RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-29_09:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.73 15.0707 0.409609
2 to 25 15.75 21.7188 0.804222
3 to 26 15.41 30.2099 0.975129
4 to 27 15.68 17.8427 0.601169
5 to 28 15.86 16.3883 0.503509
6 to 29 15.74 16.0222 0.477735
7 to 30 16.01 13.3794 0.289557
8 to 31 16.03 25.1067 0.907654
9 to 32 15.92 9.4615 0.075337
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.847494
Tough bday spacings test for dh-ranFile-2018-06-29_09:31: 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 13 38 83 96 79 67 54 39 21 9 1
(O-E)^2/E 1.6 0.1 1.3 0.0 3.6 1.6 0.1 2.9 2.5 0.9 2.3
Birthday Spacings: Sum(O-E)^2/E= 16.764, p= 0.920
RESULTS OF GCD FOR dh-ranFile-2018-06-29_09:31
Euclid's algorithm:
p-value, steps to gcd: 0.167150
p-value, dist. of gcd's: 0.610578
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-29_09:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.702 0.466 0.934 0.678 0.582 0.056 0.758 0.423
Bits 8 to 15---> 0.738 0.694 0.052 0.932 0.879 0.833 0.502 0.873
Bits 16 to 23---> 0.539 0.540 0.964 0.973 0.140 0.406 0.765 0.504
Bits 24 to 31---> 0.423 0.349 0.788 0.632 0.995 0.951 0.438 0.721
KS test for the above 32 p values: 0.986
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-29_09:31,
p-values for 5 runs: 0.3094, 0.6097, 0.2945, 0.5281, 0.7397
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-29_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 199 211.4 0.729 0.729
r= 29 5213 5134.0 1.215 1.945
r= 30 23110 23103.0 0.002 1.947
r= 31 11478 11551.5 0.468 2.415
chi-square = 2.415 with df = 3; p-value = 0.509
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-29_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 234 211.4 2.412 2.412
r= 30 5123 5134.0 0.024 2.436
r= 31 22992 23103.0 0.534 2.969
r= 32 11651 11551.5 0.857 3.826
chi-square = 3.826 with df = 3; p-value = 0.719
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-29_09:31
b-rank test for bits 1 to 8, p=0.70469
b-rank test for bits 2 to 9, p=0.45722
b-rank test for bits 3 to 10, p=0.56832
b-rank test for bits 4 to 11, p=0.50516
b-rank test for bits 5 to 12, p=0.20538
b-rank test for bits 6 to 13, p=0.73740
b-rank test for bits 7 to 14, p=0.85775
b-rank test for bits 8 to 15, p=0.91176
b-rank test for bits 9 to 16, p=0.82244
b-rank test for bits 10 to 17, p=0.73721
b-rank test for bits 11 to 18, p=0.95359
b-rank test for bits 12 to 19, p=0.94157
b-rank test for bits 13 to 20, p=0.38429
b-rank test for bits 14 to 21, p=0.34324
b-rank test for bits 15 to 22, p=0.62463
b-rank test for bits 16 to 23, p=0.45647
b-rank test for bits 17 to 24, p=0.68486
b-rank test for bits 18 to 25, p=0.34035
b-rank test for bits 19 to 26, p=0.07811
b-rank test for bits 20 to 27, p=0.81234
b-rank test for bits 21 to 28, p=0.18416
b-rank test for bits 22 to 29, p=0.16532
b-rank test for bits 23 to 30, p=0.28913
b-rank test for bits 24 to 31, p=0.74949
b-rank test for bits 25 to 32, p=0.00077
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 = 0.756212
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-29_09:31
(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 141948 0.09 0.535996
2 141370 -1.26 0.103814
3 141874 -0.08 0.467106
4 142263 0.83 0.795692
5 141647 -0.61 0.269964
6 140570 -3.13 0.000876
7 142834 2.16 0.984631
8 141825 -0.20 0.421901
9 142097 0.44 0.669481
10 141804 -0.25 0.402803
11 141860 -0.12 0.454121
12 141459 -1.05 0.146360
13 141639 -0.63 0.263820
14 141702 -0.48 0.314045
15 142921 2.36 0.990954
16 141714 -0.46 0.324059
17 141931 0.05 0.520190
18 142199 0.68 0.750733
19 141300 -1.42 0.077271
20 141761 -0.35 0.364459
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-29_09:31
Bits used No. missing words z-score p-value
23 to 32 141482 -1.4736 0.070301
22 to 31 142127 0.7506 0.773549
21 to 30 142049 0.4816 0.684962
20 to 29 141414 -1.7080 0.043815
19 to 28 141415 -1.7046 0.044136
18 to 27 140923 -3.4011 0.000336
17 to 26 142107 0.6816 0.752261
16 to 25 141804 -0.3632 0.358225
15 to 24 141498 -1.4184 0.078040
14 to 23 141756 -0.5287 0.298498
13 to 22 141956 0.1609 0.563926
12 to 21 141677 -0.8011 0.211526
11 to 20 141620 -0.9977 0.159215
10 to 19 141783 -0.4356 0.331556
9 to 18 141579 -1.1391 0.127337
8 to 17 142115 0.7092 0.760902
7 to 16 141876 -0.1149 0.454250
6 to 15 142561 2.2471 0.987684
5 to 14 141762 -0.5080 0.305715
4 to 13 141948 0.1333 0.553040
3 to 12 142218 1.0644 0.856422
2 to 11 141808 -0.3494 0.363389
1 to 10 141756 -0.5287 0.298498
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-29_09:31
Bits used No. missing words z-score p-value
28 to 32 142152 0.8226 0.794635
27 to 31 141612 -1.0079 0.156752
26 to 30 141794 -0.3909 0.347917
25 to 29 141152 -2.5672 0.005126
24 to 28 142298 1.3175 0.906169
23 to 27 141607 -1.0248 0.152718
22 to 26 142007 0.3311 0.629710
21 to 25 141397 -1.7367 0.041219
20 to 24 141716 -0.6554 0.256119
19 to 23 141928 0.0633 0.525232
18 to 22 141562 -1.1774 0.119520
17 to 21 142195 0.9684 0.833571
16 to 20 142285 1.2735 0.898572
15 to 19 141954 0.1514 0.560179
14 to 18 141682 -0.7706 0.220469
13 to 17 141914 0.0158 0.506315
12 to 16 141851 -0.1977 0.421629
11 to 15 141795 -0.3876 0.349171
10 to 14 141791 -0.4011 0.344166
9 to 13 142454 1.8463 0.967579
8 to 12 142001 0.3107 0.622003
7 to 11 142597 2.3311 0.990126
6 to 10 141767 -0.4825 0.314734
5 to 9 141780 -0.4384 0.330546
4 to 8 141717 -0.6520 0.257212
3 to 7 141874 -0.1198 0.452336
2 to 6 141666 -0.8248 0.204729
1 to 5 141762 -0.4994 0.308741
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-29_09:31
Bits used No. missing words z-score p-value
31 to 32 141914 0.0138 0.505496
30 to 31 141995 0.2527 0.599755
29 to 30 142596 2.0256 0.978596
28 to 29 141131 -2.2960 0.010839
27 to 28 142012 0.3029 0.619002
26 to 27 142802 2.6332 0.995771
25 to 26 142464 1.6362 0.949101
24 to 25 141788 -0.3579 0.360207
23 to 24 141889 -0.0600 0.476090
22 to 23 141697 -0.6263 0.265545
21 to 22 141689 -0.6499 0.257865
20 to 21 141503 -1.1986 0.115339
19 to 20 141626 -0.8358 0.201639
18 to 19 142320 1.2114 0.887132
17 to 18 142127 0.6421 0.739594
16 to 17 141584 -0.9597 0.168609
15 to 16 141487 -1.2458 0.106417
14 to 15 141873 -0.1072 0.457328
13 to 14 141762 -0.4346 0.331926
12 to 13 141890 -0.0570 0.477264
11 to 12 141723 -0.5496 0.291281
10 to 11 141672 -0.7001 0.241936
9 to 10 141255 -1.9302 0.026792
8 to 9 141517 -1.1573 0.123572
7 to 8 142302 1.1583 0.876633
6 to 7 142057 0.4356 0.668438
5 to 6 141650 -0.7650 0.222140
4 to 5 141652 -0.7591 0.223901
3 to 4 141813 -0.2842 0.388144
2 to 3 141753 -0.4612 0.322345
1 to 2 142181 0.8014 0.788546
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-29_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2518.97 0.268 0.605756
Test results for specific bytes for dh-ranFile-2018-06-29_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2561.59 0.871 0.808139
2 to 9 2542.31 0.598 0.725197
3 to 10 2502.29 0.032 0.512935
4 to 11 2522.09 0.312 0.622630
5 to 12 2632.07 1.868 0.969098
6 to 13 2381.97 -1.669 0.047537
7 to 14 2447.30 -0.745 0.228039
8 to 15 2492.50 -0.106 0.457768
9 to 16 2422.93 -1.090 0.137868
10 to 17 2580.97 1.145 0.873904
11 to 18 2648.16 2.095 0.981928
12 to 19 2392.61 -1.519 0.064417
13 to 20 2483.95 -0.227 0.410227
14 to 21 2555.46 0.784 0.783591
15 to 22 2469.81 -0.427 0.334710
16 to 23 2449.30 -0.717 0.236696
17 to 24 2533.60 0.475 0.682676
18 to 25 2474.37 -0.362 0.358520
19 to 26 2548.09 0.680 0.751767
20 to 27 2479.45 -0.291 0.385657
21 to 28 2660.32 2.267 0.988313
22 to 29 2468.39 -0.447 0.327447
23 to 30 2386.21 -1.609 0.053780
24 to 31 2435.90 -0.906 0.182345
25 to 32 2470.51 -0.417 0.338344
CDPARK for dh-ranFile-2018-06-29_09:31: 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
3502 -0.9589 0.168804
3529 0.2740 0.607947
3563 1.8265 0.966111
3501 -1.0046 0.157553
3529 0.2740 0.607947
3523 0.0000 0.500000
3544 0.9589 0.831196
3502 -0.9589 0.168804
3563 1.8265 0.966111
3518 -0.2283 0.409702
Square side=100, avg. no. parked=3527.40 sample std.=22.16
p-value of the KSTEST for those 10 p-values: 0.687520
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-29_09:31
0.1747,0.7066,0.9040,0.8003,0.5855,0.7004,0.1777,0.8778,0.8712,0.3307,
The KS test for those 10 p-values: 0.297992
The 3DSPHERES test for dh-ranFile-2018-06-29_09:31
sample no r^3 equiv. uni.
1 83.806 0.938796
2 106.023 0.970815
3 33.041 0.667579
4 39.000 0.727465
5 2.472 0.079089
6 12.291 0.336157
7 2.845 0.090482
8 33.413 0.671675
9 53.463 0.831713
10 22.467 0.527111
11 124.752 0.984367
12 9.407 0.269171
13 27.524 0.600464
14 56.805 0.849457
15 13.010 0.351869
16 25.817 0.577074
17 28.576 0.614231
18 13.445 0.361201
19 101.725 0.966320
20 14.942 0.392295
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.231585
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-29_09:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 -1.2 -0.8 -0.3 1.3 -1.1
-0.4 -1.6 -0.8 1.6 -0.0 -0.2
1.3 -1.4 1.1 -2.2 1.1 -0.8
-0.9 -0.5 0.4 0.9 0.5 0.1
1.8 0.4 0.0 1.0 1.5 -1.9
-0.3 -1.6 -0.5 0.3 0.1 -1.2
0.3 0.8 -0.8 0.4 -0.6 -1.0
-0.1
Chi-square with 42 degrees of freedom:42.534275
z-score=0.058294, p-value=0.552031
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-29_09:31
Test no p-value
1 0.720890
2 0.018485
3 0.914539
4 0.023538
5 0.941674
6 0.033072
7 0.001059
8 0.399286
9 0.249564
10 0.615739
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.027140
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-29_09:31:
(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 66531 0.28 66674 0.00
3 25000.00 25113 0.51 24932 0.18
4 6666.67 6689 0.07 6670 0.00
5 1388.89 1397 0.05 1428 1.10
6 238.10 227 0.52 261 2.20
7 34.72 36 0.05 27 1.72
8 4.96 6 0.22 7 0.84
p=0.05421 p=0.58214
Number of rngs required: 688924, p-value: 0.726
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-29_09:31
No. of wins: Observed Expected
98667 98585.9
z-score= 0.363, pvalue=0.64166
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66939 66666.7 1.112 1.112
2 37253 37654.3 4.277 5.390
3 27031 26954.7 0.216 5.606
4 19201 19313.5 0.655 6.260
5 13941 13851.4 0.579 6.840
6 9923 9943.5 0.042 6.882
7 7160 7145.0 0.031 6.914
8 5045 5139.1 1.722 8.636
9 3680 3699.9 0.107 8.742
10 2696 2666.3 0.331 9.073
11 1960 1923.3 0.699 9.772
12 1377 1388.7 0.099 9.872
13 1017 1003.7 0.176 10.047
14 767 726.1 2.299 12.347
15 569 525.8 3.543 15.890
16 406 381.2 1.620 17.510
17 269 276.5 0.206 17.715
18 222 200.8 2.232 19.947
19 156 146.0 0.687 20.634
20 109 106.2 0.073 20.707
21 279 287.1 0.229 20.936
Chisq= 20.94 for 20 degrees of freedom, p= 0.59912
SUMMARY of craptest
p-value for no. of wins: 0.641665
p-value for throws/game: 0.599118
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-29_09:31
No. of wins: Observed Expected
98444 98585.9
z-score=-0.634, pvalue=0.26289
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66699 66666.7 0.016 0.016
2 37669 37654.3 0.006 0.021
3 26982 26954.7 0.028 0.049
4 19488 19313.5 1.577 1.626
5 13815 13851.4 0.096 1.722
6 9913 9943.5 0.094 1.816
7 7073 7145.0 0.726 2.542
8 5197 5139.1 0.653 3.195
9 3615 3699.9 1.947 5.141
10 2636 2666.3 0.344 5.486
11 1899 1923.3 0.308 5.793
12 1351 1388.7 1.026 6.819
13 978 1003.7 0.659 7.478
14 751 726.1 0.851 8.329
15 560 525.8 2.220 10.549
16 385 381.2 0.039 10.588
17 265 276.5 0.482 11.069
18 175 200.8 3.322 14.391
19 155 146.0 0.557 14.948
20 105 106.2 0.014 14.962
21 289 287.1 0.012 14.974
Chisq= 14.97 for 20 degrees of freedom, p= 0.22212
SUMMARY of craptest
p-value for no. of wins: 0.262886
p-value for throws/game: 0.222123
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0003,0.0008,0.0009,0.0011,0.0051,0.0108,0.0185,0.0235,0.0268,0.0271,
0.0331,0.0412,0.0438,0.0441,0.0475,0.0518,0.0538,0.0542,0.0559,0.0644,
0.0703,0.0753,0.0773,0.0780,0.0781,0.0791,0.0905,0.1038,0.1064,0.1153,
0.1195,0.1236,0.1273,0.1379,0.1403,0.1464,0.1527,0.1568,0.1576,0.1592,
0.1653,0.1671,0.1686,0.1688,0.1688,0.1747,0.1777,0.1823,0.1842,0.2016,
0.2047,0.2054,0.2115,0.2205,0.2221,0.2221,0.2239,0.2280,0.2316,0.2367,
0.2419,0.2496,0.2561,0.2572,0.2579,0.2629,0.2638,0.2655,0.2692,0.2700,
0.2891,0.2896,0.2913,0.2945,0.2980,0.2985,0.2985,0.3057,0.3087,0.3094,
0.3140,0.3147,0.3223,0.3241,0.3274,0.3305,0.3307,0.3316,0.3319,0.3347,
0.3362,0.3383,0.3404,0.3432,0.3442,0.3479,0.3490,0.3492,0.3519,0.3582,
0.3585,0.3602,0.3612,0.3634,0.3645,0.3843,0.3857,0.3881,0.3923,0.3993,
0.4028,0.4056,0.4096,0.4097,0.4102,0.4216,0.4219,0.4232,0.4232,0.4379,
0.4523,0.4541,0.4542,0.4565,0.4572,0.4573,0.4578,0.4663,0.4671,0.4761,
0.4773,0.4777,0.5000,0.5019,0.5035,0.5039,0.5052,0.5055,0.5063,0.5091,
0.5129,0.5202,0.5252,0.5271,0.5281,0.5360,0.5395,0.5401,0.5520,0.5530,
0.5602,0.5639,0.5683,0.5771,0.5821,0.5823,0.5855,0.5991,0.5998,0.6005,
0.6012,0.6058,0.6079,0.6079,0.6097,0.6106,0.6142,0.6157,0.6190,0.6220,
0.6226,0.6246,0.6297,0.6315,0.6417,0.6676,0.6684,0.6695,0.6717,0.6777,
0.6827,0.6849,0.6850,0.6875,0.6942,0.7004,0.7022,0.7047,0.7066,0.7191,
0.7209,0.7214,0.7252,0.7260,0.7275,0.7372,0.7374,0.7377,0.7396,0.7397,
0.7495,0.7507,0.7518,0.7523,0.7562,0.7575,0.7609,0.7649,0.7735,0.7836,
0.7883,0.7885,0.7946,0.7957,0.8003,0.8042,0.8081,0.8123,0.8224,0.8312,
0.8317,0.8333,0.8336,0.8475,0.8495,0.8564,0.8577,0.8712,0.8726,0.8739,
0.8766,0.8778,0.8794,0.8871,0.8986,0.9040,0.9062,0.9077,0.9118,0.9145,
0.9203,0.9315,0.9345,0.9388,0.9416,0.9417,0.9491,0.9512,0.9536,0.9640,
0.9661,0.9661,0.9663,0.9676,0.9691,0.9708,0.9735,0.9751,0.9786,0.9819,
0.9844,0.9846,0.9862,0.9877,0.9883,0.9901,0.9910,0.9946,0.9958,
Overall p-value after applying KStest on 269 p-values = 0.548306
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.