RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-17_19:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.90 16.4708 0.509259
2 to 25 15.62 21.8194 0.808237
3 to 26 15.84 22.1949 0.822660
4 to 27 15.68 22.8593 0.846112
5 to 28 15.85 20.8408 0.766508
6 to 29 15.82 17.9987 0.611079
7 to 30 15.96 15.0260 0.406394
8 to 31 15.52 33.6471 0.990678
9 to 32 15.61 22.0079 0.815584
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.020951
Tough bday spacings test for dh-ranFile-2018-06-17_19:31: 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 10 44 72 85 108 71 50 33 16 7 4
(O-E)^2/E 0.1 1.5 0.0 1.6 1.1 0.7 0.1 0.4 0.1 0.0 0.0
Birthday Spacings: Sum(O-E)^2/E= 5.513, p= 0.146
RESULTS OF GCD FOR dh-ranFile-2018-06-17_19:31
Euclid's algorithm:
p-value, steps to gcd: 0.084659
p-value, dist. of gcd's: 0.395139
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-17_19:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.447 0.375 0.110 0.901 0.220 0.545 0.584 0.808
Bits 8 to 15---> 0.544 0.513 0.780 0.189 0.535 0.492 0.821 0.093
Bits 16 to 23---> 0.919 0.184 0.014 0.756 0.537 0.392 0.292 0.396
Bits 24 to 31---> 0.902 0.472 0.526 0.974 0.209 0.195 0.183 0.044
KS test for the above 32 p values: 0.274
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-17_19:31,
p-values for 5 runs: 0.7800, 0.9892, 0.6913, 0.1172, 0.0368
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-17_19:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 216 211.4 0.099 0.099
r= 29 5150 5134.0 0.050 0.149
r= 30 23188 23103.0 0.312 0.461
r= 31 11446 11551.5 0.964 1.425
chi-square = 1.425 with df = 3; p-value = 0.300
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-17_19:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 191 211.4 1.972 1.972
r= 30 5316 5134.0 6.451 8.423
r= 31 22952 23103.0 0.988 9.411
r= 32 11541 11551.5 0.010 9.420
chi-square = 9.420 with df = 3; p-value = 0.976
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-17_19:31
b-rank test for bits 1 to 8, p=0.22866
b-rank test for bits 2 to 9, p=0.29668
b-rank test for bits 3 to 10, p=0.70056
b-rank test for bits 4 to 11, p=0.63924
b-rank test for bits 5 to 12, p=0.67516
b-rank test for bits 6 to 13, p=0.92937
b-rank test for bits 7 to 14, p=0.78560
b-rank test for bits 8 to 15, p=0.59829
b-rank test for bits 9 to 16, p=0.54423
b-rank test for bits 10 to 17, p=0.96990
b-rank test for bits 11 to 18, p=0.99321
b-rank test for bits 12 to 19, p=0.71242
b-rank test for bits 13 to 20, p=0.38659
b-rank test for bits 14 to 21, p=0.56990
b-rank test for bits 15 to 22, p=0.08639
b-rank test for bits 16 to 23, p=0.91317
b-rank test for bits 17 to 24, p=0.98526
b-rank test for bits 18 to 25, p=0.39462
b-rank test for bits 19 to 26, p=0.13377
b-rank test for bits 20 to 27, p=0.15996
b-rank test for bits 21 to 28, p=0.19661
b-rank test for bits 22 to 29, p=0.55028
b-rank test for bits 23 to 30, p=0.76054
b-rank test for bits 24 to 31, p=0.96694
b-rank test for bits 25 to 32, p=0.71453
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 = 0.112127
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-17_19:31
(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 141647 -0.61 0.269964
2 141751 -0.37 0.355717
3 141590 -0.75 0.227804
4 142452 1.27 0.897587
5 141582 -0.76 0.222198
6 141972 0.15 0.558207
7 142274 0.85 0.802902
8 141807 -0.24 0.405518
9 142058 0.35 0.635840
10 141008 -2.11 0.017606
11 142502 1.38 0.916934
12 141892 -0.04 0.483851
13 141906 -0.01 0.496896
14 142115 0.48 0.684577
15 142314 0.95 0.827796
16 142029 0.28 0.610109
17 142196 0.67 0.748504
18 142521 1.43 0.923517
19 141610 -0.70 0.242161
20 141538 -0.87 0.192808
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-17_19:31
Bits used No. missing words z-score p-value
23 to 32 142055 0.5023 0.692275
22 to 31 142120 0.7264 0.766218
21 to 30 141537 -1.2839 0.099589
20 to 29 142278 1.2713 0.898185
19 to 28 141686 -0.7701 0.220619
18 to 27 141836 -0.2529 0.400187
17 to 26 142406 1.7127 0.956612
16 to 25 141382 -1.8184 0.034503
15 to 24 142043 0.4609 0.677576
14 to 23 141938 0.0989 0.539376
13 to 22 141574 -1.1563 0.123777
12 to 21 142362 1.5609 0.940730
11 to 20 142091 0.6264 0.734490
10 to 19 142190 0.9678 0.833435
9 to 18 141732 -0.6115 0.270440
8 to 17 141648 -0.9011 0.183758
7 to 16 142275 1.2609 0.896333
6 to 15 141718 -0.6598 0.254704
5 to 14 142266 1.2299 0.890632
4 to 13 142172 0.9058 0.817468
3 to 12 142492 2.0092 0.977742
2 to 11 141673 -0.8149 0.207556
1 to 10 141948 0.1333 0.553040
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-17_19:31
Bits used No. missing words z-score p-value
28 to 32 141473 -1.4791 0.069559
27 to 31 142437 1.7887 0.963169
26 to 30 141949 0.1345 0.553486
25 to 29 142159 0.8463 0.801318
24 to 28 142022 0.3819 0.648744
23 to 27 142015 0.3582 0.639905
22 to 26 141689 -0.7469 0.227568
21 to 25 141872 -0.1265 0.449651
20 to 24 141664 -0.8316 0.202810
19 to 23 142174 0.8972 0.815190
18 to 22 142222 1.0599 0.855405
17 to 21 141784 -0.4248 0.335474
16 to 20 141908 -0.0045 0.498201
15 to 19 142217 1.0429 0.851514
14 to 18 142363 1.5379 0.937959
13 to 17 142300 1.3243 0.907299
12 to 16 141610 -1.0147 0.155130
11 to 15 141971 0.2091 0.582796
10 to 14 141638 -0.9198 0.178848
9 to 13 141462 -1.5164 0.064713
8 to 12 141740 -0.5740 0.282984
7 to 11 141770 -0.4723 0.318355
6 to 10 141850 -0.2011 0.420303
5 to 9 141714 -0.6621 0.253942
4 to 8 141486 -1.4350 0.075641
3 to 7 141868 -0.1401 0.444290
2 to 6 141656 -0.8587 0.195240
1 to 5 141539 -1.2554 0.104675
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-17_19:31
Bits used No. missing words z-score p-value
31 to 32 141949 0.1170 0.546578
30 to 31 142108 0.5860 0.721078
29 to 30 141900 -0.0275 0.489022
28 to 29 141925 0.0462 0.518434
27 to 28 142556 1.9076 0.971777
26 to 27 141890 -0.0570 0.477264
25 to 26 141778 -0.3874 0.349229
24 to 25 141969 0.1760 0.569860
23 to 24 141897 -0.0364 0.485493
22 to 23 141807 -0.3019 0.381380
21 to 22 141868 -0.1219 0.451482
20 to 21 141666 -0.7178 0.236444
19 to 20 142796 2.6155 0.995546
18 to 19 142172 0.7748 0.780782
17 to 18 142283 1.1023 0.864828
16 to 17 142005 0.2822 0.611110
15 to 16 141653 -0.7561 0.224784
14 to 15 142206 0.8751 0.809249
13 to 14 141461 -1.3225 0.093000
12 to 13 142429 1.5329 0.937356
11 to 12 141747 -0.4788 0.316023
10 to 11 142199 0.8545 0.803582
9 to 10 142241 0.9784 0.836056
8 to 9 141956 0.1377 0.554749
7 to 8 142023 0.3353 0.631304
6 to 7 142305 1.1672 0.878429
5 to 6 141793 -0.3432 0.365740
4 to 5 141653 -0.7561 0.224784
3 to 4 141964 0.1613 0.564059
2 to 3 142320 1.2114 0.887132
1 to 2 142454 1.6067 0.945939
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-17_19:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2492.43 -0.107 0.457398
Test results for specific bytes for dh-ranFile-2018-06-17_19:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2562.58 0.885 0.811916
2 to 9 2574.91 1.059 0.855293
3 to 10 2417.19 -1.171 0.120768
4 to 11 2691.54 2.709 0.996624
5 to 12 2628.53 1.818 0.965449
6 to 13 2411.15 -1.257 0.104450
7 to 14 2478.34 -0.306 0.379671
8 to 15 2708.77 2.952 0.998424
9 to 16 2611.78 1.581 0.943034
10 to 17 2640.47 1.987 0.976515
11 to 18 2522.67 0.321 0.625759
12 to 19 2452.39 -0.673 0.250354
13 to 20 2473.33 -0.377 0.353037
14 to 21 2487.09 -0.183 0.427567
15 to 22 2497.29 -0.038 0.484718
16 to 23 2541.23 0.583 0.720071
17 to 24 2547.47 0.671 0.749006
18 to 25 2454.94 -0.637 0.261961
19 to 26 2444.47 -0.785 0.216128
20 to 27 2550.48 0.714 0.762366
21 to 28 2407.07 -1.314 0.094373
22 to 29 2454.24 -0.647 0.258763
23 to 30 2508.68 0.123 0.548869
24 to 31 2408.52 -1.294 0.097874
25 to 32 2474.34 -0.363 0.358364
CDPARK for dh-ranFile-2018-06-17_19:31: 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
3515 -0.3653 0.357445
3521 -0.0913 0.463617
3531 0.3653 0.642555
3487 -1.6438 0.050105
3516 -0.3196 0.374623
3534 0.5023 0.692266
3521 -0.0913 0.463617
3529 0.2740 0.607947
3549 1.1872 0.882429
3583 2.7397 0.996925
Square side=100, avg. no. parked=3528.60 sample std.=23.67
p-value of the KSTEST for those 10 p-values: 0.608349
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-17_19:31
0.1895,0.1749,0.4552,0.3071,0.2167,0.1285,0.4609,0.4253,0.2270,0.9739,
The KS test for those 10 p-values: 0.091750
The 3DSPHERES test for dh-ranFile-2018-06-17_19:31
sample no r^3 equiv. uni.
1 6.855 0.204278
2 29.063 0.620444
3 38.656 0.724323
4 40.591 0.741543
5 1.855 0.059963
6 8.560 0.248232
7 11.232 0.312288
8 9.056 0.260560
9 17.973 0.450702
10 3.122 0.098829
11 17.415 0.440383
12 31.731 0.652751
13 61.681 0.872039
14 17.998 0.451145
15 28.264 0.610210
16 19.696 0.481351
17 7.963 0.233115
18 14.158 0.376198
19 30.895 0.642936
20 12.191 0.333944
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.298481
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-17_19:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 0.1 -0.1 0.6 -1.1 -1.6
-1.2 -0.3 0.2 -0.7 -1.6 0.2
-0.1 0.7 -1.6 1.1 0.3 0.3
-1.0 1.6 -0.2 -0.1 0.6 -1.2
0.5 0.4 0.7 -0.3 0.6 0.1
1.4 -0.6 1.2 -0.3 1.0 -0.1
-2.1 -0.7 0.1 0.4 1.6 0.0
-0.1
Chi-square with 42 degrees of freedom:33.422644
z-score=-0.935866, p-value=0.175073
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-17_19:31
Test no p-value
1 0.480589
2 0.462745
3 0.307789
4 0.000442
5 0.670892
6 0.225964
7 0.932221
8 0.235611
9 0.043457
10 0.069603
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.080380
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-17_19:31:
(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 66562 0.16 66368 1.34
3 25000.00 25144 0.83 25161 1.04
4 6666.67 6578 1.18 6800 2.67
5 1388.89 1412 0.38 1410 0.32
6 238.10 267 3.51 223 0.96
7 34.72 35 0.00 31 0.40
8 4.96 1 3.16 6 0.22
p=0.83898 p=0.67319
Number of rngs required: 692793, p-value: 1.000
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-17_19:31
No. of wins: Observed Expected
98645 98585.9
z-score= 0.265, pvalue=0.60431
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67007 66666.7 1.737 1.737
2 37346 37654.3 2.525 4.262
3 27121 26954.7 1.026 5.288
4 19107 19313.5 2.207 7.495
5 13821 13851.4 0.067 7.561
6 9921 9943.5 0.051 7.613
7 7147 7145.0 0.001 7.613
8 5045 5139.1 1.722 9.335
9 3821 3699.9 3.966 13.301
10 2707 2666.3 0.621 13.923
11 1910 1923.3 0.092 14.015
12 1393 1388.7 0.013 14.028
13 994 1003.7 0.094 14.122
14 745 726.1 0.490 14.612
15 531 525.8 0.051 14.663
16 399 381.2 0.836 15.498
17 259 276.5 1.112 16.611
18 194 200.8 0.232 16.843
19 153 146.0 0.337 17.180
20 102 106.2 0.167 17.348
21 277 287.1 0.356 17.704
Chisq= 17.70 for 20 degrees of freedom, p= 0.39309
SUMMARY of craptest
p-value for no. of wins: 0.604308
p-value for throws/game: 0.393091
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-17_19:31
No. of wins: Observed Expected
98165 98585.9
z-score=-1.882, pvalue=0.02990
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66646 66666.7 0.006 0.006
2 37525 37654.3 0.444 0.451
3 27101 26954.7 0.794 1.244
4 19255 19313.5 0.177 1.421
5 13909 13851.4 0.239 1.661
6 9912 9943.5 0.100 1.761
7 7218 7145.0 0.745 2.506
8 5008 5139.1 3.343 5.849
9 3620 3699.9 1.724 7.573
10 2747 2666.3 2.443 10.016
11 1902 1923.3 0.237 10.252
12 1457 1388.7 3.355 13.607
13 1062 1003.7 3.385 16.992
14 710 726.1 0.359 17.351
15 518 525.8 0.117 17.467
16 356 381.2 1.660 19.127
17 261 276.5 0.873 20.000
18 215 200.8 1.000 21.000
19 154 146.0 0.440 21.440
20 114 106.2 0.571 22.011
21 310 287.1 1.824 23.835
Chisq= 23.83 for 20 degrees of freedom, p= 0.75032
SUMMARY of craptest
p-value for no. of wins: 0.029896
p-value for throws/game: 0.750320
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0004,0.0143,0.0176,0.0210,0.0299,0.0345,0.0368,0.0435,0.0436,0.0501,
0.0600,0.0647,0.0696,0.0696,0.0756,0.0804,0.0847,0.0864,0.0918,0.0929,
0.0930,0.0944,0.0979,0.0988,0.0996,0.1045,0.1047,0.1102,0.1121,0.1172,
0.1208,0.1238,0.1285,0.1338,0.1456,0.1551,0.1600,0.1749,0.1751,0.1788,
0.1834,0.1837,0.1838,0.1890,0.1895,0.1928,0.1945,0.1952,0.1966,0.2028,
0.2043,0.2076,0.2094,0.2161,0.2167,0.2199,0.2206,0.2222,0.2248,0.2248,
0.2260,0.2270,0.2276,0.2278,0.2287,0.2331,0.2356,0.2364,0.2422,0.2482,
0.2504,0.2539,0.2547,0.2588,0.2606,0.2620,0.2700,0.2704,0.2738,0.2830,
0.2920,0.2967,0.2985,0.3004,0.3071,0.3078,0.3123,0.3160,0.3184,0.3339,
0.3355,0.3492,0.3530,0.3557,0.3574,0.3584,0.3657,0.3746,0.3747,0.3762,
0.3797,0.3814,0.3866,0.3919,0.3931,0.3946,0.3951,0.3956,0.4002,0.4055,
0.4064,0.4203,0.4253,0.4276,0.4404,0.4443,0.4469,0.4497,0.4507,0.4511,
0.4515,0.4552,0.4574,0.4609,0.4627,0.4636,0.4636,0.4716,0.4773,0.4806,
0.4814,0.4839,0.4847,0.4855,0.4890,0.4917,0.4969,0.4982,0.5093,0.5126,
0.5184,0.5256,0.5348,0.5371,0.5394,0.5436,0.5442,0.5450,0.5466,0.5489,
0.5503,0.5530,0.5535,0.5547,0.5582,0.5641,0.5699,0.5699,0.5828,0.5839,
0.5983,0.6043,0.6079,0.6083,0.6101,0.6102,0.6111,0.6111,0.6204,0.6258,
0.6313,0.6358,0.6392,0.6399,0.6426,0.6429,0.6487,0.6528,0.6709,0.6732,
0.6752,0.6776,0.6846,0.6913,0.6923,0.6923,0.7006,0.7124,0.7145,0.7201,
0.7211,0.7243,0.7345,0.7415,0.7485,0.7490,0.7503,0.7562,0.7605,0.7624,
0.7662,0.7665,0.7800,0.7805,0.7808,0.7856,0.8013,0.8029,0.8036,0.8079,
0.8082,0.8092,0.8119,0.8152,0.8156,0.8175,0.8213,0.8227,0.8278,0.8334,
0.8361,0.8390,0.8461,0.8515,0.8553,0.8554,0.8648,0.8720,0.8784,0.8824,
0.8871,0.8906,0.8963,0.8976,0.8982,0.9009,0.9017,0.9073,0.9132,0.9169,
0.9192,0.9235,0.9294,0.9322,0.9374,0.9380,0.9407,0.9430,0.9459,0.9566,
0.9632,0.9654,0.9669,0.9699,0.9718,0.9739,0.9743,0.9758,0.9765,0.9777,
0.9853,0.9892,0.9907,0.9932,0.9955,0.9966,0.9969,0.9984,1.0000,
Overall p-value after applying KStest on 269 p-values = 0.408308
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.