RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-19_13:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.97 29.6418 0.970953
2 to 25 15.94 27.3157 0.946403
3 to 26 15.51 23.1951 0.856993
4 to 27 15.74 11.3456 0.161954
5 to 28 16.01 15.2099 0.419635
6 to 29 15.77 15.1589 0.415963
7 to 30 15.73 22.4841 0.833189
8 to 31 15.74 9.7574 0.086524
9 to 32 15.72 12.8950 0.256812
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.545878
Tough bday spacings test for dh-ranFile-2018-06-19_13:31: 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 7 31 72 91 109 81 57 40 7 3 2
(O-E)^2/E 0.5 0.9 0.0 0.5 1.3 0.1 0.5 3.5 4.2 2.0 1.0
Birthday Spacings: Sum(O-E)^2/E= 14.448, p= 0.846
RESULTS OF GCD FOR dh-ranFile-2018-06-19_13:31
Euclid's algorithm:
p-value, steps to gcd: 0.322442
p-value, dist. of gcd's: 0.416520
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-19_13:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.195 0.584 0.625 0.757 0.062 0.827 0.180 0.829
Bits 8 to 15---> 0.196 0.096 0.645 0.314 0.514 0.955 0.259 0.096
Bits 16 to 23---> 0.728 0.827 0.843 0.534 0.950 0.855 0.287 0.098
Bits 24 to 31---> 0.251 0.751 0.215 0.021 0.144 0.506 0.605 0.102
KS test for the above 32 p values: 0.463
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-19_13:31,
p-values for 5 runs: 0.1538, 0.4063, 0.6987, 0.7922, 0.0767
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-19_13:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 228 211.4 1.301 1.301
r= 29 5105 5134.0 0.164 1.464
r= 30 23086 23103.0 0.013 1.477
r= 31 11581 11551.5 0.075 1.552
chi-square = 1.552 with df = 3; p-value = 0.330
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-19_13:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 194 211.4 1.435 1.435
r= 30 5129 5134.0 0.005 1.440
r= 31 23156 23103.0 0.121 1.561
r= 32 11521 11551.5 0.081 1.642
chi-square = 1.642 with df = 3; p-value = 0.350
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-19_13:31
b-rank test for bits 1 to 8, p=0.39257
b-rank test for bits 2 to 9, p=0.18461
b-rank test for bits 3 to 10, p=0.06004
b-rank test for bits 4 to 11, p=0.43099
b-rank test for bits 5 to 12, p=0.50705
b-rank test for bits 6 to 13, p=0.21668
b-rank test for bits 7 to 14, p=0.39610
b-rank test for bits 8 to 15, p=0.71915
b-rank test for bits 9 to 16, p=0.17129
b-rank test for bits 10 to 17, p=0.33641
b-rank test for bits 11 to 18, p=0.58759
b-rank test for bits 12 to 19, p=0.75075
b-rank test for bits 13 to 20, p=0.78468
b-rank test for bits 14 to 21, p=0.23206
b-rank test for bits 15 to 22, p=0.83602
b-rank test for bits 16 to 23, p=0.34367
b-rank test for bits 17 to 24, p=0.46598
b-rank test for bits 18 to 25, p=0.50635
b-rank test for bits 19 to 26, p=0.51320
b-rank test for bits 20 to 27, p=0.39207
b-rank test for bits 21 to 28, p=0.97097
b-rank test for bits 22 to 29, p=0.39906
b-rank test for bits 23 to 30, p=0.47201
b-rank test for bits 24 to 31, p=0.57188
b-rank test for bits 25 to 32, p=0.24692
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 = 0.214901
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-19_13:31
(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 141939 0.07 0.527634
2 142376 1.09 0.862221
3 142135 0.53 0.700996
4 142434 1.23 0.889875
5 141574 -0.78 0.216672
6 142212 0.71 0.760271
7 141624 -0.67 0.252495
8 142754 1.97 0.975782
9 141981 0.17 0.566493
10 142237 0.77 0.778038
11 141960 0.12 0.547120
12 142233 0.76 0.775247
13 141755 -0.36 0.359205
14 141750 -0.37 0.354847
15 141609 -0.70 0.241431
16 142593 1.60 0.944907
17 141711 -0.46 0.321543
18 140801 -2.59 0.004805
19 142196 0.67 0.748504
20 141320 -1.38 0.084266
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-19_13:31
Bits used No. missing words z-score p-value
23 to 32 141654 -0.8804 0.189308
22 to 31 141657 -0.8701 0.192122
21 to 30 141679 -0.7942 0.213528
20 to 29 141692 -0.7494 0.226804
19 to 28 141529 -1.3115 0.094847
18 to 27 142287 1.3023 0.903595
17 to 26 142067 0.5437 0.706673
16 to 25 142373 1.5989 0.945074
15 to 24 142336 1.4713 0.929392
14 to 23 142055 0.5023 0.692275
13 to 22 141895 -0.0494 0.480295
12 to 21 142522 2.1127 0.982685
11 to 20 141853 -0.1942 0.422994
10 to 19 141900 -0.0322 0.487167
9 to 18 141772 -0.4736 0.317910
8 to 17 141738 -0.5908 0.277330
7 to 16 141719 -0.6563 0.255812
6 to 15 142121 0.7299 0.767273
5 to 14 142135 0.7782 0.781766
4 to 13 141886 -0.0804 0.467940
3 to 12 142388 1.6506 0.950588
2 to 11 142051 0.4885 0.687408
1 to 10 142042 0.4575 0.676338
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-19_13:31
Bits used No. missing words z-score p-value
28 to 32 142067 0.5345 0.703493
27 to 31 141661 -0.8418 0.199951
26 to 30 141702 -0.7028 0.241086
25 to 29 141764 -0.4926 0.311132
24 to 28 142602 2.3480 0.990564
23 to 27 141673 -0.8011 0.211532
22 to 26 141891 -0.0621 0.475227
21 to 25 142054 0.4904 0.688077
20 to 24 141779 -0.4418 0.329318
19 to 23 142063 0.5209 0.698787
18 to 22 141967 0.1955 0.577496
17 to 21 142038 0.4362 0.668643
16 to 20 142068 0.5379 0.704665
15 to 19 141966 0.1921 0.576169
14 to 18 142079 0.5752 0.717406
13 to 17 141911 0.0057 0.502258
12 to 16 142122 0.7209 0.764519
11 to 15 141640 -0.9130 0.180626
10 to 14 141779 -0.4418 0.329318
9 to 13 141746 -0.5537 0.289905
8 to 12 141531 -1.2825 0.099838
7 to 11 141824 -0.2893 0.386193
6 to 10 142222 1.0599 0.855405
5 to 9 141904 -0.0181 0.492792
4 to 8 142094 0.6260 0.734343
3 to 7 141861 -0.1638 0.434932
2 to 6 142197 0.9752 0.835258
1 to 5 141951 0.1413 0.556166
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-19_13:31
Bits used No. missing words z-score p-value
31 to 32 142584 1.9902 0.976714
30 to 31 142030 0.3560 0.639064
29 to 30 142820 2.6863 0.996388
28 to 29 142110 0.5919 0.723057
27 to 28 141965 0.1642 0.565220
26 to 27 142382 1.3943 0.918388
25 to 26 142070 0.4740 0.682233
24 to 25 141962 0.1554 0.561735
23 to 24 142105 0.5772 0.718097
22 to 23 142360 1.3294 0.908144
21 to 22 141823 -0.2547 0.399493
20 to 21 141704 -0.6057 0.272359
19 to 20 141929 0.0580 0.523135
18 to 19 142150 0.7099 0.761130
17 to 18 141851 -0.1721 0.431693
16 to 17 141684 -0.6647 0.253124
15 to 16 141704 -0.6057 0.272359
14 to 15 141925 0.0462 0.518434
13 to 14 141591 -0.9390 0.173859
12 to 13 141846 -0.1868 0.425903
11 to 12 141630 -0.8240 0.204975
10 to 11 142417 1.4976 0.932875
9 to 10 141035 -2.5791 0.004952
8 to 9 141877 -0.0954 0.462011
7 to 8 142373 1.3678 0.914306
6 to 7 141733 -0.5201 0.301480
5 to 6 142207 0.8781 0.810051
4 to 5 141679 -0.6794 0.248430
3 to 4 142470 1.6539 0.950925
2 to 3 142338 1.2645 0.896977
1 to 2 141724 -0.5467 0.292294
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-19_13:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2426.68 -1.037 0.149899
Test results for specific bytes for dh-ranFile-2018-06-19_13:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2406.69 -1.320 0.093482
2 to 9 2605.62 1.494 0.932374
3 to 10 2484.66 -0.217 0.414149
4 to 11 2452.81 -0.667 0.252279
5 to 12 2469.02 -0.438 0.330670
6 to 13 2526.99 0.382 0.648644
7 to 14 2576.06 1.076 0.858952
8 to 15 2428.19 -1.016 0.154908
9 to 16 2602.30 1.447 0.926019
10 to 17 2556.98 0.806 0.789822
11 to 18 2510.85 0.153 0.560960
12 to 19 2480.76 -0.272 0.392785
13 to 20 2553.35 0.754 0.774705
14 to 21 2463.40 -0.518 0.302368
15 to 22 2519.69 0.278 0.609666
16 to 23 2552.30 0.740 0.770256
17 to 24 2519.91 0.282 0.610868
18 to 25 2382.34 -1.664 0.048063
19 to 26 2456.94 -0.609 0.271284
20 to 27 2475.80 -0.342 0.366068
21 to 28 2481.94 -0.255 0.399196
22 to 29 2498.96 -0.015 0.494138
23 to 30 2404.56 -1.350 0.088551
24 to 31 2358.02 -2.008 0.022330
25 to 32 2518.37 0.260 0.602472
CDPARK for dh-ranFile-2018-06-19_13:31: 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
3510 -0.5936 0.276387
3533 0.4566 0.676028
3562 1.7808 0.962529
3523 0.0000 0.500000
3496 -1.2329 0.108811
3517 -0.2740 0.392053
3499 -1.0959 0.136563
3487 -1.6438 0.050105
3538 0.6849 0.753306
Square side=100, avg. no. parked=3516.10 sample std.=22.15
p-value of the KSTEST for those 10 p-values: 0.381459
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-19_13:31
0.8320,0.3965,0.0612,0.0754,0.1952,0.5930,0.3161,0.1617,0.4248,0.3652,
The KS test for those 10 p-values: 0.137938
The 3DSPHERES test for dh-ranFile-2018-06-19_13:31
sample no r^3 equiv. uni.
1 141.455 0.991042
2 14.147 0.375981
3 40.951 0.744628
4 78.025 0.925788
5 7.565 0.222882
6 35.206 0.690723
7 10.987 0.306660
8 14.955 0.392568
9 30.644 0.639929
10 57.708 0.853918
11 0.665 0.021909
12 28.752 0.616494
13 50.410 0.813687
14 15.776 0.408965
15 30.527 0.638526
16 6.930 0.206265
17 61.399 0.870830
18 70.998 0.906200
19 5.750 0.174430
20 35.523 0.693983
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.446580
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-19_13:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 1.8 1.1 -1.3 0.2 -1.0
0.7 -1.5 1.1 0.3 0.5 -0.0
0.1 0.5 -0.8 0.7 0.9 0.7
0.9 -1.2 -0.6 1.0 -0.6 -1.0
1.2 0.5 -0.2 -1.3 -2.4 0.1
-2.1 -2.9 -0.4 0.2 -0.6 -0.8
-0.2 -0.7 0.1 1.0 -0.6 0.0
-0.1
Chi-square with 42 degrees of freedom:45.161933
z-score=0.344995, p-value=0.658758
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-19_13:31
Test no p-value
1 0.489645
2 0.041153
3 0.224820
4 0.704598
5 0.053921
6 0.378820
7 0.043139
8 0.946368
9 0.958599
10 0.823348
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.378089
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-19_13:31:
(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 66550 0.20 66800 0.27
3 25000.00 25104 0.43 24876 0.62
4 6666.67 6770 1.60 6623 0.29
5 1388.89 1308 4.71 1428 1.10
6 238.10 234 0.07 228 0.43
7 34.72 31 0.40 40 0.80
8 4.96 2 1.77 4 0.19
p=0.83656 p=0.28090
Number of rngs required: 688192, p-value: 0.404
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-19_13:31
No. of wins: Observed Expected
98295 98585.9
z-score=-1.301, pvalue=0.09665
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66526 66666.7 0.297 0.297
2 37726 37654.3 0.136 0.433
3 26956 26954.7 0.000 0.433
4 19529 19313.5 2.405 2.839
5 13661 13851.4 2.618 5.456
6 10044 9943.5 1.015 6.471
7 7055 7145.0 1.134 7.606
8 5233 5139.1 1.717 9.322
9 3647 3699.9 0.755 10.078
10 2675 2666.3 0.028 10.106
11 1929 1923.3 0.017 10.123
12 1370 1388.7 0.253 10.376
13 1016 1003.7 0.150 10.526
14 725 726.1 0.002 10.528
15 568 525.8 3.381 13.909
16 364 381.2 0.772 14.681
17 272 276.5 0.075 14.755
18 200 200.8 0.003 14.759
19 127 146.0 2.469 17.227
20 121 106.2 2.058 19.285
21 256 287.1 3.372 22.657
Chisq= 22.66 for 20 degrees of freedom, p= 0.69406
SUMMARY of craptest
p-value for no. of wins: 0.096648
p-value for throws/game: 0.694056
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-19_13:31
No. of wins: Observed Expected
98254 98585.9
z-score=-1.484, pvalue=0.06887
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66299 66666.7 2.028 2.028
2 37784 37654.3 0.447 2.474
3 26999 26954.7 0.073 2.547
4 19300 19313.5 0.009 2.556
5 13949 13851.4 0.687 3.244
6 9989 9943.5 0.208 3.452
7 7180 7145.0 0.171 3.623
8 5077 5139.1 0.750 4.373
9 3706 3699.9 0.010 4.383
10 2686 2666.3 0.146 4.528
11 1891 1923.3 0.543 5.072
12 1418 1388.7 0.616 5.688
13 1057 1003.7 2.829 8.517
14 691 726.1 1.701 10.218
15 591 525.8 8.075 18.293
16 351 381.2 2.385 20.678
17 259 276.5 1.112 21.790
18 203 200.8 0.023 21.814
19 159 146.0 1.160 22.974
20 123 106.2 2.652 25.627
21 288 287.1 0.003 25.630
Chisq= 25.63 for 20 degrees of freedom, p= 0.82160
SUMMARY of craptest
p-value for no. of wins: 0.068869
p-value for throws/game: 0.821602
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0048,0.0050,0.0208,0.0219,0.0223,0.0412,0.0431,0.0481,0.0501,0.0539,
0.0600,0.0612,0.0618,0.0689,0.0754,0.0767,0.0843,0.0865,0.0886,0.0935,
0.0948,0.0958,0.0962,0.0966,0.0980,0.0998,0.1020,0.1088,0.1088,0.1366,
0.1379,0.1437,0.1499,0.1538,0.1549,0.1617,0.1620,0.1713,0.1739,0.1744,
0.1796,0.1806,0.1846,0.1893,0.1921,0.1952,0.1952,0.1965,0.2000,0.2050,
0.2063,0.2115,0.2135,0.2149,0.2153,0.2167,0.2167,0.2229,0.2248,0.2268,
0.2321,0.2411,0.2414,0.2469,0.2484,0.2514,0.2523,0.2525,0.2531,0.2558,
0.2568,0.2587,0.2713,0.2724,0.2724,0.2764,0.2773,0.2809,0.2866,0.2899,
0.2923,0.3015,0.3024,0.3067,0.3111,0.3142,0.3161,0.3179,0.3215,0.3224,
0.3293,0.3293,0.3297,0.3307,0.3364,0.3437,0.3501,0.3548,0.3592,0.3652,
0.3661,0.3760,0.3781,0.3788,0.3815,0.3862,0.3921,0.3921,0.3926,0.3926,
0.3928,0.3961,0.3965,0.3991,0.3992,0.3995,0.4041,0.4063,0.4090,0.4141,
0.4160,0.4165,0.4196,0.4230,0.4248,0.4259,0.4310,0.4317,0.4349,0.4466,
0.4620,0.4629,0.4660,0.4679,0.4720,0.4752,0.4803,0.4872,0.4896,0.4928,
0.4941,0.5000,0.5023,0.5060,0.5064,0.5070,0.5132,0.5139,0.5184,0.5231,
0.5276,0.5342,0.5459,0.5471,0.5562,0.5610,0.5617,0.5652,0.5665,0.5719,
0.5762,0.5775,0.5844,0.5876,0.5930,0.6025,0.6048,0.6097,0.6109,0.6165,
0.6250,0.6385,0.6391,0.6399,0.6448,0.6486,0.6588,0.6686,0.6760,0.6763,
0.6822,0.6874,0.6881,0.6907,0.6923,0.6940,0.6941,0.6987,0.6988,0.7010,
0.7035,0.7046,0.7047,0.7067,0.7174,0.7181,0.7191,0.7231,0.7280,0.7343,
0.7446,0.7485,0.7506,0.7508,0.7533,0.7574,0.7603,0.7611,0.7645,0.7673,
0.7703,0.7747,0.7752,0.7780,0.7818,0.7847,0.7898,0.7922,0.8101,0.8137,
0.8216,0.8233,0.8266,0.8273,0.8287,0.8320,0.8332,0.8353,0.8360,0.8366,
0.8426,0.8465,0.8539,0.8551,0.8554,0.8570,0.8590,0.8622,0.8708,0.8899,
0.8970,0.9036,0.9062,0.9081,0.9143,0.9184,0.9258,0.9260,0.9294,0.9324,
0.9329,0.9449,0.9451,0.9464,0.9464,0.9500,0.9506,0.9509,0.9547,0.9586,
0.9625,0.9710,0.9710,0.9758,0.9767,0.9827,0.9906,0.9910,0.9964,
Overall p-value after applying KStest on 269 p-values = 0.711023
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.