RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-29_16:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.79 15.2791 0.424614
2 to 25 15.52 16.3606 0.501570
3 to 26 15.70 19.9284 0.722090
4 to 27 15.55 19.0902 0.676618
5 to 28 15.75 17.6231 0.587018
6 to 29 15.68 14.4798 0.367107
7 to 30 15.68 15.6179 0.448935
8 to 31 15.76 24.5103 0.893781
9 to 32 15.64 18.0667 0.615357
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.248693
Tough bday spacings test for dh-ranFile-2018-06-29_16:31: 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 12 43 75 95 96 85 43 24 19 6 2
(O-E)^2/E 0.9 1.1 0.0 0.1 0.0 0.6 1.6 1.1 1.1 0.1 1.0
Birthday Spacings: Sum(O-E)^2/E= 7.686, p= 0.341
RESULTS OF GCD FOR dh-ranFile-2018-06-29_16:31
Euclid's algorithm:
p-value, steps to gcd: 0.530658
p-value, dist. of gcd's: 0.331602
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-29_16:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.235 0.598 0.628 0.301 0.504 0.621 0.763 0.821
Bits 8 to 15---> 0.674 0.191 0.288 0.469 0.908 0.043 0.020 0.143
Bits 16 to 23---> 0.295 0.397 0.799 0.588 0.966 0.845 0.421 0.885
Bits 24 to 31---> 0.571 0.125 0.842 0.885 0.550 0.989 0.539 0.344
KS test for the above 32 p values: 0.183
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-29_16:31,
p-values for 5 runs: 0.4942, 0.5068, 0.3479, 0.9226, 0.5688
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-29_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 232 211.4 2.004 2.004
r= 29 5188 5134.0 0.568 2.571
r= 30 23104 23103.0 0.000 2.571
r= 31 11476 11551.5 0.494 3.065
chi-square = 3.065 with df = 3; p-value = 0.618
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-29_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 219 211.4 0.272 0.272
r= 30 5108 5134.0 0.132 0.404
r= 31 23124 23103.0 0.019 0.423
r= 32 11549 11551.5 0.001 0.423
chi-square = 0.423 with df = 3; p-value = 0.065
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-29_16:31
b-rank test for bits 1 to 8, p=0.71934
b-rank test for bits 2 to 9, p=0.62346
b-rank test for bits 3 to 10, p=0.82845
b-rank test for bits 4 to 11, p=0.14836
b-rank test for bits 5 to 12, p=0.12280
b-rank test for bits 6 to 13, p=0.09048
b-rank test for bits 7 to 14, p=0.55210
b-rank test for bits 8 to 15, p=0.48651
b-rank test for bits 9 to 16, p=0.76465
b-rank test for bits 10 to 17, p=0.38473
b-rank test for bits 11 to 18, p=0.47538
b-rank test for bits 12 to 19, p=0.54771
b-rank test for bits 13 to 20, p=0.42511
b-rank test for bits 14 to 21, p=0.84704
b-rank test for bits 15 to 22, p=0.66526
b-rank test for bits 16 to 23, p=0.79616
b-rank test for bits 17 to 24, p=0.82270
b-rank test for bits 18 to 25, p=0.13012
b-rank test for bits 19 to 26, p=0.29257
b-rank test for bits 20 to 27, p=0.22394
b-rank test for bits 21 to 28, p=0.24190
b-rank test for bits 22 to 29, p=0.10792
b-rank test for bits 23 to 30, p=0.10114
b-rank test for bits 24 to 31, p=0.93114
b-rank test for bits 25 to 32, p=0.88175
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 = 0.875591
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-29_16:31
(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 142145 0.55 0.709057
2 141489 -0.98 0.163030
3 141780 -0.30 0.381260
4 141488 -0.98 0.162456
5 142121 0.49 0.689543
6 142016 0.25 0.598408
7 143062 2.69 0.996461
8 142168 0.60 0.727201
9 142473 1.32 0.906078
10 141761 -0.35 0.364459
11 141819 -0.21 0.416424
12 142160 0.59 0.720954
13 142397 1.14 0.872735
14 142005 0.22 0.588438
15 141527 -0.89 0.185850
16 142116 0.48 0.685407
17 142004 0.22 0.587528
18 141853 -0.13 0.447646
19 141833 -0.18 0.429228
20 141749 -0.37 0.353978
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-29_16:31
Bits used No. missing words z-score p-value
23 to 32 141966 0.1954 0.577466
22 to 31 142283 1.2885 0.901217
21 to 30 142132 0.7678 0.778705
20 to 29 142399 1.6885 0.954344
19 to 28 142097 0.6471 0.741229
18 to 27 142154 0.8437 0.800579
17 to 26 142608 2.4092 0.992006
16 to 25 141741 -0.5804 0.280806
15 to 24 142005 0.3299 0.629261
14 to 23 142238 1.1333 0.871465
13 to 22 141293 -2.1253 0.016782
12 to 21 142109 0.6885 0.754436
11 to 20 141681 -0.7873 0.215540
10 to 19 142248 1.1678 0.878562
9 to 18 141567 -1.1804 0.118911
8 to 17 141948 0.1333 0.553040
7 to 16 141708 -0.6942 0.243765
6 to 15 142288 1.3058 0.904183
5 to 14 141820 -0.3080 0.379028
4 to 13 142051 0.4885 0.687408
3 to 12 142005 0.3299 0.629261
2 to 11 141941 0.1092 0.543481
1 to 10 141610 -1.0322 0.150996
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-29_16:31
Bits used No. missing words z-score p-value
28 to 32 142032 0.4158 0.661233
27 to 31 142350 1.4938 0.932386
26 to 30 141765 -0.4893 0.312331
25 to 29 141659 -0.8486 0.198059
24 to 28 141557 -1.1943 0.116173
23 to 27 142220 1.0531 0.853857
22 to 26 141456 -1.5367 0.062182
21 to 25 141440 -1.5909 0.055811
20 to 24 142027 0.3989 0.655010
19 to 23 141958 0.1650 0.565521
18 to 22 141692 -0.7367 0.230649
17 to 21 142055 0.4938 0.689275
16 to 20 141842 -0.2282 0.409731
15 to 19 141929 0.0667 0.526581
14 to 18 142152 0.8226 0.794635
13 to 17 142307 1.3480 0.911176
12 to 16 141440 -1.5909 0.055811
11 to 15 141924 0.0497 0.519831
10 to 14 142055 0.4938 0.689275
9 to 13 142043 0.4531 0.674768
8 to 12 142027 0.3989 0.655010
7 to 11 142299 1.3209 0.906735
6 to 10 141847 -0.2113 0.416331
5 to 9 141925 0.0531 0.521181
4 to 8 141499 -1.3909 0.082120
3 to 7 142451 1.8362 0.966834
2 to 6 142016 0.3616 0.641172
1 to 5 141677 -0.7876 0.215477
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-29_16:31
Bits used No. missing words z-score p-value
31 to 32 141925 0.0462 0.518434
30 to 31 141107 -2.3668 0.008972
29 to 30 142018 0.3206 0.625728
28 to 29 142330 1.2409 0.892681
27 to 28 141506 -1.1898 0.117070
26 to 27 142380 1.3884 0.917493
25 to 26 142316 1.1996 0.884856
24 to 25 141919 0.0285 0.511378
23 to 24 141516 -1.1603 0.122970
22 to 23 141585 -0.9567 0.169353
21 to 22 141477 -1.2753 0.101100
20 to 21 142361 1.3324 0.908629
19 to 20 141639 -0.7974 0.212600
18 to 19 142437 1.5565 0.940211
17 to 18 142081 0.5064 0.693713
16 to 17 141989 0.2350 0.592901
15 to 16 142084 0.5153 0.696811
14 to 15 141411 -1.4700 0.070781
13 to 14 141982 0.2144 0.584869
12 to 13 142162 0.7453 0.771967
11 to 12 141497 -1.2163 0.111933
10 to 11 141967 0.1701 0.567541
9 to 10 142223 0.9253 0.822590
8 to 9 142001 0.2704 0.606579
7 to 8 141331 -1.7060 0.044005
6 to 7 142431 1.5388 0.938080
5 to 6 142361 1.3324 0.908629
4 to 5 142050 0.4150 0.660913
3 to 4 141992 0.2439 0.596332
2 to 3 142100 0.5624 0.713095
1 to 2 141420 -1.4435 0.074447
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-29_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2353.34 -2.074 0.019032
Test results for specific bytes for dh-ranFile-2018-06-29_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2425.37 -1.055 0.145619
2 to 9 2473.93 -0.369 0.356165
3 to 10 2481.21 -0.266 0.395236
4 to 11 2530.52 0.432 0.667001
5 to 12 2495.17 -0.068 0.472744
6 to 13 2543.67 0.618 0.731565
7 to 14 2415.38 -1.197 0.115711
8 to 15 2480.80 -0.271 0.393007
9 to 16 2581.15 1.148 0.874452
10 to 17 2569.01 0.976 0.835438
11 to 18 2327.20 -2.444 0.007267
12 to 19 2458.46 -0.587 0.278441
13 to 20 2348.86 -2.137 0.016283
14 to 21 2400.54 -1.407 0.079776
15 to 22 2564.31 0.910 0.818464
16 to 23 2518.26 0.258 0.601886
17 to 24 2549.59 0.701 0.758423
18 to 25 2367.40 -1.875 0.030379
19 to 26 2439.33 -0.858 0.195440
20 to 27 2504.80 0.068 0.527075
21 to 28 2464.17 -0.507 0.306195
22 to 29 2435.42 -0.913 0.180531
23 to 30 2534.07 0.482 0.685053
24 to 31 2564.48 0.912 0.819095
25 to 32 2700.99 2.842 0.997762
CDPARK for dh-ranFile-2018-06-29_16:31: 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
3524 0.0457 0.518210
3551 1.2785 0.899470
3506 -0.7763 0.218799
3528 0.2283 0.590298
3474 -2.2374 0.012629
3469 -2.4658 0.006836
3521 -0.0913 0.463617
3527 0.1826 0.572463
3546 1.0502 0.853193
3545 1.0046 0.842447
Square side=100, avg. no. parked=3519.10 sample std.=27.01
p-value of the KSTEST for those 10 p-values: 0.437256
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-29_16:31
0.0880,0.3792,0.6378,0.2439,0.3186,0.2008,0.3827,0.6532,0.8116,0.9102,
The KS test for those 10 p-values: 0.912202
The 3DSPHERES test for dh-ranFile-2018-06-29_16:31
sample no r^3 equiv. uni.
1 65.803 0.888466
2 9.610 0.274092
3 22.360 0.525422
4 9.764 0.277814
5 21.963 0.519105
6 7.268 0.215143
7 27.222 0.596428
8 23.149 0.537736
9 40.029 0.736655
10 74.505 0.916548
11 36.040 0.699207
12 24.119 0.552454
13 22.088 0.521108
14 2.981 0.094592
15 139.728 0.990511
16 56.468 0.847755
17 36.997 0.708647
18 16.182 0.416897
19 1.061 0.034762
20 32.841 0.665360
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.642268
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-29_16:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 0.5 1.8 0.8 0.7 1.5
-0.9 -1.7 0.7 0.1 -0.4 -2.0
0.8 -0.7 -0.6 0.5 -0.0 -2.2
1.0 2.6 0.6 -0.5 0.9 -1.4
0.2 -1.0 1.2 -0.5 0.9 1.0
-0.0 1.7 -0.0 -1.3 -0.4 0.6
0.3 -1.0 -0.8 -1.3 -0.6 1.0
-1.1
Chi-square with 42 degrees of freedom:48.579134
z-score=0.717842, p-value=0.774987
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-29_16:31
Test no p-value
1 0.002096
2 0.279942
3 0.473605
4 0.501263
5 0.094482
6 0.253522
7 0.513010
8 0.082264
9 0.401158
10 0.016126
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.008633
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-29_16:31:
(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 66714 0.03 66698 0.01
3 25000.00 24880 0.58 24936 0.16
4 6666.67 6773 1.70 6665 0.00
5 1388.89 1365 0.41 1418 0.61
6 238.10 237 0.01 242 0.06
7 34.72 27 1.72 38 0.31
8 4.96 3 0.77 2 1.77
p=0.48314 p=0.18235
Number of rngs required: 687726, p-value: 0.217
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-29_16:31
No. of wins: Observed Expected
99002 98585.9
z-score= 1.861, pvalue=0.96864
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66836 66666.7 0.430 0.430
2 37324 37654.3 2.898 3.328
3 26901 26954.7 0.107 3.435
4 19316 19313.5 0.000 3.435
5 14056 13851.4 3.022 6.457
6 10094 9943.5 2.277 8.733
7 7151 7145.0 0.005 8.738
8 5096 5139.1 0.361 9.099
9 3618 3699.9 1.811 10.911
10 2643 2666.3 0.204 11.114
11 1930 1923.3 0.023 11.138
12 1358 1388.7 0.680 11.818
13 1047 1003.7 1.867 13.685
14 711 726.1 0.316 14.000
15 541 525.8 0.437 14.438
16 338 381.2 4.885 19.323
17 261 276.5 0.873 20.196
18 197 200.8 0.073 20.269
19 144 146.0 0.027 20.296
20 116 106.2 0.901 21.197
21 322 287.1 4.239 25.436
Chisq= 25.44 for 20 degrees of freedom, p= 0.81475
SUMMARY of craptest
p-value for no. of wins: 0.968644
p-value for throws/game: 0.814751
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-29_16:31
No. of wins: Observed Expected
98279 98585.9
z-score=-1.372, pvalue=0.08496
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66298 66666.7 2.039 2.039
2 37816 37654.3 0.694 2.733
3 27069 26954.7 0.484 3.217
4 19200 19313.5 0.667 3.884
5 13797 13851.4 0.214 4.098
6 9957 9943.5 0.018 4.116
7 7164 7145.0 0.050 4.166
8 5257 5139.1 2.706 6.872
9 3772 3699.9 1.406 8.279
10 2732 2666.3 1.619 9.898
11 1982 1923.3 1.790 11.688
12 1353 1388.7 0.920 12.607
13 976 1003.7 0.765 13.373
14 741 726.1 0.304 13.677
15 505 525.8 0.826 14.502
16 359 381.2 1.287 15.790
17 276 276.5 0.001 15.791
18 206 200.8 0.133 15.924
19 159 146.0 1.160 17.084
20 99 106.2 0.490 17.574
21 282 287.1 0.091 17.665
Chisq= 17.67 for 20 degrees of freedom, p= 0.39057
SUMMARY of craptest
p-value for no. of wins: 0.084962
p-value for throws/game: 0.390567
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0021,0.0068,0.0073,0.0086,0.0090,0.0126,0.0161,0.0163,0.0168,0.0190,
0.0204,0.0304,0.0348,0.0431,0.0440,0.0558,0.0558,0.0622,0.0646,0.0708,
0.0744,0.0798,0.0821,0.0823,0.0850,0.0880,0.0905,0.0945,0.0946,0.1011,
0.1011,0.1079,0.1119,0.1157,0.1162,0.1171,0.1189,0.1228,0.1230,0.1250,
0.1301,0.1427,0.1456,0.1484,0.1510,0.1625,0.1630,0.1694,0.1805,0.1824,
0.1830,0.1858,0.1911,0.1954,0.1981,0.2008,0.2126,0.2151,0.2155,0.2155,
0.2170,0.2188,0.2239,0.2306,0.2351,0.2419,0.2438,0.2439,0.2487,0.2535,
0.2741,0.2778,0.2784,0.2799,0.2808,0.2876,0.2926,0.2952,0.3014,0.3062,
0.3123,0.3186,0.3316,0.3405,0.3443,0.3479,0.3540,0.3562,0.3645,0.3671,
0.3790,0.3792,0.3813,0.3827,0.3847,0.3906,0.3930,0.3952,0.3968,0.4012,
0.4097,0.4163,0.4164,0.4169,0.4205,0.4246,0.4251,0.4292,0.4373,0.4476,
0.4489,0.4636,0.4688,0.4727,0.4736,0.4754,0.4831,0.4865,0.4942,0.5013,
0.5016,0.5045,0.5068,0.5114,0.5130,0.5182,0.5184,0.5191,0.5198,0.5211,
0.5212,0.5254,0.5266,0.5271,0.5307,0.5377,0.5394,0.5435,0.5477,0.5496,
0.5521,0.5525,0.5530,0.5655,0.5675,0.5688,0.5715,0.5725,0.5775,0.5849,
0.5870,0.5875,0.5884,0.5884,0.5903,0.5929,0.5963,0.5964,0.5975,0.5984,
0.6019,0.6066,0.6154,0.6183,0.6207,0.6235,0.6257,0.6284,0.6293,0.6293,
0.6378,0.6412,0.6423,0.6532,0.6550,0.6550,0.6609,0.6612,0.6653,0.6654,
0.6670,0.6743,0.6748,0.6766,0.6851,0.6854,0.6874,0.6893,0.6893,0.6895,
0.6937,0.6968,0.6992,0.7086,0.7091,0.7131,0.7193,0.7210,0.7221,0.7272,
0.7316,0.7367,0.7412,0.7544,0.7584,0.7630,0.7647,0.7720,0.7750,0.7787,
0.7946,0.7962,0.7990,0.8006,0.8116,0.8148,0.8185,0.8191,0.8208,0.8226,
0.8227,0.8284,0.8354,0.8424,0.8424,0.8448,0.8470,0.8478,0.8532,0.8539,
0.8715,0.8727,0.8745,0.8756,0.8786,0.8817,0.8849,0.8854,0.8854,0.8885,
0.8927,0.8938,0.8995,0.9012,0.9042,0.9061,0.9067,0.9077,0.9086,0.9086,
0.9102,0.9112,0.9122,0.9165,0.9175,0.9226,0.9311,0.9324,0.9381,0.9402,
0.9543,0.9665,0.9668,0.9686,0.9895,0.9905,0.9920,0.9965,0.9978,
Overall p-value after applying KStest on 269 p-values = 0.555980
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.