RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-16_08:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.60 22.3216 0.827335
2 to 25 15.60 16.9834 0.544508
3 to 26 15.66 15.3328 0.428478
4 to 27 15.87 13.4134 0.291895
5 to 28 15.96 17.9234 0.606310
6 to 29 16.14 10.1113 0.101121
7 to 30 15.93 15.3711 0.431230
8 to 31 15.77 14.4387 0.364161
9 to 32 16.01 9.5142 0.077263
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.490939
Tough bday spacings test for dh-ranFile-2018-06-16_08:31: 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 11 39 76 109 86 61 66 27 12 10 3
(O-E)^2/E 0.4 0.2 0.1 1.3 1.4 3.8 3.7 0.3 0.6 1.7 0.3
Birthday Spacings: Sum(O-E)^2/E= 13.634, p= 0.810
RESULTS OF GCD FOR dh-ranFile-2018-06-16_08:31
Euclid's algorithm:
p-value, steps to gcd: 0.605831
p-value, dist. of gcd's: 0.201312
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-16_08:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.473 0.460 0.662 0.539 0.210 0.568 0.915 0.747
Bits 8 to 15---> 0.667 0.542 0.494 0.512 0.795 0.727 0.621 0.467
Bits 16 to 23---> 0.832 0.401 0.866 0.098 0.548 0.503 0.924 0.137
Bits 24 to 31---> 0.710 0.125 0.587 0.412 0.270 0.157 0.388 0.869
KS test for the above 32 p values: 0.753
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-16_08:31,
p-values for 5 runs: 0.7428, 0.4653, 0.0777, 0.6470, 0.4481
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-16_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 205 211.4 0.195 0.195
r= 29 5035 5134.0 1.909 2.104
r= 30 23105 23103.0 0.000 2.104
r= 31 11655 11551.5 0.927 3.031
chi-square = 3.031 with df = 3; p-value = 0.613
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-16_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 220 211.4 0.348 0.348
r= 30 5128 5134.0 0.007 0.355
r= 31 23200 23103.0 0.407 0.762
r= 32 11452 11551.5 0.857 1.620
chi-square = 1.620 with df = 3; p-value = 0.345
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-16_08:31
b-rank test for bits 1 to 8, p=0.24510
b-rank test for bits 2 to 9, p=0.93722
b-rank test for bits 3 to 10, p=0.85200
b-rank test for bits 4 to 11, p=0.27655
b-rank test for bits 5 to 12, p=0.32665
b-rank test for bits 6 to 13, p=0.28899
b-rank test for bits 7 to 14, p=0.70182
b-rank test for bits 8 to 15, p=0.86725
b-rank test for bits 9 to 16, p=0.38507
b-rank test for bits 10 to 17, p=0.75070
b-rank test for bits 11 to 18, p=0.17490
b-rank test for bits 12 to 19, p=0.04081
b-rank test for bits 13 to 20, p=0.34461
b-rank test for bits 14 to 21, p=0.45598
b-rank test for bits 15 to 22, p=0.69200
b-rank test for bits 16 to 23, p=0.32659
b-rank test for bits 17 to 24, p=0.37100
b-rank test for bits 18 to 25, p=0.40106
b-rank test for bits 19 to 26, p=0.47417
b-rank test for bits 20 to 27, p=0.88834
b-rank test for bits 21 to 28, p=0.55752
b-rank test for bits 22 to 29, p=0.00673
b-rank test for bits 23 to 30, p=0.57439
b-rank test for bits 24 to 31, p=0.21717
b-rank test for bits 25 to 32, p=0.18231
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 = 0.519221
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-16_08:31
(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 141347 -1.31 0.094447
2 142891 2.29 0.989094
3 142129 0.51 0.696111
4 142580 1.57 0.941441
5 141696 -0.50 0.309089
6 141636 -0.64 0.261535
7 141660 -0.58 0.280099
8 142305 0.92 0.822377
9 141681 -0.53 0.296850
10 141576 -0.78 0.218046
11 142331 0.99 0.837740
12 141697 -0.50 0.309913
13 142953 2.44 0.992625
14 142524 1.44 0.924519
15 142092 0.43 0.665237
16 141823 -0.20 0.420073
17 142256 0.81 0.791023
18 141879 -0.07 0.471753
19 142389 1.12 0.868797
20 141707 -0.47 0.318202
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-16_08:31
Bits used No. missing words z-score p-value
23 to 32 141408 -1.7287 0.041929
22 to 31 141933 0.0816 0.532526
21 to 30 141534 -1.2942 0.097791
20 to 29 141895 -0.0494 0.480295
19 to 28 142288 1.3058 0.904183
18 to 27 141669 -0.8287 0.203630
17 to 26 141628 -0.9701 0.165998
16 to 25 141971 0.2127 0.584202
15 to 24 141964 0.1885 0.574764
14 to 23 141838 -0.2460 0.402855
13 to 22 141714 -0.6736 0.250298
12 to 21 142118 0.7196 0.764100
11 to 20 142318 1.4092 0.920613
10 to 19 142229 1.1023 0.864837
9 to 18 141966 0.1954 0.577466
8 to 17 141262 -2.2322 0.012802
7 to 16 142133 0.7713 0.779728
6 to 15 141999 0.3092 0.621418
5 to 14 141619 -1.0011 0.158380
4 to 13 141652 -0.8873 0.187447
3 to 12 142068 0.5471 0.707858
2 to 11 141663 -0.8494 0.197826
1 to 10 142491 2.0058 0.977559
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-16_08:31
Bits used No. missing words z-score p-value
28 to 32 142475 1.9175 0.972414
27 to 31 141766 -0.4859 0.313532
26 to 30 142055 0.4938 0.689275
25 to 29 141904 -0.0181 0.492792
24 to 28 142196 0.9718 0.834416
23 to 27 141653 -0.8689 0.192447
22 to 26 142127 0.7379 0.769702
21 to 25 141775 -0.4554 0.324427
20 to 24 141358 -1.8689 0.030817
19 to 23 141741 -0.5706 0.284132
18 to 22 141944 0.1175 0.546778
17 to 21 141788 -0.4113 0.340431
16 to 20 141906 -0.0113 0.495497
15 to 19 142375 1.5785 0.942779
14 to 18 141880 -0.0994 0.460401
13 to 17 141646 -0.8926 0.186024
12 to 16 142274 1.2362 0.891802
11 to 15 141695 -0.7265 0.233753
10 to 14 141818 -0.3096 0.378435
9 to 13 141557 -1.1943 0.116173
8 to 12 142143 0.7921 0.785849
7 to 11 142242 1.1277 0.870276
6 to 10 142246 1.1413 0.873118
5 to 9 141468 -1.4960 0.067322
4 to 8 141205 -2.3876 0.008480
3 to 7 141768 -0.4791 0.315939
2 to 6 142001 0.3107 0.622003
1 to 5 141552 -1.2113 0.112893
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-16_08:31
Bits used No. missing words z-score p-value
31 to 32 141682 -0.6706 0.251241
30 to 31 141881 -0.0836 0.466699
29 to 30 141819 -0.2665 0.394942
28 to 29 142027 0.3471 0.635745
27 to 28 142057 0.4356 0.668438
26 to 27 141924 0.0433 0.517259
25 to 26 142082 0.5094 0.694747
24 to 25 142326 1.2291 0.890486
23 to 24 141426 -1.4258 0.076970
22 to 23 142299 1.1495 0.874819
21 to 22 141931 0.0639 0.525484
20 to 21 141882 -0.0806 0.467872
19 to 20 142439 1.5624 0.940909
18 to 19 141854 -0.1632 0.435174
17 to 18 141739 -0.5024 0.307676
16 to 17 141941 0.0934 0.537216
15 to 16 142565 1.9341 0.973451
14 to 15 142381 1.3914 0.917941
13 to 14 141834 -0.2222 0.412074
12 to 13 142005 0.2822 0.611110
11 to 12 142024 0.3383 0.632416
10 to 11 142254 1.0167 0.845358
9 to 10 141814 -0.2812 0.389275
8 to 9 141850 -0.1750 0.430534
7 to 8 141544 -1.0777 0.140591
6 to 7 141625 -0.8387 0.200810
5 to 6 141676 -0.6883 0.245635
4 to 5 141610 -0.8830 0.188624
3 to 4 141662 -0.7296 0.232821
2 to 3 141816 -0.2753 0.391539
1 to 2 141685 -0.6617 0.254069
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-16_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2536.84 0.521 0.698801
Test results for specific bytes for dh-ranFile-2018-06-16_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2389.75 -1.559 0.059480
2 to 9 2415.93 -1.189 0.117243
3 to 10 2419.83 -1.134 0.128444
4 to 11 2590.83 1.285 0.900527
5 to 12 2543.90 0.621 0.732661
6 to 13 2601.07 1.429 0.923542
7 to 14 2498.68 -0.019 0.492562
8 to 15 2473.55 -0.374 0.354190
9 to 16 2396.65 -1.462 0.071921
10 to 17 2470.42 -0.418 0.337847
11 to 18 2513.29 0.188 0.574560
12 to 19 2526.01 0.368 0.643527
13 to 20 2583.27 1.178 0.880534
14 to 21 2486.29 -0.194 0.423154
15 to 22 2379.72 -1.701 0.044464
16 to 23 2486.74 -0.188 0.425612
17 to 24 2598.13 1.388 0.917404
18 to 25 2600.67 1.424 0.922733
19 to 26 2569.26 0.979 0.836318
20 to 27 2530.69 0.434 0.667883
21 to 28 2553.37 0.755 0.774802
22 to 29 2500.16 0.002 0.500924
23 to 30 2388.07 -1.583 0.056725
24 to 31 2473.60 -0.373 0.354460
25 to 32 2501.90 0.027 0.510712
CDPARK for dh-ranFile-2018-06-16_08:31: 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
3505 -0.8219 0.205562
3510 -0.5936 0.276387
3517 -0.2740 0.392053
3547 1.0959 0.863437
3538 0.6849 0.753306
3522 -0.0457 0.481790
3528 0.2283 0.590298
3505 -0.8219 0.205562
3494 -1.3242 0.092718
3499 -1.0959 0.136563
Square side=100, avg. no. parked=3516.50 sample std.=16.35
p-value of the KSTEST for those 10 p-values: 0.460263
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-16_08:31
0.8124,0.8683,0.0061,0.3258,0.2740,0.4752,0.5608,0.9462,0.2896,0.9816,
The KS test for those 10 p-values: 0.547789
The 3DSPHERES test for dh-ranFile-2018-06-16_08:31
sample no r^3 equiv. uni.
1 16.382 0.420777
2 66.457 0.890873
3 7.604 0.223896
4 54.812 0.839115
5 7.240 0.214427
6 14.583 0.384970
7 2.477 0.079243
8 16.974 0.432100
9 30.899 0.642982
10 1.666 0.054018
11 62.441 0.875238
12 71.128 0.906605
13 8.313 0.242011
14 5.558 0.169127
15 17.171 0.435815
16 32.860 0.665569
17 81.132 0.933090
18 53.916 0.834240
19 17.864 0.448704
20 87.965 0.946719
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.689110
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-16_08:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 0.9 -0.6 -0.1 0.1 0.2
-0.3 0.7 -0.7 1.6 1.2 -0.2
0.6 1.5 -2.0 0.2 -0.4 -0.5
1.2 -0.1 -1.2 -1.9 0.5 -0.4
0.8 -0.3 1.1 -1.2 0.8 0.8
-0.6 1.7 -1.0 1.2 1.0 -1.6
-1.4 0.8 -0.4 -0.1 0.1 0.0
-0.1
Chi-square with 42 degrees of freedom:37.576581
z-score=-0.482635, p-value=0.334608
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-16_08:31
Test no p-value
1 0.015031
2 0.767623
3 0.290877
4 0.200895
5 0.551829
6 0.024242
7 0.711653
8 0.001167
9 0.148470
10 0.045259
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.004064
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-16_08:31:
(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 66496 0.44 66569 0.14
3 25000.00 25083 0.28 25089 0.32
4 6666.67 6770 1.60 6686 0.06
5 1388.89 1413 0.42 1353 0.93
6 238.10 203 5.17 253 0.93
7 34.72 31 0.40 45 3.04
8 4.96 3 0.77 4 0.19
p=0.83080 p=0.53126
Number of rngs required: 688846, p-value: 0.695
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-16_08:31
No. of wins: Observed Expected
98760 98585.9
z-score= 0.779, pvalue=0.78197
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66740 66666.7 0.081 0.081
2 37689 37654.3 0.032 0.113
3 26886 26954.7 0.175 0.288
4 19058 19313.5 3.379 3.667
5 13874 13851.4 0.037 3.704
6 9964 9943.5 0.042 3.746
7 7145 7145.0 0.000 3.746
8 5192 5139.1 0.545 4.291
9 3717 3699.9 0.079 4.370
10 2780 2666.3 4.849 9.219
11 1932 1923.3 0.039 9.258
12 1394 1388.7 0.020 9.278
13 1017 1003.7 0.176 9.454
14 709 726.1 0.405 9.858
15 510 525.8 0.477 10.335
16 383 381.2 0.009 10.344
17 286 276.5 0.324 10.668
18 187 200.8 0.952 11.620
19 144 146.0 0.027 11.647
20 104 106.2 0.046 11.694
21 289 287.1 0.012 11.706
Chisq= 11.71 for 20 degrees of freedom, p= 0.07418
SUMMARY of craptest
p-value for no. of wins: 0.781969
p-value for throws/game: 0.074175
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-16_08:31
No. of wins: Observed Expected
98107 98585.9
z-score=-2.142, pvalue=0.01611
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66591 66666.7 0.086 0.086
2 37883 37654.3 1.389 1.475
3 26813 26954.7 0.745 2.220
4 18958 19313.5 6.542 8.762
5 14172 13851.4 7.420 16.182
6 9788 9943.5 2.433 18.615
7 7084 7145.0 0.521 19.136
8 5137 5139.1 0.001 19.137
9 3799 3699.9 2.656 21.793
10 2684 2666.3 0.118 21.911
11 1948 1923.3 0.316 22.227
12 1419 1388.7 0.659 22.886
13 1036 1003.7 1.038 23.925
14 747 726.1 0.599 24.524
15 562 525.8 2.487 27.011
16 377 381.2 0.045 27.057
17 264 276.5 0.569 27.625
18 186 200.8 1.095 28.720
19 154 146.0 0.440 29.160
20 85 106.2 4.237 33.398
21 313 287.1 2.334 35.732
Chisq= 35.73 for 20 degrees of freedom, p= 0.98346
SUMMARY of craptest
p-value for no. of wins: 0.016107
p-value for throws/game: 0.983464
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0012,0.0041,0.0061,0.0067,0.0085,0.0128,0.0150,0.0161,0.0242,0.0308,
0.0408,0.0419,0.0445,0.0453,0.0540,0.0567,0.0595,0.0673,0.0719,0.0742,
0.0770,0.0773,0.0777,0.0792,0.0927,0.0944,0.0978,0.0981,0.1011,0.1129,
0.1162,0.1172,0.1253,0.1284,0.1365,0.1366,0.1406,0.1485,0.1569,0.1584,
0.1660,0.1691,0.1749,0.1823,0.1860,0.1874,0.1886,0.1924,0.1978,0.2008,
0.2009,0.2013,0.2036,0.2056,0.2056,0.2104,0.2144,0.2172,0.2180,0.2239,
0.2328,0.2338,0.2420,0.2451,0.2456,0.2503,0.2512,0.2541,0.2615,0.2697,
0.2740,0.2764,0.2765,0.2801,0.2841,0.2890,0.2896,0.2909,0.2919,0.2969,
0.3077,0.3091,0.3099,0.3135,0.3159,0.3182,0.3244,0.3258,0.3266,0.3266,
0.3346,0.3378,0.3404,0.3446,0.3451,0.3542,0.3545,0.3642,0.3710,0.3784,
0.3850,0.3851,0.3881,0.3893,0.3915,0.3921,0.3949,0.4009,0.4011,0.4029,
0.4116,0.4121,0.4201,0.4208,0.4232,0.4256,0.4285,0.4305,0.4312,0.4321,
0.4352,0.4358,0.4481,0.4487,0.4560,0.4603,0.4604,0.4604,0.4653,0.4667,
0.4674,0.4679,0.4718,0.4730,0.4742,0.4752,0.4803,0.4818,0.4909,0.4926,
0.4928,0.4942,0.4955,0.5009,0.5031,0.5107,0.5122,0.5173,0.5192,0.5255,
0.5313,0.5325,0.5372,0.5386,0.5416,0.5445,0.5468,0.5476,0.5478,0.5518,
0.5575,0.5608,0.5684,0.5744,0.5746,0.5748,0.5775,0.5842,0.5866,0.5903,
0.6058,0.6063,0.6111,0.6132,0.6210,0.6214,0.6220,0.6324,0.6357,0.6430,
0.6435,0.6470,0.6625,0.6652,0.6656,0.6668,0.6679,0.6684,0.6891,0.6893,
0.6920,0.6947,0.6952,0.6961,0.6988,0.7018,0.7079,0.7099,0.7117,0.7269,
0.7327,0.7428,0.7473,0.7507,0.7528,0.7533,0.7641,0.7676,0.7697,0.7748,
0.7797,0.7820,0.7858,0.7910,0.7950,0.8097,0.8124,0.8224,0.8273,0.8308,
0.8322,0.8342,0.8344,0.8363,0.8377,0.8391,0.8454,0.8520,0.8634,0.8648,
0.8662,0.8673,0.8683,0.8687,0.8688,0.8703,0.8731,0.8748,0.8752,0.8805,
0.8883,0.8905,0.8909,0.8918,0.9005,0.9042,0.9066,0.9150,0.9174,0.9179,
0.9206,0.9227,0.9235,0.9238,0.9245,0.9331,0.9372,0.9409,0.9414,0.9428,
0.9462,0.9467,0.9724,0.9735,0.9776,0.9816,0.9835,0.9891,0.9926,
Overall p-value after applying KStest on 269 p-values = 0.782004
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.