RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-09_05:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.72 22.8171 0.844701
2 to 25 15.49 20.0751 0.729596
3 to 26 15.64 19.6310 0.706462
4 to 27 15.68 17.5211 0.580365
5 to 28 15.58 16.2781 0.495784
6 to 29 15.81 15.9289 0.471116
7 to 30 15.81 16.2953 0.496992
8 to 31 15.65 13.8611 0.323088
9 to 32 15.71 15.5080 0.441057
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.259015
Tough bday spacings test for dh-ranFile-2018-07-09_05:31: 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 12 39 77 104 92 79 51 27 11 6 2
(O-E)^2/E 0.9 0.2 0.2 0.4 0.3 0.0 0.0 0.3 1.0 0.1 1.0
Birthday Spacings: Sum(O-E)^2/E= 4.376, p= 0.071
RESULTS OF GCD FOR dh-ranFile-2018-07-09_05:31
Euclid's algorithm:
p-value, steps to gcd: 0.828784
p-value, dist. of gcd's: 0.109396
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-09_05:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.499 0.781 0.019 0.597 0.335 0.955 0.646 0.169
Bits 8 to 15---> 0.818 0.192 0.325 0.309 0.259 0.799 0.837 0.518
Bits 16 to 23---> 0.717 0.643 0.057 0.207 0.565 0.150 0.057 0.212
Bits 24 to 31---> 0.590 0.986 0.512 0.395 0.981 0.462 0.582 0.958
KS test for the above 32 p values: 0.030
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-09_05:31,
p-values for 5 runs: 0.2000, 0.0829, 0.1768, 0.9843, 0.5190
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-09_05:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 202 211.4 0.420 0.420
r= 29 5069 5134.0 0.823 1.243
r= 30 23084 23103.0 0.016 1.258
r= 31 11645 11551.5 0.756 2.015
chi-square = 2.015 with df = 3; p-value = 0.431
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-09_05:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 211 211.4 0.001 0.001
r= 30 5056 5134.0 1.185 1.186
r= 31 23193 23103.0 0.350 1.536
r= 32 11540 11551.5 0.011 1.548
chi-square = 1.548 with df = 3; p-value = 0.329
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-09_05:31
b-rank test for bits 1 to 8, p=0.60016
b-rank test for bits 2 to 9, p=0.17292
b-rank test for bits 3 to 10, p=0.44832
b-rank test for bits 4 to 11, p=0.04315
b-rank test for bits 5 to 12, p=0.77838
b-rank test for bits 6 to 13, p=0.80770
b-rank test for bits 7 to 14, p=0.08281
b-rank test for bits 8 to 15, p=0.58946
b-rank test for bits 9 to 16, p=0.29129
b-rank test for bits 10 to 17, p=0.24764
b-rank test for bits 11 to 18, p=0.33505
b-rank test for bits 12 to 19, p=0.04741
b-rank test for bits 13 to 20, p=0.36093
b-rank test for bits 14 to 21, p=0.70925
b-rank test for bits 15 to 22, p=0.84829
b-rank test for bits 16 to 23, p=0.48479
b-rank test for bits 17 to 24, p=0.11754
b-rank test for bits 18 to 25, p=0.01416
b-rank test for bits 19 to 26, p=0.61216
b-rank test for bits 20 to 27, p=0.68370
b-rank test for bits 21 to 28, p=0.90344
b-rank test for bits 22 to 29, p=0.75606
b-rank test for bits 23 to 30, p=0.64958
b-rank test for bits 24 to 31, p=0.24766
b-rank test for bits 25 to 32, p=0.19055
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 = 0.506112
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-09_05:31
(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 142538 1.47 0.929064
2 142117 0.49 0.686236
3 141176 -1.71 0.043321
4 141593 -0.74 0.229927
5 142496 1.37 0.914770
6 142636 1.70 0.955230
7 142166 0.60 0.725646
8 141786 -0.29 0.386614
9 142350 1.03 0.848402
10 142025 0.27 0.606519
11 142569 1.54 0.938376
12 141774 -0.32 0.375929
13 141963 0.13 0.549895
14 141578 -0.77 0.219425
15 141184 -1.69 0.045067
16 142077 0.39 0.652379
17 141618 -0.68 0.248038
18 141811 -0.23 0.409146
19 141520 -0.91 0.181504
20 141894 -0.04 0.485714
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-09_05:31
Bits used No. missing words z-score p-value
23 to 32 142007 0.3368 0.631864
22 to 31 141416 -1.7011 0.044459
21 to 30 141443 -1.6080 0.053914
20 to 29 141930 0.0713 0.528411
19 to 28 142623 2.4609 0.993071
18 to 27 141822 -0.3011 0.381655
17 to 26 141358 -1.9011 0.028642
16 to 25 141344 -1.9494 0.025623
15 to 24 141785 -0.4287 0.334062
14 to 23 142301 1.3506 0.911586
13 to 22 142129 0.7575 0.775620
12 to 21 141948 0.1333 0.553040
11 to 20 142266 1.2299 0.890632
10 to 19 141822 -0.3011 0.381655
9 to 18 141806 -0.3563 0.360804
8 to 17 141675 -0.8080 0.209535
7 to 16 142035 0.4333 0.667618
6 to 15 141971 0.2127 0.584202
5 to 14 141712 -0.6804 0.248110
4 to 13 141442 -1.6115 0.053537
3 to 12 141598 -1.0736 0.141512
2 to 11 141591 -1.0977 0.136170
1 to 10 141938 0.0989 0.539376
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-09_05:31
Bits used No. missing words z-score p-value
28 to 32 141815 -0.3198 0.374574
27 to 31 141902 -0.0248 0.490088
26 to 30 142413 1.7074 0.956122
25 to 29 141476 -1.4689 0.070928
24 to 28 142131 0.7514 0.773801
23 to 27 141993 0.2836 0.611652
22 to 26 141966 0.1921 0.576169
21 to 25 141911 0.0057 0.502258
20 to 24 141394 -1.7469 0.040329
19 to 23 142171 0.8870 0.812465
18 to 22 142045 0.4599 0.677205
17 to 21 141680 -0.7774 0.218464
16 to 20 142196 0.9718 0.834416
15 to 19 142127 0.7379 0.769702
14 to 18 142196 0.9718 0.834416
13 to 17 141364 -1.8486 0.032260
12 to 16 141965 0.1887 0.574841
11 to 15 142010 0.3413 0.633544
10 to 14 142268 1.2158 0.887975
9 to 13 142077 0.5684 0.715109
8 to 12 142334 1.4396 0.925004
7 to 11 142541 2.1413 0.983873
6 to 10 141619 -0.9842 0.162516
5 to 9 141876 -0.1130 0.455022
4 to 8 141393 -1.7503 0.040036
3 to 7 141957 0.1616 0.564187
2 to 6 141812 -0.3299 0.370726
1 to 5 141662 -0.8384 0.200901
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-09_05:31
Bits used No. missing words z-score p-value
31 to 32 142033 0.3648 0.642373
30 to 31 142056 0.4327 0.667367
29 to 30 141533 -1.1101 0.133474
28 to 29 142131 0.6539 0.743410
27 to 28 141811 -0.2901 0.385886
26 to 27 141834 -0.2222 0.412074
25 to 26 141824 -0.2517 0.400632
24 to 25 142289 1.1200 0.868637
23 to 24 141903 -0.0187 0.492551
22 to 23 141645 -0.7797 0.217774
21 to 22 142144 0.6922 0.755607
20 to 21 141888 -0.0629 0.474915
19 to 20 142108 0.5860 0.721078
18 to 19 141529 -1.1219 0.130949
17 to 18 141501 -1.2045 0.114196
16 to 17 141736 -0.5113 0.304571
15 to 16 141397 -1.5113 0.065356
14 to 15 142098 0.5565 0.711082
13 to 14 141907 -0.0069 0.497258
12 to 13 141893 -0.0482 0.480790
11 to 12 141602 -0.9066 0.182315
10 to 11 141856 -0.1573 0.437498
9 to 10 141727 -0.5378 0.295342
8 to 9 141873 -0.1072 0.457328
7 to 8 141998 0.2616 0.603171
6 to 7 141843 -0.1957 0.422437
5 to 6 141841 -0.2016 0.420129
4 to 5 141783 -0.3727 0.354703
3 to 4 141718 -0.5644 0.286243
2 to 3 141276 -1.8682 0.030865
1 to 2 141715 -0.5732 0.283240
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-09_05:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2474.45 -0.361 0.358911
Test results for specific bytes for dh-ranFile-2018-07-09_05:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2385.90 -1.614 0.053303
2 to 9 2428.76 -1.008 0.156838
3 to 10 2546.05 0.651 0.742549
4 to 11 2432.22 -0.959 0.168876
5 to 12 2542.63 0.603 0.726716
6 to 13 2435.33 -0.915 0.180205
7 to 14 2435.68 -0.910 0.181499
8 to 15 2432.65 -0.953 0.170420
9 to 16 2451.22 -0.690 0.245134
10 to 17 2511.14 0.157 0.562572
11 to 18 2520.05 0.284 0.611625
12 to 19 2522.80 0.322 0.626426
13 to 20 2640.65 1.989 0.976656
14 to 21 2453.61 -0.656 0.255874
15 to 22 2489.49 -0.149 0.440936
16 to 23 2592.87 1.313 0.905462
17 to 24 2446.44 -0.757 0.224378
18 to 25 2500.30 0.004 0.501677
19 to 26 2637.79 1.949 0.974329
20 to 27 2398.51 -1.435 0.075599
21 to 28 2608.12 1.529 0.936878
22 to 29 2416.22 -1.185 0.118033
23 to 30 2508.60 0.122 0.548398
24 to 31 2472.76 -0.385 0.350022
25 to 32 2497.58 -0.034 0.486322
CDPARK for dh-ranFile-2018-07-09_05:31: 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
3502 -0.9589 0.168804
3524 0.0457 0.518210
3489 -1.5525 0.060270
3494 -1.3242 0.092718
3505 -0.8219 0.205562
3493 -1.3699 0.085365
3536 0.5936 0.723613
3496 -1.2329 0.108811
3506 -0.7763 0.218799
Square side=100, avg. no. parked=3503.20 sample std.=14.92
p-value of the KSTEST for those 10 p-values: 0.001762
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-09_05:31
0.2096,0.8423,0.0290,0.2384,0.0644,0.1059,0.8633,0.6410,0.0755,0.8538,
The KS test for those 10 p-values: 0.124675
The 3DSPHERES test for dh-ranFile-2018-07-09_05:31
sample no r^3 equiv. uni.
1 2.310 0.074098
2 15.960 0.412575
3 1.119 0.036601
4 16.457 0.422220
5 63.671 0.880251
6 30.019 0.632350
7 56.267 0.846730
8 51.338 0.819365
9 11.917 0.327825
10 8.958 0.258145
11 1.367 0.044560
12 85.052 0.941285
13 45.698 0.782004
14 24.140 0.552758
15 33.776 0.675629
16 2.692 0.085816
17 2.296 0.073667
18 35.715 0.695931
19 3.065 0.097130
20 10.662 0.299115
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.446003
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-09_05:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 1.8 0.3 0.3 -0.1 2.0
-0.4 0.8 -1.2 -2.0 0.3 1.1
-0.7 1.4 0.6 1.3 -1.1 1.9
-1.2 -0.1 1.7 -1.2 -0.9 -1.9
-0.9 0.4 -1.0 -0.3 -1.0 -0.1
0.8 0.6 1.1 1.8 -0.8 -0.1
1.0 -2.0 1.3 0.4 -0.6 -1.0
-0.1
Chi-square with 42 degrees of freedom:52.068241
z-score=1.098535, p-value=0.862752
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-09_05:31
Test no p-value
1 0.330787
2 0.793964
3 0.162210
4 0.755673
5 0.010682
6 0.987570
7 0.964677
8 0.002182
9 0.870008
10 0.041214
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.060696
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-09_05:31:
(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 66762 0.14 66476 0.55
3 25000.00 24974 0.03 25173 1.20
4 6666.67 6608 0.52 6661 0.00
5 1388.89 1386 0.01 1434 1.47
6 238.10 239 0.00 225 0.72
7 34.72 28 1.30 28 1.30
8 4.96 2 1.77 2 1.77
p=0.29038 p=0.67913
Number of rngs required: 688955, p-value: 0.738
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-09_05:31
No. of wins: Observed Expected
98636 98585.9
z-score= 0.224, pvalue=0.58872
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66654 66666.7 0.002 0.002
2 37675 37654.3 0.011 0.014
3 26920 26954.7 0.045 0.059
4 19317 19313.5 0.001 0.059
5 13856 13851.4 0.002 0.061
6 10015 9943.5 0.514 0.574
7 7191 7145.0 0.296 0.870
8 5165 5139.1 0.131 1.001
9 3638 3699.9 1.034 2.035
10 2668 2666.3 0.001 2.036
11 1869 1923.3 1.535 3.571
12 1307 1388.7 4.811 8.382
13 1038 1003.7 1.171 9.553
14 768 726.1 2.413 11.966
15 516 525.8 0.184 12.150
16 400 381.2 0.932 13.082
17 291 276.5 0.756 13.839
18 183 200.8 1.583 15.422
19 147 146.0 0.007 15.429
20 105 106.2 0.014 15.443
21 277 287.1 0.356 15.799
Chisq= 15.80 for 20 degrees of freedom, p= 0.27098
SUMMARY of craptest
p-value for no. of wins: 0.588723
p-value for throws/game: 0.270978
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-09_05:31
No. of wins: Observed Expected
99030 98585.9
z-score= 1.986, pvalue=0.97651
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66939 66666.7 1.112 1.112
2 37573 37654.3 0.176 1.288
3 26897 26954.7 0.124 1.412
4 19207 19313.5 0.587 1.999
5 13629 13851.4 3.572 5.570
6 9877 9943.5 0.445 6.015
7 7171 7145.0 0.094 6.110
8 5200 5139.1 0.722 6.832
9 3689 3699.9 0.032 6.864
10 2737 2666.3 1.875 8.739
11 1969 1923.3 1.084 9.823
12 1407 1388.7 0.240 10.064
13 1042 1003.7 1.460 11.524
14 747 726.1 0.599 12.123
15 522 525.8 0.028 12.151
16 386 381.2 0.062 12.213
17 261 276.5 0.873 13.086
18 228 200.8 3.676 16.762
19 127 146.0 2.469 19.231
20 106 106.2 0.000 19.231
21 286 287.1 0.004 19.235
Chisq= 19.24 for 20 degrees of freedom, p= 0.49342
SUMMARY of craptest
p-value for no. of wins: 0.976509
p-value for throws/game: 0.493420
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0018,0.0022,0.0107,0.0142,0.0189,0.0256,0.0286,0.0290,0.0300,0.0309,
0.0323,0.0366,0.0400,0.0403,0.0412,0.0431,0.0433,0.0445,0.0446,0.0451,
0.0474,0.0501,0.0533,0.0535,0.0539,0.0568,0.0573,0.0603,0.0607,0.0644,
0.0654,0.0709,0.0712,0.0737,0.0741,0.0755,0.0756,0.0828,0.0829,0.0854,
0.0858,0.0927,0.0971,0.1059,0.1088,0.1094,0.1142,0.1175,0.1180,0.1247,
0.1309,0.1335,0.1362,0.1415,0.1499,0.1568,0.1622,0.1625,0.1688,0.1689,
0.1693,0.1704,0.1729,0.1768,0.1802,0.1815,0.1815,0.1823,0.1905,0.1924,
0.2000,0.2009,0.2056,0.2070,0.2095,0.2096,0.2123,0.2178,0.2185,0.2188,
0.2194,0.2244,0.2299,0.2384,0.2451,0.2476,0.2477,0.2480,0.2481,0.2559,
0.2581,0.2590,0.2591,0.2710,0.2832,0.2862,0.2904,0.2913,0.2953,0.2991,
0.3046,0.3091,0.3231,0.3247,0.3278,0.3287,0.3308,0.3341,0.3350,0.3354,
0.3500,0.3547,0.3589,0.3608,0.3609,0.3707,0.3746,0.3759,0.3817,0.3817,
0.3859,0.3866,0.3949,0.4006,0.4091,0.4121,0.4126,0.4201,0.4222,0.4224,
0.4307,0.4375,0.4409,0.4411,0.4460,0.4483,0.4550,0.4573,0.4619,0.4711,
0.4749,0.4808,0.4848,0.4857,0.4863,0.4901,0.4926,0.4934,0.4958,0.4970,
0.4973,0.4987,0.5017,0.5023,0.5061,0.5122,0.5179,0.5182,0.5190,0.5284,
0.5394,0.5484,0.5499,0.5528,0.5530,0.5626,0.5642,0.5646,0.5748,0.5762,
0.5804,0.5821,0.5842,0.5887,0.5895,0.5904,0.5975,0.6002,0.6032,0.6065,
0.6116,0.6117,0.6122,0.6264,0.6319,0.6324,0.6335,0.6410,0.6424,0.6425,
0.6464,0.6496,0.6524,0.6674,0.6676,0.6756,0.6772,0.6791,0.6837,0.6862,
0.6959,0.7065,0.7092,0.7111,0.7151,0.7173,0.7211,0.7236,0.7256,0.7267,
0.7296,0.7379,0.7425,0.7434,0.7556,0.7557,0.7561,0.7697,0.7738,0.7756,
0.7784,0.7812,0.7820,0.7940,0.7988,0.8077,0.8125,0.8181,0.8194,0.8288,
0.8344,0.8344,0.8373,0.8423,0.8447,0.8467,0.8483,0.8484,0.8538,0.8628,
0.8633,0.8686,0.8700,0.8803,0.8880,0.8906,0.9034,0.9055,0.9116,0.9148,
0.9250,0.9291,0.9369,0.9384,0.9413,0.9552,0.9553,0.9561,0.9576,0.9647,
0.9743,0.9765,0.9767,0.9813,0.9839,0.9843,0.9860,0.9876,0.9931,
Overall p-value after applying KStest on 269 p-values = 0.007517
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.