RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-16_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 15.83 20.7007 0.760034
2 to 25 15.75 26.7802 0.938629
3 to 26 15.76 18.9593 0.669124
4 to 27 15.78 15.4035 0.433561
5 to 28 15.82 10.3415 0.111318
6 to 29 15.90 17.8251 0.600044
7 to 30 15.72 7.7792 0.028957
8 to 31 15.73 25.8058 0.921929
9 to 32 15.68 21.5317 0.796596
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.509281
Tough bday spacings test for dh-ranFile-2018-06-16_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 12 39 65 103 93 83 41 26 21 11 6
(O-E)^2/E 0.9 0.2 0.9 0.3 0.2 0.3 2.4 0.5 2.5 2.9 0.9
Birthday Spacings: Sum(O-E)^2/E= 11.961, p= 0.712
RESULTS OF GCD FOR dh-ranFile-2018-06-16_05:31
Euclid's algorithm:
p-value, steps to gcd: 0.825192
p-value, dist. of gcd's: 0.300296
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-16_05:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.781 0.720 0.578 0.509 0.788 0.791 0.900 0.740
Bits 8 to 15---> 0.410 0.369 0.330 0.607 0.115 0.285 0.491 0.721
Bits 16 to 23---> 0.806 0.380 0.971 0.726 0.855 0.247 0.807 0.427
Bits 24 to 31---> 0.737 0.647 0.788 0.878 0.784 0.123 0.683 0.758
KS test for the above 32 p values: 0.986
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-16_05:31,
p-values for 5 runs: 0.4377, 0.2854, 0.5040, 0.6330, 0.2826
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-16_05:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 187 211.4 2.820 2.820
r= 29 5076 5134.0 0.655 3.476
r= 30 23194 23103.0 0.358 3.834
r= 31 11543 11551.5 0.006 3.840
chi-square = 3.840 with df = 3; p-value = 0.721
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-16_05:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 226 211.4 1.006 1.006
r= 30 5103 5134.0 0.187 1.193
r= 31 23107 23103.0 0.001 1.194
r= 32 11564 11551.5 0.013 1.207
chi-square = 1.207 with df = 3; p-value = 0.249
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-16_05:31
b-rank test for bits 1 to 8, p=0.73515
b-rank test for bits 2 to 9, p=0.98760
b-rank test for bits 3 to 10, p=0.31738
b-rank test for bits 4 to 11, p=0.27899
b-rank test for bits 5 to 12, p=0.46413
b-rank test for bits 6 to 13, p=0.51071
b-rank test for bits 7 to 14, p=0.38687
b-rank test for bits 8 to 15, p=0.42798
b-rank test for bits 9 to 16, p=0.64224
b-rank test for bits 10 to 17, p=0.66863
b-rank test for bits 11 to 18, p=0.72636
b-rank test for bits 12 to 19, p=0.96587
b-rank test for bits 13 to 20, p=0.03742
b-rank test for bits 14 to 21, p=0.46385
b-rank test for bits 15 to 22, p=0.39616
b-rank test for bits 16 to 23, p=0.08606
b-rank test for bits 17 to 24, p=0.05435
b-rank test for bits 18 to 25, p=0.92282
b-rank test for bits 19 to 26, p=0.37602
b-rank test for bits 20 to 27, p=0.78436
b-rank test for bits 21 to 28, p=0.86867
b-rank test for bits 22 to 29, p=0.55536
b-rank test for bits 23 to 30, p=0.40106
b-rank test for bits 24 to 31, p=0.42013
b-rank test for bits 25 to 32, p=0.07784
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 = 0.832173
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-16_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 141935 0.06 0.523913
2 141614 -0.69 0.245090
3 141325 -1.37 0.086086
4 142809 2.10 0.982225
5 141475 -1.01 0.155103
6 142557 1.51 0.934892
7 142027 0.27 0.608315
8 141766 -0.33 0.368857
9 141660 -0.58 0.280099
10 141869 -0.09 0.462464
11 141704 -0.48 0.315705
12 141981 0.17 0.566493
13 141763 -0.34 0.366216
14 142628 1.68 0.953437
15 142231 0.75 0.773844
16 141588 -0.75 0.226395
17 142306 0.93 0.822985
18 141893 -0.04 0.484782
19 142367 1.07 0.857538
20 141236 -1.57 0.057836
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-16_05:31
Bits used No. missing words z-score p-value
23 to 32 142164 0.8782 0.810075
22 to 31 141838 -0.2460 0.402855
21 to 30 142140 0.7954 0.786814
20 to 29 142033 0.4264 0.665109
19 to 28 141838 -0.2460 0.402855
18 to 27 141894 -0.0529 0.478921
17 to 26 141785 -0.4287 0.334062
16 to 25 142052 0.4920 0.688628
15 to 24 142370 1.5885 0.943915
14 to 23 141964 0.1885 0.574764
13 to 22 141994 0.2920 0.614844
12 to 21 141729 -0.6218 0.267028
11 to 20 141936 0.0920 0.536637
10 to 19 141497 -1.4218 0.077538
9 to 18 142568 2.2713 0.988435
8 to 17 141735 -0.6011 0.273874
7 to 16 141989 0.2747 0.608236
6 to 15 142313 1.3920 0.918034
5 to 14 141785 -0.4287 0.334062
4 to 13 141778 -0.4529 0.325324
3 to 12 141939 0.1023 0.540745
2 to 11 142124 0.7402 0.770423
1 to 10 142393 1.6678 0.952325
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-16_05:31
Bits used No. missing words z-score p-value
28 to 32 141435 -1.6079 0.053929
27 to 31 141580 -1.1164 0.132131
26 to 30 142026 0.3955 0.653760
25 to 29 141761 -0.5028 0.307548
24 to 28 141674 -0.7977 0.212514
23 to 27 141273 -2.1571 0.015501
22 to 26 142231 1.0904 0.862233
21 to 25 141354 -1.8825 0.029886
20 to 24 142340 1.4599 0.927841
19 to 23 142264 1.2023 0.885371
18 to 22 141452 -1.5503 0.060538
17 to 21 142049 0.4735 0.682057
16 to 20 142096 0.6328 0.736561
15 to 19 141846 -0.2147 0.415009
14 to 18 142216 1.0396 0.850728
13 to 17 141625 -0.9638 0.167565
12 to 16 142271 1.2260 0.889901
11 to 15 142011 0.3446 0.634819
10 to 14 141677 -0.7876 0.215477
9 to 13 141260 -2.2011 0.013864
8 to 12 142252 1.1616 0.877300
7 to 11 141808 -0.3435 0.365614
6 to 10 142031 0.4124 0.659992
5 to 9 141789 -0.4079 0.341674
4 to 8 142016 0.3616 0.641172
3 to 7 141639 -0.9164 0.179736
2 to 6 141965 0.1887 0.574841
1 to 5 141854 -0.1876 0.425611
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-16_05:31
Bits used No. missing words z-score p-value
31 to 32 141957 0.1406 0.555915
30 to 31 142197 0.8486 0.801944
29 to 30 141556 -1.0423 0.148643
28 to 29 142198 0.8515 0.802764
27 to 28 142200 0.8574 0.804397
26 to 27 141465 -1.3107 0.094978
25 to 26 142835 2.7306 0.996839
24 to 25 142115 0.6067 0.727974
23 to 24 141627 -0.8328 0.202470
22 to 23 142022 0.3324 0.630191
21 to 22 141819 -0.2665 0.394942
20 to 21 141980 0.2085 0.582568
19 to 20 142056 0.4327 0.667367
18 to 19 141992 0.2439 0.596332
17 to 18 142231 0.9489 0.828659
16 to 17 141448 -1.3609 0.086780
15 to 16 141601 -0.9095 0.181536
14 to 15 141886 -0.0688 0.472566
13 to 14 141875 -0.1013 0.459669
12 to 13 142098 0.5565 0.711082
11 to 12 141037 -2.5732 0.005037
10 to 11 141882 -0.0806 0.467872
9 to 10 142043 0.3943 0.653323
8 to 9 141480 -1.2665 0.102674
7 to 8 142095 0.5477 0.708051
6 to 7 142344 1.2822 0.900116
5 to 6 141896 -0.0393 0.484317
4 to 5 142117 0.6126 0.729928
3 to 4 141796 -0.3343 0.369074
2 to 3 142211 0.8899 0.813235
1 to 2 142088 0.5271 0.700921
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-16_05:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2560.41 0.854 0.803551
Test results for specific bytes for dh-ranFile-2018-06-16_05:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2668.57 2.384 0.991437
2 to 9 2543.88 0.621 0.732554
3 to 10 2551.20 0.724 0.765487
4 to 11 2554.24 0.767 0.778469
5 to 12 2528.38 0.401 0.655932
6 to 13 2523.26 0.329 0.628886
7 to 14 2417.37 -1.169 0.121281
8 to 15 2604.71 1.481 0.930682
9 to 16 2457.39 -0.603 0.273408
10 to 17 2433.73 -0.937 0.174338
11 to 18 2509.36 0.132 0.552630
12 to 19 2477.47 -0.319 0.374994
13 to 20 2552.70 0.745 0.771961
14 to 21 2565.41 0.925 0.822526
15 to 22 2465.06 -0.494 0.310603
16 to 23 2385.80 -1.615 0.053158
17 to 24 2533.89 0.479 0.684147
18 to 25 2419.07 -1.145 0.126190
19 to 26 2491.54 -0.120 0.452376
20 to 27 2482.78 -0.244 0.403789
21 to 28 2548.95 0.692 0.755623
22 to 29 2415.17 -1.200 0.115142
23 to 30 2472.42 -0.390 0.348231
24 to 31 2518.86 0.267 0.605145
25 to 32 2498.69 -0.018 0.492633
CDPARK for dh-ranFile-2018-06-16_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
3543 0.9132 0.819442
3563 1.8265 0.966111
3486 -1.6895 0.045562
3518 -0.2283 0.409702
3538 0.6849 0.753306
3550 1.2329 0.891189
3557 1.5525 0.939730
3524 0.0457 0.518210
3534 0.5023 0.692266
3524 0.0457 0.518210
Square side=100, avg. no. parked=3533.70 sample std.=21.17
p-value of the KSTEST for those 10 p-values: 0.137758
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-16_05:31
0.1350,0.3215,0.5177,0.9545,0.5186,0.8973,0.0413,0.2026,0.8209,0.8469,
The KS test for those 10 p-values: 0.877969
The 3DSPHERES test for dh-ranFile-2018-06-16_05:31
sample no r^3 equiv. uni.
1 0.145 0.004808
2 32.069 0.656636
3 41.069 0.745627
4 5.429 0.165544
5 21.098 0.505038
6 9.523 0.271996
7 19.203 0.472768
8 6.941 0.206550
9 20.397 0.493324
10 30.032 0.632516
11 41.470 0.749008
12 8.366 0.243368
13 4.331 0.134440
14 73.207 0.912860
15 68.493 0.898033
16 84.478 0.940151
17 40.778 0.743154
18 43.315 0.763975
19 12.720 0.345581
20 48.184 0.799337
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.830886
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-16_05:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 -0.3 1.3 0.3 1.1 0.1
1.7 0.9 -1.2 1.4 -0.4 1.1
-1.0 0.1 -0.7 0.0 -1.9 1.0
-0.3 0.3 -0.2 -0.6 1.8 1.4
-0.5 -2.2 -1.2 0.2 0.3 1.9
0.7 0.4 -0.4 0.1 -0.1 0.2
0.7 -0.1 -1.2 1.0 -1.3 -1.0
1.8
Chi-square with 42 degrees of freedom:44.201913
z-score=0.240248, p-value=0.621219
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-16_05:31
Test no p-value
1 0.992513
2 0.075299
3 0.087411
4 0.967356
5 0.132651
6 0.192291
7 0.195811
8 0.355750
9 0.131979
10 0.828857
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.069010
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-16_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 66801 0.27 66596 0.07
3 25000.00 24968 0.04 25050 0.10
4 6666.67 6534 2.64 6743 0.87
5 1388.89 1445 2.27 1353 0.93
6 238.10 213 2.65 228 0.43
7 34.72 33 0.09 25 2.72
8 4.96 5 0.00 4 0.19
p=0.75815 p=0.49545
Number of rngs required: 687177, p-value: 0.076
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-16_05:31
No. of wins: Observed Expected
98206 98585.9
z-score=-1.699, pvalue=0.04466
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66136 66666.7 4.224 4.224
2 37851 37654.3 1.027 5.251
3 27059 26954.7 0.403 5.655
4 19316 19313.5 0.000 5.655
5 13856 13851.4 0.002 5.657
6 10074 9943.5 1.712 7.368
7 7212 7145.0 0.628 7.996
8 5111 5139.1 0.153 8.149
9 3778 3699.9 1.650 9.799
10 2642 2666.3 0.221 10.021
11 1860 1923.3 2.085 12.106
12 1407 1388.7 0.240 12.346
13 1038 1003.7 1.171 13.517
14 713 726.1 0.238 13.755
15 537 525.8 0.237 13.992
16 370 381.2 0.326 14.318
17 295 276.5 1.232 15.551
18 191 200.8 0.481 16.032
19 147 146.0 0.007 16.039
20 115 106.2 0.727 16.765
21 292 287.1 0.083 16.849
Chisq= 16.85 for 20 degrees of freedom, p= 0.33721
SUMMARY of craptest
p-value for no. of wins: 0.044664
p-value for throws/game: 0.337212
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-16_05:31
No. of wins: Observed Expected
98749 98585.9
z-score= 0.730, pvalue=0.76720
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66979 66666.7 1.463 1.463
2 37470 37654.3 0.902 2.366
3 26848 26954.7 0.423 2.788
4 19165 19313.5 1.141 3.929
5 13813 13851.4 0.107 4.036
6 9811 9943.5 1.767 5.803
7 7301 7145.0 3.405 9.208
8 5208 5139.1 0.924 10.132
9 3718 3699.9 0.089 10.221
10 2700 2666.3 0.426 10.647
11 1918 1923.3 0.015 10.662
12 1331 1388.7 2.401 13.062
13 1048 1003.7 1.954 15.016
14 734 726.1 0.085 15.101
15 518 525.8 0.117 15.218
16 391 381.2 0.255 15.473
17 294 276.5 1.102 16.575
18 193 200.8 0.305 16.880
19 146 146.0 0.000 16.880
20 105 106.2 0.014 16.894
21 309 287.1 1.668 18.563
Chisq= 18.56 for 20 degrees of freedom, p= 0.44960
SUMMARY of craptest
p-value for no. of wins: 0.767202
p-value for throws/game: 0.449604
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0048,0.0050,0.0139,0.0155,0.0290,0.0299,0.0374,0.0413,0.0447,0.0456,
0.0532,0.0539,0.0543,0.0578,0.0605,0.0690,0.0753,0.0763,0.0775,0.0778,
0.0861,0.0861,0.0868,0.0874,0.0950,0.1027,0.1113,0.1145,0.1151,0.1213,
0.1231,0.1262,0.1320,0.1321,0.1327,0.1344,0.1350,0.1378,0.1486,0.1551,
0.1655,0.1676,0.1743,0.1797,0.1815,0.1923,0.1958,0.2025,0.2026,0.2066,
0.2125,0.2155,0.2264,0.2434,0.2451,0.2469,0.2487,0.2670,0.2720,0.2734,
0.2739,0.2790,0.2801,0.2826,0.2854,0.2854,0.3003,0.3075,0.3106,0.3157,
0.3174,0.3215,0.3253,0.3295,0.3341,0.3341,0.3372,0.3417,0.3456,0.3482,
0.3557,0.3656,0.3662,0.3689,0.3691,0.3691,0.3750,0.3760,0.3803,0.3869,
0.3949,0.3962,0.4011,0.4029,0.4029,0.4038,0.4097,0.4099,0.4150,0.4201,
0.4256,0.4269,0.4280,0.4336,0.4377,0.4496,0.4524,0.4597,0.4625,0.4639,
0.4641,0.4679,0.4726,0.4728,0.4789,0.4843,0.4848,0.4906,0.4926,0.4933,
0.4954,0.5040,0.5050,0.5092,0.5093,0.5107,0.5177,0.5182,0.5182,0.5186,
0.5239,0.5366,0.5407,0.5526,0.5554,0.5559,0.5665,0.5748,0.5748,0.5784,
0.5826,0.5963,0.6000,0.6051,0.6068,0.6082,0.6083,0.6148,0.6212,0.6289,
0.6302,0.6325,0.6330,0.6348,0.6412,0.6422,0.6468,0.6533,0.6538,0.6559,
0.6566,0.6600,0.6651,0.6674,0.6686,0.6691,0.6821,0.6830,0.6841,0.6886,
0.6923,0.7009,0.7081,0.7111,0.7124,0.7202,0.7207,0.7214,0.7262,0.7264,
0.7280,0.7299,0.7326,0.7351,0.7366,0.7370,0.7405,0.7432,0.7456,0.7490,
0.7533,0.7556,0.7580,0.7582,0.7600,0.7640,0.7655,0.7672,0.7704,0.7720,
0.7738,0.7785,0.7810,0.7839,0.7844,0.7868,0.7877,0.7881,0.7913,0.7966,
0.7993,0.8019,0.8028,0.8036,0.8044,0.8060,0.8074,0.8101,0.8132,0.8194,
0.8209,0.8225,0.8230,0.8252,0.8287,0.8289,0.8309,0.8322,0.8469,0.8507,
0.8549,0.8575,0.8622,0.8687,0.8773,0.8778,0.8780,0.8854,0.8899,0.8912,
0.8973,0.8980,0.8999,0.9001,0.9129,0.9180,0.9219,0.9228,0.9278,0.9307,
0.9349,0.9386,0.9397,0.9402,0.9439,0.9523,0.9534,0.9545,0.9659,0.9661,
0.9674,0.9711,0.9822,0.9855,0.9876,0.9884,0.9914,0.9925,0.9968,
Overall p-value after applying KStest on 269 p-values = 0.078620
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.