RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-19_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 15.80 14.5161 0.369707
2 to 25 15.59 11.7017 0.182144
3 to 26 15.67 24.7574 0.899727
4 to 27 15.90 12.7925 0.250036
5 to 28 16.17 21.8351 0.808855
6 to 29 15.83 19.8537 0.718219
7 to 30 15.77 33.6902 0.990797
8 to 31 15.94 15.0445 0.407726
9 to 32 16.07 10.5658 0.121776
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.825420
Tough bday spacings test for dh-ranFile-2018-06-19_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 10 41 75 94 93 79 58 25 14 10 1
(O-E)^2/E 0.1 0.5 0.0 0.1 0.2 0.0 0.7 0.8 0.1 1.7 2.3
Birthday Spacings: Sum(O-E)^2/E= 6.542, p= 0.232
RESULTS OF GCD FOR dh-ranFile-2018-06-19_02:31
Euclid's algorithm:
p-value, steps to gcd: 0.224431
p-value, dist. of gcd's: 0.001841
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-19_02:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.913 0.551 0.408 0.730 0.271 0.677 0.764 0.228
Bits 8 to 15---> 0.736 0.092 0.181 0.797 0.354 0.953 0.288 0.899
Bits 16 to 23---> 0.503 0.008 0.231 0.162 0.711 0.117 0.876 0.803
Bits 24 to 31---> 0.199 0.139 0.996 0.383 0.401 0.992 0.050 0.296
KS test for the above 32 p values: 0.288
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-19_02:31,
p-values for 5 runs: 0.6282, 0.7311, 0.0178, 0.8334, 0.6860
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-19_02:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 221 211.4 0.434 0.434
r= 29 4972 5134.0 5.112 5.547
r= 30 23271 23103.0 1.221 6.768
r= 31 11536 11551.5 0.021 6.789
chi-square = 6.789 with df = 3; p-value = 0.921
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-19_02:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 204 211.4 0.260 0.260
r= 30 4989 5134.0 4.096 4.356
r= 31 23289 23103.0 1.497 5.853
r= 32 11518 11551.5 0.097 5.950
chi-square = 5.950 with df = 3; p-value = 0.886
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-19_02:31
b-rank test for bits 1 to 8, p=0.03951
b-rank test for bits 2 to 9, p=0.85014
b-rank test for bits 3 to 10, p=0.42343
b-rank test for bits 4 to 11, p=0.52468
b-rank test for bits 5 to 12, p=0.13459
b-rank test for bits 6 to 13, p=0.02310
b-rank test for bits 7 to 14, p=0.29621
b-rank test for bits 8 to 15, p=0.82481
b-rank test for bits 9 to 16, p=0.97846
b-rank test for bits 10 to 17, p=0.17025
b-rank test for bits 11 to 18, p=0.39603
b-rank test for bits 12 to 19, p=0.14498
b-rank test for bits 13 to 20, p=0.33236
b-rank test for bits 14 to 21, p=0.48586
b-rank test for bits 15 to 22, p=0.05887
b-rank test for bits 16 to 23, p=0.73501
b-rank test for bits 17 to 24, p=0.14270
b-rank test for bits 18 to 25, p=0.45941
b-rank test for bits 19 to 26, p=0.24641
b-rank test for bits 20 to 27, p=0.91178
b-rank test for bits 21 to 28, p=0.83392
b-rank test for bits 22 to 29, p=0.82337
b-rank test for bits 23 to 30, p=0.29095
b-rank test for bits 24 to 31, p=0.35097
b-rank test for bits 25 to 32, p=0.61933
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 = 0.558734
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-19_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 140922 -2.31 0.010532
2 141898 -0.03 0.489440
3 141483 -1.00 0.159601
4 140963 -2.21 0.013516
5 142045 0.32 0.624373
6 141385 -1.23 0.110274
7 141906 -0.01 0.496896
8 142076 0.39 0.651516
9 141477 -1.01 0.156220
10 141448 -1.08 0.140545
11 142132 0.52 0.698558
12 142037 0.30 0.617261
13 141748 -0.38 0.353109
14 142211 0.70 0.759544
15 142284 0.88 0.809321
16 142557 1.51 0.934892
17 141799 -0.26 0.398288
18 141936 0.06 0.524843
19 142215 0.71 0.762443
20 142216 0.72 0.763164
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-19_02:31
Bits used No. missing words z-score p-value
23 to 32 141232 -2.3356 0.009756
22 to 31 142122 0.7333 0.768326
21 to 30 141714 -0.6736 0.250298
20 to 29 142175 0.9161 0.820194
19 to 28 142419 1.7575 0.960582
18 to 27 141825 -0.2908 0.385605
17 to 26 141979 0.2402 0.594928
16 to 25 141830 -0.2736 0.392215
15 to 24 141279 -2.1736 0.014869
14 to 23 141526 -1.3218 0.093113
13 to 22 141779 -0.4494 0.326567
12 to 21 141967 0.1989 0.578815
11 to 20 142015 0.3644 0.642213
10 to 19 141487 -1.4563 0.072653
9 to 18 142176 0.9196 0.821097
8 to 17 141970 0.2092 0.582857
7 to 16 141687 -0.7667 0.221643
6 to 15 142006 0.3333 0.630563
5 to 14 142078 0.5816 0.719589
4 to 13 141887 -0.0770 0.469312
3 to 12 141583 -1.1253 0.130236
2 to 11 141517 -1.3529 0.088050
1 to 10 141819 -0.3115 0.377717
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-19_02:31
Bits used No. missing words z-score p-value
28 to 32 141904 -0.0181 0.492792
27 to 31 141758 -0.5130 0.303982
26 to 30 141771 -0.4689 0.319565
25 to 29 141878 -0.1062 0.457711
24 to 28 141886 -0.0791 0.468483
23 to 27 142009 0.3379 0.632267
22 to 26 141784 -0.4248 0.335474
21 to 25 142154 0.8294 0.796558
20 to 24 141988 0.2667 0.605141
19 to 23 141718 -0.6486 0.258306
18 to 22 142690 2.6463 0.995932
17 to 21 142054 0.4904 0.688077
16 to 20 142504 2.0158 0.978091
15 to 19 141862 -0.1604 0.436267
14 to 18 141777 -0.4486 0.326869
13 to 17 142360 1.5277 0.936706
12 to 16 142155 0.8328 0.797516
11 to 15 141854 -0.1876 0.425611
10 to 14 141970 0.2057 0.581472
9 to 13 141842 -0.2282 0.409731
8 to 12 141716 -0.6554 0.256119
7 to 11 142182 0.9243 0.822336
6 to 10 141805 -0.3537 0.361797
5 to 9 142395 1.6463 0.950153
4 to 8 141988 0.2667 0.605141
3 to 7 141286 -2.1130 0.017301
2 to 6 141208 -2.3774 0.008718
1 to 5 141560 -1.1842 0.118173
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-19_02:31
Bits used No. missing words z-score p-value
31 to 32 141944 0.1023 0.540729
30 to 31 142375 1.3737 0.915226
29 to 30 141821 -0.2606 0.397216
28 to 29 142054 0.4268 0.665221
27 to 28 142608 2.0610 0.980347
26 to 27 141712 -0.5821 0.280252
25 to 26 141844 -0.1927 0.423592
24 to 25 142686 2.2911 0.989020
23 to 24 141302 -1.7915 0.036604
22 to 23 142311 1.1849 0.881965
21 to 22 142201 0.8604 0.805211
20 to 21 142364 1.3412 0.910074
19 to 20 142169 0.7660 0.778158
18 to 19 141657 -0.7443 0.228337
17 to 18 141962 0.1554 0.561735
16 to 17 141871 -0.1131 0.454988
15 to 16 141912 0.0079 0.503142
14 to 15 142881 2.8663 0.997923
13 to 14 142196 0.8456 0.801122
12 to 13 141850 -0.1750 0.430534
11 to 12 141689 -0.6499 0.257865
10 to 11 141882 -0.0806 0.467872
9 to 10 141590 -0.9420 0.173102
8 to 9 141900 -0.0275 0.489022
7 to 8 141242 -1.9685 0.024504
6 to 7 141683 -0.6676 0.252182
5 to 6 141486 -1.2488 0.105876
4 to 5 142181 0.8014 0.788546
3 to 4 142037 0.3766 0.646767
2 to 3 141917 0.0226 0.509025
1 to 2 141966 0.1672 0.566381
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-19_02:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2441.53 -0.827 0.204153
Test results for specific bytes for dh-ranFile-2018-06-19_02:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2492.98 -0.099 0.460446
2 to 9 2604.45 1.477 0.930186
3 to 10 2452.91 -0.666 0.252741
4 to 11 2451.64 -0.684 0.247010
5 to 12 2423.52 -1.082 0.139719
6 to 13 2431.32 -0.971 0.165707
7 to 14 2423.54 -1.081 0.139781
8 to 15 2504.31 0.061 0.524293
9 to 16 2363.42 -1.932 0.026710
10 to 17 2543.97 0.622 0.732967
11 to 18 2371.26 -1.821 0.034327
12 to 19 2554.28 0.768 0.778627
13 to 20 2441.74 -0.824 0.204978
14 to 21 2473.21 -0.379 0.352405
15 to 22 2477.56 -0.317 0.375465
16 to 23 2627.62 1.805 0.964446
17 to 24 2521.93 0.310 0.621758
18 to 25 2500.53 0.008 0.503017
19 to 26 2485.60 -0.204 0.419317
20 to 27 2496.74 -0.046 0.481632
21 to 28 2518.12 0.256 0.601133
22 to 29 2621.74 1.722 0.957430
23 to 30 2585.90 1.215 0.887767
24 to 31 2519.05 0.269 0.606187
25 to 32 2422.02 -1.103 0.135047
CDPARK for dh-ranFile-2018-06-19_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
3538 0.6849 0.753306
3500 -1.0502 0.146807
3477 -2.1005 0.017844
3550 1.2329 0.891189
3551 1.2785 0.899470
3498 -1.1416 0.126820
3504 -0.8676 0.192812
3576 2.4201 0.992242
3514 -0.4110 0.340551
Square side=100, avg. no. parked=3526.30 sample std.=30.29
p-value of the KSTEST for those 10 p-values: 0.219397
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-19_02:31
0.4900,0.5046,0.7345,0.1524,0.2930,0.5784,0.6448,0.8458,0.1297,0.3553,
The KS test for those 10 p-values: 0.819060
The 3DSPHERES test for dh-ranFile-2018-06-19_02:31
sample no r^3 equiv. uni.
1 16.574 0.424464
2 11.075 0.308688
3 17.081 0.434107
4 21.385 0.509751
5 57.844 0.854578
6 11.567 0.319946
7 124.040 0.983992
8 24.789 0.562338
9 0.992 0.032529
10 85.365 0.941894
11 81.756 0.934468
12 5.919 0.179057
13 115.178 0.978491
14 18.776 0.465206
15 19.653 0.480611
16 9.815 0.279045
17 29.876 0.630591
18 18.849 0.466501
19 15.292 0.399338
20 9.951 0.282293
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.387115
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-19_02:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -0.3 0.1 -0.4 1.3 1.9
-0.9 -0.2 -1.0 -0.2 -1.3 0.4
0.5 1.3 1.3 -0.1 0.4 1.7
-0.4 -0.8 0.5 -0.3 -1.9 0.5
-1.0 -1.0 -0.5 -1.6 1.0 1.3
-1.0 -0.4 -1.8 -0.5 -0.1 0.8
1.0 -1.3 -1.6 -0.1 -0.6 -1.0
-1.1
Chi-square with 42 degrees of freedom:41.955318
z-score=-0.004875, p-value=0.527087
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-19_02:31
Test no p-value
1 0.032070
2 0.302046
3 0.073184
4 0.187277
5 0.591018
6 0.615118
7 0.018567
8 0.458538
9 0.707196
10 0.035331
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.023652
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-19_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 66884 0.71 66651 0.00
3 25000.00 24833 1.12 25058 0.13
4 6666.67 6606 0.55 6622 0.30
5 1388.89 1393 0.01 1379 0.07
6 238.10 252 0.81 257 1.50
7 34.72 26 2.19 30 0.64
8 4.96 5 0.00 2 1.77
p=0.50524 p=0.37958
Number of rngs required: 688066, p-value: 0.349
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-19_02:31
No. of wins: Observed Expected
98768 98585.9
z-score= 0.815, pvalue=0.79236
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66804 66666.7 0.283 0.283
2 37902 37654.3 1.629 1.912
3 26764 26954.7 1.350 3.262
4 19451 19313.5 0.979 4.241
5 13834 13851.4 0.022 4.263
6 9833 9943.5 1.229 5.492
7 7025 7145.0 2.016 7.508
8 5106 5139.1 0.213 7.721
9 3635 3699.9 1.137 8.858
10 2694 2666.3 0.288 9.146
11 1958 1923.3 0.625 9.771
12 1359 1388.7 0.637 10.408
13 1046 1003.7 1.781 12.189
14 682 726.1 2.683 14.873
15 516 525.8 0.184 15.057
16 342 381.2 4.021 19.078
17 287 276.5 0.396 19.474
18 201 200.8 0.000 19.474
19 159 146.0 1.160 20.634
20 111 106.2 0.216 20.850
21 291 287.1 0.053 20.902
Chisq= 20.90 for 20 degrees of freedom, p= 0.59710
SUMMARY of craptest
p-value for no. of wins: 0.792362
p-value for throws/game: 0.597103
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-19_02:31
No. of wins: Observed Expected
97960 98585.9
z-score=-2.799, pvalue=0.00256
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66427 66666.7 0.862 0.862
2 37542 37654.3 0.335 1.197
3 27170 26954.7 1.719 2.916
4 19443 19313.5 0.869 3.785
5 13950 13851.4 0.702 4.486
6 9996 9943.5 0.277 4.763
7 7207 7145.0 0.538 5.301
8 5114 5139.1 0.122 5.423
9 3605 3699.9 2.432 7.855
10 2672 2666.3 0.012 7.867
11 1918 1923.3 0.015 7.882
12 1372 1388.7 0.202 8.084
13 1001 1003.7 0.007 8.091
14 740 726.1 0.265 8.356
15 518 525.8 0.117 8.473
16 365 381.2 0.684 9.157
17 272 276.5 0.075 9.231
18 195 200.8 0.169 9.401
19 135 146.0 0.827 10.227
20 96 106.2 0.982 11.210
21 262 287.1 2.197 13.406
Chisq= 13.41 for 20 degrees of freedom, p= 0.14073
SUMMARY of craptest
p-value for no. of wins: 0.002561
p-value for throws/game: 0.140725
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0018,0.0026,0.0078,0.0087,0.0098,0.0105,0.0135,0.0149,0.0173,0.0178,
0.0178,0.0186,0.0231,0.0237,0.0245,0.0267,0.0321,0.0325,0.0343,0.0353,
0.0366,0.0395,0.0503,0.0589,0.0727,0.0732,0.0880,0.0918,0.0931,0.1059,
0.1103,0.1171,0.1182,0.1218,0.1268,0.1297,0.1302,0.1346,0.1350,0.1388,
0.1397,0.1398,0.1405,0.1407,0.1427,0.1450,0.1468,0.1524,0.1562,0.1596,
0.1617,0.1657,0.1703,0.1731,0.1791,0.1812,0.1821,0.1873,0.1928,0.1992,
0.2042,0.2050,0.2194,0.2216,0.2244,0.2283,0.2285,0.2308,0.2321,0.2464,
0.2470,0.2500,0.2503,0.2522,0.2527,0.2561,0.2579,0.2583,0.2714,0.2790,
0.2803,0.2823,0.2879,0.2882,0.2910,0.2930,0.2959,0.2962,0.3020,0.3040,
0.3087,0.3196,0.3199,0.3266,0.3269,0.3324,0.3355,0.3406,0.3490,0.3510,
0.3524,0.3531,0.3544,0.3553,0.3618,0.3697,0.3755,0.3777,0.3796,0.3832,
0.3856,0.3871,0.3922,0.3960,0.3972,0.3983,0.3993,0.4009,0.4077,0.4078,
0.4097,0.4193,0.4234,0.4236,0.4245,0.4256,0.4305,0.4341,0.4363,0.4550,
0.4577,0.4585,0.4594,0.4604,0.4652,0.4665,0.4679,0.4685,0.4693,0.4806,
0.4816,0.4859,0.4890,0.4894,0.4900,0.4928,0.4969,0.5030,0.5030,0.5031,
0.5046,0.5052,0.5090,0.5098,0.5243,0.5247,0.5248,0.5271,0.5407,0.5513,
0.5587,0.5617,0.5623,0.5664,0.5784,0.5788,0.5815,0.5829,0.5910,0.5949,
0.5971,0.6011,0.6051,0.6051,0.6062,0.6151,0.6173,0.6193,0.6218,0.6244,
0.6282,0.6306,0.6306,0.6323,0.6422,0.6448,0.6468,0.6515,0.6652,0.6770,
0.6860,0.6881,0.6986,0.7072,0.7113,0.7182,0.7196,0.7300,0.7311,0.7330,
0.7345,0.7350,0.7360,0.7533,0.7595,0.7624,0.7632,0.7641,0.7683,0.7782,
0.7786,0.7885,0.7924,0.7966,0.7966,0.7975,0.8011,0.8028,0.8052,0.8089,
0.8093,0.8191,0.8202,0.8211,0.8223,0.8234,0.8248,0.8254,0.8334,0.8339,
0.8458,0.8501,0.8546,0.8759,0.8820,0.8859,0.8878,0.8912,0.8990,0.8995,
0.8997,0.9101,0.9118,0.9126,0.9152,0.9210,0.9280,0.9302,0.9345,0.9349,
0.9367,0.9419,0.9502,0.9529,0.9574,0.9606,0.9644,0.9781,0.9785,0.9785,
0.9803,0.9840,0.9890,0.9908,0.9922,0.9922,0.9959,0.9960,0.9979,
Overall p-value after applying KStest on 269 p-values = 0.222292
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.