RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-28_21:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.53 17.2689 0.563701
2 to 25 15.81 12.0963 0.205730
3 to 26 15.81 16.7129 0.526025
4 to 27 15.73 22.0690 0.817920
5 to 28 15.84 18.9350 0.667726
6 to 29 15.83 21.0444 0.775687
7 to 30 15.54 25.3310 0.912458
8 to 31 15.55 22.0791 0.818303
9 to 32 15.87 13.8156 0.319889
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.313348
Tough bday spacings test for dh-ranFile-2018-06-28_21:31: 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 5 31 73 124 89 68 43 36 17 9 5
(O-E)^2/E 1.9 0.9 0.0 7.1 0.8 1.3 1.6 1.3 0.3 0.9 0.2
Birthday Spacings: Sum(O-E)^2/E= 16.200, p= 0.906
RESULTS OF GCD FOR dh-ranFile-2018-06-28_21:31
Euclid's algorithm:
p-value, steps to gcd: 0.890692
p-value, dist. of gcd's: 0.977629
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-28_21:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.605 0.952 0.928 0.638 0.968 0.942 0.771 0.824
Bits 8 to 15---> 0.950 0.237 0.656 0.721 0.539 0.288 0.790 0.275
Bits 16 to 23---> 0.163 0.547 0.910 0.806 0.003 0.306 0.596 0.627
Bits 24 to 31---> 0.413 0.983 0.531 0.214 0.496 0.296 0.888 0.964
KS test for the above 32 p values: 0.978
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-28_21:31,
p-values for 5 runs: 0.2441, 0.8171, 0.8399, 0.5919, 0.8528
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-28_21:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 208 211.4 0.055 0.055
r= 29 5035 5134.0 1.909 1.965
r= 30 23361 23103.0 2.880 4.845
r= 31 11396 11551.5 2.094 6.939
chi-square = 6.939 with df = 3; p-value = 0.926
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-28_21:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 227 211.4 1.148 1.148
r= 30 5213 5134.0 1.215 2.364
r= 31 22980 23103.0 0.655 3.019
r= 32 11580 11551.5 0.070 3.089
chi-square = 3.089 with df = 3; p-value = 0.622
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-28_21:31
b-rank test for bits 1 to 8, p=0.80519
b-rank test for bits 2 to 9, p=0.07107
b-rank test for bits 3 to 10, p=0.40344
b-rank test for bits 4 to 11, p=0.35623
b-rank test for bits 5 to 12, p=0.33660
b-rank test for bits 6 to 13, p=0.95424
b-rank test for bits 7 to 14, p=0.02433
b-rank test for bits 8 to 15, p=0.79685
b-rank test for bits 9 to 16, p=0.14027
b-rank test for bits 10 to 17, p=0.33500
b-rank test for bits 11 to 18, p=0.23346
b-rank test for bits 12 to 19, p=0.01908
b-rank test for bits 13 to 20, p=0.26747
b-rank test for bits 14 to 21, p=0.62364
b-rank test for bits 15 to 22, p=0.31453
b-rank test for bits 16 to 23, p=0.41051
b-rank test for bits 17 to 24, p=0.08468
b-rank test for bits 18 to 25, p=0.66518
b-rank test for bits 19 to 26, p=0.79011
b-rank test for bits 20 to 27, p=0.37350
b-rank test for bits 21 to 28, p=0.26061
b-rank test for bits 22 to 29, p=0.78962
b-rank test for bits 23 to 30, p=0.08040
b-rank test for bits 24 to 31, p=0.57710
b-rank test for bits 25 to 32, p=0.29220
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 = 0.119103
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-28_21:31
(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 141126 -1.83 0.033609
2 141286 -1.46 0.072644
3 141717 -0.45 0.326583
4 142029 0.28 0.610109
5 141699 -0.49 0.311563
6 143093 2.77 0.997159
7 143103 2.79 0.997356
8 141684 -0.53 0.299280
9 142005 0.22 0.588438
10 141744 -0.39 0.349643
11 142928 2.38 0.991345
12 141666 -0.57 0.284838
13 141862 -0.11 0.455973
14 141426 -1.13 0.129391
15 142366 1.07 0.857011
16 141524 -0.90 0.183979
17 141358 -1.29 0.098846
18 141278 -1.48 0.070097
19 142324 0.97 0.833691
20 142930 2.38 0.991454
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-28_21:31
Bits used No. missing words z-score p-value
23 to 32 141738 -0.5908 0.277330
22 to 31 141617 -1.0080 0.156719
21 to 30 142004 0.3264 0.627957
20 to 29 141584 -1.1218 0.130968
19 to 28 141756 -0.5287 0.298498
18 to 27 141621 -0.9942 0.160053
17 to 26 141822 -0.3011 0.381655
16 to 25 141565 -1.1873 0.117546
15 to 24 142327 1.4402 0.925100
14 to 23 142062 0.5264 0.700712
13 to 22 141787 -0.4218 0.336575
12 to 21 141652 -0.8873 0.187447
11 to 20 141351 -1.9253 0.027097
10 to 19 141770 -0.4804 0.315454
9 to 18 142060 0.5196 0.698312
8 to 17 141593 -1.0908 0.137682
7 to 16 141492 -1.4391 0.075066
6 to 15 141621 -0.9942 0.160053
5 to 14 141982 0.2506 0.598933
4 to 13 142202 1.0092 0.843562
3 to 12 142057 0.5092 0.694696
2 to 11 142673 2.6333 0.995773
1 to 10 141882 -0.0942 0.462459
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-28_21:31
Bits used No. missing words z-score p-value
28 to 32 141755 -0.5232 0.300434
27 to 31 141915 0.0192 0.507667
26 to 30 141793 -0.3943 0.346665
25 to 29 141993 0.2836 0.611652
24 to 28 142218 1.0463 0.852298
23 to 27 142118 0.7074 0.760327
22 to 26 142309 1.3548 0.912262
21 to 25 141619 -0.9842 0.162516
20 to 24 141991 0.2768 0.609051
19 to 23 142042 0.4497 0.673547
18 to 22 142140 0.7819 0.782873
17 to 21 141671 -0.8079 0.209575
16 to 20 141876 -0.1130 0.455022
15 to 19 141441 -1.5876 0.056193
14 to 18 141719 -0.6452 0.259403
13 to 17 141943 0.1141 0.545435
12 to 16 141876 -0.1130 0.455022
11 to 15 142387 1.6192 0.947300
10 to 14 141675 -0.7943 0.213499
9 to 13 142006 0.3277 0.628429
8 to 12 141507 -1.3638 0.086310
7 to 11 141796 -0.3842 0.350426
6 to 10 141943 0.1141 0.545435
5 to 9 142168 0.8768 0.809715
4 to 8 142059 0.5074 0.694048
3 to 7 141506 -1.3672 0.085778
2 to 6 141572 -1.1435 0.126417
1 to 5 141714 -0.6621 0.253942
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-28_21:31
Bits used No. missing words z-score p-value
31 to 32 141877 -0.0954 0.462011
30 to 31 142125 0.6362 0.737675
29 to 30 141817 -0.2724 0.392673
28 to 29 141843 -0.1957 0.422437
27 to 28 141332 -1.7030 0.044280
26 to 27 142591 2.0108 0.977828
25 to 26 142210 0.8869 0.812442
24 to 25 141955 0.1347 0.553583
23 to 24 142023 0.3353 0.631304
22 to 23 140908 -2.9538 0.001570
21 to 22 141984 0.2203 0.587168
20 to 21 141457 -1.3343 0.091052
19 to 20 141626 -0.8358 0.201639
18 to 19 142142 0.6863 0.753751
17 to 18 141956 0.1377 0.554749
16 to 17 141989 0.2350 0.592901
15 to 16 142023 0.3353 0.631304
14 to 15 141614 -0.8712 0.191828
13 to 14 141751 -0.4671 0.320232
12 to 13 142021 0.3294 0.629077
11 to 12 142020 0.3265 0.627962
10 to 11 142042 0.3914 0.652233
9 to 10 142429 1.5329 0.937356
8 to 9 142069 0.4710 0.681181
7 to 8 142115 0.6067 0.727974
6 to 7 142380 1.3884 0.917493
5 to 6 141895 -0.0423 0.483141
4 to 5 142205 0.8722 0.808446
3 to 4 141664 -0.7237 0.234629
2 to 3 142079 0.5005 0.691639
1 to 2 141452 -1.3491 0.088660
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-28_21:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2686.59 2.639 0.995840
Test results for specific bytes for dh-ranFile-2018-06-28_21:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2497.48 -0.036 0.485794
2 to 9 2502.71 0.038 0.515260
3 to 10 2481.47 -0.262 0.396630
4 to 11 2553.24 0.753 0.774267
5 to 12 2395.46 -1.478 0.069641
6 to 13 2482.72 -0.244 0.403458
7 to 14 2479.29 -0.293 0.384814
8 to 15 2504.01 0.057 0.522594
9 to 16 2543.35 0.613 0.730098
10 to 17 2622.52 1.733 0.958429
11 to 18 2541.48 0.587 0.721257
12 to 19 2527.83 0.394 0.653050
13 to 20 2593.99 1.329 0.908101
14 to 21 2604.58 1.479 0.930436
15 to 22 2472.41 -0.390 0.348213
16 to 23 2462.16 -0.535 0.296277
17 to 24 2614.35 1.617 0.947077
18 to 25 2611.18 1.572 0.942070
19 to 26 2511.80 0.167 0.566286
20 to 27 2476.25 -0.336 0.368496
21 to 28 2431.74 -0.965 0.167189
22 to 29 2472.80 -0.385 0.350235
23 to 30 2596.10 1.359 0.912939
24 to 31 2551.88 0.734 0.768416
25 to 32 2433.79 -0.936 0.174541
CDPARK for dh-ranFile-2018-06-28_21:31: 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
3515 -0.3653 0.357445
3513 -0.4566 0.323972
3500 -1.0502 0.146807
3519 -0.1826 0.427537
3524 0.0457 0.518210
3516 -0.3196 0.374623
3571 2.1918 0.985802
3502 -0.9589 0.168804
3542 0.8676 0.807188
3554 1.4155 0.921543
Square side=100, avg. no. parked=3525.60 sample std.=21.81
p-value of the KSTEST for those 10 p-values: 0.757625
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-28_21:31
0.1931,0.9180,0.7665,0.8170,0.8073,0.9143,0.0142,0.7296,0.6070,0.2691,
The KS test for those 10 p-values: 0.263615
The 3DSPHERES test for dh-ranFile-2018-06-28_21:31
sample no r^3 equiv. uni.
1 53.431 0.831536
2 95.655 0.958766
3 31.896 0.654653
4 24.932 0.564421
5 81.295 0.933453
6 11.255 0.312816
7 4.562 0.141070
8 47.365 0.793784
9 8.475 0.246093
10 14.130 0.375621
11 6.743 0.201287
12 11.075 0.308698
13 25.006 0.565494
14 5.451 0.166146
15 4.781 0.147307
16 45.733 0.782256
17 40.182 0.737997
18 2.543 0.081260
19 12.721 0.345596
20 39.759 0.734273
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.937388
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-28_21:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 2.2 -0.8 1.6 -0.2 1.7
0.5 0.0 -1.3 -1.4 -1.3 0.1
0.6 1.3 0.7 -0.7 -0.1 2.4
0.1 -0.9 -0.8 -0.4 -0.4 -1.1
2.5 -1.5 0.2 0.5 -0.2 -2.7
0.9 -0.9 1.5 -0.8 0.2 -1.0
0.7 -0.1 0.5 -0.1 -1.3 0.0
-0.1
Chi-square with 42 degrees of freedom:53.095654
z-score=1.210635, p-value=0.882836
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-28_21:31
Test no p-value
1 0.004666
2 0.229910
3 0.032152
4 0.102386
5 0.641382
6 0.241522
7 0.834010
8 0.919749
9 0.825196
10 0.390595
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.318170
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-28_21:31:
(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 66562 0.16 66485 0.50
3 25000.00 25082 0.27 25171 1.17
4 6666.67 6681 0.03 6734 0.68
5 1388.89 1378 0.09 1323 3.13
6 238.10 251 0.70 246 0.26
7 34.72 42 1.53 38 0.31
8 4.96 3 0.77 2 1.77
p=0.26268 p=0.74759
Number of rngs required: 690745, p-value: 0.998
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-28_21:31
No. of wins: Observed Expected
98936 98585.9
z-score= 1.566, pvalue=0.94133
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66641 66666.7 0.010 0.010
2 37769 37654.3 0.349 0.359
3 26890 26954.7 0.155 0.515
4 19058 19313.5 3.379 3.894
5 13888 13851.4 0.097 3.990
6 10007 9943.5 0.405 4.395
7 7185 7145.0 0.224 4.619
8 5272 5139.1 3.438 8.057
9 3706 3699.9 0.010 8.067
10 2657 2666.3 0.032 8.100
11 1874 1923.3 1.265 9.365
12 1385 1388.7 0.010 9.375
13 979 1003.7 0.609 9.984
14 759 726.1 1.487 11.471
15 510 525.8 0.477 11.947
16 399 381.2 0.836 12.783
17 279 276.5 0.022 12.805
18 187 200.8 0.952 13.758
19 150 146.0 0.110 13.868
20 101 106.2 0.256 14.124
21 304 287.1 0.993 15.117
Chisq= 15.12 for 20 degrees of freedom, p= 0.23034
SUMMARY of craptest
p-value for no. of wins: 0.941330
p-value for throws/game: 0.230341
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-28_21:31
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 66861 66666.7 0.566 0.566
2 37763 37654.3 0.314 0.880
3 26912 26954.7 0.068 0.948
4 19341 19313.5 0.039 0.987
5 13934 13851.4 0.492 1.479
6 9932 9943.5 0.013 1.493
7 7037 7145.0 1.633 3.126
8 4999 5139.1 3.818 6.944
9 3662 3699.9 0.388 7.331
10 2730 2666.3 1.522 8.853
11 1859 1923.3 2.152 11.005
12 1367 1388.7 0.340 11.345
13 988 1003.7 0.246 11.591
14 701 726.1 0.870 12.462
15 544 525.8 0.627 13.089
16 381 381.2 0.000 13.089
17 265 276.5 0.482 13.571
18 185 200.8 1.248 14.819
19 137 146.0 0.553 15.372
20 110 106.2 0.135 15.506
21 292 287.1 0.083 15.590
Chisq= 15.59 for 20 degrees of freedom, p= 0.25826
SUMMARY of craptest
p-value for no. of wins: 0.443346
p-value for throws/game: 0.258264
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0016,0.0034,0.0047,0.0142,0.0191,0.0243,0.0271,0.0322,0.0336,0.0443,
0.0562,0.0696,0.0701,0.0711,0.0726,0.0751,0.0804,0.0813,0.0847,0.0858,
0.0863,0.0887,0.0911,0.0988,0.1024,0.1175,0.1191,0.1264,0.1294,0.1310,
0.1377,0.1403,0.1411,0.1468,0.1473,0.1567,0.1601,0.1601,0.1625,0.1630,
0.1661,0.1672,0.1688,0.1745,0.1840,0.1874,0.1918,0.1931,0.2013,0.2016,
0.2057,0.2096,0.2135,0.2138,0.2299,0.2303,0.2335,0.2346,0.2367,0.2415,
0.2441,0.2461,0.2539,0.2583,0.2594,0.2606,0.2627,0.2636,0.2675,0.2691,
0.2753,0.2773,0.2848,0.2883,0.2922,0.2963,0.2963,0.2985,0.2993,0.3004,
0.3056,0.3087,0.3116,0.3128,0.3133,0.3145,0.3155,0.3182,0.3199,0.3202,
0.3240,0.3266,0.3350,0.3366,0.3366,0.3456,0.3467,0.3482,0.3496,0.3502,
0.3504,0.3562,0.3574,0.3685,0.3735,0.3746,0.3756,0.3817,0.3848,0.3906,
0.3927,0.3966,0.4034,0.4035,0.4105,0.4127,0.4224,0.4275,0.4433,0.4550,
0.4550,0.4560,0.4620,0.4625,0.4831,0.4858,0.4962,0.5077,0.5153,0.5182,
0.5226,0.5260,0.5306,0.5388,0.5454,0.5454,0.5471,0.5536,0.5547,0.5637,
0.5644,0.5655,0.5663,0.5771,0.5872,0.5884,0.5919,0.5929,0.5963,0.5989,
0.6054,0.6070,0.6091,0.6101,0.6117,0.6219,0.6236,0.6267,0.6280,0.6280,
0.6284,0.6291,0.6313,0.6313,0.6379,0.6414,0.6522,0.6530,0.6547,0.6559,
0.6652,0.6677,0.6735,0.6812,0.6916,0.6940,0.6947,0.6983,0.7007,0.7207,
0.7213,0.7280,0.7296,0.7301,0.7343,0.7377,0.7380,0.7476,0.7538,0.7576,
0.7603,0.7665,0.7684,0.7709,0.7743,0.7757,0.7823,0.7829,0.7896,0.7896,
0.7901,0.7938,0.7968,0.8052,0.8063,0.8072,0.8073,0.8084,0.8097,0.8124,
0.8170,0.8171,0.8179,0.8183,0.8245,0.8252,0.8315,0.8337,0.8340,0.8399,
0.8436,0.8523,0.8528,0.8570,0.8828,0.8881,0.8907,0.9060,0.9081,0.9104,
0.9123,0.9125,0.9129,0.9143,0.9175,0.9180,0.9197,0.9215,0.9251,0.9261,
0.9279,0.9304,0.9335,0.9374,0.9374,0.9413,0.9420,0.9421,0.9471,0.9473,
0.9497,0.9519,0.9542,0.9584,0.9588,0.9637,0.9685,0.9776,0.9778,0.9780,
0.9830,0.9858,0.9913,0.9915,0.9958,0.9958,0.9972,0.9974,0.9975,
Overall p-value after applying KStest on 269 p-values = 0.131748
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.