RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-29_00:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.67 16.0804 0.481855
2 to 25 15.48 19.7113 0.710739
3 to 26 15.58 22.8156 0.844649
4 to 27 15.63 17.0625 0.549862
5 to 28 15.72 17.0483 0.548899
6 to 29 15.67 22.0194 0.816027
7 to 30 15.57 15.1167 0.412922
8 to 31 15.93 22.8723 0.846546
9 to 32 15.62 10.7541 0.130942
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.410509
Tough bday spacings test for dh-ranFile-2018-06-29_00:31: 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 9 39 80 95 94 83 40 37 13 8 2
(O-E)^2/E 0.0 0.2 0.6 0.1 0.1 0.3 2.8 1.8 0.2 0.3 1.0
Birthday Spacings: Sum(O-E)^2/E= 7.433, p= 0.316
RESULTS OF GCD FOR dh-ranFile-2018-06-29_00:31
Euclid's algorithm:
p-value, steps to gcd: 0.274597
p-value, dist. of gcd's: 0.292687
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-29_00:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.353 0.415 0.559 0.267 0.309 0.739 0.134 0.187
Bits 8 to 15---> 0.734 0.791 0.302 0.396 0.135 0.493 0.915 0.125
Bits 16 to 23---> 0.652 0.607 0.582 0.617 0.940 0.961 0.723 0.866
Bits 24 to 31---> 0.683 0.174 0.624 0.296 0.535 0.729 0.892 0.676
KS test for the above 32 p values: 0.553
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-29_00:31,
p-values for 5 runs: 0.7021, 0.9909, 0.4787, 0.5119, 0.7247
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-29_00:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 211 211.4 0.001 0.001
r= 29 5225 5134.0 1.613 1.613
r= 30 23123 23103.0 0.017 1.631
r= 31 11441 11551.5 1.057 2.688
chi-square = 2.688 with df = 3; p-value = 0.558
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-29_00:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 188 211.4 2.594 2.594
r= 30 5170 5134.0 0.252 2.846
r= 31 23102 23103.0 0.000 2.846
r= 32 11540 11551.5 0.011 2.858
chi-square = 2.858 with df = 3; p-value = 0.586
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-29_00:31
b-rank test for bits 1 to 8, p=0.79631
b-rank test for bits 2 to 9, p=0.57979
b-rank test for bits 3 to 10, p=0.56064
b-rank test for bits 4 to 11, p=0.05432
b-rank test for bits 5 to 12, p=0.35453
b-rank test for bits 6 to 13, p=0.67665
b-rank test for bits 7 to 14, p=0.96311
b-rank test for bits 8 to 15, p=0.95479
b-rank test for bits 9 to 16, p=0.38068
b-rank test for bits 10 to 17, p=0.17771
b-rank test for bits 11 to 18, p=0.83607
b-rank test for bits 12 to 19, p=0.46648
b-rank test for bits 13 to 20, p=0.22039
b-rank test for bits 14 to 21, p=0.82816
b-rank test for bits 15 to 22, p=0.06689
b-rank test for bits 16 to 23, p=0.01972
b-rank test for bits 17 to 24, p=0.06461
b-rank test for bits 18 to 25, p=0.50008
b-rank test for bits 19 to 26, p=0.21684
b-rank test for bits 20 to 27, p=0.02815
b-rank test for bits 21 to 28, p=0.13740
b-rank test for bits 22 to 29, p=0.65485
b-rank test for bits 23 to 30, p=0.98316
b-rank test for bits 24 to 31, p=0.79327
b-rank test for bits 25 to 32, p=0.90830
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 = 0.550116
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-29_00:31
(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 141982 0.17 0.567412
2 142122 0.50 0.690368
3 142064 0.36 0.641092
4 142100 0.45 0.672017
5 141137 -1.80 0.035576
6 140946 -2.25 0.012200
7 142493 1.36 0.913671
8 142223 0.73 0.768182
9 142434 1.23 0.889875
10 141573 -0.79 0.215987
11 141514 -0.92 0.177830
12 141600 -0.72 0.234922
13 141147 -1.78 0.037444
14 142237 0.77 0.778038
15 142784 2.04 0.979505
16 142881 2.27 0.988404
17 141740 -0.40 0.346189
18 141453 -1.07 0.143169
19 141992 0.19 0.576581
20 142434 1.23 0.889875
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-29_00:31
Bits used No. missing words z-score p-value
23 to 32 141692 -0.7494 0.226804
22 to 31 141515 -1.3598 0.086953
21 to 30 141457 -1.5598 0.059408
20 to 29 141885 -0.0839 0.466569
19 to 28 142004 0.3264 0.627957
18 to 27 141756 -0.5287 0.298498
17 to 26 141938 0.0989 0.539376
16 to 25 142163 0.8747 0.809138
15 to 24 142028 0.4092 0.658806
14 to 23 142121 0.7299 0.767273
13 to 22 141911 0.0058 0.502297
12 to 21 141638 -0.9356 0.174734
11 to 20 141777 -0.4563 0.324083
10 to 19 142328 1.4437 0.925587
9 to 18 141979 0.2402 0.594928
8 to 17 142034 0.4299 0.666365
7 to 16 141509 -1.3804 0.083724
6 to 15 142135 0.7782 0.781766
5 to 14 142128 0.7540 0.774586
4 to 13 141369 -1.8632 0.031217
3 to 12 142064 0.5333 0.703103
2 to 11 141760 -0.5149 0.303301
1 to 10 141988 0.2713 0.606911
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-29_00:31
Bits used No. missing words z-score p-value
28 to 32 141974 0.2192 0.586761
27 to 31 142328 1.4192 0.922083
26 to 30 142264 1.2023 0.885371
25 to 29 142029 0.4057 0.657504
24 to 28 142633 2.4531 0.992919
23 to 27 141578 -1.1232 0.130686
22 to 26 141863 -0.1571 0.437602
21 to 25 141649 -0.8825 0.188760
20 to 24 142030 0.4091 0.658749
19 to 23 141787 -0.4147 0.339189
18 to 22 141844 -0.2215 0.412368
17 to 21 142275 1.2396 0.892431
16 to 20 141878 -0.1062 0.457711
15 to 19 142443 1.8091 0.964778
14 to 18 142202 0.9921 0.839426
13 to 17 141498 -1.3943 0.081608
12 to 16 141707 -0.6859 0.246399
11 to 15 141355 -1.8791 0.030116
10 to 14 142128 0.7413 0.770730
9 to 13 142301 1.3277 0.907861
8 to 12 141992 0.2802 0.610352
7 to 11 141774 -0.4587 0.323208
6 to 10 141988 0.2667 0.605141
5 to 9 141870 -0.1333 0.446969
4 to 8 142065 0.5277 0.701145
3 to 7 141735 -0.5909 0.277277
2 to 6 141634 -0.9333 0.175327
1 to 5 142374 1.5752 0.942389
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-29_00:31
Bits used No. missing words z-score p-value
31 to 32 142490 1.7129 0.956634
30 to 31 141797 -0.3314 0.370187
29 to 30 142512 1.7778 0.962281
28 to 29 142192 0.8338 0.797813
27 to 28 141746 -0.4818 0.314974
26 to 27 141919 0.0285 0.511378
25 to 26 141513 -1.1691 0.121179
24 to 25 142260 1.0344 0.849531
23 to 24 141665 -0.7207 0.235536
22 to 23 142315 1.1967 0.884282
21 to 22 141639 -0.7974 0.212600
20 to 21 141670 -0.7060 0.240098
19 to 20 141959 0.1465 0.558244
18 to 19 141896 -0.0393 0.484317
17 to 18 142169 0.7660 0.778158
16 to 17 142068 0.4681 0.680127
15 to 16 142351 1.3029 0.903689
14 to 15 141978 0.2026 0.580263
13 to 14 141589 -0.9449 0.172348
12 to 13 142065 0.4592 0.676956
11 to 12 142183 0.8073 0.790249
10 to 11 141801 -0.3196 0.374652
9 to 10 141507 -1.1868 0.117650
8 to 9 141971 0.1819 0.572176
7 to 8 142230 0.9459 0.827908
6 to 7 141193 -2.1131 0.017297
5 to 6 141650 -0.7650 0.222140
4 to 5 141541 -1.0865 0.138625
3 to 4 142340 1.2704 0.898031
2 to 3 142329 1.2380 0.892135
1 to 2 141689 -0.6499 0.257865
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-29_00:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2430.55 -0.982 0.163016
Test results for specific bytes for dh-ranFile-2018-06-29_00:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2643.97 2.036 0.979126
2 to 9 2504.19 0.059 0.523625
3 to 10 2393.57 -1.505 0.066134
4 to 11 2561.73 0.873 0.808673
5 to 12 2558.26 0.824 0.795016
6 to 13 2453.88 -0.652 0.257118
7 to 14 2572.82 1.030 0.848456
8 to 15 2409.61 -1.278 0.100582
9 to 16 2492.15 -0.111 0.455823
10 to 17 2546.16 0.653 0.743041
11 to 18 2509.85 0.139 0.555386
12 to 19 2583.56 1.182 0.881348
13 to 20 2402.76 -1.375 0.084545
14 to 21 2555.36 0.783 0.783165
15 to 22 2615.75 1.637 0.949182
16 to 23 2525.36 0.359 0.640073
17 to 24 2417.39 -1.168 0.121343
18 to 25 2540.07 0.567 0.714512
19 to 26 2450.44 -0.701 0.241687
20 to 27 2489.83 -0.144 0.442795
21 to 28 2554.12 0.765 0.777990
22 to 29 2496.22 -0.053 0.478690
23 to 30 2364.98 -1.909 0.028104
24 to 31 2427.52 -1.025 0.152685
25 to 32 2408.04 -1.301 0.096705
CDPARK for dh-ranFile-2018-06-29_00:31: 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
3509 -0.6393 0.261324
3557 1.5525 0.939730
3518 -0.2283 0.409702
3538 0.6849 0.753306
3564 1.8721 0.969407
3590 3.0594 0.998891
3544 0.9589 0.831196
3504 -0.8676 0.192812
3503 -0.9132 0.180558
3528 0.2283 0.590298
Square side=100, avg. no. parked=3535.50 sample std.=27.27
p-value of the KSTEST for those 10 p-values: 0.147185
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-29_00:31
0.6091,0.0074,0.3665,0.6275,0.1956,0.4643,0.3252,0.7971,0.9385,0.4153,
The KS test for those 10 p-values: 0.889669
The 3DSPHERES test for dh-ranFile-2018-06-29_00:31
sample no r^3 equiv. uni.
1 60.223 0.865669
2 45.225 0.778538
3 15.586 0.405195
4 7.813 0.229292
5 29.858 0.630373
6 61.929 0.873093
7 26.085 0.580833
8 32.106 0.657066
9 33.905 0.677020
10 50.557 0.814602
11 7.495 0.221066
12 29.440 0.625186
13 33.387 0.671396
14 2.282 0.073255
15 19.896 0.484791
16 47.140 0.792231
17 0.882 0.028957
18 13.098 0.353774
19 54.510 0.837488
20 4.682 0.144499
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.611231
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-29_00:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 0.5 -0.6 1.1 -0.4 1.7
-0.1 0.2 -0.6 -0.3 0.0 -0.2
0.8 0.2 0.3 0.4 -2.0 0.8
-0.3 -1.6 -0.5 -0.6 0.9 1.3
0.4 -0.0 -0.1 -0.0 -0.1 1.8
-0.9 2.0 2.5 -0.9 -0.5 0.4
0.5 -0.7 0.1 0.4 -0.6 0.0
1.8
Chi-square with 42 degrees of freedom:39.082718
z-score=-0.318302, p-value=0.400236
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-29_00:31
Test no p-value
1 0.042193
2 0.003574
3 0.769267
4 0.593886
5 0.678533
6 0.006399
7 0.038601
8 0.639007
9 0.181272
10 0.425026
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.017517
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-29_00:31:
(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 66490 0.47 66673 0.00
3 25000.00 25138 0.76 25048 0.09
4 6666.67 6709 0.27 6671 0.00
5 1388.89 1371 0.23 1342 1.58
6 238.10 259 1.84 215 2.24
7 34.72 26 2.19 45 3.04
8 4.96 6 0.22 5 0.00
p=0.57375 p=0.67571
Number of rngs required: 688249, p-value: 0.430
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-29_00:31
No. of wins: Observed Expected
98767 98585.9
z-score= 0.810, pvalue=0.79108
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66364 66666.7 1.374 1.374
2 37924 37654.3 1.931 3.306
3 26898 26954.7 0.119 3.425
4 19283 19313.5 0.048 3.473
5 13974 13851.4 1.085 4.558
6 9841 9943.5 1.057 5.615
7 7169 7145.0 0.080 5.696
8 5167 5139.1 0.152 5.847
9 3759 3699.9 0.945 6.793
10 2666 2666.3 0.000 6.793
11 1857 1923.3 2.287 9.080
12 1400 1388.7 0.091 9.171
13 1040 1003.7 1.312 10.483
14 724 726.1 0.006 10.489
15 534 525.8 0.127 10.616
16 394 381.2 0.433 11.049
17 309 276.5 3.810 14.860
18 202 200.8 0.007 14.866
19 139 146.0 0.334 15.201
20 113 106.2 0.433 15.634
21 243 287.1 6.778 22.412
Chisq= 22.41 for 20 degrees of freedom, p= 0.68142
SUMMARY of craptest
p-value for no. of wins: 0.791079
p-value for throws/game: 0.681419
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-29_00:31
No. of wins: Observed Expected
98805 98585.9
z-score= 0.980, pvalue=0.83649
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66841 66666.7 0.456 0.456
2 37573 37654.3 0.176 0.632
3 26948 26954.7 0.002 0.633
4 19428 19313.5 0.679 1.312
5 13865 13851.4 0.013 1.326
6 9891 9943.5 0.278 1.603
7 7133 7145.0 0.020 1.624
8 5139 5139.1 0.000 1.624
9 3590 3699.9 3.262 4.886
10 2687 2666.3 0.161 5.047
11 1927 1923.3 0.007 5.054
12 1406 1388.7 0.215 5.268
13 1003 1003.7 0.001 5.269
14 677 726.1 3.326 8.594
15 481 525.8 3.823 12.417
16 383 381.2 0.009 12.426
17 270 276.5 0.155 12.581
18 218 200.8 1.468 14.049
19 131 146.0 1.538 15.587
20 117 106.2 1.095 16.682
21 292 287.1 0.083 16.765
Chisq= 16.77 for 20 degrees of freedom, p= 0.33183
SUMMARY of craptest
p-value for no. of wins: 0.836489
p-value for throws/game: 0.331832
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0036,0.0064,0.0074,0.0122,0.0173,0.0175,0.0197,0.0281,0.0281,0.0290,
0.0301,0.0312,0.0356,0.0374,0.0386,0.0422,0.0543,0.0594,0.0646,0.0661,
0.0669,0.0733,0.0816,0.0837,0.0845,0.0870,0.0967,0.1006,0.1177,0.1212,
0.1213,0.1255,0.1307,0.1309,0.1345,0.1346,0.1374,0.1386,0.1432,0.1445,
0.1472,0.1527,0.1630,0.1723,0.1737,0.1747,0.1753,0.1777,0.1778,0.1806,
0.1813,0.1866,0.1888,0.1928,0.1956,0.2126,0.2160,0.2168,0.2204,0.2211,
0.2221,0.2268,0.2293,0.2349,0.2355,0.2401,0.2417,0.2464,0.2571,0.2579,
0.2613,0.2666,0.2746,0.2773,0.2927,0.2962,0.2985,0.3023,0.3033,0.3088,
0.3150,0.3160,0.3232,0.3241,0.3252,0.3318,0.3392,0.3462,0.3534,0.3538,
0.3545,0.3665,0.3702,0.3747,0.3807,0.3964,0.4002,0.4052,0.4097,0.4105,
0.4124,0.4129,0.4146,0.4153,0.4250,0.4297,0.4376,0.4428,0.4470,0.4558,
0.4577,0.4643,0.4665,0.4666,0.4787,0.4787,0.4819,0.4843,0.4848,0.4935,
0.5001,0.5023,0.5114,0.5119,0.5236,0.5355,0.5394,0.5489,0.5499,0.5501,
0.5532,0.5554,0.5578,0.5582,0.5585,0.5606,0.5674,0.5722,0.5737,0.5766,
0.5798,0.5803,0.5808,0.5815,0.5859,0.5868,0.5903,0.5939,0.5949,0.6051,
0.6069,0.6074,0.6091,0.6104,0.6112,0.6171,0.6239,0.6252,0.6275,0.6280,
0.6304,0.6390,0.6401,0.6411,0.6524,0.6549,0.6571,0.6575,0.6587,0.6588,
0.6664,0.6714,0.6720,0.6757,0.6757,0.6766,0.6770,0.6770,0.6785,0.6801,
0.6814,0.6835,0.6904,0.7011,0.7021,0.7031,0.7107,0.7145,0.7227,0.7247,
0.7286,0.7345,0.7391,0.7430,0.7533,0.7673,0.7682,0.7693,0.7707,0.7746,
0.7780,0.7780,0.7782,0.7785,0.7818,0.7832,0.7902,0.7910,0.7911,0.7922,
0.7933,0.7950,0.7963,0.7971,0.7978,0.8087,0.8091,0.8146,0.8160,0.8279,
0.8282,0.8312,0.8361,0.8365,0.8375,0.8394,0.8446,0.8465,0.8485,0.8495,
0.8657,0.8657,0.8731,0.8813,0.8843,0.8854,0.8897,0.8899,0.8899,0.8917,
0.8921,0.8924,0.8980,0.9037,0.9079,0.9083,0.9137,0.9154,0.9221,0.9256,
0.9385,0.9395,0.9397,0.9424,0.9492,0.9548,0.9566,0.9615,0.9623,0.9631,
0.9648,0.9694,0.9791,0.9795,0.9832,0.9884,0.9909,0.9929,0.9989,
Overall p-value after applying KStest on 269 p-values = 0.381560
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.