RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-15_11:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.59 24.3375 0.889448
2 to 25 15.72 22.8016 0.844179
3 to 26 15.76 15.4153 0.434406
4 to 27 15.64 21.5224 0.796211
5 to 28 15.65 26.4380 0.933158
6 to 29 16.00 15.8174 0.463188
7 to 30 15.19 31.6800 0.983514
8 to 31 15.79 18.1312 0.619393
9 to 32 15.81 20.3847 0.744974
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.017386
Tough bday spacings test for dh-ranFile-2018-06-15_11:31: 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 39 80 92 101 78 45 37 11 6 8
(O-E)^2/E 4.1 0.2 0.6 0.3 0.1 0.0 1.0 1.8 1.0 0.1 3.8
Birthday Spacings: Sum(O-E)^2/E= 12.957, p= 0.774
RESULTS OF GCD FOR dh-ranFile-2018-06-15_11:31
Euclid's algorithm:
p-value, steps to gcd: 0.128364
p-value, dist. of gcd's: 0.407187
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-15_11:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.861 0.983 0.026 0.817 0.409 0.088 0.296 0.344
Bits 8 to 15---> 0.301 0.339 0.222 0.573 0.823 0.529 0.322 0.561
Bits 16 to 23---> 0.052 0.035 0.495 0.910 0.454 0.982 0.779 0.769
Bits 24 to 31---> 0.439 0.968 0.910 0.347 0.201 0.698 0.495 0.346
KS test for the above 32 p values: 0.188
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-15_11:31,
p-values for 5 runs: 0.1337, 0.3645, 0.5558, 0.1347, 0.9739
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-15_11:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 175 211.4 6.273 6.273
r= 29 5034 5134.0 1.948 8.221
r= 30 23081 23103.0 0.021 8.242
r= 31 11710 11551.5 2.174 10.417
chi-square = 10.417 with df = 3; p-value = 0.985
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-15_11:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 235 211.4 2.630 2.630
r= 30 5104 5134.0 0.175 2.806
r= 31 23230 23103.0 0.698 3.503
r= 32 11431 11551.5 1.257 4.761
chi-square = 4.761 with df = 3; p-value = 0.810
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-15_11:31
b-rank test for bits 1 to 8, p=0.72136
b-rank test for bits 2 to 9, p=0.15620
b-rank test for bits 3 to 10, p=0.34515
b-rank test for bits 4 to 11, p=0.82658
b-rank test for bits 5 to 12, p=0.76699
b-rank test for bits 6 to 13, p=0.03409
b-rank test for bits 7 to 14, p=0.42309
b-rank test for bits 8 to 15, p=0.87841
b-rank test for bits 9 to 16, p=0.98831
b-rank test for bits 10 to 17, p=0.38874
b-rank test for bits 11 to 18, p=0.69997
b-rank test for bits 12 to 19, p=0.48358
b-rank test for bits 13 to 20, p=0.31395
b-rank test for bits 14 to 21, p=0.85722
b-rank test for bits 15 to 22, p=0.10920
b-rank test for bits 16 to 23, p=0.41385
b-rank test for bits 17 to 24, p=0.38492
b-rank test for bits 18 to 25, p=0.15902
b-rank test for bits 19 to 26, p=0.07704
b-rank test for bits 20 to 27, p=0.43916
b-rank test for bits 21 to 28, p=0.23241
b-rank test for bits 22 to 29, p=0.09028
b-rank test for bits 23 to 30, p=0.29815
b-rank test for bits 24 to 31, p=0.78434
b-rank test for bits 25 to 32, p=0.73208
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 = 0.790185
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-15_11:31
(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 142109 0.47 0.679578
2 142131 0.52 0.697743
3 141870 -0.09 0.463392
4 142400 1.15 0.874190
5 141662 -0.58 0.281675
6 141898 -0.03 0.489440
7 142480 1.33 0.908790
8 141730 -0.42 0.337610
9 142366 1.07 0.857011
10 141901 -0.02 0.492236
11 141950 0.10 0.537852
12 141788 -0.28 0.388404
13 141437 -1.10 0.134889
14 141724 -0.43 0.332502
15 141918 0.02 0.508081
16 141512 -0.93 0.176615
17 142266 0.83 0.797674
18 141894 -0.04 0.485714
19 142323 0.97 0.833108
20 142565 1.53 0.937231
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-15_11:31
Bits used No. missing words z-score p-value
23 to 32 141659 -0.8632 0.194012
22 to 31 142000 0.3127 0.622729
21 to 30 141863 -0.1598 0.436536
20 to 29 141870 -0.1356 0.446061
19 to 28 141930 0.0713 0.528411
18 to 27 141777 -0.4563 0.324083
17 to 26 142106 0.6782 0.751169
16 to 25 142220 1.0713 0.857977
15 to 24 141756 -0.5287 0.298498
14 to 23 142109 0.6885 0.754436
13 to 22 141829 -0.2770 0.390890
12 to 21 141797 -0.3873 0.349251
11 to 20 141899 -0.0356 0.485792
10 to 19 142005 0.3299 0.629261
9 to 18 141908 -0.0046 0.498170
8 to 17 142101 0.6609 0.745672
7 to 16 142115 0.7092 0.760902
6 to 15 142402 1.6989 0.955327
5 to 14 141895 -0.0494 0.480295
4 to 13 141918 0.0299 0.511925
3 to 12 141525 -1.3253 0.092540
2 to 11 141506 -1.3908 0.082144
1 to 10 141753 -0.5391 0.294920
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-15_11:31
Bits used No. missing words z-score p-value
28 to 32 141440 -1.5909 0.055811
27 to 31 141643 -0.9028 0.183312
26 to 30 142412 1.7040 0.955806
25 to 29 141669 -0.8147 0.207628
24 to 28 141771 -0.4689 0.319565
23 to 27 141481 -1.4520 0.073256
22 to 26 141799 -0.3740 0.354202
21 to 25 142452 1.8396 0.967084
20 to 24 141913 0.0124 0.504963
19 to 23 142103 0.6565 0.744252
18 to 22 142038 0.4362 0.668643
17 to 21 142078 0.5718 0.716259
16 to 20 141256 -2.2147 0.013391
15 to 19 142385 1.6124 0.946567
14 to 18 142369 1.5582 0.940407
13 to 17 142266 1.2091 0.886678
12 to 16 142396 1.6497 0.950501
11 to 15 141677 -0.7876 0.215477
10 to 14 141764 -0.4926 0.311132
9 to 13 141673 -0.8011 0.211532
8 to 12 141814 -0.3232 0.373290
7 to 11 141529 -1.2893 0.098655
6 to 10 141235 -2.2859 0.011131
5 to 9 142123 0.7243 0.765561
4 to 8 142414 1.7107 0.956436
3 to 7 142460 1.8667 0.969027
2 to 6 142106 0.6667 0.747511
1 to 5 142133 0.7582 0.775835
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-15_11:31
Bits used No. missing words z-score p-value
31 to 32 141730 -0.5290 0.298404
30 to 31 142055 0.4297 0.666295
29 to 30 142054 0.4268 0.665221
28 to 29 141930 0.0610 0.524310
27 to 28 141769 -0.4140 0.339454
26 to 27 142593 2.0167 0.978138
25 to 26 141486 -1.2488 0.105876
24 to 25 142048 0.4091 0.658751
23 to 24 141611 -0.8800 0.189422
22 to 23 142090 0.5329 0.702966
21 to 22 141560 -1.0305 0.151394
20 to 21 142519 1.7984 0.963946
19 to 20 141964 0.1613 0.564059
18 to 19 142009 0.2940 0.615626
17 to 18 141342 -1.6735 0.047111
16 to 17 142499 1.7394 0.959021
15 to 16 141541 -1.0865 0.138625
14 to 15 142349 1.2970 0.902678
13 to 14 141689 -0.6499 0.257865
12 to 13 141792 -0.3461 0.364632
11 to 12 141834 -0.2222 0.412074
10 to 11 141279 -1.8594 0.031487
9 to 10 142169 0.7660 0.778158
8 to 9 141906 -0.0098 0.496081
7 to 8 141850 -0.1750 0.430534
6 to 7 141823 -0.2547 0.399493
5 to 6 141380 -1.5614 0.059209
4 to 5 142160 0.7394 0.770180
3 to 4 142169 0.7660 0.778158
2 to 3 142361 1.3324 0.908629
1 to 2 141912 0.0079 0.503142
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-15_11:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2512.41 0.175 0.569649
Test results for specific bytes for dh-ranFile-2018-06-15_11:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2498.82 -0.017 0.493332
2 to 9 2499.30 -0.010 0.496074
3 to 10 2652.41 2.155 0.984436
4 to 11 2426.16 -1.044 0.148179
5 to 12 2509.34 0.132 0.552527
6 to 13 2435.01 -0.919 0.179009
7 to 14 2498.49 -0.021 0.491469
8 to 15 2439.67 -0.853 0.196777
9 to 16 2628.52 1.817 0.965428
10 to 17 2428.61 -1.010 0.156325
11 to 18 2550.10 0.709 0.760709
12 to 19 2516.46 0.233 0.592061
13 to 20 2461.26 -0.548 0.291879
14 to 21 2499.58 -0.006 0.497655
15 to 22 2440.66 -0.839 0.200695
16 to 23 2399.08 -1.427 0.076766
17 to 24 2440.39 -0.843 0.199624
18 to 25 2527.07 0.383 0.649053
19 to 26 2600.19 1.417 0.921741
20 to 27 2467.01 -0.467 0.320390
21 to 28 2531.53 0.446 0.672147
22 to 29 2518.55 0.262 0.603465
23 to 30 2563.42 0.897 0.815105
24 to 31 2434.16 -0.931 0.175882
25 to 32 2451.38 -0.688 0.245840
CDPARK for dh-ranFile-2018-06-15_11:31: 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
3518 -0.2283 0.409702
3520 -0.1370 0.445521
3541 0.8219 0.794438
3500 -1.0502 0.146807
3504 -0.8676 0.192812
3521 -0.0913 0.463617
3513 -0.4566 0.323972
3481 -1.9178 0.027568
3509 -0.6393 0.261324
3544 0.9589 0.831196
Square side=100, avg. no. parked=3515.10 sample std.=17.69
p-value of the KSTEST for those 10 p-values: 0.379103
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-15_11:31
0.6434,0.3304,0.3321,0.4845,0.3516,0.6314,0.7177,0.4025,0.3092,0.6087,
The KS test for those 10 p-values: 0.210317
The 3DSPHERES test for dh-ranFile-2018-06-15_11:31
sample no r^3 equiv. uni.
1 6.289 0.189124
2 12.365 0.337775
3 29.213 0.622337
4 17.706 0.445775
5 15.635 0.406181
6 0.801 0.026340
7 3.219 0.101754
8 6.365 0.191169
9 32.022 0.656097
10 0.822 0.027016
11 20.305 0.491778
12 2.445 0.078277
13 20.160 0.489317
14 21.318 0.508645
15 0.889 0.029191
16 1.235 0.040338
17 29.786 0.629484
18 18.409 0.458616
19 75.633 0.919630
20 86.782 0.944575
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.057237
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-15_11:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 -1.2 3.2 -0.1 0.0 1.1
-0.6 -1.5 -1.1 0.3 0.7 -1.0
-0.6 0.7 0.7 -0.2 -1.2 0.4
0.6 0.4 1.3 0.8 -0.1 -0.6
-0.5 -0.1 -0.3 -0.7 -0.5 -0.2
-0.3 -0.6 -0.0 1.8 -1.9 -0.5
-0.5 -1.0 0.1 -0.1 0.1 -1.0
-1.1
Chi-square with 42 degrees of freedom:36.703965
z-score=-0.577845, p-value=0.297890
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-15_11:31
Test no p-value
1 0.006162
2 0.067747
3 0.470323
4 0.089522
5 0.069455
6 0.229408
7 0.439771
8 0.153451
9 0.001868
10 0.465852
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000470
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-15_11:31:
(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 66813 0.32 66584 0.10
3 25000.00 24883 0.55 25132 0.70
4 6666.67 6684 0.05 6616 0.39
5 1388.89 1359 0.64 1398 0.06
6 238.10 223 0.96 233 0.11
7 34.72 34 0.01 33 0.09
8 4.96 3 0.77 3 0.77
p=0.23010 p=0.10091
Number of rngs required: 687699, p-value: 0.208
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-15_11:31
No. of wins: Observed Expected
98330 98585.9
z-score=-1.144, pvalue=0.12624
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66455 66666.7 0.672 0.672
2 37716 37654.3 0.101 0.773
3 27165 26954.7 1.640 2.413
4 19186 19313.5 0.841 3.255
5 13813 13851.4 0.107 3.361
6 9864 9943.5 0.636 3.997
7 7043 7145.0 1.457 5.454
8 5211 5139.1 1.007 6.461
9 3719 3699.9 0.099 6.560
10 2715 2666.3 0.890 7.450
11 1967 1923.3 0.992 8.441
12 1405 1388.7 0.190 8.631
13 1082 1003.7 6.106 14.737
14 762 726.1 1.771 16.508
15 485 525.8 3.171 19.679
16 377 381.2 0.045 19.725
17 307 276.5 3.355 23.080
18 212 200.8 0.621 23.701
19 137 146.0 0.553 24.254
20 118 106.2 1.308 25.562
21 261 287.1 2.375 27.937
Chisq= 27.94 for 20 degrees of freedom, p= 0.88910
SUMMARY of craptest
p-value for no. of wins: 0.126240
p-value for throws/game: 0.889095
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-15_11:31
No. of wins: Observed Expected
98646 98585.9
z-score= 0.269, pvalue=0.60603
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66475 66666.7 0.551 0.551
2 37575 37654.3 0.167 0.718
3 27193 26954.7 2.106 2.824
4 19318 19313.5 0.001 2.825
5 13712 13851.4 1.403 4.229
6 9906 9943.5 0.142 4.370
7 7193 7145.0 0.322 4.693
8 5216 5139.1 1.152 5.844
9 3728 3699.9 0.214 6.058
10 2645 2666.3 0.170 6.228
11 1976 1923.3 1.442 7.671
12 1392 1388.7 0.008 7.678
13 1040 1003.7 1.312 8.990
14 717 726.1 0.115 9.105
15 529 525.8 0.019 9.124
16 381 381.2 0.000 9.124
17 278 276.5 0.008 9.132
18 199 200.8 0.017 9.149
19 138 146.0 0.437 9.585
20 100 106.2 0.364 9.949
21 289 287.1 0.012 9.961
Chisq= 9.96 for 20 degrees of freedom, p= 0.03113
SUMMARY of craptest
p-value for no. of wins: 0.606030
p-value for throws/game: 0.031131
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0005,0.0019,0.0062,0.0111,0.0134,0.0174,0.0261,0.0263,0.0270,0.0276,
0.0292,0.0311,0.0315,0.0341,0.0348,0.0403,0.0471,0.0521,0.0558,0.0572,
0.0592,0.0677,0.0695,0.0733,0.0768,0.0770,0.0783,0.0821,0.0879,0.0895,
0.0903,0.0925,0.0987,0.1009,0.1018,0.1059,0.1092,0.1262,0.1284,0.1337,
0.1347,0.1349,0.1386,0.1468,0.1482,0.1514,0.1535,0.1562,0.1563,0.1590,
0.1759,0.1766,0.1790,0.1833,0.1883,0.1891,0.1894,0.1912,0.1928,0.1940,
0.1968,0.1996,0.2007,0.2010,0.2076,0.2079,0.2103,0.2115,0.2155,0.2216,
0.2294,0.2301,0.2324,0.2458,0.2579,0.2613,0.2817,0.2919,0.2949,0.2958,
0.2979,0.2981,0.2984,0.2985,0.3012,0.3092,0.3111,0.3139,0.3196,0.3204,
0.3222,0.3240,0.3241,0.3304,0.3321,0.3325,0.3376,0.3378,0.3391,0.3395,
0.3444,0.3452,0.3456,0.3465,0.3493,0.3516,0.3542,0.3645,0.3646,0.3733,
0.3791,0.3849,0.3884,0.3887,0.3909,0.3995,0.4025,0.4062,0.4072,0.4089,
0.4097,0.4121,0.4138,0.4231,0.4305,0.4344,0.4365,0.4392,0.4394,0.4398,
0.4455,0.4458,0.4461,0.4537,0.4586,0.4632,0.4634,0.4636,0.4659,0.4703,
0.4803,0.4836,0.4845,0.4857,0.4858,0.4893,0.4894,0.4915,0.4918,0.4922,
0.4933,0.4945,0.4951,0.4961,0.4961,0.4977,0.4982,0.5031,0.5050,0.5081,
0.5086,0.5119,0.5243,0.5284,0.5289,0.5379,0.5525,0.5558,0.5605,0.5641,
0.5696,0.5731,0.5921,0.6035,0.6060,0.6087,0.6156,0.6194,0.6223,0.6227,
0.6293,0.6295,0.6314,0.6434,0.6491,0.6561,0.6588,0.6652,0.6663,0.6686,
0.6721,0.6796,0.6977,0.6979,0.7000,0.7030,0.7163,0.7177,0.7214,0.7321,
0.7443,0.7450,0.7457,0.7475,0.7512,0.7544,0.7607,0.7609,0.7656,0.7670,
0.7688,0.7702,0.7739,0.7758,0.7782,0.7782,0.7790,0.7843,0.7902,0.7944,
0.7962,0.7977,0.8098,0.8151,0.8172,0.8233,0.8266,0.8312,0.8331,0.8442,
0.8570,0.8572,0.8580,0.8614,0.8742,0.8784,0.8867,0.8891,0.8894,0.9027,
0.9086,0.9088,0.9097,0.9098,0.9196,0.9217,0.9332,0.9372,0.9404,0.9446,
0.9466,0.9505,0.9553,0.9558,0.9564,0.9590,0.9639,0.9654,0.9671,0.9684,
0.9690,0.9739,0.9781,0.9822,0.9833,0.9835,0.9844,0.9847,0.9883,
Overall p-value after applying KStest on 269 p-values = 0.181496
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.