RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-25_21:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 16.02 9.9299 0.093477
2 to 25 15.83 17.8898 0.604176
3 to 26 15.94 17.8121 0.599213
4 to 27 15.68 28.8756 0.964310
5 to 28 15.76 23.4643 0.865263
6 to 29 15.86 18.2320 0.625652
7 to 30 16.21 23.4656 0.865303
8 to 31 15.69 24.0596 0.882175
9 to 32 15.70 33.3816 0.989920
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.019693
Tough bday spacings test for dh-ranFile-2018-06-25_21:31: 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 43 70 111 83 88 51 30 15 2 2
(O-E)^2/E 1.9 1.1 0.1 1.8 2.2 1.2 0.0 0.0 0.0 3.2 1.0
Birthday Spacings: Sum(O-E)^2/E= 12.701, p= 0.759
RESULTS OF GCD FOR dh-ranFile-2018-06-25_21:31
Euclid's algorithm:
p-value, steps to gcd: 0.976256
p-value, dist. of gcd's: 0.322527
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-25_21:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.398 0.107 0.760 0.529 0.800 0.473 0.046 0.673
Bits 8 to 15---> 0.088 0.404 0.746 0.769 0.483 0.044 0.890 0.691
Bits 16 to 23---> 0.585 0.905 0.288 0.274 0.633 0.471 0.754 0.334
Bits 24 to 31---> 0.361 0.748 0.399 0.412 0.933 0.015 0.585 0.825
KS test for the above 32 p values: 0.310
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-25_21:31,
p-values for 5 runs: 0.6940, 0.5137, 0.3653, 0.2305, 0.7345
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-25_21:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 200 211.4 0.617 0.617
r= 29 5198 5134.0 0.798 1.414
r= 30 22986 23103.0 0.593 2.007
r= 31 11616 11551.5 0.360 2.367
chi-square = 2.367 with df = 3; p-value = 0.500
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-25_21:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 211 211.4 0.001 0.001
r= 30 5184 5134.0 0.487 0.488
r= 31 22994 23103.0 0.515 1.002
r= 32 11611 11551.5 0.306 1.309
chi-square = 1.309 with df = 3; p-value = 0.273
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-25_21:31
b-rank test for bits 1 to 8, p=0.02878
b-rank test for bits 2 to 9, p=0.22461
b-rank test for bits 3 to 10, p=0.84415
b-rank test for bits 4 to 11, p=0.13363
b-rank test for bits 5 to 12, p=0.30987
b-rank test for bits 6 to 13, p=0.00079
b-rank test for bits 7 to 14, p=0.14110
b-rank test for bits 8 to 15, p=0.10789
b-rank test for bits 9 to 16, p=0.06960
b-rank test for bits 10 to 17, p=0.60180
b-rank test for bits 11 to 18, p=0.82112
b-rank test for bits 12 to 19, p=0.81624
b-rank test for bits 13 to 20, p=0.99839
b-rank test for bits 14 to 21, p=0.68364
b-rank test for bits 15 to 22, p=0.25398
b-rank test for bits 16 to 23, p=0.80848
b-rank test for bits 17 to 24, p=0.42757
b-rank test for bits 18 to 25, p=0.61109
b-rank test for bits 19 to 26, p=0.76255
b-rank test for bits 20 to 27, p=0.83968
b-rank test for bits 21 to 28, p=0.46359
b-rank test for bits 22 to 29, p=0.30987
b-rank test for bits 23 to 30, p=0.35719
b-rank test for bits 24 to 31, p=0.32476
b-rank test for bits 25 to 32, p=0.63288
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 = 0.629150
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-25_21:31
(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 142413 1.18 0.880362
2 142115 0.48 0.684577
3 142628 1.68 0.953437
4 141544 -0.85 0.196670
5 142013 0.24 0.595695
6 142160 0.59 0.720954
7 140816 -2.55 0.005317
8 141358 -1.29 0.098846
9 142403 1.15 0.875634
10 141382 -1.23 0.108960
11 142105 0.46 0.676227
12 141886 -0.05 0.478265
13 142368 1.07 0.858063
14 141642 -0.62 0.266116
15 142397 1.14 0.872735
16 142258 0.81 0.792364
17 141598 -0.73 0.233489
18 140954 -2.23 0.012805
19 141509 -0.94 0.174804
20 141850 -0.14 0.444875
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-25_21:31
Bits used No. missing words z-score p-value
23 to 32 141723 -0.6425 0.260269
22 to 31 141633 -0.9529 0.170330
21 to 30 141864 -0.1563 0.437894
20 to 29 142113 0.7023 0.758757
19 to 28 141754 -0.5356 0.296110
18 to 27 141768 -0.4873 0.313007
17 to 26 142058 0.5127 0.695904
16 to 25 142029 0.4127 0.660070
15 to 24 142210 1.0368 0.850084
14 to 23 141813 -0.3322 0.369880
13 to 22 142280 1.2782 0.899406
12 to 21 141837 -0.2494 0.401520
11 to 20 141746 -0.5632 0.286647
10 to 19 141675 -0.8080 0.209535
9 to 18 141648 -0.9011 0.183758
8 to 17 142156 0.8506 0.802500
7 to 16 141254 -2.2598 0.011918
6 to 15 142422 1.7678 0.961455
5 to 14 141718 -0.6598 0.254704
4 to 13 142213 1.0471 0.852482
3 to 12 141928 0.0644 0.525666
2 to 11 141894 -0.0529 0.478921
1 to 10 141722 -0.6460 0.259151
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-25_21:31
Bits used No. missing words z-score p-value
28 to 32 141790 -0.4045 0.342919
27 to 31 141531 -1.2825 0.099838
26 to 30 141930 0.0701 0.527930
25 to 29 141896 -0.0452 0.481979
24 to 28 141753 -0.5299 0.298080
23 to 27 141583 -1.1062 0.134319
22 to 26 142023 0.3853 0.650001
21 to 25 142143 0.7921 0.785849
20 to 24 142267 1.2124 0.887328
19 to 23 141814 -0.3232 0.373290
18 to 22 141791 -0.4011 0.344166
17 to 21 142211 1.0226 0.846754
16 to 20 141468 -1.4960 0.067322
15 to 19 142399 1.6599 0.951533
14 to 18 142017 0.3650 0.642438
13 to 17 142201 0.9887 0.838598
12 to 16 141808 -0.3435 0.365614
11 to 15 142190 0.9514 0.829305
10 to 14 141308 -2.0384 0.020755
9 to 13 141824 -0.2893 0.386193
8 to 12 141526 -1.2994 0.096899
7 to 11 141904 -0.0181 0.492792
6 to 10 141377 -1.8045 0.035576
5 to 9 141990 0.2735 0.607749
4 to 8 141185 -2.4554 0.007037
3 to 7 141567 -1.1604 0.122935
2 to 6 141985 0.2565 0.601221
1 to 5 141791 -0.4011 0.344166
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-25_21:31
Bits used No. missing words z-score p-value
31 to 32 142079 0.5005 0.691639
30 to 31 142011 0.2999 0.617878
29 to 30 141567 -1.0098 0.156290
28 to 29 142066 0.4622 0.678014
27 to 28 141511 -1.1750 0.119994
26 to 27 141759 -0.4435 0.328720
25 to 26 141910 0.0020 0.500789
24 to 25 141998 0.2616 0.603171
23 to 24 142180 0.7984 0.787691
22 to 23 142484 1.6952 0.954980
21 to 22 141586 -0.9538 0.170099
20 to 21 142056 0.4327 0.667367
19 to 20 141777 -0.3904 0.348137
18 to 19 141832 -0.2281 0.409780
17 to 18 141827 -0.2429 0.404056
16 to 17 141471 -1.2930 0.098004
15 to 16 141504 -1.1957 0.115914
14 to 15 142619 2.0934 0.981844
13 to 14 143236 3.9135 0.999955
12 to 13 141684 -0.6647 0.253124
11 to 12 141409 -1.4759 0.069985
10 to 11 140979 -2.7443 0.003032
9 to 10 141627 -0.8328 0.202470
8 to 9 141666 -0.7178 0.236444
7 to 8 141608 -0.8889 0.187034
6 to 7 142194 0.8397 0.799471
5 to 6 142156 0.7276 0.766583
4 to 5 142362 1.3353 0.909113
3 to 4 141855 -0.1603 0.436336
2 to 3 142310 1.1819 0.881381
1 to 2 141727 -0.5378 0.295342
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-25_21:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2334.24 -2.344 0.009533
Test results for specific bytes for dh-ranFile-2018-06-25_21:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2521.56 0.305 0.619795
2 to 9 2427.37 -1.027 0.152177
3 to 10 2558.84 0.832 0.797330
4 to 11 2476.41 -0.334 0.369310
5 to 12 2431.26 -0.972 0.165503
6 to 13 2468.70 -0.443 0.329020
7 to 14 2526.50 0.375 0.646082
8 to 15 2474.49 -0.361 0.359118
9 to 16 2532.58 0.461 0.677534
10 to 17 2509.55 0.135 0.553735
11 to 18 2464.36 -0.504 0.307114
12 to 19 2470.76 -0.414 0.339612
13 to 20 2477.79 -0.314 0.376743
14 to 21 2514.61 0.207 0.581843
15 to 22 2467.07 -0.466 0.320708
16 to 23 2553.57 0.758 0.775663
17 to 24 2487.84 -0.172 0.431744
18 to 25 2570.31 0.994 0.839964
19 to 26 2560.32 0.853 0.803203
20 to 27 2629.87 1.837 0.966864
21 to 28 2524.01 0.340 0.632899
22 to 29 2577.26 1.093 0.862727
23 to 30 2542.64 0.603 0.726775
24 to 31 2575.06 1.061 0.855762
25 to 32 2479.47 -0.290 0.385763
CDPARK for dh-ranFile-2018-06-25_21:31: 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
3521 -0.0913 0.463617
3544 0.9589 0.831196
3556 1.5068 0.934075
3484 -1.7808 0.037471
3474 -2.2374 0.012629
3502 -0.9589 0.168804
3548 1.1416 0.873180
3532 0.4110 0.659449
3502 -0.9589 0.168804
3522 -0.0457 0.481790
Square side=100, avg. no. parked=3518.50 sample std.=26.16
p-value of the KSTEST for those 10 p-values: 0.602292
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-25_21:31
0.4454,0.4379,0.2133,0.7609,0.4418,0.2561,0.2460,0.3143,0.5455,0.8306,
The KS test for those 10 p-values: 0.397208
The 3DSPHERES test for dh-ranFile-2018-06-25_21:31
sample no r^3 equiv. uni.
1 58.662 0.858494
2 26.426 0.585576
3 8.167 0.238325
4 9.307 0.266732
5 14.863 0.390691
6 10.875 0.304067
7 4.389 0.136090
8 80.383 0.931398
9 13.743 0.367510
10 126.366 0.985186
11 25.534 0.573064
12 20.736 0.499028
13 29.674 0.628099
14 5.474 0.166779
15 34.913 0.687692
16 97.650 0.961419
17 67.065 0.893062
18 29.142 0.621450
19 6.276 0.188768
20 11.209 0.311782
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.710415
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-25_21:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -0.7 0.6 -0.3 0.1 0.3
-1.3 0.2 -0.1 -0.6 0.0 -0.9
-0.1 -0.0 -1.5 1.3 0.7 0.8
0.6 0.3 -0.6 -0.5 -2.0 1.0
0.3 -0.4 1.5 1.2 -0.6 -0.8
0.3 0.5 0.1 -1.4 0.2 1.0
0.5 -0.4 1.3 -0.1 -1.3 0.0
-1.1
Chi-square with 42 degrees of freedom:28.391067
z-score=-1.484856, p-value=0.053737
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-25_21:31
Test no p-value
1 0.583549
2 0.031714
3 0.884592
4 0.017063
5 0.790420
6 0.035672
7 0.353346
8 0.122908
9 0.658536
10 0.444018
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.171423
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-25_21:31:
(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 66624 0.03 66706 0.02
3 25000.00 24969 0.04 24948 0.11
4 6666.67 6631 0.19 6733 0.66
5 1388.89 1509 10.39 1341 1.65
6 238.10 225 0.72 227 0.52
7 34.72 36 0.05 40 0.80
8 4.96 5 0.00 4 0.19
p=0.92353 p=0.31634
Number of rngs required: 687960, p-value: 0.305
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-25_21:31
No. of wins: Observed Expected
98499 98585.9
z-score=-0.388, pvalue=0.34883
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66101 66666.7 4.800 4.800
2 37372 37654.3 2.117 6.916
3 27228 26954.7 2.770 9.687
4 19352 19313.5 0.077 9.764
5 13899 13851.4 0.163 9.927
6 10188 9943.5 6.010 15.937
7 7200 7145.0 0.423 16.360
8 5185 5139.1 0.410 16.770
9 3766 3699.9 1.182 17.953
10 2711 2666.3 0.749 18.702
11 1954 1923.3 0.489 19.191
12 1402 1388.7 0.127 19.318
13 974 1003.7 0.880 20.198
14 728 726.1 0.005 20.202
15 541 525.8 0.437 20.640
16 359 381.2 1.287 21.927
17 287 276.5 0.396 22.323
18 205 200.8 0.087 22.409
19 144 146.0 0.027 22.436
20 106 106.2 0.000 22.437
21 298 287.1 0.413 22.849
Chisq= 22.85 for 20 degrees of freedom, p= 0.70375
SUMMARY of craptest
p-value for no. of wins: 0.348830
p-value for throws/game: 0.703745
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-25_21:31
No. of wins: Observed Expected
98988 98585.9
z-score= 1.799, pvalue=0.96396
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66674 66666.7 0.001 0.001
2 37692 37654.3 0.038 0.039
3 26723 26954.7 1.992 2.031
4 19314 19313.5 0.000 2.031
5 13871 13851.4 0.028 2.058
6 9872 9943.5 0.515 2.573
7 7242 7145.0 1.316 3.889
8 5218 5139.1 1.212 5.102
9 3721 3699.9 0.121 5.222
10 2682 2666.3 0.092 5.315
11 1944 1923.3 0.222 5.537
12 1425 1388.7 0.947 6.484
13 978 1003.7 0.659 7.142
14 735 726.1 0.108 7.251
15 493 525.8 2.050 9.301
16 381 381.2 0.000 9.301
17 278 276.5 0.008 9.309
18 210 200.8 0.419 9.727
19 136 146.0 0.683 10.410
20 101 106.2 0.256 10.666
21 310 287.1 1.824 12.491
Chisq= 12.49 for 20 degrees of freedom, p= 0.10185
SUMMARY of craptest
p-value for no. of wins: 0.963960
p-value for throws/game: 0.101847
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0008,0.0030,0.0053,0.0070,0.0095,0.0119,0.0126,0.0128,0.0150,0.0171,
0.0197,0.0208,0.0288,0.0317,0.0356,0.0357,0.0375,0.0441,0.0460,0.0537,
0.0673,0.0696,0.0700,0.0876,0.0935,0.0969,0.0980,0.0988,0.0998,0.1018,
0.1066,0.1079,0.1090,0.1159,0.1200,0.1229,0.1229,0.1336,0.1343,0.1361,
0.1411,0.1522,0.1563,0.1655,0.1668,0.1688,0.1688,0.1701,0.1703,0.1714,
0.1748,0.1838,0.1870,0.1888,0.1967,0.2025,0.2095,0.2133,0.2246,0.2305,
0.2335,0.2364,0.2383,0.2460,0.2531,0.2540,0.2547,0.2561,0.2592,0.2603,
0.2661,0.2667,0.2729,0.2739,0.2866,0.2875,0.2953,0.2961,0.2981,0.3041,
0.3048,0.3071,0.3099,0.3099,0.3102,0.3118,0.3130,0.3143,0.3163,0.3207,
0.3225,0.3248,0.3287,0.3290,0.3336,0.3396,0.3429,0.3442,0.3442,0.3481,
0.3488,0.3533,0.3572,0.3591,0.3611,0.3653,0.3656,0.3675,0.3693,0.3699,
0.3733,0.3767,0.3858,0.3862,0.3907,0.3972,0.3981,0.3990,0.4015,0.4038,
0.4041,0.4098,0.4121,0.4276,0.4317,0.4363,0.4379,0.4379,0.4418,0.4440,
0.4449,0.4454,0.4636,0.4636,0.4712,0.4734,0.4783,0.4789,0.4818,0.4820,
0.4827,0.4928,0.4990,0.5002,0.5008,0.5137,0.5257,0.5279,0.5288,0.5455,
0.5537,0.5731,0.5818,0.5835,0.5853,0.5853,0.5856,0.5957,0.5992,0.6012,
0.6018,0.6023,0.6032,0.6042,0.6077,0.6111,0.6179,0.6198,0.6215,0.6257,
0.6281,0.6291,0.6329,0.6329,0.6333,0.6424,0.6461,0.6500,0.6585,0.6594,
0.6601,0.6674,0.6734,0.6762,0.6775,0.6780,0.6836,0.6846,0.6877,0.6915,
0.6916,0.6940,0.6959,0.7037,0.7104,0.7210,0.7268,0.7345,0.7460,0.7484,
0.7540,0.7588,0.7591,0.7605,0.7609,0.7626,0.7666,0.7693,0.7757,0.7858,
0.7877,0.7904,0.7924,0.7973,0.7995,0.8002,0.8025,0.8032,0.8085,0.8162,
0.8211,0.8247,0.8293,0.8306,0.8312,0.8386,0.8397,0.8400,0.8441,0.8468,
0.8501,0.8525,0.8558,0.8581,0.8585,0.8627,0.8653,0.8653,0.8727,0.8732,
0.8756,0.8804,0.8814,0.8822,0.8846,0.8873,0.8896,0.8931,0.8994,0.9047,
0.9091,0.9235,0.9314,0.9328,0.9341,0.9515,0.9534,0.9550,0.9614,0.9615,
0.9640,0.9643,0.9669,0.9763,0.9818,0.9852,0.9899,0.9984,1.0000,
Overall p-value after applying KStest on 269 p-values = 0.658689
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.