RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-09_08:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.63 18.3028 0.630019
2 to 25 15.87 10.6287 0.124795
3 to 26 15.73 23.6787 0.871569
4 to 27 15.63 17.1973 0.558922
5 to 28 15.67 22.2500 0.824706
6 to 29 15.77 10.7714 0.131804
7 to 30 15.92 12.4847 0.230061
8 to 31 15.75 11.1499 0.151335
9 to 32 15.91 15.6885 0.453985
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.752849
Tough bday spacings test for dh-ranFile-2018-07-09_08:31: 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 14 28 94 91 88 81 51 22 17 9 5
(O-E)^2/E 2.6 2.0 5.9 0.5 1.0 0.1 0.0 2.0 0.3 0.9 0.2
Birthday Spacings: Sum(O-E)^2/E= 15.411, p= 0.882
RESULTS OF GCD FOR dh-ranFile-2018-07-09_08:31
Euclid's algorithm:
p-value, steps to gcd: 0.017673
p-value, dist. of gcd's: 0.029104
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-09_08:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.565 0.762 0.403 0.883 0.001 0.871 0.290 0.029
Bits 8 to 15---> 0.436 0.118 0.898 0.119 0.483 0.529 0.399 0.113
Bits 16 to 23---> 0.023 0.568 0.871 0.131 0.123 0.557 0.997 0.958
Bits 24 to 31---> 0.943 0.821 0.890 0.562 0.200 0.490 0.012 0.864
KS test for the above 32 p values: 0.739
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-09_08:31,
p-values for 5 runs: 0.9061, 0.9676, 0.3229, 0.8486, 0.1454
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-09_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 226 211.4 1.006 1.006
r= 29 5019 5134.0 2.576 3.582
r= 30 23220 23103.0 0.592 4.174
r= 31 11535 11551.5 0.024 4.198
chi-square = 4.198 with df = 3; p-value = 0.759
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-09_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 210 211.4 0.010 0.010
r= 30 5158 5134.0 0.112 0.122
r= 31 23069 23103.0 0.050 0.172
r= 32 11563 11551.5 0.011 0.183
chi-square = 0.183 with df = 3; p-value = 0.020
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-09_08:31
b-rank test for bits 1 to 8, p=0.60616
b-rank test for bits 2 to 9, p=0.07391
b-rank test for bits 3 to 10, p=0.87751
b-rank test for bits 4 to 11, p=0.22134
b-rank test for bits 5 to 12, p=0.67836
b-rank test for bits 6 to 13, p=0.39071
b-rank test for bits 7 to 14, p=0.50921
b-rank test for bits 8 to 15, p=0.96936
b-rank test for bits 9 to 16, p=0.66888
b-rank test for bits 10 to 17, p=0.91375
b-rank test for bits 11 to 18, p=0.03325
b-rank test for bits 12 to 19, p=0.53070
b-rank test for bits 13 to 20, p=0.51949
b-rank test for bits 14 to 21, p=0.55350
b-rank test for bits 15 to 22, p=0.64653
b-rank test for bits 16 to 23, p=0.96497
b-rank test for bits 17 to 24, p=0.32617
b-rank test for bits 18 to 25, p=0.47912
b-rank test for bits 19 to 26, p=0.36400
b-rank test for bits 20 to 27, p=0.72035
b-rank test for bits 21 to 28, p=0.88839
b-rank test for bits 22 to 29, p=0.89703
b-rank test for bits 23 to 30, p=0.53412
b-rank test for bits 24 to 31, p=0.96067
b-rank test for bits 25 to 32, p=0.93260
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 = 0.069246
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-09_08:31
(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 141728 -0.42 0.335904
2 141770 -0.33 0.372387
3 142279 0.86 0.806128
4 142294 0.90 0.815610
5 141470 -1.03 0.152335
6 141992 0.19 0.576581
7 140622 -3.01 0.001316
8 140659 -2.92 0.001743
9 142208 0.70 0.757357
10 141521 -0.91 0.182121
11 141554 -0.83 0.203210
12 141390 -1.21 0.112491
13 141297 -1.43 0.076261
14 141626 -0.66 0.253990
15 142114 0.48 0.683746
16 141422 -1.14 0.127431
17 141778 -0.31 0.379480
18 141681 -0.53 0.296850
19 142801 2.08 0.981390
20 141985 0.18 0.570167
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-09_08:31
Bits used No. missing words z-score p-value
23 to 32 142042 0.4575 0.676338
22 to 31 142006 0.3333 0.630563
21 to 30 141922 0.0437 0.517424
20 to 29 142127 0.7506 0.773549
19 to 28 141672 -0.8184 0.206570
18 to 27 142183 0.9437 0.827336
17 to 26 141961 0.1782 0.570706
16 to 25 142052 0.4920 0.688628
15 to 24 141545 -1.2563 0.104502
14 to 23 141755 -0.5322 0.297303
13 to 22 141942 0.1127 0.544848
12 to 21 141976 0.2299 0.590914
11 to 20 141749 -0.5529 0.290179
10 to 19 141608 -1.0391 0.149386
9 to 18 142401 1.6954 0.955002
8 to 17 142185 0.9506 0.829093
7 to 16 142055 0.5023 0.692275
6 to 15 141966 0.1954 0.577466
5 to 14 142056 0.5058 0.693487
4 to 13 141730 -0.6184 0.268163
3 to 12 142050 0.4851 0.686186
2 to 11 142399 1.6885 0.954344
1 to 10 142610 2.4161 0.992156
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-09_08:31
Bits used No. missing words z-score p-value
28 to 32 141636 -0.9265 0.177082
27 to 31 141427 -1.6350 0.051023
26 to 30 141550 -1.2181 0.111599
25 to 29 141985 0.2565 0.601221
24 to 28 141498 -1.3943 0.081608
23 to 27 141951 0.1413 0.556166
22 to 26 141613 -1.0045 0.157567
21 to 25 142292 1.2972 0.902717
20 to 24 142228 1.0802 0.859982
19 to 23 141912 0.0091 0.503611
18 to 22 141627 -0.9571 0.169271
17 to 21 141570 -1.1503 0.125016
16 to 20 141730 -0.6079 0.271628
15 to 19 141506 -1.3672 0.085778
14 to 18 142379 1.5921 0.944319
13 to 17 142232 1.0938 0.862978
12 to 16 141796 -0.3842 0.350426
11 to 15 141668 -0.8181 0.206659
10 to 14 141619 -0.9842 0.162516
9 to 13 141908 -0.0045 0.498201
8 to 12 142245 1.1379 0.872411
7 to 11 142012 0.3480 0.636093
6 to 10 142004 0.3209 0.625863
5 to 9 141856 -0.1808 0.428270
4 to 8 141591 -1.0791 0.140275
3 to 7 141937 0.0938 0.537365
2 to 6 142263 1.1989 0.884713
1 to 5 141833 -0.2587 0.397916
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-09_08:31
Bits used No. missing words z-score p-value
31 to 32 141374 -1.5791 0.057151
30 to 31 142231 0.9489 0.828659
29 to 30 141803 -0.3137 0.376891
28 to 29 141482 -1.2606 0.103734
27 to 28 142131 0.6539 0.743410
26 to 27 141928 0.0551 0.521960
25 to 26 141955 0.1347 0.553583
24 to 25 142458 1.6185 0.947222
23 to 24 142383 1.3973 0.918832
22 to 23 141599 -0.9154 0.179984
21 to 22 141681 -0.6735 0.250302
20 to 21 141747 -0.4788 0.316023
19 to 20 141780 -0.3815 0.351415
18 to 19 141758 -0.4464 0.327654
17 to 18 141347 -1.6588 0.048579
16 to 17 142154 0.7217 0.764773
15 to 16 141459 -1.3284 0.092022
14 to 15 141880 -0.0865 0.465527
13 to 14 141284 -1.8446 0.032546
12 to 13 141870 -0.1160 0.453819
11 to 12 141984 0.2203 0.587168
10 to 11 142078 0.4976 0.690600
9 to 10 142041 0.3884 0.651143
8 to 9 141924 0.0433 0.517259
7 to 8 142520 1.8014 0.964179
6 to 7 142090 0.5329 0.702966
5 to 6 141939 0.0875 0.534872
4 to 5 142235 0.9607 0.831643
3 to 4 141645 -0.7797 0.217774
2 to 3 141085 -2.4317 0.007515
1 to 2 142007 0.2881 0.613370
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-09_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2399.61 -1.420 0.077837
Test results for specific bytes for dh-ranFile-2018-07-09_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2494.35 -0.080 0.468168
2 to 9 2435.38 -0.914 0.180388
3 to 10 2480.07 -0.282 0.389021
4 to 11 2460.92 -0.553 0.290258
5 to 12 2558.03 0.821 0.794081
6 to 13 2492.20 -0.110 0.456108
7 to 14 2575.85 1.073 0.858289
8 to 15 2416.29 -1.184 0.118226
9 to 16 2501.84 0.026 0.510396
10 to 17 2504.32 0.061 0.524371
11 to 18 2493.88 -0.087 0.465498
12 to 19 2482.19 -0.252 0.400567
13 to 20 2428.69 -1.008 0.156622
14 to 21 2513.59 0.192 0.576200
15 to 22 2524.63 0.348 0.636191
16 to 23 2388.73 -1.574 0.057790
17 to 24 2446.69 -0.754 0.225438
18 to 25 2470.56 -0.416 0.338559
19 to 26 2460.73 -0.555 0.289303
20 to 27 2422.89 -1.091 0.137736
21 to 28 2408.33 -1.296 0.097416
22 to 29 2663.64 2.314 0.989673
23 to 30 2378.24 -1.722 0.042535
24 to 31 2567.64 0.957 0.830623
25 to 32 2473.40 -0.376 0.353365
CDPARK for dh-ranFile-2018-07-09_08:31: 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
3487 -1.6438 0.050105
3506 -0.7763 0.218799
3555 1.4612 0.928018
3505 -0.8219 0.205562
3506 -0.7763 0.218799
3535 0.5479 0.708135
3562 1.7808 0.962529
3524 0.0457 0.518210
3534 0.5023 0.692266
3500 -1.0502 0.146807
Square side=100, avg. no. parked=3521.40 sample std.=23.48
p-value of the KSTEST for those 10 p-values: 0.709442
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-09_08:31
0.2729,0.1295,0.6560,0.9173,0.9019,0.7207,0.2761,0.4627,0.4311,0.8442,
The KS test for those 10 p-values: 0.810077
The 3DSPHERES test for dh-ranFile-2018-07-09_08:31
sample no r^3 equiv. uni.
1 57.956 0.855122
2 13.037 0.352455
3 8.174 0.238508
4 10.331 0.291342
5 2.604 0.083154
6 36.816 0.706886
7 6.654 0.198936
8 3.348 0.105592
9 3.957 0.123571
10 10.203 0.288302
11 26.323 0.584156
12 30.214 0.634733
13 11.586 0.320362
14 16.185 0.416955
15 17.289 0.438021
16 37.122 0.709861
17 23.769 0.547204
18 80.679 0.932071
19 8.508 0.246928
20 4.461 0.138178
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.228669
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-09_08:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -0.3 -1.3 0.5 -1.4 -0.4
-1.2 1.7 1.1 0.8 0.2 -1.0
1.3 -0.9 -1.4 -1.8 -1.2 -0.9
-0.5 0.3 0.4 2.6 1.2 -0.2
0.1 1.9 0.9 1.3 0.2 0.2
-0.4 0.4 -0.2 -1.7 -1.6 -0.7
0.7 0.2 1.3 0.4 0.9 1.0
-1.1
Chi-square with 42 degrees of freedom:48.358944
z-score=0.693818, p-value=0.768389
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-09_08:31
Test no p-value
1 0.658919
2 0.011397
3 0.013589
4 0.047696
5 0.033391
6 0.547471
7 0.925196
8 0.343403
9 0.124129
10 0.145337
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.005360
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-09_08:31:
(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 66804 0.28 66522 0.31
3 25000.00 24762 2.27 25131 0.69
4 6666.67 6720 0.43 6754 1.14
5 1388.89 1409 0.29 1328 2.67
6 238.10 255 1.20 214 2.44
7 34.72 43 1.97 48 5.08
8 4.96 6 0.22 2 1.77
p=0.64650 p=0.97144
Number of rngs required: 688922, p-value: 0.725
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-09_08:31
No. of wins: Observed Expected
98392 98585.9
z-score=-0.867, pvalue=0.19296
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66758 66666.7 0.125 0.125
2 37474 37654.3 0.864 0.989
3 26991 26954.7 0.049 1.037
4 19358 19313.5 0.103 1.140
5 13846 13851.4 0.002 1.142
6 10007 9943.5 0.405 1.547
7 7135 7145.0 0.014 1.561
8 5070 5139.1 0.928 2.490
9 3692 3699.9 0.017 2.506
10 2762 2666.3 3.435 5.942
11 1987 1923.3 2.108 8.049
12 1341 1388.7 1.641 9.690
13 986 1003.7 0.313 10.003
14 654 726.1 7.167 17.170
15 547 525.8 0.852 18.022
16 361 381.2 1.065 19.087
17 281 276.5 0.072 19.159
18 221 200.8 2.026 21.185
19 147 146.0 0.007 21.192
20 114 106.2 0.571 21.763
21 268 287.1 1.272 23.035
Chisq= 23.04 for 20 degrees of freedom, p= 0.71293
SUMMARY of craptest
p-value for no. of wins: 0.192958
p-value for throws/game: 0.712926
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-09_08:31
No. of wins: Observed Expected
98406 98585.9
z-score=-0.804, pvalue=0.21057
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66746 66666.7 0.094 0.094
2 37551 37654.3 0.284 0.378
3 26867 26954.7 0.286 0.663
4 19379 19313.5 0.222 0.886
5 13722 13851.4 1.209 2.095
6 10009 9943.5 0.431 2.526
7 7079 7145.0 0.610 3.136
8 5253 5139.1 2.526 5.662
9 3777 3699.9 1.608 7.270
10 2703 2666.3 0.505 7.775
11 1928 1923.3 0.011 7.786
12 1381 1388.7 0.043 7.830
13 1031 1003.7 0.742 8.571
14 750 726.1 0.784 9.355
15 517 525.8 0.148 9.504
16 379 381.2 0.012 9.516
17 245 276.5 3.597 13.113
18 189 200.8 0.697 13.810
19 133 146.0 1.155 14.965
20 103 106.2 0.097 15.062
21 258 287.1 2.952 18.014
Chisq= 18.01 for 20 degrees of freedom, p= 0.41353
SUMMARY of craptest
p-value for no. of wins: 0.210574
p-value for throws/game: 0.413531
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0013,0.0013,0.0017,0.0054,0.0075,0.0114,0.0123,0.0136,0.0177,0.0197,
0.0225,0.0289,0.0291,0.0325,0.0332,0.0334,0.0425,0.0477,0.0486,0.0501,
0.0510,0.0572,0.0578,0.0692,0.0739,0.0763,0.0778,0.0816,0.0832,0.0858,
0.0920,0.0974,0.1037,0.1045,0.1056,0.1116,0.1125,0.1133,0.1176,0.1182,
0.1187,0.1235,0.1236,0.1241,0.1248,0.1250,0.1274,0.1295,0.1310,0.1318,
0.1377,0.1382,0.1403,0.1453,0.1454,0.1468,0.1494,0.1513,0.1523,0.1566,
0.1576,0.1625,0.1693,0.1771,0.1800,0.1804,0.1821,0.1930,0.1989,0.2004,
0.2032,0.2056,0.2066,0.2067,0.2106,0.2178,0.2188,0.2188,0.2213,0.2254,
0.2287,0.2301,0.2385,0.2469,0.2503,0.2540,0.2682,0.2716,0.2729,0.2761,
0.2883,0.2893,0.2902,0.2903,0.2905,0.2913,0.2969,0.2973,0.3160,0.3204,
0.3229,0.3262,0.3277,0.3359,0.3386,0.3434,0.3504,0.3514,0.3525,0.3534,
0.3640,0.3724,0.3769,0.3795,0.3890,0.3907,0.3979,0.3989,0.4006,0.4029,
0.4135,0.4170,0.4283,0.4311,0.4362,0.4380,0.4538,0.4540,0.4561,0.4627,
0.4655,0.4655,0.4682,0.4791,0.4827,0.4896,0.4982,0.5036,0.5092,0.5104,
0.5173,0.5174,0.5182,0.5195,0.5220,0.5244,0.5287,0.5307,0.5341,0.5349,
0.5374,0.5448,0.5472,0.5475,0.5535,0.5536,0.5562,0.5566,0.5589,0.5618,
0.5654,0.5684,0.5702,0.5707,0.5762,0.5766,0.5775,0.5842,0.5872,0.5909,
0.6012,0.6062,0.6134,0.6259,0.6300,0.6306,0.6347,0.6361,0.6362,0.6465,
0.6465,0.6511,0.6560,0.6589,0.6689,0.6763,0.6784,0.6837,0.6862,0.6886,
0.6906,0.6923,0.6923,0.6935,0.7030,0.7069,0.7081,0.7094,0.7099,0.7129,
0.7203,0.7207,0.7253,0.7388,0.7434,0.7528,0.7574,0.7591,0.7619,0.7648,
0.7684,0.7735,0.7941,0.8061,0.8101,0.8156,0.8211,0.8247,0.8273,0.8287,
0.8291,0.8306,0.8316,0.8442,0.8486,0.8551,0.8583,0.8600,0.8630,0.8637,
0.8712,0.8715,0.8716,0.8724,0.8775,0.8822,0.8832,0.8847,0.8884,0.8898,
0.8970,0.8981,0.9019,0.9027,0.9061,0.9137,0.9173,0.9188,0.9252,0.9280,
0.9321,0.9326,0.9429,0.9443,0.9472,0.9543,0.9550,0.9582,0.9607,0.9625,
0.9642,0.9650,0.9676,0.9694,0.9714,0.9814,0.9897,0.9922,0.9971,
Overall p-value after applying KStest on 269 p-values = 0.096492
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.