Pocock-type sequential boundaries for binary outcomes (version 1.1)
          (c) Bahjat Qaqish (2004)

Defintions:
  K     = the maximum planned sample size
  THETA = the event probability
  PHI   = the desired probability of early stopping
  ALPHA = the pointwsie stopping probability (computed)


This file contains a list of boundaries for:
  K     = 2, 3, ..., 40
  THETA = 0.1, 0.2, 0.3
  PHI   = 0.05


------------------------------------------------------
K     = 2
THETA = 0.1
PHI   = 0.05
pr(Hitting the upper boundary) = 0.01
ALPHA = 0.055

The upper boundary b_1, ..., b_K:
2
2
------------------------------------------------------
K     = 2
THETA = 0.2
PHI   = 0.05
pr(Hitting the upper boundary) = 0.04
ALPHA = 0.12

The upper boundary b_1, ..., b_K:
2
2
------------------------------------------------------
K     = 2
THETA = 0.3
PHI   = 0.05
pr(Hitting the upper boundary) = 0
ALPHA = 0

The upper boundary b_1, ..., b_K:
2
3
------------------------------------------------------
K     = 3
THETA = 0.1
PHI   = 0.05
pr(Hitting the upper boundary) = 0.028
ALPHA = 0.064

The upper boundary b_1, ..., b_K:
2
2
2
------------------------------------------------------
K     = 3
THETA = 0.2
PHI   = 0.05
pr(Hitting the upper boundary) = 0.04
ALPHA = 0.072

The upper boundary b_1, ..., b_K:
2
2
3
------------------------------------------------------
K     = 3
THETA = 0.3
PHI   = 0.05
pr(Hitting the upper boundary) = 0.027
ALPHA = 0.0585

The upper boundary b_1, ..., b_K:
2
3
3
------------------------------------------------------
K     = 4
THETA = 0.1
PHI   = 0.05
pr(Hitting the upper boundary) = 0.028
ALPHA = 0.04015

The upper boundary b_1, ..., b_K:
2
2
2
3
------------------------------------------------------
K     = 4
THETA = 0.2
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0272
ALPHA = 0.0336

The upper boundary b_1, ..., b_K:
2
3
3
3
------------------------------------------------------
K     = 4
THETA = 0.3
PHI   = 0.05
pr(Hitting the upper boundary) = 0.027
ALPHA = 0.05535

The upper boundary b_1, ..., b_K:
2
3
3
4
------------------------------------------------------
K     = 5
THETA = 0.1
PHI   = 0.05
pr(Hitting the upper boundary) = 0.03043
ALPHA = 0.04015

The upper boundary b_1, ..., b_K:
2
2
2
3
3
------------------------------------------------------
K     = 5
THETA = 0.2
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0272
ALPHA = 0.0336

The upper boundary b_1, ..., b_K:
2
3
3
3
4
------------------------------------------------------
K     = 5
THETA = 0.3
PHI   = 0.05
pr(Hitting the upper boundary) = 0.04401
ALPHA = 0.05724

The upper boundary b_1, ..., b_K:
2
3
3
4
4
------------------------------------------------------
K     = 6
THETA = 0.1
PHI   = 0.05
pr(Hitting the upper boundary) = 0.035533
ALPHA = 0.04015

The upper boundary b_1, ..., b_K:
2
2
2
3
3
3
------------------------------------------------------
K     = 6
THETA = 0.2
PHI   = 0.05
pr(Hitting the upper boundary) = 0.033344
ALPHA = 0.0336

The upper boundary b_1, ..., b_K:
2
3
3
3
4
4
------------------------------------------------------
K     = 6
THETA = 0.3
PHI   = 0.05
pr(Hitting the upper boundary) = 0.04401
ALPHA = 0.050625

The upper boundary b_1, ..., b_K:
2
3
3
4
4
5
------------------------------------------------------
K     = 7
THETA = 0.1
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0434062
ALPHA = 0.04015

The upper boundary b_1, ..., b_K:
2
2
2
3
3
3
3
------------------------------------------------------
K     = 7
THETA = 0.2
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0464512
ALPHA = 0.036672

The upper boundary b_1, ..., b_K:
2
3
3
3
4
4
4
------------------------------------------------------
K     = 7
THETA = 0.3
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0463914
ALPHA = 0.0297877

The upper boundary b_1, ..., b_K:
2
3
3
4
5
5
5
------------------------------------------------------
K     = 8
THETA = 0.1
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0434062
ALPHA = 0.0330459

The upper boundary b_1, ..., b_K:
2
2
2
3
3
3
3
4
------------------------------------------------------
K     = 8
THETA = 0.2
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0464512
ALPHA = 0.036672

The upper boundary b_1, ..., b_K:
2
3
3
3
4
4
4
5
------------------------------------------------------
K     = 8
THETA = 0.3
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0463914
ALPHA = 0.0297877

The upper boundary b_1, ..., b_K:
2
3
3
4
5
5
5
6
------------------------------------------------------
K     = 9
THETA = 0.1
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0444691
ALPHA = 0.0330459

The upper boundary b_1, ..., b_K:
2
2
2
3
3
3
3
4
4
------------------------------------------------------
K     = 9
THETA = 0.2
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0421258
ALPHA = 0.030272

The upper boundary b_1, ..., b_K:
2
3
3
3
4
4
5
5
5
------------------------------------------------------
K     = 9
THETA = 0.3
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0471415
ALPHA = 0.0278977

The upper boundary b_1, ..., b_K:
2
3
3
4
5
5
6
6
6
------------------------------------------------------
K     = 10
THETA = 0.1
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0467543
ALPHA = 0.0330459

The upper boundary b_1, ..., b_K:
2
2
2
3
3
3
3
4
4
4
------------------------------------------------------
K     = 10
THETA = 0.2
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0421258
ALPHA = 0.0299967

The upper boundary b_1, ..., b_K:
2
3
3
3
4
4
5
5
5
6
------------------------------------------------------
K     = 10
THETA = 0.3
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0471415
ALPHA = 0.0278977

The upper boundary b_1, ..., b_K:
2
3
3
4
5
5
6
6
6
7
------------------------------------------------------
K     = 11
THETA = 0.1
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0391972
ALPHA = 0.0268458

The upper boundary b_1, ..., b_K:
2
2
3
3
3
3
3
4
4
4
4
------------------------------------------------------
K     = 11
THETA = 0.2
PHI   = 0.05
pr(Hitting the upper boundary) = 0.044202
ALPHA = 0.0299967

The upper boundary b_1, ..., b_K:
2
3
3
3
4
4
5
5
5
6
6
------------------------------------------------------
K     = 11
THETA = 0.3
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0380509
ALPHA = 0.0261474

The upper boundary b_1, ..., b_K:
2
3
4
4
5
5
6
6
6
7
7
------------------------------------------------------
K     = 12
THETA = 0.1
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0446211
ALPHA = 0.0268458

The upper boundary b_1, ..., b_K:
2
2
3
3
3
3
3
4
4
4
4
4
------------------------------------------------------
K     = 12
THETA = 0.2
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0488661
ALPHA = 0.0299967

The upper boundary b_1, ..., b_K:
2
3
3
3
4
4
5
5
5
6
6
6
------------------------------------------------------
K     = 12
THETA = 0.3
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0380509
ALPHA = 0.0261474

The upper boundary b_1, ..., b_K:
2
3
4
4
5
5
6
6
6
7
7
8
------------------------------------------------------
K     = 13
THETA = 0.1
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0446211
ALPHA = 0.0268458

The upper boundary b_1, ..., b_K:
2
2
3
3
3
3
3
4
4
4
4
4
5
------------------------------------------------------
K     = 13
THETA = 0.2
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0488661
ALPHA = 0.0286177

The upper boundary b_1, ..., b_K:
2
3
3
3
4
4
5
5
5
6
6
6
7
------------------------------------------------------
K     = 13
THETA = 0.3
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0420096
ALPHA = 0.0261474

The upper boundary b_1, ..., b_K:
2
3
4
4
5
5
6
6
6
7
7
8
8
------------------------------------------------------
K     = 14
THETA = 0.1
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0453184
ALPHA = 0.0268458

The upper boundary b_1, ..., b_K:
2
2
3
3
3
3
3
4
4
4
4
4
5
5
------------------------------------------------------
K     = 14
THETA = 0.2
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0400319
ALPHA = 0.0233907

The upper boundary b_1, ..., b_K:
2
3
3
4
4
4
5
5
5
6
6
6
7
7
------------------------------------------------------
K     = 14
THETA = 0.3
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0420096
ALPHA = 0.0261474

The upper boundary b_1, ..., b_K:
2
3
4
4
5
5
6
6
6
7
7
8
8
9
------------------------------------------------------
K     = 15
THETA = 0.1
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0468003
ALPHA = 0.0268458

The upper boundary b_1, ..., b_K:
2
2
3
3
3
3
3
4
4
4
4
4
5
5
5
------------------------------------------------------
K     = 15
THETA = 0.2
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0436654
ALPHA = 0.0233907

The upper boundary b_1, ..., b_K:
2
3
3
4
4
4
5
5
5
6
6
6
7
7
7
------------------------------------------------------
K     = 15
THETA = 0.3
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0447166
ALPHA = 0.0261474

The upper boundary b_1, ..., b_K:
2
3
4
4
5
5
6
6
6
7
7
8
8
9
9
------------------------------------------------------
K     = 16
THETA = 0.1
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0491445
ALPHA = 0.0268458

The upper boundary b_1, ..., b_K:
2
2
3
3
3
3
3
4
4
4
4
4
5
5
5
5
------------------------------------------------------
K     = 16
THETA = 0.2
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0496234
ALPHA = 0.0269287

The upper boundary b_1, ..., b_K:
2
3
3
4
4
4
5
5
5
6
6
6
7
7
7
7
------------------------------------------------------
K     = 16
THETA = 0.3
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0447166
ALPHA = 0.0254842

The upper boundary b_1, ..., b_K:
2
3
4
4
5
5
6
6
6
7
7
8
8
9
9
10
------------------------------------------------------
K     = 17
THETA = 0.1
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0474358
ALPHA = 0.0256645

The upper boundary b_1, ..., b_K:
2
2
3
3
3
3
4
4
4
4
4
4
5
5
5
5
5
------------------------------------------------------
K     = 17
THETA = 0.2
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0496234
ALPHA = 0.0269287

The upper boundary b_1, ..., b_K:
2
3
3
4
4
4
5
5
5
6
6
6
7
7
7
7
8
------------------------------------------------------
K     = 17
THETA = 0.3
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0466268
ALPHA = 0.0254842

The upper boundary b_1, ..., b_K:
2
3
4
4
5
5
6
6
6
7
7
8
8
9
9
10
10
------------------------------------------------------
K     = 18
THETA = 0.1
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0474358
ALPHA = 0.0256645

The upper boundary b_1, ..., b_K:
2
2
3
3
3
3
4
4
4
4
4
4
5
5
5
5
5
6
------------------------------------------------------
K     = 18
THETA = 0.2
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0475206
ALPHA = 0.0231194

The upper boundary b_1, ..., b_K:
2
3
3
4
4
4
5
5
5
6
6
6
7
7
7
8
8
8
------------------------------------------------------
K     = 18
THETA = 0.3
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0464311
ALPHA = 0.023457

The upper boundary b_1, ..., b_K:
2
3
4
4
5
5
6
6
7
7
7
8
8
9
9
10
10
10
------------------------------------------------------
K     = 19
THETA = 0.1
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0478793
ALPHA = 0.0256645

The upper boundary b_1, ..., b_K:
2
2
3
3
3
3
4
4
4
4
4
4
5
5
5
5
5
6
6
------------------------------------------------------
K     = 19
THETA = 0.2
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0475206
ALPHA = 0.0214299

The upper boundary b_1, ..., b_K:
2
3
3
4
4
4
5
5
5
6
6
6
7
7
7
8
8
8
9
------------------------------------------------------
K     = 19
THETA = 0.3
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0464311
ALPHA = 0.023457

The upper boundary b_1, ..., b_K:
2
3
4
4
5
5
6
6
7
7
7
8
8
9
9
10
10
10
11
------------------------------------------------------
K     = 20
THETA = 0.1
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0488262
ALPHA = 0.0256645

The upper boundary b_1, ..., b_K:
2
2
3
3
3
3
4
4
4
4
4
4
5
5
5
5
5
6
6
6
------------------------------------------------------
K     = 20
THETA = 0.2
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0484005
ALPHA = 0.0214299

The upper boundary b_1, ..., b_K:
2
3
3
4
4
4
5
5
5
6
6
6
7
7
7
8
8
8
9
9
------------------------------------------------------
K     = 20
THETA = 0.3
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0489222
ALPHA = 0.023457

The upper boundary b_1, ..., b_K:
2
3
4
4
5
5
6
6
7
7
7
8
8
9
9
10
10
10
11
11
------------------------------------------------------
K     = 21
THETA = 0.1
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0469602
ALPHA = 0.0238908

The upper boundary b_1, ..., b_K:
2
2
3
3
3
3
4
4
4
4
4
5
5
5
5
5
5
6
6
6
6
------------------------------------------------------
K     = 21
THETA = 0.2
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0474322
ALPHA = 0.0194934

The upper boundary b_1, ..., b_K:
2
3
3
4
4
4
5
5
6
6
6
6
7
7
7
8
8
8
9
9
9
------------------------------------------------------
K     = 21
THETA = 0.3
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0489222
ALPHA = 0.023457

The upper boundary b_1, ..., b_K:
2
3
4
4
5
5
6
6
7
7
7
8
8
9
9
10
10
10
11
11
12
------------------------------------------------------
K     = 22
THETA = 0.1
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0491822
ALPHA = 0.0238908

The upper boundary b_1, ..., b_K:
2
2
3
3
3
3
4
4
4
4
4
5
5
5
5
5
5
6
6
6
6
6
------------------------------------------------------
K     = 22
THETA = 0.2
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0474322
ALPHA = 0.0194934

The upper boundary b_1, ..., b_K:
2
3
3
4
4
4
5
5
6
6
6
6
7
7
7
8
8
8
9
9
9
10
------------------------------------------------------
K     = 22
THETA = 0.3
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0472996
ALPHA = 0.0212936

The upper boundary b_1, ..., b_K:
2
3
4
4
5
5
6
6
7
7
8
8
8
9
9
10
10
10
11
11
12
12
------------------------------------------------------
K     = 23
THETA = 0.1
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0491822
ALPHA = 0.022376

The upper boundary b_1, ..., b_K:
2
2
3
3
3
3
4
4
4
4
4
5
5
5
5
5
5
6
6
6
6
6
7
------------------------------------------------------
K     = 23
THETA = 0.2
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0481067
ALPHA = 0.0194934

The upper boundary b_1, ..., b_K:
2
3
3
4
4
4
5
5
6
6
6
6
7
7
7
8
8
8
9
9
9
10
10
------------------------------------------------------
K     = 23
THETA = 0.3
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0472996
ALPHA = 0.021208

The upper boundary b_1, ..., b_K:
2
3
4
4
5
5
6
6
7
7
8
8
8
9
9
10
10
10
11
11
12
12
13
------------------------------------------------------
K     = 24
THETA = 0.1
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0494715
ALPHA = 0.022376

The upper boundary b_1, ..., b_K:
2
2
3
3
3
3
4
4
4
4
4
5
5
5
5
5
5
6
6
6
6
6
7
7
------------------------------------------------------
K     = 24
THETA = 0.2
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0496277
ALPHA = 0.0194934

The upper boundary b_1, ..., b_K:
2
3
3
4
4
4
5
5
6
6
6
6
7
7
7
8
8
8
9
9
9
10
10
10
------------------------------------------------------
K     = 24
THETA = 0.3
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0484761
ALPHA = 0.021208

The upper boundary b_1, ..., b_K:
2
3
4
4
5
5
6
6
7
7
8
8
8
9
9
10
10
10
11
11
12
12
13
13
------------------------------------------------------
K     = 25
THETA = 0.1
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0478958
ALPHA = 0.0203395

The upper boundary b_1, ..., b_K:
2
2
3
3
3
3
4
4
4
4
4
5
5
5
5
5
6
6
6
6
6
6
7
7
7
------------------------------------------------------
K     = 25
THETA = 0.2
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0497334
ALPHA = 0.018732

The upper boundary b_1, ..., b_K:
2
3
3
4
4
4
5
5
6
6
6
7
7
7
7
8
8
8
9
9
9
10
10
10
10
------------------------------------------------------
K     = 25
THETA = 0.3
PHI   = 0.05
pr(Hitting the upper boundary) = 0.049276
ALPHA = 0.0195954

The upper boundary b_1, ..., b_K:
2
3
4
4
5
5
6
6
7
7
8
8
8
9
9
10
10
11
11
11
12
12
13
13
13
------------------------------------------------------
K     = 26
THETA = 0.1
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0489439
ALPHA = 0.0203395

The upper boundary b_1, ..., b_K:
2
2
3
3
3
3
4
4
4
4
4
5
5
5
5
5
6
6
6
6
6
6
7
7
7
7
------------------------------------------------------
K     = 26
THETA = 0.2
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0497334
ALPHA = 0.018732

The upper boundary b_1, ..., b_K:
2
3
3
4
4
4
5
5
6
6
6
7
7
7
7
8
8
8
9
9
9
10
10
10
10
11
------------------------------------------------------
K     = 26
THETA = 0.3
PHI   = 0.05
pr(Hitting the upper boundary) = 0.049276
ALPHA = 0.0195954

The upper boundary b_1, ..., b_K:
2
3
4
4
5
5
6
6
7
7
8
8
8
9
9
10
10
11
11
11
12
12
13
13
13
14
------------------------------------------------------
K     = 27
THETA = 0.1
PHI   = 0.05
pr(Hitting the upper boundary) = 0.048104
ALPHA = 0.0183754

The upper boundary b_1, ..., b_K:
2
2
3
3
3
3
4
4
4
4
5
5
5
5
5
5
6
6
6
6
6
6
7
7
7
7
7
------------------------------------------------------
K     = 27
THETA = 0.2
PHI   = 0.05
pr(Hitting the upper boundary) = 0.048598
ALPHA = 0.0176953

The upper boundary b_1, ..., b_K:
2
3
3
4
4
4
5
5
6
6
6
7
7
7
8
8
8
8
9
9
9
10
10
10
10
11
11
------------------------------------------------------
K     = 27
THETA = 0.3
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0485545
ALPHA = 0.0178463

The upper boundary b_1, ..., b_K:
2
3
4
4
5
5
6
6
7
7
8
8
9
9
9
10
10
11
11
11
12
12
13
13
13
14
14
------------------------------------------------------
K     = 28
THETA = 0.1
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0487135
ALPHA = 0.0180613

The upper boundary b_1, ..., b_K:
2
2
3
3
3
3
4
4
4
4
5
5
5
5
5
5
6
6
6
6
6
7
7
7
7
7
7
7
------------------------------------------------------
K     = 28
THETA = 0.2
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0489028
ALPHA = 0.0171459

The upper boundary b_1, ..., b_K:
2
3
3
4
4
4
5
5
6
6
6
7
7
7
8
8
8
8
9
9
9
10
10
10
11
11
11
11
------------------------------------------------------
K     = 28
THETA = 0.3
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0485545
ALPHA = 0.0178463

The upper boundary b_1, ..., b_K:
2
3
4
4
5
5
6
6
7
7
8
8
9
9
9
10
10
11
11
11
12
12
13
13
13
14
14
15
------------------------------------------------------
K     = 29
THETA = 0.1
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0487135
ALPHA = 0.0180613

The upper boundary b_1, ..., b_K:
2
2
3
3
3
3
4
4
4
4
5
5
5
5
5
5
6
6
6
6
6
7
7
7
7
7
7
7
8
------------------------------------------------------
K     = 29
THETA = 0.2
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0489028
ALPHA = 0.0171459

The upper boundary b_1, ..., b_K:
2
3
3
4
4
4
5
5
6
6
6
7
7
7
8
8
8
8
9
9
9
10
10
10
11
11
11
11
12
------------------------------------------------------
K     = 29
THETA = 0.3
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0495828
ALPHA = 0.0178463

The upper boundary b_1, ..., b_K:
2
3
4
4
5
5
6
6
7
7
8
8
9
9
9
10
10
11
11
11
12
12
13
13
13
14
14
15
15
------------------------------------------------------
K     = 30
THETA = 0.1
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0489739
ALPHA = 0.0180613

The upper boundary b_1, ..., b_K:
2
2
3
3
3
3
4
4
4
4
5
5
5
5
5
5
6
6
6
6
6
7
7
7
7
7
7
7
8
8
------------------------------------------------------
K     = 30
THETA = 0.2
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0495007
ALPHA = 0.0171459

The upper boundary b_1, ..., b_K:
2
3
3
4
4
4
5
5
6
6
6
7
7
7
8
8
8
8
9
9
9
10
10
10
11
11
11
11
12
12
------------------------------------------------------
K     = 30
THETA = 0.3
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0494063
ALPHA = 0.0170411

The upper boundary b_1, ..., b_K:
2
3
4
4
5
5
6
6
7
7
8
8
9
9
9
10
10
11
11
12
12
12
13
13
14
14
14
15
15
15
------------------------------------------------------
K     = 31
THETA = 0.1
PHI   = 0.05
pr(Hitting the upper boundary) = 0.04952
ALPHA = 0.0180613

The upper boundary b_1, ..., b_K:
2
2
3
3
3
3
4
4
4
4
5
5
5
5
5
5
6
6
6
6
6
7
7
7
7
7
7
7
8
8
8
------------------------------------------------------
K     = 31
THETA = 0.2
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0463336
ALPHA = 0.0166201

The upper boundary b_1, ..., b_K:
2
3
3
4
4
5
5
5
6
6
6
7
7
7
8
8
8
8
9
9
9
10
10
10
11
11
11
11
12
12
12
------------------------------------------------------
K     = 31
THETA = 0.3
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0494063
ALPHA = 0.0170411

The upper boundary b_1, ..., b_K:
2
3
4
4
5
5
6
6
7
7
8
8
9
9
9
10
10
11
11
12
12
12
13
13
14
14
14
15
15
15
16
------------------------------------------------------
K     = 32
THETA = 0.1
PHI   = 0.05
pr(Hitting the upper boundary) = 0.048985
ALPHA = 0.0174553

The upper boundary b_1, ..., b_K:
2
2
3
3
3
3
4
4
4
4
5
5
5
5
5
5
6
6
6
6
6
7
7
7
7
7
7
8
8
8
8
8
------------------------------------------------------
K     = 32
THETA = 0.2
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0484649
ALPHA = 0.0168381

The upper boundary b_1, ..., b_K:
2
3
3
4
4
5
5
5
6
6
6
7
7
7
8
8
8
8
9
9
9
10
10
10
11
11
11
11
12
12
12
12
------------------------------------------------------
K     = 32
THETA = 0.3
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0494177
ALPHA = 0.0160899

The upper boundary b_1, ..., b_K:
2
3
4
4
5
5
6
6
7
7
8
8
9
9
9
10
10
11
11
12
12
12
13
13
14
14
14
15
15
16
16
16
------------------------------------------------------
K     = 33
THETA = 0.1
PHI   = 0.05
pr(Hitting the upper boundary) = 0.048729
ALPHA = 0.016427

The upper boundary b_1, ..., b_K:
2
2
3
3
3
3
4
4
4
4
5
5
5
5
5
6
6
6
6
6
6
7
7
7
7
7
7
8
8
8
8
8
8
------------------------------------------------------
K     = 33
THETA = 0.2
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0484649
ALPHA = 0.0168381

The upper boundary b_1, ..., b_K:
2
3
3
4
4
5
5
5
6
6
6
7
7
7
8
8
8
8
9
9
9
10
10
10
11
11
11
11
12
12
12
12
13
------------------------------------------------------
K     = 33
THETA = 0.3
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0494177
ALPHA = 0.0160899

The upper boundary b_1, ..., b_K:
2
3
4
4
5
5
6
6
7
7
8
8
9
9
9
10
10
11
11
12
12
12
13
13
14
14
14
15
15
16
16
16
17
------------------------------------------------------
K     = 34
THETA = 0.1
PHI   = 0.05
pr(Hitting the upper boundary) = 0.048729
ALPHA = 0.016356

The upper boundary b_1, ..., b_K:
2
2
3
3
3
3
4
4
4
4
5
5
5
5
5
6
6
6
6
6
6
7
7
7
7
7
7
8
8
8
8
8
8
9
------------------------------------------------------
K     = 34
THETA = 0.2
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0490746
ALPHA = 0.0168381

The upper boundary b_1, ..., b_K:
2
3
3
4
4
5
5
5
6
6
6
7
7
7
8
8
8
8
9
9
9
10
10
10
11
11
11
11
12
12
12
12
13
13
------------------------------------------------------
K     = 34
THETA = 0.3
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0487959
ALPHA = 0.0147495

The upper boundary b_1, ..., b_K:
2
3
4
4
5
5
6
6
7
7
8
8
9
9
10
10
10
11
11
12
12
12
13
13
14
14
14
15
15
16
16
16
17
17
------------------------------------------------------
K     = 35
THETA = 0.1
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0489005
ALPHA = 0.016356

The upper boundary b_1, ..., b_K:
2
2
3
3
3
3
4
4
4
4
5
5
5
5
5
6
6
6
6
6
6
7
7
7
7
7
7
8
8
8
8
8
8
9
9
------------------------------------------------------
K     = 35
THETA = 0.2
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0492849
ALPHA = 0.0164982

The upper boundary b_1, ..., b_K:
2
3
3
4
4
5
5
5
6
6
6
7
7
7
8
8
8
8
9
9
9
10
10
10
11
11
11
11
12
12
12
13
13
13
13
------------------------------------------------------
K     = 35
THETA = 0.3
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0487959
ALPHA = 0.0147495

The upper boundary b_1, ..., b_K:
2
3
4
4
5
5
6
6
7
7
8
8
9
9
10
10
10
11
11
12
12
12
13
13
14
14
14
15
15
16
16
16
17
17
18
------------------------------------------------------
K     = 36
THETA = 0.1
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0492641
ALPHA = 0.016356

The upper boundary b_1, ..., b_K:
2
2
3
3
3
3
4
4
4
4
5
5
5
5
5
6
6
6
6
6
6
7
7
7
7
7
7
8
8
8
8
8
8
9
9
9
------------------------------------------------------
K     = 36
THETA = 0.2
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0492849
ALPHA = 0.0164982

The upper boundary b_1, ..., b_K:
2
3
3
4
4
5
5
5
6
6
6
7
7
7
8
8
8
8
9
9
9
10
10
10
11
11
11
11
12
12
12
13
13
13
13
14
------------------------------------------------------
K     = 36
THETA = 0.3
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0494466
ALPHA = 0.0147495

The upper boundary b_1, ..., b_K:
2
3
4
4
5
5
6
6
7
7
8
8
9
9
10
10
10
11
11
12
12
12
13
13
14
14
14
15
15
16
16
16
17
17
18
18
------------------------------------------------------
K     = 37
THETA = 0.1
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0498408
ALPHA = 0.016356

The upper boundary b_1, ..., b_K:
2
2
3
3
3
3
4
4
4
4
5
5
5
5
5
6
6
6
6
6
6
7
7
7
7
7
7
8
8
8
8
8
8
9
9
9
9
------------------------------------------------------
K     = 37
THETA = 0.2
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0497442
ALPHA = 0.0164982

The upper boundary b_1, ..., b_K:
2
3
3
4
4
5
5
5
6
6
6
7
7
7
8
8
8
8
9
9
9
10
10
10
11
11
11
11
12
12
12
13
13
13
13
14
14
------------------------------------------------------
K     = 37
THETA = 0.3
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0491643
ALPHA = 0.0139375

The upper boundary b_1, ..., b_K:
2
3
4
4
5
5
6
6
7
7
8
8
9
9
10
10
10
11
11
12
12
13
13
13
14
14
15
15
15
16
16
16
17
17
18
18
18
------------------------------------------------------
K     = 38
THETA = 0.1
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0471144
ALPHA = 0.0152589

The upper boundary b_1, ..., b_K:
2
2
3
3
3
4
4
4
4
4
5
5
5
5
5
6
6
6
6
6
6
7
7
7
7
7
7
8
8
8
8
8
8
9
9
9
9
9
------------------------------------------------------
K     = 38
THETA = 0.2
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0493351
ALPHA = 0.0155715

The upper boundary b_1, ..., b_K:
2
3
3
4
4
5
5
5
6
6
6
7
7
7
8
8
8
9
9
9
9
10
10
10
11
11
11
11
12
12
12
13
13
13
13
14
14
14
------------------------------------------------------
K     = 38
THETA = 0.3
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0491643
ALPHA = 0.0139375

The upper boundary b_1, ..., b_K:
2
3
4
4
5
5
6
6
7
7
8
8
9
9
10
10
10
11
11
12
12
13
13
13
14
14
15
15
15
16
16
16
17
17
18
18
18
19
------------------------------------------------------
K     = 39
THETA = 0.1
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0481967
ALPHA = 0.0152589

The upper boundary b_1, ..., b_K:
2
2
3
3
3
4
4
4
4
4
5
5
5
5
5
6
6
6
6
6
6
7
7
7
7
7
7
8
8
8
8
8
8
9
9
9
9
9
9
------------------------------------------------------
K     = 39
THETA = 0.2
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0493351
ALPHA = 0.0151241

The upper boundary b_1, ..., b_K:
2
3
3
4
4
5
5
5
6
6
6
7
7
7
8
8
8
9
9
9
9
10
10
10
11
11
11
11
12
12
12
13
13
13
13
14
14
14
15
------------------------------------------------------
K     = 39
THETA = 0.3
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0499812
ALPHA = 0.0139375

The upper boundary b_1, ..., b_K:
2
3
4
4
5
5
6
6
7
7
8
8
9
9
10
10
10
11
11
12
12
13
13
13
14
14
15
15
15
16
16
16
17
17
18
18
18
19
19
------------------------------------------------------
K     = 40
THETA = 0.1
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0495586
ALPHA = 0.0156727

The upper boundary b_1, ..., b_K:
2
2
3
3
3
4
4
4
4
4
5
5
5
5
5
6
6
6
6
6
6
7
7
7
7
7
7
8
8
8
8
8
8
9
9
9
9
9
9
9
------------------------------------------------------
K     = 40
THETA = 0.2
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0496594
ALPHA = 0.0151241

The upper boundary b_1, ..., b_K:
2
3
3
4
4
5
5
5
6
6
6
7
7
7
8
8
8
9
9
9
9
10
10
10
11
11
11
11
12
12
12
13
13
13
13
14
14
14
15
15
------------------------------------------------------
K     = 40
THETA = 0.3
PHI   = 0.05
pr(Hitting the upper boundary) = 0.0499812
ALPHA = 0.0139375

The upper boundary b_1, ..., b_K:
2
3
4
4
5
5
6
6
7
7
8
8
9
9
10
10
10
11
11
12
12
13
13
13
14
14
15
15
15
16
16
16
17
17
18
18
18
19
19
20
------------------------------------------------------