RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-18_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 15.64 23.4020 0.863385
2 to 25 15.64 32.2588 0.986029
3 to 26 15.82 14.8817 0.396000
4 to 27 15.49 25.2689 0.911150
5 to 28 15.82 10.2378 0.106655
6 to 29 15.78 36.0738 0.995516
7 to 30 16.02 7.7218 0.027860
8 to 31 16.06 29.4131 0.969098
9 to 32 15.54 28.7480 0.963078
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.001994
Tough bday spacings test for dh-ranFile-2018-06-18_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 35 73 100 90 71 61 32 21 7 1
(O-E)^2/E 0.0 0.1 0.0 0.1 0.6 0.7 1.5 0.2 2.5 0.0 2.3
Birthday Spacings: Sum(O-E)^2/E= 7.924, p= 0.364
RESULTS OF GCD FOR dh-ranFile-2018-06-18_06:31
Euclid's algorithm:
p-value, steps to gcd: 0.571487
p-value, dist. of gcd's: 0.492050
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-18_06:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.960 0.776 0.042 0.415 0.533 0.850 0.316 0.648
Bits 8 to 15---> 0.678 0.575 0.442 0.149 0.765 0.613 0.459 0.070
Bits 16 to 23---> 0.716 0.423 0.778 0.700 0.540 0.609 0.618 0.219
Bits 24 to 31---> 0.934 0.550 0.396 0.245 0.947 0.670 0.591 0.596
KS test for the above 32 p values: 0.823
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-18_06:31,
p-values for 5 runs: 0.4864, 0.2802, 0.5729, 0.5225, 0.3376
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-18_06:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 216 211.4 0.099 0.099
r= 29 5080 5134.0 0.568 0.668
r= 30 23118 23103.0 0.010 0.677
r= 31 11586 11551.5 0.103 0.780
chi-square = 0.780 with df = 3; p-value = 0.146
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-18_06:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 203 211.4 0.335 0.335
r= 30 5008 5134.0 3.093 3.428
r= 31 23157 23103.0 0.126 3.554
r= 32 11632 11551.5 0.561 4.115
chi-square = 4.115 with df = 3; p-value = 0.751
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-18_06:31
b-rank test for bits 1 to 8, p=0.33778
b-rank test for bits 2 to 9, p=0.55849
b-rank test for bits 3 to 10, p=0.60184
b-rank test for bits 4 to 11, p=0.16012
b-rank test for bits 5 to 12, p=0.60922
b-rank test for bits 6 to 13, p=0.66997
b-rank test for bits 7 to 14, p=0.70782
b-rank test for bits 8 to 15, p=0.52374
b-rank test for bits 9 to 16, p=0.43339
b-rank test for bits 10 to 17, p=0.79051
b-rank test for bits 11 to 18, p=0.01366
b-rank test for bits 12 to 19, p=0.70046
b-rank test for bits 13 to 20, p=0.03788
b-rank test for bits 14 to 21, p=0.10316
b-rank test for bits 15 to 22, p=0.32564
b-rank test for bits 16 to 23, p=0.58749
b-rank test for bits 17 to 24, p=0.76341
b-rank test for bits 18 to 25, p=0.50566
b-rank test for bits 19 to 26, p=0.99266
b-rank test for bits 20 to 27, p=0.83627
b-rank test for bits 21 to 28, p=0.12354
b-rank test for bits 22 to 29, p=0.81710
b-rank test for bits 23 to 30, p=0.17630
b-rank test for bits 24 to 31, p=0.71793
b-rank test for bits 25 to 32, p=0.47383
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 = 0.764374
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-18_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 141435 -1.11 0.133877
2 142244 0.78 0.782875
3 141377 -1.24 0.106794
4 142037 0.30 0.617261
5 141207 -1.64 0.050403
6 141505 -0.94 0.172407
7 141426 -1.13 0.129391
8 142445 1.25 0.894636
9 141350 -1.31 0.095633
10 141457 -1.06 0.145291
11 141442 -1.09 0.137440
12 142305 0.92 0.822377
13 141538 -0.87 0.192808
14 142380 1.10 0.864268
15 142407 1.16 0.877541
16 141379 -1.24 0.107656
17 141427 -1.13 0.129884
18 142167 0.60 0.726424
19 141673 -0.55 0.290415
20 142112 0.47 0.682082
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-18_06:31
Bits used No. missing words z-score p-value
23 to 32 142034 0.4299 0.666365
22 to 31 141904 -0.0184 0.492668
21 to 30 141803 -0.3667 0.356938
20 to 29 141685 -0.7736 0.219598
19 to 28 141899 -0.0356 0.485792
18 to 27 141536 -1.2873 0.098987
17 to 26 142074 0.5678 0.714924
16 to 25 141762 -0.5080 0.305715
15 to 24 141754 -0.5356 0.296110
14 to 23 141684 -0.7770 0.218579
13 to 22 141576 -1.1494 0.125193
12 to 21 141863 -0.1598 0.436536
11 to 20 141589 -1.1046 0.134669
10 to 19 141756 -0.5287 0.298498
9 to 18 141458 -1.5563 0.059817
8 to 17 141901 -0.0287 0.488542
7 to 16 141953 0.1506 0.559849
6 to 15 142619 2.4471 0.992800
5 to 14 142216 1.0575 0.854854
4 to 13 141793 -0.4011 0.344159
3 to 12 141796 -0.3908 0.347975
2 to 11 141719 -0.6563 0.255812
1 to 10 141125 -2.7046 0.003419
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-18_06:31
Bits used No. missing words z-score p-value
28 to 32 141967 0.1955 0.577496
27 to 31 142427 1.7548 0.960354
26 to 30 141791 -0.4011 0.344166
25 to 29 142537 2.1277 0.983319
24 to 28 141993 0.2836 0.611652
23 to 27 141857 -0.1774 0.429601
22 to 26 141783 -0.4282 0.334239
21 to 25 142178 0.9107 0.818785
20 to 24 141879 -0.1028 0.459056
19 to 23 141328 -1.9706 0.024384
18 to 22 141653 -0.8689 0.192447
17 to 21 142022 0.3819 0.648744
16 to 20 141798 -0.3774 0.352942
15 to 19 142096 0.6328 0.736561
14 to 18 141400 -1.7265 0.042125
13 to 17 141475 -1.4723 0.070469
12 to 16 141904 -0.0181 0.492792
11 to 15 142026 0.3955 0.653760
10 to 14 141650 -0.8791 0.189678
9 to 13 141407 -1.7028 0.044301
8 to 12 141520 -1.3198 0.093457
7 to 11 141903 -0.0215 0.491440
6 to 10 141352 -1.8893 0.029429
5 to 9 141940 0.1040 0.541402
4 to 8 141772 -0.4655 0.320778
3 to 7 141219 -2.3401 0.009639
2 to 6 142377 1.5853 0.943553
1 to 5 141677 -0.7876 0.215477
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-18_06:31
Bits used No. missing words z-score p-value
31 to 32 141631 -0.8210 0.205814
30 to 31 141893 -0.0482 0.480790
29 to 30 142232 0.9518 0.829408
28 to 29 141373 -1.5821 0.056814
27 to 28 141888 -0.0629 0.474915
26 to 27 141442 -1.3786 0.084016
25 to 26 141873 -0.1072 0.457328
24 to 25 142109 0.5890 0.722068
23 to 24 142069 0.4710 0.681181
22 to 23 141143 -2.2606 0.011893
21 to 22 142464 1.6362 0.949101
20 to 21 141785 -0.3668 0.356901
19 to 20 141774 -0.3992 0.344872
18 to 19 142169 0.7660 0.778158
17 to 18 141994 0.2498 0.598615
16 to 17 141999 0.2645 0.604308
15 to 16 141552 -1.0541 0.145925
14 to 15 141959 0.1465 0.558244
13 to 14 141620 -0.8535 0.196696
12 to 13 141625 -0.8387 0.200810
11 to 12 141926 0.0492 0.519610
10 to 11 141861 -0.1426 0.443316
9 to 10 141612 -0.8771 0.190222
8 to 9 141863 -0.1367 0.445647
7 to 8 142512 1.7778 0.962281
6 to 7 141790 -0.3520 0.362417
5 to 6 141569 -1.0039 0.157708
4 to 5 142397 1.4386 0.924862
3 to 4 141557 -1.0393 0.149328
2 to 3 141746 -0.4818 0.314974
1 to 2 141593 -0.9331 0.175377
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-18_06:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2507.05 0.100 0.539702
Test results for specific bytes for dh-ranFile-2018-06-18_06:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2469.65 -0.429 0.333880
2 to 9 2481.82 -0.257 0.398527
3 to 10 2521.00 0.297 0.616765
4 to 11 2460.52 -0.558 0.288299
5 to 12 2486.90 -0.185 0.426522
6 to 13 2494.29 -0.081 0.467794
7 to 14 2306.04 -2.743 0.003044
8 to 15 2579.53 1.125 0.869652
9 to 16 2601.04 1.429 0.923477
10 to 17 2566.15 0.936 0.825245
11 to 18 2507.43 0.105 0.541819
12 to 19 2517.07 0.241 0.595363
13 to 20 2524.07 0.340 0.633217
14 to 21 2479.31 -0.293 0.384909
15 to 22 2416.98 -1.174 0.120183
16 to 23 2468.97 -0.439 0.330406
17 to 24 2520.22 0.286 0.612536
18 to 25 2374.72 -1.772 0.038215
19 to 26 2416.07 -1.187 0.117625
20 to 27 2431.93 -0.963 0.167870
21 to 28 2411.12 -1.257 0.104378
22 to 29 2534.84 0.493 0.688873
23 to 30 2514.20 0.201 0.579587
24 to 31 2444.43 -0.786 0.215986
25 to 32 2591.92 1.300 0.903188
CDPARK for dh-ranFile-2018-06-18_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
3506 -0.7763 0.218799
3509 -0.6393 0.261324
3525 0.0913 0.536383
3546 1.0502 0.853193
3580 2.6027 0.995376
3516 -0.3196 0.374623
3548 1.1416 0.873180
3569 2.1005 0.982156
3486 -1.6895 0.045562
3496 -1.2329 0.108811
Square side=100, avg. no. parked=3528.10 sample std.=29.82
p-value of the KSTEST for those 10 p-values: 0.322749
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-18_06:31
0.3667,0.2913,0.1015,0.5882,0.3814,0.0815,0.5349,0.9383,0.7453,0.8984,
The KS test for those 10 p-values: 0.993691
The 3DSPHERES test for dh-ranFile-2018-06-18_06:31
sample no r^3 equiv. uni.
1 139.614 0.990475
2 68.288 0.897332
3 39.949 0.735954
4 10.008 0.283659
5 42.748 0.759477
6 13.684 0.366264
7 6.895 0.205332
8 29.519 0.626171
9 6.561 0.196438
10 38.881 0.726386
11 44.382 0.772223
12 6.308 0.189621
13 93.888 0.956265
14 21.318 0.508655
15 51.218 0.818642
16 19.583 0.479404
17 59.096 0.860525
18 1.210 0.039518
19 4.474 0.138553
20 34.458 0.682915
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.571841
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-18_06:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -1.6 -1.6 -0.1 -1.3 -0.2
1.2 1.3 -0.8 -1.7 0.7 0.0
-0.5 0.4 -0.9 -0.8 0.3 0.4
-0.4 -0.4 0.3 1.3 -0.7 -0.4
0.5 1.9 -0.9 0.8 0.6 -0.9
0.7 1.7 -0.1 0.9 2.0 0.1
-1.4 -0.7 -1.6 -0.1 -0.6 0.0
-1.1
Chi-square with 42 degrees of freedom:40.491221
z-score=-0.164621, p-value=0.462715
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-18_06:31
Test no p-value
1 0.110044
2 0.134565
3 0.019412
4 0.005431
5 0.240930
6 0.056631
7 0.114184
8 0.849011
9 0.049629
10 0.631088
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000515
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-18_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 66747 0.10 66734 0.07
3 25000.00 24957 0.07 24930 0.20
4 6666.67 6630 0.20 6673 0.01
5 1388.89 1376 0.12 1380 0.06
6 238.10 232 0.16 244 0.15
7 34.72 50 6.72 36 0.05
8 4.96 7 0.84 2 1.77
p=0.77700 p=0.10850
Number of rngs required: 687503, p-value: 0.148
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-18_06:31
No. of wins: Observed Expected
98489 98585.9
z-score=-0.433, pvalue=0.33243
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66881 66666.7 0.689 0.689
2 37550 37654.3 0.289 0.978
3 26944 26954.7 0.004 0.982
4 19427 19313.5 0.667 1.650
5 13645 13851.4 3.076 4.726
6 9943 9943.5 0.000 4.726
7 7123 7145.0 0.068 4.794
8 5139 5139.1 0.000 4.794
9 3753 3699.9 0.763 5.557
10 2713 2666.3 0.818 6.375
11 1948 1923.3 0.316 6.692
12 1373 1388.7 0.178 6.870
13 963 1003.7 1.652 8.521
14 658 726.1 6.394 14.916
15 547 525.8 0.852 15.768
16 361 381.2 1.065 16.833
17 260 276.5 0.989 17.822
18 230 200.8 4.237 22.059
19 131 146.0 1.538 23.597
20 124 106.2 2.978 26.575
21 287 287.1 0.000 26.575
Chisq= 26.58 for 20 degrees of freedom, p= 0.85235
SUMMARY of craptest
p-value for no. of wins: 0.332432
p-value for throws/game: 0.852350
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-18_06:31
No. of wins: Observed Expected
98296 98585.9
z-score=-1.296, pvalue=0.09742
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66557 66666.7 0.180 0.180
2 37486 37654.3 0.752 0.933
3 26768 26954.7 1.294 2.226
4 19556 19313.5 3.046 5.272
5 13794 13851.4 0.238 5.510
6 9975 9943.5 0.100 5.610
7 7223 7145.0 0.851 6.461
8 5114 5139.1 0.122 6.583
9 3793 3699.9 2.344 8.927
10 2662 2666.3 0.007 8.934
11 2010 1923.3 3.906 12.840
12 1355 1388.7 0.820 13.660
13 1036 1003.7 1.038 14.698
14 722 726.1 0.024 14.722
15 533 525.8 0.098 14.819
16 372 381.2 0.220 15.039
17 282 276.5 0.108 15.147
18 198 200.8 0.040 15.187
19 145 146.0 0.007 15.193
20 123 106.2 2.652 17.846
21 296 287.1 0.275 18.121
Chisq= 18.12 for 20 degrees of freedom, p= 0.42056
SUMMARY of craptest
p-value for no. of wins: 0.097416
p-value for throws/game: 0.420559
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0005,0.0020,0.0030,0.0034,0.0054,0.0096,0.0119,0.0137,0.0194,0.0244,
0.0279,0.0294,0.0379,0.0382,0.0395,0.0419,0.0421,0.0443,0.0456,0.0496,
0.0504,0.0566,0.0568,0.0598,0.0697,0.0705,0.0815,0.0840,0.0935,0.0956,
0.0974,0.0990,0.1015,0.1032,0.1044,0.1067,0.1068,0.1077,0.1085,0.1088,
0.1100,0.1142,0.1176,0.1202,0.1235,0.1252,0.1294,0.1299,0.1339,0.1346,
0.1347,0.1374,0.1386,0.1453,0.1458,0.1459,0.1484,0.1488,0.1493,0.1577,
0.1601,0.1679,0.1724,0.1754,0.1763,0.1896,0.1897,0.1902,0.1924,0.1928,
0.1964,0.1967,0.2008,0.2053,0.2058,0.2155,0.2160,0.2185,0.2186,0.2188,
0.2196,0.2409,0.2453,0.2558,0.2613,0.2802,0.2837,0.2883,0.2904,0.2913,
0.2961,0.2985,0.3057,0.3150,0.3155,0.3208,0.3227,0.3256,0.3304,0.3324,
0.3339,0.3342,0.3376,0.3378,0.3442,0.3442,0.3449,0.3480,0.3529,0.3569,
0.3569,0.3624,0.3637,0.3663,0.3667,0.3746,0.3814,0.3849,0.3960,0.3964,
0.3985,0.4149,0.4206,0.4227,0.4265,0.4296,0.4334,0.4365,0.4422,0.4433,
0.4456,0.4573,0.4587,0.4591,0.4627,0.4678,0.4738,0.4749,0.4794,0.4808,
0.4858,0.4864,0.4885,0.4914,0.4920,0.4927,0.4928,0.5057,0.5087,0.5196,
0.5225,0.5237,0.5332,0.5349,0.5364,0.5397,0.5399,0.5414,0.5418,0.5499,
0.5582,0.5585,0.5598,0.5715,0.5718,0.5729,0.5749,0.5775,0.5796,0.5875,
0.5882,0.5908,0.5954,0.5962,0.5986,0.6018,0.6043,0.6090,0.6092,0.6117,
0.6125,0.6130,0.6168,0.6173,0.6179,0.6262,0.6311,0.6332,0.6482,0.6487,
0.6538,0.6664,0.6695,0.6700,0.6782,0.6812,0.6821,0.6829,0.6889,0.6995,
0.7005,0.7078,0.7149,0.7158,0.7179,0.7221,0.7264,0.7264,0.7360,0.7366,
0.7453,0.7507,0.7595,0.7634,0.7644,0.7650,0.7722,0.7763,0.7770,0.7779,
0.7782,0.7829,0.7905,0.8171,0.8186,0.8188,0.8224,0.8235,0.8252,0.8294,
0.8363,0.8490,0.8497,0.8524,0.8532,0.8549,0.8605,0.8634,0.8643,0.8697,
0.8732,0.8775,0.8946,0.8973,0.8984,0.9032,0.9112,0.9235,0.9249,0.9340,
0.9383,0.9436,0.9469,0.9491,0.9563,0.9603,0.9604,0.9623,0.9631,0.9691,
0.9822,0.9833,0.9860,0.9905,0.9927,0.9928,0.9937,0.9954,0.9955,
Overall p-value after applying KStest on 269 p-values = 0.041776
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.