RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-12_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 15.77 12.8373 0.252993
2 to 25 15.71 19.6060 0.705123
3 to 26 15.84 18.5540 0.645277
4 to 27 15.64 18.1037 0.617673
5 to 28 15.87 20.0675 0.729211
6 to 29 15.80 13.8563 0.322753
7 to 30 15.98 9.9931 0.096102
8 to 31 16.04 7.2413 0.019796
9 to 32 15.80 16.1791 0.488822
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.623168
Tough bday spacings test for dh-ranFile-2018-07-12_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 11 42 70 86 88 91 53 29 16 7 7
(O-E)^2/E 0.4 0.8 0.1 1.4 1.0 2.1 0.0 0.0 0.1 0.0 2.1
Birthday Spacings: Sum(O-E)^2/E= 8.032, p= 0.374
RESULTS OF GCD FOR dh-ranFile-2018-07-12_02:31
Euclid's algorithm:
p-value, steps to gcd: 0.670821
p-value, dist. of gcd's: 0.558784
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-12_02:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.472 0.084 0.489 0.376 0.355 0.170 0.253 0.466
Bits 8 to 15---> 0.123 0.341 0.776 0.324 0.603 0.828 0.454 0.493
Bits 16 to 23---> 0.566 0.727 0.128 0.431 0.173 0.573 0.660 0.704
Bits 24 to 31---> 0.632 0.977 0.744 0.858 0.882 0.972 0.855 0.568
KS test for the above 32 p values: 0.405
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-12_02:31,
p-values for 5 runs: 0.5115, 0.0773, 0.3032, 0.7867, 0.1219
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-12_02:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 228 211.4 1.301 1.301
r= 29 5096 5134.0 0.281 1.582
r= 30 22925 23103.0 1.372 2.954
r= 31 11751 11551.5 3.445 6.399
chi-square = 6.399 with df = 3; p-value = 0.906
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-12_02:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 203 211.4 0.335 0.335
r= 30 5152 5134.0 0.063 0.398
r= 31 23069 23103.0 0.050 0.448
r= 32 11576 11551.5 0.052 0.500
chi-square = 0.500 with df = 3; p-value = 0.081
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-12_02:31
b-rank test for bits 1 to 8, p=0.95855
b-rank test for bits 2 to 9, p=0.12208
b-rank test for bits 3 to 10, p=0.17631
b-rank test for bits 4 to 11, p=0.12475
b-rank test for bits 5 to 12, p=0.69108
b-rank test for bits 6 to 13, p=0.29975
b-rank test for bits 7 to 14, p=0.89691
b-rank test for bits 8 to 15, p=0.37057
b-rank test for bits 9 to 16, p=0.92390
b-rank test for bits 10 to 17, p=0.15226
b-rank test for bits 11 to 18, p=0.01270
b-rank test for bits 12 to 19, p=0.18106
b-rank test for bits 13 to 20, p=0.19017
b-rank test for bits 14 to 21, p=0.14066
b-rank test for bits 15 to 22, p=0.36877
b-rank test for bits 16 to 23, p=0.59835
b-rank test for bits 17 to 24, p=0.09061
b-rank test for bits 18 to 25, p=0.00079
b-rank test for bits 19 to 26, p=0.70270
b-rank test for bits 20 to 27, p=0.64736
b-rank test for bits 21 to 28, p=0.52288
b-rank test for bits 22 to 29, p=0.05757
b-rank test for bits 23 to 30, p=0.32564
b-rank test for bits 24 to 31, p=0.18369
b-rank test for bits 25 to 32, p=0.26273
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 = 0.014091
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-12_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 142254 0.81 0.789678
2 141936 0.06 0.524843
3 142238 0.77 0.778733
4 142039 0.30 0.619043
5 141628 -0.66 0.255490
6 140932 -2.28 0.011201
7 142160 0.59 0.720954
8 141895 -0.03 0.486645
9 141413 -1.16 0.123096
10 141678 -0.54 0.294429
11 143073 2.72 0.996725
12 142135 0.53 0.700996
13 141968 0.14 0.554516
14 142094 0.43 0.666937
15 142180 0.63 0.736439
16 142114 0.48 0.683746
17 141812 -0.23 0.410054
18 141287 -1.45 0.072967
19 141888 -0.05 0.480126
20 141518 -0.91 0.180274
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-12_02:31
Bits used No. missing words z-score p-value
23 to 32 142551 2.2127 0.986539
22 to 31 141607 -1.0425 0.148586
21 to 30 142012 0.3540 0.638344
20 to 29 141642 -0.9218 0.178309
19 to 28 141859 -0.1736 0.431109
18 to 27 142191 0.9713 0.834295
17 to 26 141749 -0.5529 0.290179
16 to 25 142490 2.0023 0.977374
15 to 24 142391 1.6609 0.951636
14 to 23 141632 -0.9563 0.169458
13 to 22 141886 -0.0804 0.467940
12 to 21 142225 1.0885 0.861817
11 to 20 142025 0.3989 0.655003
10 to 19 142033 0.4264 0.665109
9 to 18 141995 0.2954 0.616161
8 to 17 141676 -0.8046 0.210529
7 to 16 141663 -0.8494 0.197826
6 to 15 142320 1.4161 0.921627
5 to 14 141778 -0.4529 0.325324
4 to 13 141810 -0.3425 0.365981
3 to 12 142130 0.7609 0.776651
2 to 11 141890 -0.0667 0.473428
1 to 10 142280 1.2782 0.899406
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-12_02:31
Bits used No. missing words z-score p-value
28 to 32 141755 -0.5232 0.300434
27 to 31 142058 0.5040 0.692857
26 to 30 141691 -0.7401 0.229619
25 to 29 142054 0.4904 0.688077
24 to 28 141387 -1.7706 0.038313
23 to 27 141485 -1.4384 0.075159
22 to 26 141175 -2.4893 0.006401
21 to 25 142824 3.1006 0.999034
20 to 24 141566 -1.1638 0.122246
19 to 23 141558 -1.1909 0.116837
18 to 22 142144 0.7955 0.786836
17 to 21 142239 1.1175 0.868115
16 to 20 142166 0.8701 0.807868
15 to 19 142040 0.4429 0.671099
14 to 18 141749 -0.5435 0.293396
13 to 17 141689 -0.7469 0.227568
12 to 16 142202 0.9921 0.839426
11 to 15 142028 0.4023 0.656258
10 to 14 142426 1.7514 0.960064
9 to 13 141673 -0.8011 0.211532
8 to 12 141701 -0.7062 0.240031
7 to 11 142269 1.2192 0.888620
6 to 10 142346 1.4802 0.930595
5 to 9 142662 2.5514 0.994636
4 to 8 141752 -0.5333 0.296905
3 to 7 141853 -0.1909 0.424283
2 to 6 141598 -1.0554 0.145631
1 to 5 142165 0.8667 0.806941
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-12_02:31
Bits used No. missing words z-score p-value
31 to 32 141780 -0.3815 0.351415
30 to 31 142221 0.9194 0.821052
29 to 30 141889 -0.0600 0.476090
28 to 29 142018 0.3206 0.625728
27 to 28 142079 0.5005 0.691639
26 to 27 142167 0.7601 0.776399
25 to 26 141997 0.2586 0.602033
24 to 25 141644 -0.7827 0.216906
23 to 24 141900 -0.0275 0.489022
22 to 23 141353 -1.6411 0.050389
21 to 22 142170 0.7689 0.779035
20 to 21 142456 1.6126 0.946584
19 to 20 141657 -0.7443 0.228337
18 to 19 141995 0.2527 0.599755
17 to 18 141775 -0.3963 0.345959
16 to 17 141852 -0.1691 0.432853
15 to 16 142366 1.3471 0.911027
14 to 15 141990 0.2380 0.594046
13 to 14 141726 -0.5408 0.294324
12 to 13 141624 -0.8417 0.199983
11 to 12 141575 -0.9862 0.162012
10 to 11 141892 -0.0511 0.479615
9 to 10 141634 -0.8122 0.208343
8 to 9 142412 1.4828 0.930937
7 to 8 142401 1.4504 0.926520
6 to 7 142758 2.5035 0.993851
5 to 6 142734 2.4327 0.992506
4 to 5 142359 1.3265 0.907656
3 to 4 141709 -0.5909 0.277279
2 to 3 141624 -0.8417 0.199983
1 to 2 141531 -1.1160 0.132207
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-12_02:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2582.29 1.164 0.877746
Test results for specific bytes for dh-ranFile-2018-07-12_02:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2716.66 3.064 0.998908
2 to 9 2458.73 -0.584 0.279721
3 to 10 2355.04 -2.050 0.020183
4 to 11 2435.05 -0.919 0.179163
5 to 12 2457.39 -0.603 0.273412
6 to 13 2573.00 1.032 0.849065
7 to 14 2469.83 -0.427 0.334786
8 to 15 2475.10 -0.352 0.362387
9 to 16 2542.02 0.594 0.723826
10 to 17 2503.70 0.052 0.520874
11 to 18 2536.08 0.510 0.695051
12 to 19 2484.91 -0.213 0.415500
13 to 20 2448.00 -0.735 0.231037
14 to 21 2553.66 0.759 0.776036
15 to 22 2461.21 -0.549 0.291649
16 to 23 2451.17 -0.691 0.244912
17 to 24 2409.42 -1.281 0.100099
18 to 25 2417.42 -1.168 0.121446
19 to 26 2548.32 0.683 0.752819
20 to 27 2406.81 -1.318 0.093774
21 to 28 2421.91 -1.104 0.134720
22 to 29 2615.32 1.631 0.948537
23 to 30 2474.67 -0.358 0.360084
24 to 31 2474.92 -0.355 0.361423
25 to 32 2546.35 0.656 0.743934
CDPARK for dh-ranFile-2018-07-12_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
3518 -0.2283 0.409702
3578 2.5114 0.993988
3565 1.9178 0.972432
3528 0.2283 0.590298
3503 -0.9132 0.180558
3520 -0.1370 0.445521
3514 -0.4110 0.340551
3532 0.4110 0.659449
3551 1.2785 0.899470
3508 -0.6849 0.246694
Square side=100, avg. no. parked=3531.70 sample std.=23.80
p-value of the KSTEST for those 10 p-values: 0.393830
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-12_02:31
0.3842,0.6540,0.4367,0.4882,0.2974,0.0648,0.0821,0.6072,0.8338,0.1304,
The KS test for those 10 p-values: 0.455371
The 3DSPHERES test for dh-ranFile-2018-07-12_02:31
sample no r^3 equiv. uni.
1 4.511 0.139617
2 25.384 0.570935
3 27.322 0.597774
4 22.832 0.532831
5 1.925 0.062148
6 11.135 0.310065
7 11.633 0.321440
8 5.939 0.179606
9 46.695 0.789128
10 1.532 0.049774
11 12.863 0.348686
12 4.220 0.131225
13 20.621 0.497108
14 0.663 0.021868
15 127.433 0.985704
16 1.971 0.063576
17 0.146 0.004855
18 20.788 0.499895
19 23.135 0.537533
20 70.535 0.904741
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.059302
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-12_02:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -0.3 -1.1 0.0 -1.0 0.4
1.4 0.2 1.3 -0.8 -0.1 -1.0
0.2 -0.1 -1.0 0.6 -0.5 -0.1
2.1 -1.1 1.4 -1.0 -2.1 0.7
-0.2 1.3 0.7 -0.6 0.1 -0.1
0.5 0.4 0.1 -1.3 1.3 0.2
2.4 -0.1 -1.2 1.0 0.9 -1.0
-1.1
Chi-square with 42 degrees of freedom:40.472193
z-score=-0.166697, p-value=0.461871
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-12_02:31
Test no p-value
1 0.302341
2 0.626374
3 0.374430
4 0.004311
5 0.494730
6 0.145993
7 0.758484
8 0.903805
9 0.375462
10 0.034571
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.392108
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-12_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 66691 0.01 66735 0.07
3 25000.00 25053 0.11 24930 0.20
4 6666.67 6596 0.75 6677 0.02
5 1388.89 1409 0.29 1360 0.60
6 238.10 207 4.06 243 0.10
7 34.72 37 0.15 46 3.66
8 4.96 6 0.22 8 1.86
p=0.52940 p=0.63165
Number of rngs required: 688803, p-value: 0.678
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-12_02:31
No. of wins: Observed Expected
98441 98585.9
z-score=-0.648, pvalue=0.25853
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66792 66666.7 0.236 0.236
2 37763 37654.3 0.314 0.549
3 26869 26954.7 0.273 0.822
4 19153 19313.5 1.333 2.155
5 13832 13851.4 0.027 2.182
6 9728 9943.5 4.672 6.855
7 7243 7145.0 1.343 8.198
8 5189 5139.1 0.485 8.683
9 3762 3699.9 1.043 9.727
10 2626 2666.3 0.609 10.336
11 1948 1923.3 0.316 10.652
12 1433 1388.7 1.411 12.063
13 1008 1003.7 0.018 12.081
14 745 726.1 0.490 12.571
15 560 525.8 2.220 14.790
16 368 381.2 0.454 15.244
17 255 276.5 1.678 16.922
18 200 200.8 0.003 16.925
19 159 146.0 1.160 18.086
20 89 106.2 2.790 20.876
21 278 287.1 0.289 21.165
Chisq= 21.17 for 20 degrees of freedom, p= 0.61254
SUMMARY of craptest
p-value for no. of wins: 0.258527
p-value for throws/game: 0.612540
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-12_02:31
No. of wins: Observed Expected
98999 98585.9
z-score= 1.848, pvalue=0.96769
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66716 66666.7 0.037 0.037
2 37827 37654.3 0.792 0.828
3 26768 26954.7 1.294 2.122
4 19314 19313.5 0.000 2.122
5 13875 13851.4 0.040 2.162
6 10048 9943.5 1.097 3.259
7 6999 7145.0 2.984 6.244
8 5147 5139.1 0.012 6.256
9 3663 3699.9 0.367 6.623
10 2678 2666.3 0.051 6.675
11 1945 1923.3 0.244 6.919
12 1399 1388.7 0.076 6.995
13 983 1003.7 0.428 7.422
14 701 726.1 0.870 8.293
15 540 525.8 0.382 8.674
16 368 381.2 0.454 9.128
17 265 276.5 0.482 9.609
18 208 200.8 0.256 9.865
19 164 146.0 2.223 12.089
20 117 106.2 1.095 13.184
21 275 287.1 0.511 13.695
Chisq= 13.69 for 20 degrees of freedom, p= 0.15438
SUMMARY of craptest
p-value for no. of wins: 0.967685
p-value for throws/game: 0.154378
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0008,0.0043,0.0049,0.0064,0.0112,0.0127,0.0141,0.0198,0.0202,0.0219,
0.0346,0.0383,0.0498,0.0504,0.0576,0.0593,0.0621,0.0636,0.0648,0.0730,
0.0752,0.0773,0.0812,0.0821,0.0837,0.0906,0.0938,0.0961,0.1001,0.1168,
0.1214,0.1219,0.1221,0.1222,0.1231,0.1231,0.1247,0.1276,0.1304,0.1312,
0.1322,0.1347,0.1396,0.1407,0.1456,0.1460,0.1486,0.1523,0.1544,0.1620,
0.1695,0.1703,0.1733,0.1763,0.1783,0.1792,0.1796,0.1803,0.1806,0.1811,
0.1837,0.1902,0.1978,0.2000,0.2000,0.2083,0.2105,0.2115,0.2169,0.2276,
0.2283,0.2296,0.2310,0.2400,0.2449,0.2467,0.2530,0.2532,0.2555,0.2585,
0.2627,0.2734,0.2773,0.2797,0.2902,0.2916,0.2934,0.2943,0.2944,0.2969,
0.2974,0.2998,0.3004,0.3023,0.3032,0.3101,0.3214,0.3228,0.3244,0.3253,
0.3256,0.3348,0.3405,0.3406,0.3460,0.3487,0.3514,0.3554,0.3601,0.3614,
0.3624,0.3660,0.3688,0.3706,0.3743,0.3744,0.3755,0.3756,0.3842,0.3921,
0.3938,0.4053,0.4097,0.4101,0.4155,0.4243,0.4311,0.4314,0.4329,0.4367,
0.4455,0.4539,0.4554,0.4619,0.4660,0.4679,0.4722,0.4734,0.4761,0.4796,
0.4801,0.4866,0.4882,0.4888,0.4890,0.4893,0.4926,0.4947,0.4971,0.4999,
0.5115,0.5209,0.5229,0.5248,0.5294,0.5328,0.5375,0.5545,0.5588,0.5664,
0.5678,0.5709,0.5731,0.5903,0.5940,0.5978,0.5983,0.5998,0.6020,0.6026,
0.6072,0.6125,0.6162,0.6177,0.6190,0.6232,0.6257,0.6264,0.6316,0.6317,
0.6383,0.6453,0.6474,0.6540,0.6550,0.6563,0.6594,0.6596,0.6651,0.6669,
0.6708,0.6711,0.6775,0.6837,0.6881,0.6911,0.6916,0.6929,0.6951,0.7010,
0.7027,0.7041,0.7051,0.7210,0.7238,0.7275,0.7292,0.7364,0.7439,0.7443,
0.7528,0.7585,0.7760,0.7763,0.7764,0.7767,0.7787,0.7790,0.7867,0.7868,
0.7891,0.7897,0.8069,0.8079,0.8211,0.8282,0.8338,0.8343,0.8394,0.8491,
0.8553,0.8584,0.8618,0.8681,0.8777,0.8825,0.8886,0.8969,0.8994,0.8995,
0.9038,0.9047,0.9063,0.9077,0.9110,0.9216,0.9239,0.9265,0.9306,0.9309,
0.9466,0.9485,0.9516,0.9586,0.9601,0.9677,0.9724,0.9725,0.9773,0.9774,
0.9857,0.9865,0.9925,0.9939,0.9940,0.9946,0.9967,0.9989,0.9990,
Overall p-value after applying KStest on 269 p-values = 0.193670
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.