RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-12_13:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.84 11.8088 0.188427
2 to 25 15.71 18.9645 0.669425
3 to 26 15.85 13.0605 0.267875
4 to 27 15.83 16.5777 0.516689
5 to 28 15.84 13.2040 0.277573
6 to 29 15.58 17.5354 0.581297
7 to 30 15.74 20.4404 0.747675
8 to 31 16.01 10.7263 0.129569
9 to 32 15.53 17.0105 0.546343
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.543630
Tough bday spacings test for dh-ranFile-2018-07-12_13:31: 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 8 38 62 109 94 89 45 32 11 8 4
(O-E)^2/E 0.1 0.1 1.7 1.3 0.1 1.5 1.0 0.2 1.0 0.3 0.0
Birthday Spacings: Sum(O-E)^2/E= 7.325, p= 0.306
RESULTS OF GCD FOR dh-ranFile-2018-07-12_13:31
Euclid's algorithm:
p-value, steps to gcd: 0.285716
p-value, dist. of gcd's: 0.552013
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-12_13:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.613 0.896 0.686 0.424 0.002 0.562 0.646 0.204
Bits 8 to 15---> 0.967 0.002 0.210 0.274 0.508 0.895 0.080 0.216
Bits 16 to 23---> 0.461 0.906 0.025 0.374 0.494 0.100 0.921 0.398
Bits 24 to 31---> 0.237 0.099 0.024 0.248 0.413 0.308 0.415 0.589
KS test for the above 32 p values: 0.916
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-12_13:31,
p-values for 5 runs: 0.9289, 0.0623, 0.2762, 0.7145, 0.6656
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-12_13:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 213 211.4 0.012 0.012
r= 29 5100 5134.0 0.225 0.237
r= 30 23115 23103.0 0.006 0.243
r= 31 11572 11551.5 0.036 0.280
chi-square = 0.280 with df = 3; p-value = 0.036
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-12_13:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 221 211.4 0.434 0.434
r= 30 5211 5134.0 1.155 1.589
r= 31 23011 23103.0 0.367 1.956
r= 32 11557 11551.5 0.003 1.958
chi-square = 1.958 with df = 3; p-value = 0.419
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-12_13:31
b-rank test for bits 1 to 8, p=0.98562
b-rank test for bits 2 to 9, p=0.28514
b-rank test for bits 3 to 10, p=0.93638
b-rank test for bits 4 to 11, p=0.15328
b-rank test for bits 5 to 12, p=0.60399
b-rank test for bits 6 to 13, p=0.87637
b-rank test for bits 7 to 14, p=0.23734
b-rank test for bits 8 to 15, p=0.77638
b-rank test for bits 9 to 16, p=0.17395
b-rank test for bits 10 to 17, p=0.55274
b-rank test for bits 11 to 18, p=0.58702
b-rank test for bits 12 to 19, p=0.75540
b-rank test for bits 13 to 20, p=0.58054
b-rank test for bits 14 to 21, p=0.65428
b-rank test for bits 15 to 22, p=0.29532
b-rank test for bits 16 to 23, p=0.13330
b-rank test for bits 17 to 24, p=0.10839
b-rank test for bits 18 to 25, p=0.56145
b-rank test for bits 19 to 26, p=0.82951
b-rank test for bits 20 to 27, p=0.40328
b-rank test for bits 21 to 28, p=0.09125
b-rank test for bits 22 to 29, p=0.30002
b-rank test for bits 23 to 30, p=0.14879
b-rank test for bits 24 to 31, p=0.67541
b-rank test for bits 25 to 32, p=0.70999
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 = 0.921921
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-12_13:31
(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 141908 -0.00 0.498760
2 141745 -0.38 0.350508
3 142179 0.63 0.735676
4 142127 0.51 0.694475
5 142074 0.38 0.649786
6 141452 -1.07 0.142641
7 141709 -0.47 0.319871
8 142391 1.13 0.869790
9 141744 -0.39 0.349643
10 142689 1.82 0.965747
11 142225 0.74 0.769605
12 142083 0.41 0.657545
13 142111 0.47 0.681248
14 142428 1.21 0.887214
15 141892 -0.04 0.483851
16 142094 0.43 0.666937
17 142208 0.70 0.757357
18 142077 0.39 0.652379
19 141720 -0.44 0.329114
20 141453 -1.07 0.143169
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-12_13:31
Bits used No. missing words z-score p-value
23 to 32 141982 0.2506 0.598933
22 to 31 141878 -0.1080 0.456984
21 to 30 141438 -1.6253 0.052052
20 to 29 142088 0.6161 0.731087
19 to 28 141756 -0.5287 0.298498
18 to 27 142002 0.3196 0.625346
17 to 26 141973 0.2196 0.586890
16 to 25 141566 -1.1839 0.118227
15 to 24 141996 0.2989 0.617477
14 to 23 141857 -0.1804 0.428400
13 to 22 142164 0.8782 0.810075
12 to 21 141647 -0.9046 0.182842
11 to 20 141887 -0.0770 0.469312
10 to 19 141809 -0.3460 0.364684
9 to 18 141357 -1.9046 0.028417
8 to 17 142005 0.3299 0.629261
7 to 16 142259 1.2058 0.886045
6 to 15 142110 0.6920 0.755521
5 to 14 142139 0.7920 0.785810
4 to 13 142018 0.3747 0.646067
3 to 12 142018 0.3747 0.646067
2 to 11 142113 0.7023 0.758757
1 to 10 142178 0.9264 0.822894
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-12_13:31
Bits used No. missing words z-score p-value
28 to 32 142032 0.4158 0.661233
27 to 31 142201 0.9887 0.838598
26 to 30 141603 -1.0384 0.149540
25 to 29 141965 0.1887 0.574841
24 to 28 141323 -1.9876 0.023430
23 to 27 141571 -1.1469 0.125715
22 to 26 141704 -0.6960 0.243204
21 to 25 141607 -1.0248 0.152718
20 to 24 142071 0.5480 0.708166
19 to 23 141588 -1.0893 0.138021
18 to 22 141856 -0.1808 0.428270
17 to 21 141807 -0.3469 0.364340
16 to 20 142418 1.7243 0.957674
15 to 19 141892 -0.0587 0.476577
14 to 18 141745 -0.5571 0.288746
13 to 17 142185 0.9345 0.824970
12 to 16 142388 1.6226 0.947664
11 to 15 141788 -0.4113 0.340431
10 to 14 142339 1.4565 0.927374
9 to 13 141935 0.0870 0.534671
8 to 12 142231 1.0904 0.862233
7 to 11 141590 -1.0825 0.139521
6 to 10 141023 -3.0045 0.001330
5 to 9 141590 -1.0825 0.139521
4 to 8 141939 0.1006 0.540057
3 to 7 142581 2.2768 0.988602
2 to 6 142256 1.1752 0.880033
1 to 5 142524 2.0836 0.981403
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-12_13:31
Bits used No. missing words z-score p-value
31 to 32 141476 -1.2783 0.100579
30 to 31 141979 0.2055 0.581416
29 to 30 142091 0.5359 0.703986
28 to 29 142107 0.5831 0.720086
27 to 28 141609 -0.8859 0.187828
26 to 27 142495 1.7276 0.957974
25 to 26 142128 0.6450 0.740551
24 to 25 142272 1.0698 0.857651
23 to 24 141606 -0.8948 0.185453
22 to 23 141217 -2.0423 0.020562
21 to 22 141818 -0.2694 0.393807
20 to 21 141780 -0.3815 0.351415
19 to 20 142162 0.7453 0.771967
18 to 19 141199 -2.0954 0.018069
17 to 18 142062 0.4504 0.673772
16 to 17 141907 -0.0069 0.497258
15 to 16 141672 -0.7001 0.241936
14 to 15 141875 -0.1013 0.459669
13 to 14 142303 1.1613 0.877234
12 to 13 141899 -0.0305 0.487845
11 to 12 141928 0.0551 0.521960
10 to 11 142023 0.3353 0.631304
9 to 10 141824 -0.2517 0.400632
8 to 9 142120 0.6214 0.732847
7 to 8 142059 0.4415 0.670576
6 to 7 141817 -0.2724 0.392673
5 to 6 141729 -0.5319 0.297381
4 to 5 141498 -1.2134 0.112496
3 to 4 142556 1.9076 0.971777
2 to 3 141256 -1.9272 0.026976
1 to 2 141675 -0.6912 0.244708
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-12_13:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2510.21 0.144 0.557429
Test results for specific bytes for dh-ranFile-2018-07-12_13:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2413.45 -1.224 0.110468
2 to 9 2529.04 0.411 0.659325
3 to 10 2435.62 -0.911 0.181272
4 to 11 2625.01 1.768 0.961464
5 to 12 2586.16 1.218 0.888479
6 to 13 2555.02 0.778 0.781736
7 to 14 2676.51 2.496 0.993723
8 to 15 2519.05 0.269 0.606180
9 to 16 2606.27 1.503 0.933573
10 to 17 2441.01 -0.834 0.202075
11 to 18 2475.97 -0.340 0.366994
12 to 19 2616.49 1.647 0.950257
13 to 20 2455.59 -0.628 0.264990
14 to 21 2600.47 1.421 0.922316
15 to 22 2555.85 0.790 0.785181
16 to 23 2584.82 1.200 0.884853
17 to 24 2513.56 0.192 0.576020
18 to 25 2524.19 0.342 0.633888
19 to 26 2589.39 1.264 0.896917
20 to 27 2437.30 -0.887 0.187628
21 to 28 2560.75 0.859 0.804854
22 to 29 2375.44 -1.762 0.039068
23 to 30 2496.21 -0.054 0.478652
24 to 31 2409.46 -1.280 0.100207
25 to 32 2404.12 -1.356 0.087548
CDPARK for dh-ranFile-2018-07-12_13:31: 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
3563 1.8265 0.966111
3542 0.8676 0.807188
3517 -0.2740 0.392053
3551 1.2785 0.899470
3537 0.6393 0.738676
3511 -0.5479 0.291865
3499 -1.0959 0.136563
3530 0.3196 0.625377
3517 -0.2740 0.392053
3540 0.7763 0.781201
Square side=100, avg. no. parked=3530.70 sample std.=18.65
p-value of the KSTEST for those 10 p-values: 0.483051
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-12_13:31
0.5081,0.1056,0.3469,0.9556,0.0917,0.6547,0.6822,0.7702,0.4144,0.4599,
The KS test for those 10 p-values: 0.969803
The 3DSPHERES test for dh-ranFile-2018-07-12_13:31
sample no r^3 equiv. uni.
1 5.399 0.164698
2 24.357 0.555982
3 0.444 0.014675
4 6.400 0.192116
5 1.814 0.058669
6 22.330 0.524954
7 31.854 0.654164
8 2.525 0.080716
9 35.880 0.697598
10 14.618 0.385692
11 10.811 0.302584
12 55.911 0.844900
13 18.998 0.469148
14 6.577 0.196853
15 40.869 0.743926
16 26.530 0.587010
17 9.388 0.268690
18 8.815 0.254590
19 18.012 0.451401
20 69.938 0.902826
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.385960
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-12_13:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
2.7 -0.3 -3.2 -0.3 -0.2 -0.4
0.6 -1.4 1.3 0.1 -0.2 -1.3
0.2 -1.0 0.4 1.6 -0.4 -1.1
0.6 2.0 0.3 -0.8 -0.2 1.6
-1.4 -1.3 -2.1 0.4 0.8 0.8
-0.3 0.2 -0.9 -0.1 1.9 1.5
-0.7 -0.4 -0.4 -0.7 0.1 -1.0
-1.1
Chi-square with 42 degrees of freedom:56.458303
z-score=1.577530, p-value=0.932788
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-12_13:31
Test no p-value
1 0.025612
2 0.325181
3 0.667866
4 0.848461
5 0.685997
6 0.033317
7 0.623081
8 0.048540
9 0.397615
10 0.459573
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.300250
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-12_13:31:
(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 66548 0.21 66621 0.03
3 25000.00 24982 0.01 24971 0.03
4 6666.67 6743 0.87 6697 0.14
5 1388.89 1435 1.53 1414 0.45
6 238.10 243 0.10 263 2.61
7 34.72 43 1.97 28 1.30
8 4.96 5 0.00 5 0.00
p=0.41782 p=0.39904
Number of rngs required: 688330, p-value: 0.467
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-12_13:31
No. of wins: Observed Expected
98985 98585.9
z-score= 1.785, pvalue=0.96289
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66804 66666.7 0.283 0.283
2 37643 37654.3 0.003 0.286
3 26915 26954.7 0.059 0.345
4 19314 19313.5 0.000 0.345
5 13900 13851.4 0.170 0.515
6 9949 9943.5 0.003 0.518
7 7069 7145.0 0.809 1.327
8 5067 5139.1 1.011 2.338
9 3760 3699.9 0.977 3.315
10 2630 2666.3 0.494 3.809
11 1911 1923.3 0.079 3.889
12 1359 1388.7 0.637 4.525
13 984 1003.7 0.387 4.913
14 756 726.1 1.228 6.141
15 508 525.8 0.605 6.745
16 381 381.2 0.000 6.746
17 279 276.5 0.022 6.767
18 206 200.8 0.133 6.901
19 149 146.0 0.062 6.963
20 114 106.2 0.571 7.533
21 302 287.1 0.772 8.305
Chisq= 8.31 for 20 degrees of freedom, p= 0.01035
SUMMARY of craptest
p-value for no. of wins: 0.962885
p-value for throws/game: 0.010352
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-12_13:31
No. of wins: Observed Expected
98349 98585.9
z-score=-1.059, pvalue=0.14472
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66754 66666.7 0.114 0.114
2 37917 37654.3 1.832 1.947
3 26810 26954.7 0.777 2.724
4 19255 19313.5 0.177 2.901
5 13998 13851.4 1.551 4.452
6 9901 9943.5 0.182 4.634
7 7018 7145.0 2.258 6.892
8 5142 5139.1 0.002 6.894
9 3641 3699.9 0.937 7.831
10 2687 2666.3 0.161 7.991
11 1952 1923.3 0.427 8.419
12 1371 1388.7 0.227 8.645
13 970 1003.7 1.132 9.778
14 656 726.1 6.775 16.553
15 493 525.8 2.050 18.603
16 380 381.2 0.003 18.607
17 264 276.5 0.569 19.176
18 202 200.8 0.007 19.182
19 149 146.0 0.062 19.245
20 116 106.2 0.901 20.146
21 324 287.1 4.739 24.885
Chisq= 24.88 for 20 degrees of freedom, p= 0.79413
SUMMARY of craptest
p-value for no. of wins: 0.144716
p-value for throws/game: 0.794129
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0013,0.0021,0.0022,0.0104,0.0147,0.0181,0.0206,0.0234,0.0242,0.0250,
0.0256,0.0270,0.0284,0.0333,0.0362,0.0391,0.0485,0.0521,0.0587,0.0623,
0.0801,0.0807,0.0875,0.0912,0.0917,0.0990,0.1001,0.1002,0.1006,0.1056,
0.1084,0.1105,0.1125,0.1182,0.1257,0.1296,0.1333,0.1366,0.1380,0.1395,
0.1395,0.1426,0.1432,0.1447,0.1488,0.1495,0.1527,0.1533,0.1647,0.1739,
0.1813,0.1828,0.1855,0.1876,0.1878,0.1884,0.1921,0.1969,0.2021,0.2044,
0.2098,0.2165,0.2371,0.2373,0.2419,0.2432,0.2447,0.2485,0.2546,0.2650,
0.2679,0.2687,0.2741,0.2762,0.2776,0.2851,0.2857,0.2887,0.2919,0.2953,
0.2974,0.2985,0.3000,0.3002,0.3026,0.3056,0.3085,0.3199,0.3252,0.3291,
0.3404,0.3469,0.3496,0.3505,0.3514,0.3643,0.3647,0.3670,0.3740,0.3857,
0.3860,0.3921,0.3921,0.3927,0.3938,0.3976,0.3976,0.3990,0.4006,0.4033,
0.4126,0.4144,0.4153,0.4178,0.4189,0.4243,0.4283,0.4284,0.4514,0.4570,
0.4596,0.4597,0.4599,0.4611,0.4665,0.4691,0.4693,0.4766,0.4787,0.4831,
0.4839,0.4878,0.4943,0.4973,0.4988,0.5081,0.5082,0.5167,0.5220,0.5250,
0.5347,0.5401,0.5436,0.5463,0.5520,0.5527,0.5560,0.5574,0.5615,0.5620,
0.5748,0.5760,0.5805,0.5813,0.5814,0.5869,0.5870,0.5870,0.5888,0.5989,
0.6040,0.6062,0.6129,0.6175,0.6231,0.6253,0.6254,0.6293,0.6313,0.6339,
0.6461,0.6461,0.6463,0.6498,0.6524,0.6542,0.6543,0.6547,0.6575,0.6593,
0.6612,0.6656,0.6669,0.6679,0.6694,0.6706,0.6738,0.6754,0.6812,0.6822,
0.6856,0.6860,0.6945,0.6976,0.7040,0.7082,0.7100,0.7145,0.7201,0.7311,
0.7328,0.7357,0.7387,0.7406,0.7439,0.7477,0.7554,0.7555,0.7574,0.7588,
0.7696,0.7702,0.7720,0.7764,0.7812,0.7817,0.7852,0.7858,0.7941,0.8049,
0.8072,0.8101,0.8229,0.8250,0.8295,0.8386,0.8449,0.8485,0.8577,0.8622,
0.8698,0.8764,0.8772,0.8800,0.8849,0.8860,0.8872,0.8885,0.8946,0.8960,
0.8969,0.8995,0.9028,0.9056,0.9158,0.9211,0.9219,0.9223,0.9274,0.9289,
0.9328,0.9336,0.9364,0.9477,0.9503,0.9556,0.9577,0.9580,0.9615,0.9629,
0.9657,0.9661,0.9675,0.9698,0.9718,0.9814,0.9856,0.9886,0.9937,
Overall p-value after applying KStest on 269 p-values = 0.962849
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.