RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-28_04:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.91 24.0944 0.883107
2 to 25 15.60 22.8352 0.845307
3 to 26 15.78 18.5448 0.644725
4 to 27 15.73 16.7634 0.529498
5 to 28 15.58 17.5683 0.583452
6 to 29 16.00 18.1920 0.623172
7 to 30 15.77 24.7246 0.898954
8 to 31 15.70 11.7096 0.182605
9 to 32 15.73 14.6497 0.379301
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.323421
Tough bday spacings test for dh-ranFile-2018-06-28_04:31: 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 8 36 58 92 110 72 62 30 20 7 5
(O-E)^2/E 0.1 0.0 3.2 0.3 1.6 0.5 1.9 0.0 1.8 0.0 0.2
Birthday Spacings: Sum(O-E)^2/E= 9.582, p= 0.522
RESULTS OF GCD FOR dh-ranFile-2018-06-28_04:31
Euclid's algorithm:
p-value, steps to gcd: 0.297859
p-value, dist. of gcd's: 0.857977
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-28_04:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.423 0.704 0.861 0.159 0.944 0.541 0.407 0.814
Bits 8 to 15---> 0.943 0.797 0.890 0.533 0.362 0.900 0.584 0.148
Bits 16 to 23---> 0.710 0.085 0.596 0.541 0.448 0.666 0.248 0.785
Bits 24 to 31---> 0.438 0.537 0.805 0.569 0.861 0.918 0.604 0.523
KS test for the above 32 p values: 0.955
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-28_04:31,
p-values for 5 runs: 0.2857, 0.1719, 0.4719, 0.3202, 0.1769
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-28_04:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 214 211.4 0.032 0.032
r= 29 5076 5134.0 0.655 0.687
r= 30 23087 23103.0 0.011 0.698
r= 31 11623 11551.5 0.442 1.140
chi-square = 1.140 with df = 3; p-value = 0.233
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-28_04:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 197 211.4 0.983 0.983
r= 30 5130 5134.0 0.003 0.986
r= 31 23064 23103.0 0.066 1.052
r= 32 11609 11551.5 0.286 1.338
chi-square = 1.338 with df = 3; p-value = 0.280
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-28_04:31
b-rank test for bits 1 to 8, p=0.57703
b-rank test for bits 2 to 9, p=0.32133
b-rank test for bits 3 to 10, p=0.85472
b-rank test for bits 4 to 11, p=0.45519
b-rank test for bits 5 to 12, p=0.37105
b-rank test for bits 6 to 13, p=0.27966
b-rank test for bits 7 to 14, p=0.97727
b-rank test for bits 8 to 15, p=0.86239
b-rank test for bits 9 to 16, p=0.18866
b-rank test for bits 10 to 17, p=0.40780
b-rank test for bits 11 to 18, p=0.12360
b-rank test for bits 12 to 19, p=0.30036
b-rank test for bits 13 to 20, p=0.12434
b-rank test for bits 14 to 21, p=0.40292
b-rank test for bits 15 to 22, p=0.09676
b-rank test for bits 16 to 23, p=0.15296
b-rank test for bits 17 to 24, p=0.80489
b-rank test for bits 18 to 25, p=0.74575
b-rank test for bits 19 to 26, p=0.95466
b-rank test for bits 20 to 27, p=0.59205
b-rank test for bits 21 to 28, p=0.68342
b-rank test for bits 22 to 29, p=0.47474
b-rank test for bits 23 to 30, p=0.90655
b-rank test for bits 24 to 31, p=0.74569
b-rank test for bits 25 to 32, p=0.52975
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 = 0.964973
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-28_04:31
(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 142174 0.62 0.731840
2 142355 1.04 0.851128
3 141656 -0.59 0.276961
4 141643 -0.62 0.266883
5 141385 -1.23 0.110274
6 142307 0.93 0.823591
7 141829 -0.19 0.425561
8 142070 0.38 0.646317
9 141450 -1.07 0.141591
10 142173 0.62 0.731070
11 141630 -0.65 0.256994
12 141645 -0.62 0.268422
13 141771 -0.32 0.373272
14 141582 -0.76 0.222198
15 142011 0.24 0.593884
16 142311 0.94 0.826001
17 141457 -1.06 0.145291
18 141853 -0.13 0.447646
19 141903 -0.01 0.494100
20 141672 -0.55 0.289615
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-28_04:31
Bits used No. missing words z-score p-value
23 to 32 141753 -0.5391 0.294920
22 to 31 141533 -1.2977 0.097197
21 to 30 141878 -0.1080 0.456984
20 to 29 141684 -0.7770 0.218579
19 to 28 141814 -0.3287 0.371182
18 to 27 141486 -1.4598 0.072178
17 to 26 141943 0.1161 0.546215
16 to 25 141978 0.2368 0.593591
15 to 24 141502 -1.4046 0.080072
14 to 23 141969 0.2058 0.581510
13 to 22 141899 -0.0356 0.485792
12 to 21 141457 -1.5598 0.059408
11 to 20 141560 -1.2046 0.114182
10 to 19 142648 2.5471 0.994569
9 to 18 141783 -0.4356 0.331556
8 to 17 141871 -0.1322 0.447424
7 to 16 141409 -1.7253 0.042239
6 to 15 141452 -1.5770 0.057398
5 to 14 142227 1.0954 0.863332
4 to 13 142557 2.2333 0.987237
3 to 12 141920 0.0368 0.514675
2 to 11 141821 -0.3046 0.380341
1 to 10 141825 -0.2908 0.385605
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-28_04:31
Bits used No. missing words z-score p-value
28 to 32 142329 1.4226 0.922575
27 to 31 141540 -1.2520 0.105291
26 to 30 141788 -0.4113 0.340431
25 to 29 141204 -2.3909 0.008402
24 to 28 142202 0.9921 0.839426
23 to 27 142128 0.7413 0.770730
22 to 26 141855 -0.1842 0.426940
21 to 25 141708 -0.6825 0.247470
20 to 24 141885 -0.0825 0.467135
19 to 23 142125 0.7311 0.767636
18 to 22 141507 -1.3638 0.086310
17 to 21 141839 -0.2384 0.405783
16 to 20 141695 -0.7265 0.233753
15 to 19 141853 -0.1909 0.424283
14 to 18 142178 0.9107 0.818785
13 to 17 142106 0.6667 0.747511
12 to 16 141622 -0.9740 0.165028
11 to 15 141675 -0.7943 0.213499
10 to 14 142058 0.5040 0.692857
9 to 13 141574 -1.1367 0.127829
8 to 12 141916 0.0226 0.509019
7 to 11 142126 0.7345 0.768670
6 to 10 142331 1.4294 0.923554
5 to 9 142302 1.3311 0.908419
4 to 8 142190 0.9514 0.829305
3 to 7 141744 -0.5604 0.287589
2 to 6 141642 -0.9062 0.182414
1 to 5 142196 0.9718 0.834416
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-28_04:31
Bits used No. missing words z-score p-value
31 to 32 142000 0.2675 0.605444
30 to 31 141300 -1.7974 0.036133
29 to 30 141610 -0.8830 0.188624
28 to 29 141526 -1.1308 0.129077
27 to 28 141917 0.0226 0.509025
26 to 27 141926 0.0492 0.519610
25 to 26 141491 -1.2340 0.108599
24 to 25 141367 -1.5998 0.054822
23 to 24 141570 -1.0010 0.158420
22 to 23 142264 1.0462 0.852271
21 to 22 141513 -1.1691 0.121179
20 to 21 142166 0.7571 0.775517
19 to 20 141757 -0.4494 0.326589
18 to 19 141869 -0.1190 0.452651
17 to 18 141576 -0.9833 0.162736
16 to 17 141817 -0.2724 0.392673
15 to 16 141893 -0.0482 0.480790
14 to 15 141760 -0.4405 0.329787
13 to 14 142251 1.0079 0.843243
12 to 13 142137 0.6716 0.749079
11 to 12 141372 -1.5850 0.056478
10 to 11 141438 -1.3904 0.082211
9 to 10 141270 -1.8859 0.029652
8 to 9 141285 -1.8417 0.032761
7 to 8 142304 1.1642 0.877832
6 to 7 142730 2.4209 0.992258
5 to 6 141862 -0.1396 0.444482
4 to 5 141851 -0.1721 0.431693
3 to 4 142206 0.8751 0.809249
2 to 3 142143 0.6893 0.754680
1 to 2 142356 1.3176 0.906183
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-28_04:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2420.62 -1.123 0.130801
Test results for specific bytes for dh-ranFile-2018-06-28_04:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2588.53 1.252 0.894716
2 to 9 2413.39 -1.225 0.110316
3 to 10 2426.01 -1.046 0.147703
4 to 11 2440.43 -0.842 0.199788
5 to 12 2526.55 0.375 0.646337
6 to 13 2549.90 0.706 0.759789
7 to 14 2559.34 0.839 0.799300
8 to 15 2541.56 0.588 0.721659
9 to 16 2516.27 0.230 0.590982
10 to 17 2521.47 0.304 0.619297
11 to 18 2404.33 -1.353 0.088026
12 to 19 2453.55 -0.657 0.255606
13 to 20 2385.74 -1.616 0.053059
14 to 21 2407.15 -1.313 0.094580
15 to 22 2517.73 0.251 0.598981
16 to 23 2582.59 1.168 0.878589
17 to 24 2566.71 0.943 0.827251
18 to 25 2493.06 -0.098 0.460886
19 to 26 2491.52 -0.120 0.452272
20 to 27 2471.42 -0.404 0.343039
21 to 28 2445.91 -0.765 0.222151
22 to 29 2495.14 -0.069 0.472627
23 to 30 2484.15 -0.224 0.411342
24 to 31 2505.62 0.079 0.531677
25 to 32 2546.21 0.654 0.743297
CDPARK for dh-ranFile-2018-06-28_04:31: 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
3499 -1.0959 0.136563
3530 0.3196 0.625377
3531 0.3653 0.642555
3490 -1.5068 0.065925
3507 -0.7306 0.232514
3558 1.5982 0.944998
3500 -1.0502 0.146807
3501 -1.0046 0.157553
3556 1.5068 0.934075
3527 0.1826 0.572463
Square side=100, avg. no. parked=3519.90 sample std.=22.98
p-value of the KSTEST for those 10 p-values: 0.518977
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-28_04:31
0.4045,0.2777,0.4259,0.7425,0.8047,0.9074,0.8707,0.8087,0.8564,0.2172,
The KS test for those 10 p-values: 0.180778
The 3DSPHERES test for dh-ranFile-2018-06-28_04:31
sample no r^3 equiv. uni.
1 2.820 0.089720
2 6.664 0.199193
3 12.968 0.350963
4 12.624 0.343471
5 36.513 0.703912
6 11.743 0.323910
7 42.137 0.754523
8 5.097 0.156240
9 24.349 0.555872
10 55.307 0.841750
11 28.717 0.616042
12 10.048 0.284624
13 12.152 0.333060
14 69.791 0.902350
15 42.884 0.760565
16 17.589 0.443609
17 32.986 0.666973
18 2.632 0.083984
19 15.339 0.400294
20 40.187 0.738037
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.751564
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-28_04:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 0.5 0.8 1.1 -0.2 -0.6
-0.1 -0.2 -2.3 0.8 0.1 0.0
-0.0 -1.7 2.3 -0.0 1.7 -1.4
0.7 -1.0 1.4 -0.5 0.4 1.6
-2.0 0.7 -1.0 -0.8 -1.1 -0.0
-0.7 -1.4 0.2 -0.8 0.6 -0.7
0.7 -0.4 0.1 -1.3 0.1 -1.0
-1.1
Chi-square with 42 degrees of freedom:43.869064
z-score=0.203932, p-value=0.607780
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-28_04:31
Test no p-value
1 0.308200
2 0.071632
3 0.347606
4 0.866536
5 0.092232
6 0.696430
7 0.002116
8 0.103110
9 0.021406
10 0.609901
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.022825
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-28_04:31:
(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 66343 1.57 66582 0.11
3 25000.00 25228 2.08 25026 0.03
4 6666.67 6689 0.07 6705 0.22
5 1388.89 1458 3.44 1422 0.79
6 238.10 243 0.10 224 0.83
7 34.72 34 0.01 36 0.05
8 4.96 4 0.19 4 0.19
p=0.72013 p=0.10076
Number of rngs required: 688195, p-value: 0.405
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-28_04:31
No. of wins: Observed Expected
98305 98585.9
z-score=-1.256, pvalue=0.10453
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66344 66666.7 1.562 1.562
2 37670 37654.3 0.007 1.568
3 26888 26954.7 0.165 1.733
4 19637 19313.5 5.420 7.153
5 13873 13851.4 0.034 7.187
6 10013 9943.5 0.485 7.672
7 7094 7145.0 0.364 8.037
8 5187 5139.1 0.447 8.483
9 3674 3699.9 0.181 8.664
10 2725 2666.3 1.292 9.957
11 1872 1923.3 1.370 11.327
12 1401 1388.7 0.108 11.435
13 993 1003.7 0.114 11.549
14 744 726.1 0.439 11.988
15 572 525.8 4.053 16.041
16 342 381.2 4.021 20.063
17 246 276.5 3.373 23.435
18 180 200.8 2.160 25.596
19 137 146.0 0.553 26.149
20 109 106.2 0.073 26.222
21 299 287.1 0.492 26.714
Chisq= 26.71 for 20 degrees of freedom, p= 0.85649
SUMMARY of craptest
p-value for no. of wins: 0.104528
p-value for throws/game: 0.856490
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-28_04:31
No. of wins: Observed Expected
98798 98585.9
z-score= 0.949, pvalue=0.82864
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66843 66666.7 0.466 0.466
2 37585 37654.3 0.128 0.594
3 26798 26954.7 0.911 1.505
4 19285 19313.5 0.042 1.547
5 13730 13851.4 1.064 2.612
6 9930 9943.5 0.018 2.630
7 7200 7145.0 0.423 3.053
8 5111 5139.1 0.153 3.206
9 3799 3699.9 2.656 5.863
10 2669 2666.3 0.003 5.865
11 1960 1923.3 0.699 6.565
12 1412 1388.7 0.390 6.954
13 989 1003.7 0.216 7.170
14 706 726.1 0.559 7.729
15 534 525.8 0.127 7.855
16 362 381.2 0.962 8.817
17 304 276.5 2.727 11.544
18 213 200.8 0.737 12.282
19 144 146.0 0.027 12.309
20 111 106.2 0.216 12.524
21 315 287.1 2.708 15.233
Chisq= 15.23 for 20 degrees of freedom, p= 0.23706
SUMMARY of craptest
p-value for no. of wins: 0.828644
p-value for throws/game: 0.237064
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0021,0.0084,0.0214,0.0228,0.0297,0.0328,0.0361,0.0422,0.0531,0.0548,
0.0565,0.0574,0.0594,0.0659,0.0716,0.0722,0.0801,0.0822,0.0840,0.0849,
0.0863,0.0880,0.0897,0.0922,0.0946,0.0968,0.0972,0.1008,0.1031,0.1045,
0.1053,0.1086,0.1103,0.1103,0.1142,0.1212,0.1236,0.1243,0.1278,0.1291,
0.1308,0.1366,0.1416,0.1453,0.1468,0.1477,0.1480,0.1530,0.1562,0.1576,
0.1584,0.1590,0.1627,0.1650,0.1719,0.1769,0.1808,0.1824,0.1826,0.1886,
0.1887,0.1992,0.1998,0.2135,0.2172,0.2186,0.2222,0.2222,0.2325,0.2327,
0.2338,0.2371,0.2475,0.2476,0.2556,0.2570,0.2669,0.2684,0.2770,0.2777,
0.2797,0.2800,0.2846,0.2857,0.2876,0.2896,0.2949,0.2979,0.3004,0.3082,
0.3202,0.3213,0.3234,0.3239,0.3266,0.3298,0.3316,0.3331,0.3404,0.3430,
0.3435,0.3476,0.3510,0.3621,0.3711,0.3712,0.3733,0.3793,0.3803,0.3856,
0.3927,0.4003,0.4029,0.4045,0.4054,0.4058,0.4071,0.4078,0.4113,0.4234,
0.4243,0.4256,0.4259,0.4269,0.4317,0.4378,0.4436,0.4445,0.4474,0.4476,
0.4484,0.4523,0.4527,0.4552,0.4570,0.4609,0.4671,0.4719,0.4726,0.4747,
0.4808,0.4858,0.4941,0.5090,0.5090,0.5147,0.5190,0.5196,0.5221,0.5231,
0.5295,0.5297,0.5317,0.5328,0.5368,0.5407,0.5411,0.5462,0.5559,0.5686,
0.5725,0.5770,0.5815,0.5835,0.5843,0.5910,0.5920,0.5936,0.5939,0.5955,
0.5990,0.6036,0.6054,0.6078,0.6099,0.6160,0.6193,0.6232,0.6254,0.6426,
0.6447,0.6463,0.6463,0.6665,0.6670,0.6834,0.6929,0.6964,0.7039,0.7040,
0.7104,0.7201,0.7217,0.7311,0.7318,0.7380,0.7425,0.7433,0.7457,0.7458,
0.7475,0.7491,0.7516,0.7545,0.7547,0.7598,0.7606,0.7676,0.7687,0.7707,
0.7755,0.7849,0.7965,0.7993,0.8047,0.8049,0.8049,0.8087,0.8092,0.8139,
0.8188,0.8236,0.8260,0.8273,0.8286,0.8293,0.8344,0.8394,0.8418,0.8432,
0.8453,0.8511,0.8523,0.8547,0.8564,0.8565,0.8580,0.8609,0.8609,0.8624,
0.8633,0.8665,0.8707,0.8778,0.8786,0.8831,0.8902,0.8947,0.8990,0.8996,
0.9024,0.9062,0.9065,0.9074,0.9084,0.9182,0.9226,0.9236,0.9341,0.9431,
0.9442,0.9450,0.9547,0.9552,0.9650,0.9773,0.9872,0.9923,0.9946,
Overall p-value after applying KStest on 269 p-values = 0.338450
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.