RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-24_21:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.68 15.8680 0.466786
2 to 25 15.55 15.6270 0.449584
3 to 26 15.82 19.5901 0.704269
4 to 27 16.09 20.0019 0.725869
5 to 28 15.91 18.1962 0.623435
6 to 29 15.73 26.5990 0.935782
7 to 30 15.71 19.2131 0.683560
8 to 31 15.75 17.4907 0.578370
9 to 32 15.69 12.9064 0.257569
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.276764
Tough bday spacings test for dh-ranFile-2018-06-24_21:31: 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 43 72 87 111 77 39 25 19 4 14
(O-E)^2/E 0.0 1.1 0.0 1.2 1.8 0.0 3.3 0.8 1.1 1.0 24.3
Birthday Spacings: Sum(O-E)^2/E= 34.631, p= 1.000
RESULTS OF GCD FOR dh-ranFile-2018-06-24_21:31
Euclid's algorithm:
p-value, steps to gcd: 0.637388
p-value, dist. of gcd's: 0.849501
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-24_21:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.631 0.313 0.508 0.382 0.014 0.344 0.065 0.739
Bits 8 to 15---> 0.683 0.650 0.273 0.017 0.467 0.048 0.893 0.117
Bits 16 to 23---> 0.850 0.124 0.548 0.230 0.236 0.920 0.014 0.107
Bits 24 to 31---> 0.616 0.516 0.812 0.261 0.441 0.361 0.422 0.031
KS test for the above 32 p values: 0.950
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-24_21:31,
p-values for 5 runs: 0.4781, 0.4604, 0.7489, 0.2296, 0.0476
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-24_21:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 245 211.4 5.334 5.334
r= 29 5154 5134.0 0.078 5.412
r= 30 23024 23103.0 0.270 5.683
r= 31 11577 11551.5 0.056 5.739
chi-square = 5.739 with df = 3; p-value = 0.875
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-24_21:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 224 211.4 0.749 0.749
r= 30 5019 5134.0 2.576 3.325
r= 31 23243 23103.0 0.848 4.173
r= 32 11514 11551.5 0.122 4.295
chi-square = 4.295 with df = 3; p-value = 0.769
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-24_21:31
b-rank test for bits 1 to 8, p=0.79925
b-rank test for bits 2 to 9, p=0.82223
b-rank test for bits 3 to 10, p=0.26196
b-rank test for bits 4 to 11, p=0.72864
b-rank test for bits 5 to 12, p=0.21366
b-rank test for bits 6 to 13, p=0.35861
b-rank test for bits 7 to 14, p=0.44481
b-rank test for bits 8 to 15, p=0.70195
b-rank test for bits 9 to 16, p=0.69550
b-rank test for bits 10 to 17, p=0.57591
b-rank test for bits 11 to 18, p=0.96464
b-rank test for bits 12 to 19, p=0.45189
b-rank test for bits 13 to 20, p=0.75710
b-rank test for bits 14 to 21, p=0.83155
b-rank test for bits 15 to 22, p=0.09267
b-rank test for bits 16 to 23, p=0.78184
b-rank test for bits 17 to 24, p=0.03210
b-rank test for bits 18 to 25, p=0.55137
b-rank test for bits 19 to 26, p=0.01908
b-rank test for bits 20 to 27, p=0.97029
b-rank test for bits 21 to 28, p=0.78828
b-rank test for bits 22 to 29, p=0.63203
b-rank test for bits 23 to 30, p=0.88677
b-rank test for bits 24 to 31, p=0.00988
b-rank test for bits 25 to 32, p=0.87198
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 = 0.198602
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-24_21:31
(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 141943 0.08 0.531352
2 141776 -0.31 0.377703
3 141742 -0.39 0.347914
4 142400 1.15 0.874190
5 141373 -1.25 0.105083
6 142073 0.38 0.648920
7 142999 2.55 0.994551
8 141576 -0.78 0.218046
9 141595 -0.73 0.231348
10 142450 1.26 0.896750
11 141971 0.14 0.557285
12 141287 -1.45 0.072967
13 141813 -0.23 0.410962
14 142884 2.28 0.988615
15 142594 1.60 0.945167
16 142136 0.53 0.701806
17 141494 -0.97 0.165924
18 142154 0.57 0.716223
19 141418 -1.15 0.125491
20 142258 0.81 0.792364
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-24_21:31
Bits used No. missing words z-score p-value
23 to 32 141629 -0.9667 0.166858
22 to 31 142008 0.3402 0.633163
21 to 30 141849 -0.2080 0.417601
20 to 29 142482 1.9747 0.975850
19 to 28 141807 -0.3529 0.362096
18 to 27 142403 1.7023 0.955651
17 to 26 141911 0.0058 0.502297
16 to 25 142325 1.4333 0.924120
15 to 24 142323 1.4264 0.923131
14 to 23 141801 -0.3736 0.354369
13 to 22 142229 1.1023 0.864837
12 to 21 141902 -0.0253 0.489918
11 to 20 142147 0.8196 0.793764
10 to 19 142228 1.0989 0.864086
9 to 18 142233 1.1161 0.867811
8 to 17 141669 -0.8287 0.203630
7 to 16 142260 1.2092 0.886708
6 to 15 142393 1.6678 0.952325
5 to 14 141783 -0.4356 0.331556
4 to 13 141457 -1.5598 0.059408
3 to 12 141511 -1.3736 0.084790
2 to 11 141589 -1.1046 0.134669
1 to 10 142011 0.3506 0.637051
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-24_21:31
Bits used No. missing words z-score p-value
28 to 32 142053 0.4870 0.686877
27 to 31 142083 0.5887 0.721973
26 to 30 141686 -0.7571 0.224510
25 to 29 141682 -0.7706 0.220469
24 to 28 142750 2.8497 0.997812
23 to 27 141969 0.2023 0.580148
22 to 26 141921 0.0396 0.515778
21 to 25 141867 -0.1435 0.442951
20 to 24 141502 -1.3808 0.083673
19 to 23 141696 -0.7232 0.234793
18 to 22 142447 1.8226 0.965819
17 to 21 142113 0.6904 0.755031
16 to 20 141954 0.1514 0.560179
15 to 19 142054 0.4904 0.688077
14 to 18 141775 -0.4554 0.324427
13 to 17 142021 0.3785 0.647486
12 to 16 142223 1.0633 0.856174
11 to 15 141839 -0.2384 0.405783
10 to 14 141602 -1.0418 0.148753
9 to 13 141741 -0.5706 0.284132
8 to 12 141866 -0.1469 0.441613
7 to 11 142544 2.1514 0.984279
6 to 10 142033 0.4192 0.662473
5 to 9 141406 -1.7062 0.043985
4 to 8 141485 -1.4384 0.075159
3 to 7 142288 1.2836 0.900364
2 to 6 141716 -0.6554 0.256119
1 to 5 141615 -0.9977 0.159205
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-24_21:31
Bits used No. missing words z-score p-value
31 to 32 141796 -0.3343 0.369074
30 to 31 142207 0.8781 0.810051
29 to 30 141812 -0.2871 0.387014
28 to 29 141710 -0.5880 0.278268
27 to 28 141950 0.1200 0.547747
26 to 27 141500 -1.2075 0.113627
25 to 26 142002 0.2734 0.607713
24 to 25 141248 -1.9508 0.025539
23 to 24 142036 0.3737 0.645671
22 to 23 142324 1.2232 0.889376
21 to 22 142095 0.5477 0.708051
20 to 21 141827 -0.2429 0.404056
19 to 20 142207 0.8781 0.810051
18 to 19 141688 -0.6529 0.256913
17 to 18 141475 -1.2812 0.100060
16 to 17 141889 -0.0600 0.476090
15 to 16 142300 1.1524 0.875426
14 to 15 141900 -0.0275 0.489022
13 to 14 141603 -0.9036 0.183096
12 to 13 142642 2.1613 0.984663
11 to 12 142427 1.5271 0.936626
10 to 11 142009 0.2940 0.615626
9 to 10 142143 0.6893 0.754680
8 to 9 141741 -0.4965 0.309754
7 to 8 142408 1.4710 0.929355
6 to 7 141517 -1.1573 0.123572
5 to 6 142126 0.6391 0.738636
4 to 5 141900 -0.0275 0.489022
3 to 4 141566 -1.0128 0.155584
2 to 3 141652 -0.7591 0.223901
1 to 2 142355 1.3147 0.905688
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-24_21:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2529.85 0.422 0.663540
Test results for specific bytes for dh-ranFile-2018-06-24_21:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2425.54 -1.053 0.146165
2 to 9 2498.68 -0.019 0.492552
3 to 10 2571.24 1.007 0.843148
4 to 11 2581.60 1.154 0.875739
5 to 12 2506.69 0.095 0.537669
6 to 13 2476.72 -0.329 0.370970
7 to 14 2524.72 0.350 0.636696
8 to 15 2640.32 1.984 0.976393
9 to 16 2572.68 1.028 0.848004
10 to 17 2604.90 1.484 0.931038
11 to 18 2520.73 0.293 0.615290
12 to 19 2615.28 1.630 0.948476
13 to 20 2507.43 0.105 0.541861
14 to 21 2636.48 1.930 0.973200
15 to 22 2520.71 0.293 0.615201
16 to 23 2587.12 1.232 0.891029
17 to 24 2408.26 -1.297 0.097249
18 to 25 2526.21 0.371 0.644577
19 to 26 2564.46 0.912 0.819027
20 to 27 2521.65 0.306 0.620243
21 to 28 2563.10 0.892 0.813892
22 to 29 2490.69 -0.132 0.447601
23 to 30 2580.75 1.142 0.873274
24 to 31 2553.84 0.761 0.776805
25 to 32 2411.49 -1.252 0.105340
CDPARK for dh-ranFile-2018-06-24_21:31: 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
3511 -0.5479 0.291865
3521 -0.0913 0.463617
3545 1.0046 0.842447
3543 0.9132 0.819442
3532 0.4110 0.659449
3572 2.2374 0.987371
3542 0.8676 0.807188
3525 0.0913 0.536383
3514 -0.4110 0.340551
3581 2.6484 0.995956
Square side=100, avg. no. parked=3538.60 sample std.=22.11
p-value of the KSTEST for those 10 p-values: 0.057975
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-24_21:31
0.3549,0.1787,0.8081,0.7698,0.0527,0.7309,0.3055,0.8684,0.7259,0.7879,
The KS test for those 10 p-values: 0.517562
The 3DSPHERES test for dh-ranFile-2018-06-24_21:31
sample no r^3 equiv. uni.
1 79.163 0.928552
2 49.143 0.805653
3 1.938 0.062565
4 7.790 0.228699
5 2.846 0.090506
6 72.059 0.909462
7 0.984 0.032253
8 57.375 0.852291
9 15.501 0.403520
10 11.519 0.318841
11 1.747 0.056560
12 1.912 0.061741
13 16.526 0.423543
14 11.800 0.325187
15 2.382 0.076324
16 23.157 0.537864
17 80.634 0.931969
18 66.731 0.891863
19 33.059 0.667788
20 25.456 0.571956
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.304712
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-24_21:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 -1.2 0.8 0.3 1.3 -0.8
-0.3 1.3 0.5 0.8 0.3 -0.6
-1.3 -0.2 -0.6 -0.3 1.4 -0.3
-0.7 -0.7 0.1 -0.1 1.5 -0.2
0.6 -0.5 0.3 1.2 0.0 0.3
-1.8 1.0 0.5 -1.3 1.3 -0.8
1.9 0.2 0.5 -0.7 -1.3 0.0
-1.1
Chi-square with 42 degrees of freedom:35.022057
z-score=-0.761356, p-value=0.231392
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-24_21:31
Test no p-value
1 0.455947
2 0.275126
3 0.128812
4 0.416646
5 0.192022
6 0.964089
7 0.957475
8 0.063791
9 0.926253
10 0.615419
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.601386
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-24_21:31:
(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 66722 0.05 66701 0.02
3 25000.00 25020 0.02 25060 0.14
4 6666.67 6587 0.95 6642 0.09
5 1388.89 1400 0.09 1342 1.58
6 238.10 229 0.35 216 2.05
7 34.72 36 0.05 31 0.40
8 4.96 5 0.00 7 0.84
p=0.04036 p=0.47200
Number of rngs required: 688015, p-value: 0.327
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-24_21:31
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 66595 66666.7 0.077 0.077
2 37700 37654.3 0.055 0.132
3 26991 26954.7 0.049 0.181
4 19249 19313.5 0.215 0.396
5 13667 13851.4 2.455 2.852
6 10172 9943.5 5.249 8.101
7 7029 7145.0 1.884 9.985
8 5232 5139.1 1.680 11.665
9 3627 3699.9 1.435 13.100
10 2715 2666.3 0.890 13.990
11 1952 1923.3 0.427 14.417
12 1373 1388.7 0.178 14.596
13 1005 1003.7 0.002 14.597
14 697 726.1 1.169 15.767
15 542 525.8 0.497 16.264
16 384 381.2 0.021 16.285
17 279 276.5 0.022 16.307
18 240 200.8 7.640 23.947
19 160 146.0 1.346 25.292
20 106 106.2 0.000 25.293
21 285 287.1 0.016 25.308
Chisq= 25.31 for 20 degrees of freedom, p= 0.81010
SUMMARY of craptest
p-value for no. of wins: 0.448650
p-value for throws/game: 0.810104
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-24_21:31
No. of wins: Observed Expected
98554 98585.9
z-score=-0.142, pvalue=0.44335
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66518 66666.7 0.332 0.332
2 38048 37654.3 4.116 4.447
3 26813 26954.7 0.745 5.193
4 19392 19313.5 0.319 5.512
5 13809 13851.4 0.130 5.642
6 9942 9943.5 0.000 5.642
7 7077 7145.0 0.648 6.290
8 5189 5139.1 0.485 6.775
9 3775 3699.9 1.526 8.301
10 2629 2666.3 0.522 8.823
11 1881 1923.3 0.932 9.754
12 1310 1388.7 4.465 14.219
13 1073 1003.7 4.783 19.001
14 662 726.1 5.666 24.667
15 532 525.8 0.072 24.739
16 379 381.2 0.012 24.751
17 258 276.5 1.243 25.994
18 198 200.8 0.040 26.034
19 141 146.0 0.170 26.204
20 108 106.2 0.030 26.234
21 266 287.1 1.553 27.787
Chisq= 27.79 for 20 degrees of freedom, p= 0.88546
SUMMARY of craptest
p-value for no. of wins: 0.443346
p-value for throws/game: 0.885459
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0099,0.0141,0.0143,0.0166,0.0191,0.0255,0.0308,0.0321,0.0323,0.0404,
0.0440,0.0476,0.0485,0.0527,0.0566,0.0580,0.0594,0.0617,0.0626,0.0638,
0.0649,0.0730,0.0752,0.0763,0.0837,0.0848,0.0905,0.0927,0.0972,0.1001,
0.1051,0.1053,0.1071,0.1136,0.1173,0.1236,0.1240,0.1255,0.1288,0.1347,
0.1462,0.1488,0.1556,0.1592,0.1659,0.1669,0.1787,0.1831,0.1920,0.1986,
0.2036,0.2137,0.2180,0.2205,0.2239,0.2245,0.2287,0.2296,0.2297,0.2313,
0.2314,0.2348,0.2359,0.2561,0.2569,0.2576,0.2610,0.2620,0.2733,0.2751,
0.2768,0.2783,0.2841,0.2919,0.3047,0.3055,0.3098,0.3129,0.3188,0.3244,
0.3252,0.3274,0.3316,0.3406,0.3441,0.3479,0.3544,0.3549,0.3586,0.3610,
0.3621,0.3691,0.3710,0.3777,0.3816,0.3870,0.4035,0.4041,0.4058,0.4110,
0.4166,0.4176,0.4219,0.4235,0.4406,0.4416,0.4430,0.4433,0.4448,0.4476,
0.4487,0.4496,0.4519,0.4559,0.4604,0.4636,0.4667,0.4668,0.4720,0.4761,
0.4781,0.4890,0.4890,0.4899,0.4926,0.5023,0.5084,0.5156,0.5158,0.5176,
0.5314,0.5364,0.5377,0.5379,0.5419,0.5477,0.5479,0.5514,0.5573,0.5602,
0.5720,0.5759,0.5784,0.5801,0.6014,0.6077,0.6152,0.6153,0.6154,0.6156,
0.6157,0.6202,0.6234,0.6310,0.6320,0.6332,0.6367,0.6371,0.6374,0.6446,
0.6457,0.6475,0.6489,0.6500,0.6594,0.6625,0.6635,0.6678,0.6830,0.6836,
0.6869,0.6881,0.6955,0.7018,0.7019,0.7043,0.7081,0.7162,0.7220,0.7259,
0.7259,0.7286,0.7309,0.7386,0.7388,0.7489,0.7547,0.7550,0.7571,0.7687,
0.7698,0.7768,0.7818,0.7879,0.7883,0.7924,0.7938,0.7993,0.8057,0.8072,
0.8081,0.8101,0.8101,0.8101,0.8123,0.8139,0.8190,0.8194,0.8222,0.8315,
0.8424,0.8431,0.8480,0.8495,0.8503,0.8523,0.8562,0.8641,0.8648,0.8678,
0.8684,0.8720,0.8733,0.8742,0.8750,0.8754,0.8757,0.8855,0.8867,0.8868,
0.8894,0.8910,0.8919,0.8932,0.8967,0.9004,0.9057,0.9095,0.9197,0.9231,
0.9241,0.9263,0.9286,0.9294,0.9310,0.9320,0.9358,0.9366,0.9452,0.9485,
0.9499,0.9523,0.9557,0.9575,0.9641,0.9646,0.9658,0.9703,0.9732,0.9759,
0.9764,0.9843,0.9847,0.9874,0.9886,0.9946,0.9960,0.9978,0.9999,
Overall p-value after applying KStest on 269 p-values = 0.073288
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.