RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-19_16:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.55 25.0054 0.905412
2 to 25 15.90 15.2619 0.423379
3 to 26 15.63 26.6792 0.937057
4 to 27 15.74 25.2133 0.909964
5 to 28 15.40 24.1573 0.884777
6 to 29 15.73 23.5666 0.868304
7 to 30 16.04 10.3337 0.110964
8 to 31 15.82 15.1987 0.418831
9 to 32 15.92 29.7584 0.971859
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.012027
Tough bday spacings test for dh-ranFile-2018-06-19_16:31: 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 30 74 93 102 88 61 21 13 4 5
(O-E)^2/E 0.0 1.2 0.0 0.2 0.2 1.2 1.5 2.6 0.2 1.0 0.2
Birthday Spacings: Sum(O-E)^2/E= 8.460, p= 0.416
RESULTS OF GCD FOR dh-ranFile-2018-06-19_16:31
Euclid's algorithm:
p-value, steps to gcd: 0.470560
p-value, dist. of gcd's: 0.116142
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-19_16:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.456 0.846 0.149 0.009 0.714 0.809 0.836 0.040
Bits 8 to 15---> 0.233 0.916 0.227 0.404 0.947 0.586 0.855 0.782
Bits 16 to 23---> 0.299 0.675 0.924 0.346 0.380 0.550 0.417 0.452
Bits 24 to 31---> 0.079 0.989 0.413 0.673 0.072 0.653 0.934 0.959
KS test for the above 32 p values: 0.517
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-19_16:31,
p-values for 5 runs: 0.7580, 0.7969, 0.8606, 0.1835, 0.9134
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-19_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 232 211.4 2.004 2.004
r= 29 5205 5134.0 0.982 2.985
r= 30 23119 23103.0 0.011 2.996
r= 31 11444 11551.5 1.001 3.997
chi-square = 3.997 with df = 3; p-value = 0.738
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-19_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 184 211.4 3.556 3.556
r= 30 5174 5134.0 0.311 3.867
r= 31 23110 23103.0 0.002 3.869
r= 32 11532 11551.5 0.033 3.902
chi-square = 3.902 with df = 3; p-value = 0.728
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-19_16:31
b-rank test for bits 1 to 8, p=0.15841
b-rank test for bits 2 to 9, p=0.35285
b-rank test for bits 3 to 10, p=0.38109
b-rank test for bits 4 to 11, p=0.22418
b-rank test for bits 5 to 12, p=0.06259
b-rank test for bits 6 to 13, p=0.33916
b-rank test for bits 7 to 14, p=0.27253
b-rank test for bits 8 to 15, p=0.81749
b-rank test for bits 9 to 16, p=0.62845
b-rank test for bits 10 to 17, p=0.50398
b-rank test for bits 11 to 18, p=0.23683
b-rank test for bits 12 to 19, p=0.19637
b-rank test for bits 13 to 20, p=0.56649
b-rank test for bits 14 to 21, p=0.80517
b-rank test for bits 15 to 22, p=0.96099
b-rank test for bits 16 to 23, p=0.08354
b-rank test for bits 17 to 24, p=0.79638
b-rank test for bits 18 to 25, p=0.36286
b-rank test for bits 19 to 26, p=0.83619
b-rank test for bits 20 to 27, p=0.92066
b-rank test for bits 21 to 28, p=0.06954
b-rank test for bits 22 to 29, p=0.93803
b-rank test for bits 23 to 30, p=0.91527
b-rank test for bits 24 to 31, p=0.99285
b-rank test for bits 25 to 32, p=0.70382
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 = 0.663912
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-19_16:31
(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 142055 0.34 0.633204
2 141854 -0.13 0.448570
3 141918 0.02 0.508081
4 141446 -1.08 0.139505
5 142695 1.84 0.966797
6 142238 0.77 0.778733
7 141694 -0.50 0.307444
8 141915 0.01 0.505285
9 141810 -0.23 0.408238
10 142068 0.37 0.644579
11 141526 -0.90 0.185225
12 141142 -1.79 0.036500
13 142715 1.88 0.970110
14 142558 1.52 0.935188
15 141840 -0.16 0.435658
16 141205 -1.65 0.049920
17 142159 0.58 0.720168
18 142272 0.85 0.801603
19 142173 0.62 0.731070
20 142025 0.27 0.606519
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-19_16:31
Bits used No. missing words z-score p-value
23 to 32 142198 0.9954 0.840233
22 to 31 142226 1.0920 0.862576
21 to 30 141586 -1.1149 0.132440
20 to 29 141884 -0.0873 0.465199
19 to 28 142021 0.3851 0.649907
18 to 27 142098 0.6506 0.742343
17 to 26 141806 -0.3563 0.360804
16 to 25 141480 -1.4804 0.069377
15 to 24 141822 -0.3011 0.381655
14 to 23 141603 -1.0563 0.145413
13 to 22 141929 0.0678 0.527039
12 to 21 142094 0.6368 0.737870
11 to 20 142038 0.4437 0.671367
10 to 19 141971 0.2127 0.584202
9 to 18 141748 -0.5563 0.288999
8 to 17 142163 0.8747 0.809138
7 to 16 141950 0.1402 0.555765
6 to 15 142104 0.6713 0.748978
5 to 14 141963 0.1851 0.573413
4 to 13 141535 -1.2908 0.098388
3 to 12 141974 0.2230 0.588232
2 to 11 141407 -1.7322 0.041621
1 to 10 141342 -1.9563 0.025214
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-19_16:31
Bits used No. missing words z-score p-value
28 to 32 141967 0.1955 0.577496
27 to 31 141772 -0.4655 0.320778
26 to 30 142255 1.1718 0.879354
25 to 29 142216 1.0396 0.850728
24 to 28 142334 1.4396 0.925004
23 to 27 141979 0.2362 0.593349
22 to 26 141642 -0.9062 0.182414
21 to 25 142118 0.7074 0.760327
20 to 24 142263 1.1989 0.884713
19 to 23 142529 2.1006 0.982161
18 to 22 141824 -0.2893 0.386193
17 to 21 142146 0.8023 0.788802
16 to 20 142345 1.4768 0.930142
15 to 19 141835 -0.2520 0.400534
14 to 18 141731 -0.6045 0.272753
13 to 17 141598 -1.0554 0.145631
12 to 16 142151 0.8192 0.793670
11 to 15 142185 0.9345 0.824970
10 to 14 141781 -0.4350 0.331775
9 to 13 142004 0.3209 0.625863
8 to 12 141421 -1.6554 0.048926
7 to 11 141584 -1.1028 0.135054
6 to 10 141696 -0.7232 0.234793
5 to 9 141917 0.0260 0.510371
4 to 8 141908 -0.0045 0.498201
3 to 7 141591 -1.0791 0.140275
2 to 6 141743 -0.5638 0.286435
1 to 5 141324 -1.9842 0.023618
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-19_16:31
Bits used No. missing words z-score p-value
31 to 32 142077 0.4946 0.689559
30 to 31 142280 1.0934 0.862896
29 to 30 142075 0.4887 0.687474
28 to 29 142177 0.7896 0.785116
27 to 28 141963 0.1583 0.562897
26 to 27 141953 0.1288 0.551250
25 to 26 141119 -2.3314 0.009867
24 to 25 142401 1.4504 0.926520
23 to 24 141961 0.1524 0.560572
22 to 23 141540 -1.0895 0.137974
21 to 22 141581 -0.9685 0.166391
20 to 21 141714 -0.5762 0.282242
19 to 20 141281 -1.8535 0.031907
18 to 19 141515 -1.1632 0.122371
17 to 18 142181 0.8014 0.788546
16 to 17 142118 0.6155 0.730903
15 to 16 142533 1.8397 0.967096
14 to 15 142341 1.2734 0.898555
13 to 14 142109 0.5890 0.722068
12 to 13 142220 0.9164 0.820280
11 to 12 141303 -1.7886 0.036841
10 to 11 142113 0.6008 0.726012
9 to 10 141188 -2.1278 0.016676
8 to 9 142253 1.0138 0.844655
7 to 8 141603 -0.9036 0.183096
6 to 7 141604 -0.9007 0.183880
5 to 6 141849 -0.1780 0.429375
4 to 5 141573 -0.9921 0.160569
3 to 4 141047 -2.5437 0.005484
2 to 3 142196 0.8456 0.801122
1 to 2 142268 1.0580 0.854978
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-19_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2516.56 0.234 0.592592
Test results for specific bytes for dh-ranFile-2018-06-19_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2479.10 -0.296 0.383797
2 to 9 2550.39 0.713 0.761951
3 to 10 2535.44 0.501 0.691876
4 to 11 2486.45 -0.192 0.423995
5 to 12 2527.74 0.392 0.652583
6 to 13 2560.02 0.849 0.802025
7 to 14 2540.97 0.579 0.718833
8 to 15 2579.31 1.122 0.868998
9 to 16 2536.11 0.511 0.695229
10 to 17 2435.13 -0.917 0.179459
11 to 18 2604.92 1.484 0.931072
12 to 19 2553.22 0.753 0.774152
13 to 20 2421.20 -1.114 0.132568
14 to 21 2451.77 -0.682 0.247615
15 to 22 2429.16 -1.002 0.158228
16 to 23 2574.01 1.047 0.852381
17 to 24 2480.79 -0.272 0.392936
18 to 25 2569.16 0.978 0.835987
19 to 26 2508.96 0.127 0.550408
20 to 27 2412.54 -1.237 0.108072
21 to 28 2431.98 -0.962 0.168021
22 to 29 2549.09 0.694 0.756213
23 to 30 2439.87 -0.850 0.197574
24 to 31 2408.65 -1.292 0.098191
25 to 32 2561.22 0.866 0.806704
CDPARK for dh-ranFile-2018-06-19_16:31: 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
3507 -0.7306 0.232514
3525 0.0913 0.536383
3515 -0.3653 0.357445
3551 1.2785 0.899470
3544 0.9589 0.831196
3534 0.5023 0.692266
3522 -0.0457 0.481790
3527 0.1826 0.572463
3484 -1.7808 0.037471
3485 -1.7352 0.041356
Square side=100, avg. no. parked=3519.40 sample std.=21.27
p-value of the KSTEST for those 10 p-values: 0.898925
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-19_16:31
0.6031,0.0623,0.2192,0.0663,0.1950,0.1391,0.2124,0.3767,0.9163,0.6897,
The KS test for those 10 p-values: 0.128983
The 3DSPHERES test for dh-ranFile-2018-06-19_16:31
sample no r^3 equiv. uni.
1 16.666 0.426232
2 9.270 0.265811
3 7.643 0.224898
4 2.565 0.081940
5 7.097 0.210665
6 10.759 0.301366
7 31.019 0.644411
8 36.141 0.700222
9 33.273 0.670145
10 24.055 0.551491
11 65.458 0.887176
12 43.812 0.767856
13 26.784 0.590488
14 66.680 0.891681
15 22.614 0.529432
16 32.663 0.663371
17 58.844 0.859347
18 18.083 0.452701
19 23.504 0.543186
20 42.815 0.760012
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.407944
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-19_16:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -0.7 0.8 1.8 -1.0 -0.1
-1.1 1.5 -0.8 0.3 -0.0 0.5
0.9 0.0 1.3 0.6 0.6 -0.8
-1.4 0.3 2.1 -1.0 -0.7 -0.4
0.6 -1.4 0.4 -0.4 -1.9 -0.9
-2.3 -2.0 0.7 -1.4 -0.4 -1.0
1.4 -0.1 -0.4 1.0 0.1 0.0
0.8
Chi-square with 42 degrees of freedom:45.699087
z-score=0.403604, p-value=0.678903
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-19_16:31
Test no p-value
1 0.397306
2 0.015964
3 0.426363
4 0.359817
5 0.300325
6 0.096423
7 0.551296
8 0.576328
9 0.192288
10 0.344627
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.070165
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-19_16:31:
(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 66538 0.25 66602 0.06
3 25000.00 25074 0.22 24916 0.28
4 6666.67 6757 1.22 6771 1.63
5 1388.89 1355 0.83 1422 0.79
6 238.10 236 0.02 251 0.70
7 34.72 36 0.05 34 0.01
8 4.96 3 0.77 3 0.77
p=0.23730 p=0.35791
Number of rngs required: 688842, p-value: 0.694
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-19_16:31
No. of wins: Observed Expected
98692 98585.9
z-score= 0.475, pvalue=0.68251
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66933 66666.7 1.064 1.064
2 37596 37654.3 0.090 1.154
3 26960 26954.7 0.001 1.155
4 19423 19313.5 0.621 1.777
5 13844 13851.4 0.004 1.781
6 9675 9943.5 7.252 9.033
7 7273 7145.0 2.292 11.325
8 4978 5139.1 5.048 16.374
9 3743 3699.9 0.503 16.877
10 2691 2666.3 0.229 17.105
11 1914 1923.3 0.045 17.151
12 1402 1388.7 0.127 17.277
13 998 1003.7 0.033 17.310
14 725 726.1 0.002 17.312
15 518 525.8 0.117 17.428
16 370 381.2 0.326 17.755
17 251 276.5 2.359 20.113
18 210 200.8 0.419 20.532
19 131 146.0 1.538 22.070
20 100 106.2 0.364 22.434
21 265 287.1 1.703 24.137
Chisq= 24.14 for 20 degrees of freedom, p= 0.76354
SUMMARY of craptest
p-value for no. of wins: 0.682509
p-value for throws/game: 0.763539
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-19_16:31
No. of wins: Observed Expected
98619 98585.9
z-score= 0.148, pvalue=0.55892
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66494 66666.7 0.447 0.447
2 37559 37654.3 0.241 0.689
3 27154 26954.7 1.473 2.162
4 19335 19313.5 0.024 2.186
5 13817 13851.4 0.086 2.271
6 9976 9943.5 0.106 2.377
7 7068 7145.0 0.830 3.207
8 5200 5139.1 0.722 3.930
9 3686 3699.9 0.052 3.982
10 2671 2666.3 0.008 3.990
11 1903 1923.3 0.215 4.205
12 1404 1388.7 0.168 4.373
13 1054 1003.7 2.519 6.892
14 743 726.1 0.391 7.283
15 535 525.8 0.160 7.443
16 372 381.2 0.220 7.663
17 268 276.5 0.264 7.926
18 202 200.8 0.007 7.933
19 142 146.0 0.109 8.042
20 102 106.2 0.167 8.209
21 315 287.1 2.708 10.918
Chisq= 10.92 for 20 degrees of freedom, p= 0.05167
SUMMARY of craptest
p-value for no. of wins: 0.558918
p-value for throws/game: 0.051670
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0055,0.0092,0.0099,0.0120,0.0160,0.0167,0.0236,0.0252,0.0319,0.0365,
0.0368,0.0375,0.0401,0.0414,0.0416,0.0489,0.0499,0.0517,0.0623,0.0626,
0.0663,0.0694,0.0695,0.0702,0.0720,0.0787,0.0819,0.0835,0.0964,0.0982,
0.0984,0.1081,0.1110,0.1161,0.1224,0.1290,0.1324,0.1326,0.1351,0.1380,
0.1391,0.1395,0.1403,0.1454,0.1456,0.1489,0.1582,0.1584,0.1606,0.1664,
0.1680,0.1795,0.1824,0.1831,0.1835,0.1839,0.1852,0.1923,0.1950,0.1964,
0.1976,0.2107,0.2124,0.2192,0.2242,0.2249,0.2273,0.2325,0.2329,0.2348,
0.2368,0.2373,0.2476,0.2658,0.2725,0.2728,0.2822,0.2864,0.2890,0.2986,
0.3003,0.3014,0.3074,0.3208,0.3318,0.3392,0.3446,0.3462,0.3528,0.3574,
0.3579,0.3598,0.3608,0.3629,0.3767,0.3804,0.3811,0.3817,0.3838,0.3862,
0.3929,0.3973,0.4005,0.4038,0.4079,0.4082,0.4132,0.4160,0.4167,0.4188,
0.4234,0.4240,0.4262,0.4264,0.4294,0.4357,0.4486,0.4518,0.4527,0.4561,
0.4652,0.4706,0.4818,0.4982,0.5040,0.5053,0.5081,0.5104,0.5169,0.5270,
0.5294,0.5364,0.5432,0.5495,0.5504,0.5513,0.5513,0.5515,0.5558,0.5589,
0.5606,0.5629,0.5665,0.5725,0.5734,0.5763,0.5775,0.5842,0.5860,0.5882,
0.5905,0.5926,0.5933,0.6031,0.6065,0.6259,0.6284,0.6332,0.6444,0.6446,
0.6499,0.6526,0.6533,0.6634,0.6639,0.6701,0.6714,0.6727,0.6750,0.6789,
0.6825,0.6875,0.6896,0.6897,0.6919,0.6923,0.6935,0.6952,0.7002,0.7038,
0.7136,0.7188,0.7202,0.7221,0.7260,0.7278,0.7309,0.7311,0.7379,0.7382,
0.7423,0.7490,0.7562,0.7580,0.7600,0.7603,0.7620,0.7635,0.7679,0.7742,
0.7787,0.7820,0.7851,0.7885,0.7888,0.7937,0.7964,0.7969,0.8011,0.8016,
0.8020,0.8052,0.8067,0.8091,0.8091,0.8175,0.8203,0.8250,0.8312,0.8358,
0.8360,0.8362,0.8402,0.8447,0.8464,0.8507,0.8524,0.8550,0.8554,0.8593,
0.8606,0.8626,0.8629,0.8683,0.8690,0.8794,0.8847,0.8848,0.8872,0.8917,
0.8986,0.8989,0.8995,0.9054,0.9100,0.9134,0.9153,0.9156,0.9163,0.9207,
0.9241,0.9250,0.9265,0.9301,0.9311,0.9345,0.9352,0.9371,0.9380,0.9473,
0.9591,0.9610,0.9668,0.9671,0.9701,0.9719,0.9822,0.9890,0.9928,
Overall p-value after applying KStest on 269 p-values = 0.375025
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.