RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-05_19:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 16.00 19.0183 0.672517
2 to 25 16.05 16.5646 0.515778
3 to 26 16.22 12.4564 0.228252
4 to 27 16.23 20.7003 0.760016
5 to 28 15.83 13.7541 0.315572
6 to 29 15.76 10.9276 0.139699
7 to 30 15.50 23.7475 0.873541
8 to 31 15.69 11.2901 0.158908
9 to 32 15.42 23.9415 0.878966
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.950635
Tough bday spacings test for dh-ranFile-2018-07-05_19:31: 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 38 93 85 86 85 50 37 10 6 1
(O-E)^2/E 0.0 0.1 5.3 1.6 1.4 0.6 0.1 1.8 1.6 0.1 2.3
Birthday Spacings: Sum(O-E)^2/E= 14.829, p= 0.862
RESULTS OF GCD FOR dh-ranFile-2018-07-05_19:31
Euclid's algorithm:
p-value, steps to gcd: 0.512221
p-value, dist. of gcd's: 0.540989
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-05_19:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.631 0.135 0.294 0.018 0.428 0.869 0.317 0.900
Bits 8 to 15---> 0.408 0.969 0.440 0.184 0.241 0.381 0.294 0.942
Bits 16 to 23---> 0.808 0.220 0.108 0.424 0.402 0.082 0.939 0.678
Bits 24 to 31---> 0.419 0.528 0.710 0.436 0.398 0.696 0.998 0.795
KS test for the above 32 p values: 0.231
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-05_19:31,
p-values for 5 runs: 0.0459, 0.8000, 0.4996, 0.6980, 0.0958
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-05_19:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 207 211.4 0.092 0.092
r= 29 4989 5134.0 4.096 4.188
r= 30 23156 23103.0 0.121 4.310
r= 31 11648 11551.5 0.806 5.115
chi-square = 5.115 with df = 3; p-value = 0.836
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-05_19:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 210 211.4 0.010 0.010
r= 30 4987 5134.0 4.210 4.219
r= 31 23386 23103.0 3.465 7.685
r= 32 11417 11551.5 1.567 9.251
chi-square = 9.251 with df = 3; p-value = 0.974
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-05_19:31
b-rank test for bits 1 to 8, p=0.81698
b-rank test for bits 2 to 9, p=0.99201
b-rank test for bits 3 to 10, p=0.90051
b-rank test for bits 4 to 11, p=0.99009
b-rank test for bits 5 to 12, p=0.47162
b-rank test for bits 6 to 13, p=0.75757
b-rank test for bits 7 to 14, p=0.67755
b-rank test for bits 8 to 15, p=0.78528
b-rank test for bits 9 to 16, p=0.77342
b-rank test for bits 10 to 17, p=0.52815
b-rank test for bits 11 to 18, p=0.96859
b-rank test for bits 12 to 19, p=0.86082
b-rank test for bits 13 to 20, p=0.46253
b-rank test for bits 14 to 21, p=0.73692
b-rank test for bits 15 to 22, p=0.39624
b-rank test for bits 16 to 23, p=0.05269
b-rank test for bits 17 to 24, p=0.84680
b-rank test for bits 18 to 25, p=0.64331
b-rank test for bits 19 to 26, p=0.76945
b-rank test for bits 20 to 27, p=0.37353
b-rank test for bits 21 to 28, p=0.38992
b-rank test for bits 22 to 29, p=0.31554
b-rank test for bits 23 to 30, p=0.08251
b-rank test for bits 24 to 31, p=0.16486
b-rank test for bits 25 to 32, p=0.75665
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 = 0.048778
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-05_19:31
(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 141969 0.14 0.555439
2 142626 1.67 0.952980
3 141978 0.16 0.563734
4 142596 1.60 0.945684
5 142719 1.89 0.970738
6 142855 2.21 0.986430
7 141822 -0.20 0.419160
8 142820 2.13 0.983320
9 141808 -0.24 0.406425
10 141726 -0.43 0.334201
11 142524 1.44 0.924519
12 143148 2.89 0.998099
13 142330 0.98 0.837165
14 142006 0.23 0.589347
15 142078 0.39 0.653242
16 141576 -0.78 0.218046
17 141906 -0.01 0.496896
18 141846 -0.15 0.441184
19 141701 -0.49 0.313217
20 141975 0.15 0.560972
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-05_19:31
Bits used No. missing words z-score p-value
23 to 32 141907 -0.0080 0.496795
22 to 31 142111 0.6954 0.756602
21 to 30 141900 -0.0322 0.487167
20 to 29 142274 1.2575 0.895711
19 to 28 141835 -0.2563 0.398856
18 to 27 141570 -1.1701 0.120980
17 to 26 141536 -1.2873 0.098987
16 to 25 141651 -0.8908 0.186520
15 to 24 141444 -1.6046 0.054292
14 to 23 142166 0.8851 0.811940
13 to 22 142296 1.3333 0.908791
12 to 21 142209 1.0333 0.849279
11 to 20 142190 0.9678 0.833435
10 to 19 141675 -0.8080 0.209535
9 to 18 142343 1.4954 0.932597
8 to 17 141836 -0.2529 0.400187
7 to 16 141894 -0.0529 0.478921
6 to 15 142049 0.4816 0.684962
5 to 14 141821 -0.3046 0.380341
4 to 13 142230 1.1058 0.865585
3 to 12 142083 0.5989 0.725368
2 to 11 141687 -0.7667 0.221643
1 to 10 142141 0.7989 0.787815
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-05_19:31
Bits used No. missing words z-score p-value
28 to 32 141892 -0.0587 0.476577
27 to 31 142125 0.7311 0.767636
26 to 30 141698 -0.7164 0.236881
25 to 29 142129 0.7446 0.771757
24 to 28 141904 -0.0181 0.492792
23 to 27 142150 0.8158 0.792702
22 to 26 141446 -1.5706 0.058137
21 to 25 142242 1.1277 0.870276
20 to 24 141350 -1.8960 0.028978
19 to 23 141947 0.1277 0.550805
18 to 22 142127 0.7379 0.769702
17 to 21 141939 0.1006 0.540057
16 to 20 142094 0.6260 0.734343
15 to 19 141543 -1.2418 0.107156
14 to 18 141740 -0.5740 0.282984
13 to 17 141843 -0.2248 0.411049
12 to 16 141491 -1.4181 0.078086
11 to 15 142259 1.1853 0.882055
10 to 14 142332 1.4328 0.924040
9 to 13 141914 0.0158 0.506315
8 to 12 141965 0.1887 0.574841
7 to 11 142068 0.5379 0.704665
6 to 10 142315 1.3752 0.915458
5 to 9 141931 0.0735 0.529279
4 to 8 141819 -0.3062 0.379725
3 to 7 141631 -0.9435 0.172715
2 to 6 141854 -0.1876 0.425611
1 to 5 142558 2.1989 0.986057
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-05_19:31
Bits used No. missing words z-score p-value
31 to 32 141765 -0.4258 0.335144
30 to 31 141908 -0.0039 0.498435
29 to 30 141703 -0.6086 0.271381
28 to 29 142273 1.0728 0.858314
27 to 28 141365 -1.6057 0.054171
26 to 27 142009 0.2940 0.615626
25 to 26 142400 1.4474 0.926108
24 to 25 141724 -0.5467 0.292294
23 to 24 141687 -0.6558 0.255963
22 to 23 141856 -0.1573 0.437498
21 to 22 141841 -0.2016 0.420129
20 to 21 142339 1.2675 0.897505
19 to 20 142087 0.5241 0.699896
18 to 19 142131 0.6539 0.743410
17 to 18 142156 0.7276 0.766583
16 to 17 142040 0.3855 0.650051
15 to 16 142417 1.4976 0.932875
14 to 15 141582 -0.9656 0.167128
13 to 14 141749 -0.4729 0.318125
12 to 13 141891 -0.0541 0.478439
11 to 12 141573 -0.9921 0.160569
10 to 11 142017 0.3176 0.624610
9 to 10 141612 -0.8771 0.190222
8 to 9 142095 0.5477 0.708051
7 to 8 142162 0.7453 0.771967
6 to 7 141996 0.2557 0.600895
5 to 6 141238 -1.9803 0.023834
4 to 5 141628 -0.8299 0.203303
3 to 4 142225 0.9312 0.824120
2 to 3 142050 0.4150 0.660913
1 to 2 142348 1.2940 0.902169
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-05_19:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2549.66 0.702 0.758767
Test results for specific bytes for dh-ranFile-2018-07-05_19:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2474.48 -0.361 0.359070
2 to 9 2408.05 -1.300 0.096727
3 to 10 2497.13 -0.041 0.483817
4 to 11 2562.86 0.889 0.813002
5 to 12 2390.84 -1.544 0.061327
6 to 13 2404.65 -1.349 0.088746
7 to 14 2386.88 -1.600 0.054828
8 to 15 2444.12 -0.790 0.214693
9 to 16 2546.65 0.660 0.745265
10 to 17 2433.06 -0.947 0.171900
11 to 18 2491.82 -0.116 0.453956
12 to 19 2524.33 0.344 0.634629
13 to 20 2410.18 -1.270 0.102008
14 to 21 2597.75 1.382 0.916573
15 to 22 2495.69 -0.061 0.475696
16 to 23 2461.12 -0.550 0.291214
17 to 24 2573.46 1.039 0.850566
18 to 25 2603.02 1.457 0.927425
19 to 26 2417.03 -1.173 0.120324
20 to 27 2422.27 -1.099 0.135822
21 to 28 2599.23 1.403 0.919739
22 to 29 2373.72 -1.786 0.037061
23 to 30 2628.72 1.820 0.965647
24 to 31 2392.75 -1.517 0.064659
25 to 32 2494.25 -0.081 0.467603
CDPARK for dh-ranFile-2018-07-05_19:31: 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
3549 1.1872 0.882429
3551 1.2785 0.899470
3525 0.0913 0.536383
3529 0.2740 0.607947
3515 -0.3653 0.357445
3550 1.2329 0.891189
3528 0.2283 0.590298
3514 -0.4110 0.340551
3535 0.5479 0.708135
3513 -0.4566 0.323972
Square side=100, avg. no. parked=3530.90 sample std.=14.21
p-value of the KSTEST for those 10 p-values: 0.264494
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-05_19:31
0.0868,0.7511,0.9582,0.7349,0.9159,0.2144,0.3854,0.9854,0.9843,0.2909,
The KS test for those 10 p-values: 0.067281
The 3DSPHERES test for dh-ranFile-2018-07-05_19:31
sample no r^3 equiv. uni.
1 6.440 0.193187
2 97.803 0.961615
3 9.869 0.280325
4 32.160 0.657682
5 37.969 0.717943
6 12.747 0.346164
7 8.481 0.246251
8 8.198 0.239104
9 26.485 0.586392
10 24.287 0.554945
11 6.493 0.194625
12 1.916 0.061868
13 18.964 0.468545
14 67.524 0.894687
15 14.928 0.392009
16 58.725 0.858790
17 39.165 0.728964
18 26.919 0.592329
19 6.145 0.185221
20 9.328 0.267226
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.762790
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-05_19:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 1.3 0.6 1.2 -0.9 -1.5
-0.4 0.8 0.9 1.5 -0.9 0.6
0.2 1.0 -0.2 -1.0 -0.7 -0.3
-0.3 1.6 -1.4 1.1 0.4 -1.3
-0.7 0.4 -1.1 1.2 -0.6 1.1
-1.1 0.4 2.4 -0.3 -0.8 0.1
0.7 -1.0 0.1 -1.8 0.1 0.0
-1.1
Chi-square with 42 degrees of freedom:40.221547
z-score=-0.194045, p-value=0.450747
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-05_19:31
Test no p-value
1 0.109195
2 0.446915
3 0.867502
4 0.111906
5 0.048433
6 0.127222
7 0.045688
8 0.840062
9 0.003204
10 0.000519
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000554
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-05_19:31:
(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 67010 1.77 66419 0.92
3 25000.00 24649 4.93 25127 0.65
4 6666.67 6700 0.17 6771 1.63
5 1388.89 1375 0.14 1421 0.74
6 238.10 229 0.35 233 0.11
7 34.72 34 0.01 26 2.19
8 4.96 2 1.77 2 1.77
p=0.83363 p=0.76233
Number of rngs required: 687672, p-value: 0.199
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-05_19:31
No. of wins: Observed Expected
98157 98585.9
z-score=-1.918, pvalue=0.02755
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66354 66666.7 1.466 1.466
2 37780 37654.3 0.419 1.886
3 27081 26954.7 0.591 2.477
4 19152 19313.5 1.350 3.827
5 14089 13851.4 4.075 7.902
6 10102 9943.5 2.525 10.427
7 7076 7145.0 0.667 11.094
8 5074 5139.1 0.824 11.918
9 3606 3699.9 2.381 14.299
10 2631 2666.3 0.467 14.767
11 1973 1923.3 1.283 16.049
12 1449 1388.7 2.615 18.664
13 1011 1003.7 0.053 18.717
14 714 726.1 0.203 18.920
15 570 525.8 3.709 22.629
16 338 381.2 4.885 27.515
17 256 276.5 1.526 29.040
18 210 200.8 0.419 29.459
19 147 146.0 0.007 29.466
20 83 106.2 5.074 34.540
21 304 287.1 0.993 35.533
Chisq= 35.53 for 20 degrees of freedom, p= 0.98256
SUMMARY of craptest
p-value for no. of wins: 0.027549
p-value for throws/game: 0.982558
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-05_19:31
No. of wins: Observed Expected
98762 98585.9
z-score= 0.788, pvalue=0.78460
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66763 66666.7 0.139 0.139
2 37585 37654.3 0.128 0.267
3 26916 26954.7 0.056 0.322
4 19302 19313.5 0.007 0.329
5 13717 13851.4 1.304 1.634
6 9950 9943.5 0.004 1.638
7 7121 7145.0 0.081 1.719
8 5273 5139.1 3.490 5.209
9 3806 3699.9 3.045 8.254
10 2669 2666.3 0.003 8.256
11 1936 1923.3 0.083 8.340
12 1340 1388.7 1.711 10.050
13 989 1003.7 0.216 10.266
14 727 726.1 0.001 10.267
15 514 525.8 0.266 10.534
16 356 381.2 1.660 12.193
17 293 276.5 0.980 13.173
18 184 200.8 1.410 14.583
19 147 146.0 0.007 14.590
20 110 106.2 0.135 14.725
21 302 287.1 0.772 15.497
Chisq= 15.50 for 20 degrees of freedom, p= 0.25271
SUMMARY of craptest
p-value for no. of wins: 0.784595
p-value for throws/game: 0.252706
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0005,0.0006,0.0032,0.0178,0.0238,0.0275,0.0290,0.0371,0.0457,0.0459,
0.0484,0.0488,0.0527,0.0542,0.0543,0.0548,0.0581,0.0613,0.0619,0.0647,
0.0673,0.0781,0.0822,0.0825,0.0868,0.0887,0.0958,0.0967,0.0990,0.1020,
0.1072,0.1080,0.1092,0.1119,0.1203,0.1210,0.1272,0.1351,0.1358,0.1397,
0.1589,0.1606,0.1649,0.1671,0.1719,0.1727,0.1842,0.1852,0.1865,0.1902,
0.1932,0.1946,0.1990,0.2033,0.2095,0.2144,0.2147,0.2180,0.2201,0.2216,
0.2283,0.2307,0.2369,0.2391,0.2406,0.2463,0.2527,0.2560,0.2645,0.2672,
0.2714,0.2803,0.2830,0.2909,0.2912,0.2923,0.2943,0.2943,0.3132,0.3155,
0.3156,0.3171,0.3181,0.3240,0.3342,0.3351,0.3406,0.3462,0.3574,0.3591,
0.3735,0.3797,0.3803,0.3811,0.3854,0.3899,0.3920,0.3962,0.3977,0.3989,
0.4002,0.4016,0.4064,0.4085,0.4110,0.4187,0.4192,0.4201,0.4243,0.4256,
0.4283,0.4355,0.4375,0.4402,0.4412,0.4469,0.4507,0.4540,0.4625,0.4676,
0.4685,0.4716,0.4757,0.4766,0.4784,0.4789,0.4838,0.4872,0.4928,0.4968,
0.4969,0.4984,0.4996,0.5063,0.5122,0.5158,0.5278,0.5282,0.5293,0.5364,
0.5401,0.5410,0.5508,0.5549,0.5554,0.5610,0.5637,0.5748,0.5864,0.5893,
0.5903,0.5923,0.6009,0.6079,0.6156,0.6246,0.6311,0.6346,0.6433,0.6501,
0.6532,0.6577,0.6609,0.6725,0.6775,0.6783,0.6850,0.6959,0.6980,0.6999,
0.7047,0.7081,0.7081,0.7102,0.7179,0.7254,0.7290,0.7343,0.7349,0.7369,
0.7434,0.7453,0.7511,0.7566,0.7566,0.7576,0.7588,0.7600,0.7623,0.7628,
0.7666,0.7676,0.7694,0.7697,0.7718,0.7720,0.7734,0.7846,0.7853,0.7878,
0.7927,0.7954,0.8000,0.8075,0.8119,0.8130,0.8170,0.8241,0.8334,0.8336,
0.8365,0.8372,0.8401,0.8468,0.8493,0.8506,0.8583,0.8588,0.8608,0.8616,
0.8656,0.8675,0.8687,0.8703,0.8735,0.8790,0.8821,0.8824,0.8912,0.8947,
0.8957,0.8975,0.8995,0.8997,0.9005,0.9022,0.9088,0.9155,0.9159,0.9166,
0.9197,0.9240,0.9245,0.9261,0.9274,0.9326,0.9329,0.9393,0.9422,0.9457,
0.9506,0.9530,0.9582,0.9616,0.9656,0.9686,0.9689,0.9707,0.9739,0.9826,
0.9833,0.9843,0.9854,0.9861,0.9864,0.9901,0.9920,0.9981,0.9982,
Overall p-value after applying KStest on 269 p-values = 0.106214
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.