RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-19_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 15.81 22.5347 0.834978
2 to 25 16.10 15.3051 0.426485
3 to 26 15.93 14.6914 0.382300
4 to 27 15.89 20.1251 0.732117
5 to 28 15.81 30.4479 0.976710
6 to 29 15.81 9.0901 0.062607
7 to 30 15.86 8.5541 0.046778
8 to 31 15.89 16.8427 0.534926
9 to 32 15.57 22.0778 0.818254
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.816738
Tough bday spacings test for dh-ranFile-2018-06-19_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 13 32 79 87 109 84 49 28 9 6 4
(O-E)^2/E 1.6 0.6 0.4 1.2 1.3 0.4 0.2 0.1 2.3 0.1 0.0
Birthday Spacings: Sum(O-E)^2/E= 8.239, p= 0.395
RESULTS OF GCD FOR dh-ranFile-2018-06-19_05:31
Euclid's algorithm:
p-value, steps to gcd: 0.973898
p-value, dist. of gcd's: 0.922076
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-19_05:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.650 0.785 0.754 0.378 0.341 0.726 0.211 0.302
Bits 8 to 15---> 0.507 0.921 0.745 0.623 0.760 0.445 0.124 0.384
Bits 16 to 23---> 0.659 0.081 0.789 0.964 0.626 0.485 0.013 0.702
Bits 24 to 31---> 0.450 0.203 0.779 0.086 0.283 0.458 0.780 0.393
KS test for the above 32 p values: 0.341
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-19_05:31,
p-values for 5 runs: 0.2098, 0.2835, 0.8500, 0.5586, 0.4632
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-19_05:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 223 211.4 0.634 0.634
r= 29 5179 5134.0 0.394 1.029
r= 30 23092 23103.0 0.005 1.034
r= 31 11506 11551.5 0.179 1.213
chi-square = 1.213 with df = 3; p-value = 0.250
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-19_05:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 219 211.4 0.272 0.272
r= 30 5113 5134.0 0.086 0.358
r= 31 22932 23103.0 1.266 1.624
r= 32 11736 11551.5 2.946 4.570
chi-square = 4.570 with df = 3; p-value = 0.794
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-19_05:31
b-rank test for bits 1 to 8, p=0.64977
b-rank test for bits 2 to 9, p=0.60738
b-rank test for bits 3 to 10, p=0.90062
b-rank test for bits 4 to 11, p=0.32779
b-rank test for bits 5 to 12, p=0.45428
b-rank test for bits 6 to 13, p=0.17461
b-rank test for bits 7 to 14, p=0.41378
b-rank test for bits 8 to 15, p=0.18244
b-rank test for bits 9 to 16, p=0.85720
b-rank test for bits 10 to 17, p=0.81322
b-rank test for bits 11 to 18, p=0.56156
b-rank test for bits 12 to 19, p=0.41051
b-rank test for bits 13 to 20, p=0.83621
b-rank test for bits 14 to 21, p=0.70849
b-rank test for bits 15 to 22, p=0.70774
b-rank test for bits 16 to 23, p=0.50299
b-rank test for bits 17 to 24, p=0.83607
b-rank test for bits 18 to 25, p=0.47919
b-rank test for bits 19 to 26, p=0.60595
b-rank test for bits 20 to 27, p=0.65882
b-rank test for bits 21 to 28, p=0.30178
b-rank test for bits 22 to 29, p=0.92241
b-rank test for bits 23 to 30, p=0.63982
b-rank test for bits 24 to 31, p=0.03968
b-rank test for bits 25 to 32, p=0.58901
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 = 0.223376
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-19_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 141642 -0.62 0.266116
2 141838 -0.17 0.433819
3 141663 -0.58 0.282464
4 141762 -0.34 0.365337
5 142012 0.24 0.594790
6 142166 0.60 0.725646
7 141905 -0.01 0.495964
8 142028 0.28 0.609212
9 141406 -1.18 0.119797
10 141931 0.05 0.520190
11 142741 1.94 0.974001
12 141616 -0.69 0.246561
13 142052 0.33 0.630562
14 142375 1.09 0.861706
15 140837 -2.51 0.006115
16 141945 0.08 0.533210
17 142255 0.81 0.790351
18 141657 -0.59 0.277744
19 141538 -0.87 0.192808
20 141666 -0.57 0.284838
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-19_05:31
Bits used No. missing words z-score p-value
23 to 32 141838 -0.2460 0.402855
22 to 31 141721 -0.6494 0.258036
21 to 30 141679 -0.7942 0.213528
20 to 29 142114 0.7058 0.759831
19 to 28 141690 -0.7563 0.224732
18 to 27 142053 0.4954 0.689846
17 to 26 142204 1.0161 0.845210
16 to 25 142254 1.1885 0.882685
15 to 24 141882 -0.0942 0.462459
14 to 23 141570 -1.1701 0.120980
13 to 22 141978 0.2368 0.593591
12 to 21 142271 1.2471 0.893827
11 to 20 141949 0.1368 0.554403
10 to 19 141827 -0.2839 0.388245
9 to 18 142288 1.3058 0.904183
8 to 17 141480 -1.4804 0.069377
7 to 16 141313 -2.0563 0.019876
6 to 15 141744 -0.5701 0.284304
5 to 14 142413 1.7368 0.958788
4 to 13 141954 0.1540 0.561209
3 to 12 142010 0.3471 0.635756
2 to 11 141983 0.2540 0.600266
1 to 10 141744 -0.5701 0.284304
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-19_05:31
Bits used No. missing words z-score p-value
28 to 32 141932 0.0768 0.530628
27 to 31 141959 0.1684 0.566855
26 to 30 141980 0.2396 0.594664
25 to 29 142149 0.8124 0.791731
24 to 28 141749 -0.5435 0.293396
23 to 27 141977 0.2294 0.590717
22 to 26 141725 -0.6248 0.266036
21 to 25 142187 0.9413 0.826713
20 to 24 142038 0.4362 0.668643
19 to 23 141579 -1.1198 0.131407
18 to 22 141739 -0.5774 0.281838
17 to 21 142016 0.3616 0.641172
16 to 20 142087 0.6023 0.726503
15 to 19 141684 -0.7638 0.222484
14 to 18 142357 1.5175 0.935433
13 to 17 141626 -0.9604 0.168417
12 to 16 141782 -0.4316 0.333006
11 to 15 142045 0.4599 0.677205
10 to 14 141895 -0.0486 0.480629
9 to 13 142225 1.0701 0.857706
8 to 12 141690 -0.7435 0.228592
7 to 11 141644 -0.8994 0.184214
6 to 10 142361 1.5311 0.937126
5 to 9 141592 -1.0757 0.141032
4 to 8 141860 -0.1672 0.433598
3 to 7 142364 1.5413 0.938373
2 to 6 142206 1.0057 0.842711
1 to 5 141807 -0.3469 0.364340
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-19_05:31
Bits used No. missing words z-score p-value
31 to 32 141822 -0.2576 0.398354
30 to 31 141754 -0.4582 0.323404
29 to 30 142197 0.8486 0.801944
28 to 29 142017 0.3176 0.624610
27 to 28 142213 0.8958 0.814815
26 to 27 141919 0.0285 0.511378
25 to 26 141966 0.1672 0.566381
24 to 25 141949 0.1170 0.546578
23 to 24 141984 0.2203 0.587168
22 to 23 141725 -0.5437 0.293308
21 to 22 141941 0.0934 0.537216
20 to 21 142113 0.6008 0.726012
19 to 20 141823 -0.2547 0.399493
18 to 19 141566 -1.0128 0.155584
17 to 18 142222 0.9223 0.821822
16 to 17 142003 0.2763 0.608846
15 to 16 141861 -0.1426 0.443316
14 to 15 143055 3.3796 0.999637
13 to 14 142316 1.1996 0.884856
12 to 13 142178 0.7925 0.785976
11 to 12 141644 -0.7827 0.216906
10 to 11 142348 1.2940 0.902169
9 to 10 142153 0.7188 0.763865
8 to 9 141428 -1.4199 0.077825
7 to 8 141712 -0.5821 0.280252
6 to 7 142286 1.1111 0.866742
5 to 6 141553 -1.0511 0.146602
4 to 5 142135 0.6657 0.747196
3 to 4 141646 -0.7768 0.218643
2 to 3 142161 0.7424 0.771074
1 to 2 141621 -0.8505 0.197515
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-19_05:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2509.18 0.130 0.551657
Test results for specific bytes for dh-ranFile-2018-06-19_05:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2487.63 -0.175 0.430539
2 to 9 2460.87 -0.553 0.290012
3 to 10 2444.10 -0.791 0.214594
4 to 11 2600.29 1.418 0.921952
5 to 12 2482.26 -0.251 0.400964
6 to 13 2475.55 -0.346 0.364751
7 to 14 2470.43 -0.418 0.337925
8 to 15 2601.18 1.431 0.923774
9 to 16 2475.72 -0.343 0.365675
10 to 17 2516.95 0.240 0.594738
11 to 18 2354.89 -2.052 0.020077
12 to 19 2559.11 0.836 0.798413
13 to 20 2470.82 -0.413 0.339929
14 to 21 2423.30 -1.085 0.139036
15 to 22 2538.26 0.541 0.705784
16 to 23 2497.47 -0.036 0.485715
17 to 24 2534.97 0.495 0.689549
18 to 25 2541.89 0.592 0.723198
19 to 26 2588.07 1.245 0.893524
20 to 27 2461.15 -0.549 0.291355
21 to 28 2622.72 1.735 0.958671
22 to 29 2533.35 0.472 0.681412
23 to 30 2545.95 0.650 0.742081
24 to 31 2367.69 -1.871 0.030659
25 to 32 2491.39 -0.122 0.451515
CDPARK for dh-ranFile-2018-06-19_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
3521 -0.0913 0.463617
3531 0.3653 0.642555
3539 0.7306 0.767486
3524 0.0457 0.518210
3520 -0.1370 0.445521
3519 -0.1826 0.427537
3524 0.0457 0.518210
3555 1.4612 0.928018
3511 -0.5479 0.291865
3521 -0.0913 0.463617
Square side=100, avg. no. parked=3526.50 sample std.=11.83
p-value of the KSTEST for those 10 p-values: 0.262810
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-19_05:31
0.7232,0.0707,0.4110,0.3242,0.4393,0.7466,0.4316,0.0780,0.6131,0.4833,
The KS test for those 10 p-values: 0.468715
The 3DSPHERES test for dh-ranFile-2018-06-19_05:31
sample no r^3 equiv. uni.
1 17.359 0.439335
2 27.085 0.594581
3 9.567 0.273046
4 73.046 0.912391
5 9.529 0.272130
6 10.904 0.304739
7 8.176 0.238552
8 46.978 0.791109
9 78.949 0.928040
10 0.361 0.011950
11 10.006 0.283616
12 63.359 0.879000
13 22.473 0.527202
14 10.850 0.303484
15 109.620 0.974113
16 9.437 0.269883
17 30.199 0.634555
18 1.581 0.051321
19 2.343 0.075122
20 2.535 0.081043
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.414856
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-19_05:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -0.7 -0.6 0.3 1.1 0.1
0.8 0.4 1.1 -0.1 -1.2 2.2
0.6 1.3 -0.1 1.4 0.1 -1.8
-0.8 0.5 0.6 -0.5 0.6 -0.2
-3.1 -1.5 0.4 0.0 0.7 -0.7
-1.7 0.1 -0.4 -1.3 0.2 -0.5
-0.7 0.2 0.9 -0.7 0.1 0.0
-1.1
Chi-square with 42 degrees of freedom:40.262757
z-score=-0.189549, p-value=0.452577
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-19_05:31
Test no p-value
1 0.330698
2 0.154195
3 0.041080
4 0.481728
5 0.994037
6 0.260298
7 0.235243
8 0.004786
9 0.421678
10 0.068685
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.023114
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-19_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 66609 0.05 66575 0.13
3 25000.00 24900 0.40 25080 0.26
4 6666.67 6794 2.43 6716 0.37
5 1388.89 1423 0.84 1343 1.52
6 238.10 247 0.33 240 0.02
7 34.72 23 3.96 41 1.14
8 4.96 3 0.77 4 0.19
p=0.81386 p=0.26941
Number of rngs required: 687810, p-value: 0.247
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-19_05:31
No. of wins: Observed Expected
98368 98585.9
z-score=-0.974, pvalue=0.16493
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66699 66666.7 0.016 0.016
2 37649 37654.3 0.001 0.016
3 27166 26954.7 1.656 1.672
4 19291 19313.5 0.026 1.698
5 13831 13851.4 0.030 1.729
6 9881 9943.5 0.393 2.122
7 7181 7145.0 0.181 2.303
8 5098 5139.1 0.328 2.631
9 3654 3699.9 0.569 3.200
10 2585 2666.3 2.479 5.679
11 1963 1923.3 0.818 6.497
12 1408 1388.7 0.267 6.764
13 1030 1003.7 0.688 7.452
14 717 726.1 0.115 7.567
15 546 525.8 0.773 8.341
16 355 381.2 1.794 10.135
17 268 276.5 0.264 10.399
18 183 200.8 1.583 11.982
19 153 146.0 0.337 12.319
20 100 106.2 0.364 12.682
21 242 287.1 7.089 19.771
Chisq= 19.77 for 20 degrees of freedom, p= 0.52767
SUMMARY of craptest
p-value for no. of wins: 0.164931
p-value for throws/game: 0.527671
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-19_05:31
No. of wins: Observed Expected
98386 98585.9
z-score=-0.894, pvalue=0.18569
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66758 66666.7 0.125 0.125
2 37540 37654.3 0.347 0.472
3 27129 26954.7 1.127 1.599
4 19152 19313.5 1.350 2.949
5 13990 13851.4 1.386 4.335
6 9934 9943.5 0.009 4.344
7 7113 7145.0 0.144 4.488
8 5128 5139.1 0.024 4.512
9 3666 3699.9 0.310 4.822
10 2713 2666.3 0.818 5.640
11 1891 1923.3 0.543 6.183
12 1364 1388.7 0.441 6.624
13 1005 1003.7 0.002 6.626
14 736 726.1 0.134 6.759
15 490 525.8 2.442 9.202
16 371 381.2 0.270 9.472
17 295 276.5 1.232 10.704
18 204 200.8 0.050 10.754
19 143 146.0 0.061 10.815
20 104 106.2 0.046 10.862
21 274 287.1 0.599 11.461
Chisq= 11.46 for 20 degrees of freedom, p= 0.06661
SUMMARY of craptest
p-value for no. of wins: 0.185692
p-value for throws/game: 0.066606
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0048,0.0061,0.0120,0.0127,0.0199,0.0201,0.0231,0.0307,0.0397,0.0411,
0.0468,0.0513,0.0626,0.0666,0.0687,0.0694,0.0707,0.0751,0.0778,0.0780,
0.0808,0.0810,0.0864,0.1198,0.1210,0.1239,0.1314,0.1390,0.1410,0.1466,
0.1542,0.1556,0.1649,0.1684,0.1746,0.1824,0.1842,0.1857,0.1928,0.1975,
0.2026,0.2098,0.2113,0.2135,0.2146,0.2169,0.2186,0.2225,0.2234,0.2247,
0.2286,0.2352,0.2386,0.2466,0.2468,0.2502,0.2580,0.2603,0.2628,0.2660,
0.2661,0.2694,0.2699,0.2721,0.2730,0.2777,0.2803,0.2818,0.2825,0.2829,
0.2835,0.2836,0.2843,0.2843,0.2848,0.2900,0.2914,0.2919,0.2933,0.2934,
0.3017,0.3018,0.3035,0.3047,0.3234,0.3242,0.3278,0.3307,0.3330,0.3379,
0.3399,0.3408,0.3413,0.3643,0.3648,0.3653,0.3657,0.3783,0.3823,0.3845,
0.3882,0.3929,0.3945,0.3984,0.3995,0.4010,0.4029,0.4105,0.4110,0.4138,
0.4149,0.4217,0.4265,0.4275,0.4305,0.4316,0.4336,0.4338,0.4393,0.4393,
0.4433,0.4452,0.4455,0.4505,0.4515,0.4526,0.4543,0.4584,0.4625,0.4632,
0.4636,0.4636,0.4687,0.4792,0.4806,0.4817,0.4833,0.4849,0.4857,0.4960,
0.5030,0.5072,0.5114,0.5182,0.5182,0.5202,0.5272,0.5277,0.5306,0.5332,
0.5349,0.5372,0.5466,0.5517,0.5544,0.5586,0.5612,0.5616,0.5664,0.5669,
0.5872,0.5890,0.5907,0.5936,0.5946,0.5947,0.5947,0.5948,0.6003,0.6059,
0.6074,0.6088,0.6092,0.6131,0.6227,0.6246,0.6260,0.6306,0.6346,0.6358,
0.6398,0.6412,0.6426,0.6498,0.6499,0.6586,0.6588,0.6686,0.6772,0.6814,
0.6895,0.6898,0.7021,0.7058,0.7077,0.7085,0.7232,0.7232,0.7256,0.7260,
0.7262,0.7265,0.7321,0.7421,0.7453,0.7466,0.7472,0.7540,0.7598,0.7603,
0.7639,0.7675,0.7711,0.7791,0.7796,0.7849,0.7860,0.7893,0.7904,0.7911,
0.7917,0.7939,0.7984,0.8019,0.8132,0.8139,0.8148,0.8167,0.8183,0.8218,
0.8267,0.8350,0.8361,0.8362,0.8427,0.8452,0.8500,0.8572,0.8577,0.8617,
0.8667,0.8790,0.8827,0.8849,0.8935,0.8938,0.9006,0.9022,0.9042,0.9124,
0.9210,0.9220,0.9221,0.9224,0.9238,0.9280,0.9280,0.9354,0.9371,0.9384,
0.9587,0.9588,0.9636,0.9739,0.9740,0.9741,0.9767,0.9940,0.9996,
Overall p-value after applying KStest on 269 p-values = 0.310228
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.