RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-15_02:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.65 23.1460 0.855443
2 to 25 15.50 15.7081 0.455384
3 to 26 15.89 16.2785 0.495816
4 to 27 15.78 15.1898 0.418188
5 to 28 16.00 14.3985 0.361281
6 to 29 15.87 19.4292 0.695541
7 to 30 15.46 25.1321 0.908209
8 to 31 15.57 32.3930 0.986558
9 to 32 15.47 17.5603 0.582928
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.203725
Tough bday spacings test for dh-ranFile-2018-06-15_02:31: 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 8 35 77 90 102 76 63 21 18 4 6
(O-E)^2/E 0.1 0.1 0.2 0.6 0.2 0.1 2.3 2.6 0.7 1.0 0.9
Birthday Spacings: Sum(O-E)^2/E= 8.735, p= 0.443
RESULTS OF GCD FOR dh-ranFile-2018-06-15_02:31
Euclid's algorithm:
p-value, steps to gcd: 0.576803
p-value, dist. of gcd's: 0.042372
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-15_02:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.755 0.822 0.226 0.638 0.906 0.003 0.179 0.917
Bits 8 to 15---> 0.876 0.896 0.399 0.435 0.535 0.432 0.307 0.874
Bits 16 to 23---> 0.021 0.155 0.100 0.434 0.159 0.214 0.566 0.952
Bits 24 to 31---> 0.944 0.794 0.689 0.574 0.005 0.288 0.537 0.069
KS test for the above 32 p values: 0.359
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-15_02:31,
p-values for 5 runs: 0.5837, 0.1591, 0.4584, 0.6374, 0.8044
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-15_02:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 213 211.4 0.012 0.012
r= 29 5158 5134.0 0.112 0.124
r= 30 22984 23103.0 0.613 0.737
r= 31 11645 11551.5 0.756 1.494
chi-square = 1.494 with df = 3; p-value = 0.316
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-15_02:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 220 211.4 0.348 0.348
r= 30 5201 5134.0 0.874 1.222
r= 31 23159 23103.0 0.136 1.358
r= 32 11420 11551.5 1.498 2.855
chi-square = 2.855 with df = 3; p-value = 0.586
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-15_02:31
b-rank test for bits 1 to 8, p=0.91521
b-rank test for bits 2 to 9, p=0.23149
b-rank test for bits 3 to 10, p=0.09721
b-rank test for bits 4 to 11, p=0.84682
b-rank test for bits 5 to 12, p=0.51805
b-rank test for bits 6 to 13, p=0.93624
b-rank test for bits 7 to 14, p=0.11472
b-rank test for bits 8 to 15, p=0.55233
b-rank test for bits 9 to 16, p=0.10270
b-rank test for bits 10 to 17, p=0.51352
b-rank test for bits 11 to 18, p=0.89320
b-rank test for bits 12 to 19, p=0.76586
b-rank test for bits 13 to 20, p=0.64936
b-rank test for bits 14 to 21, p=0.93451
b-rank test for bits 15 to 22, p=0.15133
b-rank test for bits 16 to 23, p=0.67629
b-rank test for bits 17 to 24, p=0.29323
b-rank test for bits 18 to 25, p=0.85507
b-rank test for bits 19 to 26, p=0.66968
b-rank test for bits 20 to 27, p=0.05107
b-rank test for bits 21 to 28, p=0.02861
b-rank test for bits 22 to 29, p=0.41776
b-rank test for bits 23 to 30, p=0.69359
b-rank test for bits 24 to 31, p=0.57754
b-rank test for bits 25 to 32, p=0.52437
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 = 0.815887
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-15_02:31
(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 141785 -0.29 0.385720
2 142069 0.37 0.645448
3 141847 -0.15 0.442106
4 143093 2.77 0.997159
5 140960 -2.22 0.013275
6 142136 0.53 0.701806
7 142053 0.34 0.631443
8 142174 0.62 0.731840
9 141869 -0.09 0.462464
10 141973 0.15 0.559129
11 141705 -0.48 0.316536
12 142173 0.62 0.731070
13 141176 -1.71 0.043321
14 140561 -3.15 0.000816
15 141451 -1.07 0.142115
16 142005 0.22 0.588438
17 141965 0.13 0.551745
18 141924 0.03 0.513671
19 142065 0.36 0.641965
20 142378 1.10 0.863247
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-15_02:31
Bits used No. missing words z-score p-value
23 to 32 141766 -0.4942 0.310568
22 to 31 141594 -1.0873 0.138442
21 to 30 141678 -0.7977 0.212525
20 to 29 142068 0.5471 0.707858
19 to 28 141752 -0.5425 0.293731
18 to 27 142040 0.4506 0.673856
17 to 26 141639 -0.9322 0.175624
16 to 25 142175 0.9161 0.820194
15 to 24 142271 1.2471 0.893827
14 to 23 142217 1.0609 0.855639
13 to 22 142089 0.6196 0.732224
12 to 21 142136 0.7816 0.782781
11 to 20 141738 -0.5908 0.277330
10 to 19 142017 0.3713 0.644784
9 to 18 142201 1.0058 0.842734
8 to 17 141819 -0.3115 0.377717
7 to 16 141921 0.0402 0.516050
6 to 15 141572 -1.1632 0.122373
5 to 14 141310 -2.0667 0.019383
4 to 13 141538 -1.2804 0.100194
3 to 12 141694 -0.7425 0.228887
2 to 11 142051 0.4885 0.687408
1 to 10 141884 -0.0873 0.465199
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-15_02:31
Bits used No. missing words z-score p-value
28 to 32 141761 -0.5028 0.307548
27 to 31 142271 1.2260 0.889901
26 to 30 141801 -0.3672 0.356727
25 to 29 141601 -1.0452 0.147968
24 to 28 142103 0.6565 0.744252
23 to 27 141634 -0.9333 0.175327
22 to 26 141810 -0.3367 0.368167
21 to 25 141996 0.2938 0.615543
20 to 24 142204 0.9989 0.841074
19 to 23 141771 -0.4689 0.319565
18 to 22 142112 0.6870 0.753964
17 to 21 142044 0.4565 0.675988
16 to 20 141980 0.2396 0.594664
15 to 19 141963 0.1819 0.572182
14 to 18 142154 0.8294 0.796558
13 to 17 141381 -1.7909 0.036651
12 to 16 141914 0.0158 0.506315
11 to 15 142169 0.8802 0.810635
10 to 14 141857 -0.1774 0.429601
9 to 13 141616 -0.9943 0.160029
8 to 12 142251 1.1582 0.876610
7 to 11 142282 1.2633 0.896757
6 to 10 141466 -1.5028 0.066444
5 to 9 142194 0.9650 0.832723
4 to 8 141868 -0.1401 0.444290
3 to 7 141624 -0.9672 0.166717
2 to 6 142275 1.2396 0.892431
1 to 5 142231 1.0904 0.862233
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-15_02:31
Bits used No. missing words z-score p-value
31 to 32 141913 0.0108 0.504319
30 to 31 141439 -1.3874 0.082659
29 to 30 142036 0.3737 0.645671
28 to 29 141523 -1.1396 0.127223
27 to 28 141967 0.1701 0.567541
26 to 27 141499 -1.2104 0.113060
25 to 26 142152 0.7158 0.762955
24 to 25 141745 -0.4847 0.313927
23 to 24 141615 -0.8682 0.192634
22 to 23 141765 -0.4258 0.335144
21 to 22 142055 0.4297 0.666295
20 to 21 141677 -0.6853 0.246565
19 to 20 141666 -0.7178 0.236444
18 to 19 142358 1.3235 0.907167
17 to 18 142155 0.7247 0.765679
16 to 17 141391 -1.5290 0.063133
15 to 16 141887 -0.0659 0.473741
14 to 15 141610 -0.8830 0.188624
13 to 14 142444 1.5772 0.942625
12 to 13 141872 -0.1101 0.456158
11 to 12 141821 -0.2606 0.397216
10 to 11 141362 -1.6145 0.053205
9 to 10 141387 -1.5408 0.061683
8 to 9 141477 -1.2753 0.101100
7 to 8 141990 0.2380 0.594046
6 to 7 142041 0.3884 0.651143
5 to 6 141036 -2.5762 0.004995
4 to 5 141412 -1.4671 0.071181
3 to 4 141336 -1.6912 0.045396
2 to 3 141721 -0.5555 0.289261
1 to 2 141640 -0.7945 0.213457
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-15_02:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2567.83 0.959 0.831292
Test results for specific bytes for dh-ranFile-2018-06-15_02:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2568.90 0.974 0.835058
2 to 9 2391.31 -1.537 0.062141
3 to 10 2415.31 -1.198 0.115508
4 to 11 2574.93 1.060 0.855366
5 to 12 2441.42 -0.828 0.203716
6 to 13 2438.22 -0.874 0.191122
7 to 14 2403.52 -1.364 0.086212
8 to 15 2546.08 0.652 0.742695
9 to 16 2446.29 -0.760 0.223767
10 to 17 2516.32 0.231 0.591262
11 to 18 2444.91 -0.779 0.217943
12 to 19 2468.65 -0.443 0.328765
13 to 20 2524.85 0.351 0.637355
14 to 21 2542.40 0.600 0.725610
15 to 22 2547.82 0.676 0.750559
16 to 23 2570.09 0.991 0.839199
17 to 24 2547.00 0.665 0.746862
18 to 25 2643.04 2.023 0.978456
19 to 26 2434.40 -0.928 0.176765
20 to 27 2570.42 0.996 0.840339
21 to 28 2487.16 -0.182 0.427974
22 to 29 2522.44 0.317 0.624509
23 to 30 2517.86 0.253 0.599677
24 to 31 2601.80 1.440 0.925021
25 to 32 2461.73 -0.541 0.294201
CDPARK for dh-ranFile-2018-06-15_02:31: 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
3515 -0.3653 0.357445
3488 -1.5982 0.055002
3516 -0.3196 0.374623
3515 -0.3653 0.357445
3545 1.0046 0.842447
3504 -0.8676 0.192812
3544 0.9589 0.831196
3516 -0.3196 0.374623
3514 -0.4110 0.340551
3504 -0.8676 0.192812
Square side=100, avg. no. parked=3516.10 sample std.=16.44
p-value of the KSTEST for those 10 p-values: 0.229607
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-15_02:31
0.7478,0.9839,0.4313,0.9593,0.3081,0.1903,0.3581,0.0119,0.7515,0.4073,
The KS test for those 10 p-values: 0.729175
The 3DSPHERES test for dh-ranFile-2018-06-15_02:31
sample no r^3 equiv. uni.
1 43.483 0.765298
2 13.764 0.367964
3 134.626 0.988752
4 13.694 0.366489
5 7.466 0.220315
6 7.437 0.219556
7 41.320 0.747748
8 32.052 0.656443
9 45.633 0.781530
10 89.428 0.949255
11 69.242 0.900545
12 20.034 0.487169
13 2.862 0.090988
14 2.930 0.093051
15 16.964 0.431898
16 48.963 0.804481
17 19.013 0.469415
18 0.645 0.021267
19 37.471 0.713219
20 28.717 0.616050
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.933422
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-15_02:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 0.5 0.6 -1.3 -0.5 1.3
-0.2 1.4 -1.5 0.2 0.2 0.7
0.3 0.1 -0.5 2.7 0.0 1.1
-0.3 -2.2 -0.7 0.3 -0.7 0.3
-1.9 0.1 0.9 0.3 -0.5 -0.3
-0.1 -0.9 0.4 -0.3 0.3 0.1
0.0 -0.7 0.9 -1.8 0.1 0.0
-1.1
Chi-square with 42 degrees of freedom:35.555055
z-score=-0.703201, p-value=0.251752
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-15_02:31
Test no p-value
1 0.970589
2 0.031374
3 0.023832
4 0.392665
5 0.124279
6 0.209078
7 0.034339
8 0.279334
9 0.163373
10 0.225480
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.002931
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-15_02:31:
(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 66667 0.00 66671 0.00
3 25000.00 24881 0.57 25173 1.20
4 6666.67 6735 0.70 6546 2.18
5 1388.89 1438 1.74 1345 1.39
6 238.10 238 0.00 233 0.11
7 34.72 37 0.15 28 1.30
8 4.96 3 0.77 3 0.77
p=0.31352 p=0.67476
Number of rngs required: 688897, p-value: 0.716
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-15_02:31
No. of wins: Observed Expected
98537 98585.9
z-score=-0.219, pvalue=0.41351
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66571 66666.7 0.137 0.137
2 37917 37654.3 1.832 1.970
3 26750 26954.7 1.555 3.525
4 19253 19313.5 0.189 3.714
5 13921 13851.4 0.350 4.064
6 9899 9943.5 0.200 4.263
7 7176 7145.0 0.134 4.397
8 5242 5139.1 2.061 6.459
9 3770 3699.9 1.329 7.788
10 2620 2666.3 0.804 8.592
11 1935 1923.3 0.071 8.663
12 1355 1388.7 0.820 9.483
13 981 1003.7 0.514 9.997
14 725 726.1 0.002 9.999
15 502 525.8 1.080 11.079
16 378 381.2 0.026 11.105
17 277 276.5 0.001 11.106
18 176 200.8 3.070 14.176
19 158 146.0 0.989 15.165
20 96 106.2 0.982 16.147
21 298 287.1 0.413 16.560
Chisq= 16.56 for 20 degrees of freedom, p= 0.31867
SUMMARY of craptest
p-value for no. of wins: 0.413510
p-value for throws/game: 0.318669
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-15_02:31
No. of wins: Observed Expected
98492 98585.9
z-score=-0.420, pvalue=0.33732
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66470 66666.7 0.580 0.580
2 37426 37654.3 1.384 1.965
3 27368 26954.7 6.336 8.301
4 19350 19313.5 0.069 8.370
5 13837 13851.4 0.015 8.385
6 9958 9943.5 0.021 8.406
7 7183 7145.0 0.202 8.608
8 5108 5139.1 0.188 8.796
9 3745 3699.9 0.551 9.346
10 2640 2666.3 0.259 9.606
11 1890 1923.3 0.578 10.183
12 1360 1388.7 0.595 10.778
13 1013 1003.7 0.086 10.864
14 644 726.1 9.292 20.156
15 551 525.8 1.204 21.360
16 359 381.2 1.287 22.647
17 288 276.5 0.475 23.122
18 219 200.8 1.644 24.766
19 177 146.0 6.590 31.356
20 106 106.2 0.000 31.356
21 308 287.1 1.519 32.875
Chisq= 32.88 for 20 degrees of freedom, p= 0.96518
SUMMARY of craptest
p-value for no. of wins: 0.337319
p-value for throws/game: 0.965181
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0008,0.0029,0.0030,0.0049,0.0050,0.0119,0.0133,0.0194,0.0211,0.0213,
0.0238,0.0286,0.0314,0.0343,0.0367,0.0424,0.0433,0.0454,0.0511,0.0532,
0.0550,0.0617,0.0621,0.0631,0.0664,0.0688,0.0712,0.0827,0.0862,0.0910,
0.0931,0.0972,0.0997,0.1002,0.1011,0.1027,0.1131,0.1147,0.1155,0.1224,
0.1243,0.1272,0.1384,0.1421,0.1480,0.1513,0.1554,0.1591,0.1595,0.1600,
0.1634,0.1667,0.1753,0.1756,0.1768,0.1791,0.1886,0.1903,0.1911,0.1926,
0.1928,0.1928,0.2037,0.2037,0.2091,0.2125,0.2135,0.2138,0.2179,0.2196,
0.2203,0.2238,0.2255,0.2261,0.2289,0.2296,0.2315,0.2364,0.2466,0.2518,
0.2773,0.2793,0.2878,0.2893,0.2932,0.2937,0.2942,0.3066,0.3075,0.3081,
0.3106,0.3135,0.3139,0.3163,0.3165,0.3187,0.3196,0.3288,0.3351,0.3373,
0.3406,0.3567,0.3574,0.3574,0.3581,0.3592,0.3613,0.3665,0.3680,0.3682,
0.3746,0.3746,0.3777,0.3857,0.3927,0.3972,0.3995,0.4073,0.4135,0.4178,
0.4182,0.4280,0.4296,0.4313,0.4319,0.4319,0.4336,0.4346,0.4421,0.4425,
0.4443,0.4554,0.4562,0.4584,0.4625,0.4652,0.4694,0.4737,0.4872,0.4958,
0.5043,0.5063,0.5135,0.5137,0.5160,0.5181,0.5244,0.5353,0.5367,0.5517,
0.5523,0.5591,0.5655,0.5675,0.5722,0.5736,0.5768,0.5775,0.5829,0.5837,
0.5856,0.5884,0.5913,0.5940,0.5947,0.5997,0.6155,0.6161,0.6245,0.6314,
0.6374,0.6374,0.6379,0.6420,0.6448,0.6454,0.6457,0.6494,0.6511,0.6564,
0.6663,0.6697,0.6739,0.6748,0.6760,0.6763,0.6874,0.6887,0.6936,0.6955,
0.7018,0.7079,0.7132,0.7155,0.7256,0.7292,0.7311,0.7318,0.7322,0.7427,
0.7443,0.7469,0.7477,0.7478,0.7506,0.7515,0.7540,0.7552,0.7630,0.7653,
0.7657,0.7659,0.7815,0.7828,0.7937,0.7966,0.8044,0.8045,0.8106,0.8159,
0.8202,0.8216,0.8312,0.8313,0.8327,0.8351,0.8392,0.8403,0.8411,0.8424,
0.8427,0.8468,0.8551,0.8554,0.8554,0.8556,0.8622,0.8632,0.8743,0.8758,
0.8766,0.8899,0.8924,0.8932,0.8938,0.8960,0.8968,0.9005,0.9064,0.9072,
0.9082,0.9152,0.9171,0.9250,0.9334,0.9345,0.9362,0.9426,0.9436,0.9493,
0.9518,0.9593,0.9652,0.9706,0.9785,0.9839,0.9866,0.9888,0.9972,
Overall p-value after applying KStest on 269 p-values = 0.384864
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.