RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-02_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 15.86 10.7335 0.129921
2 to 25 15.60 21.0423 0.775596
3 to 26 15.81 11.7047 0.182322
4 to 27 15.70 16.2733 0.495453
5 to 28 15.73 15.0402 0.407415
6 to 29 16.17 22.2295 0.823948
7 to 30 15.85 13.1831 0.276158
8 to 31 15.99 15.1019 0.411856
9 to 32 15.86 8.5889 0.047718
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.504715
Tough bday spacings test for dh-ranFile-2018-07-02_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 10 43 86 89 94 65 50 32 24 6 1
(O-E)^2/E 0.1 1.1 2.2 0.8 0.1 2.2 0.1 0.2 5.6 0.1 2.3
Birthday Spacings: Sum(O-E)^2/E= 14.724, p= 0.858
RESULTS OF GCD FOR dh-ranFile-2018-07-02_16:31
Euclid's algorithm:
p-value, steps to gcd: 0.986859
p-value, dist. of gcd's: 0.436130
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-02_16:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.171 0.253 0.558 0.623 0.142 0.039 0.263 0.517
Bits 8 to 15---> 0.842 0.431 0.755 0.508 0.117 0.842 0.742 0.806
Bits 16 to 23---> 0.445 0.658 0.764 0.591 0.816 0.604 0.063 0.314
Bits 24 to 31---> 0.967 0.646 0.884 0.845 0.078 0.323 0.379 0.046
KS test for the above 32 p values: 0.056
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-02_16:31,
p-values for 5 runs: 0.0616, 0.6090, 0.5568, 0.6808, 0.8668
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-02_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 199 211.4 0.729 0.729
r= 29 5129 5134.0 0.005 0.734
r= 30 23151 23103.0 0.100 0.834
r= 31 11521 11551.5 0.081 0.914
chi-square = 0.914 with df = 3; p-value = 0.178
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-02_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 207 211.4 0.092 0.092
r= 30 5025 5134.0 2.315 2.407
r= 31 23199 23103.0 0.399 2.805
r= 32 11569 11551.5 0.026 2.832
chi-square = 2.832 with df = 3; p-value = 0.582
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-02_16:31
b-rank test for bits 1 to 8, p=0.29028
b-rank test for bits 2 to 9, p=0.12377
b-rank test for bits 3 to 10, p=0.59722
b-rank test for bits 4 to 11, p=0.11939
b-rank test for bits 5 to 12, p=0.71957
b-rank test for bits 6 to 13, p=0.52677
b-rank test for bits 7 to 14, p=0.21969
b-rank test for bits 8 to 15, p=0.46259
b-rank test for bits 9 to 16, p=0.01311
b-rank test for bits 10 to 17, p=0.25669
b-rank test for bits 11 to 18, p=0.40881
b-rank test for bits 12 to 19, p=0.17650
b-rank test for bits 13 to 20, p=0.27605
b-rank test for bits 14 to 21, p=0.48362
b-rank test for bits 15 to 22, p=0.10152
b-rank test for bits 16 to 23, p=0.48804
b-rank test for bits 17 to 24, p=0.02843
b-rank test for bits 18 to 25, p=0.01797
b-rank test for bits 19 to 26, p=0.36906
b-rank test for bits 20 to 27, p=0.66911
b-rank test for bits 21 to 28, p=0.49419
b-rank test for bits 22 to 29, p=0.40607
b-rank test for bits 23 to 30, p=0.92450
b-rank test for bits 24 to 31, p=0.40781
b-rank test for bits 25 to 32, p=0.06979
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 = 0.010964
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-02_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 141977 0.16 0.562814
2 142450 1.26 0.896750
3 141220 -1.61 0.053635
4 141525 -0.90 0.184602
5 140973 -2.19 0.014346
6 141993 0.20 0.577496
7 141999 0.21 0.582975
8 142099 0.44 0.671173
9 142383 1.11 0.865789
10 141841 -0.16 0.436579
11 141281 -1.47 0.071044
12 141500 -0.96 0.169441
13 142052 0.33 0.630562
14 141702 -0.48 0.314045
15 141502 -0.95 0.170623
16 141920 0.02 0.509945
17 141899 -0.02 0.490372
18 141838 -0.17 0.433819
19 142307 0.93 0.823591
20 142873 2.25 0.987825
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-02_16:31
Bits used No. missing words z-score p-value
23 to 32 141981 0.2471 0.597599
22 to 31 142230 1.1058 0.865585
21 to 30 142253 1.1851 0.882005
20 to 29 141448 -1.5908 0.055828
19 to 28 142066 0.5402 0.705485
18 to 27 141862 -0.1632 0.435178
17 to 26 141666 -0.8391 0.200715
16 to 25 142030 0.4161 0.661333
15 to 24 141620 -0.9977 0.159215
14 to 23 142056 0.5058 0.693487
13 to 22 141398 -1.7632 0.038933
12 to 21 141817 -0.3184 0.375099
11 to 20 141933 0.0816 0.532526
10 to 19 141975 0.2264 0.589574
9 to 18 141911 0.0058 0.502297
8 to 17 142208 1.0299 0.848471
7 to 16 141498 -1.4184 0.078040
6 to 15 141638 -0.9356 0.174734
5 to 14 141593 -1.0908 0.137682
4 to 13 141362 -1.8873 0.029557
3 to 12 141651 -0.8908 0.186520
2 to 11 142065 0.5368 0.704295
1 to 10 141411 -1.7184 0.042864
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-02_16:31
Bits used No. missing words z-score p-value
28 to 32 141545 -1.2350 0.108412
27 to 31 141844 -0.2215 0.412368
26 to 30 142258 1.1819 0.881384
25 to 29 141925 0.0531 0.521181
24 to 28 141971 0.2091 0.582796
23 to 27 142253 1.1650 0.877987
22 to 26 141996 0.2938 0.615543
21 to 25 142112 0.6870 0.753964
20 to 24 142105 0.6633 0.746427
19 to 23 141196 -2.4181 0.007802
18 to 22 142293 1.3006 0.903298
17 to 21 141756 -0.5198 0.301615
16 to 20 142144 0.7955 0.786836
15 to 19 142184 0.9311 0.824095
14 to 18 141906 -0.0113 0.495497
13 to 17 141680 -0.7774 0.218464
12 to 16 142007 0.3311 0.629710
11 to 15 141950 0.1379 0.554826
10 to 14 141948 0.1311 0.552146
9 to 13 142327 1.4158 0.921587
8 to 12 141978 0.2328 0.592034
7 to 11 141530 -1.2859 0.099245
6 to 10 141435 -1.6079 0.053929
5 to 9 141762 -0.4994 0.308741
4 to 8 142217 1.0429 0.851514
3 to 7 141656 -0.8587 0.195240
2 to 6 142114 0.6938 0.756095
1 to 5 141759 -0.5096 0.305168
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-02_16:31
Bits used No. missing words z-score p-value
31 to 32 141767 -0.4199 0.337297
30 to 31 141123 -2.3196 0.010182
29 to 30 142416 1.4946 0.932491
28 to 29 141515 -1.1632 0.122371
27 to 28 142212 0.8928 0.814026
26 to 27 141859 -0.1485 0.440988
25 to 26 141433 -1.4051 0.079995
24 to 25 141612 -0.8771 0.190222
23 to 24 141745 -0.4847 0.313927
22 to 23 141889 -0.0600 0.476090
21 to 22 142195 0.8427 0.800298
20 to 21 142077 0.4946 0.689559
19 to 20 142062 0.4504 0.673772
18 to 19 141779 -0.3845 0.350321
17 to 18 141750 -0.4700 0.319178
16 to 17 141976 0.1967 0.577956
15 to 16 141626 -0.8358 0.201639
14 to 15 141798 -0.3284 0.371302
13 to 14 141657 -0.7443 0.228337
12 to 13 141812 -0.2871 0.387014
11 to 12 142250 1.0049 0.842534
10 to 11 141648 -0.7709 0.220388
9 to 10 141193 -2.1131 0.017297
8 to 9 141805 -0.3078 0.379133
7 to 8 142163 0.7483 0.772857
6 to 7 142221 0.9194 0.821052
5 to 6 141371 -1.5880 0.056144
4 to 5 142011 0.2999 0.617878
3 to 4 142011 0.2999 0.617878
2 to 3 142011 0.2999 0.617878
1 to 2 142364 1.3412 0.910074
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-02_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2544.92 0.635 0.737351
Test results for specific bytes for dh-ranFile-2018-07-02_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2515.10 0.214 0.584555
2 to 9 2533.99 0.481 0.684640
3 to 10 2429.11 -1.003 0.158050
4 to 11 2520.26 0.287 0.612753
5 to 12 2550.40 0.713 0.761995
6 to 13 2462.15 -0.535 0.296252
7 to 14 2619.18 1.685 0.954049
8 to 15 2440.30 -0.844 0.199269
9 to 16 2520.96 0.296 0.616525
10 to 17 2521.56 0.305 0.619758
11 to 18 2631.51 1.860 0.968546
12 to 19 2436.82 -0.893 0.185810
13 to 20 2530.12 0.426 0.664916
14 to 21 2551.64 0.730 0.767386
15 to 22 2476.44 -0.333 0.369506
16 to 23 2462.37 -0.532 0.297301
17 to 24 2438.85 -0.865 0.193594
18 to 25 2446.27 -0.760 0.223676
19 to 26 2512.09 0.171 0.567892
20 to 27 2549.70 0.703 0.758921
21 to 28 2551.91 0.734 0.768582
22 to 29 2552.11 0.737 0.769409
23 to 30 2516.14 0.228 0.590260
24 to 31 2539.99 0.566 0.714170
25 to 32 2404.51 -1.350 0.088438
CDPARK for dh-ranFile-2018-07-02_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
3497 -1.1872 0.117571
3525 0.0913 0.536383
3513 -0.4566 0.323972
3519 -0.1826 0.427537
3552 1.3242 0.907282
3514 -0.4110 0.340551
3545 1.0046 0.842447
3489 -1.5525 0.060270
3529 0.2740 0.607947
3507 -0.7306 0.232514
Square side=100, avg. no. parked=3519.00 sample std.=18.68
p-value of the KSTEST for those 10 p-values: 0.874628
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-02_16:31
0.7685,0.5098,0.4944,0.8664,0.1624,0.4075,0.0286,0.1981,0.3630,0.4643,
The KS test for those 10 p-values: 0.644785
The 3DSPHERES test for dh-ranFile-2018-07-02_16:31
sample no r^3 equiv. uni.
1 5.682 0.172531
2 6.883 0.205005
3 9.148 0.262821
4 24.834 0.562991
5 7.796 0.228841
6 41.178 0.746555
7 0.475 0.015717
8 15.456 0.402618
9 15.491 0.403319
10 15.208 0.397665
11 16.973 0.432075
12 6.422 0.192712
13 15.312 0.399750
14 47.009 0.791321
15 15.072 0.394918
16 39.863 0.735198
17 42.196 0.755013
18 22.811 0.532506
19 23.305 0.540133
20 0.990 0.032453
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.160096
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-02_16:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 0.5 -0.1 0.0 -0.5 0.4
2.1 0.8 1.5 0.4 0.4 -0.1
-0.5 0.5 -1.4 0.7 -0.7 -1.5
-0.2 0.8 -0.0 -1.0 -1.2 0.3
2.8 0.5 -0.1 -0.8 -0.9 -0.7
0.9 0.8 0.6 -0.8 1.3 1.1
0.5 1.5 3.0 1.0 0.9 0.0
1.8
Chi-square with 42 degrees of freedom:50.624328
z-score=0.940991, p-value=0.830211
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-02_16:31
Test no p-value
1 0.047268
2 0.074121
3 0.109060
4 0.085980
5 0.662716
6 0.097219
7 0.000104
8 0.101418
9 0.046537
10 0.429572
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000028
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-02_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 66626 0.02 66408 1.00
3 25000.00 24928 0.21 25187 1.40
4 6666.67 6765 1.45 6723 0.48
5 1388.89 1406 0.21 1403 0.14
6 238.10 233 0.11 242 0.06
7 34.72 37 0.15 33 0.09
8 4.96 4 0.19 3 0.77
p=0.11384 p=0.31595
Number of rngs required: 690743, p-value: 0.998
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-02_16:31
No. of wins: Observed Expected
98557 98585.9
z-score=-0.129, pvalue=0.44865
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66632 66666.7 0.018 0.018
2 37883 37654.3 1.389 1.407
3 26992 26954.7 0.052 1.458
4 19248 19313.5 0.222 1.680
5 13756 13851.4 0.657 2.338
6 9954 9943.5 0.011 2.349
7 7055 7145.0 1.134 3.483
8 5116 5139.1 0.104 3.586
9 3739 3699.9 0.414 4.000
10 2713 2666.3 0.818 4.818
11 1887 1923.3 0.686 5.505
12 1378 1388.7 0.083 5.588
13 1010 1003.7 0.039 5.627
14 715 726.1 0.171 5.798
15 545 525.8 0.698 6.496
16 379 381.2 0.012 6.509
17 256 276.5 1.526 8.034
18 194 200.8 0.232 8.266
19 153 146.0 0.337 8.604
20 115 106.2 0.727 9.330
21 280 287.1 0.176 9.506
Chisq= 9.51 for 20 degrees of freedom, p= 0.02373
SUMMARY of craptest
p-value for no. of wins: 0.448650
p-value for throws/game: 0.023734
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-02_16:31
No. of wins: Observed Expected
98521 98585.9
z-score=-0.290, pvalue=0.38588
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66656 66666.7 0.002 0.002
2 37577 37654.3 0.159 0.160
3 26969 26954.7 0.008 0.168
4 19293 19313.5 0.022 0.190
5 13844 13851.4 0.004 0.194
6 9921 9943.5 0.051 0.245
7 7158 7145.0 0.024 0.268
8 5166 5139.1 0.141 0.409
9 3768 3699.9 1.255 1.664
10 2616 2666.3 0.949 2.613
11 1908 1923.3 0.122 2.735
12 1428 1388.7 1.110 3.845
13 1006 1003.7 0.005 3.850
14 721 726.1 0.036 3.887
15 529 525.8 0.019 3.906
16 408 381.2 1.891 5.797
17 260 276.5 0.989 6.786
18 187 200.8 0.952 7.739
19 162 146.0 1.757 9.496
20 112 106.2 0.315 9.811
21 311 287.1 1.987 11.798
Chisq= 11.80 for 20 degrees of freedom, p= 0.07714
SUMMARY of craptest
p-value for no. of wins: 0.385875
p-value for throws/game: 0.077143
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0000,0.0001,0.0078,0.0102,0.0110,0.0131,0.0143,0.0157,0.0173,0.0180,
0.0237,0.0284,0.0286,0.0296,0.0325,0.0389,0.0390,0.0429,0.0462,0.0465,
0.0473,0.0477,0.0536,0.0539,0.0558,0.0561,0.0562,0.0603,0.0616,0.0626,
0.0698,0.0710,0.0741,0.0771,0.0777,0.0780,0.0800,0.0860,0.0884,0.0972,
0.0992,0.1014,0.1015,0.1084,0.1091,0.1138,0.1168,0.1176,0.1194,0.1224,
0.1238,0.1299,0.1377,0.1420,0.1581,0.1592,0.1601,0.1624,0.1694,0.1706,
0.1714,0.1725,0.1747,0.1765,0.1781,0.1823,0.1846,0.1858,0.1865,0.1902,
0.1927,0.1936,0.1952,0.1981,0.1993,0.2007,0.2016,0.2050,0.2185,0.2197,
0.2204,0.2237,0.2283,0.2288,0.2325,0.2525,0.2567,0.2626,0.2628,0.2761,
0.2762,0.2903,0.2963,0.2973,0.3016,0.3052,0.3087,0.3139,0.3140,0.3144,
0.3159,0.3192,0.3230,0.3240,0.3373,0.3406,0.3503,0.3630,0.3691,0.3695,
0.3713,0.3751,0.3791,0.3792,0.3859,0.3870,0.3949,0.3977,0.3997,0.4026,
0.4033,0.4061,0.4074,0.4075,0.4078,0.4088,0.4119,0.4124,0.4275,0.4296,
0.4311,0.4321,0.4338,0.4352,0.4361,0.4366,0.4410,0.4452,0.4487,0.4626,
0.4643,0.4761,0.4836,0.4880,0.4904,0.4942,0.4944,0.4955,0.4955,0.5023,
0.5047,0.5080,0.5098,0.5099,0.5168,0.5212,0.5268,0.5325,0.5325,0.5364,
0.5401,0.5521,0.5548,0.5568,0.5583,0.5628,0.5630,0.5679,0.5775,0.5780,
0.5817,0.5828,0.5830,0.5846,0.5896,0.5903,0.5908,0.5920,0.5972,0.5976,
0.6037,0.6079,0.6090,0.6128,0.6155,0.6165,0.6179,0.6179,0.6179,0.6198,
0.6227,0.6297,0.6306,0.6448,0.6458,0.6577,0.6613,0.6627,0.6649,0.6691,
0.6712,0.6738,0.6808,0.6846,0.6896,0.6935,0.7043,0.7055,0.7142,0.7196,
0.7352,0.7374,0.7425,0.7464,0.7466,0.7540,0.7550,0.7550,0.7561,0.7589,
0.7620,0.7643,0.7674,0.7685,0.7686,0.7694,0.7729,0.7756,0.7868,0.7913,
0.8003,0.8058,0.8140,0.8164,0.8211,0.8236,0.8239,0.8241,0.8302,0.8418,
0.8424,0.8425,0.8425,0.8446,0.8485,0.8515,0.8576,0.8656,0.8658,0.8664,
0.8668,0.8746,0.8780,0.8814,0.8820,0.8841,0.8967,0.9033,0.9073,0.9101,
0.9216,0.9245,0.9325,0.9540,0.9665,0.9685,0.9869,0.9878,0.9975,
Overall p-value after applying KStest on 269 p-values = 0.001894
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.