RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-01-27_02:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.75 12.6860 0.243060
2 to 25 15.80 11.7632 0.185742
3 to 26 16.01 30.3424 0.976021
4 to 27 15.76 15.0016 0.404636
5 to 28 15.62 16.0421 0.479145
6 to 29 15.70 19.6792 0.709036
7 to 30 15.63 23.0394 0.852027
8 to 31 15.65 24.0469 0.881833
9 to 32 15.96 14.9427 0.400388
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.707584
Tough bday spacings test for dh-ranFile-2018-01-27_02:31: 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 11 27 71 88 115 72 60 32 19 4 1
(O-E)^2/E 0.4 2.5 0.1 1.0 3.1 0.5 1.2 0.2 1.1 1.0 2.3
Birthday Spacings: Sum(O-E)^2/E= 13.335, p= 0.794
RESULTS OF GCD FOR dh-ranFile-2018-01-27_02:31
Euclid's algorithm:
p-value, steps to gcd: 0.587562
p-value, dist. of gcd's: 0.981410
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-01-27_02:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.834 0.329 0.008 0.559 0.232 0.368 0.387 0.013
Bits 8 to 15---> 0.829 0.155 0.875 0.747 0.593 0.719 0.073 0.188
Bits 16 to 23---> 0.198 0.856 0.547 0.193 0.417 0.390 0.036 0.054
Bits 24 to 31---> 0.940 0.408 0.036 0.804 0.387 0.097 0.860 0.193
KS test for the above 32 p values: 0.896
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-01-27_02:31,
p-values for 5 runs: 0.6686, 0.6851, 0.4333, 0.3596, 0.3345
Rank test for binary matrices (31x31) for dh-ranFile-2018-01-27_02:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 202 211.4 0.420 0.420
r= 29 5056 5134.0 1.185 1.605
r= 30 23123 23103.0 0.017 1.622
r= 31 11619 11551.5 0.394 2.016
chi-square = 2.016 with df = 3; p-value = 0.431
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-01-27_02:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 212 211.4 0.002 0.002
r= 30 5048 5134.0 1.441 1.443
r= 31 23303 23103.0 1.731 3.173
r= 32 11437 11551.5 1.135 4.309
chi-square = 4.309 with df = 3; p-value = 0.770
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-01-27_02:31
b-rank test for bits 1 to 8, p=0.20688
b-rank test for bits 2 to 9, p=0.06445
b-rank test for bits 3 to 10, p=0.31732
b-rank test for bits 4 to 11, p=0.58999
b-rank test for bits 5 to 12, p=0.04527
b-rank test for bits 6 to 13, p=0.86527
b-rank test for bits 7 to 14, p=0.83393
b-rank test for bits 8 to 15, p=0.92434
b-rank test for bits 9 to 16, p=0.35241
b-rank test for bits 10 to 17, p=0.74725
b-rank test for bits 11 to 18, p=0.82387
b-rank test for bits 12 to 19, p=0.10323
b-rank test for bits 13 to 20, p=0.56554
b-rank test for bits 14 to 21, p=0.87076
b-rank test for bits 15 to 22, p=0.98952
b-rank test for bits 16 to 23, p=0.70292
b-rank test for bits 17 to 24, p=0.99679
b-rank test for bits 18 to 25, p=0.97161
b-rank test for bits 19 to 26, p=0.84287
b-rank test for bits 20 to 27, p=0.63909
b-rank test for bits 21 to 28, p=0.88015
b-rank test for bits 22 to 29, p=0.39255
b-rank test for bits 23 to 30, p=0.13876
b-rank test for bits 24 to 31, p=0.29165
b-rank test for bits 25 to 32, p=0.91181
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 = 0.051756
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-01-27_02:31
(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 141837 -0.17 0.432900
2 141907 -0.01 0.497828
3 141337 -1.34 0.090575
4 141906 -0.01 0.496896
5 141779 -0.30 0.380370
6 141411 -1.16 0.122147
7 142078 0.39 0.653242
8 141951 0.10 0.538780
9 142317 0.95 0.829578
10 141823 -0.20 0.420073
11 141667 -0.57 0.285632
12 142218 0.72 0.764604
13 142029 0.28 0.610109
14 141712 -0.46 0.322381
15 141191 -1.68 0.046640
16 142601 1.62 0.946958
17 141626 -0.66 0.253990
18 141724 -0.43 0.332502
19 141757 -0.36 0.360954
20 141625 -0.66 0.253242
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-01-27_02:31
Bits used No. missing words z-score p-value
23 to 32 142133 0.7713 0.779728
22 to 31 142189 0.9644 0.832572
21 to 30 141942 0.1127 0.544848
20 to 29 142313 1.3920 0.918034
19 to 28 142183 0.9437 0.827336
18 to 27 141651 -0.8908 0.186520
17 to 26 142348 1.5127 0.934816
16 to 25 142392 1.6644 0.951982
15 to 24 141708 -0.6942 0.243765
14 to 23 141457 -1.5598 0.059408
13 to 22 141684 -0.7770 0.218579
12 to 21 141448 -1.5908 0.055828
11 to 20 141426 -1.6667 0.047792
10 to 19 142385 1.6402 0.949523
9 to 18 142084 0.6023 0.726516
8 to 17 142487 1.9920 0.976813
7 to 16 142044 0.4644 0.678812
6 to 15 142198 0.9954 0.840233
5 to 14 142030 0.4161 0.661333
4 to 13 142014 0.3609 0.640925
3 to 12 141837 -0.2494 0.401520
2 to 11 141521 -1.3391 0.090274
1 to 10 141779 -0.4494 0.326567
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-01-27_02:31
Bits used No. missing words z-score p-value
28 to 32 140962 -3.2113 0.000661
27 to 31 142100 0.6463 0.740970
26 to 30 142263 1.1989 0.884713
25 to 29 141810 -0.3367 0.368167
24 to 28 141986 0.2599 0.602529
23 to 27 141909 -0.0011 0.499554
22 to 26 141429 -1.6282 0.051737
21 to 25 141780 -0.4384 0.330546
20 to 24 142062 0.5175 0.697605
19 to 23 141276 -2.1469 0.015901
18 to 22 141742 -0.5672 0.285282
17 to 21 141994 0.2870 0.612950
16 to 20 141988 0.2667 0.605141
15 to 19 141999 0.3040 0.619423
14 to 18 142321 1.3955 0.918566
13 to 17 141317 -2.0079 0.022327
12 to 16 141512 -1.3469 0.089009
11 to 15 141292 -2.0926 0.018190
10 to 14 141396 -1.7401 0.040921
9 to 13 142169 0.8802 0.810635
8 to 12 141454 -1.5435 0.061356
7 to 11 142062 0.5175 0.697605
6 to 10 141413 -1.6825 0.046238
5 to 9 142351 1.4972 0.932828
4 to 8 141985 0.2565 0.601221
3 to 7 141513 -1.3435 0.089556
2 to 6 141835 -0.2520 0.400534
1 to 5 142439 1.7955 0.963712
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-01-27_02:31
Bits used No. missing words z-score p-value
31 to 32 141528 -1.1249 0.130323
30 to 31 141773 -0.4022 0.343786
29 to 30 141316 -1.7502 0.040039
28 to 29 141864 -0.1337 0.446813
27 to 28 142015 0.3117 0.622370
26 to 27 141237 -1.9833 0.023668
25 to 26 141993 0.2468 0.597474
24 to 25 141455 -1.3402 0.090089
23 to 24 142078 0.4976 0.690600
22 to 23 142195 0.8427 0.800298
21 to 22 141622 -0.8476 0.198336
20 to 21 141604 -0.9007 0.183880
19 to 20 141532 -1.1131 0.132840
18 to 19 142237 0.9666 0.833123
17 to 18 141902 -0.0216 0.491375
16 to 17 142000 0.2675 0.605444
15 to 16 141610 -0.8830 0.188624
14 to 15 141630 -0.8240 0.204975
13 to 14 141683 -0.6676 0.252182
12 to 13 141850 -0.1750 0.430534
11 to 12 142342 1.2763 0.899078
10 to 11 142307 1.1731 0.879616
9 to 10 142026 0.3442 0.634637
8 to 9 142067 0.4651 0.679071
7 to 8 141646 -0.7768 0.218643
6 to 7 141838 -0.2104 0.416673
5 to 6 141752 -0.4641 0.321288
4 to 5 141631 -0.8210 0.205814
3 to 4 141716 -0.5703 0.284239
2 to 3 141675 -0.6912 0.244708
1 to 2 141642 -0.7886 0.215178
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-01-27_02:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2613.73 1.608 0.946118
Test results for specific bytes for dh-ranFile-2018-01-27_02:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2592.69 1.311 0.905040
2 to 9 2618.08 1.670 0.952531
3 to 10 2593.01 1.315 0.905817
4 to 11 2416.46 -1.181 0.118713
5 to 12 2442.42 -0.814 0.207721
6 to 13 2628.24 1.814 0.965126
7 to 14 2512.97 0.183 0.572779
8 to 15 2469.61 -0.430 0.333654
9 to 16 2480.68 -0.273 0.392357
10 to 17 2461.58 -0.543 0.293448
11 to 18 2510.25 0.145 0.557648
12 to 19 2465.98 -0.481 0.315232
13 to 20 2582.30 1.164 0.877770
14 to 21 2569.15 0.978 0.835952
15 to 22 2475.31 -0.349 0.363458
16 to 23 2445.91 -0.765 0.222152
17 to 24 2596.78 1.369 0.914460
18 to 25 2414.25 -1.213 0.112616
19 to 26 2350.91 -2.108 0.017499
20 to 27 2349.29 -2.131 0.016527
21 to 28 2503.38 0.048 0.519035
22 to 29 2549.42 0.699 0.757707
23 to 30 2513.97 0.198 0.578329
24 to 31 2413.19 -1.228 0.109791
25 to 32 2564.45 0.912 0.818985
CDPARK for dh-ranFile-2018-01-27_02:31: 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
3505 -0.8219 0.205562
3506 -0.7763 0.218799
3504 -0.8676 0.192812
3530 0.3196 0.625377
3465 -2.6484 0.004044
3522 -0.0457 0.481790
3538 0.6849 0.753306
3518 -0.2283 0.409702
3515 -0.3653 0.357445
3532 0.4110 0.659449
Square side=100, avg. no. parked=3513.50 sample std.=19.70
p-value of the KSTEST for those 10 p-values: 0.300071
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-01-27_02:31
0.4208,0.2854,0.2801,0.3256,0.3286,0.3298,0.5082,0.1775,0.7573,0.1850,
The KS test for those 10 p-values: 0.071964
The 3DSPHERES test for dh-ranFile-2018-01-27_02:31
sample no r^3 equiv. uni.
1 19.995 0.486489
2 21.086 0.504834
3 41.095 0.745853
4 22.563 0.528627
5 43.025 0.761686
6 37.841 0.716735
7 8.175 0.238516
8 55.112 0.840717
9 32.126 0.657287
10 7.161 0.212345
11 131.706 0.987602
12 59.290 0.861422
13 73.041 0.912376
14 47.028 0.791457
15 50.701 0.815486
16 66.866 0.892350
17 48.912 0.804149
18 5.121 0.156914
19 23.885 0.548940
20 19.420 0.476565
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.031662
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-01-27_02:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 1.8 -1.1 0.2 -0.7 -0.6
1.3 0.7 -0.2 0.7 -0.4 0.3
-0.3 0.5 -1.3 1.6 0.8 -0.5
1.6 -0.3 -1.2 0.7 -0.2 0.3
-1.5 0.3 0.4 -1.0 -1.4 -2.0
-0.8 -0.9 1.0 -0.5 -0.2 -1.6
1.9 -0.4 -0.8 0.4 -0.6 0.0
0.8
Chi-square with 42 degrees of freedom:39.516348
z-score=-0.270989, p-value=0.419435
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-01-27_02:31
Test no p-value
1 0.014329
2 0.005650
3 0.551869
4 0.581969
5 0.018734
6 0.264852
7 0.664175
8 0.276491
9 0.009666
10 0.460127
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.003099
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-01-27_02:31:
(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 66713 0.03 66762 0.14
3 25000.00 25001 0.00 24858 0.81
4 6666.67 6606 0.55 6702 0.19
5 1388.89 1414 0.45 1403 0.14
6 238.10 236 0.02 240 0.02
7 34.72 26 2.19 28 1.30
8 4.96 3 0.77 6 0.22
p=0.32621 p=0.16740
Number of rngs required: 688925, p-value: 0.726
RESULTS OF CRAPS TEST for dh-ranFile-2018-01-27_02:31
No. of wins: Observed Expected
98406 98585.9
z-score=-0.804, pvalue=0.21057
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66329 66666.7 1.710 1.710
2 37717 37654.3 0.104 1.815
3 27072 26954.7 0.510 2.325
4 19389 19313.5 0.295 2.620
5 13959 13851.4 0.836 3.456
6 9923 9943.5 0.042 3.498
7 7096 7145.0 0.336 3.835
8 5106 5139.1 0.213 4.047
9 3789 3699.9 2.147 6.195
10 2737 2666.3 1.875 8.070
11 1929 1923.3 0.017 8.086
12 1340 1388.7 1.711 9.797
13 977 1003.7 0.711 10.508
14 741 726.1 0.304 10.812
15 500 525.8 1.269 12.082
16 375 381.2 0.099 12.181
17 264 276.5 0.569 12.749
18 204 200.8 0.050 12.799
19 163 146.0 1.983 14.783
20 101 106.2 0.256 15.039
21 289 287.1 0.012 15.051
Chisq= 15.05 for 20 degrees of freedom, p= 0.22653
SUMMARY of craptest
p-value for no. of wins: 0.210574
p-value for throws/game: 0.226529
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-01-27_02:31
No. of wins: Observed Expected
98472 98585.9
z-score=-0.509, pvalue=0.30529
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66806 66666.7 0.291 0.291
2 37533 37654.3 0.391 0.682
3 26948 26954.7 0.002 0.684
4 19395 19313.5 0.344 1.028
5 13845 13851.4 0.003 1.031
6 9910 9943.5 0.113 1.144
7 7172 7145.0 0.102 1.246
8 5115 5139.1 0.113 1.359
9 3564 3699.9 4.989 6.348
10 2617 2666.3 0.911 7.259
11 1966 1923.3 0.947 8.206
12 1345 1388.7 1.378 9.584
13 1010 1003.7 0.039 9.623
14 810 726.1 9.685 19.308
15 518 525.8 0.117 19.424
16 379 381.2 0.012 19.437
17 288 276.5 0.475 19.912
18 213 200.8 0.737 20.649
19 139 146.0 0.334 20.983
20 120 106.2 1.789 22.772
21 307 287.1 1.377 24.150
Chisq= 24.15 for 20 degrees of freedom, p= 0.76408
SUMMARY of craptest
p-value for no. of wins: 0.305291
p-value for throws/game: 0.764080
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0007,0.0031,0.0040,0.0056,0.0083,0.0097,0.0133,0.0143,0.0159,0.0165,
0.0175,0.0182,0.0187,0.0223,0.0237,0.0317,0.0359,0.0363,0.0400,0.0409,
0.0453,0.0462,0.0466,0.0478,0.0517,0.0518,0.0543,0.0558,0.0594,0.0614,
0.0644,0.0720,0.0730,0.0890,0.0896,0.0901,0.0903,0.0906,0.0966,0.1032,
0.1098,0.1126,0.1187,0.1221,0.1303,0.1328,0.1388,0.1551,0.1569,0.1674,
0.1775,0.1839,0.1850,0.1857,0.1865,0.1877,0.1886,0.1928,0.1930,0.1934,
0.1977,0.1983,0.2050,0.2056,0.2058,0.2069,0.2077,0.2106,0.2123,0.2152,
0.2186,0.2186,0.2188,0.2222,0.2265,0.2318,0.2385,0.2431,0.2438,0.2447,
0.2522,0.2532,0.2540,0.2649,0.2765,0.2801,0.2842,0.2853,0.2854,0.2856,
0.2916,0.2934,0.3001,0.3053,0.3152,0.3173,0.3213,0.3224,0.3256,0.3262,
0.3266,0.3286,0.3292,0.3298,0.3305,0.3325,0.3337,0.3345,0.3438,0.3524,
0.3574,0.3596,0.3610,0.3635,0.3678,0.3682,0.3804,0.3867,0.3870,0.3897,
0.3924,0.3926,0.4004,0.4005,0.4015,0.4046,0.4080,0.4097,0.4165,0.4167,
0.4194,0.4201,0.4208,0.4305,0.4310,0.4329,0.4333,0.4468,0.4601,0.4766,
0.4791,0.4818,0.4865,0.4914,0.4969,0.4978,0.4996,0.5048,0.5082,0.5190,
0.5286,0.5388,0.5448,0.5472,0.5489,0.5519,0.5576,0.5593,0.5655,0.5728,
0.5783,0.5820,0.5876,0.5900,0.5928,0.5975,0.6012,0.6025,0.6051,0.6054,
0.6101,0.6130,0.6194,0.6224,0.6254,0.6346,0.6391,0.6409,0.6532,0.6573,
0.6594,0.6613,0.6642,0.6686,0.6788,0.6791,0.6851,0.6906,0.6976,0.6976,
0.7029,0.7076,0.7090,0.7167,0.7187,0.7264,0.7265,0.7410,0.7459,0.7465,
0.7473,0.7533,0.7573,0.7577,0.7617,0.7641,0.7646,0.7700,0.7797,0.7915,
0.7945,0.8003,0.8041,0.8042,0.8106,0.8155,0.8190,0.8239,0.8273,0.8295,
0.8296,0.8326,0.8331,0.8339,0.8345,0.8360,0.8402,0.8407,0.8429,0.8520,
0.8561,0.8602,0.8614,0.8653,0.8708,0.8752,0.8778,0.8796,0.8801,0.8818,
0.8847,0.8924,0.8964,0.8991,0.9050,0.9058,0.9118,0.9124,0.9145,0.9180,
0.9186,0.9243,0.9328,0.9348,0.9395,0.9461,0.9470,0.9495,0.9520,0.9525,
0.9637,0.9651,0.9716,0.9760,0.9768,0.9814,0.9876,0.9895,0.9968,
Overall p-value after applying KStest on 269 p-values = 0.083583
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.