RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-08_07:31
(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 14.4440 0.364540
2 to 25 15.77 14.4791 0.367052
3 to 26 15.55 27.7729 0.952338
4 to 27 15.64 24.2276 0.886619
5 to 28 15.67 19.7945 0.715127
6 to 29 15.52 15.1769 0.417261
7 to 30 15.80 15.8964 0.468812
8 to 31 15.74 15.0741 0.409853
9 to 32 15.83 14.6550 0.379681
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.356345
Tough bday spacings test for dh-ranFile-2018-07-08_07:31: 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 13 39 75 110 84 69 59 23 21 4 3
(O-E)^2/E 1.6 0.2 0.0 1.6 1.9 1.1 0.9 1.5 2.5 1.0 0.3
Birthday Spacings: Sum(O-E)^2/E= 12.626, p= 0.755
RESULTS OF GCD FOR dh-ranFile-2018-07-08_07:31
Euclid's algorithm:
p-value, steps to gcd: 0.558349
p-value, dist. of gcd's: 0.581697
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-08_07:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.101 0.462 0.133 0.703 0.712 0.606 0.683 0.639
Bits 8 to 15---> 0.944 0.230 0.386 0.018 0.164 0.671 0.533 0.097
Bits 16 to 23---> 0.077 0.505 0.987 0.295 0.139 0.163 0.459 0.139
Bits 24 to 31---> 0.260 0.486 0.417 0.241 0.025 0.338 0.442 0.594
KS test for the above 32 p values: 0.941
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-08_07:31,
p-values for 5 runs: 0.7168, 0.6191, 0.2648, 0.7668, 0.2773
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-08_07:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 200 211.4 0.617 0.617
r= 29 5031 5134.0 2.067 2.683
r= 30 23370 23103.0 3.085 5.768
r= 31 11399 11551.5 2.014 7.782
chi-square = 7.782 with df = 3; p-value = 0.949
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-08_07:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 228 211.4 1.301 1.301
r= 30 5136 5134.0 0.001 1.301
r= 31 22958 23103.0 0.911 2.212
r= 32 11678 11551.5 1.385 3.597
chi-square = 3.597 with df = 3; p-value = 0.692
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-08_07:31
b-rank test for bits 1 to 8, p=0.58897
b-rank test for bits 2 to 9, p=0.47224
b-rank test for bits 3 to 10, p=0.15985
b-rank test for bits 4 to 11, p=0.36811
b-rank test for bits 5 to 12, p=0.97066
b-rank test for bits 6 to 13, p=0.61347
b-rank test for bits 7 to 14, p=0.35740
b-rank test for bits 8 to 15, p=0.01891
b-rank test for bits 9 to 16, p=0.96666
b-rank test for bits 10 to 17, p=0.70466
b-rank test for bits 11 to 18, p=0.58848
b-rank test for bits 12 to 19, p=0.59498
b-rank test for bits 13 to 20, p=0.74295
b-rank test for bits 14 to 21, p=0.90673
b-rank test for bits 15 to 22, p=0.43734
b-rank test for bits 16 to 23, p=0.41792
b-rank test for bits 17 to 24, p=0.14680
b-rank test for bits 18 to 25, p=0.75671
b-rank test for bits 19 to 26, p=0.30974
b-rank test for bits 20 to 27, p=0.47816
b-rank test for bits 21 to 28, p=0.68182
b-rank test for bits 22 to 29, p=0.65382
b-rank test for bits 23 to 30, p=0.96516
b-rank test for bits 24 to 31, p=0.58621
b-rank test for bits 25 to 32, p=0.87190
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 = 0.252629
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-08_07:31
(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 142550 1.50 0.932789
2 142216 0.72 0.763164
3 142450 1.26 0.896750
4 142065 0.36 0.641965
5 141973 0.15 0.559129
6 141439 -1.10 0.135905
7 142009 0.23 0.592070
8 142046 0.32 0.625259
9 141941 0.07 0.529493
10 142557 1.51 0.934892
11 142393 1.13 0.870777
12 141764 -0.34 0.367095
13 142045 0.32 0.624373
14 141566 -0.80 0.211227
15 141889 -0.05 0.481057
16 141130 -1.82 0.034314
17 141909 -0.00 0.499692
18 142339 1.00 0.842287
19 142218 0.72 0.764604
20 141447 -1.08 0.140024
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-08_07:31
Bits used No. missing words z-score p-value
23 to 32 141944 0.1196 0.547581
22 to 31 142326 1.4368 0.924612
21 to 30 142027 0.4058 0.657540
20 to 29 142359 1.5506 0.939500
19 to 28 142036 0.4368 0.668869
18 to 27 141175 -2.5322 0.005668
17 to 26 141408 -1.7287 0.041929
16 to 25 141485 -1.4632 0.071705
15 to 24 141917 0.0264 0.510550
14 to 23 142029 0.4127 0.660070
13 to 22 142490 2.0023 0.977374
12 to 21 142605 2.3989 0.991777
11 to 20 142359 1.5506 0.939500
10 to 19 141890 -0.0667 0.473428
9 to 18 141715 -0.6701 0.251396
8 to 17 141633 -0.9529 0.170330
7 to 16 142192 0.9747 0.835151
6 to 15 142129 0.7575 0.775620
5 to 14 142150 0.8299 0.796701
4 to 13 142013 0.3575 0.639635
3 to 12 141824 -0.2942 0.384287
2 to 11 142240 1.1402 0.872907
1 to 10 142056 0.5058 0.693487
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-08_07:31
Bits used No. missing words z-score p-value
28 to 32 141668 -0.8181 0.206659
27 to 31 141740 -0.5740 0.282984
26 to 30 141568 -1.1571 0.123626
25 to 29 141909 -0.0011 0.499554
24 to 28 141811 -0.3333 0.369446
23 to 27 141464 -1.5096 0.065574
22 to 26 141864 -0.1537 0.438939
21 to 25 141820 -0.3028 0.381016
20 to 24 141961 0.1752 0.569520
19 to 23 142008 0.3345 0.630989
18 to 22 141529 -1.2893 0.098655
17 to 21 141824 -0.2893 0.386193
16 to 20 142333 1.4362 0.924523
15 to 19 141883 -0.0893 0.464440
14 to 18 141436 -1.6045 0.054301
13 to 17 141632 -0.9401 0.173583
12 to 16 142106 0.6667 0.747511
11 to 15 141849 -0.2045 0.418978
10 to 14 141138 -2.6147 0.004466
9 to 13 141287 -2.1096 0.017447
8 to 12 141482 -1.4486 0.073728
7 to 11 141652 -0.8723 0.191521
6 to 10 141538 -1.2587 0.104061
5 to 9 141176 -2.4859 0.006462
4 to 8 141823 -0.2926 0.384897
3 to 7 141372 -1.8215 0.034269
2 to 6 142322 1.3989 0.919076
1 to 5 141506 -1.3672 0.085778
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-08_07:31
Bits used No. missing words z-score p-value
31 to 32 141715 -0.5732 0.283240
30 to 31 141613 -0.8741 0.191024
29 to 30 142011 0.2999 0.617878
28 to 29 141270 -1.8859 0.029652
27 to 28 142480 1.6834 0.953850
26 to 27 142213 0.8958 0.814815
25 to 26 141954 0.1318 0.552417
24 to 25 141612 -0.8771 0.190222
23 to 24 141659 -0.7384 0.230125
22 to 23 141575 -0.9862 0.162012
21 to 22 141119 -2.3314 0.009867
20 to 21 141353 -1.6411 0.050389
19 to 20 142082 0.5094 0.694747
18 to 19 141647 -0.7738 0.219514
17 to 18 141993 0.2468 0.597474
16 to 17 142346 1.2881 0.901147
15 to 16 142046 0.4032 0.656583
14 to 15 141724 -0.5467 0.292294
13 to 14 141174 -2.1691 0.015037
12 to 13 142330 1.2409 0.892681
11 to 12 141498 -1.2134 0.112496
10 to 11 141453 -1.3461 0.089134
9 to 10 141818 -0.2694 0.393807
8 to 9 141575 -0.9862 0.162012
7 to 8 141935 0.0757 0.530180
6 to 7 141597 -0.9213 0.178440
5 to 6 142046 0.4032 0.656583
4 to 5 141462 -1.3196 0.093491
3 to 4 141778 -0.3874 0.349229
2 to 3 141810 -0.2930 0.384758
1 to 2 141519 -1.1514 0.124781
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-08_07:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2521.51 0.304 0.619501
Test results for specific bytes for dh-ranFile-2018-07-08_07:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2390.48 -1.549 0.060713
2 to 9 2388.09 -1.583 0.056757
3 to 10 2501.11 0.016 0.506279
4 to 11 2437.02 -0.891 0.186534
5 to 12 2489.30 -0.151 0.439886
6 to 13 2318.88 -2.561 0.005212
7 to 14 2644.79 2.048 0.979705
8 to 15 2477.77 -0.314 0.376600
9 to 16 2416.82 -1.176 0.119734
10 to 17 2512.85 0.182 0.572120
11 to 18 2472.30 -0.392 0.347618
12 to 19 2296.66 -2.876 0.002016
13 to 20 2537.18 0.526 0.700486
14 to 21 2675.49 2.482 0.993463
15 to 22 2462.87 -0.525 0.299743
16 to 23 2552.26 0.739 0.770061
17 to 24 2617.48 1.661 0.951678
18 to 25 2613.85 1.610 0.946313
19 to 26 2516.00 0.226 0.589532
20 to 27 2454.85 -0.638 0.261586
21 to 28 2435.88 -0.907 0.182268
22 to 29 2462.84 -0.525 0.299622
23 to 30 2452.53 -0.671 0.251004
24 to 31 2400.07 -1.413 0.078799
25 to 32 2415.39 -1.197 0.115734
CDPARK for dh-ranFile-2018-07-08_07:31: 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
3531 0.3653 0.642555
3505 -0.8219 0.205562
3515 -0.3653 0.357445
3494 -1.3242 0.092718
3513 -0.4566 0.323972
3548 1.1416 0.873180
3525 0.0913 0.536383
3541 0.8219 0.794438
3555 1.4612 0.928018
3547 1.0959 0.863437
Square side=100, avg. no. parked=3527.40 sample std.=19.37
p-value of the KSTEST for those 10 p-values: 0.818016
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-08_07:31
0.2893,0.5276,0.9125,0.7304,0.1441,0.3403,0.0351,0.2533,0.0368,0.3628,
The KS test for those 10 p-values: 0.212308
The 3DSPHERES test for dh-ranFile-2018-07-08_07:31
sample no r^3 equiv. uni.
1 5.817 0.176258
2 115.180 0.978492
3 12.186 0.333815
4 10.802 0.302370
5 1.597 0.051835
6 0.943 0.030948
7 13.390 0.360033
8 1.089 0.035649
9 12.907 0.349650
10 49.344 0.806948
11 22.542 0.528297
12 30.619 0.639631
13 40.799 0.743327
14 16.169 0.416644
15 0.417 0.013790
16 14.134 0.375702
17 17.004 0.432655
18 13.748 0.367630
19 8.705 0.251855
20 20.507 0.495186
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.082248
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-08_07:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 0.1 0.1 -1.4 -0.8 -0.2
-1.5 0.6 2.3 0.4 1.0 0.9
-1.1 -0.0 1.3 -0.5 -0.7 1.0
-0.2 0.5 1.7 -2.8 -1.2 1.7
-1.8 -1.5 2.0 -2.2 0.4 0.0
-2.3 1.0 0.8 0.8 -0.8 0.1
-0.5 -0.4 0.5 -0.7 0.1 0.0
-1.1
Chi-square with 42 degrees of freedom:57.562758
z-score=1.698036, p-value=0.944678
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-08_07:31
Test no p-value
1 0.034527
2 0.000218
3 0.017114
4 0.585285
5 0.463220
6 0.042322
7 0.145160
8 0.642993
9 0.033151
10 0.758156
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.001183
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-08_07:31:
(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 66844 0.47 66815 0.33
3 25000.00 25050 0.10 24840 1.02
4 6666.67 6438 7.84 6676 0.01
5 1388.89 1390 0.00 1401 0.11
6 238.10 233 0.11 222 1.09
7 34.72 36 0.05 37 0.15
8 4.96 8 1.86 8 1.86
p=0.89253 p=0.40047
Number of rngs required: 687939, p-value: 0.296
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-08_07:31
No. of wins: Observed Expected
98229 98585.9
z-score=-1.596, pvalue=0.05524
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66852 66666.7 0.515 0.515
2 37459 37654.3 1.013 1.528
3 26960 26954.7 0.001 1.529
4 19267 19313.5 0.112 1.641
5 13976 13851.4 1.120 2.762
6 9956 9943.5 0.016 2.777
7 7146 7145.0 0.000 2.777
8 5005 5139.1 3.498 6.275
9 3679 3699.9 0.118 6.393
10 2663 2666.3 0.004 6.397
11 1990 1923.3 2.311 8.708
12 1362 1388.7 0.515 9.223
13 1066 1003.7 3.865 13.088
14 714 726.1 0.203 13.291
15 551 525.8 1.204 14.495
16 336 381.2 5.348 19.844
17 276 276.5 0.001 19.845
18 221 200.8 2.026 21.871
19 142 146.0 0.109 21.979
20 104 106.2 0.046 22.025
21 275 287.1 0.511 22.537
Chisq= 22.54 for 20 degrees of freedom, p= 0.68788
SUMMARY of craptest
p-value for no. of wins: 0.055235
p-value for throws/game: 0.687881
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-08_07:31
No. of wins: Observed Expected
98642 98585.9
z-score= 0.251, pvalue=0.59913
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66509 66666.7 0.373 0.373
2 37575 37654.3 0.167 0.540
3 27027 26954.7 0.194 0.734
4 19232 19313.5 0.344 1.077
5 13809 13851.4 0.130 1.207
6 10063 9943.5 1.435 2.642
7 7142 7145.0 0.001 2.644
8 5133 5139.1 0.007 2.651
9 3812 3699.9 3.399 6.049
10 2724 2666.3 1.249 7.298
11 1883 1923.3 0.846 8.144
12 1427 1388.7 1.054 9.198
13 987 1003.7 0.278 9.476
14 710 726.1 0.359 9.835
15 513 525.8 0.313 10.148
16 419 381.2 3.759 13.907
17 260 276.5 0.989 14.896
18 203 200.8 0.023 14.920
19 147 146.0 0.007 14.927
20 112 106.2 0.315 15.242
21 313 287.1 2.334 17.575
Chisq= 17.58 for 20 degrees of freedom, p= 0.38465
SUMMARY of craptest
p-value for no. of wins: 0.599130
p-value for throws/game: 0.384649
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0002,0.0012,0.0020,0.0045,0.0052,0.0057,0.0065,0.0099,0.0138,0.0150,
0.0171,0.0174,0.0177,0.0189,0.0250,0.0297,0.0309,0.0332,0.0343,0.0343,
0.0345,0.0351,0.0356,0.0368,0.0419,0.0423,0.0504,0.0518,0.0543,0.0552,
0.0568,0.0607,0.0656,0.0717,0.0737,0.0768,0.0788,0.0822,0.0858,0.0891,
0.0927,0.0935,0.0975,0.0987,0.1012,0.1041,0.1125,0.1157,0.1197,0.1236,
0.1248,0.1332,0.1359,0.1393,0.1395,0.1400,0.1441,0.1452,0.1468,0.1598,
0.1620,0.1620,0.1627,0.1639,0.1703,0.1736,0.1763,0.1784,0.1823,0.1865,
0.1902,0.1910,0.1915,0.2056,0.2067,0.2112,0.2123,0.2195,0.2296,0.2301,
0.2410,0.2510,0.2514,0.2519,0.2526,0.2533,0.2600,0.2616,0.2648,0.2773,
0.2830,0.2832,0.2893,0.2923,0.2954,0.2964,0.2996,0.2997,0.3024,0.3097,
0.3240,0.3338,0.3383,0.3403,0.3476,0.3492,0.3497,0.3563,0.3574,0.3574,
0.3600,0.3628,0.3645,0.3671,0.3671,0.3676,0.3681,0.3694,0.3757,0.3766,
0.3797,0.3810,0.3843,0.3846,0.3848,0.3849,0.3858,0.3862,0.3938,0.4005,
0.4099,0.4166,0.4167,0.4173,0.4179,0.4190,0.4327,0.4373,0.4389,0.4399,
0.4424,0.4590,0.4624,0.4632,0.4644,0.4688,0.4722,0.4734,0.4782,0.4811,
0.4863,0.4952,0.4996,0.4997,0.5053,0.5063,0.5106,0.5276,0.5283,0.5295,
0.5302,0.5325,0.5364,0.5476,0.5524,0.5583,0.5591,0.5695,0.5721,0.5817,
0.5853,0.5862,0.5885,0.5890,0.5895,0.5921,0.5937,0.5950,0.5975,0.5991,
0.6057,0.6135,0.6179,0.6191,0.6195,0.6244,0.6253,0.6310,0.6395,0.6396,
0.6396,0.6420,0.6426,0.6430,0.6538,0.6566,0.6566,0.6575,0.6601,0.6689,
0.6713,0.6818,0.6835,0.6879,0.6916,0.6935,0.6947,0.7005,0.7033,0.7047,
0.7120,0.7151,0.7168,0.7304,0.7429,0.7433,0.7475,0.7547,0.7567,0.7582,
0.7632,0.7646,0.7668,0.7701,0.7756,0.7944,0.7967,0.8069,0.8148,0.8180,
0.8352,0.8423,0.8634,0.8708,0.8719,0.8729,0.8732,0.8866,0.8925,0.8927,
0.8967,0.9011,0.9067,0.9125,0.9191,0.9245,0.9246,0.9280,0.9328,0.9349,
0.9395,0.9395,0.9413,0.9437,0.9447,0.9463,0.9493,0.9517,0.9523,0.9539,
0.9652,0.9667,0.9707,0.9774,0.9785,0.9797,0.9869,0.9918,0.9935,
Overall p-value after applying KStest on 269 p-values = 0.001959
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.