RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-26_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 15.72 12.7878 0.249729
2 to 25 15.58 24.4512 0.892316
3 to 26 15.48 24.7143 0.898711
4 to 27 15.68 17.0998 0.552375
5 to 28 15.78 14.0766 0.338326
6 to 29 15.61 37.2829 0.996920
7 to 30 15.57 31.0936 0.980545
8 to 31 15.73 12.6770 0.242475
9 to 32 15.84 21.3313 0.788181
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.059513
Tough bday spacings test for dh-ranFile-2018-06-26_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 6 37 68 87 106 97 48 22 18 8 3
(O-E)^2/E 1.1 0.0 0.4 1.2 0.7 4.5 0.3 2.0 0.7 0.3 0.3
Birthday Spacings: Sum(O-E)^2/E= 11.467, p= 0.678
RESULTS OF GCD FOR dh-ranFile-2018-06-26_19:31
Euclid's algorithm:
p-value, steps to gcd: 0.156166
p-value, dist. of gcd's: 0.481251
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-26_19:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.496 0.630 0.619 0.338 0.926 0.482 0.559 0.228
Bits 8 to 15---> 0.412 0.058 0.967 0.833 0.686 0.703 0.842 0.377
Bits 16 to 23---> 0.586 0.286 0.288 0.337 0.341 0.450 0.618 0.062
Bits 24 to 31---> 0.436 0.157 0.909 0.912 0.312 0.761 0.448 0.341
KS test for the above 32 p values: 0.442
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-26_19:31,
p-values for 5 runs: 0.0580, 0.9473, 0.6228, 0.5669, 0.6558
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-26_19:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 193 211.4 1.605 1.605
r= 29 5124 5134.0 0.020 1.624
r= 30 23080 23103.0 0.023 1.647
r= 31 11603 11551.5 0.229 1.876
chi-square = 1.876 with df = 3; p-value = 0.402
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-26_19:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 190 211.4 2.170 2.170
r= 30 5069 5134.0 0.823 2.993
r= 31 23201 23103.0 0.415 3.408
r= 32 11540 11551.5 0.011 3.420
chi-square = 3.420 with df = 3; p-value = 0.669
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-26_19:31
b-rank test for bits 1 to 8, p=0.97935
b-rank test for bits 2 to 9, p=0.59154
b-rank test for bits 3 to 10, p=0.14104
b-rank test for bits 4 to 11, p=0.74393
b-rank test for bits 5 to 12, p=0.03968
b-rank test for bits 6 to 13, p=0.65179
b-rank test for bits 7 to 14, p=0.62642
b-rank test for bits 8 to 15, p=0.07472
b-rank test for bits 9 to 16, p=0.13919
b-rank test for bits 10 to 17, p=0.35518
b-rank test for bits 11 to 18, p=0.91135
b-rank test for bits 12 to 19, p=0.12154
b-rank test for bits 13 to 20, p=0.73296
b-rank test for bits 14 to 21, p=0.31413
b-rank test for bits 15 to 22, p=0.70906
b-rank test for bits 16 to 23, p=0.14187
b-rank test for bits 17 to 24, p=0.00245
b-rank test for bits 18 to 25, p=0.00805
b-rank test for bits 19 to 26, p=0.90087
b-rank test for bits 20 to 27, p=0.98219
b-rank test for bits 21 to 28, p=0.77253
b-rank test for bits 22 to 29, p=0.97422
b-rank test for bits 23 to 30, p=0.87962
b-rank test for bits 24 to 31, p=0.58548
b-rank test for bits 25 to 32, p=0.17902
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 = 0.190788
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-26_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 141850 -0.14 0.444875
2 142373 1.08 0.860672
3 142134 0.52 0.700184
4 141437 -1.10 0.134889
5 141989 0.19 0.573834
6 140759 -2.69 0.003597
7 142436 1.23 0.890752
8 141464 -1.04 0.149056
9 141277 -1.48 0.069783
10 142074 0.38 0.649786
11 141968 0.14 0.554516
12 142091 0.42 0.664386
13 141419 -1.15 0.125974
14 141122 -1.84 0.032917
15 141232 -1.58 0.056762
16 141088 -1.92 0.027492
17 142369 1.07 0.858588
18 143112 2.81 0.997523
19 141903 -0.01 0.494100
20 142461 1.29 0.901292
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-26_19:31
Bits used No. missing words z-score p-value
23 to 32 141981 0.2471 0.597599
22 to 31 142161 0.8678 0.807256
21 to 30 141435 -1.6356 0.050960
20 to 29 142012 0.3540 0.638344
19 to 28 142276 1.2644 0.896953
18 to 27 142432 1.8023 0.964252
17 to 26 141227 -2.3529 0.009315
16 to 25 142143 0.8058 0.789809
15 to 24 141763 -0.5046 0.306925
14 to 23 141950 0.1402 0.555765
13 to 22 142368 1.5816 0.943132
12 to 21 141600 -1.0667 0.143064
11 to 20 141695 -0.7391 0.229933
10 to 19 142057 0.5092 0.694696
9 to 18 142117 0.7161 0.763036
8 to 17 142416 1.7471 0.959693
7 to 16 141535 -1.2908 0.098388
6 to 15 142094 0.6368 0.737870
5 to 14 141695 -0.7391 0.229933
4 to 13 141808 -0.3494 0.363389
3 to 12 142175 0.9161 0.820194
2 to 11 141875 -0.1184 0.452884
1 to 10 142206 1.0230 0.846846
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-26_19:31
Bits used No. missing words z-score p-value
28 to 32 141654 -0.8655 0.193375
27 to 31 141634 -0.9333 0.175327
26 to 30 141715 -0.6587 0.255030
25 to 29 142061 0.5141 0.696421
24 to 28 141420 -1.6587 0.048584
23 to 27 142069 0.5413 0.705834
22 to 26 141754 -0.5265 0.299256
21 to 25 142173 0.8938 0.814285
20 to 24 142058 0.5040 0.692857
19 to 23 141807 -0.3469 0.364340
18 to 22 141979 0.2362 0.593349
17 to 21 142206 1.0057 0.842711
16 to 20 141963 0.1819 0.572182
15 to 19 141606 -1.0282 0.151919
14 to 18 141512 -1.3469 0.089009
13 to 17 142053 0.4870 0.686877
12 to 16 142371 1.5650 0.941207
11 to 15 142247 1.1446 0.873822
10 to 14 142454 1.8463 0.967579
9 to 13 142365 1.5446 0.938784
8 to 12 141331 -1.9604 0.024972
7 to 11 141862 -0.1604 0.436267
6 to 10 142178 0.9107 0.818785
5 to 9 141120 -2.6757 0.003729
4 to 8 141668 -0.8181 0.206659
3 to 7 141646 -0.8926 0.186024
2 to 6 141697 -0.7198 0.235836
1 to 5 142062 0.5175 0.697605
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-26_19:31
Bits used No. missing words z-score p-value
31 to 32 142064 0.4563 0.675896
30 to 31 141745 -0.4847 0.313927
29 to 30 141987 0.2291 0.590610
28 to 29 141221 -2.0305 0.021154
27 to 28 141829 -0.2370 0.406343
26 to 27 142214 0.8987 0.815602
25 to 26 141785 -0.3668 0.356901
24 to 25 142088 0.5271 0.700921
23 to 24 141435 -1.3992 0.080876
22 to 23 141948 0.1141 0.545409
21 to 22 141854 -0.1632 0.435174
20 to 21 141605 -0.8977 0.184665
19 to 20 142347 1.2911 0.901659
18 to 19 141487 -1.2458 0.106417
17 to 18 141464 -1.3137 0.094481
16 to 17 141701 -0.6145 0.269428
15 to 16 141670 -0.7060 0.240098
14 to 15 142243 0.9843 0.837510
13 to 14 142406 1.4651 0.928554
12 to 13 142285 1.1082 0.866106
11 to 12 141705 -0.6027 0.273340
10 to 11 142480 1.6834 0.953850
9 to 10 141204 -2.0806 0.018734
8 to 9 142438 1.5595 0.940561
7 to 8 142379 1.3855 0.917044
6 to 7 141955 0.1347 0.553583
5 to 6 141584 -0.9597 0.168609
4 to 5 141894 -0.0452 0.481966
3 to 4 142229 0.9430 0.827154
2 to 3 141863 -0.1367 0.445647
1 to 2 142611 2.0698 0.980766
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-26_19:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2628.31 1.815 0.965208
Test results for specific bytes for dh-ranFile-2018-06-26_19:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2451.31 -0.689 0.245543
2 to 9 2609.15 1.544 0.938652
3 to 10 2545.82 0.648 0.741514
4 to 11 2497.72 -0.032 0.487151
5 to 12 2515.49 0.219 0.586696
6 to 13 2496.46 -0.050 0.480025
7 to 14 2500.80 0.011 0.504528
8 to 15 2729.31 3.243 0.999409
9 to 16 2568.40 0.967 0.833303
10 to 17 2325.35 -2.470 0.006757
11 to 18 2508.25 0.117 0.546423
12 to 19 2546.29 0.655 0.743666
13 to 20 2452.63 -0.670 0.251453
14 to 21 2523.34 0.330 0.629312
15 to 22 2442.08 -0.819 0.206358
16 to 23 2362.06 -1.951 0.025543
17 to 24 2572.67 1.028 0.847950
18 to 25 2360.54 -1.972 0.024286
19 to 26 2560.26 0.852 0.802967
20 to 27 2521.21 0.300 0.617898
21 to 28 2510.20 0.144 0.557360
22 to 29 2444.84 -0.780 0.217671
23 to 30 2545.02 0.637 0.737833
24 to 31 2450.13 -0.705 0.240336
25 to 32 2476.55 -0.332 0.370082
CDPARK for dh-ranFile-2018-06-26_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
3570 2.1461 0.984068
3540 0.7763 0.781201
3498 -1.1416 0.126820
3522 -0.0457 0.481790
3505 -0.8219 0.205562
3531 0.3653 0.642555
3564 1.8721 0.969407
3556 1.5068 0.934075
3500 -1.0502 0.146807
3537 0.6393 0.738676
Square side=100, avg. no. parked=3532.30 sample std.=24.78
p-value of the KSTEST for those 10 p-values: 0.241452
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-26_19:31
0.6485,0.9278,0.3411,0.8526,0.3033,0.1993,0.9043,0.7177,0.4996,0.9042,
The KS test for those 10 p-values: 0.232376
The 3DSPHERES test for dh-ranFile-2018-06-26_19:31
sample no r^3 equiv. uni.
1 12.276 0.335811
2 13.757 0.367804
3 3.097 0.098072
4 92.308 0.953900
5 6.403 0.192206
6 67.178 0.893464
7 71.420 0.907510
8 4.563 0.141108
9 35.990 0.698706
10 28.389 0.611825
11 46.296 0.786306
12 18.412 0.458680
13 134.238 0.988605
14 34.308 0.681326
15 84.295 0.939785
16 25.893 0.578151
17 15.101 0.395499
18 2.218 0.071255
19 60.168 0.865422
20 35.671 0.695482
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.317178
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-26_19:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -0.3 -0.8 1.5 0.0 -0.1
0.1 -0.0 -0.6 -0.7 -0.5 -0.8
0.3 -0.0 1.1 -0.2 0.2 0.9
0.8 -0.3 1.6 -1.9 0.9 -1.8
-0.6 1.6 -1.8 0.1 -0.9 0.1
-0.9 0.1 0.0 0.8 -1.0 0.2
0.5 0.2 0.5 -0.7 -1.3 -1.0
-0.1
Chi-square with 42 degrees of freedom:31.148164
z-score=-1.184032, p-value=0.109292
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-26_19:31
Test no p-value
1 0.679712
2 0.034995
3 0.526508
4 0.317215
5 0.005385
6 0.837014
7 0.011234
8 0.020297
9 0.858378
10 0.445779
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.027947
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-26_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 66564 0.16 66614 0.04
3 25000.00 24982 0.01 24922 0.24
4 6666.67 6727 0.55 6718 0.40
5 1388.89 1447 2.43 1474 5.22
6 238.10 245 0.20 226 0.61
7 34.72 28 1.30 38 0.31
8 4.96 6 0.22 7 0.84
p=0.43905 p=0.73583
Number of rngs required: 688863, p-value: 0.702
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-26_19:31
No. of wins: Observed Expected
98586 98585.9
z-score= 0.001, pvalue=0.50025
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66413 66666.7 0.965 0.965
2 37747 37654.3 0.228 1.193
3 26963 26954.7 0.003 1.196
4 19475 19313.5 1.351 2.547
5 13705 13851.4 1.548 4.095
6 9944 9943.5 0.000 4.095
7 7174 7145.0 0.117 4.212
8 5161 5139.1 0.094 4.306
9 3700 3699.9 0.000 4.306
10 2649 2666.3 0.112 4.418
11 1986 1923.3 2.042 6.460
12 1431 1388.7 1.286 7.746
13 1008 1003.7 0.018 7.764
14 721 726.1 0.036 7.801
15 558 525.8 1.967 9.768
16 357 381.2 1.530 11.298
17 288 276.5 0.475 11.773
18 208 200.8 0.256 12.029
19 136 146.0 0.683 12.712
20 94 106.2 1.405 14.117
21 282 287.1 0.091 14.208
Chisq= 14.21 for 20 degrees of freedom, p= 0.18021
SUMMARY of craptest
p-value for no. of wins: 0.500252
p-value for throws/game: 0.180212
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-26_19:31
No. of wins: Observed Expected
98282 98585.9
z-score=-1.359, pvalue=0.08707
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66483 66666.7 0.506 0.506
2 37711 37654.3 0.085 0.591
3 27024 26954.7 0.178 0.769
4 19319 19313.5 0.002 0.771
5 13802 13851.4 0.176 0.947
6 10149 9943.5 4.245 5.192
7 7151 7145.0 0.005 5.197
8 5258 5139.1 2.752 7.950
9 3641 3699.9 0.937 8.886
10 2630 2666.3 0.494 9.380
11 1871 1923.3 1.424 10.804
12 1371 1388.7 0.227 11.031
13 1013 1003.7 0.086 11.117
14 675 726.1 3.602 14.718
15 524 525.8 0.006 14.725
16 383 381.2 0.009 14.734
17 278 276.5 0.008 14.741
18 203 200.8 0.023 14.765
19 155 146.0 0.557 15.322
20 84 106.2 4.646 19.968
21 275 287.1 0.511 20.479
Chisq= 20.48 for 20 degrees of freedom, p= 0.57166
SUMMARY of craptest
p-value for no. of wins: 0.087068
p-value for throws/game: 0.571662
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0024,0.0036,0.0037,0.0054,0.0068,0.0080,0.0093,0.0112,0.0187,0.0203,
0.0212,0.0243,0.0250,0.0255,0.0275,0.0279,0.0329,0.0350,0.0397,0.0486,
0.0510,0.0568,0.0580,0.0584,0.0595,0.0618,0.0698,0.0713,0.0747,0.0809,
0.0871,0.0890,0.0945,0.0981,0.0984,0.1064,0.1093,0.1215,0.1260,0.1268,
0.1349,0.1392,0.1410,0.1411,0.1419,0.1431,0.1468,0.1491,0.1519,0.1562,
0.1570,0.1686,0.1753,0.1790,0.1802,0.1847,0.1860,0.1908,0.1922,0.1934,
0.1993,0.2056,0.2064,0.2067,0.2177,0.2278,0.2299,0.2299,0.2324,0.2358,
0.2401,0.2403,0.2415,0.2425,0.2455,0.2497,0.2515,0.2550,0.2694,0.2733,
0.2859,0.2877,0.2993,0.3033,0.3069,0.3121,0.3139,0.3141,0.3172,0.3172,
0.3358,0.3367,0.3377,0.3383,0.3411,0.3412,0.3413,0.3552,0.3569,0.3634,
0.3643,0.3678,0.3701,0.3765,0.3955,0.4016,0.4063,0.4121,0.4352,0.4359,
0.4363,0.4391,0.4423,0.4449,0.4456,0.4458,0.4484,0.4504,0.4529,0.4587,
0.4800,0.4813,0.4818,0.4820,0.4824,0.4872,0.4941,0.4956,0.4996,0.5003,
0.5045,0.5265,0.5454,0.5464,0.5524,0.5536,0.5545,0.5558,0.5574,0.5588,
0.5669,0.5717,0.5722,0.5738,0.5782,0.5855,0.5861,0.5867,0.5906,0.5915,
0.5933,0.5976,0.6118,0.6178,0.6179,0.6194,0.6228,0.6264,0.6293,0.6296,
0.6383,0.6426,0.6485,0.6498,0.6518,0.6558,0.6644,0.6687,0.6759,0.6777,
0.6797,0.6813,0.6863,0.6869,0.6929,0.6947,0.6955,0.6964,0.6976,0.6987,
0.7002,0.7009,0.7020,0.7029,0.7058,0.7091,0.7177,0.7330,0.7358,0.7378,
0.7379,0.7387,0.7415,0.7437,0.7439,0.7615,0.7630,0.7725,0.7812,0.7863,
0.7882,0.7898,0.8030,0.8073,0.8143,0.8156,0.8188,0.8202,0.8272,0.8331,
0.8333,0.8370,0.8375,0.8417,0.8427,0.8468,0.8479,0.8526,0.8584,0.8586,
0.8607,0.8654,0.8661,0.8738,0.8796,0.8908,0.8923,0.8935,0.8970,0.8987,
0.9009,0.9013,0.9017,0.9042,0.9043,0.9075,0.9093,0.9113,0.9122,0.9170,
0.9262,0.9278,0.9286,0.9341,0.9387,0.9388,0.9398,0.9406,0.9412,0.9431,
0.9473,0.9539,0.9539,0.9597,0.9643,0.9652,0.9669,0.9676,0.9694,0.9742,
0.9794,0.9805,0.9808,0.9822,0.9841,0.9886,0.9969,0.9975,0.9994,
Overall p-value after applying KStest on 269 p-values = 0.100741
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.