RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-15_10:31
(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 26.6004 0.935806
2 to 25 15.88 18.6842 0.653046
3 to 26 15.93 11.1345 0.150514
4 to 27 15.98 25.5431 0.916804
5 to 28 15.78 8.8260 0.054438
6 to 29 15.78 22.8079 0.844390
7 to 30 15.81 10.9391 0.140289
8 to 31 15.89 21.0716 0.776896
9 to 32 16.02 13.1997 0.277285
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.593189
Tough bday spacings test for dh-ranFile-2018-06-15_10:31: 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 35 59 85 95 97 61 28 20 7 4
(O-E)^2/E 0.0 0.1 2.8 1.6 0.1 4.5 1.5 0.1 1.8 0.0 0.0
Birthday Spacings: Sum(O-E)^2/E= 12.528, p= 0.749
RESULTS OF GCD FOR dh-ranFile-2018-06-15_10:31
Euclid's algorithm:
p-value, steps to gcd: 0.511141
p-value, dist. of gcd's: 0.324327
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-15_10:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.629 0.736 0.706 0.621 0.298 0.087 0.882 0.127
Bits 8 to 15---> 0.653 0.615 0.074 0.540 0.854 0.200 0.815 0.933
Bits 16 to 23---> 0.504 0.088 0.125 0.694 0.961 0.571 0.904 0.860
Bits 24 to 31---> 0.322 0.435 0.530 0.440 0.244 0.136 0.711 0.665
KS test for the above 32 p values: 0.271
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-15_10:31,
p-values for 5 runs: 0.0153, 0.4729, 0.8859, 0.5630, 0.3597
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-15_10:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 232 211.4 2.004 2.004
r= 29 5092 5134.0 0.344 2.347
r= 30 23179 23103.0 0.250 2.597
r= 31 11497 11551.5 0.257 2.855
chi-square = 2.855 with df = 3; p-value = 0.585
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-15_10:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 200 211.4 0.617 0.617
r= 30 5125 5134.0 0.016 0.632
r= 31 23185 23103.0 0.291 0.923
r= 32 11490 11551.5 0.328 1.251
chi-square = 1.251 with df = 3; p-value = 0.259
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-15_10:31
b-rank test for bits 1 to 8, p=0.35794
b-rank test for bits 2 to 9, p=0.75758
b-rank test for bits 3 to 10, p=0.95412
b-rank test for bits 4 to 11, p=0.67947
b-rank test for bits 5 to 12, p=0.01487
b-rank test for bits 6 to 13, p=0.17049
b-rank test for bits 7 to 14, p=0.52054
b-rank test for bits 8 to 15, p=0.56159
b-rank test for bits 9 to 16, p=0.18948
b-rank test for bits 10 to 17, p=0.27605
b-rank test for bits 11 to 18, p=0.09024
b-rank test for bits 12 to 19, p=0.45058
b-rank test for bits 13 to 20, p=0.89793
b-rank test for bits 14 to 21, p=0.95393
b-rank test for bits 15 to 22, p=0.20998
b-rank test for bits 16 to 23, p=0.19165
b-rank test for bits 17 to 24, p=0.56487
b-rank test for bits 18 to 25, p=0.10126
b-rank test for bits 19 to 26, p=0.44429
b-rank test for bits 20 to 27, p=0.24198
b-rank test for bits 21 to 28, p=0.56338
b-rank test for bits 22 to 29, p=0.31928
b-rank test for bits 23 to 30, p=0.65257
b-rank test for bits 24 to 31, p=0.58994
b-rank test for bits 25 to 32, p=0.63235
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 = 0.664903
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-15_10:31
(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 141653 -0.60 0.274619
2 143083 2.74 0.996949
3 142340 1.01 0.842850
4 142061 0.35 0.638469
5 141871 -0.09 0.464320
6 141494 -0.97 0.165924
7 141772 -0.32 0.374157
8 141949 0.09 0.536924
9 141552 -0.83 0.201892
10 141774 -0.32 0.375929
11 142593 1.60 0.944907
12 142290 0.89 0.813110
13 141817 -0.22 0.414601
14 142360 1.05 0.853822
15 142415 1.18 0.881292
16 141783 -0.30 0.383935
17 141673 -0.55 0.290415
18 141582 -0.76 0.222198
19 142063 0.36 0.640218
20 141735 -0.41 0.341889
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-15_10:31
Bits used No. missing words z-score p-value
23 to 32 142339 1.4816 0.930779
22 to 31 141829 -0.2770 0.390890
21 to 30 141880 -0.1011 0.459721
20 to 29 142199 0.9989 0.841069
19 to 28 141702 -0.7149 0.237326
18 to 27 141948 0.1333 0.553040
17 to 26 142257 1.1989 0.884709
16 to 25 142024 0.3954 0.653731
15 to 24 141660 -0.8598 0.194961
14 to 23 142096 0.6437 0.740112
13 to 22 141824 -0.2942 0.384287
12 to 21 142713 2.7713 0.997208
11 to 20 141635 -0.9460 0.172083
10 to 19 141847 -0.2149 0.414911
9 to 18 141830 -0.2736 0.392215
8 to 17 142168 0.8920 0.813794
7 to 16 141898 -0.0391 0.484418
6 to 15 140851 -3.6494 0.000131
5 to 14 141854 -0.1908 0.424344
4 to 13 141642 -0.9218 0.178309
3 to 12 141978 0.2368 0.593591
2 to 11 141493 -1.4356 0.075555
1 to 10 141591 -1.0977 0.136170
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-15_10:31
Bits used No. missing words z-score p-value
28 to 32 142554 2.1853 0.985567
27 to 31 142306 1.3446 0.910630
26 to 30 141854 -0.1876 0.425611
25 to 29 142009 0.3379 0.632267
24 to 28 142106 0.6667 0.747511
23 to 27 142302 1.3311 0.908419
22 to 26 141375 -1.8113 0.035048
21 to 25 142310 1.3582 0.912800
20 to 24 141693 -0.7333 0.231681
19 to 23 142220 1.0531 0.853857
18 to 22 141556 -1.1977 0.115511
17 to 21 141876 -0.1130 0.455022
16 to 20 142296 1.3107 0.905028
15 to 19 142234 1.1006 0.864459
14 to 18 141856 -0.1808 0.428270
13 to 17 141626 -0.9604 0.168417
12 to 16 142057 0.5006 0.691665
11 to 15 141796 -0.3842 0.350426
10 to 14 141786 -0.4181 0.337949
9 to 13 141653 -0.8689 0.192447
8 to 12 142081 0.5819 0.719694
7 to 11 141923 0.0463 0.518480
6 to 10 142179 0.9141 0.819677
5 to 9 141628 -0.9537 0.170128
4 to 8 141954 0.1514 0.560179
3 to 7 141976 0.2260 0.589399
2 to 6 142112 0.6870 0.753964
1 to 5 141999 0.3040 0.619423
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-15_10:31
Bits used No. missing words z-score p-value
31 to 32 141563 -1.0216 0.153480
30 to 31 141458 -1.3314 0.091536
29 to 30 142059 0.4415 0.670576
28 to 29 142064 0.4563 0.675896
27 to 28 141508 -1.1839 0.118233
26 to 27 141951 0.1229 0.548915
25 to 26 141649 -0.7679 0.221263
24 to 25 142116 0.6096 0.728952
23 to 24 141879 -0.0895 0.464355
22 to 23 141865 -0.1308 0.447980
21 to 22 141887 -0.0659 0.473741
20 to 21 141963 0.1583 0.562897
19 to 20 142740 2.4504 0.992864
18 to 19 142345 1.2852 0.900632
17 to 18 141354 -1.6381 0.050696
16 to 17 142598 2.0315 0.978897
15 to 16 141177 -2.1603 0.015376
14 to 15 141931 0.0639 0.525484
13 to 14 141609 -0.8859 0.187828
12 to 13 142508 1.7660 0.961301
11 to 12 142036 0.3737 0.645671
10 to 11 141506 -1.1898 0.117070
9 to 10 141795 -0.3373 0.367962
8 to 9 142105 0.5772 0.718097
7 to 8 142163 0.7483 0.772857
6 to 7 141844 -0.1927 0.423592
5 to 6 142262 1.0403 0.850905
4 to 5 142158 0.7335 0.768385
3 to 4 141703 -0.6086 0.271381
2 to 3 141254 -1.9331 0.026610
1 to 2 142107 0.5831 0.720086
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-15_10:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2505.97 0.084 0.533621
Test results for specific bytes for dh-ranFile-2018-06-15_10:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2459.28 -0.576 0.282348
2 to 9 2549.50 0.700 0.758044
3 to 10 2607.81 1.525 0.936337
4 to 11 2412.71 -1.234 0.108519
5 to 12 2434.64 -0.924 0.177642
6 to 13 2466.91 -0.468 0.319892
7 to 14 2432.19 -0.959 0.168789
8 to 15 2632.72 1.877 0.969741
9 to 16 2496.43 -0.050 0.479880
10 to 17 2556.60 0.800 0.788288
11 to 18 2470.29 -0.420 0.337183
12 to 19 2456.52 -0.615 0.269307
13 to 20 2444.52 -0.785 0.216351
14 to 21 2583.86 1.186 0.882181
15 to 22 2527.52 0.389 0.651427
16 to 23 2439.94 -0.849 0.197817
17 to 24 2514.55 0.206 0.581519
18 to 25 2574.64 1.056 0.854426
19 to 26 2475.33 -0.349 0.363597
20 to 27 2408.03 -1.301 0.096689
21 to 28 2499.61 -0.006 0.497799
22 to 29 2501.52 0.021 0.508569
23 to 30 2546.08 0.652 0.742706
24 to 31 2375.44 -1.762 0.039068
25 to 32 2601.42 1.434 0.924259
CDPARK for dh-ranFile-2018-06-15_10:31: 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
3514 -0.4110 0.340551
3503 -0.9132 0.180558
3510 -0.5936 0.276387
3543 0.9132 0.819442
3520 -0.1370 0.445521
3502 -0.9589 0.168804
3556 1.5068 0.934075
3517 -0.2740 0.392053
3536 0.5936 0.723613
3557 1.5525 0.939730
Square side=100, avg. no. parked=3525.80 sample std.=19.68
p-value of the KSTEST for those 10 p-values: 0.827658
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-15_10:31
0.5789,0.3502,0.1913,0.5319,0.3765,0.4527,0.6254,0.6514,0.0633,0.8635,
The KS test for those 10 p-values: 0.732245
The 3DSPHERES test for dh-ranFile-2018-06-15_10:31
sample no r^3 equiv. uni.
1 38.517 0.723041
2 2.048 0.065982
3 8.044 0.235186
4 31.673 0.652078
5 12.211 0.334379
6 76.768 0.922614
7 48.185 0.799342
8 56.000 0.845360
9 13.060 0.352949
10 21.163 0.506112
11 0.227 0.007529
12 24.716 0.561264
13 7.469 0.220395
14 37.875 0.717050
15 28.380 0.611704
16 1.804 0.058353
17 14.358 0.380350
18 14.324 0.379642
19 1.055 0.034569
20 42.179 0.754873
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.687194
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-15_10:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -1.2 1.8 -1.1 1.0 -0.4
0.1 0.2 -0.3 1.2 -1.7 1.3
-0.2 0.7 0.3 0.7 -1.8 -0.6
-0.4 -0.5 -1.1 0.9 1.0 0.9
-0.1 -0.8 0.4 -0.5 0.4 2.1
-1.0 0.3 -0.4 -0.5 -0.1 1.3
2.1 -0.1 -0.8 1.0 -0.6 1.0
-0.1
Chi-square with 42 degrees of freedom:38.583135
z-score=-0.372811, p-value=0.378241
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-15_10:31
Test no p-value
1 0.547069
2 0.162322
3 0.318456
4 0.517194
5 0.052089
6 0.001483
7 0.937287
8 0.146566
9 0.570397
10 0.126350
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.078098
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-15_10:31:
(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 66757 0.12 66502 0.41
3 25000.00 24845 0.96 25202 1.63
4 6666.67 6694 0.11 6588 0.93
5 1388.89 1438 1.74 1447 2.43
6 238.10 235 0.04 227 0.52
7 34.72 26 2.19 28 1.30
8 4.96 4 0.19 5 0.00
p=0.49999 p=0.69871
Number of rngs required: 687505, p-value: 0.149
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-15_10:31
No. of wins: Observed Expected
98798 98585.9
z-score= 0.949, pvalue=0.82864
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66757 66666.7 0.122 0.122
2 37423 37654.3 1.421 1.543
3 26980 26954.7 0.024 1.567
4 19358 19313.5 0.103 1.670
5 13755 13851.4 0.671 2.341
6 10085 9943.5 2.012 4.353
7 7147 7145.0 0.001 4.354
8 5232 5139.1 1.680 6.034
9 3684 3699.9 0.068 6.102
10 2653 2666.3 0.066 6.169
11 1850 1923.3 2.796 8.964
12 1413 1388.7 0.424 9.388
13 986 1003.7 0.313 9.701
14 736 726.1 0.134 9.835
15 583 525.8 6.214 16.049
16 350 381.2 2.546 18.595
17 292 276.5 0.864 19.459
18 206 200.8 0.133 19.592
19 142 146.0 0.109 19.701
20 98 106.2 0.635 20.337
21 270 287.1 1.020 21.357
Chisq= 21.36 for 20 degrees of freedom, p= 0.62359
SUMMARY of craptest
p-value for no. of wins: 0.828644
p-value for throws/game: 0.623589
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-15_10:31
No. of wins: Observed Expected
98127 98585.9
z-score=-2.052, pvalue=0.02007
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66480 66666.7 0.523 0.523
2 37896 37654.3 1.551 2.074
3 26831 26954.7 0.568 2.642
4 19379 19313.5 0.222 2.864
5 13772 13851.4 0.455 3.320
6 9903 9943.5 0.165 3.485
7 7256 7145.0 1.724 5.209
8 5109 5139.1 0.176 5.384
9 3734 3699.9 0.315 5.699
10 2725 2666.3 1.292 6.992
11 1901 1923.3 0.259 7.251
12 1361 1388.7 0.554 7.805
13 1014 1003.7 0.105 7.911
14 734 726.1 0.085 7.996
15 507 525.8 0.675 8.670
16 365 381.2 0.684 9.355
17 293 276.5 0.980 10.335
18 194 200.8 0.232 10.567
19 113 146.0 7.453 18.019
20 114 106.2 0.571 18.590
21 319 287.1 3.541 22.131
Chisq= 22.13 for 20 degrees of freedom, p= 0.66656
SUMMARY of craptest
p-value for no. of wins: 0.020071
p-value for throws/game: 0.666564
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0001,0.0015,0.0075,0.0149,0.0153,0.0154,0.0201,0.0266,0.0346,0.0350,
0.0391,0.0507,0.0521,0.0544,0.0584,0.0633,0.0660,0.0740,0.0756,0.0781,
0.0873,0.0878,0.0902,0.0915,0.0967,0.1013,0.1085,0.1155,0.1171,0.1182,
0.1253,0.1264,0.1273,0.1362,0.1363,0.1403,0.1466,0.1489,0.1505,0.1535,
0.1623,0.1659,0.1684,0.1688,0.1688,0.1701,0.1705,0.1721,0.1776,0.1783,
0.1806,0.1878,0.1895,0.1913,0.1916,0.1924,0.1950,0.1978,0.1996,0.2019,
0.2100,0.2164,0.2204,0.2213,0.2222,0.2317,0.2352,0.2373,0.2420,0.2437,
0.2592,0.2693,0.2712,0.2714,0.2746,0.2761,0.2764,0.2773,0.2823,0.2904,
0.2977,0.3185,0.3193,0.3199,0.3218,0.3243,0.3344,0.3372,0.3379,0.3406,
0.3419,0.3502,0.3504,0.3529,0.3579,0.3597,0.3636,0.3680,0.3742,0.3759,
0.3765,0.3782,0.3796,0.3804,0.3839,0.3843,0.3909,0.3921,0.3922,0.4146,
0.4149,0.4236,0.4243,0.4256,0.4283,0.4348,0.4398,0.4443,0.4455,0.4480,
0.4506,0.4527,0.4550,0.4597,0.4643,0.4644,0.4729,0.4737,0.4799,0.4844,
0.4978,0.5000,0.5038,0.5061,0.5086,0.5111,0.5172,0.5185,0.5205,0.5255,
0.5302,0.5319,0.5336,0.5369,0.5399,0.5471,0.5489,0.5530,0.5602,0.5613,
0.5616,0.5629,0.5630,0.5634,0.5649,0.5704,0.5708,0.5789,0.5815,0.5854,
0.5894,0.5899,0.5932,0.5936,0.6117,0.6153,0.6194,0.6215,0.6236,0.6254,
0.6286,0.6323,0.6323,0.6385,0.6402,0.6457,0.6514,0.6514,0.6521,0.6526,
0.6530,0.6533,0.6537,0.6649,0.6654,0.6666,0.6706,0.6759,0.6795,0.6872,
0.6917,0.6945,0.6987,0.7059,0.7108,0.7171,0.7181,0.7197,0.7201,0.7230,
0.7236,0.7290,0.7322,0.7358,0.7401,0.7427,0.7475,0.7488,0.7540,0.7549,
0.7576,0.7580,0.7684,0.7729,0.7769,0.7883,0.7993,0.8131,0.8138,0.8151,
0.8194,0.8197,0.8277,0.8286,0.8411,0.8428,0.8444,0.8454,0.8509,0.8538,
0.8539,0.8542,0.8544,0.8595,0.8635,0.8645,0.8813,0.8817,0.8822,0.8847,
0.8859,0.8979,0.9006,0.9044,0.9050,0.9084,0.9106,0.9128,0.9168,0.9226,
0.9243,0.9308,0.9325,0.9341,0.9358,0.9363,0.9373,0.9397,0.9449,0.9539,
0.9541,0.9613,0.9615,0.9697,0.9789,0.9856,0.9929,0.9969,0.9972,
Overall p-value after applying KStest on 269 p-values = 0.983473
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.