beta: 0.2
preprocessing time for sampling: 0.0449678897857666
amortized time for sample size  5 is:  0.0001246805191040039
preprocessing time for sampling: 0.044982194900512695
amortized time for sample size  10 is:  0.00012468433380126954
preprocessing time for sampling: 0.044814109802246094
amortized time for sample size  15 is:  0.00012487745285034182
preprocessing time for sampling: 0.04538583755493164
amortized time for sample size  20 is:  0.00012461423873901366
preprocessing time for sampling: 0.04479789733886719
amortized time for sample size  25 is:  0.00012478742599487307
preprocessing time for sampling: 0.04481101036071777
amortized time for sample size  30 is:  0.00012425390879313152
preprocessing time for sampling: 0.0448451042175293
amortized time for sample size  35 is:  0.00012347936630249025
preprocessing time for sampling: 0.04479622840881348
amortized time for sample size  40 is:  0.00012352937459945678
preprocessing time for sampling: 0.04475903511047363
amortized time for sample size  45 is:  0.00012385373645358618
preprocessing time for sampling: 0.044831037521362305
amortized time for sample size  50 is:  0.00012579259872436523
preprocessing time for sampling: 0.04483294486999512
amortized time for sample size  55 is:  0.0001247266422618519
preprocessing time for sampling: 0.044985055923461914
amortized time for sample size  60 is:  0.00012505181630452473
preprocessing time for sampling: 0.045510292053222656
amortized time for sample size  65 is:  0.00012547841438880335
preprocessing time for sampling: 0.04637503623962402
amortized time for sample size  70 is:  0.00012561443873814176
preprocessing time for sampling: 0.04546928405761719
amortized time for sample size  75 is:  0.00012590160369873048
preprocessing time for sampling: 0.04560399055480957
amortized time for sample size  80 is:  0.00012710902094841003
preprocessing time for sampling: 0.04606914520263672
amortized time for sample size  85 is:  0.0001247720998876235
preprocessing time for sampling: 0.04484081268310547
amortized time for sample size  90 is:  0.00012423197428385415
preprocessing time for sampling: 0.04491305351257324
amortized time for sample size  95 is:  0.00012483343325163187
preprocessing time for sampling: 0.045300960540771484
amortized time for sample size  100 is:  0.0001261078119277954
preprocessing time for sampling: 0.0458528995513916
amortized time for sample size  105 is:  0.00012726079849969773
preprocessing time for sampling: 0.046682119369506836
amortized time for sample size  110 is:  0.00012463864413174718
preprocessing time for sampling: 0.04480791091918945
amortized time for sample size  115 is:  0.00012359175474747366
preprocessing time for sampling: 0.044899702072143555
amortized time for sample size  120 is:  0.00012359253565470378
preprocessing time for sampling: 0.044921875
amortized time for sample size  125 is:  0.00012376367568969727
preprocessing time for sampling: 0.044957876205444336
amortized time for sample size  130 is:  0.00012384774134709285
preprocessing time for sampling: 0.044957876205444336
amortized time for sample size  135 is:  0.00012408487885086624
preprocessing time for sampling: 0.04474592208862305
amortized time for sample size  140 is:  0.00012401243618556432
preprocessing time for sampling: 0.04479098320007324
amortized time for sample size  145 is:  0.00012366819381713867
preprocessing time for sampling: 0.04499197006225586
amortized time for sample size  150 is:  0.0001238164265950521
preprocessing time for sampling: 0.04478096961975098
amortized time for sample size  155 is:  0.00012361697227724136
preprocessing time for sampling: 0.04482316970825195
amortized time for sample size  160 is:  0.00012390361726284028
preprocessing time for sampling: 0.04478096961975098
amortized time for sample size  165 is:  0.0001240280324762518
preprocessing time for sampling: 0.04499006271362305
amortized time for sample size  170 is:  0.00012339275023516485
preprocessing time for sampling: 0.04471015930175781
amortized time for sample size  175 is:  0.00012349459784371513
preprocessing time for sampling: 0.04482388496398926
amortized time for sample size  180 is:  0.00012360698646969267
preprocessing time for sampling: 0.04487800598144531
amortized time for sample size  185 is:  0.0001233882646302919
preprocessing time for sampling: 0.04490399360656738
amortized time for sample size  190 is:  0.00012319686538294743
preprocessing time for sampling: 0.04473233222961426
amortized time for sample size  195 is:  0.0001232244295951648
preprocessing time for sampling: 0.04473996162414551
amortized time for sample size  200 is:  0.0001234165072441101
preprocessing time for sampling: 0.044847965240478516
amortized time for sample size  205 is:  0.0001232381448513124
preprocessing time for sampling: 0.04500079154968262
amortized time for sample size  210 is:  0.00012316131591796873
preprocessing time for sampling: 0.04477405548095703
amortized time for sample size  215 is:  0.0001246605584787768
preprocessing time for sampling: 0.04514145851135254
amortized time for sample size  220 is:  0.0001245012391697277
preprocessing time for sampling: 0.0451350212097168
amortized time for sample size  225 is:  0.00012411023245917428
preprocessing time for sampling: 0.04522705078125
amortized time for sample size  230 is:  0.00012442658258521037
preprocessing time for sampling: 0.04479408264160156
amortized time for sample size  235 is:  0.0001234575941207561
preprocessing time for sampling: 0.044734954833984375
amortized time for sample size  240 is:  0.00012366303801536558
preprocessing time for sampling: 0.04527902603149414
amortized time for sample size  245 is:  0.00012915422478500677
preprocessing time for sampling: 0.044799089431762695
amortized time for sample size  250 is:  0.00012306588172912597
*** results for plotting, beta= 0.2 

mean_list= [np.float64(0.26), np.float64(0.36), np.float64(0.49000000000000005), np.float64(0.6300000000000001), np.float64(0.48), np.float64(0.53), np.float64(0.5799999999999998), np.float64(0.55), np.float64(0.57), np.float64(0.56), np.float64(0.6), np.float64(0.5499999999999999), np.float64(0.6799999999999999), np.float64(0.62), np.float64(0.57), np.float64(0.6100000000000001), np.float64(0.6399999999999999), np.float64(0.65), np.float64(0.63), np.float64(0.68), np.float64(0.6799999999999999), np.float64(0.5900000000000001), np.float64(0.7100000000000001), np.float64(0.76), np.float64(0.5900000000000001), np.float64(0.6499999999999999), np.float64(0.65), np.float64(0.69), np.float64(0.71), np.float64(0.6900000000000001), np.float64(0.65), np.float64(0.74), np.float64(0.72), np.float64(0.77), np.float64(0.63), np.float64(0.7100000000000001), np.float64(0.73), np.float64(0.71), np.float64(0.74), np.float64(0.62), np.float64(0.65), np.float64(0.62), np.float64(0.7099999999999999), np.float64(0.6399999999999999), np.float64(0.7), np.float64(0.6699999999999999), np.float64(0.76), np.float64(0.6599999999999999), np.float64(0.76), np.float64(0.79)]
std_list= [np.float64(0.14282856857085702), np.float64(0.11999999999999998), np.float64(0.12999999999999998), np.float64(0.16763054614240208), np.float64(0.15999999999999998), np.float64(0.16763054614240208), np.float64(0.11661903789690602), np.float64(0.12041594578792293), np.float64(0.14866068747318506), np.float64(0.17435595774162693), np.float64(0.2), np.float64(0.1857417562100671), np.float64(0.18867962264113208), np.float64(0.15362291495737218), np.float64(0.16155494421403513), np.float64(0.23), np.float64(0.14282856857085702), np.float64(0.14317821063276354), np.float64(0.1846618531261939), np.float64(0.14696938456699069), np.float64(0.1077032961426901), np.float64(0.18138357147217052), np.float64(0.16999999999999998), np.float64(0.1685229954635272), np.float64(0.14456832294800961), np.float64(0.15000000000000002), np.float64(0.14317821063276354), np.float64(0.09433981132056606), np.float64(0.13000000000000003), np.float64(0.13000000000000003), np.float64(0.16278820596099708), np.float64(0.11135528725660046), np.float64(0.09797958971132717), np.float64(0.10049875621120892), np.float64(0.1268857754044952), np.float64(0.13000000000000003), np.float64(0.16155494421403513), np.float64(0.11357816691600549), np.float64(0.11135528725660046), np.float64(0.15362291495737218), np.float64(0.10246950765959598), np.float64(0.16613247725836153), np.float64(0.1135781669160055), np.float64(0.10198039027185571), np.float64(0.10954451150103324), np.float64(0.11), np.float64(0.1562049935181331), np.float64(0.1356465996625054), np.float64(0.11135528725660046), np.float64(0.09433981132056607)]
beta: 0.4
preprocessing time for sampling: 0.04483294486999512
amortized time for sample size  5 is:  0.00012339305877685547
preprocessing time for sampling: 0.04483199119567871
amortized time for sample size  10 is:  0.00012345457077026368
preprocessing time for sampling: 0.04485607147216797
amortized time for sample size  15 is:  0.00012352593739827473
preprocessing time for sampling: 0.04489898681640625
amortized time for sample size  20 is:  0.00012353253364562986
preprocessing time for sampling: 0.04493975639343262
amortized time for sample size  25 is:  0.00012349891662597658
preprocessing time for sampling: 0.04481077194213867
amortized time for sample size  30 is:  0.00012341086069742838
preprocessing time for sampling: 0.04479217529296875
amortized time for sample size  35 is:  0.00012333427156720843
preprocessing time for sampling: 0.04480171203613281
amortized time for sample size  40 is:  0.00012360668182373046
preprocessing time for sampling: 0.04494190216064453
amortized time for sample size  45 is:  0.00012347592247856988
preprocessing time for sampling: 0.04479575157165527
amortized time for sample size  50 is:  0.00013164200782775877
preprocessing time for sampling: 0.04872298240661621
amortized time for sample size  55 is:  0.00012410818446766247
preprocessing time for sampling: 0.04488992691040039
amortized time for sample size  60 is:  0.00012409385045369467
preprocessing time for sampling: 0.047567129135131836
amortized time for sample size  65 is:  0.0001299163744999812
preprocessing time for sampling: 0.04848194122314453
amortized time for sample size  70 is:  0.00012583664485386442
preprocessing time for sampling: 0.04495692253112793
amortized time for sample size  75 is:  0.00012408164342244467
preprocessing time for sampling: 0.04488182067871094
amortized time for sample size  80 is:  0.0001249542832374573
preprocessing time for sampling: 0.04665398597717285
amortized time for sample size  85 is:  0.00012985897064208985
preprocessing time for sampling: 0.044875144958496094
amortized time for sample size  90 is:  0.00012674644258287216
preprocessing time for sampling: 0.047094106674194336
amortized time for sample size  95 is:  0.00012817254819368063
preprocessing time for sampling: 0.04849839210510254
amortized time for sample size  100 is:  0.0001241255283355713
preprocessing time for sampling: 0.04508376121520996
amortized time for sample size  105 is:  0.0001243179412115188
preprocessing time for sampling: 0.06454610824584961
amortized time for sample size  110 is:  0.0001238131523132324
preprocessing time for sampling: 0.044838905334472656
amortized time for sample size  115 is:  0.00012348811522774073
preprocessing time for sampling: 0.04491281509399414
amortized time for sample size  120 is:  0.00012359813849131265
preprocessing time for sampling: 0.04502606391906738
amortized time for sample size  125 is:  0.000123549747467041
preprocessing time for sampling: 0.04489493370056152
amortized time for sample size  130 is:  0.00012896855060870834
preprocessing time for sampling: 0.04920220375061035
amortized time for sample size  135 is:  0.0001325622664557563
preprocessing time for sampling: 0.047425031661987305
amortized time for sample size  140 is:  0.00012578272819519044
preprocessing time for sampling: 0.04575991630554199
amortized time for sample size  145 is:  0.00012377719221443964
preprocessing time for sampling: 0.04480576515197754
amortized time for sample size  150 is:  0.000123586368560791
preprocessing time for sampling: 0.04485297203063965
amortized time for sample size  155 is:  0.00012354929216446412
preprocessing time for sampling: 0.04476284980773926
amortized time for sample size  160 is:  0.00012397982180118561
preprocessing time for sampling: 0.052681922912597656
amortized time for sample size  165 is:  0.0001237160364786784
preprocessing time for sampling: 0.04483294486999512
amortized time for sample size  170 is:  0.0001234139414394603
preprocessing time for sampling: 0.04485607147216797
amortized time for sample size  175 is:  0.00012347474779401507
preprocessing time for sampling: 0.04498696327209473
amortized time for sample size  180 is:  0.00012335716353522406
preprocessing time for sampling: 0.04478168487548828
amortized time for sample size  185 is:  0.000123536457886567
preprocessing time for sampling: 0.0448000431060791
amortized time for sample size  190 is:  0.0001232443232285349
preprocessing time for sampling: 0.04506111145019531
amortized time for sample size  195 is:  0.0001236583391825358
preprocessing time for sampling: 0.045831918716430664
amortized time for sample size  200 is:  0.00012335659265518188
preprocessing time for sampling: 0.05170392990112305
amortized time for sample size  205 is:  0.00012309678007916704
preprocessing time for sampling: 0.04481816291809082
amortized time for sample size  210 is:  0.00012291727747235976
preprocessing time for sampling: 0.04488825798034668
amortized time for sample size  215 is:  0.0001236526134402253
preprocessing time for sampling: 0.0448458194732666
amortized time for sample size  220 is:  0.00012329968539151278
preprocessing time for sampling: 0.04481673240661621
amortized time for sample size  225 is:  0.0001232135984632704
preprocessing time for sampling: 0.04482769966125488
amortized time for sample size  230 is:  0.0001232967065728229
preprocessing time for sampling: 0.04496288299560547
amortized time for sample size  235 is:  0.000123160017297623
preprocessing time for sampling: 0.04488015174865723
amortized time for sample size  240 is:  0.00012346528967221575
preprocessing time for sampling: 0.044831037521362305
amortized time for sample size  245 is:  0.00012308514848047373
preprocessing time for sampling: 0.04487490653991699
amortized time for sample size  250 is:  0.0001233030891418457
*** results for plotting, beta= 0.4 

mean_list= [np.float64(0.51), np.float64(0.75), np.float64(0.74), np.float64(0.69), np.float64(0.8400000000000001), np.float64(0.8100000000000002), np.float64(0.89), np.float64(0.7500000000000001), np.float64(0.8600000000000001), np.float64(0.93), np.float64(0.86), np.float64(0.8699999999999999), np.float64(0.8800000000000001), np.float64(0.9000000000000001), np.float64(0.8400000000000001), np.float64(0.8699999999999999), np.float64(0.9400000000000001), np.float64(0.9099999999999999), np.float64(0.9099999999999999), np.float64(0.9400000000000001), np.float64(0.93), np.float64(0.9199999999999999), np.float64(0.9200000000000002), np.float64(0.9400000000000001), np.float64(0.95), np.float64(0.9700000000000001), np.float64(0.89), np.float64(0.95), np.float64(0.93), np.float64(0.9400000000000001), np.float64(0.9800000000000001), np.float64(0.93), np.float64(0.93), np.float64(0.97), np.float64(0.9400000000000001), np.float64(0.96), np.float64(0.9200000000000002), np.float64(0.9800000000000001), np.float64(0.96), np.float64(0.9400000000000001), np.float64(0.95), np.float64(0.96), np.float64(0.99), np.float64(0.97), np.float64(0.97), np.float64(0.99), np.float64(0.96), np.float64(0.9700000000000001), np.float64(0.97), np.float64(0.96)]
std_list= [np.float64(0.11357816691600546), np.float64(0.12041594578792297), np.float64(0.14966629547095767), np.float64(0.09433981132056608), np.float64(0.12000000000000001), np.float64(0.17), np.float64(0.05385164807134503), np.float64(0.10246950765959602), np.float64(0.10198039027185571), np.float64(0.09), np.float64(0.1562049935181331), np.float64(0.07810249675906655), np.float64(0.039999999999999994), np.float64(0.07745966692414831), np.float64(0.11135528725660045), np.float64(0.11000000000000001), np.float64(0.04898979485566354), np.float64(0.12206555615733704), np.float64(0.08306623862918072), np.float64(0.04898979485566355), np.float64(0.06403124237432847), np.float64(0.10770329614269009), np.float64(0.0748331477354788), np.float64(0.04898979485566356), np.float64(0.08062257748298547), np.float64(0.04582575694955839), np.float64(0.1044030650891055), np.float64(0.08062257748298547), np.float64(0.07810249675906653), np.float64(0.06633249580710798), np.float64(0.039999999999999994), np.float64(0.06403124237432847), np.float64(0.07810249675906653), np.float64(0.04582575694955839), np.float64(0.07999999999999999), np.float64(0.04898979485566355), np.float64(0.09797958971132713), np.float64(0.039999999999999994), np.float64(0.04898979485566356), np.float64(0.04898979485566355), np.float64(0.04999999999999999), np.float64(0.04898979485566355), np.float64(0.029999999999999992), np.float64(0.06403124237432847), np.float64(0.06403124237432847), np.float64(0.029999999999999992), np.float64(0.04898979485566356), np.float64(0.04582575694955839), np.float64(0.04582575694955839), np.float64(0.06633249580710798)]
beta: 0.6
preprocessing time for sampling: 0.04488706588745117
amortized time for sample size  5 is:  0.000123227596282959
preprocessing time for sampling: 0.044870853424072266
amortized time for sample size  10 is:  0.00012332725524902342
preprocessing time for sampling: 0.04487800598144531
amortized time for sample size  15 is:  0.00012299172083536785
preprocessing time for sampling: 0.04488706588745117
amortized time for sample size  20 is:  0.0001231250762939453
preprocessing time for sampling: 0.04543495178222656
amortized time for sample size  25 is:  0.00012297649383544921
preprocessing time for sampling: 0.04488682746887207
amortized time for sample size  30 is:  0.0001228007475535075
preprocessing time for sampling: 0.04488325119018555
amortized time for sample size  35 is:  0.00012268407004220144
preprocessing time for sampling: 0.04486489295959473
amortized time for sample size  40 is:  0.0001228272318840027
preprocessing time for sampling: 0.044866085052490234
amortized time for sample size  45 is:  0.00012319257524278428
preprocessing time for sampling: 0.04484224319458008
amortized time for sample size  50 is:  0.0001230257511138916
preprocessing time for sampling: 0.04486703872680664
amortized time for sample size  55 is:  0.0001230609200217507
preprocessing time for sampling: 0.04468894004821777
amortized time for sample size  60 is:  0.0001231034199396769
preprocessing time for sampling: 0.04454803466796875
amortized time for sample size  65 is:  0.00012314202235295225
preprocessing time for sampling: 0.0448760986328125
amortized time for sample size  70 is:  0.000124302795955113
preprocessing time for sampling: 0.044973134994506836
amortized time for sample size  75 is:  0.00012307415008544923
preprocessing time for sampling: 0.04493093490600586
amortized time for sample size  80 is:  0.00012296995520591736
preprocessing time for sampling: 0.04491376876831055
amortized time for sample size  85 is:  0.00012297459209666532
preprocessing time for sampling: 0.044940948486328125
amortized time for sample size  90 is:  0.0001230208608839247
preprocessing time for sampling: 0.04487800598144531
amortized time for sample size  95 is:  0.0001231697484066612
preprocessing time for sampling: 0.04491686820983887
amortized time for sample size  100 is:  0.0001232657432556152
preprocessing time for sampling: 0.04487204551696777
amortized time for sample size  105 is:  0.00012337130591982885
preprocessing time for sampling: 0.04493308067321777
amortized time for sample size  110 is:  0.00012310099601745605
preprocessing time for sampling: 0.044875144958496094
amortized time for sample size  115 is:  0.0001233791683031165
preprocessing time for sampling: 0.04490804672241211
amortized time for sample size  120 is:  0.0001231554945309957
preprocessing time for sampling: 0.04488706588745117
amortized time for sample size  125 is:  0.00012322521209716798
preprocessing time for sampling: 0.044899940490722656
amortized time for sample size  130 is:  0.00012328010339003346
preprocessing time for sampling: 0.04493403434753418
amortized time for sample size  135 is:  0.0001233244295473452
preprocessing time for sampling: 0.04488706588745117
amortized time for sample size  140 is:  0.00012330526965005057
preprocessing time for sampling: 0.04484915733337402
amortized time for sample size  145 is:  0.00012322762916828025
preprocessing time for sampling: 0.044862985610961914
amortized time for sample size  150 is:  0.00012351442972819012
preprocessing time for sampling: 0.04482316970825195
amortized time for sample size  155 is:  0.0001228662767717915
preprocessing time for sampling: 0.04488492012023926
amortized time for sample size  160 is:  0.00012320363521575928
preprocessing time for sampling: 0.044915199279785156
amortized time for sample size  165 is:  0.00012375146692449396
preprocessing time for sampling: 0.044975996017456055
amortized time for sample size  170 is:  0.0001233509849099552
preprocessing time for sampling: 0.04488706588745117
amortized time for sample size  175 is:  0.00012335075650896345
preprocessing time for sampling: 0.044877052307128906
amortized time for sample size  180 is:  0.00012337240907880993
preprocessing time for sampling: 0.04484724998474121
amortized time for sample size  185 is:  0.00012305719788010055
preprocessing time for sampling: 0.04492497444152832
amortized time for sample size  190 is:  0.0001234346816414281
preprocessing time for sampling: 0.04486894607543945
amortized time for sample size  195 is:  0.00012326868986472107
preprocessing time for sampling: 0.04485797882080078
amortized time for sample size  200 is:  0.00012331796884536744
preprocessing time for sampling: 0.04484701156616211
amortized time for sample size  205 is:  0.00012315203503864567
preprocessing time for sampling: 0.045152902603149414
amortized time for sample size  210 is:  0.00012311466534932453
preprocessing time for sampling: 0.044806718826293945
amortized time for sample size  215 is:  0.00012322911550832348
preprocessing time for sampling: 0.04496169090270996
amortized time for sample size  220 is:  0.00012366552786393598
preprocessing time for sampling: 0.044866085052490234
amortized time for sample size  225 is:  0.00012390419642130537
preprocessing time for sampling: 0.04567408561706543
amortized time for sample size  230 is:  0.0001238768411719281
preprocessing time for sampling: 0.04489493370056152
amortized time for sample size  235 is:  0.000123053621738515
preprocessing time for sampling: 0.04483199119567871
amortized time for sample size  240 is:  0.00012293491760889688
preprocessing time for sampling: 0.04495596885681152
amortized time for sample size  245 is:  0.0001228585437852509
preprocessing time for sampling: 0.0448918342590332
amortized time for sample size  250 is:  0.00012308758735656738
*** results for plotting, beta= 0.6 

mean_list= [np.float64(0.76), np.float64(0.7499999999999999), np.float64(0.8700000000000001), np.float64(0.9200000000000002), np.float64(0.9399999999999998), np.float64(0.9), np.float64(0.9200000000000002), np.float64(0.95), np.float64(0.99), np.float64(0.99), np.float64(1.0), np.float64(0.9700000000000001), np.float64(0.9800000000000001), np.float64(0.9800000000000001), np.float64(1.0), np.float64(1.0), np.float64(0.99), np.float64(1.0), np.float64(0.9800000000000001), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(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(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)]
std_list= [np.float64(0.1562049935181331), np.float64(0.14317821063276354), np.float64(0.11000000000000001), np.float64(0.059999999999999984), np.float64(0.09165151389911681), np.float64(0.1), np.float64(0.0748331477354788), np.float64(0.04999999999999999), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.04582575694955839), np.float64(0.039999999999999994), np.float64(0.039999999999999994), np.float64(0.0), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.039999999999999994), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.029999999999999992), 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(0.0), 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)]
beta: 0.8
preprocessing time for sampling: 0.04482579231262207
amortized time for sample size  5 is:  0.00012294626235961914
preprocessing time for sampling: 0.04489493370056152
amortized time for sample size  10 is:  0.00012281680107116696
preprocessing time for sampling: 0.04483294486999512
amortized time for sample size  15 is:  0.0001228623390197754
preprocessing time for sampling: 0.04484820365905762
amortized time for sample size  20 is:  0.0001229053735733032
preprocessing time for sampling: 0.04480886459350586
amortized time for sample size  25 is:  0.00012281894683837893
preprocessing time for sampling: 0.044821977615356445
amortized time for sample size  30 is:  0.00012279899915059405
preprocessing time for sampling: 0.04482316970825195
amortized time for sample size  35 is:  0.00012271247591291154
preprocessing time for sampling: 0.04484987258911133
amortized time for sample size  40 is:  0.00012269192934036255
preprocessing time for sampling: 0.04483318328857422
amortized time for sample size  45 is:  0.00012274222903781466
preprocessing time for sampling: 0.04482388496398926
amortized time for sample size  50 is:  0.0001226518154144287
preprocessing time for sampling: 0.0448451042175293
amortized time for sample size  55 is:  0.0001226846521550959
preprocessing time for sampling: 0.04471993446350098
amortized time for sample size  60 is:  0.00012289675076802573
preprocessing time for sampling: 0.04449200630187988
amortized time for sample size  65 is:  0.0001229864267202524
preprocessing time for sampling: 0.04489421844482422
amortized time for sample size  70 is:  0.00012449410983494347
preprocessing time for sampling: 0.04574179649353027
amortized time for sample size  75 is:  0.00012402989069620768
preprocessing time for sampling: 0.04488682746887207
amortized time for sample size  80 is:  0.00012305259704589844
preprocessing time for sampling: 0.04486393928527832
amortized time for sample size  85 is:  0.00012301327200496897
preprocessing time for sampling: 0.04486227035522461
amortized time for sample size  90 is:  0.00012300803926255967
preprocessing time for sampling: 0.04495716094970703
amortized time for sample size  95 is:  0.0001234366768284848
preprocessing time for sampling: 0.04485011100769043
amortized time for sample size  100 is:  0.00012344191074371337
preprocessing time for sampling: 0.04492473602294922
amortized time for sample size  105 is:  0.0001239043417431059
preprocessing time for sampling: 0.04484391212463379
amortized time for sample size  110 is:  0.00012433364174582742
preprocessing time for sampling: 0.04493594169616699
amortized time for sample size  115 is:  0.00012444210052490234
preprocessing time for sampling: 0.04485511779785156
amortized time for sample size  120 is:  0.00012335179249445597
preprocessing time for sampling: 0.04488968849182129
amortized time for sample size  125 is:  0.0001234524917602539
preprocessing time for sampling: 0.044838905334472656
amortized time for sample size  130 is:  0.0001234587339254526
preprocessing time for sampling: 0.0448911190032959
amortized time for sample size  135 is:  0.00012361183872929325
preprocessing time for sampling: 0.044875144958496094
amortized time for sample size  140 is:  0.0001236177853175572
preprocessing time for sampling: 0.044899940490722656
amortized time for sample size  145 is:  0.00012354503828903725
preprocessing time for sampling: 0.04502296447753906
amortized time for sample size  150 is:  0.0001252848943074544
preprocessing time for sampling: 0.0458369255065918
amortized time for sample size  155 is:  0.00012382147389073525
preprocessing time for sampling: 0.044914960861206055
amortized time for sample size  160 is:  0.00012435351312160492
preprocessing time for sampling: 0.04507184028625488
amortized time for sample size  165 is:  0.0001257220326047955
preprocessing time for sampling: 0.04498791694641113
amortized time for sample size  170 is:  0.00012558808046228746
preprocessing time for sampling: 0.04535412788391113
amortized time for sample size  175 is:  0.00012457477024623327
preprocessing time for sampling: 0.04485297203063965
amortized time for sample size  180 is:  0.00012471552689870198
preprocessing time for sampling: 0.04574108123779297
amortized time for sample size  185 is:  0.000123402028470426
preprocessing time for sampling: 0.04487919807434082
amortized time for sample size  190 is:  0.0001230708548897191
preprocessing time for sampling: 0.04482674598693848
amortized time for sample size  195 is:  0.00012290021700736803
preprocessing time for sampling: 0.044795989990234375
amortized time for sample size  200 is:  0.0001232778191566467
preprocessing time for sampling: 0.044821977615356445
amortized time for sample size  205 is:  0.00012285637274021057
preprocessing time for sampling: 0.04481387138366699
amortized time for sample size  210 is:  0.0001229502246493385
preprocessing time for sampling: 0.044786930084228516
amortized time for sample size  215 is:  0.0001229527495628179
preprocessing time for sampling: 0.044793128967285156
amortized time for sample size  220 is:  0.00012295526807958428
preprocessing time for sampling: 0.044892311096191406
amortized time for sample size  225 is:  0.0001228863716125488
preprocessing time for sampling: 0.044877052307128906
amortized time for sample size  230 is:  0.00012401082204735795
preprocessing time for sampling: 0.04491782188415527
amortized time for sample size  235 is:  0.00012311279012801798
preprocessing time for sampling: 0.04488492012023926
amortized time for sample size  240 is:  0.0001242806613445282
preprocessing time for sampling: 0.04672574996948242
amortized time for sample size  245 is:  0.00012591284148547114
preprocessing time for sampling: 0.04487299919128418
amortized time for sample size  250 is:  0.0001231753158569336
*** results for plotting, beta= 0.8 

mean_list= [np.float64(0.8400000000000001), np.float64(0.93), np.float64(0.9199999999999999), np.float64(0.95), np.float64(0.97), np.float64(0.9800000000000001), np.float64(1.0), np.float64(0.99), np.float64(0.9700000000000001), np.float64(0.99), np.float64(0.99), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(0.99), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), 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(0.06403124237432847), np.float64(0.059999999999999984), np.float64(0.06708203932499368), np.float64(0.04582575694955839), np.float64(0.039999999999999994), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.06403124237432847), np.float64(0.029999999999999992), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0)]
beta: 1
preprocessing time for sampling: 0.05132484436035156
amortized time for sample size  5 is:  0.00013223695755004884
preprocessing time for sampling: 0.051342010498046875
amortized time for sample size  10 is:  0.00013238978385925293
preprocessing time for sampling: 0.05067014694213867
amortized time for sample size  15 is:  0.00013124243418375652
preprocessing time for sampling: 0.05051922798156738
amortized time for sample size  20 is:  0.0001312086582183838
preprocessing time for sampling: 0.05037522315979004
amortized time for sample size  25 is:  0.0001311562538146973
preprocessing time for sampling: 0.05158591270446777
amortized time for sample size  30 is:  0.0001308290163675944
preprocessing time for sampling: 0.05046200752258301
amortized time for sample size  35 is:  0.00013126305171421598
preprocessing time for sampling: 0.05024576187133789
amortized time for sample size  40 is:  0.0001313645839691162
preprocessing time for sampling: 0.050466060638427734
amortized time for sample size  45 is:  0.00013124942779541013
preprocessing time for sampling: 0.050477027893066406
amortized time for sample size  50 is:  0.00013113832473754883
preprocessing time for sampling: 0.05028700828552246
amortized time for sample size  55 is:  0.00013118397105823867
preprocessing time for sampling: 0.05049276351928711
amortized time for sample size  60 is:  0.00013112080097198487
preprocessing time for sampling: 0.05050373077392578
amortized time for sample size  65 is:  0.00013279460026667669
preprocessing time for sampling: 0.050351858139038086
amortized time for sample size  70 is:  0.00013148229462759835
preprocessing time for sampling: 0.05051088333129883
amortized time for sample size  75 is:  0.00013134358723958334
preprocessing time for sampling: 0.05050492286682129
amortized time for sample size  80 is:  0.0001315417289733887
preprocessing time for sampling: 0.05028796195983887
amortized time for sample size  85 is:  0.0001314081865198472
preprocessing time for sampling: 0.050522804260253906
amortized time for sample size  90 is:  0.0001314562956492106
preprocessing time for sampling: 0.051412105560302734
amortized time for sample size  95 is:  0.00013205297369706006
preprocessing time for sampling: 0.05125093460083008
amortized time for sample size  100 is:  0.00013213253021240233
preprocessing time for sampling: 0.0513768196105957
amortized time for sample size  105 is:  0.0001318469728742327
preprocessing time for sampling: 0.051509857177734375
amortized time for sample size  110 is:  0.000132081075148149
preprocessing time for sampling: 0.05124521255493164
amortized time for sample size  115 is:  0.0001321793431821077
preprocessing time for sampling: 0.05140876770019531
amortized time for sample size  120 is:  0.0001322280764579773
preprocessing time for sampling: 0.0514218807220459
amortized time for sample size  125 is:  0.0001314811897277832
preprocessing time for sampling: 0.05034184455871582
amortized time for sample size  130 is:  0.00013144810383136456
preprocessing time for sampling: 0.05060100555419922
amortized time for sample size  135 is:  0.0001314547856648763
preprocessing time for sampling: 0.05141592025756836
amortized time for sample size  140 is:  0.00013219002314976283
preprocessing time for sampling: 0.051191091537475586
amortized time for sample size  145 is:  0.00013214433604273306
preprocessing time for sampling: 0.05048513412475586
amortized time for sample size  150 is:  0.00013123793601989747
preprocessing time for sampling: 0.05127286911010742
amortized time for sample size  155 is:  0.00013180808098085464
preprocessing time for sampling: 0.05037188529968262
amortized time for sample size  160 is:  0.00013164979219436643
preprocessing time for sampling: 0.05048179626464844
amortized time for sample size  165 is:  0.00013260394876653497
preprocessing time for sampling: 0.05078601837158203
amortized time for sample size  170 is:  0.00013433676607468552
preprocessing time for sampling: 0.05112600326538086
amortized time for sample size  175 is:  0.00013463133403233122
preprocessing time for sampling: 0.05129814147949219
amortized time for sample size  180 is:  0.00013202777173784044
preprocessing time for sampling: 0.05091404914855957
amortized time for sample size  185 is:  0.0001312080331750818
preprocessing time for sampling: 0.05035901069641113
amortized time for sample size  190 is:  0.00013231853434914038
preprocessing time for sampling: 0.05054736137390137
amortized time for sample size  195 is:  0.00013280307329618013
preprocessing time for sampling: 0.05109810829162598
amortized time for sample size  200 is:  0.00013311109542846677
preprocessing time for sampling: 0.05025219917297363
amortized time for sample size  205 is:  0.00013370719770105873
preprocessing time for sampling: 0.05051994323730469
amortized time for sample size  210 is:  0.00013302640687851678
preprocessing time for sampling: 0.051712989807128906
amortized time for sample size  215 is:  0.00013287665123163267
preprocessing time for sampling: 0.05089306831359863
amortized time for sample size  220 is:  0.00013378770784898238
preprocessing time for sampling: 0.05160999298095703
amortized time for sample size  225 is:  0.000132635498046875
preprocessing time for sampling: 0.05153703689575195
amortized time for sample size  230 is:  0.00013243529070978578
preprocessing time for sampling: 0.051483869552612305
amortized time for sample size  235 is:  0.00013302042129191945
preprocessing time for sampling: 0.051470279693603516
amortized time for sample size  240 is:  0.0001330345670382182
preprocessing time for sampling: 0.053420066833496094
amortized time for sample size  245 is:  0.00013261603335944976
preprocessing time for sampling: 0.0511469841003418
amortized time for sample size  250 is:  0.0001326777076721191
*** results for plotting, beta= 1 

mean_list= [np.float64(0.8699999999999999), np.float64(0.9800000000000001), np.float64(0.99), np.float64(0.97), np.float64(0.99), np.float64(0.9800000000000001), 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)]
std_list= [np.float64(0.14177446878757824), np.float64(0.039999999999999994), np.float64(0.029999999999999992), np.float64(0.04582575694955839), np.float64(0.029999999999999992), np.float64(0.039999999999999994), 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)]
beta: 1.2
preprocessing time for sampling: 0.04559683799743652
amortized time for sample size  5 is:  0.00012334537506103517
preprocessing time for sampling: 0.04485297203063965
amortized time for sample size  10 is:  0.0001229872703552246
preprocessing time for sampling: 0.044805049896240234
amortized time for sample size  15 is:  0.00012292766571044922
preprocessing time for sampling: 0.044838905334472656
amortized time for sample size  20 is:  0.0001230957508087158
preprocessing time for sampling: 0.04445481300354004
amortized time for sample size  25 is:  0.00012327175140380858
preprocessing time for sampling: 0.04451107978820801
amortized time for sample size  30 is:  0.00012292925516764323
preprocessing time for sampling: 0.04494619369506836
amortized time for sample size  35 is:  0.00012300661631992887
preprocessing time for sampling: 0.04495716094970703
amortized time for sample size  40 is:  0.0001230277419090271
preprocessing time for sampling: 0.04483985900878906
amortized time for sample size  45 is:  0.00012307739257812498
preprocessing time for sampling: 0.04519510269165039
amortized time for sample size  50 is:  0.0001260791778564453
preprocessing time for sampling: 0.04539322853088379
amortized time for sample size  55 is:  0.0001257866079157049
preprocessing time for sampling: 0.051117897033691406
amortized time for sample size  60 is:  0.00012420721848805747
preprocessing time for sampling: 0.04467892646789551
amortized time for sample size  65 is:  0.00012501368155846227
preprocessing time for sampling: 0.04500317573547363
amortized time for sample size  70 is:  0.00012430555479867118
preprocessing time for sampling: 0.04487872123718262
amortized time for sample size  75 is:  0.0001237157185872396
preprocessing time for sampling: 0.045545101165771484
amortized time for sample size  80 is:  0.00012553298473358155
preprocessing time for sampling: 0.04465222358703613
amortized time for sample size  85 is:  0.00012468783995684454
preprocessing time for sampling: 0.04523801803588867
amortized time for sample size  90 is:  0.0001251398457421197
preprocessing time for sampling: 0.04563784599304199
amortized time for sample size  95 is:  0.00012525515807302372
preprocessing time for sampling: 0.045320987701416016
amortized time for sample size  100 is:  0.00012766602039337158
preprocessing time for sampling: 0.045212745666503906
amortized time for sample size  105 is:  0.00012542645136515298
preprocessing time for sampling: 0.04522895812988281
amortized time for sample size  110 is:  0.00012636910785328258
preprocessing time for sampling: 0.04482769966125488
amortized time for sample size  115 is:  0.00012474764948305878
preprocessing time for sampling: 0.04532599449157715
amortized time for sample size  120 is:  0.0001256213585535685
preprocessing time for sampling: 0.04574918746948242
amortized time for sample size  125 is:  0.0001255950164794922
preprocessing time for sampling: 0.044975996017456055
amortized time for sample size  130 is:  0.00012489881882300744
preprocessing time for sampling: 0.04515576362609863
amortized time for sample size  135 is:  0.00012466292911105686
preprocessing time for sampling: 0.045213937759399414
amortized time for sample size  140 is:  0.00012469090734209333
preprocessing time for sampling: 0.04479098320007324
amortized time for sample size  145 is:  0.0001278205082334321
preprocessing time for sampling: 0.04493594169616699
amortized time for sample size  150 is:  0.00012598055203755698
preprocessing time for sampling: 0.04638314247131348
amortized time for sample size  155 is:  0.00012751779248637538
preprocessing time for sampling: 0.04493999481201172
amortized time for sample size  160 is:  0.00012494407594203948
preprocessing time for sampling: 0.044870853424072266
amortized time for sample size  165 is:  0.00012371305985884232
preprocessing time for sampling: 0.044945716857910156
amortized time for sample size  170 is:  0.00012784096773932964
preprocessing time for sampling: 0.04539608955383301
amortized time for sample size  175 is:  0.0001264864649091448
preprocessing time for sampling: 0.045371055603027344
amortized time for sample size  180 is:  0.00012537916501363118
preprocessing time for sampling: 0.04570603370666504
amortized time for sample size  185 is:  0.0001263604292998443
preprocessing time for sampling: 0.04600214958190918
amortized time for sample size  190 is:  0.00012653872841282893
preprocessing time for sampling: 0.0452420711517334
amortized time for sample size  195 is:  0.00012437709172566732
preprocessing time for sampling: 0.0451807975769043
amortized time for sample size  200 is:  0.0001249405384063721
preprocessing time for sampling: 0.045159101486206055
amortized time for sample size  205 is:  0.0001252263580880514
preprocessing time for sampling: 0.046628713607788086
amortized time for sample size  210 is:  0.0001260398342495873
preprocessing time for sampling: 0.04543018341064453
amortized time for sample size  215 is:  0.0001250702281330907
preprocessing time for sampling: 0.045446157455444336
amortized time for sample size  220 is:  0.0001260264570062811
preprocessing time for sampling: 0.04600882530212402
amortized time for sample size  225 is:  0.00012612587610880534
preprocessing time for sampling: 0.04572010040283203
amortized time for sample size  230 is:  0.00012697510097337808
preprocessing time for sampling: 0.047338008880615234
amortized time for sample size  235 is:  0.00012776022769035177
preprocessing time for sampling: 0.04503488540649414
amortized time for sample size  240 is:  0.00012588724493980407
preprocessing time for sampling: 0.045706748962402344
amortized time for sample size  245 is:  0.00012577244700217734
preprocessing time for sampling: 0.04575204849243164
amortized time for sample size  250 is:  0.00012491196632385254
*** results for plotting, beta= 1.2 

mean_list= [np.float64(0.9299999999999999), np.float64(0.97), np.float64(0.99), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(0.99), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0), np.float64(1.0)]
std_list= [np.float64(0.09000000000000001), np.float64(0.045825756949558386), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.029999999999999992), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0), np.float64(0.0)]
