RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-12_14:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.65 23.6540 0.870854
2 to 25 15.76 13.7567 0.315760
3 to 26 15.83 13.8824 0.324591
4 to 27 15.65 17.8990 0.604762
5 to 28 15.68 31.0005 0.980031
6 to 29 15.46 21.6312 0.800678
7 to 30 15.51 20.8501 0.766931
8 to 31 15.81 15.5968 0.447427
9 to 32 15.71 16.2614 0.494615
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.331858
Tough bday spacings test for dh-ranFile-2018-07-12_14:31: 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 11 38 74 97 103 62 49 39 13 11 3
(O-E)^2/E 0.4 0.1 0.0 0.0 0.3 3.3 0.2 2.9 0.2 2.9 0.3
Birthday Spacings: Sum(O-E)^2/E= 10.529, p= 0.605
RESULTS OF GCD FOR dh-ranFile-2018-07-12_14:31
Euclid's algorithm:
p-value, steps to gcd: 0.493642
p-value, dist. of gcd's: 0.846183
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-12_14:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.742 0.992 0.092 0.743 0.573 0.535 0.402 0.829
Bits 8 to 15---> 0.292 0.498 0.814 0.103 0.494 0.407 0.228 0.928
Bits 16 to 23---> 0.742 0.135 0.861 0.573 0.494 0.073 0.532 0.641
Bits 24 to 31---> 0.837 0.994 0.233 0.569 0.390 0.795 0.474 0.041
KS test for the above 32 p values: 0.302
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-12_14:31,
p-values for 5 runs: 0.0543, 0.5751, 0.6673, 0.6957, 0.1661
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-12_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 207 211.4 0.092 0.092
r= 29 5190 5134.0 0.611 0.703
r= 30 23047 23103.0 0.136 0.839
r= 31 11556 11551.5 0.002 0.841
chi-square = 0.841 with df = 3; p-value = 0.160
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-12_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 217 211.4 0.147 0.147
r= 30 5076 5134.0 0.655 0.803
r= 31 23266 23103.0 1.149 1.952
r= 32 11441 11551.5 1.057 3.010
chi-square = 3.010 with df = 3; p-value = 0.610
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-12_14:31
b-rank test for bits 1 to 8, p=0.04329
b-rank test for bits 2 to 9, p=0.70247
b-rank test for bits 3 to 10, p=0.73273
b-rank test for bits 4 to 11, p=0.02124
b-rank test for bits 5 to 12, p=0.15541
b-rank test for bits 6 to 13, p=0.47905
b-rank test for bits 7 to 14, p=0.14363
b-rank test for bits 8 to 15, p=0.12343
b-rank test for bits 9 to 16, p=0.51088
b-rank test for bits 10 to 17, p=0.87286
b-rank test for bits 11 to 18, p=0.49673
b-rank test for bits 12 to 19, p=0.39235
b-rank test for bits 13 to 20, p=0.56003
b-rank test for bits 14 to 21, p=0.18499
b-rank test for bits 15 to 22, p=0.36054
b-rank test for bits 16 to 23, p=0.38353
b-rank test for bits 17 to 24, p=0.21461
b-rank test for bits 18 to 25, p=0.21197
b-rank test for bits 19 to 26, p=0.25451
b-rank test for bits 20 to 27, p=0.15481
b-rank test for bits 21 to 28, p=0.59527
b-rank test for bits 22 to 29, p=0.03616
b-rank test for bits 23 to 30, p=0.16929
b-rank test for bits 24 to 31, p=0.44743
b-rank test for bits 25 to 32, p=0.02388
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 = 0.005029
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-12_14:31
(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 141469 -1.03 0.151785
2 141777 -0.31 0.378591
3 142420 1.19 0.883596
4 142160 0.59 0.720954
5 141128 -1.83 0.033960
6 142791 2.06 0.980300
7 142244 0.78 0.782875
8 142431 1.22 0.888550
9 141880 -0.07 0.472683
10 142682 1.81 0.964486
11 142027 0.27 0.608315
12 141155 -1.76 0.038996
13 142789 2.06 0.980075
14 141277 -1.48 0.069783
15 142344 1.02 0.845086
16 141966 0.13 0.552669
17 142155 0.57 0.717015
18 141466 -1.04 0.150144
19 141764 -0.34 0.367095
20 142442 1.24 0.893353
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-12_14:31
Bits used No. missing words z-score p-value
23 to 32 142676 2.6437 0.995900
22 to 31 141490 -1.4460 0.074093
21 to 30 142391 1.6609 0.951636
20 to 29 142260 1.2092 0.886708
19 to 28 142058 0.5127 0.695904
18 to 27 142081 0.5920 0.723063
17 to 26 142251 1.1782 0.880636
16 to 25 142035 0.4333 0.667618
15 to 24 141919 0.0333 0.513300
14 to 23 142105 0.6747 0.750075
13 to 22 141995 0.2954 0.616161
12 to 21 142121 0.7299 0.767273
11 to 20 142438 1.8230 0.965848
10 to 19 141891 -0.0632 0.474801
9 to 18 142212 1.0437 0.851686
8 to 17 140827 -3.7322 0.000095
7 to 16 141716 -0.6667 0.252496
6 to 15 141773 -0.4701 0.319141
5 to 14 141689 -0.7598 0.223699
4 to 13 141718 -0.6598 0.254704
3 to 12 141845 -0.2218 0.412224
2 to 11 141828 -0.2804 0.389567
1 to 10 141978 0.2368 0.593591
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-12_14:31
Bits used No. missing words z-score p-value
28 to 32 141870 -0.1333 0.446969
27 to 31 141988 0.2667 0.605141
26 to 30 142379 1.5921 0.944319
25 to 29 141273 -2.1571 0.015501
24 to 28 142159 0.8463 0.801318
23 to 27 141519 -1.3232 0.092892
22 to 26 141687 -0.7537 0.225526
21 to 25 141828 -0.2757 0.391391
20 to 24 141945 0.1209 0.548121
19 to 23 141921 0.0396 0.515778
18 to 22 142540 2.1379 0.983736
17 to 21 141905 -0.0147 0.494145
16 to 20 142350 1.4938 0.932386
15 to 19 142413 1.7074 0.956122
14 to 18 141847 -0.2113 0.416331
13 to 17 141506 -1.3672 0.085778
12 to 16 141544 -1.2384 0.107783
11 to 15 141411 -1.6893 0.045585
10 to 14 142689 2.6429 0.995891
9 to 13 142282 1.2633 0.896757
8 to 12 141954 0.1514 0.560179
7 to 11 141946 0.1243 0.549463
6 to 10 141955 0.1548 0.561516
5 to 9 142191 0.9548 0.830164
4 to 8 141496 -1.4011 0.080589
3 to 7 141591 -1.0791 0.140275
2 to 6 142005 0.3243 0.627147
1 to 5 141766 -0.4859 0.313532
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-12_14:31
Bits used No. missing words z-score p-value
31 to 32 142630 2.1259 0.983243
30 to 31 142151 0.7129 0.762043
29 to 30 141966 0.1672 0.566381
28 to 29 142075 0.4887 0.687474
27 to 28 141339 -1.6824 0.046247
26 to 27 141695 -0.6322 0.263614
25 to 26 141817 -0.2724 0.392673
24 to 25 141805 -0.3078 0.379133
23 to 24 141337 -1.6883 0.045678
22 to 23 142347 1.2911 0.901659
21 to 22 141526 -1.1308 0.129077
20 to 21 141953 0.1288 0.551250
19 to 20 142400 1.4474 0.926108
18 to 19 141803 -0.3137 0.376891
17 to 18 141876 -0.0983 0.460840
16 to 17 141766 -0.4228 0.336220
15 to 16 142452 1.6008 0.945289
14 to 15 141571 -0.9980 0.159134
13 to 14 142276 1.0816 0.860290
12 to 13 141790 -0.3520 0.362417
11 to 12 142034 0.3678 0.643473
10 to 11 141414 -1.4612 0.071987
9 to 10 142213 0.8958 0.814815
8 to 9 141936 0.0787 0.531354
7 to 8 141954 0.1318 0.552417
6 to 7 142097 0.5536 0.710073
5 to 6 141614 -0.8712 0.191828
4 to 5 141839 -0.2075 0.417824
3 to 4 142062 0.4504 0.673772
2 to 3 142464 1.6362 0.949101
1 to 2 142120 0.6214 0.732847
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-12_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2459.51 -0.573 0.283455
Test results for specific bytes for dh-ranFile-2018-07-12_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2671.99 2.432 0.992499
2 to 9 2482.70 -0.245 0.403371
3 to 10 2588.28 1.249 0.894081
4 to 11 2541.88 0.592 0.723156
5 to 12 2388.79 -1.573 0.057887
6 to 13 2413.27 -1.227 0.110003
7 to 14 2505.17 0.073 0.529166
8 to 15 2426.94 -1.033 0.150752
9 to 16 2588.64 1.254 0.894997
10 to 17 2549.03 0.693 0.755969
11 to 18 2448.19 -0.733 0.231888
12 to 19 2369.31 -1.848 0.032280
13 to 20 2504.80 0.068 0.527078
14 to 21 2556.80 0.803 0.789091
15 to 22 2545.80 0.648 0.741426
16 to 23 2415.01 -1.202 0.114701
17 to 24 2464.48 -0.502 0.307702
18 to 25 2410.19 -1.270 0.102024
19 to 26 2630.00 1.838 0.967005
20 to 27 2506.69 0.095 0.537673
21 to 28 2519.83 0.280 0.610437
22 to 29 2509.44 0.133 0.553096
23 to 30 2492.96 -0.100 0.460357
24 to 31 2432.75 -0.951 0.170796
25 to 32 2442.78 -0.809 0.209193
CDPARK for dh-ranFile-2018-07-12_14:31: 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
3562 1.7808 0.962529
3513 -0.4566 0.323972
3545 1.0046 0.842447
3472 -2.3288 0.009936
3535 0.5479 0.708135
3552 1.3242 0.907282
3514 -0.4110 0.340551
3490 -1.5068 0.065925
3503 -0.9132 0.180558
3551 1.2785 0.899470
Square side=100, avg. no. parked=3523.70 sample std.=28.36
p-value of the KSTEST for those 10 p-values: 0.424369
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-12_14:31
0.4293,0.8161,0.8319,0.1474,0.7218,0.7029,0.4087,0.0451,0.7619,0.4247,
The KS test for those 10 p-values: 0.765888
The 3DSPHERES test for dh-ranFile-2018-07-12_14:31
sample no r^3 equiv. uni.
1 41.145 0.746275
2 35.930 0.698099
3 80.378 0.931388
4 10.327 0.291228
5 6.915 0.205867
6 42.648 0.758675
7 24.584 0.559328
8 12.217 0.334509
9 41.452 0.748855
10 20.282 0.491394
11 70.305 0.904010
12 17.541 0.442721
13 26.507 0.586699
14 23.716 0.546395
15 25.689 0.575268
16 13.799 0.368693
17 21.398 0.509957
18 1.013 0.033197
19 4.781 0.147325
20 4.510 0.139584
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.846003
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-12_14:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -1.2 0.1 -1.0 1.2 -1.9
0.9 0.0 -0.5 -0.1 -0.1 -0.4
-0.1 -0.0 1.6 -0.2 -0.6 0.9
-0.1 -0.9 1.4 -1.3 1.7 0.3
1.7 -1.6 -1.2 -2.0 -0.3 -0.6
-0.9 0.4 -0.4 0.3 0.2 -0.7
-0.7 0.8 -0.4 -0.1 0.1 -1.0
-0.1
Chi-square with 42 degrees of freedom:34.706902
z-score=-0.795742, p-value=0.219706
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-12_14:31
Test no p-value
1 0.632750
2 0.058065
3 0.368016
4 0.828375
5 0.486247
6 0.281538
7 0.029573
8 0.302288
9 0.808175
10 0.045506
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.262636
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-12_14:31:
(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 66729 0.06 66747 0.10
3 25000.00 25028 0.03 25092 0.34
4 6666.67 6593 0.81 6554 1.90
5 1388.89 1380 0.06 1343 1.52
6 238.10 232 0.16 222 1.09
7 34.72 32 0.21 38 0.31
8 4.96 5 0.00 3 0.77
p=0.03003 p=0.57996
Number of rngs required: 688439, p-value: 0.517
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-12_14:31
No. of wins: Observed Expected
98214 98585.9
z-score=-1.663, pvalue=0.04814
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66991 66666.7 1.578 1.578
2 37524 37654.3 0.451 2.029
3 26826 26954.7 0.615 2.644
4 19229 19313.5 0.369 3.013
5 13979 13851.4 1.175 4.188
6 9910 9943.5 0.113 4.301
7 7221 7145.0 0.808 5.109
8 5150 5139.1 0.023 5.132
9 3699 3699.9 0.000 5.133
10 2635 2666.3 0.367 5.500
11 1854 1923.3 2.499 7.999
12 1380 1388.7 0.055 8.054
13 1020 1003.7 0.264 8.318
14 700 726.1 0.941 9.259
15 479 525.8 4.172 13.431
16 354 381.2 1.934 15.365
17 283 276.5 0.151 15.516
18 227 200.8 3.410 18.926
19 135 146.0 0.827 19.753
20 107 106.2 0.006 19.758
21 297 287.1 0.340 20.099
Chisq= 20.10 for 20 degrees of freedom, p= 0.54824
SUMMARY of craptest
p-value for no. of wins: 0.048139
p-value for throws/game: 0.548239
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-12_14:31
No. of wins: Observed Expected
98569 98585.9
z-score=-0.075, pvalue=0.46995
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66696 66666.7 0.013 0.013
2 37605 37654.3 0.065 0.078
3 27159 26954.7 1.548 1.625
4 19245 19313.5 0.243 1.868
5 13885 13851.4 0.081 1.950
6 9969 9943.5 0.065 2.015
7 7172 7145.0 0.102 2.117
8 5114 5139.1 0.122 2.239
9 3653 3699.9 0.594 2.833
10 2612 2666.3 1.106 3.938
11 1838 1923.3 3.786 7.724
12 1352 1388.7 0.972 8.696
13 1018 1003.7 0.203 8.899
14 750 726.1 0.784 9.683
15 489 525.8 2.580 12.264
16 377 381.2 0.045 12.309
17 305 276.5 2.929 15.238
18 193 200.8 0.305 15.543
19 148 146.0 0.028 15.571
20 118 106.2 1.308 16.879
21 302 287.1 0.772 17.650
Chisq= 17.65 for 20 degrees of freedom, p= 0.38957
SUMMARY of craptest
p-value for no. of wins: 0.469948
p-value for throws/game: 0.389567
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0001,0.0050,0.0099,0.0155,0.0212,0.0239,0.0296,0.0300,0.0323,0.0332,
0.0340,0.0362,0.0390,0.0406,0.0433,0.0451,0.0455,0.0456,0.0457,0.0462,
0.0481,0.0543,0.0579,0.0581,0.0659,0.0698,0.0720,0.0733,0.0741,0.0806,
0.0858,0.0923,0.0929,0.1020,0.1029,0.1078,0.1100,0.1147,0.1234,0.1291,
0.1348,0.1396,0.1403,0.1436,0.1473,0.1474,0.1501,0.1508,0.1518,0.1548,
0.1554,0.1591,0.1603,0.1661,0.1693,0.1708,0.1806,0.1850,0.1918,0.2059,
0.2092,0.2120,0.2146,0.2197,0.2237,0.2255,0.2281,0.2319,0.2331,0.2525,
0.2545,0.2547,0.2626,0.2636,0.2815,0.2835,0.2912,0.2919,0.3017,0.3023,
0.3077,0.3135,0.3158,0.3191,0.3240,0.3246,0.3319,0.3345,0.3362,0.3406,
0.3605,0.3624,0.3671,0.3680,0.3687,0.3769,0.3786,0.3791,0.3835,0.3896,
0.3896,0.3903,0.3914,0.3923,0.3927,0.4024,0.4034,0.4075,0.4087,0.4122,
0.4163,0.4178,0.4244,0.4247,0.4293,0.4427,0.4470,0.4474,0.4474,0.4604,
0.4608,0.4699,0.4727,0.4738,0.4748,0.4790,0.4862,0.4914,0.4936,0.4937,
0.4941,0.4942,0.4946,0.4967,0.4975,0.5100,0.5109,0.5133,0.5158,0.5165,
0.5271,0.5292,0.5314,0.5316,0.5352,0.5377,0.5464,0.5481,0.5482,0.5495,
0.5513,0.5524,0.5527,0.5531,0.5593,0.5600,0.5602,0.5615,0.5664,0.5693,
0.5730,0.5733,0.5751,0.5753,0.5800,0.5867,0.5936,0.5953,0.6047,0.6048,
0.6051,0.6083,0.6099,0.6104,0.6162,0.6271,0.6328,0.6414,0.6435,0.6673,
0.6676,0.6738,0.6875,0.6957,0.6959,0.6981,0.7025,0.7029,0.7081,0.7101,
0.7170,0.7210,0.7218,0.7231,0.7232,0.7327,0.7328,0.7414,0.7420,0.7425,
0.7426,0.7463,0.7489,0.7501,0.7560,0.7587,0.7619,0.7620,0.7659,0.7669,
0.7673,0.7829,0.7891,0.7947,0.8007,0.8013,0.8082,0.8138,0.8148,0.8161,
0.8284,0.8289,0.8302,0.8319,0.8371,0.8424,0.8451,0.8460,0.8462,0.8517,
0.8603,0.8608,0.8709,0.8729,0.8806,0.8836,0.8867,0.8886,0.8934,0.8941,
0.8950,0.8968,0.8995,0.9017,0.9040,0.9073,0.9261,0.9278,0.9314,0.9324,
0.9443,0.9453,0.9491,0.9516,0.9561,0.9625,0.9645,0.9658,0.9670,0.9800,
0.9801,0.9803,0.9832,0.9837,0.9922,0.9925,0.9939,0.9959,0.9959,
Overall p-value after applying KStest on 269 p-values = 0.700618
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.