RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-08_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 15.74 18.2797 0.628597
2 to 25 15.94 11.8978 0.193715
3 to 26 15.95 18.7736 0.658321
4 to 27 15.82 18.6472 0.650847
5 to 28 15.62 14.2155 0.348205
6 to 29 15.64 15.7746 0.460135
7 to 30 15.75 16.2983 0.497208
8 to 31 15.51 19.5423 0.701696
9 to 32 15.56 18.9353 0.667741
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.266668
Tough bday spacings test for dh-ranFile-2018-07-08_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 5 27 64 103 98 101 51 26 13 5 7
(O-E)^2/E 1.9 2.5 1.2 0.3 0.0 6.7 0.0 0.5 0.2 0.4 2.1
Birthday Spacings: Sum(O-E)^2/E= 15.816, p= 0.895
RESULTS OF GCD FOR dh-ranFile-2018-07-08_02:31
Euclid's algorithm:
p-value, steps to gcd: 0.328586
p-value, dist. of gcd's: 0.433590
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-08_02:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.460 0.212 0.674 0.259 0.755 0.112 0.706 0.470
Bits 8 to 15---> 0.650 0.470 0.104 0.802 0.355 0.211 0.031 0.551
Bits 16 to 23---> 0.770 0.713 0.219 0.385 0.544 0.951 0.730 0.657
Bits 24 to 31---> 0.766 0.779 0.988 0.313 0.970 0.269 0.117 0.092
KS test for the above 32 p values: 0.065
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-08_02:31,
p-values for 5 runs: 0.6204, 0.3885, 0.4662, 0.7471, 0.2989
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-08_02:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 240 211.4 3.864 3.864
r= 29 5222 5134.0 1.508 5.372
r= 30 22947 23103.0 1.054 6.426
r= 31 11591 11551.5 0.135 6.561
chi-square = 6.561 with df = 3; p-value = 0.913
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-08_02:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 230 211.4 1.633 1.633
r= 30 5276 5134.0 3.927 5.560
r= 31 23086 23103.0 0.013 5.573
r= 32 11408 11551.5 1.783 7.356
chi-square = 7.356 with df = 3; p-value = 0.939
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-08_02:31
b-rank test for bits 1 to 8, p=0.36121
b-rank test for bits 2 to 9, p=0.53562
b-rank test for bits 3 to 10, p=0.68209
b-rank test for bits 4 to 11, p=0.05643
b-rank test for bits 5 to 12, p=0.22674
b-rank test for bits 6 to 13, p=0.88660
b-rank test for bits 7 to 14, p=0.94496
b-rank test for bits 8 to 15, p=0.25303
b-rank test for bits 9 to 16, p=0.82919
b-rank test for bits 10 to 17, p=0.67474
b-rank test for bits 11 to 18, p=0.69145
b-rank test for bits 12 to 19, p=0.47383
b-rank test for bits 13 to 20, p=0.43707
b-rank test for bits 14 to 21, p=0.29304
b-rank test for bits 15 to 22, p=0.26346
b-rank test for bits 16 to 23, p=0.25299
b-rank test for bits 17 to 24, p=0.87224
b-rank test for bits 18 to 25, p=0.50957
b-rank test for bits 19 to 26, p=0.50059
b-rank test for bits 20 to 27, p=0.22689
b-rank test for bits 21 to 28, p=0.31143
b-rank test for bits 22 to 29, p=0.13907
b-rank test for bits 23 to 30, p=0.68975
b-rank test for bits 24 to 31, p=0.71332
b-rank test for bits 25 to 32, p=0.35211
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 = 0.644665
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-08_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 142511 1.41 0.920104
2 141912 0.01 0.502489
3 142625 1.67 0.952750
4 141658 -0.59 0.278528
5 141479 -1.01 0.157342
6 141901 -0.02 0.492236
7 141112 -1.86 0.031237
8 142357 1.05 0.852210
9 143569 3.88 0.999947
10 141662 -0.58 0.281675
11 141835 -0.17 0.431063
12 140690 -2.85 0.002194
13 141240 -1.56 0.058926
14 141279 -1.47 0.070411
15 141493 -0.97 0.165343
16 141870 -0.09 0.463392
17 142383 1.11 0.865789
18 141853 -0.13 0.447646
19 141208 -1.64 0.050646
20 141509 -0.94 0.174804
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-08_02:31
Bits used No. missing words z-score p-value
23 to 32 141624 -0.9839 0.162583
22 to 31 141641 -0.9253 0.177411
21 to 30 141669 -0.8287 0.203630
20 to 29 142392 1.6644 0.951982
19 to 28 141666 -0.8391 0.200715
18 to 27 141716 -0.6667 0.252496
17 to 26 141766 -0.4942 0.310568
16 to 25 141718 -0.6598 0.254704
15 to 24 141922 0.0437 0.517424
14 to 23 141770 -0.4804 0.315454
13 to 22 142128 0.7540 0.774586
12 to 21 141789 -0.4149 0.339096
11 to 20 141758 -0.5218 0.300895
10 to 19 141475 -1.4977 0.067107
9 to 18 142152 0.8368 0.798646
8 to 17 142378 1.6161 0.946964
7 to 16 142057 0.5092 0.694696
6 to 15 142033 0.4264 0.665109
5 to 14 141738 -0.5908 0.277330
4 to 13 141865 -0.1529 0.439254
3 to 12 141348 -1.9356 0.026457
2 to 11 141652 -0.8873 0.187447
1 to 10 142190 0.9678 0.833435
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-08_02:31
Bits used No. missing words z-score p-value
28 to 32 142044 0.4565 0.675988
27 to 31 142222 1.0599 0.855405
26 to 30 141842 -0.2282 0.409731
25 to 29 141366 -1.8418 0.032752
24 to 28 141759 -0.5096 0.305168
23 to 27 141805 -0.3537 0.361797
22 to 26 141899 -0.0350 0.486033
21 to 25 141648 -0.8859 0.187845
20 to 24 141283 -2.1232 0.016871
19 to 23 142472 1.9074 0.971763
18 to 22 142282 1.2633 0.896757
17 to 21 141804 -0.3571 0.360527
16 to 20 141792 -0.3977 0.345415
15 to 19 141449 -1.5604 0.059328
14 to 18 142470 1.9006 0.971321
13 to 17 142142 0.7887 0.784860
12 to 16 142308 1.3514 0.911720
11 to 15 142112 0.6870 0.753964
10 to 14 142059 0.5074 0.694048
9 to 13 141597 -1.0587 0.144858
8 to 12 142163 0.8599 0.805077
7 to 11 142139 0.7785 0.781875
6 to 10 141802 -0.3638 0.357992
5 to 9 141709 -0.6791 0.248542
4 to 8 141952 0.1446 0.557504
3 to 7 142102 0.6531 0.743160
2 to 6 142080 0.5785 0.718551
1 to 5 141904 -0.0181 0.492792
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-08_02:31
Bits used No. missing words z-score p-value
31 to 32 141828 -0.2399 0.405199
30 to 31 142538 1.8545 0.968165
29 to 30 140981 -2.7384 0.003087
28 to 29 141958 0.1436 0.557080
27 to 28 141939 0.0875 0.534872
26 to 27 141619 -0.8564 0.195880
25 to 26 142148 0.7040 0.759297
24 to 25 142710 2.3619 0.990908
23 to 24 141889 -0.0600 0.476090
22 to 23 141597 -0.9213 0.178440
21 to 22 141762 -0.4346 0.331926
20 to 21 141604 -0.9007 0.183880
19 to 20 142286 1.1111 0.866742
18 to 19 142101 0.5654 0.714099
17 to 18 142266 1.0521 0.853629
16 to 17 141652 -0.7591 0.223901
15 to 16 142012 0.3029 0.619002
14 to 15 141847 -0.1839 0.427060
13 to 14 141947 0.1111 0.544240
12 to 13 142041 0.3884 0.651143
11 to 12 141722 -0.5526 0.290270
10 to 11 141761 -0.4376 0.330856
9 to 10 141494 -1.2252 0.110257
8 to 9 141216 -2.0452 0.020417
7 to 8 141779 -0.3845 0.350321
6 to 7 142584 1.9902 0.976714
5 to 6 142213 0.8958 0.814815
4 to 5 141634 -0.8122 0.208343
3 to 4 141768 -0.4169 0.338375
2 to 3 141939 0.0875 0.534872
1 to 2 142511 1.7748 0.962038
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-08_02:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2503.67 0.052 0.520708
Test results for specific bytes for dh-ranFile-2018-07-08_02:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2489.23 -0.152 0.439489
2 to 9 2505.39 0.076 0.530382
3 to 10 2595.30 1.348 0.911137
4 to 11 2351.80 -2.096 0.018049
5 to 12 2529.72 0.420 0.662881
6 to 13 2409.66 -1.278 0.100707
7 to 14 2475.58 -0.345 0.364910
8 to 15 2480.58 -0.275 0.391817
9 to 16 2472.74 -0.386 0.349933
10 to 17 2519.37 0.274 0.607939
11 to 18 2484.51 -0.219 0.413274
12 to 19 2630.81 1.850 0.967843
13 to 20 2474.71 -0.358 0.360276
14 to 21 2451.80 -0.682 0.247725
15 to 22 2631.12 1.854 0.968157
16 to 23 2519.88 0.281 0.610702
17 to 24 2517.84 0.252 0.599606
18 to 25 2472.59 -0.388 0.349151
19 to 26 2428.17 -1.016 0.154861
20 to 27 2409.38 -1.282 0.099997
21 to 28 2326.26 -2.457 0.007004
22 to 29 2406.62 -1.321 0.093314
23 to 30 2522.34 0.316 0.623954
24 to 31 2517.69 0.250 0.598770
25 to 32 2657.10 2.222 0.986847
CDPARK for dh-ranFile-2018-07-08_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
3555 1.4612 0.928018
3518 -0.2283 0.409702
3517 -0.2740 0.392053
3530 0.3196 0.625377
3492 -1.4155 0.078457
3529 0.2740 0.607947
3553 1.3699 0.914635
3550 1.2329 0.891189
3510 -0.5936 0.276387
3515 -0.3653 0.357445
Square side=100, avg. no. parked=3526.90 sample std.=19.60
p-value of the KSTEST for those 10 p-values: 0.774203
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-08_02:31
0.0828,0.0919,0.4789,0.3703,0.2910,0.5407,0.4273,0.0319,0.0843,0.8197,
The KS test for those 10 p-values: 0.069991
The 3DSPHERES test for dh-ranFile-2018-07-08_02:31
sample no r^3 equiv. uni.
1 54.388 0.836823
2 23.811 0.547831
3 14.314 0.379442
4 57.870 0.854704
5 14.178 0.376619
6 44.498 0.773105
7 30.941 0.643483
8 7.919 0.232000
9 109.343 0.973873
10 3.170 0.100283
11 23.731 0.546624
12 12.650 0.344040
13 23.906 0.549257
14 43.143 0.762623
15 39.053 0.727950
16 67.861 0.895861
17 2.489 0.079633
18 13.798 0.368675
19 21.310 0.508519
20 6.622 0.198076
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.875740
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-08_02:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 1.3 0.3 1.6 -0.1 -1.4
0.2 1.4 0.1 0.3 0.1 -0.5
-2.0 -1.7 -0.4 0.2 0.3 -1.4
1.2 0.0 0.6 -0.3 1.1 -0.2
-0.3 1.7 0.5 -0.3 0.7 2.7
0.0 0.8 -0.2 1.6 -0.2 -1.4
0.7 1.8 1.3 -0.7 0.1 2.0
0.8
Chi-square with 42 degrees of freedom:48.468342
z-score=0.705754, p-value=0.771683
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-08_02:31
Test no p-value
1 0.518914
2 0.041363
3 0.018124
4 0.004159
5 0.250852
6 0.006081
7 0.863445
8 0.173251
9 0.071080
10 0.190052
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000236
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-08_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 66783 0.20 66732 0.06
3 25000.00 24845 0.96 24907 0.35
4 6666.67 6725 0.51 6745 0.92
5 1388.89 1362 0.52 1326 2.85
6 238.10 244 0.15 252 0.81
7 34.72 35 0.00 32 0.21
8 4.96 5 0.00 5 0.00
p=0.11450 p=0.48201
Number of rngs required: 689728, p-value: 0.939
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-08_02:31
No. of wins: Observed Expected
98823 98585.9
z-score= 1.061, pvalue=0.85557
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66981 66666.7 1.482 1.482
2 37774 37654.3 0.380 1.862
3 26808 26954.7 0.799 2.661
4 19358 19313.5 0.103 2.764
5 13718 13851.4 1.285 4.049
6 9934 9943.5 0.009 4.058
7 7155 7145.0 0.014 4.072
8 4972 5139.1 5.432 9.504
9 3674 3699.9 0.181 9.685
10 2681 2666.3 0.081 9.766
11 1876 1923.3 1.165 10.930
12 1400 1388.7 0.091 11.022
13 969 1003.7 1.201 12.222
14 705 726.1 0.615 12.838
15 558 525.8 1.967 14.805
16 344 381.2 3.621 18.426
17 304 276.5 2.727 21.153
18 249 200.8 11.554 32.707
19 154 146.0 0.440 33.147
20 91 106.2 2.180 35.327
21 295 287.1 0.217 35.543
Chisq= 35.54 for 20 degrees of freedom, p= 0.98260
SUMMARY of craptest
p-value for no. of wins: 0.855572
p-value for throws/game: 0.982605
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-08_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 67018 66666.7 1.852 1.852
2 37563 37654.3 0.221 2.073
3 27038 26954.7 0.257 2.330
4 19182 19313.5 0.895 3.225
5 13840 13851.4 0.009 3.234
6 9822 9943.5 1.486 4.720
7 7079 7145.0 0.610 5.330
8 5144 5139.1 0.005 5.335
9 3748 3699.9 0.626 5.961
10 2685 2666.3 0.131 6.092
11 1913 1923.3 0.055 6.148
12 1416 1388.7 0.535 6.683
13 964 1003.7 1.571 8.254
14 687 726.1 2.110 10.364
15 525 525.8 0.001 10.366
16 348 381.2 2.883 13.249
17 255 276.5 1.678 14.926
18 202 200.8 0.007 14.933
19 151 146.0 0.172 15.106
20 108 106.2 0.030 15.136
21 312 287.1 2.157 17.293
Chisq= 17.29 for 20 degrees of freedom, p= 0.36610
SUMMARY of craptest
p-value for no. of wins: 0.305291
p-value for throws/game: 0.366102
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0002,0.0022,0.0031,0.0042,0.0061,0.0070,0.0169,0.0180,0.0181,0.0204,
0.0265,0.0307,0.0312,0.0319,0.0328,0.0414,0.0506,0.0564,0.0589,0.0593,
0.0650,0.0671,0.0700,0.0704,0.0711,0.0785,0.0796,0.0828,0.0843,0.0919,
0.0923,0.0933,0.1000,0.1003,0.1007,0.1041,0.1103,0.1124,0.1145,0.1174,
0.1391,0.1449,0.1549,0.1573,0.1626,0.1653,0.1733,0.1748,0.1774,0.1784,
0.1839,0.1874,0.1878,0.1901,0.1937,0.1959,0.1981,0.2007,0.2036,0.2083,
0.2112,0.2123,0.2194,0.2239,0.2267,0.2269,0.2320,0.2477,0.2485,0.2509,
0.2525,0.2530,0.2530,0.2547,0.2591,0.2635,0.2667,0.2689,0.2764,0.2773,
0.2785,0.2817,0.2903,0.2910,0.2930,0.2989,0.3009,0.3052,0.3053,0.3106,
0.3114,0.3127,0.3155,0.3286,0.3309,0.3319,0.3384,0.3391,0.3440,0.3454,
0.3482,0.3492,0.3499,0.3503,0.3521,0.3553,0.3574,0.3580,0.3603,0.3605,
0.3612,0.3618,0.3649,0.3661,0.3687,0.3703,0.3766,0.3794,0.3851,0.3885,
0.3918,0.3921,0.4052,0.4097,0.4097,0.4133,0.4271,0.4273,0.4311,0.4336,
0.4371,0.4393,0.4395,0.4476,0.4601,0.4601,0.4634,0.4662,0.4700,0.4702,
0.4738,0.4761,0.4789,0.4820,0.4860,0.4922,0.4928,0.4972,0.5006,0.5025,
0.5085,0.5096,0.5174,0.5189,0.5207,0.5304,0.5349,0.5349,0.5356,0.5407,
0.5442,0.5443,0.5466,0.5478,0.5493,0.5509,0.5571,0.5575,0.5988,0.5996,
0.6079,0.6079,0.6107,0.6190,0.6204,0.6240,0.6254,0.6286,0.6435,0.6447,
0.6497,0.6508,0.6511,0.6570,0.6583,0.6629,0.6651,0.6677,0.6738,0.6747,
0.6760,0.6821,0.6898,0.6915,0.6940,0.6947,0.7017,0.7062,0.7126,0.7133,
0.7141,0.7186,0.7279,0.7300,0.7432,0.7471,0.7540,0.7551,0.7593,0.7626,
0.7658,0.7696,0.7717,0.7731,0.7742,0.7746,0.7787,0.7819,0.7849,0.7986,
0.8022,0.8051,0.8148,0.8197,0.8292,0.8334,0.8368,0.8522,0.8536,0.8547,
0.8554,0.8556,0.8634,0.8658,0.8667,0.8722,0.8757,0.8866,0.8912,0.8950,
0.8959,0.8968,0.9111,0.9117,0.9127,0.9146,0.9201,0.9280,0.9386,0.9393,
0.9450,0.9470,0.9513,0.9520,0.9528,0.9620,0.9678,0.9682,0.9682,0.9700,
0.9713,0.9718,0.9739,0.9767,0.9826,0.9868,0.9884,0.9909,0.9999,
Overall p-value after applying KStest on 269 p-values = 0.248698
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.