RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-20_07:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 16.03 13.4528 0.294614
2 to 25 15.91 18.3481 0.632795
3 to 26 15.81 13.0386 0.266400
4 to 27 15.94 12.7202 0.245295
5 to 28 15.73 22.0223 0.816137
6 to 29 15.39 25.6064 0.918063
7 to 30 15.70 15.3965 0.433057
8 to 31 15.84 17.8873 0.604017
9 to 32 15.71 17.7287 0.593856
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.755369
Tough bday spacings test for dh-ranFile-2018-06-20_07:31: 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 39 81 104 89 77 48 25 16 9 3
(O-E)^2/E 0.0 0.2 0.8 0.4 0.8 0.0 0.3 0.8 0.1 0.9 0.3
Birthday Spacings: Sum(O-E)^2/E= 4.479, p= 0.077
RESULTS OF GCD FOR dh-ranFile-2018-06-20_07:31
Euclid's algorithm:
p-value, steps to gcd: 0.962640
p-value, dist. of gcd's: 0.618922
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-20_07:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.142 0.771 0.093 0.531 0.786 0.767 0.420 0.608
Bits 8 to 15---> 0.376 0.143 0.579 0.676 0.925 0.416 0.640 0.117
Bits 16 to 23---> 0.367 0.543 0.009 0.446 0.654 0.236 0.064 0.493
Bits 24 to 31---> 0.400 0.097 0.946 0.364 0.954 0.745 0.996 0.552
KS test for the above 32 p values: 0.078
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-20_07:31,
p-values for 5 runs: 0.8276, 0.3378, 0.0823, 0.3644, 0.7834
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-20_07:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 228 211.4 1.301 1.301
r= 29 5175 5134.0 0.327 1.628
r= 30 23071 23103.0 0.044 1.672
r= 31 11526 11551.5 0.056 1.729
chi-square = 1.729 with df = 3; p-value = 0.369
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-20_07:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 199 211.4 0.729 0.729
r= 30 5082 5134.0 0.527 1.256
r= 31 23139 23103.0 0.056 1.312
r= 32 11580 11551.5 0.070 1.382
chi-square = 1.382 with df = 3; p-value = 0.290
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-20_07:31
b-rank test for bits 1 to 8, p=0.23560
b-rank test for bits 2 to 9, p=0.88652
b-rank test for bits 3 to 10, p=0.98995
b-rank test for bits 4 to 11, p=0.63248
b-rank test for bits 5 to 12, p=0.80696
b-rank test for bits 6 to 13, p=0.16853
b-rank test for bits 7 to 14, p=0.03910
b-rank test for bits 8 to 15, p=0.30532
b-rank test for bits 9 to 16, p=0.11072
b-rank test for bits 10 to 17, p=0.95182
b-rank test for bits 11 to 18, p=0.95814
b-rank test for bits 12 to 19, p=0.89773
b-rank test for bits 13 to 20, p=0.56136
b-rank test for bits 14 to 21, p=0.36938
b-rank test for bits 15 to 22, p=0.07111
b-rank test for bits 16 to 23, p=0.52846
b-rank test for bits 17 to 24, p=0.01156
b-rank test for bits 18 to 25, p=0.15537
b-rank test for bits 19 to 26, p=0.95474
b-rank test for bits 20 to 27, p=0.70204
b-rank test for bits 21 to 28, p=0.93128
b-rank test for bits 22 to 29, p=0.21677
b-rank test for bits 23 to 30, p=0.78610
b-rank test for bits 24 to 31, p=0.89507
b-rank test for bits 25 to 32, p=0.61505
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 = 0.169543
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-20_07:31
(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 141849 -0.14 0.443952
2 141705 -0.48 0.316536
3 142103 0.45 0.674546
4 141569 -0.80 0.213259
5 142242 0.78 0.781499
6 142166 0.60 0.725646
7 141952 0.10 0.539707
8 142521 1.43 0.923517
9 141982 0.17 0.567412
10 141601 -0.72 0.235640
11 142952 2.44 0.992578
12 141326 -1.36 0.086454
13 142571 1.55 0.938943
14 141371 -1.26 0.104236
15 142875 2.26 0.987972
16 141777 -0.31 0.378591
17 141927 0.04 0.516466
18 142787 2.05 0.979849
19 141655 -0.59 0.276180
20 142353 1.04 0.850042
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-20_07:31
Bits used No. missing words z-score p-value
23 to 32 141375 -1.8425 0.032700
22 to 31 141971 0.2127 0.584202
21 to 30 141827 -0.2839 0.388245
20 to 29 142443 1.8402 0.967134
19 to 28 142032 0.4230 0.663852
18 to 27 142087 0.6127 0.729948
17 to 26 141666 -0.8391 0.200715
16 to 25 141416 -1.7011 0.044459
15 to 24 141770 -0.4804 0.315454
14 to 23 141629 -0.9667 0.166858
13 to 22 142077 0.5782 0.718426
12 to 21 141538 -1.2804 0.100194
11 to 20 141824 -0.2942 0.384287
10 to 19 142111 0.6954 0.756602
9 to 18 142311 1.3851 0.916984
8 to 17 141738 -0.5908 0.277330
7 to 16 141691 -0.7529 0.225766
6 to 15 141797 -0.3873 0.349251
5 to 14 141848 -0.2115 0.416255
4 to 13 141738 -0.5908 0.277330
3 to 12 141602 -1.0598 0.144627
2 to 11 141771 -0.4770 0.316681
1 to 10 141873 -0.1253 0.450153
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-20_07:31
Bits used No. missing words z-score p-value
28 to 32 141853 -0.1909 0.424283
27 to 31 142378 1.5887 0.943937
26 to 30 141845 -0.2181 0.413688
25 to 29 141978 0.2328 0.592034
24 to 28 142162 0.8565 0.804142
23 to 27 141841 -0.2316 0.408414
22 to 26 142563 2.2158 0.986648
21 to 25 141870 -0.1333 0.446969
20 to 24 142011 0.3446 0.634819
19 to 23 141599 -1.0520 0.146408
18 to 22 141890 -0.0655 0.473878
17 to 21 141853 -0.1909 0.424283
16 to 20 141371 -1.8248 0.034012
15 to 19 141888 -0.0723 0.471180
14 to 18 141686 -0.7571 0.224510
13 to 17 141950 0.1379 0.554826
12 to 16 141941 0.1074 0.542747
11 to 15 141488 -1.4282 0.076612
10 to 14 141941 0.1074 0.542747
9 to 13 141700 -0.7096 0.238978
8 to 12 141437 -1.6011 0.054675
7 to 11 141771 -0.4689 0.319565
6 to 10 142447 1.8226 0.965819
5 to 9 142174 0.8972 0.815190
4 to 8 142157 0.8396 0.799422
3 to 7 141948 0.1311 0.552146
2 to 6 142481 1.9379 0.973680
1 to 5 141760 -0.5062 0.306357
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-20_07:31
Bits used No. missing words z-score p-value
31 to 32 141978 0.2026 0.580263
30 to 31 141925 0.0462 0.518434
29 to 30 142198 0.8515 0.802764
28 to 29 141519 -1.1514 0.124781
27 to 28 142037 0.3766 0.646767
26 to 27 141830 -0.2340 0.407488
25 to 26 141553 -1.0511 0.146602
24 to 25 141754 -0.4582 0.323404
23 to 24 142001 0.2704 0.606579
22 to 23 141921 0.0344 0.513731
21 to 22 141846 -0.1868 0.425903
20 to 21 142048 0.4091 0.658751
19 to 20 141774 -0.3992 0.344872
18 to 19 141752 -0.4641 0.321288
17 to 18 141690 -0.6470 0.258819
16 to 17 141276 -1.8682 0.030865
15 to 16 141328 -1.7148 0.043188
14 to 15 141924 0.0433 0.517259
13 to 14 142057 0.4356 0.668438
12 to 13 141689 -0.6499 0.257865
11 to 12 141894 -0.0452 0.481966
10 to 11 141735 -0.5142 0.303539
9 to 10 141723 -0.5496 0.291281
8 to 9 141895 -0.0423 0.483141
7 to 8 141983 0.2173 0.586019
6 to 7 141615 -0.8682 0.192634
5 to 6 141783 -0.3727 0.354703
4 to 5 142404 1.4592 0.927745
3 to 4 141453 -1.3461 0.089134
2 to 3 141544 -1.0777 0.140591
1 to 2 141833 -0.2252 0.410927
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-20_07:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2543.08 0.609 0.728837
Test results for specific bytes for dh-ranFile-2018-06-20_07:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2681.96 2.573 0.994964
2 to 9 2446.06 -0.763 0.222768
3 to 10 2519.08 0.270 0.606356
4 to 11 2419.67 -1.136 0.127971
5 to 12 2511.10 0.157 0.562366
6 to 13 2444.07 -0.791 0.214496
7 to 14 2611.57 1.578 0.942693
8 to 15 2345.65 -2.183 0.014526
9 to 16 2383.93 -1.642 0.050347
10 to 17 2419.95 -1.132 0.128805
11 to 18 2538.78 0.548 0.708297
12 to 19 2423.58 -1.081 0.139916
13 to 20 2504.70 0.066 0.526471
14 to 21 2659.22 2.252 0.987832
15 to 22 2458.11 -0.592 0.276777
16 to 23 2602.13 1.444 0.925674
17 to 24 2477.89 -0.313 0.377261
18 to 25 2382.28 -1.665 0.047970
19 to 26 2585.53 1.210 0.886782
20 to 27 2600.62 1.423 0.922626
21 to 28 2534.24 0.484 0.685864
22 to 29 2560.25 0.852 0.802897
23 to 30 2449.29 -0.717 0.236658
24 to 31 2359.11 -1.992 0.023159
25 to 32 2394.65 -1.490 0.068123
CDPARK for dh-ranFile-2018-06-20_07:31: 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
3501 -1.0046 0.157553
3514 -0.4110 0.340551
3509 -0.6393 0.261324
3497 -1.1872 0.117571
3542 0.8676 0.807188
3521 -0.0913 0.463617
3470 -2.4201 0.007758
3546 1.0502 0.853193
3542 0.8676 0.807188
3495 -1.2785 0.100530
Square side=100, avg. no. parked=3513.70 sample std.=23.28
p-value of the KSTEST for those 10 p-values: 0.276692
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-20_07:31
0.3407,0.9352,0.4963,0.9295,0.9759,0.5273,0.1832,0.8953,0.2481,0.2543,
The KS test for those 10 p-values: 0.285998
The 3DSPHERES test for dh-ranFile-2018-06-20_07:31
sample no r^3 equiv. uni.
1 32.253 0.658736
2 24.172 0.553241
3 5.144 0.157577
4 53.796 0.833573
5 28.118 0.608302
6 70.793 0.905559
7 16.137 0.416035
8 44.335 0.771865
9 57.604 0.853413
10 35.032 0.688933
11 21.063 0.504462
12 8.786 0.253868
13 9.558 0.272839
14 8.789 0.253951
15 2.548 0.081413
16 22.009 0.519841
17 46.032 0.784413
18 48.671 0.802569
19 58.074 0.855689
20 26.215 0.582645
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.354253
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-20_07:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 0.9 1.8 -0.4 -0.9 -2.3
-1.3 -0.8 0.1 0.3 0.9 0.1
1.2 0.3 0.8 1.2 -1.4 0.3
-0.1 0.1 -1.0 0.8 -0.1 -1.7
-1.2 0.8 -1.1 0.3 -0.8 0.5
-0.4 1.5 1.7 -0.2 0.3 -0.8
-0.5 -1.3 0.1 -1.3 -0.6 2.0
1.8
Chi-square with 42 degrees of freedom:45.515495
z-score=0.383572, p-value=0.672090
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-20_07:31
Test no p-value
1 0.712581
2 0.146001
3 0.042284
4 0.006811
5 0.018720
6 0.428026
7 0.132484
8 0.444309
9 0.458892
10 0.055479
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.002880
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-20_07:31:
(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 66563 0.16 66750 0.10
3 25000.00 25006 0.00 25018 0.01
4 6666.67 6680 0.03 6575 1.26
5 1388.89 1452 2.87 1375 0.14
6 238.10 246 0.26 228 0.43
7 34.72 48 5.08 48 5.08
8 4.96 4 0.19 5 0.00
p=0.80168 p=0.68140
Number of rngs required: 688435, p-value: 0.515
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-20_07:31
No. of wins: Observed Expected
98451 98585.9
z-score=-0.603, pvalue=0.27320
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66576 66666.7 0.123 0.123
2 37664 37654.3 0.002 0.126
3 27036 26954.7 0.245 0.371
4 19187 19313.5 0.828 1.199
5 14004 13851.4 1.681 2.880
6 10231 9943.5 8.310 11.190
7 7019 7145.0 2.223 13.413
8 5012 5139.1 3.142 16.555
9 3697 3699.9 0.002 16.557
10 2670 2666.3 0.005 16.562
11 1918 1923.3 0.015 16.577
12 1363 1388.7 0.477 17.054
13 1029 1003.7 0.637 17.691
14 687 726.1 2.110 19.801
15 519 525.8 0.089 19.889
16 369 381.2 0.387 20.277
17 276 276.5 0.001 20.278
18 222 200.8 2.232 22.509
19 139 146.0 0.334 22.844
20 100 106.2 0.364 23.207
21 282 287.1 0.091 23.298
Chisq= 23.30 for 20 degrees of freedom, p= 0.72562
SUMMARY of craptest
p-value for no. of wins: 0.273199
p-value for throws/game: 0.725618
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-20_07:31
No. of wins: Observed Expected
98600 98585.9
z-score= 0.063, pvalue=0.52522
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67097 66666.7 2.778 2.778
2 37526 37654.3 0.437 3.215
3 27004 26954.7 0.090 3.305
4 19219 19313.5 0.462 3.767
5 13943 13851.4 0.605 4.373
6 9721 9943.5 4.981 9.353
7 7103 7145.0 0.247 9.601
8 5240 5139.1 1.982 11.583
9 3587 3699.9 3.443 15.026
10 2629 2666.3 0.522 15.547
11 1873 1923.3 1.317 16.864
12 1464 1388.7 4.079 20.943
13 994 1003.7 0.094 21.037
14 666 726.1 4.981 26.018
15 505 525.8 0.826 26.843
16 392 381.2 0.309 27.152
17 296 276.5 1.369 28.522
18 190 200.8 0.584 29.106
19 153 146.0 0.337 29.443
20 88 106.2 3.124 32.567
21 310 287.1 1.824 34.391
Chisq= 34.39 for 20 degrees of freedom, p= 0.97640
SUMMARY of craptest
p-value for no. of wins: 0.525216
p-value for throws/game: 0.976402
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0029,0.0068,0.0078,0.0085,0.0116,0.0145,0.0187,0.0232,0.0309,0.0327,
0.0340,0.0391,0.0423,0.0432,0.0445,0.0480,0.0503,0.0547,0.0555,0.0636,
0.0681,0.0711,0.0766,0.0769,0.0776,0.0814,0.0823,0.0865,0.0891,0.0932,
0.0967,0.1002,0.1005,0.1042,0.1107,0.1171,0.1176,0.1248,0.1280,0.1288,
0.1325,0.1399,0.1406,0.1421,0.1429,0.1446,0.1460,0.1464,0.1466,0.1554,
0.1576,0.1576,0.1669,0.1685,0.1695,0.1832,0.1926,0.2007,0.2133,0.2145,
0.2168,0.2228,0.2245,0.2258,0.2356,0.2356,0.2364,0.2367,0.2390,0.2453,
0.2481,0.2539,0.2540,0.2543,0.2579,0.2588,0.2613,0.2664,0.2728,0.2732,
0.2762,0.2767,0.2768,0.2773,0.2773,0.2860,0.2903,0.2913,0.2946,0.3035,
0.3053,0.3064,0.3155,0.3165,0.3167,0.3196,0.3213,0.3234,0.3378,0.3406,
0.3407,0.3449,0.3493,0.3543,0.3547,0.3642,0.3644,0.3666,0.3694,0.3694,
0.3759,0.3773,0.3786,0.3843,0.3882,0.4004,0.4075,0.4084,0.4109,0.4137,
0.4160,0.4163,0.4164,0.4198,0.4243,0.4243,0.4259,0.4280,0.4331,0.4440,
0.4443,0.4457,0.4470,0.4502,0.4589,0.4636,0.4712,0.4739,0.4820,0.4831,
0.4933,0.4963,0.5045,0.5137,0.5147,0.5165,0.5173,0.5184,0.5198,0.5252,
0.5265,0.5273,0.5285,0.5309,0.5397,0.5427,0.5427,0.5429,0.5516,0.5521,
0.5532,0.5548,0.5614,0.5624,0.5674,0.5794,0.5803,0.5826,0.5842,0.5860,
0.5920,0.5939,0.6040,0.6064,0.6066,0.6083,0.6084,0.6150,0.6189,0.6325,
0.6328,0.6348,0.6403,0.6468,0.6541,0.6587,0.6588,0.6639,0.6684,0.6721,
0.6745,0.6763,0.6814,0.6859,0.6889,0.7020,0.7083,0.7126,0.7184,0.7256,
0.7256,0.7288,0.7299,0.7453,0.7554,0.7566,0.7672,0.7714,0.7719,0.7815,
0.7834,0.7844,0.7858,0.7861,0.7994,0.8017,0.8026,0.8028,0.8029,0.8041,
0.8070,0.8072,0.8072,0.8152,0.8161,0.8276,0.8336,0.8500,0.8532,0.8534,
0.8557,0.8865,0.8868,0.8951,0.8953,0.8977,0.9056,0.9170,0.9181,0.9226,
0.9235,0.9249,0.9257,0.9277,0.9295,0.9313,0.9352,0.9389,0.9427,0.9439,
0.9459,0.9518,0.9539,0.9547,0.9581,0.9626,0.9658,0.9671,0.9737,0.9759,
0.9764,0.9798,0.9866,0.9878,0.9880,0.9900,0.9926,0.9950,0.9961,
Overall p-value after applying KStest on 269 p-values = 0.323473
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.