RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-17_06:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.80 22.8566 0.846024
2 to 25 15.67 27.3479 0.946841
3 to 26 15.73 14.0823 0.338732
4 to 27 15.85 15.2438 0.422074
5 to 28 15.82 8.5161 0.045769
6 to 29 15.73 9.0119 0.060113
7 to 30 15.97 16.8988 0.538756
8 to 31 16.05 17.6005 0.585547
9 to 32 15.84 13.5635 0.302276
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.881270
Tough bday spacings test for dh-ranFile-2018-06-17_06:31: 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 32 66 94 107 71 55 44 14 6 2
(O-E)^2/E 0.0 0.6 0.7 0.1 0.9 0.7 0.2 6.8 0.1 0.1 1.0
Birthday Spacings: Sum(O-E)^2/E= 11.112, p= 0.651
RESULTS OF GCD FOR dh-ranFile-2018-06-17_06:31
Euclid's algorithm:
p-value, steps to gcd: 0.367759
p-value, dist. of gcd's: 0.211731
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-17_06:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.074 0.793 0.645 0.810 0.592 0.924 0.100 0.476
Bits 8 to 15---> 0.424 0.247 0.736 0.982 0.161 0.468 0.347 0.831
Bits 16 to 23---> 0.903 0.859 0.134 0.414 0.897 0.554 0.426 0.057
Bits 24 to 31---> 0.107 0.926 0.221 0.795 0.454 0.347 0.301 0.499
KS test for the above 32 p values: 0.057
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-17_06:31,
p-values for 5 runs: 0.7942, 0.2685, 0.7601, 0.0479, 0.5933
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-17_06:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 215 211.4 0.061 0.061
r= 29 5123 5134.0 0.024 0.084
r= 30 23303 23103.0 1.731 1.815
r= 31 11359 11551.5 3.209 5.024
chi-square = 5.024 with df = 3; p-value = 0.830
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-17_06:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 242 211.4 4.424 4.424
r= 30 5168 5134.0 0.225 4.649
r= 31 23150 23103.0 0.095 4.744
r= 32 11440 11551.5 1.077 5.821
chi-square = 5.821 with df = 3; p-value = 0.879
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-17_06:31
b-rank test for bits 1 to 8, p=0.75647
b-rank test for bits 2 to 9, p=0.80274
b-rank test for bits 3 to 10, p=0.21220
b-rank test for bits 4 to 11, p=0.75423
b-rank test for bits 5 to 12, p=0.94143
b-rank test for bits 6 to 13, p=0.23824
b-rank test for bits 7 to 14, p=0.19702
b-rank test for bits 8 to 15, p=0.17170
b-rank test for bits 9 to 16, p=0.00031
b-rank test for bits 10 to 17, p=0.67474
b-rank test for bits 11 to 18, p=0.90161
b-rank test for bits 12 to 19, p=0.70446
b-rank test for bits 13 to 20, p=0.22772
b-rank test for bits 14 to 21, p=0.98299
b-rank test for bits 15 to 22, p=0.94862
b-rank test for bits 16 to 23, p=0.03066
b-rank test for bits 17 to 24, p=0.73026
b-rank test for bits 18 to 25, p=0.85187
b-rank test for bits 19 to 26, p=0.98021
b-rank test for bits 20 to 27, p=0.78210
b-rank test for bits 21 to 28, p=0.45218
b-rank test for bits 22 to 29, p=0.75209
b-rank test for bits 23 to 30, p=0.73252
b-rank test for bits 24 to 31, p=0.37504
b-rank test for bits 25 to 32, p=0.42495
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 = 0.105069
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-17_06:31
(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 141801 -0.25 0.400093
2 141843 -0.15 0.438420
3 141247 -1.55 0.060871
4 141255 -1.53 0.063156
5 141768 -0.33 0.370621
6 142178 0.63 0.734911
7 142184 0.64 0.739483
8 141945 0.08 0.533210
9 141499 -0.96 0.168851
10 141483 -1.00 0.159601
11 141671 -0.56 0.288816
12 141201 -1.65 0.048965
13 141123 -1.84 0.033089
14 142489 1.35 0.912191
15 141776 -0.31 0.377703
16 142268 0.84 0.798989
17 141985 0.18 0.570167
18 141543 -0.86 0.196023
19 141696 -0.50 0.309089
20 141865 -0.10 0.458753
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-17_06:31
Bits used No. missing words z-score p-value
23 to 32 141676 -0.8046 0.210529
22 to 31 141511 -1.3736 0.084790
21 to 30 141834 -0.2598 0.397525
20 to 29 141952 0.1471 0.558488
19 to 28 141816 -0.3218 0.373792
18 to 27 142169 0.8954 0.814717
17 to 26 141595 -1.0839 0.139205
16 to 25 142210 1.0368 0.850084
15 to 24 142456 1.8851 0.970290
14 to 23 141987 0.2678 0.605584
13 to 22 142328 1.4437 0.925587
12 to 21 141817 -0.3184 0.375099
11 to 20 141731 -0.6149 0.269300
10 to 19 141993 0.2885 0.613525
9 to 18 141758 -0.5218 0.300895
8 to 17 142346 1.5058 0.933935
7 to 16 142085 0.6058 0.727663
6 to 15 142099 0.6540 0.743455
5 to 14 142439 1.8264 0.966109
4 to 13 141467 -1.5253 0.063595
3 to 12 142468 1.9264 0.972976
2 to 11 142004 0.3264 0.627957
1 to 10 141967 0.1989 0.578815
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-17_06:31
Bits used No. missing words z-score p-value
28 to 32 141720 -0.6418 0.260503
27 to 31 141586 -1.0960 0.136532
26 to 30 142059 0.5074 0.694048
25 to 29 141856 -0.1808 0.428270
24 to 28 141842 -0.2282 0.409731
23 to 27 141428 -1.6316 0.051379
22 to 26 141894 -0.0520 0.479278
21 to 25 141804 -0.3571 0.360527
20 to 24 142035 0.4260 0.664946
19 to 23 141616 -0.9943 0.160029
18 to 22 142222 1.0599 0.855405
17 to 21 141883 -0.0893 0.464440
16 to 20 142119 0.7107 0.761379
15 to 19 142240 1.1209 0.868838
14 to 18 142230 1.0870 0.861485
13 to 17 141758 -0.5130 0.303982
12 to 16 141713 -0.6655 0.252857
11 to 15 142021 0.3785 0.647486
10 to 14 142073 0.5548 0.710489
9 to 13 142119 0.7107 0.761379
8 to 12 141883 -0.0893 0.464440
7 to 11 141216 -2.3503 0.009380
6 to 10 142029 0.4057 0.657504
5 to 9 141989 0.2701 0.606446
4 to 8 141790 -0.4045 0.342919
3 to 7 142058 0.5040 0.692857
2 to 6 142171 0.8870 0.812465
1 to 5 141727 -0.6181 0.268265
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-17_06:31
Bits used No. missing words z-score p-value
31 to 32 142041 0.3884 0.651143
30 to 31 142408 1.4710 0.929355
29 to 30 141844 -0.1927 0.423592
28 to 29 141946 0.1082 0.543070
27 to 28 141930 0.0610 0.524310
26 to 27 142506 1.7601 0.960804
25 to 26 141879 -0.0895 0.464355
24 to 25 141816 -0.2753 0.391539
23 to 24 141911 0.0049 0.501965
22 to 23 141741 -0.4965 0.309754
21 to 22 142155 0.7247 0.765679
20 to 21 142657 2.2055 0.986291
19 to 20 142008 0.2911 0.614498
18 to 19 141981 0.2114 0.583719
17 to 18 141209 -2.0659 0.019420
16 to 17 142582 1.9843 0.976388
15 to 16 141876 -0.0983 0.460840
14 to 15 142079 0.5005 0.691639
13 to 14 142606 2.0551 0.980064
12 to 13 142604 2.0492 0.979777
11 to 12 142701 2.3353 0.990236
10 to 11 142024 0.3383 0.632416
9 to 10 141808 -0.2989 0.382505
8 to 9 141199 -2.0954 0.018069
7 to 8 141757 -0.4494 0.326589
6 to 7 141590 -0.9420 0.173102
5 to 6 141716 -0.5703 0.284239
4 to 5 142233 0.9548 0.830155
3 to 4 142062 0.4504 0.673772
2 to 3 141791 -0.3491 0.363524
1 to 2 141603 -0.9036 0.183096
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-17_06:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2565.20 0.922 0.821758
Test results for specific bytes for dh-ranFile-2018-06-17_06:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2520.28 0.287 0.612870
2 to 9 2530.69 0.434 0.667881
3 to 10 2532.11 0.454 0.675111
4 to 11 2454.09 -0.649 0.258101
5 to 12 2541.91 0.593 0.723310
6 to 13 2564.38 0.910 0.818705
7 to 14 2582.90 1.172 0.879473
8 to 15 2377.00 -1.739 0.040978
9 to 16 2537.23 0.526 0.700714
10 to 17 2483.05 -0.240 0.405284
11 to 18 2556.56 0.800 0.788127
12 to 19 2605.56 1.493 0.932261
13 to 20 2516.83 0.238 0.594060
14 to 21 2459.02 -0.580 0.281096
15 to 22 2492.62 -0.104 0.458442
16 to 23 2449.77 -0.710 0.238725
17 to 24 2499.92 -0.001 0.499574
18 to 25 2519.58 0.277 0.609089
19 to 26 2498.90 -0.016 0.493779
20 to 27 2495.95 -0.057 0.477140
21 to 28 2448.97 -0.722 0.235244
22 to 29 2472.62 -0.387 0.349320
23 to 30 2350.21 -2.118 0.017075
24 to 31 2545.06 0.637 0.738031
25 to 32 2584.67 1.197 0.884441
CDPARK for dh-ranFile-2018-06-17_06:31: 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
3540 0.7763 0.781201
3516 -0.3196 0.374623
3533 0.4566 0.676028
3505 -0.8219 0.205562
3501 -1.0046 0.157553
3543 0.9132 0.819442
3529 0.2740 0.607947
3549 1.1872 0.882429
3499 -1.0959 0.136563
3500 -1.0502 0.146807
Square side=100, avg. no. parked=3521.50 sample std.=18.55
p-value of the KSTEST for those 10 p-values: 0.815106
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-17_06:31
0.0754,0.9574,0.9817,0.8740,0.3081,0.7356,0.0221,0.2850,0.8549,0.6134,
The KS test for those 10 p-values: 0.339169
The 3DSPHERES test for dh-ranFile-2018-06-17_06:31
sample no r^3 equiv. uni.
1 7.255 0.214818
2 50.404 0.813652
3 28.721 0.616101
4 29.629 0.627540
5 31.535 0.650467
6 58.926 0.859732
7 3.559 0.111869
8 39.620 0.733046
9 2.031 0.065456
10 51.745 0.821798
11 37.088 0.709538
12 32.623 0.662917
13 4.020 0.125418
14 23.269 0.539595
15 6.562 0.196459
16 26.515 0.586809
17 39.973 0.736165
18 3.793 0.118762
19 14.023 0.373391
20 11.611 0.320941
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.626624
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-17_06:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 -0.7 -1.8 -1.9 -0.1 1.8
0.5 -0.4 -1.5 -0.1 0.8 -0.9
-0.3 1.6 -0.4 -1.2 0.5 2.2
-0.2 -0.1 0.4 -0.3 -0.2 1.0
-0.2 -0.8 -1.0 -0.6 -1.2 0.6
0.0 -0.8 -1.0 -0.4 -1.3 -0.1
0.3 0.2 0.1 -0.1 -0.6 0.0
0.8
Chi-square with 42 degrees of freedom:35.095384
z-score=-0.753355, p-value=0.234150
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-17_06:31
Test no p-value
1 0.415125
2 0.583577
3 0.016161
4 0.053071
5 0.025068
6 0.151049
7 0.327401
8 0.582128
9 0.068599
10 0.383778
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.008335
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-17_06:31:
(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 66646 0.01 66806 0.29
3 25000.00 25045 0.08 24827 1.20
4 6666.67 6611 0.46 6729 0.58
5 1388.89 1423 0.84 1329 2.58
6 238.10 235 0.04 273 5.12
7 34.72 30 0.64 29 0.94
8 4.96 9 3.29 6 0.22
p=0.50178 p=0.90947
Number of rngs required: 688975, p-value: 0.745
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-17_06:31
No. of wins: Observed Expected
98673 98585.9
z-score= 0.390, pvalue=0.65164
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66612 66666.7 0.045 0.045
2 37718 37654.3 0.108 0.153
3 26900 26954.7 0.111 0.264
4 19121 19313.5 1.918 2.182
5 13922 13851.4 0.360 2.541
6 10056 9943.5 1.272 3.813
7 7219 7145.0 0.766 4.579
8 5058 5139.1 1.279 5.858
9 3721 3699.9 0.121 5.979
10 2695 2666.3 0.309 6.288
11 1932 1923.3 0.039 6.327
12 1351 1388.7 1.026 7.352
13 1004 1003.7 0.000 7.352
14 742 726.1 0.346 7.699
15 514 525.8 0.266 7.965
16 399 381.2 0.836 8.801
17 285 276.5 0.259 9.060
18 213 200.8 0.737 9.797
19 139 146.0 0.334 10.132
20 102 106.2 0.167 10.299
21 297 287.1 0.340 10.639
Chisq= 10.64 for 20 degrees of freedom, p= 0.04495
SUMMARY of craptest
p-value for no. of wins: 0.651638
p-value for throws/game: 0.044954
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-17_06:31
No. of wins: Observed Expected
98635 98585.9
z-score= 0.220, pvalue=0.58698
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66786 66666.7 0.214 0.214
2 37672 37654.3 0.008 0.222
3 26924 26954.7 0.035 0.257
4 19270 19313.5 0.098 0.355
5 13867 13851.4 0.018 0.372
6 9931 9943.5 0.016 0.388
7 7116 7145.0 0.118 0.506
8 5116 5139.1 0.104 0.610
9 3681 3699.9 0.096 0.706
10 2655 2666.3 0.048 0.754
11 1954 1923.3 0.489 1.243
12 1399 1388.7 0.076 1.319
13 976 1003.7 0.765 2.084
14 707 726.1 0.505 2.588
15 533 525.8 0.098 2.686
16 404 381.2 1.370 4.056
17 271 276.5 0.111 4.167
18 206 200.8 0.133 4.300
19 145 146.0 0.007 4.306
20 108 106.2 0.030 4.336
21 279 287.1 0.229 4.566
Chisq= 4.57 for 20 degrees of freedom, p= 0.00014
SUMMARY of craptest
p-value for no. of wins: 0.586982
p-value for throws/game: 0.000136
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0001,0.0003,0.0083,0.0094,0.0162,0.0171,0.0181,0.0194,0.0221,0.0251,
0.0307,0.0331,0.0410,0.0450,0.0458,0.0479,0.0490,0.0514,0.0531,0.0569,
0.0569,0.0601,0.0609,0.0632,0.0636,0.0655,0.0686,0.0743,0.0754,0.0848,
0.0995,0.1051,0.1069,0.1119,0.1188,0.1254,0.1338,0.1365,0.1366,0.1392,
0.1468,0.1510,0.1576,0.1596,0.1600,0.1613,0.1689,0.1717,0.1731,0.1831,
0.1960,0.1965,0.1970,0.2056,0.2105,0.2117,0.2122,0.2148,0.2207,0.2277,
0.2341,0.2352,0.2382,0.2387,0.2470,0.2529,0.2581,0.2605,0.2683,0.2685,
0.2693,0.2811,0.2842,0.2850,0.2888,0.3008,0.3009,0.3023,0.3040,0.3081,
0.3091,0.3098,0.3209,0.3266,0.3274,0.3387,0.3392,0.3429,0.3467,0.3473,
0.3493,0.3605,0.3635,0.3678,0.3706,0.3734,0.3738,0.3746,0.3750,0.3751,
0.3777,0.3825,0.3838,0.3915,0.3975,0.4001,0.4053,0.4097,0.4135,0.4151,
0.4221,0.4236,0.4240,0.4250,0.4260,0.4283,0.4384,0.4522,0.4542,0.4584,
0.4588,0.4608,0.4644,0.4644,0.4644,0.4683,0.4765,0.4771,0.4793,0.4938,
0.4989,0.4996,0.5018,0.5020,0.5243,0.5332,0.5388,0.5396,0.5431,0.5535,
0.5585,0.5702,0.5788,0.5821,0.5836,0.5837,0.5855,0.5868,0.5870,0.5923,
0.5933,0.5941,0.6056,0.6064,0.6079,0.6091,0.6129,0.6134,0.6135,0.6145,
0.6161,0.6266,0.6275,0.6280,0.6324,0.6451,0.6475,0.6505,0.6511,0.6512,
0.6516,0.6575,0.6629,0.6649,0.6679,0.6738,0.6747,0.6751,0.6760,0.6916,
0.6929,0.6940,0.7007,0.7045,0.7095,0.7105,0.7233,0.7277,0.7303,0.7325,
0.7330,0.7349,0.7356,0.7359,0.7362,0.7380,0.7395,0.7435,0.7454,0.7521,
0.7542,0.7565,0.7601,0.7614,0.7614,0.7657,0.7812,0.7821,0.7881,0.7926,
0.7942,0.7947,0.7990,0.8027,0.8104,0.8125,0.8137,0.8147,0.8151,0.8187,
0.8194,0.8218,0.8218,0.8299,0.8302,0.8308,0.8460,0.8501,0.8519,0.8549,
0.8554,0.8592,0.8597,0.8615,0.8688,0.8740,0.8793,0.8795,0.8813,0.8824,
0.8844,0.8967,0.9016,0.9029,0.9095,0.9122,0.9239,0.9256,0.9263,0.9294,
0.9323,0.9339,0.9414,0.9468,0.9486,0.9574,0.9608,0.9661,0.9703,0.9730,
0.9764,0.9798,0.9801,0.9802,0.9817,0.9818,0.9830,0.9863,0.9902,
Overall p-value after applying KStest on 269 p-values = 0.746709
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.