RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-05_01:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.70 39.4112 0.998434
2 to 25 15.36 26.5421 0.934866
3 to 26 15.36 27.8746 0.953576
4 to 27 15.43 23.3149 0.860725
5 to 28 15.71 25.5997 0.917931
6 to 29 16.07 14.9048 0.397661
7 to 30 15.57 27.3653 0.947077
8 to 31 15.66 21.4350 0.792567
9 to 32 15.77 16.1455 0.486456
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.000473
Tough bday spacings test for dh-ranFile-2018-07-05_01:31: 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 3 43 69 97 96 74 60 32 16 7 3
(O-E)^2/E 4.1 1.1 0.2 0.0 0.0 0.2 1.2 0.2 0.1 0.0 0.3
Birthday Spacings: Sum(O-E)^2/E= 7.501, p= 0.323
RESULTS OF GCD FOR dh-ranFile-2018-07-05_01:31
Euclid's algorithm:
p-value, steps to gcd: 0.790747
p-value, dist. of gcd's: 0.927255
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-05_01:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.284 0.286 0.528 0.171 0.380 0.704 0.268 0.975
Bits 8 to 15---> 0.149 0.233 0.424 0.961 0.650 0.653 0.764 0.879
Bits 16 to 23---> 0.126 0.256 0.268 0.507 0.068 0.690 0.918 0.593
Bits 24 to 31---> 0.767 0.814 0.867 0.265 0.448 0.054 0.332 0.967
KS test for the above 32 p values: 0.078
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-05_01:31,
p-values for 5 runs: 0.6186, 0.2217, 0.8976, 0.0839, 0.3046
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-05_01:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 222 211.4 0.530 0.530
r= 29 5214 5134.0 1.246 1.776
r= 30 23045 23103.0 0.146 1.922
r= 31 11519 11551.5 0.092 2.013
chi-square = 2.013 with df = 3; p-value = 0.430
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-05_01:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 226 211.4 1.006 1.006
r= 30 5121 5134.0 0.033 1.039
r= 31 23126 23103.0 0.023 1.062
r= 32 11527 11551.5 0.052 1.114
chi-square = 1.114 with df = 3; p-value = 0.226
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-05_01:31
b-rank test for bits 1 to 8, p=0.17337
b-rank test for bits 2 to 9, p=0.24833
b-rank test for bits 3 to 10, p=0.23771
b-rank test for bits 4 to 11, p=0.92974
b-rank test for bits 5 to 12, p=0.09024
b-rank test for bits 6 to 13, p=0.54637
b-rank test for bits 7 to 14, p=0.79038
b-rank test for bits 8 to 15, p=0.71680
b-rank test for bits 9 to 16, p=0.72261
b-rank test for bits 10 to 17, p=0.93713
b-rank test for bits 11 to 18, p=0.81469
b-rank test for bits 12 to 19, p=0.95079
b-rank test for bits 13 to 20, p=0.36279
b-rank test for bits 14 to 21, p=0.40872
b-rank test for bits 15 to 22, p=0.55992
b-rank test for bits 16 to 23, p=0.09088
b-rank test for bits 17 to 24, p=0.79963
b-rank test for bits 18 to 25, p=0.38921
b-rank test for bits 19 to 26, p=0.41671
b-rank test for bits 20 to 27, p=0.14143
b-rank test for bits 21 to 28, p=0.00546
b-rank test for bits 22 to 29, p=0.81725
b-rank test for bits 23 to 30, p=0.23933
b-rank test for bits 24 to 31, p=0.25865
b-rank test for bits 25 to 32, p=0.13934
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 = 0.781253
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-05_01:31
(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 141771 -0.32 0.373272
2 141208 -1.64 0.050646
3 141902 -0.02 0.493168
4 142037 0.30 0.617261
5 141664 -0.57 0.283254
6 141759 -0.35 0.362705
7 141751 -0.37 0.355717
8 141921 0.03 0.510876
9 141515 -0.92 0.178439
10 141858 -0.12 0.452269
11 141401 -1.19 0.117478
12 141877 -0.08 0.469894
13 143012 2.58 0.995007
14 141841 -0.16 0.436579
15 141574 -0.78 0.216672
16 141756 -0.36 0.360079
17 141911 0.00 0.501557
18 142237 0.77 0.778038
19 142226 0.74 0.770315
20 142063 0.36 0.640218
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-05_01:31
Bits used No. missing words z-score p-value
23 to 32 141405 -1.7391 0.041011
22 to 31 141349 -1.9322 0.026669
21 to 30 141519 -1.3460 0.089157
20 to 29 142368 1.5816 0.943132
19 to 28 141867 -0.1460 0.441974
18 to 27 142122 0.7333 0.768326
17 to 26 142072 0.5609 0.712578
16 to 25 141398 -1.7632 0.038933
15 to 24 142380 1.6230 0.947705
14 to 23 141695 -0.7391 0.229933
13 to 22 142444 1.8437 0.967386
12 to 21 142109 0.6885 0.754436
11 to 20 142266 1.2299 0.890632
10 to 19 142349 1.5161 0.935253
9 to 18 142085 0.6058 0.727663
8 to 17 142140 0.7954 0.786814
7 to 16 141878 -0.1080 0.456984
6 to 15 141773 -0.4701 0.319141
5 to 14 141653 -0.8839 0.188376
4 to 13 141708 -0.6942 0.243765
3 to 12 142219 1.0678 0.857201
2 to 11 141815 -0.3253 0.372486
1 to 10 141570 -1.1701 0.120980
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-05_01:31
Bits used No. missing words z-score p-value
28 to 32 141339 -1.9333 0.026598
27 to 31 141283 -2.1232 0.016871
26 to 30 142186 0.9379 0.825843
25 to 29 141978 0.2328 0.592034
24 to 28 142132 0.7548 0.774820
23 to 27 141964 0.1853 0.573512
22 to 26 142336 1.4463 0.925959
21 to 25 142124 0.7277 0.766600
20 to 24 141821 -0.2994 0.382308
19 to 23 141869 -0.1367 0.445629
18 to 22 141615 -0.9977 0.159205
17 to 21 142207 1.0091 0.843525
16 to 20 141572 -1.1435 0.126417
15 to 19 141735 -0.5909 0.277277
14 to 18 141859 -0.1706 0.432265
13 to 17 141870 -0.1333 0.446969
12 to 16 142168 0.8768 0.809715
11 to 15 141901 -0.0282 0.488737
10 to 14 141983 0.2497 0.598602
9 to 13 141723 -0.6316 0.263815
8 to 12 141731 -0.6045 0.272753
7 to 11 141554 -1.2045 0.114197
6 to 10 141975 0.2226 0.588081
5 to 9 142056 0.4972 0.690471
4 to 8 142044 0.4565 0.675988
3 to 7 141786 -0.4181 0.337949
2 to 6 141779 -0.4418 0.329318
1 to 5 142176 0.9040 0.816993
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-05_01:31
Bits used No. missing words z-score p-value
31 to 32 141468 -1.3019 0.096482
30 to 31 141550 -1.0600 0.144579
29 to 30 142288 1.1170 0.868007
28 to 29 142251 1.0079 0.843243
27 to 28 141339 -1.6824 0.046247
26 to 27 141667 -0.7148 0.237355
25 to 26 142142 0.6863 0.753751
24 to 25 141709 -0.5909 0.277279
23 to 24 141833 -0.2252 0.410927
22 to 23 141756 -0.4523 0.325526
21 to 22 141180 -2.1514 0.015722
20 to 21 142117 0.6126 0.729928
19 to 20 141720 -0.5585 0.288253
18 to 19 141674 -0.6942 0.243782
17 to 18 142214 0.8987 0.815602
16 to 17 142174 0.7807 0.782522
15 to 16 142112 0.5978 0.725029
14 to 15 142323 1.2203 0.888818
13 to 14 142065 0.4592 0.676956
12 to 13 141832 -0.2281 0.409780
11 to 12 142017 0.3176 0.624610
10 to 11 142026 0.3442 0.634637
9 to 10 142202 0.8633 0.806023
8 to 9 141662 -0.7296 0.232821
7 to 8 141866 -0.1278 0.449147
6 to 7 141589 -0.9449 0.172348
5 to 6 142121 0.6244 0.733816
4 to 5 141997 0.2586 0.602033
3 to 4 141652 -0.7591 0.223901
2 to 3 141880 -0.0865 0.465527
1 to 2 141903 -0.0187 0.492551
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-05_01:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2387.32 -1.594 0.055516
Test results for specific bytes for dh-ranFile-2018-07-05_01:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2431.63 -0.967 0.166808
2 to 9 2422.40 -1.097 0.136232
3 to 10 2589.17 1.261 0.896361
4 to 11 2582.00 1.160 0.876904
5 to 12 2521.40 0.303 0.618908
6 to 13 2489.31 -0.151 0.439940
7 to 14 2594.60 1.338 0.909522
8 to 15 2540.05 0.566 0.714416
9 to 16 2515.83 0.224 0.588598
10 to 17 2538.26 0.541 0.705782
11 to 18 2419.50 -1.138 0.127474
12 to 19 2573.50 1.039 0.850711
13 to 20 2564.69 0.915 0.819853
14 to 21 2390.27 -1.552 0.060351
15 to 22 2428.53 -1.011 0.156067
16 to 23 2466.91 -0.468 0.319914
17 to 24 2499.16 -0.012 0.495265
18 to 25 2491.66 -0.118 0.453030
19 to 26 2356.17 -2.034 0.020970
20 to 27 2548.37 0.684 0.753046
21 to 28 2428.32 -1.014 0.155347
22 to 29 2579.47 1.124 0.869471
23 to 30 2582.10 1.161 0.877195
24 to 31 2638.66 1.961 0.975061
25 to 32 2516.22 0.229 0.590736
CDPARK for dh-ranFile-2018-07-05_01:31: 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
3519 -0.1826 0.427537
3517 -0.2740 0.392053
3520 -0.1370 0.445521
3501 -1.0046 0.157553
3469 -2.4658 0.006836
3520 -0.1370 0.445521
3493 -1.3699 0.085365
3570 2.1461 0.984068
3543 0.9132 0.819442
3513 -0.4566 0.323972
Square side=100, avg. no. parked=3516.50 sample std.=25.80
p-value of the KSTEST for those 10 p-values: 0.370311
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-05_01:31
0.1943,0.4755,0.6595,0.3135,0.9051,0.8995,0.1958,0.6622,0.0842,0.2798,
The KS test for those 10 p-values: 0.904893
The 3DSPHERES test for dh-ranFile-2018-07-05_01:31
sample no r^3 equiv. uni.
1 28.742 0.616370
2 51.715 0.821621
3 38.366 0.721651
4 16.699 0.426862
5 69.394 0.901049
6 7.908 0.231713
7 54.073 0.835102
8 160.897 0.995314
9 79.039 0.928255
10 9.850 0.279874
11 41.284 0.747448
12 2.890 0.091827
13 130.685 0.987173
14 6.044 0.182466
15 26.381 0.584959
16 14.342 0.380017
17 35.963 0.698431
18 17.672 0.445153
19 36.056 0.699369
20 33.659 0.674366
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.127987
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-05_01:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 1.8 -0.6 0.2 -0.3 0.1
0.8 1.5 0.0 -0.1 -0.9 0.1
0.5 -0.0 0.1 -0.6 -0.2 -1.7
-0.3 0.6 1.5 -0.8 0.4 0.1
0.5 -1.1 2.1 -1.3 -1.2 0.5
2.0 0.4 -0.1 2.4 -1.0 -0.8
-0.9 -0.1 -0.8 3.2 -0.6 1.0
-0.1
Chi-square with 42 degrees of freedom:49.604614
z-score=0.829731, p-value=0.804041
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-05_01:31
Test no p-value
1 0.832770
2 0.691716
3 0.617842
4 0.039168
5 0.435797
6 0.932970
7 0.438493
8 0.128949
9 0.023904
10 0.418539
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.748124
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-05_01:31:
(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 66634 0.02 66510 0.37
3 25000.00 25029 0.03 25143 0.82
4 6666.67 6661 0.00 6731 0.62
5 1388.89 1393 0.01 1353 0.93
6 238.10 239 0.00 231 0.21
7 34.72 41 1.14 29 0.94
8 4.96 2 1.77 2 1.77
p=0.18770 p=0.53702
Number of rngs required: 688255, p-value: 0.432
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-05_01:31
No. of wins: Observed Expected
98611 98585.9
z-score= 0.112, pvalue=0.54477
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66849 66666.7 0.499 0.499
2 37378 37654.3 2.028 2.526
3 27105 26954.7 0.838 3.364
4 19464 19313.5 1.173 4.537
5 13771 13851.4 0.467 5.004
6 10034 9943.5 0.823 5.827
7 6957 7145.0 4.948 10.775
8 5127 5139.1 0.028 10.804
9 3733 3699.9 0.297 11.100
10 2627 2666.3 0.579 11.680
11 1953 1923.3 0.458 12.137
12 1353 1388.7 0.920 13.057
13 1028 1003.7 0.588 13.645
14 691 726.1 1.701 15.345
15 528 525.8 0.009 15.354
16 392 381.2 0.309 15.663
17 271 276.5 0.111 15.774
18 196 200.8 0.116 15.890
19 137 146.0 0.553 16.443
20 128 106.2 4.468 20.911
21 278 287.1 0.289 21.200
Chisq= 21.20 for 20 degrees of freedom, p= 0.61458
SUMMARY of craptest
p-value for no. of wins: 0.544766
p-value for throws/game: 0.614580
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-05_01:31
No. of wins: Observed Expected
98846 98585.9
z-score= 1.164, pvalue=0.87769
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66596 66666.7 0.075 0.075
2 37620 37654.3 0.031 0.106
3 26976 26954.7 0.017 0.123
4 19349 19313.5 0.065 0.188
5 13764 13851.4 0.552 0.740
6 9880 9943.5 0.406 1.146
7 7191 7145.0 0.296 1.442
8 5286 5139.1 4.201 5.643
9 3770 3699.9 1.329 6.972
10 2665 2666.3 0.001 6.973
11 1883 1923.3 0.846 7.818
12 1351 1388.7 1.026 8.844
13 1010 1003.7 0.039 8.883
14 761 726.1 1.673 10.557
15 501 525.8 1.173 11.730
16 379 381.2 0.012 11.742
17 273 276.5 0.045 11.787
18 207 200.8 0.190 11.977
19 148 146.0 0.028 12.005
20 102 106.2 0.167 12.172
21 288 287.1 0.003 12.175
Chisq= 12.17 for 20 degrees of freedom, p= 0.09007
SUMMARY of craptest
p-value for no. of wins: 0.877687
p-value for throws/game: 0.090071
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0005,0.0055,0.0068,0.0157,0.0169,0.0210,0.0239,0.0266,0.0267,0.0389,
0.0392,0.0410,0.0462,0.0506,0.0543,0.0555,0.0604,0.0681,0.0775,0.0839,
0.0842,0.0854,0.0892,0.0901,0.0902,0.0909,0.0918,0.0965,0.1142,0.1175,
0.1210,0.1262,0.1264,0.1275,0.1280,0.1289,0.1362,0.1393,0.1414,0.1446,
0.1493,0.1553,0.1561,0.1576,0.1592,0.1668,0.1714,0.1723,0.1734,0.1784,
0.1825,0.1877,0.1884,0.1943,0.1958,0.2167,0.2217,0.2239,0.2262,0.2299,
0.2317,0.2328,0.2328,0.2374,0.2377,0.2393,0.2438,0.2438,0.2483,0.2563,
0.2586,0.2638,0.2652,0.2677,0.2682,0.2728,0.2773,0.2773,0.2798,0.2799,
0.2833,0.2838,0.2863,0.2883,0.3046,0.3135,0.3191,0.3199,0.3225,0.3240,
0.3255,0.3293,0.3320,0.3379,0.3557,0.3601,0.3627,0.3628,0.3703,0.3725,
0.3733,0.3800,0.3804,0.3823,0.3892,0.3921,0.3977,0.4087,0.4098,0.4109,
0.4167,0.4185,0.4244,0.4269,0.4275,0.4304,0.4323,0.4324,0.4358,0.4366,
0.4385,0.4399,0.4420,0.4452,0.4455,0.4455,0.4456,0.4470,0.4476,0.4491,
0.4523,0.4530,0.4570,0.4655,0.4699,0.4755,0.4865,0.4887,0.4926,0.4932,
0.4953,0.5016,0.5071,0.5109,0.5275,0.5370,0.5448,0.5464,0.5599,0.5735,
0.5850,0.5881,0.5886,0.5907,0.5920,0.5935,0.5986,0.6020,0.6146,0.6164,
0.6173,0.6178,0.6186,0.6189,0.6246,0.6346,0.6402,0.6502,0.6535,0.6595,
0.6622,0.6744,0.6760,0.6770,0.6898,0.6905,0.6917,0.6984,0.6994,0.7040,
0.7058,0.7126,0.7144,0.7168,0.7217,0.7226,0.7250,0.7277,0.7299,0.7338,
0.7474,0.7481,0.7530,0.7538,0.7544,0.7644,0.7666,0.7667,0.7683,0.7703,
0.7748,0.7780,0.7813,0.7825,0.7868,0.7904,0.7907,0.7926,0.7996,0.8040,
0.8060,0.8097,0.8143,0.8147,0.8156,0.8170,0.8173,0.8194,0.8199,0.8216,
0.8258,0.8328,0.8351,0.8432,0.8435,0.8507,0.8572,0.8607,0.8668,0.8680,
0.8695,0.8769,0.8772,0.8777,0.8785,0.8888,0.8906,0.8964,0.8976,0.8995,
0.9010,0.9049,0.9051,0.9095,0.9179,0.9183,0.9260,0.9273,0.9283,0.9297,
0.9330,0.9349,0.9353,0.9371,0.9431,0.9471,0.9477,0.9508,0.9536,0.9608,
0.9665,0.9674,0.9748,0.9751,0.9841,0.9872,0.9950,0.9953,0.9984,
Overall p-value after applying KStest on 269 p-values = 0.829617
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.