RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-04_18:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.64 22.0643 0.817740
2 to 25 15.95 22.2737 0.825580
3 to 26 15.77 14.5777 0.374129
4 to 27 15.49 27.3764 0.947227
5 to 28 15.32 19.3773 0.692689
6 to 29 15.58 11.9807 0.198695
7 to 30 15.66 16.1181 0.484523
8 to 31 15.63 28.7138 0.962742
9 to 32 15.83 19.8316 0.717069
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.132472
Tough bday spacings test for dh-ranFile-2018-07-04_18:31: 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 9 28 74 89 93 90 49 41 13 11 3
(O-E)^2/E 0.0 2.0 0.0 0.8 0.2 1.8 0.2 4.2 0.2 2.9 0.3
Birthday Spacings: Sum(O-E)^2/E= 12.682, p= 0.758
RESULTS OF GCD FOR dh-ranFile-2018-07-04_18:31
Euclid's algorithm:
p-value, steps to gcd: 0.887163
p-value, dist. of gcd's: 0.362852
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-04_18:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.621 0.760 0.169 0.123 0.207 0.179 0.672 0.371
Bits 8 to 15---> 0.136 0.398 0.147 0.333 0.656 0.802 0.511 0.019
Bits 16 to 23---> 0.792 0.343 0.414 0.409 0.874 0.648 0.863 0.729
Bits 24 to 31---> 0.283 0.313 0.950 0.834 0.029 0.225 0.484 0.081
KS test for the above 32 p values: 0.423
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-04_18:31,
p-values for 5 runs: 0.6221, 0.5171, 0.2652, 0.5363, 0.3675
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-04_18:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 225 211.4 0.873 0.873
r= 29 5167 5134.0 0.212 1.085
r= 30 22875 23103.0 2.251 3.336
r= 31 11733 11551.5 2.851 6.187
chi-square = 6.187 with df = 3; p-value = 0.897
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-04_18:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 211 211.4 0.001 0.001
r= 30 5164 5134.0 0.175 0.176
r= 31 23084 23103.0 0.016 0.192
r= 32 11541 11551.5 0.010 0.201
chi-square = 0.201 with df = 3; p-value = 0.023
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-04_18:31
b-rank test for bits 1 to 8, p=0.27168
b-rank test for bits 2 to 9, p=0.16110
b-rank test for bits 3 to 10, p=0.23270
b-rank test for bits 4 to 11, p=0.91942
b-rank test for bits 5 to 12, p=0.93945
b-rank test for bits 6 to 13, p=0.14973
b-rank test for bits 7 to 14, p=0.72560
b-rank test for bits 8 to 15, p=0.79944
b-rank test for bits 9 to 16, p=0.74483
b-rank test for bits 10 to 17, p=0.93746
b-rank test for bits 11 to 18, p=0.97631
b-rank test for bits 12 to 19, p=0.35011
b-rank test for bits 13 to 20, p=0.92833
b-rank test for bits 14 to 21, p=0.78749
b-rank test for bits 15 to 22, p=0.74669
b-rank test for bits 16 to 23, p=0.72558
b-rank test for bits 17 to 24, p=0.66520
b-rank test for bits 18 to 25, p=0.13045
b-rank test for bits 19 to 26, p=0.64340
b-rank test for bits 20 to 27, p=0.56909
b-rank test for bits 21 to 28, p=0.68019
b-rank test for bits 22 to 29, p=0.29185
b-rank test for bits 23 to 30, p=0.16139
b-rank test for bits 24 to 31, p=0.30173
b-rank test for bits 25 to 32, p=0.05323
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 = 0.368449
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-04_18:31
(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 141966 0.13 0.552669
2 141599 -0.73 0.234205
3 141496 -0.97 0.167091
4 141889 -0.05 0.481057
5 141980 0.17 0.565574
6 141448 -1.08 0.140545
7 141641 -0.63 0.265350
8 142403 1.15 0.875634
9 142190 0.66 0.744014
10 142051 0.33 0.629680
11 142095 0.43 0.667786
12 142263 0.83 0.795692
13 142592 1.60 0.944647
14 142263 0.83 0.795692
15 141569 -0.80 0.213259
16 141838 -0.17 0.433819
17 142317 0.95 0.829578
18 141287 -1.45 0.072967
19 141756 -0.36 0.360079
20 142471 1.31 0.905293
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-04_18:31
Bits used No. missing words z-score p-value
23 to 32 142248 1.1678 0.878562
22 to 31 141815 -0.3253 0.372486
21 to 30 141451 -1.5804 0.057002
20 to 29 141803 -0.3667 0.356938
19 to 28 141376 -1.8391 0.032953
18 to 27 141623 -0.9873 0.161737
17 to 26 142144 0.8092 0.790802
16 to 25 141989 0.2747 0.608236
15 to 24 142036 0.4368 0.668869
14 to 23 142335 1.4678 0.928924
13 to 22 141806 -0.3563 0.360804
12 to 21 141826 -0.2873 0.386924
11 to 20 141673 -0.8149 0.207556
10 to 19 141493 -1.4356 0.075555
9 to 18 141600 -1.0667 0.143064
8 to 17 142305 1.3644 0.913776
7 to 16 142685 2.6747 0.996260
6 to 15 141644 -0.9149 0.180114
5 to 14 141971 0.2127 0.584202
4 to 13 142186 0.9540 0.829967
3 to 12 142422 1.7678 0.961455
2 to 11 141750 -0.5494 0.291361
1 to 10 142200 1.0023 0.841903
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-04_18:31
Bits used No. missing words z-score p-value
28 to 32 141341 -1.9265 0.027018
27 to 31 141866 -0.1469 0.441613
26 to 30 141750 -0.5401 0.294564
25 to 29 141763 -0.4960 0.309935
24 to 28 141247 -2.2452 0.012378
23 to 27 141965 0.1887 0.574841
22 to 26 141429 -1.6282 0.051737
21 to 25 141413 -1.6825 0.046238
20 to 24 141772 -0.4655 0.320778
19 to 23 142145 0.7989 0.787820
18 to 22 142074 0.5582 0.711647
17 to 21 142020 0.3752 0.646227
16 to 20 141472 -1.4825 0.069107
15 to 19 141668 -0.8181 0.206659
14 to 18 141348 -1.9028 0.028532
13 to 17 141602 -1.0418 0.148753
12 to 16 142071 0.5480 0.708166
11 to 15 141816 -0.3164 0.375860
10 to 14 141594 -1.0689 0.142554
9 to 13 141843 -0.2248 0.411049
8 to 12 141916 0.0226 0.509019
7 to 11 142206 1.0057 0.842711
6 to 10 141786 -0.4181 0.337949
5 to 9 142125 0.7311 0.767636
4 to 8 142454 1.8463 0.967579
3 to 7 141405 -1.7096 0.043671
2 to 6 142172 0.8904 0.813376
1 to 5 141672 -0.8045 0.210552
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-04_18:31
Bits used No. missing words z-score p-value
31 to 32 141941 0.0934 0.537216
30 to 31 142099 0.5595 0.712089
29 to 30 142077 0.4946 0.689559
28 to 29 141840 -0.2045 0.418976
27 to 28 141897 -0.0364 0.485493
26 to 27 141720 -0.5585 0.288253
25 to 26 141605 -0.8977 0.184665
24 to 25 141710 -0.5880 0.278268
23 to 24 142142 0.6863 0.753751
22 to 23 141833 -0.2252 0.410927
21 to 22 141870 -0.1160 0.453819
20 to 21 142267 1.0551 0.854304
19 to 20 142015 0.3117 0.622370
18 to 19 141708 -0.5939 0.276292
17 to 18 141966 0.1672 0.566381
16 to 17 141590 -0.9420 0.173102
15 to 16 141359 -1.6234 0.052253
14 to 15 142654 2.1967 0.985978
13 to 14 141966 0.1672 0.566381
12 to 13 142197 0.8486 0.801944
11 to 12 142394 1.4297 0.923599
10 to 11 141349 -1.6529 0.049177
9 to 10 142216 0.9046 0.817170
8 to 9 141781 -0.3786 0.352509
7 to 8 141339 -1.6824 0.046247
6 to 7 141567 -1.0098 0.156290
5 to 6 142466 1.6421 0.949715
4 to 5 141449 -1.3579 0.087247
3 to 4 141600 -0.9125 0.180759
2 to 3 141808 -0.2989 0.382505
1 to 2 142553 1.8987 0.971200
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-04_18:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2432.41 -0.956 0.169579
Test results for specific bytes for dh-ranFile-2018-07-04_18:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2538.85 0.549 0.708647
2 to 9 2530.35 0.429 0.666098
3 to 10 2492.33 -0.108 0.456811
4 to 11 2493.03 -0.099 0.460750
5 to 12 2514.08 0.199 0.578931
6 to 13 2503.23 0.046 0.518240
7 to 14 2507.45 0.105 0.541943
8 to 15 2492.48 -0.106 0.457673
9 to 16 2595.49 1.350 0.911562
10 to 17 2596.52 1.365 0.913878
11 to 18 2483.98 -0.227 0.410368
12 to 19 2453.24 -0.661 0.254225
13 to 20 2384.89 -1.628 0.051767
14 to 21 2570.68 1.000 0.841254
15 to 22 2614.73 1.622 0.947649
16 to 23 2451.48 -0.686 0.246285
17 to 24 2510.16 0.144 0.557110
18 to 25 2568.67 0.971 0.834255
19 to 26 2528.32 0.401 0.655633
20 to 27 2555.26 0.782 0.782750
21 to 28 2398.13 -1.441 0.074839
22 to 29 2497.34 -0.038 0.484988
23 to 30 2575.93 1.074 0.858553
24 to 31 2437.02 -0.891 0.186547
25 to 32 2453.84 -0.653 0.256928
CDPARK for dh-ranFile-2018-07-04_18:31: 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
3496 -1.2329 0.108811
3505 -0.8219 0.205562
3508 -0.6849 0.246694
3502 -0.9589 0.168804
3523 0.0000 0.500000
3533 0.4566 0.676028
3523 0.0000 0.500000
3568 2.0548 0.980051
3532 0.4110 0.659449
3525 0.0913 0.536383
Square side=100, avg. no. parked=3521.50 sample std.=19.76
p-value of the KSTEST for those 10 p-values: 0.757078
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-04_18:31
0.7236,0.4652,0.9070,0.9645,0.2964,0.2848,0.3896,0.7122,0.6364,0.4638,
The KS test for those 10 p-values: 0.486839
The 3DSPHERES test for dh-ranFile-2018-07-04_18:31
sample no r^3 equiv. uni.
1 51.137 0.818147
2 1.462 0.047553
3 14.212 0.377321
4 15.845 0.410314
5 0.358 0.011860
6 14.830 0.390023
7 1.771 0.057330
8 11.399 0.316107
9 10.510 0.295540
10 15.005 0.393578
11 6.397 0.192043
12 9.674 0.275632
13 6.248 0.188000
14 22.836 0.532893
15 17.288 0.438011
16 0.161 0.005349
17 11.752 0.324118
18 44.444 0.772693
19 64.817 0.884739
20 80.686 0.932086
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.075432
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-04_18:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
2.0 -0.3 0.1 0.8 -0.6 2.5
0.8 0.5 -0.5 0.1 -0.5 0.5
-0.5 -0.2 -0.1 0.1 0.3 -0.4
-0.5 0.9 -0.2 1.0 -0.1 -0.0
0.7 -1.9 0.5 -0.5 -0.8 -0.2
0.3 -2.8 -0.0 3.5 -0.9 -0.1
0.5 -0.1 -1.2 -0.7 0.1 0.0
-1.1
Chi-square with 42 degrees of freedom:45.324718
z-score=0.362756, p-value=0.664931
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-04_18:31
Test no p-value
1 0.040387
2 0.004388
3 0.585103
4 0.082317
5 0.001317
6 0.183029
7 0.005059
8 0.677820
9 0.002413
10 0.133649
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000002
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-04_18:31:
(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 66765 0.15 66845 0.48
3 25000.00 24871 0.67 24847 0.94
4 6666.67 6704 0.21 6620 0.33
5 1388.89 1406 0.21 1393 0.01
6 238.10 209 3.56 255 1.20
7 34.72 40 0.80 35 0.00
8 4.96 4 0.19 4 0.19
p=0.55110 p=0.20899
Number of rngs required: 687483, p-value: 0.143
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-04_18:31
No. of wins: Observed Expected
98612 98585.9
z-score= 0.117, pvalue=0.54654
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66882 66666.7 0.696 0.696
2 37234 37654.3 4.692 5.387
3 26938 26954.7 0.010 5.398
4 19069 19313.5 3.094 8.492
5 13969 13851.4 0.998 9.490
6 9925 9943.5 0.035 9.525
7 7149 7145.0 0.002 9.527
8 5145 5139.1 0.007 9.534
9 3819 3699.9 3.836 13.370
10 2721 2666.3 1.122 14.492
11 1960 1923.3 0.699 15.191
12 1450 1388.7 2.702 17.894
13 1080 1003.7 5.798 23.692
14 730 726.1 0.021 23.712
15 511 525.8 0.419 24.131
16 399 381.2 0.836 24.967
17 273 276.5 0.045 25.012
18 210 200.8 0.419 25.431
19 144 146.0 0.027 25.458
20 103 106.2 0.097 25.555
21 289 287.1 0.012 25.567
Chisq= 25.57 for 20 degrees of freedom, p= 0.81942
SUMMARY of craptest
p-value for no. of wins: 0.546538
p-value for throws/game: 0.819415
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-04_18:31
No. of wins: Observed Expected
98348 98585.9
z-score=-1.064, pvalue=0.14370
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66218 66666.7 3.020 3.020
2 37971 37654.3 2.663 5.683
3 26820 26954.7 0.673 6.356
4 19169 19313.5 1.081 7.437
5 14006 13851.4 1.725 9.162
6 10120 9943.5 3.131 12.293
7 7048 7145.0 1.318 13.611
8 5242 5139.1 2.061 15.672
9 3679 3699.9 0.118 15.790
10 2670 2666.3 0.005 15.795
11 1956 1923.3 0.555 16.350
12 1398 1388.7 0.062 16.412
13 990 1003.7 0.187 16.599
14 775 726.1 3.288 19.887
15 525 525.8 0.001 19.888
16 374 381.2 0.134 20.022
17 304 276.5 2.727 22.749
18 206 200.8 0.133 22.882
19 148 146.0 0.028 22.910
20 104 106.2 0.046 22.956
21 277 287.1 0.356 23.313
Chisq= 23.31 for 20 degrees of freedom, p= 0.72629
SUMMARY of craptest
p-value for no. of wins: 0.143700
p-value for throws/game: 0.726293
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0000,0.0013,0.0024,0.0044,0.0051,0.0053,0.0119,0.0124,0.0195,0.0226,
0.0270,0.0285,0.0292,0.0330,0.0404,0.0437,0.0462,0.0462,0.0476,0.0492,
0.0517,0.0518,0.0523,0.0532,0.0570,0.0573,0.0691,0.0730,0.0748,0.0754,
0.0756,0.0806,0.0823,0.0872,0.1088,0.1227,0.1305,0.1325,0.1336,0.1362,
0.1405,0.1426,0.1430,0.1431,0.1437,0.1473,0.1488,0.1497,0.1563,0.1611,
0.1614,0.1617,0.1671,0.1688,0.1693,0.1696,0.1731,0.1791,0.1801,0.1808,
0.1830,0.1847,0.1865,0.1880,0.1920,0.1987,0.2056,0.2066,0.2067,0.2076,
0.2090,0.2106,0.2133,0.2248,0.2327,0.2342,0.2463,0.2467,0.2542,0.2569,
0.2652,0.2653,0.2717,0.2756,0.2763,0.2783,0.2834,0.2848,0.2883,0.2914,
0.2919,0.2946,0.2955,0.2964,0.3017,0.3099,0.3135,0.3161,0.3208,0.3241,
0.3326,0.3379,0.3429,0.3501,0.3525,0.3569,0.3601,0.3608,0.3629,0.3675,
0.3684,0.3711,0.3725,0.3741,0.3759,0.3773,0.3825,0.3869,0.3896,0.3900,
0.3936,0.3978,0.4090,0.4103,0.4104,0.4109,0.4110,0.4138,0.4190,0.4235,
0.4338,0.4380,0.4416,0.4538,0.4568,0.4577,0.4607,0.4638,0.4652,0.4811,
0.4838,0.4845,0.4850,0.4855,0.4868,0.5000,0.5000,0.5090,0.5106,0.5171,
0.5182,0.5329,0.5363,0.5364,0.5372,0.5419,0.5465,0.5511,0.5527,0.5571,
0.5656,0.5664,0.5664,0.5691,0.5748,0.5789,0.5842,0.5851,0.6082,0.6211,
0.6221,0.6224,0.6297,0.6364,0.6434,0.6462,0.6476,0.6556,0.6558,0.6594,
0.6649,0.6652,0.6661,0.6678,0.6689,0.6717,0.6760,0.6778,0.6802,0.6896,
0.6927,0.7082,0.7086,0.7116,0.7121,0.7122,0.7171,0.7236,0.7256,0.7256,
0.7263,0.7287,0.7440,0.7448,0.7467,0.7538,0.7571,0.7580,0.7600,0.7676,
0.7727,0.7828,0.7875,0.7878,0.7908,0.7922,0.7957,0.7957,0.7994,0.8019,
0.8024,0.8134,0.8172,0.8177,0.8181,0.8194,0.8256,0.8296,0.8300,0.8338,
0.8343,0.8413,0.8419,0.8427,0.8543,0.8586,0.8630,0.8739,0.8756,0.8786,
0.8847,0.8872,0.8971,0.9053,0.9070,0.9116,0.9138,0.9139,0.9194,0.9236,
0.9283,0.9289,0.9321,0.9375,0.9394,0.9446,0.9472,0.9476,0.9497,0.9504,
0.9615,0.9627,0.9645,0.9676,0.9712,0.9763,0.9801,0.9860,0.9963,
Overall p-value after applying KStest on 269 p-values = 0.147584
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.