RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-29_14:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.74 19.8749 0.719321
2 to 25 15.85 16.4426 0.507294
3 to 26 15.79 23.8602 0.876718
4 to 27 15.91 16.8272 0.533865
5 to 28 16.00 13.1027 0.270719
6 to 29 15.84 16.6778 0.523604
7 to 30 15.57 19.9579 0.723614
8 to 31 15.79 13.0264 0.265586
9 to 32 16.16 38.0629 0.997591
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.329102
Tough bday spacings test for dh-ranFile-2018-06-29_14:31: 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 5 37 76 93 103 83 61 22 10 9 1
(O-E)^2/E 1.9 0.0 0.1 0.2 0.3 0.3 1.5 2.0 1.6 0.9 2.3
Birthday Spacings: Sum(O-E)^2/E= 11.133, p= 0.653
RESULTS OF GCD FOR dh-ranFile-2018-06-29_14:31
Euclid's algorithm:
p-value, steps to gcd: 0.124952
p-value, dist. of gcd's: 0.388087
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-29_14:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.502 0.522 0.799 0.668 0.314 0.058 0.396 0.643
Bits 8 to 15---> 0.109 0.717 0.271 0.523 0.085 0.472 0.554 0.671
Bits 16 to 23---> 0.245 0.441 0.196 0.120 0.841 0.932 0.316 0.196
Bits 24 to 31---> 0.529 0.621 0.909 0.379 0.261 0.939 0.017 0.640
KS test for the above 32 p values: 0.249
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-29_14:31,
p-values for 5 runs: 0.1422, 0.9772, 0.7679, 0.7371, 0.3543
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-29_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 234 211.4 2.412 2.412
r= 29 5139 5134.0 0.005 2.417
r= 30 23125 23103.0 0.021 2.438
r= 31 11502 11551.5 0.212 2.650
chi-square = 2.650 with df = 3; p-value = 0.551
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-29_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 177 211.4 5.603 5.603
r= 30 5126 5134.0 0.012 5.616
r= 31 23186 23103.0 0.298 5.913
r= 32 11511 11551.5 0.142 6.056
chi-square = 6.056 with df = 3; p-value = 0.891
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-29_14:31
b-rank test for bits 1 to 8, p=0.03121
b-rank test for bits 2 to 9, p=0.00172
b-rank test for bits 3 to 10, p=0.21714
b-rank test for bits 4 to 11, p=0.80910
b-rank test for bits 5 to 12, p=0.96400
b-rank test for bits 6 to 13, p=0.88614
b-rank test for bits 7 to 14, p=0.80440
b-rank test for bits 8 to 15, p=0.25717
b-rank test for bits 9 to 16, p=0.67360
b-rank test for bits 10 to 17, p=0.02813
b-rank test for bits 11 to 18, p=0.10052
b-rank test for bits 12 to 19, p=0.99637
b-rank test for bits 13 to 20, p=0.33646
b-rank test for bits 14 to 21, p=0.59356
b-rank test for bits 15 to 22, p=0.03139
b-rank test for bits 16 to 23, p=0.97576
b-rank test for bits 17 to 24, p=0.40133
b-rank test for bits 18 to 25, p=0.55945
b-rank test for bits 19 to 26, p=0.51092
b-rank test for bits 20 to 27, p=0.11315
b-rank test for bits 21 to 28, p=0.77749
b-rank test for bits 22 to 29, p=0.24562
b-rank test for bits 23 to 30, p=0.02205
b-rank test for bits 24 to 31, p=0.66887
b-rank test for bits 25 to 32, p=0.68462
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 = 0.175064
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-29_14:31
(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 142601 1.62 0.946958
2 141858 -0.12 0.452269
3 141352 -1.30 0.096429
4 141682 -0.53 0.297659
5 142248 0.79 0.785611
6 141983 0.17 0.568331
7 142736 1.93 0.973288
8 142077 0.39 0.652379
9 142427 1.21 0.886766
10 142584 1.58 0.942525
11 141595 -0.73 0.231348
12 141821 -0.21 0.418248
13 142319 0.96 0.830760
14 140959 -2.22 0.013196
15 142515 1.42 0.921483
16 142222 0.73 0.767469
17 141544 -0.85 0.196670
18 141731 -0.42 0.338464
19 141503 -0.95 0.171216
20 141457 -1.06 0.145291
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-29_14:31
Bits used No. missing words z-score p-value
23 to 32 141364 -1.8804 0.030024
22 to 31 141819 -0.3115 0.377717
21 to 30 141736 -0.5977 0.275024
20 to 29 141995 0.2954 0.616161
19 to 28 141770 -0.4804 0.315454
18 to 27 142068 0.5471 0.707858
17 to 26 141921 0.0402 0.516050
16 to 25 141725 -0.6356 0.262512
15 to 24 141617 -1.0080 0.156719
14 to 23 141494 -1.4322 0.076047
13 to 22 141894 -0.0529 0.478921
12 to 21 142162 0.8713 0.808198
11 to 20 142610 2.4161 0.992156
10 to 19 141350 -1.9287 0.026883
9 to 18 141573 -1.1598 0.123074
8 to 17 142026 0.4023 0.656272
7 to 16 141430 -1.6529 0.049179
6 to 15 141628 -0.9701 0.165998
5 to 14 141888 -0.0736 0.470684
4 to 13 142405 1.7092 0.956294
3 to 12 142021 0.3851 0.649907
2 to 11 141730 -0.6184 0.268163
1 to 10 142165 0.8816 0.811009
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-29_14:31
Bits used No. missing words z-score p-value
28 to 32 141430 -1.6248 0.052098
27 to 31 141428 -1.6316 0.051379
26 to 30 141839 -0.2384 0.405783
25 to 29 142104 0.6599 0.745341
24 to 28 141143 -2.5977 0.004692
23 to 27 142045 0.4599 0.677205
22 to 26 142316 1.3785 0.915982
21 to 25 141755 -0.5232 0.300434
20 to 24 141542 -1.2452 0.106532
19 to 23 141852 -0.1943 0.422955
18 to 22 141809 -0.3401 0.366890
17 to 21 141643 -0.9028 0.183312
16 to 20 142076 0.5650 0.713957
15 to 19 141788 -0.4113 0.340431
14 to 18 142300 1.3243 0.907299
13 to 17 141895 -0.0486 0.480629
12 to 16 141962 0.1785 0.570852
11 to 15 141427 -1.6350 0.051023
10 to 14 141611 -1.0113 0.155939
9 to 13 141883 -0.0893 0.464440
8 to 12 142014 0.3548 0.638635
7 to 11 142260 1.1887 0.882723
6 to 10 141996 0.2938 0.615543
5 to 9 142079 0.5752 0.717406
4 to 8 141838 -0.2418 0.404469
3 to 7 141484 -1.4418 0.074680
2 to 6 142041 0.4463 0.672324
1 to 5 141687 -0.7537 0.225526
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-29_14:31
Bits used No. missing words z-score p-value
31 to 32 141862 -0.1396 0.444482
30 to 31 141874 -0.1042 0.458498
29 to 30 142076 0.4917 0.688517
28 to 29 142322 1.2173 0.888258
27 to 28 142145 0.6952 0.756532
26 to 27 142013 0.3058 0.620126
25 to 26 142268 1.0580 0.854978
24 to 25 142116 0.6096 0.728952
23 to 24 142039 0.3825 0.648958
22 to 23 142683 2.2822 0.988762
21 to 22 142633 2.1347 0.983608
20 to 21 141702 -0.6116 0.270404
19 to 20 141968 0.1731 0.568701
18 to 19 142133 0.6598 0.745307
17 to 18 142140 0.6804 0.751888
16 to 17 142097 0.5536 0.710073
15 to 16 141602 -0.9066 0.182315
14 to 15 142669 2.2409 0.987484
13 to 14 141440 -1.3845 0.083110
12 to 13 141868 -0.1219 0.451482
11 to 12 142250 1.0049 0.842534
10 to 11 141814 -0.2812 0.389275
9 to 10 141392 -1.5260 0.063499
8 to 9 141837 -0.2134 0.415522
7 to 8 141975 0.1937 0.576801
6 to 7 142197 0.8486 0.801944
5 to 6 142288 1.1170 0.868007
4 to 5 141818 -0.2694 0.393807
3 to 4 141672 -0.7001 0.241936
2 to 3 142150 0.7099 0.761130
1 to 2 142210 0.8869 0.812442
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-29_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2544.11 0.624 0.733644
Test results for specific bytes for dh-ranFile-2018-06-29_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2402.60 -1.377 0.084198
2 to 9 2568.41 0.967 0.833329
3 to 10 2380.22 -1.694 0.045139
4 to 11 2481.85 -0.257 0.398707
5 to 12 2525.06 0.354 0.638455
6 to 13 2531.84 0.450 0.673754
7 to 14 2407.61 -1.307 0.095686
8 to 15 2529.68 0.420 0.662640
9 to 16 2402.74 -1.375 0.084500
10 to 17 2531.34 0.443 0.671209
11 to 18 2540.89 0.578 0.718463
12 to 19 2575.94 1.074 0.858580
13 to 20 2584.13 1.190 0.882926
14 to 21 2538.10 0.539 0.705011
15 to 22 2456.19 -0.620 0.267779
16 to 23 2517.16 0.243 0.595885
17 to 24 2460.87 -0.553 0.289985
18 to 25 2571.52 1.011 0.844105
19 to 26 2548.80 0.690 0.754926
20 to 27 2383.62 -1.646 0.049895
21 to 28 2371.84 -1.812 0.034955
22 to 29 2447.96 -0.736 0.230869
23 to 30 2500.07 0.001 0.500379
24 to 31 2471.38 -0.405 0.342850
25 to 32 2380.86 -1.685 0.046003
CDPARK for dh-ranFile-2018-06-29_14:31: 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
3558 1.5982 0.944998
3543 0.9132 0.819442
3491 -1.4612 0.071982
3561 1.7352 0.958644
3546 1.0502 0.853193
3542 0.8676 0.807188
3539 0.7306 0.767486
3519 -0.1826 0.427537
3496 -1.2329 0.108811
3563 1.8265 0.966111
Square side=100, avg. no. parked=3535.80 sample std.=24.38
p-value of the KSTEST for those 10 p-values: 0.031184
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-29_14:31
0.4822,0.1214,0.6334,0.1856,0.3805,0.5381,0.9679,0.6377,0.5252,0.7477,
The KS test for those 10 p-values: 0.801996
The 3DSPHERES test for dh-ranFile-2018-06-29_14:31
sample no r^3 equiv. uni.
1 23.843 0.548315
2 26.996 0.593375
3 4.657 0.143770
4 27.377 0.598504
5 6.995 0.207973
6 9.735 0.277100
7 7.313 0.216330
8 4.075 0.127007
9 101.445 0.966004
10 62.826 0.876830
11 3.239 0.102351
12 13.220 0.356395
13 1.792 0.057990
14 71.295 0.907126
15 53.549 0.832196
16 18.658 0.463088
17 24.588 0.559389
18 65.764 0.888322
19 48.746 0.803062
20 51.196 0.818508
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.894816
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-29_14:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -1.6 -1.3 0.9 -0.3 -0.5
-0.1 -0.6 1.2 0.1 1.2 -1.2
1.1 -2.5 -0.1 0.8 -0.6 -0.1
0.9 1.8 0.1 -0.4 -0.2 1.2
1.5 0.9 -3.8 -1.7 0.3 -0.7
-0.9 0.0 -2.4 -1.3 -0.1 0.2
-0.5 -1.0 -0.4 -1.8 0.1 2.0
-1.1
Chi-square with 42 degrees of freedom:63.552269
z-score=2.351545, p-value=0.982519
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-29_14:31
Test no p-value
1 0.031945
2 0.003622
3 0.046957
4 0.363612
5 0.352794
6 0.638692
7 0.319269
8 0.868308
9 0.483646
10 0.899283
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.213137
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-29_14:31:
(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 66865 0.59 66553 0.19
3 25000.00 24893 0.46 25138 0.76
4 6666.67 6555 1.87 6602 0.63
5 1388.89 1442 2.03 1429 1.16
6 238.10 212 2.86 236 0.02
7 34.72 28 1.30 35 0.00
8 4.96 4 0.19 6 0.22
p=0.84239 p=0.18865
Number of rngs required: 687864, p-value: 0.267
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-29_14:31
No. of wins: Observed Expected
98635 98585.9
z-score= 0.220, pvalue=0.58698
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66793 66666.7 0.239 0.239
2 37689 37654.3 0.032 0.271
3 26948 26954.7 0.002 0.273
4 19124 19313.5 1.859 2.132
5 13711 13851.4 1.424 3.555
6 10024 9943.5 0.651 4.206
7 7188 7145.0 0.258 4.465
8 5087 5139.1 0.528 4.992
9 3739 3699.9 0.414 5.406
10 2733 2666.3 1.669 7.075
11 1864 1923.3 1.830 8.905
12 1404 1388.7 0.168 9.073
13 994 1003.7 0.094 9.167
14 756 726.1 1.228 10.395
15 525 525.8 0.001 10.396
16 362 381.2 0.962 11.358
17 296 276.5 1.369 12.728
18 206 200.8 0.133 12.861
19 158 146.0 0.989 13.850
20 118 106.2 1.308 15.157
21 281 287.1 0.130 15.287
Chisq= 15.29 for 20 degrees of freedom, p= 0.24027
SUMMARY of craptest
p-value for no. of wins: 0.586982
p-value for throws/game: 0.240266
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-29_14:31
No. of wins: Observed Expected
98399 98585.9
z-score=-0.836, pvalue=0.20165
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66356 66666.7 1.448 1.448
2 37726 37654.3 0.136 1.584
3 27054 26954.7 0.366 1.950
4 19258 19313.5 0.159 2.109
5 13845 13851.4 0.003 2.112
6 10182 9943.5 5.718 7.830
7 7080 7145.0 0.592 8.422
8 5151 5139.1 0.028 8.450
9 3666 3699.9 0.310 8.760
10 2761 2666.3 3.364 12.124
11 1900 1923.3 0.283 12.407
12 1389 1388.7 0.000 12.407
13 984 1003.7 0.387 12.794
14 721 726.1 0.036 12.830
15 536 525.8 0.196 13.027
16 375 381.2 0.099 13.126
17 285 276.5 0.259 13.385
18 182 200.8 1.765 15.150
19 144 146.0 0.027 15.177
20 115 106.2 0.727 15.904
21 290 287.1 0.029 15.933
Chisq= 15.93 for 20 degrees of freedom, p= 0.27922
SUMMARY of craptest
p-value for no. of wins: 0.201650
p-value for throws/game: 0.279217
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0017,0.0036,0.0047,0.0132,0.0170,0.0221,0.0269,0.0281,0.0300,0.0312,
0.0312,0.0314,0.0319,0.0350,0.0451,0.0460,0.0470,0.0492,0.0499,0.0510,
0.0514,0.0521,0.0576,0.0580,0.0635,0.0720,0.0747,0.0760,0.0831,0.0842,
0.0845,0.0848,0.0957,0.0964,0.1005,0.1024,0.1065,0.1088,0.1090,0.1131,
0.1197,0.1214,0.1231,0.1250,0.1270,0.1422,0.1438,0.1453,0.1559,0.1567,
0.1660,0.1712,0.1751,0.1823,0.1833,0.1856,0.1886,0.1956,0.1958,0.1967,
0.2017,0.2080,0.2131,0.2163,0.2171,0.2255,0.2309,0.2313,0.2403,0.2419,
0.2445,0.2456,0.2493,0.2572,0.2614,0.2625,0.2656,0.2670,0.2678,0.2682,
0.2704,0.2707,0.2712,0.2750,0.2771,0.2792,0.2900,0.2977,0.3004,0.3140,
0.3155,0.3160,0.3193,0.3291,0.3365,0.3385,0.3404,0.3428,0.3528,0.3543,
0.3564,0.3636,0.3669,0.3777,0.3787,0.3805,0.3881,0.3893,0.3938,0.3955,
0.3987,0.4013,0.4045,0.4058,0.4155,0.4182,0.4230,0.4275,0.4412,0.4445,
0.4515,0.4523,0.4585,0.4631,0.4644,0.4707,0.4718,0.4789,0.4806,0.4822,
0.4836,0.5004,0.5022,0.5073,0.5109,0.5160,0.5221,0.5228,0.5236,0.5252,
0.5290,0.5339,0.5381,0.5483,0.5512,0.5541,0.5594,0.5595,0.5683,0.5687,
0.5709,0.5768,0.5870,0.5934,0.5936,0.5959,0.5985,0.6155,0.6162,0.6201,
0.6206,0.6334,0.6377,0.6385,0.6386,0.6387,0.6398,0.6433,0.6490,0.6499,
0.6524,0.6527,0.6563,0.6626,0.6682,0.6689,0.6706,0.6712,0.6723,0.6736,
0.6738,0.6772,0.6846,0.6885,0.7050,0.7079,0.7101,0.7140,0.7174,0.7174,
0.7185,0.7193,0.7236,0.7290,0.7336,0.7371,0.7453,0.7453,0.7477,0.7519,
0.7549,0.7565,0.7611,0.7675,0.7675,0.7679,0.7775,0.7856,0.7992,0.8019,
0.8020,0.8031,0.8044,0.8072,0.8082,0.8091,0.8110,0.8124,0.8185,0.8194,
0.8308,0.8322,0.8333,0.8414,0.8424,0.8425,0.8441,0.8532,0.8550,0.8586,
0.8680,0.8683,0.8767,0.8768,0.8827,0.8829,0.8861,0.8868,0.8883,0.8883,
0.8911,0.8948,0.8993,0.9071,0.9073,0.9088,0.9160,0.9215,0.9322,0.9386,
0.9425,0.9450,0.9470,0.9563,0.9586,0.9640,0.9660,0.9661,0.9679,0.9733,
0.9758,0.9772,0.9825,0.9836,0.9875,0.9888,0.9922,0.9964,0.9976,
Overall p-value after applying KStest on 269 p-values = 0.620663
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.