time for sample size  235 is:  0.0029174194538846925
preprocessing time for sampling: 7.576496839523315
amortized time for sample size  240 is:  0.0029316146671771997
preprocessing time for sampling: 7.563643932342529
amortized time for sample size  245 is:  0.0029593172462619084
preprocessing time for sampling: 7.601725101470947
amortized time for sample size  250 is:  0.002910182266235351
*** results for plotting, beta= 0.6 

mean_list= [np.float64(0.6599999999999999), np.float64(0.78), np.float64(0.93), np.float64(0.96), np.float64(0.9), np.float64(0.97), np.float64(0.97), np.float64(0.96), np.float64(0.97), np.float64(1.0), np.float64(0.9800000000000001), np.float64(1.0), np.float64(0.9800000000000001), np.float64(1.0), np.float64(0.9800000000000001), np.float64(0.99), np.float64(0.9800000000000001), np.float64(1.0), np.float64(0.9800000000000001), 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(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)]
std_list= [np.float64(0.1562049935181331), np.float64(0.18330302779823363), np.float64(0.09), np.float64(0.06633249580710798), np.float64(0.08944271909999159), np.float64(0.045825756949558386), np.float64(0.06403124237432847), np.float64(0.04898979485566355), np.float64(0.045825756949558386), np.float64(0.0), np.float64(0.039999999999999994), np.float64(0.0), np.float64(0.039999999999999994), np.float64(0.0), np.float64(0.039999999999999994), np.float64(0.029999999999999992), np.float64(0.039999999999999994), np.float64(0.0), np.float64(0.039999999999999994), 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(0.029999999999999992), 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)]
beta: 0.8
preprocessing time for sampling: 7.568537950515747
amortized time for sample size  5 is:  0.0029575724601745602
preprocessing time for sampling: 7.608444929122925
amortized time for sample size  10 is:  0.0029891202449798594
preprocessing time for sampling: 7.578488826751709
amortized time for sample size  15 is:  0.0029515574773152664
preprocessing time for sampling: 7.573861122131348
amortized time for sample size  20 is:  0.002963603377342224
preprocessing time for sampling: 7.511682748794556
amortized time for sample size  25 is:  0.002984126377105713
preprocessing time for sampling: 7.530478000640869
amortized time for sample size  30 is:  0.0029513598283131912
preprocessing time for sampling: 7.553167104721069
amortized time for sample size  35 is:  0.002991570745195662
preprocessing time for sampling: 7.53331995010376
amortized time for sample size  40 is:  0.002880941867828369
preprocessing time for sampling: 7.466750860214233
amortized time for sample size  45 is:  0.002958151234520806
preprocessing time for sampling: 7.548074007034302
amortized time for sample size  50 is:  0.0029191798686981196
preprocessing time for sampling: 7.319617986679077
amortized time for sample size  55 is:  0.0029067925539883704
preprocessing time for sampling: 7.2795000076293945
amortized time for sample size  60 is:  0.0029029908577601123
preprocessing time for sampling: 7.547389030456543
amortized time for sample size  65 is:  0.0029224662780761718
preprocessing time for sampling: 7.490230083465576
amortized time for sample size  70 is:  0.0029199837275913783
preprocessing time for sampling: 7.500805139541626
amortized time for sample size  75 is:  0.0028990057945251476
preprocessing time for sampling: 7.418036937713623
amortized time for sample size  80 is:  0.0029048262834548955
preprocessing time for sampling: 7.472176790237427
amortized time for sample size  85 is:  0.002913676682640524
preprocessing time for sampling: 7.495529890060425
amortized time for sample size  90 is:  0.002925698571734959
preprocessing time for sampling: 7.549722909927368
amortized time for sample size  95 is:  0.002975307991630152
preprocessing time for sampling: 7.590944051742554
amortized time for sample size  100 is:  0.0028902338027954107
preprocessing time for sampling: 7.429126977920532
amortized time for sample size  105 is:  0.002894320896693639
preprocessing time for sampling: 7.5233941078186035
amortized time for sample size  110 is:  0.0029654928337443953
preprocessing time for sampling: 7.473015069961548
amortized time for sample size  115 is:  0.0029704461926999296
preprocessing time for sampling: 7.595707893371582
amortized time for sample size  120 is:  0.0029381864865620933
preprocessing time for sampling: 7.480062961578369
amortized time for sample size  125 is:  0.0028914238548278814
preprocessing time for sampling: 7.603876829147339
amortized time for sample size  130 is:  0.002928443761972281
preprocessing time for sampling: 7.424289226531982
amortized time for sample size  135 is:  0.0028991755379570855
preprocessing time for sampling: 7.467311859130859
amortized time for sample size  140 is:  0.002916266271046229
preprocessing time for sampling: 7.468660116195679
amortized time for sample size  145 is:  0.0029361004993833347
preprocessing time for sampling: 7.634308099746704
amortized time for sample size  150 is:  0.002885643180211385
preprocessing time for sampling: 7.509140968322754
amortized time for sample size  155 is:  0.002905957037402738
preprocessing time for sampling: 8.048835039138794
amortized time for sample size  160 is:  0.002939121901988983
preprocessing time for sampling: 7.718987941741943
amortized time for sample size  165 is:  0.0028883792125817508
preprocessing time for sampling: 7.537461996078491
amortized time for sample size  170 is:  0.0029231895839466754
preprocessing time for sampling: 7.5911009311676025
amortized time for sample size  175 is:  0.0029437338965279712
preprocessing time for sampling: 7.548064947128296
amortized time for sample size  180 is:  0.002908644715944926
preprocessing time for sampling: 7.553095102310181
amortized time for sample size  185 is:  0.002901229549098659
preprocessing time for sampling: 7.526640892028809
amortized time for sample size  190 is:  0.0028987126350402833
preprocessing time for sampling: 7.482417106628418
amortized time for sample size  195 is:  0.0029140547972459057
preprocessing time for sampling: 7.46884298324585
amortized time for sample size  200 is:  0.0029162121534347537
preprocessing time for sampling: 7.48737096786499
amortized time for sample size  205 is:  0.0029120256261127757
preprocessing time for sampling: 7.505367040634155
amortized time for sample size  210 is:  0.002933631874266125
preprocessing time for sampling: 7.510965824127197
amortized time for sample size  215 is:  0.0029218937186307687
preprocessing time for sampling: 7.5291619300842285
amortized time for sample size  220 is:  0.002889442194591869
preprocessing time for sampling: 7.534919738769531
amortized time for sample size  225 is:  0.0029063410758972175
preprocessing time for sampling: 7.448785066604614
amortized time for sample size  230 is:  0.0029145554770594064
preprocessing time for sampling: 7.586491823196411
amortized time for sample size  235 is:  0.002934549280937682
preprocessing time for sampling: 7.514394998550415
amortized time for sample size  240 is:  0.002882982581853867
preprocessing time for sampling: 7.469266891479492
amortized time for sample size  245 is:  0.00289791912935218
preprocessing time for sampling: 7.500935077667236
amortized time for sample size  250 is:  0.0029304237174987784
*** results for plotting, beta= 0.8 

mean_list= [np.float64(0.8), np.float64(0.93), np.float64(0.99), np.float64(0.9200000000000002), np.float64(0.99), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(0.99), np.float64(0.99), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(0.99), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(0.99), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), 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(0.14142135623730953), np.float64(0.1004987562112089), np.float64(0.029999999999999992), np.float64(0.0748331477354788), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), 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: 8.462492942810059
amortized time for sample size  5 is:  0.003072775363922119
preprocessing time for sampling: 8.404585123062134
amortized time for sample size  10 is:  0.0031435554027557373
preprocessing time for sampling: 8.423661947250366
amortized time for sample size  15 is:  0.003107432047526042
preprocessing time for sampling: 8.399262189865112
amortized time for sample size  20 is:  0.0031382206678390507
preprocessing time for sampling: 8.44105076789856
amortized time for sample size  25 is:  0.003085105323791504
preprocessing time for sampling: 8.403621196746826
amortized time for sample size  30 is:  0.0030175048510233567
preprocessing time for sampling: 8.469158172607422
amortized time for sample size  35 is:  0.003006851605006627
preprocessing time for sampling: 8.359031200408936
amortized time for sample size  40 is:  0.00295586520433426
preprocessing time for sampling: 8.321885824203491
amortized time for sample size  45 is:  0.002993994924757215
preprocessing time for sampling: 8.373736143112183
amortized time for sample size  50 is:  0.002980358982086181
preprocessing time for sampling: 8.532782077789307
amortized time for sample size  55 is:  0.0029954145604913877
preprocessing time for sampling: 8.462559938430786
amortized time for sample size  60 is:  0.0029917080005009973
preprocessing time for sampling: 8.468615055084229
amortized time for sample size  65 is:  0.0029223333138685957
preprocessing time for sampling: 8.465054988861084
amortized time for sample size  70 is:  0.0029639893259320936
preprocessing time for sampling: 8.721262216567993
amortized time for sample size  75 is:  0.002966862869262696
preprocessing time for sampling: 8.544320106506348
amortized time for sample size  80 is:  0.002961525827646256
preprocessing time for sampling: 8.495781898498535
amortized time for sample size  85 is:  0.0029687048968146824
preprocessing time for sampling: 8.582169771194458
amortized time for sample size  90 is:  0.002923243602116902
preprocessing time for sampling: 8.520244836807251
amortized time for sample size  95 is:  0.0029309202746341106
preprocessing time for sampling: 8.48476791381836
amortized time for sample size  100 is:  0.0029104579448699947
preprocessing time for sampling: 8.48344612121582
amortized time for sample size  105 is:  0.0029378843307495115
preprocessing time for sampling: 8.479516983032227
amortized time for sample size  110 is:  0.002899783242832531
preprocessing time for sampling: 8.423465251922607
amortized time for sample size  115 is:  0.002912969838018003
preprocessing time for sampling: 8.45202898979187
amortized time for sample size  120 is:  0.002907628873984019
preprocessing time for sampling: 8.409811973571777
amortized time for sample size  125 is:  0.0029043055725097655
preprocessing time for sampling: 8.357330799102783
amortized time for sample size  130 is:  0.0029274264849149263
preprocessing time for sampling: 8.383613109588623
amortized time for sample size  135 is:  0.0029146709795351377
preprocessing time for sampling: 8.495484113693237
amortized time for sample size  140 is:  0.0028979970557349065
preprocessing time for sampling: 8.368026733398438
amortized time for sample size  145 is:  0.002906907328243914
preprocessing time for sampling: 8.425700187683105
amortized time for sample size  150 is:  0.0029413538138071695
preprocessing time for sampling: 8.515038013458252
amortized time for sample size  155 is:  0.00296569481203633
preprocessing time for sampling: 8.45416522026062
amortized time for sample size  160 is:  0.002944076880812645
preprocessing time for sampling: 8.451061010360718
amortized time for sample size  165 is:  0.002939067277041348
preprocessing time for sampling: 8.462815046310425
amortized time for sample size  170 is:  0.002933103084564209
preprocessing time for sampling: 8.412360906600952
amortized time for sample size  175 is:  0.0029066856520516536
preprocessing time for sampling: 8.369364976882935
amortized time for sample size  180 is:  0.002924869047270881
preprocessing time for sampling: 8.417834043502808
amortized time for sample size  185 is:  0.0029324848200823804
preprocessing time for sampling: 8.454070091247559
amortized time for sample size  190 is:  0.002940817619624891
preprocessing time for sampling: 8.434792757034302
amortized time for sample size  195 is:  0.0029392217733921148
preprocessing time for sampling: 8.41874098777771
amortized time for sample size  200 is:  0.002946539688110352
preprocessing time for sampling: 8.398963928222656
amortized time for sample size  205 is:  0.0029216379537815008
preprocessing time for sampling: 8.386992692947388
amortized time for sample size  210 is:  0.0029569616885412302
preprocessing time for sampling: 8.504925012588501
amortized time for sample size  215 is:  0.00294606275336687
preprocessing time for sampling: 8.441008806228638
amortized time for sample size  220 is:  0.002962815208868547
preprocessing time for sampling: 8.470216035842896
amortized time for sample size  225 is:  0.0029424862967597117
preprocessing time for sampling: 8.514490127563477
amortized time for sample size  230 is:  0.0029992347385572344
preprocessing time for sampling: 8.495648860931396
amortized time for sample size  235 is:  0.002931884714897643
preprocessing time for sampling: 8.431905031204224
amortized time for sample size  240 is:  0.002981584320465724
preprocessing time for sampling: 8.40929102897644
amortized time for sample size  245 is:  0.002928012409988715
preprocessing time for sampling: 8.420144081115723
amortized time for sample size  250 is:  0.0029021782588958735
*** results for plotting, beta= 1 

mean_list= [np.float64(0.8800000000000001), np.float64(0.95), np.float64(0.99), np.float64(1.0), np.float64(0.99), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0)]
std_list= [np.float64(0.08717797887081347), np.float64(0.08062257748298547), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0)]
beta: 1.2
preprocessing time for sampling: 7.49822998046875
amortized time for sample size  5 is:  0.002981600284576415
preprocessing time for sampling: 7.56295919418335
amortized time for sample size  10 is:  0.0028977265357971196
preprocessing time for sampling: 7.484470844268799
amortized time for sample size  15 is:  0.0030563818613688148
preprocessing time for sampling: 7.486763954162598
amortized time for sample size  20 is:  0.002875683665275573
preprocessing time for sampling: 7.46047306060791
amortized time for sample size  25 is:  0.003025667190551758
preprocessing time for sampling: 7.525693893432617
amortized time for sample size  30 is:  0.002967881361643473
preprocessing time for sampling: 7.647162914276123
amortized time for sample size  35 is:  0.002873787879943848
preprocessing time for sampling: 7.467020034790039
amortized time for sample size  40 is:  0.0028952726125717173
preprocessing time for sampling: 7.487311124801636
amortized time for sample size  45 is:  0.0029520300759209523
preprocessing time for sampling: 7.49267315864563
amortized time for sample size  50 is:  0.0028834675312042236
preprocessing time for sampling: 7.515844106674194
amortized time for sample size  55 is:  0.0029166129719127303
preprocessing time for sampling: 7.528589963912964
amortized time for sample size  60 is:  0.0028895232280095415
preprocessing time for sampling: 7.469549894332886
amortized time for sample size  65 is:  0.002928195109734169
preprocessing time for sampling: 7.539271831512451
amortized time for sample size  70 is:  0.002908503975187029
preprocessing time for sampling: 7.512894868850708
amortized time for sample size  75 is:  0.0028792741775512704
preprocessing time for sampling: 7.536593914031982
amortized time for sample size  80 is:  0.0029245409071445468
preprocessing time for sampling: 7.560522079467773
amortized time for sample size  85 is:  0.002866617735694436
preprocessing time for sampling: 7.56099796295166
amortized time for sample size  90 is:  0.0028669016891055632
preprocessing time for sampling: 7.497759819030762
amortized time for sample size  95 is:  0.0028811908019216437
preprocessing time for sampling: 7.527351140975952
amortized time for sample size  100 is:  0.0028664619684219354
preprocessing time for sampling: 7.553225994110107
amortized time for sample size  105 is:  0.0029066653024582634
preprocessing time for sampling: 7.597442150115967
amortized time for sample size  110 is:  0.002924790924245661
preprocessing time for sampling: 7.567925930023193
amortized time for sample size  115 is:  0.0029553182436072314
preprocessing time for sampling: 7.7651917934417725
amortized time for sample size  120 is:  0.0029249836206436163
preprocessing time for sampling: 7.612123966217041
amortized time for sample size  125 is:  0.002896551723480224
preprocessing time for sampling: 7.494976043701172
amortized time for sample size  130 is:  0.0029302992270543032
preprocessing time for sampling: 7.528475284576416
amortized time for sample size  135 is:  0.002903676439214636
preprocessing time for sampling: 7.488723278045654
amortized time for sample size  140 is:  0.002888240456581116
preprocessing time for sampling: 7.492681980133057
amortized time for sample size  145 is:  0.0029141801636794525
preprocessing time for sampling: 7.442439794540405
amortized time for sample size  150 is:  0.002869371414184571
preprocessing time for sampling: 7.426958084106445
amortized time for sample size  155 is:  0.002959784277023808
preprocessing time for sampling: 7.489682912826538
amortized time for sample size  160 is:  0.0029255812764167784
preprocessing time for sampling: 7.493114948272705
amortized time for sample size  165 is:  0.0029537377212986793
preprocessing time for sampling: 7.492356061935425
amortized time for sample size  170 is:  0.0029550235411700083
preprocessing time for sampling: 7.540946960449219
amortized time for sample size  175 is:  0.0029039762360709054
preprocessing time for sampling: 7.465309143066406
amortized time for sample size  180 is:  0.0029357888566123114
preprocessing time for sampling: 7.514909029006958
amortized time for sample size  185 is:  0.002905974903622189
preprocessing time for sampling: 7.50852108001709
amortized time for sample size  190 is:  0.0029068897397894616
preprocessing time for sampling: 7.7097718715667725
amortized time for sample size  195 is:  0.0029232102418557194
preprocessing time for sampling: 7.534970045089722
amortized time for sample size  200 is:  0.0029922421813011173
preprocessing time for sampling: 7.585386037826538
amortized time for sample size  205 is:  0.0029536093618811633
preprocessing time for sampling: 7.504333972930908
amortized time for sample size  210 is:  0.0028914825008029034
preprocessing time for sampling: 7.519120216369629
amortized time for sample size  215 is:  0.0029353178711824636
preprocessing time for sampling: 7.508761167526245
amortized time for sample size  220 is:  0.002900802298025651
preprocessing time for sampling: 7.507975101470947
amortized time for sample size  225 is:  0.002875092538197835
preprocessing time for sampling: 7.468756914138794
amortized time for sample size  230 is:  0.0030089219860408617
preprocessing time for sampling: 7.5684309005737305
amortized time for sample size  235 is:  0.002903998141593121
preprocessing time for sampling: 7.478862047195435
amortized time for sample size  240 is:  0.0029045855303605397
preprocessing time for sampling: 7.556614875793457
amortized time for sample size  245 is:  0.002900339613155443
preprocessing time for sampling: 7.521275997161865
amortized time for sample size  250 is:  0.002936205024719239
*** results for plotting, beta= 1.2 

mean_list= [np.float64(0.9), np.float64(0.9800000000000001), 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), np.float64(1.0), np.float64(1.0), 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(0.08944271909999159), np.float64(0.039999999999999994), 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), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0)]
