RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-05_21:31
(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 20.2010 0.735922
2 to 25 15.65 18.2040 0.623915
3 to 26 15.81 14.8155 0.391228
4 to 27 15.51 22.1496 0.820966
5 to 28 15.85 10.3046 0.109649
6 to 29 15.79 16.8943 0.538452
7 to 30 15.82 15.8277 0.463919
8 to 31 16.10 15.2147 0.419981
9 to 32 15.89 11.8994 0.193807
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.805640
Tough bday spacings test for dh-ranFile-2018-07-05_21:31: 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 10 38 72 99 94 78 55 26 11 11 6
(O-E)^2/E 0.1 0.1 0.0 0.0 0.1 0.0 0.2 0.5 1.0 2.9 0.9
Birthday Spacings: Sum(O-E)^2/E= 5.786, p= 0.167
RESULTS OF GCD FOR dh-ranFile-2018-07-05_21:31
Euclid's algorithm:
p-value, steps to gcd: 0.938292
p-value, dist. of gcd's: 0.187689
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-05_21:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.254 0.333 0.232 0.342 0.916 0.693 0.838 0.998
Bits 8 to 15---> 0.012 0.644 0.308 0.712 0.724 0.950 0.296 0.652
Bits 16 to 23---> 0.657 0.218 0.647 0.541 0.058 0.206 0.583 0.153
Bits 24 to 31---> 0.088 0.783 0.408 0.502 0.359 0.122 0.751 0.493
KS test for the above 32 p values: 0.057
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-05_21:31,
p-values for 5 runs: 0.8777, 0.6365, 0.6634, 0.9120, 0.1947
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-05_21:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 208 211.4 0.055 0.055
r= 29 5051 5134.0 1.342 1.397
r= 30 23060 23103.0 0.080 1.478
r= 31 11681 11551.5 1.451 2.929
chi-square = 2.929 with df = 3; p-value = 0.597
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-05_21:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 210 211.4 0.010 0.010
r= 30 5222 5134.0 1.508 1.518
r= 31 23123 23103.0 0.017 1.535
r= 32 11445 11551.5 0.982 2.517
chi-square = 2.517 with df = 3; p-value = 0.528
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-05_21:31
b-rank test for bits 1 to 8, p=0.40405
b-rank test for bits 2 to 9, p=0.13599
b-rank test for bits 3 to 10, p=0.16860
b-rank test for bits 4 to 11, p=0.06106
b-rank test for bits 5 to 12, p=0.18890
b-rank test for bits 6 to 13, p=0.25583
b-rank test for bits 7 to 14, p=0.70521
b-rank test for bits 8 to 15, p=0.19420
b-rank test for bits 9 to 16, p=0.11858
b-rank test for bits 10 to 17, p=0.73863
b-rank test for bits 11 to 18, p=0.40614
b-rank test for bits 12 to 19, p=0.58081
b-rank test for bits 13 to 20, p=0.70637
b-rank test for bits 14 to 21, p=0.79062
b-rank test for bits 15 to 22, p=0.24085
b-rank test for bits 16 to 23, p=0.66996
b-rank test for bits 17 to 24, p=0.08468
b-rank test for bits 18 to 25, p=0.33133
b-rank test for bits 19 to 26, p=0.00499
b-rank test for bits 20 to 27, p=0.26957
b-rank test for bits 21 to 28, p=0.49627
b-rank test for bits 22 to 29, p=0.66868
b-rank test for bits 23 to 30, p=0.93902
b-rank test for bits 24 to 31, p=0.63658
b-rank test for bits 25 to 32, p=0.86415
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 = 0.336959
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-05_21:31
(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 142248 0.79 0.785611
2 141803 -0.25 0.401899
3 142115 0.48 0.684577
4 141006 -2.11 0.017404
5 142216 0.72 0.763164
6 141662 -0.58 0.281675
7 141511 -0.93 0.176010
8 142188 0.65 0.742508
9 141673 -0.55 0.290415
10 141648 -0.61 0.270738
11 141424 -1.13 0.128408
12 141799 -0.26 0.398288
13 142061 0.35 0.638469
14 142618 1.66 0.951116
15 142238 0.77 0.778733
16 142605 1.63 0.947961
17 141586 -0.76 0.224991
18 141560 -0.82 0.207195
19 142036 0.30 0.616369
20 141947 0.09 0.535067
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-05_21:31
Bits used No. missing words z-score p-value
23 to 32 141501 -1.4080 0.079560
22 to 31 142060 0.5196 0.698312
21 to 30 141964 0.1885 0.574764
20 to 29 141766 -0.4942 0.310568
19 to 28 141742 -0.5770 0.281970
18 to 27 142519 2.1023 0.982237
17 to 26 141949 0.1368 0.554403
16 to 25 141593 -1.0908 0.137682
15 to 24 141620 -0.9977 0.159215
14 to 23 141726 -0.6322 0.263637
13 to 22 142085 0.6058 0.727663
12 to 21 142283 1.2885 0.901217
11 to 20 142088 0.6161 0.731087
10 to 19 141756 -0.5287 0.298498
9 to 18 141773 -0.4701 0.319141
8 to 17 141674 -0.8115 0.208544
7 to 16 142564 2.2575 0.988011
6 to 15 141452 -1.5770 0.057398
5 to 14 141463 -1.5391 0.061894
4 to 13 141716 -0.6667 0.252496
3 to 12 141819 -0.3115 0.377717
2 to 11 141742 -0.5770 0.281970
1 to 10 141758 -0.5218 0.300895
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-05_21:31
Bits used No. missing words z-score p-value
28 to 32 141834 -0.2554 0.399224
27 to 31 142020 0.3752 0.646227
26 to 30 141595 -1.0655 0.143319
25 to 29 142058 0.5040 0.692857
24 to 28 142394 1.6429 0.949803
23 to 27 141703 -0.6994 0.242144
22 to 26 142096 0.6328 0.736561
21 to 25 141766 -0.4859 0.313532
20 to 24 141801 -0.3672 0.356727
19 to 23 142755 2.8667 0.997926
18 to 22 141987 0.2633 0.603836
17 to 21 142123 0.7243 0.765561
16 to 20 141717 -0.6520 0.257212
15 to 19 141582 -1.1096 0.133587
14 to 18 141780 -0.4384 0.330546
13 to 17 142095 0.6294 0.735453
12 to 16 142492 1.9752 0.975875
11 to 15 142139 0.7785 0.781875
10 to 14 141507 -1.3638 0.086310
9 to 13 142294 1.3040 0.903877
8 to 12 141719 -0.6452 0.259403
7 to 11 141701 -0.7062 0.240031
6 to 10 141885 -0.0825 0.467135
5 to 9 141927 0.0599 0.523882
4 to 8 141862 -0.1604 0.436267
3 to 7 141721 -0.6384 0.261605
2 to 6 142258 1.1819 0.881384
1 to 5 142481 1.9379 0.973680
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-05_21:31
Bits used No. missing words z-score p-value
31 to 32 141599 -0.9154 0.179984
30 to 31 142474 1.6657 0.952113
29 to 30 142099 0.5595 0.712089
28 to 29 142264 1.0462 0.852271
27 to 28 141333 -1.7001 0.044557
26 to 27 141796 -0.3343 0.369074
25 to 26 142020 0.3265 0.627962
24 to 25 142095 0.5477 0.708051
23 to 24 142279 1.0905 0.862247
22 to 23 141522 -1.1426 0.126609
21 to 22 141891 -0.0541 0.478439
20 to 21 141523 -1.1396 0.127223
19 to 20 141478 -1.2724 0.101623
18 to 19 141345 -1.6647 0.047987
17 to 18 141870 -0.1160 0.453819
16 to 17 141965 0.1642 0.565220
15 to 16 141850 -0.1750 0.430534
14 to 15 141502 -1.2016 0.114766
13 to 14 141572 -0.9951 0.159850
12 to 13 142113 0.6008 0.726012
11 to 12 142349 1.2970 0.902678
10 to 11 141959 0.1465 0.558244
9 to 10 141959 0.1465 0.558244
8 to 9 141516 -1.1603 0.122970
7 to 8 141678 -0.6824 0.247496
6 to 7 141540 -1.0895 0.137974
5 to 6 141693 -0.6381 0.261691
4 to 5 142016 0.3147 0.623490
3 to 4 141678 -0.6824 0.247496
2 to 3 141043 -2.5555 0.005301
1 to 2 141651 -0.7620 0.223019
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-05_21:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2548.97 0.693 0.755703
Test results for specific bytes for dh-ranFile-2018-07-05_21:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2505.37 0.076 0.530281
2 to 9 2441.16 -0.832 0.202676
3 to 10 2447.53 -0.742 0.229014
4 to 11 2506.85 0.097 0.538584
5 to 12 2532.32 0.457 0.676187
6 to 13 2545.71 0.646 0.741013
7 to 14 2517.54 0.248 0.597974
8 to 15 2498.75 -0.018 0.492957
9 to 16 2599.94 1.413 0.921219
10 to 17 2495.00 -0.071 0.471825
11 to 18 2500.49 0.007 0.502742
12 to 19 2493.90 -0.086 0.465646
13 to 20 2517.81 0.252 0.599435
14 to 21 2475.02 -0.353 0.361963
15 to 22 2383.44 -1.648 0.049634
16 to 23 2535.51 0.502 0.692243
17 to 24 2477.64 -0.316 0.375918
18 to 25 2453.48 -0.658 0.255312
19 to 26 2518.37 0.260 0.602513
20 to 27 2515.39 0.218 0.586141
21 to 28 2562.51 0.884 0.811644
22 to 29 2650.46 2.128 0.983322
23 to 30 2510.89 0.154 0.561201
24 to 31 2488.22 -0.167 0.433817
25 to 32 2574.05 1.047 0.852492
CDPARK for dh-ranFile-2018-07-05_21:31: 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
3490 -1.5068 0.065925
3521 -0.0913 0.463617
3523 0.0000 0.500000
3514 -0.4110 0.340551
3455 -3.1050 0.000951
3518 -0.2283 0.409702
3530 0.3196 0.625377
3515 -0.3653 0.357445
3528 0.2283 0.590298
Square side=100, avg. no. parked=3511.80 sample std.=21.70
p-value of the KSTEST for those 10 p-values: 0.123488
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-05_21:31
0.5397,0.0892,0.3865,0.1934,0.5270,0.4735,0.6313,0.3914,0.5280,0.3202,
The KS test for those 10 p-values: 0.185747
The 3DSPHERES test for dh-ranFile-2018-07-05_21:31
sample no r^3 equiv. uni.
1 72.718 0.911427
2 29.998 0.632098
3 1.152 0.037688
4 11.560 0.319782
5 16.605 0.425059
6 91.384 0.952457
7 19.800 0.483154
8 13.551 0.363462
9 13.532 0.363052
10 45.050 0.777239
11 16.713 0.427132
12 110.082 0.974508
13 18.738 0.464520
14 106.589 0.971361
15 1.329 0.043330
16 9.565 0.272992
17 11.869 0.326747
18 12.911 0.349738
19 25.279 0.569429
20 4.791 0.147609
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.569006
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-05_21:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 1.3 0.8 -0.8 0.5 1.8
-1.2 -0.6 0.4 -1.0 1.6 -2.7
-0.6 0.7 -0.1 -0.4 -1.3 -0.2
1.1 0.1 0.8 -0.2 -0.7 0.8
-0.1 2.3 0.1 0.3 -0.2 -0.1
-0.5 0.6 1.1 1.1 0.3 1.1
-0.5 1.1 -1.2 2.1 0.1 0.0
2.7
Chi-square with 42 degrees of freedom:49.945406
z-score=0.866915, p-value=0.813087
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-05_21:31
Test no p-value
1 0.093293
2 0.382485
3 0.476603
4 0.058057
5 0.637965
6 0.531293
7 0.259953
8 0.617379
9 0.387968
10 0.187924
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.189984
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-05_21:31:
(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 66669 0.00 66706 0.02
3 25000.00 24988 0.01 25013 0.01
4 6666.67 6717 0.38 6641 0.10
5 1388.89 1381 0.04 1375 0.14
6 238.10 207 4.06 223 0.96
7 34.72 33 0.09 37 0.15
8 4.96 4 0.19 4 0.19
p=0.42541 p=0.04461
Number of rngs required: 688264, p-value: 0.436
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-05_21:31
No. of wins: Observed Expected
98903 98585.9
z-score= 1.418, pvalue=0.92197
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66804 66666.7 0.283 0.283
2 37575 37654.3 0.167 0.450
3 26904 26954.7 0.095 0.545
4 19313 19313.5 0.000 0.545
5 13936 13851.4 0.516 1.062
6 9896 9943.5 0.227 1.289
7 7164 7145.0 0.050 1.340
8 5176 5139.1 0.265 1.605
9 3746 3699.9 0.575 2.180
10 2612 2666.3 1.106 3.286
11 1966 1923.3 0.947 4.233
12 1291 1388.7 6.879 11.112
13 1001 1003.7 0.007 11.119
14 723 726.1 0.014 11.133
15 501 525.8 1.173 12.306
16 354 381.2 1.934 14.240
17 301 276.5 2.164 16.403
18 194 200.8 0.232 16.636
19 138 146.0 0.437 17.072
20 110 106.2 0.135 17.207
21 295 287.1 0.217 17.424
Chisq= 17.42 for 20 degrees of freedom, p= 0.37469
SUMMARY of craptest
p-value for no. of wins: 0.921969
p-value for throws/game: 0.374688
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-05_21:31
No. of wins: Observed Expected
98683 98585.9
z-score= 0.434, pvalue=0.66803
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66793 66666.7 0.239 0.239
2 37789 37654.3 0.482 0.721
3 26907 26954.7 0.085 0.806
4 19376 19313.5 0.203 1.008
5 13714 13851.4 1.363 2.371
6 9868 9943.5 0.574 2.945
7 7181 7145.0 0.181 3.127
8 5061 5139.1 1.186 4.313
9 3726 3699.9 0.185 4.497
10 2711 2666.3 0.749 5.247
11 1850 1923.3 2.796 8.042
12 1374 1388.7 0.156 8.199
13 998 1003.7 0.033 8.231
14 728 726.1 0.005 8.236
15 518 525.8 0.117 8.353
16 379 381.2 0.012 8.365
17 276 276.5 0.001 8.366
18 195 200.8 0.169 8.535
19 146 146.0 0.000 8.535
20 115 106.2 0.727 9.262
21 295 287.1 0.217 9.479
Chisq= 9.48 for 20 degrees of freedom, p= 0.02333
SUMMARY of craptest
p-value for no. of wins: 0.668028
p-value for throws/game: 0.023327
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0010,0.0050,0.0053,0.0115,0.0174,0.0233,0.0377,0.0433,0.0446,0.0446,
0.0480,0.0496,0.0566,0.0574,0.0581,0.0584,0.0611,0.0619,0.0659,0.0796,
0.0847,0.0863,0.0885,0.0892,0.0933,0.1016,0.1096,0.1148,0.1186,0.1216,
0.1230,0.1235,0.1266,0.1272,0.1284,0.1336,0.1360,0.1377,0.1380,0.1433,
0.1476,0.1528,0.1592,0.1599,0.1671,0.1686,0.1760,0.1800,0.1857,0.1877,
0.1879,0.1889,0.1900,0.1934,0.1938,0.1942,0.1947,0.2027,0.2063,0.2072,
0.2085,0.2184,0.2230,0.2250,0.2290,0.2322,0.2400,0.2408,0.2421,0.2475,
0.2475,0.2525,0.2539,0.2553,0.2558,0.2572,0.2594,0.2600,0.2616,0.2617,
0.2636,0.2696,0.2707,0.2730,0.2817,0.2820,0.2820,0.2904,0.2957,0.2985,
0.3009,0.3084,0.3106,0.3135,0.3191,0.3198,0.3202,0.3267,0.3305,0.3313,
0.3334,0.3370,0.3406,0.3416,0.3497,0.3567,0.3574,0.3593,0.3620,0.3631,
0.3635,0.3691,0.3747,0.3759,0.3777,0.3825,0.3865,0.3880,0.3912,0.3914,
0.3983,0.3992,0.4019,0.4040,0.4061,0.4084,0.4097,0.4200,0.4251,0.4254,
0.4271,0.4305,0.4338,0.4363,0.4365,0.4538,0.4636,0.4639,0.4645,0.4656,
0.4671,0.4718,0.4735,0.4766,0.4784,0.4832,0.4930,0.4930,0.4963,0.5000,
0.5018,0.5027,0.5182,0.5239,0.5270,0.5278,0.5280,0.5303,0.5313,0.5351,
0.5385,0.5386,0.5397,0.5407,0.5544,0.5582,0.5582,0.5612,0.5652,0.5690,
0.5694,0.5748,0.5808,0.5826,0.5861,0.5903,0.5973,0.5980,0.5994,0.6025,
0.6038,0.6164,0.6174,0.6235,0.6239,0.6254,0.6280,0.6313,0.6321,0.6365,
0.6366,0.6380,0.6385,0.6442,0.6462,0.6467,0.6520,0.6566,0.6634,0.6680,
0.6687,0.6700,0.6762,0.6846,0.6922,0.6925,0.6929,0.6983,0.7052,0.7064,
0.7081,0.7119,0.7121,0.7241,0.7260,0.7277,0.7311,0.7355,0.7359,0.7366,
0.7386,0.7410,0.7425,0.7513,0.7557,0.7632,0.7656,0.7772,0.7787,0.7819,
0.7834,0.7856,0.7906,0.8056,0.8116,0.8131,0.8210,0.8378,0.8523,0.8525,
0.8622,0.8642,0.8777,0.8814,0.9012,0.9027,0.9039,0.9114,0.9120,0.9159,
0.9212,0.9220,0.9383,0.9390,0.9480,0.9498,0.9498,0.9511,0.9521,0.9525,
0.9714,0.9737,0.9745,0.9759,0.9822,0.9833,0.9880,0.9979,0.9982,
Overall p-value after applying KStest on 269 p-values = 0.033144
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.