RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-17_08:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.52 16.5772 0.516649
2 to 25 15.81 13.2786 0.282657
3 to 26 15.65 14.9735 0.402612
4 to 27 15.76 10.0934 0.100352
5 to 28 15.87 16.9147 0.539838
6 to 29 15.70 21.6088 0.799764
7 to 30 15.93 14.8423 0.393161
8 to 31 15.92 12.1676 0.210117
9 to 32 15.51 18.1593 0.621139
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.539095
Tough bday spacings test for dh-ranFile-2018-06-17_08:31: 4096 birthdays, year=2^32 days
Table of Expected vs. Observed counts:
Duplicates 0 1 2 3 4 5 6 7 8 9 >=10
Expected 9.2 36.6 73.3 97.7 97.7 78.1 52.1 29.8 14.9 6.6 4.1
Observed 6 45 67 102 95 87 44 27 18 6 3
(O-E)^2/E 1.1 1.9 0.5 0.2 0.1 1.0 1.3 0.3 0.7 0.1 0.3
Birthday Spacings: Sum(O-E)^2/E= 7.309, p= 0.304
RESULTS OF GCD FOR dh-ranFile-2018-06-17_08:31
Euclid's algorithm:
p-value, steps to gcd: 0.064273
p-value, dist. of gcd's: 0.239188
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-17_08:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.614 0.747 0.231 0.162 0.672 0.742 0.479 0.861
Bits 8 to 15---> 0.574 0.893 0.488 0.448 0.157 0.221 0.911 0.045
Bits 16 to 23---> 0.736 0.331 0.297 0.636 0.025 0.018 0.827 0.990
Bits 24 to 31---> 0.600 0.206 0.680 0.206 0.047 0.184 0.421 0.286
KS test for the above 32 p values: 0.265
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-17_08:31,
p-values for 5 runs: 0.4772, 0.4714, 0.3887, 0.1394, 0.0089
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-17_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 211 211.4 0.001 0.001
r= 29 5060 5134.0 1.067 1.068
r= 30 23258 23103.0 1.039 2.107
r= 31 11471 11551.5 0.561 2.668
chi-square = 2.668 with df = 3; p-value = 0.554
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-17_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 214 211.4 0.032 0.032
r= 30 5228 5134.0 1.721 1.752
r= 31 23103 23103.0 0.000 1.752
r= 32 11455 11551.5 0.807 2.559
chi-square = 2.559 with df = 3; p-value = 0.535
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-17_08:31
b-rank test for bits 1 to 8, p=0.94289
b-rank test for bits 2 to 9, p=0.09419
b-rank test for bits 3 to 10, p=0.23475
b-rank test for bits 4 to 11, p=0.54976
b-rank test for bits 5 to 12, p=0.34426
b-rank test for bits 6 to 13, p=0.81240
b-rank test for bits 7 to 14, p=0.87731
b-rank test for bits 8 to 15, p=0.21366
b-rank test for bits 9 to 16, p=0.53205
b-rank test for bits 10 to 17, p=0.20597
b-rank test for bits 11 to 18, p=0.76321
b-rank test for bits 12 to 19, p=0.12706
b-rank test for bits 13 to 20, p=0.66226
b-rank test for bits 14 to 21, p=0.85610
b-rank test for bits 15 to 22, p=0.88376
b-rank test for bits 16 to 23, p=0.88809
b-rank test for bits 17 to 24, p=0.34068
b-rank test for bits 18 to 25, p=0.80660
b-rank test for bits 19 to 26, p=0.32850
b-rank test for bits 20 to 27, p=0.18435
b-rank test for bits 21 to 28, p=0.38053
b-rank test for bits 22 to 29, p=0.45404
b-rank test for bits 23 to 30, p=0.62438
b-rank test for bits 24 to 31, p=0.29421
b-rank test for bits 25 to 32, p=0.03669
TEST SUMMARY, 25 tests, each on 100,000 random 6x8 matrices
The above should be 25 uniform [0,1] random variables:
The KS test for those 25 supposed UNI's yields p = 0.940749
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-17_08:31
(20 bits/word, 2097152 words 20 bitstreams. No. missing words
should average 141909.33 with sigma=428.00.)
----------------------------------------------------------------
BITSTREAM test results.
Bitstream No. missing words z-score p-value
1 141422 -1.14 0.127431
2 141795 -0.27 0.394686
3 141719 -0.44 0.328270
4 141582 -0.76 0.222198
5 141557 -0.82 0.205197
6 142137 0.53 0.702616
7 142407 1.16 0.877541
8 141516 -0.92 0.179049
9 141894 -0.04 0.485714
10 142322 0.96 0.832523
11 140867 -2.44 0.007439
12 140867 -2.44 0.007439
13 142496 1.37 0.914770
14 142086 0.41 0.660116
15 142145 0.55 0.709057
16 141662 -0.58 0.281675
17 141774 -0.32 0.375929
18 141423 -1.14 0.127919
19 141666 -0.57 0.284838
20 141795 -0.27 0.394686
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-17_08:31
Bits used No. missing words z-score p-value
23 to 32 141785 -0.4287 0.334062
22 to 31 141823 -0.2977 0.382970
21 to 30 142215 1.0540 0.854066
20 to 29 142275 1.2609 0.896333
19 to 28 142068 0.5471 0.707858
18 to 27 142238 1.1333 0.871465
17 to 26 141676 -0.8046 0.210529
16 to 25 141786 -0.4253 0.335318
15 to 24 141746 -0.5632 0.286647
14 to 23 142306 1.3678 0.914317
13 to 22 142177 0.9230 0.821996
12 to 21 141946 0.1264 0.550312
11 to 20 142367 1.5782 0.942737
10 to 19 141805 -0.3598 0.359514
9 to 18 142213 1.0471 0.852482
8 to 17 141806 -0.3563 0.360804
7 to 16 142056 0.5058 0.693487
6 to 15 141939 0.1023 0.540745
5 to 14 141915 0.0196 0.507800
4 to 13 142455 1.8816 0.970056
3 to 12 142307 1.3713 0.914856
2 to 11 141838 -0.2460 0.402855
1 to 10 141708 -0.6942 0.243765
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-17_08:31
Bits used No. missing words z-score p-value
28 to 32 141459 -1.5265 0.063437
27 to 31 142079 0.5752 0.717406
26 to 30 141586 -1.0960 0.136532
25 to 29 141718 -0.6486 0.258306
24 to 28 141905 -0.0147 0.494145
23 to 27 141795 -0.3876 0.349171
22 to 26 141793 -0.3943 0.346665
21 to 25 141447 -1.5672 0.058532
20 to 24 141535 -1.2689 0.102236
19 to 23 141739 -0.5774 0.281838
18 to 22 142125 0.7311 0.767636
17 to 21 142086 0.5989 0.725374
16 to 20 141915 0.0192 0.507667
15 to 19 142279 1.2531 0.894919
14 to 18 141870 -0.1333 0.446969
13 to 17 141991 0.2768 0.609051
12 to 16 142199 0.9819 0.836933
11 to 15 142148 0.8091 0.790757
10 to 14 141398 -1.7333 0.041519
9 to 13 142457 1.8565 0.968309
8 to 12 141968 0.1989 0.578822
7 to 11 141450 -1.5571 0.059729
6 to 10 142006 0.3277 0.628429
5 to 9 141864 -0.1537 0.438939
4 to 8 141793 -0.3943 0.346665
3 to 7 141886 -0.0791 0.468483
2 to 6 141536 -1.2655 0.102842
1 to 5 141754 -0.5265 0.299256
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-17_08:31
Bits used No. missing words z-score p-value
31 to 32 142193 0.8368 0.798643
30 to 31 142404 1.4592 0.927745
29 to 30 141733 -0.5201 0.301480
28 to 29 141679 -0.6794 0.248430
27 to 28 142290 1.1229 0.869264
26 to 27 141315 -1.7532 0.039785
25 to 26 142208 0.8810 0.810850
24 to 25 142403 1.4563 0.927339
23 to 24 141442 -1.3786 0.084016
22 to 23 142117 0.6126 0.729928
21 to 22 141755 -0.4553 0.324464
20 to 21 142259 1.0315 0.848841
19 to 20 142305 1.1672 0.878429
18 to 19 141852 -0.1691 0.432853
17 to 18 142747 2.4710 0.993263
16 to 17 142080 0.5035 0.692677
15 to 16 141872 -0.1101 0.456158
14 to 15 141766 -0.4228 0.336220
13 to 14 142000 0.2675 0.605444
12 to 13 141509 -1.1809 0.118818
11 to 12 142269 1.0610 0.855649
10 to 11 142093 0.5418 0.706022
9 to 10 142145 0.6952 0.756532
8 to 9 142402 1.4533 0.926930
7 to 8 142197 0.8486 0.801944
6 to 7 141811 -0.2901 0.385886
5 to 6 142007 0.2881 0.613370
4 to 5 142401 1.4504 0.926520
3 to 4 142193 0.8368 0.798643
2 to 3 141782 -0.3756 0.353605
1 to 2 142103 0.5713 0.716101
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-17_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2506.71 0.095 0.537790
Test results for specific bytes for dh-ranFile-2018-06-17_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2474.04 -0.367 0.356783
2 to 9 2296.14 -2.883 0.001970
3 to 10 2426.94 -1.033 0.150762
4 to 11 2497.10 -0.041 0.483640
5 to 12 2533.48 0.474 0.682083
6 to 13 2456.05 -0.622 0.267131
7 to 14 2563.43 0.897 0.815151
8 to 15 2465.36 -0.490 0.312101
9 to 16 2482.38 -0.249 0.401619
10 to 17 2581.64 1.155 0.875872
11 to 18 2387.27 -1.594 0.055446
12 to 19 2380.35 -1.692 0.045312
13 to 20 2530.76 0.435 0.668221
14 to 21 2514.15 0.200 0.579322
15 to 22 2471.18 -0.408 0.341768
16 to 23 2513.87 0.196 0.577742
17 to 24 2516.10 0.228 0.590038
18 to 25 2449.81 -0.710 0.238905
19 to 26 2435.54 -0.912 0.181003
20 to 27 2654.51 2.185 0.985558
21 to 28 2372.44 -1.804 0.035619
22 to 29 2455.65 -0.627 0.265262
23 to 30 2545.20 0.639 0.738644
24 to 31 2527.08 0.383 0.649122
25 to 32 2631.45 1.859 0.968484
CDPARK for dh-ranFile-2018-06-17_08:31: result of 10 tests
(Of 12000 tries, the average no. of successes should be
3523.0 with sigma=21.9)
No. succeses z-score p-value
3510 -0.5936 0.276387
3516 -0.3196 0.374623
3531 0.3653 0.642555
3533 0.4566 0.676028
3503 -0.9132 0.180558
3542 0.8676 0.807188
3545 1.0046 0.842447
3516 -0.3196 0.374623
3519 -0.1826 0.427537
3509 -0.6393 0.261324
Square side=100, avg. no. parked=3522.40 sample std.=13.73
p-value of the KSTEST for those 10 p-values: 0.702425
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-17_08:31
0.3138,0.7035,0.4230,0.7266,0.3254,0.6450,0.3151,0.8497,0.5582,0.7682,
The KS test for those 10 p-values: 0.384749
The 3DSPHERES test for dh-ranFile-2018-06-17_08:31
sample no r^3 equiv. uni.
1 17.673 0.445176
2 64.426 0.883230
3 21.132 0.505589
4 25.689 0.575272
5 56.042 0.845579
6 7.797 0.228872
7 15.461 0.402726
8 50.102 0.811768
9 91.516 0.952667
10 0.462 0.015272
11 12.331 0.337043
12 34.135 0.679491
13 79.684 0.929780
14 74.074 0.915342
15 4.718 0.145522
16 1.258 0.041059
17 8.013 0.234391
18 34.418 0.682495
19 69.686 0.902008
20 45.449 0.780187
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.424950
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-17_08:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -1.6 2.0 0.3 0.4 -0.2
-1.4 -1.0 0.2 1.6 1.6 -1.3
0.4 0.4 2.8 0.4 0.1 -0.9
-0.8 -1.1 -0.0 -0.2 1.2 -0.9
-0.5 -0.9 -0.5 -1.0 0.6 -0.2
-0.9 -0.3 -1.1 0.9 0.1 -0.8
-0.9 -0.1 2.1 -0.1 -0.6 0.0
-0.1
Chi-square with 42 degrees of freedom:43.147168
z-score=0.125166, p-value=0.577970
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-17_08:31
Test no p-value
1 0.070019
2 0.713377
3 0.419536
4 0.078599
5 0.722559
6 0.234975
7 0.421833
8 0.064609
9 0.935913
10 0.273699
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.348877
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-17_08:31:
(for k>=2, the prob. of a run of length k is 2*k/(k+1)!)
Length Expected UpRuns (O-E)^2/E DownRuns (O-E)^2/E
2 66666.67 66649 0.00 66897 0.80
3 25000.00 24975 0.03 24865 0.73
4 6666.67 6651 0.04 6627 0.24
5 1388.89 1433 1.40 1337 1.94
6 238.10 259 1.84 233 0.11
7 34.72 29 0.94 37 0.15
8 4.96 3 0.77 3 0.77
p=0.45871 p=0.42148
Number of rngs required: 687620, p-value: 0.182
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-17_08:31
No. of wins: Observed Expected
98554 98585.9
z-score=-0.142, pvalue=0.44335
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66648 66666.7 0.005 0.005
2 37527 37654.3 0.431 0.436
3 27017 26954.7 0.144 0.580
4 19520 19313.5 2.209 2.788
5 13832 13851.4 0.027 2.816
6 9855 9943.5 0.788 3.604
7 7157 7145.0 0.020 3.624
8 5229 5139.1 1.574 5.198
9 3713 3699.9 0.047 5.244
10 2625 2666.3 0.640 5.884
11 1900 1923.3 0.283 6.167
12 1348 1388.7 1.195 7.362
13 933 1003.7 4.982 12.344
14 710 726.1 0.359 12.703
15 515 525.8 0.223 12.926
16 414 381.2 2.831 15.757
17 286 276.5 0.324 16.081
18 210 200.8 0.419 16.500
19 139 146.0 0.334 16.834
20 115 106.2 0.727 17.560
21 307 287.1 1.377 18.938
Chisq= 18.94 for 20 degrees of freedom, p= 0.47413
SUMMARY of craptest
p-value for no. of wins: 0.443346
p-value for throws/game: 0.474127
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-17_08:31
No. of wins: Observed Expected
98407 98585.9
z-score=-0.800, pvalue=0.21187
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66642 66666.7 0.009 0.009
2 37347 37654.3 2.508 2.517
3 27180 26954.7 1.883 4.400
4 19277 19313.5 0.069 4.469
5 14023 13851.4 2.125 6.594
6 9857 9943.5 0.753 7.347
7 7176 7145.0 0.134 7.482
8 5125 5139.1 0.039 7.520
9 3666 3699.9 0.310 7.830
10 2691 2666.3 0.229 8.059
11 1957 1923.3 0.589 8.649
12 1437 1388.7 1.677 10.326
13 1005 1003.7 0.002 10.327
14 706 726.1 0.559 10.886
15 522 525.8 0.028 10.914
16 382 381.2 0.002 10.916
17 264 276.5 0.569 11.484
18 188 200.8 0.820 12.304
19 149 146.0 0.062 12.366
20 115 106.2 0.727 13.093
21 291 287.1 0.053 13.145
Chisq= 13.15 for 20 degrees of freedom, p= 0.12894
SUMMARY of craptest
p-value for no. of wins: 0.211867
p-value for throws/game: 0.128942
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0020,0.0074,0.0074,0.0089,0.0153,0.0184,0.0251,0.0356,0.0367,0.0398,
0.0411,0.0415,0.0451,0.0453,0.0471,0.0554,0.0585,0.0597,0.0634,0.0643,
0.0646,0.0700,0.0786,0.0840,0.0942,0.1004,0.1022,0.1028,0.1188,0.1271,
0.1274,0.1279,0.1289,0.1365,0.1394,0.1455,0.1508,0.1572,0.1622,0.1790,
0.1806,0.1810,0.1824,0.1837,0.1844,0.2052,0.2060,0.2061,0.2063,0.2101,
0.2105,0.2119,0.2137,0.2207,0.2222,0.2289,0.2313,0.2344,0.2347,0.2350,
0.2389,0.2392,0.2438,0.2484,0.2583,0.2613,0.2648,0.2653,0.2671,0.2737,
0.2764,0.2817,0.2818,0.2827,0.2848,0.2860,0.2866,0.2942,0.2971,0.2993,
0.3015,0.3040,0.3121,0.3138,0.3151,0.3245,0.3254,0.3283,0.3285,0.3306,
0.3341,0.3353,0.3362,0.3370,0.3407,0.3418,0.3443,0.3467,0.3467,0.3489,
0.3492,0.3536,0.3568,0.3595,0.3608,0.3746,0.3746,0.3759,0.3805,0.3830,
0.3847,0.3859,0.3887,0.3932,0.3947,0.3947,0.4016,0.4026,0.4027,0.4029,
0.4195,0.4212,0.4215,0.4218,0.4230,0.4250,0.4275,0.4329,0.4389,0.4433,
0.4452,0.4470,0.4478,0.4540,0.4562,0.4587,0.4685,0.4714,0.4741,0.4772,
0.4790,0.4836,0.4857,0.4883,0.4941,0.5056,0.5077,0.5078,0.5166,0.5321,
0.5352,0.5378,0.5391,0.5398,0.5407,0.5498,0.5503,0.5544,0.5582,0.5743,
0.5753,0.5777,0.5780,0.5788,0.5793,0.5900,0.5997,0.6054,0.6091,0.6134,
0.6135,0.6211,0.6244,0.6284,0.6361,0.6426,0.6450,0.6491,0.6601,0.6623,
0.6682,0.6721,0.6760,0.6795,0.6801,0.6821,0.6825,0.6927,0.6935,0.7024,
0.7026,0.7035,0.7060,0.7079,0.7091,0.7134,0.7161,0.7174,0.7226,0.7254,
0.7266,0.7299,0.7365,0.7386,0.7425,0.7475,0.7565,0.7632,0.7676,0.7682,
0.7802,0.7908,0.7986,0.7986,0.7998,0.8019,0.8066,0.8072,0.8108,0.8118,
0.8124,0.8152,0.8220,0.8270,0.8325,0.8369,0.8424,0.8456,0.8488,0.8497,
0.8525,0.8541,0.8556,0.8561,0.8607,0.8693,0.8715,0.8759,0.8773,0.8775,
0.8784,0.8832,0.8838,0.8881,0.8929,0.8949,0.8963,0.9020,0.9114,0.9143,
0.9148,0.9149,0.9153,0.9265,0.9269,0.9273,0.9277,0.9298,0.9359,0.9407,
0.9427,0.9429,0.9527,0.9683,0.9685,0.9701,0.9856,0.9900,0.9933,
Overall p-value after applying KStest on 269 p-values = 0.563836
In response to requests, we have provided a list of all the p-values
produced by the tests you have chosen for this run. The individual
p-values are supposed to be uniform in [0,1), but they are not necessarily
independent. So even though we have applied a KSTEST to the accumulated
p-values, the result is not necessarily---even if your file contains truly
random bits---uniform in [0,1). But it is probably pretty close, so take
that last p-value with a grain of salt. In particular, there may be some
values so close to 0 or 1 that the tests they came from should be applied
several more times, or new, related tests should be undertaken.