RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-03-26_21:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.62 31.6735 0.983484
2 to 25 16.10 13.5017 0.297995
3 to 26 15.76 18.0608 0.614983
4 to 27 15.83 16.7092 0.525769
5 to 28 15.38 22.4206 0.830920
6 to 29 15.79 24.7560 0.899694
7 to 30 15.83 8.2674 0.039509
8 to 31 15.60 20.0463 0.728131
9 to 32 15.83 14.4847 0.367456
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.662698
Tough bday spacings test for dh-ranFile-2018-03-26_21:31: 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 43 66 105 92 68 60 32 11 8 5
(O-E)^2/E 0.1 1.1 0.7 0.5 0.3 1.3 1.2 0.2 1.0 0.3 0.2
Birthday Spacings: Sum(O-E)^2/E= 6.985, p= 0.273
RESULTS OF GCD FOR dh-ranFile-2018-03-26_21:31
Euclid's algorithm:
p-value, steps to gcd: 0.311527
p-value, dist. of gcd's: 0.960202
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-03-26_21:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.918 0.018 0.566 0.722 0.527 0.126 0.609 0.168
Bits 8 to 15---> 0.820 0.975 0.126 0.430 0.794 0.658 0.512 0.524
Bits 16 to 23---> 0.657 0.338 0.213 0.683 0.792 0.044 0.915 0.615
Bits 24 to 31---> 0.642 0.768 0.068 0.994 0.741 0.159 0.889 0.463
KS test for the above 32 p values: 0.479
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-03-26_21:31,
p-values for 5 runs: 0.1322, 0.5776, 0.1323, 0.1455, 0.7276
Rank test for binary matrices (31x31) for dh-ranFile-2018-03-26_21:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 227 211.4 1.148 1.148
r= 29 5001 5134.0 3.446 4.594
r= 30 23184 23103.0 0.284 4.878
r= 31 11588 11551.5 0.115 4.993
chi-square = 4.993 with df = 3; p-value = 0.828
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-03-26_21:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 202 211.4 0.420 0.420
r= 30 5086 5134.0 0.449 0.869
r= 31 23335 23103.0 2.329 3.197
r= 32 11377 11551.5 2.637 5.834
chi-square = 5.834 with df = 3; p-value = 0.880
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-03-26_21:31
b-rank test for bits 1 to 8, p=0.33889
b-rank test for bits 2 to 9, p=0.82270
b-rank test for bits 3 to 10, p=0.79341
b-rank test for bits 4 to 11, p=0.25366
b-rank test for bits 5 to 12, p=0.23011
b-rank test for bits 6 to 13, p=0.08905
b-rank test for bits 7 to 14, p=0.73757
b-rank test for bits 8 to 15, p=0.28324
b-rank test for bits 9 to 16, p=0.20201
b-rank test for bits 10 to 17, p=0.04081
b-rank test for bits 11 to 18, p=0.30779
b-rank test for bits 12 to 19, p=0.14694
b-rank test for bits 13 to 20, p=0.61718
b-rank test for bits 14 to 21, p=0.22768
b-rank test for bits 15 to 22, p=0.54721
b-rank test for bits 16 to 23, p=0.45578
b-rank test for bits 17 to 24, p=0.95599
b-rank test for bits 18 to 25, p=0.54655
b-rank test for bits 19 to 26, p=0.61413
b-rank test for bits 20 to 27, p=0.37668
b-rank test for bits 21 to 28, p=0.69443
b-rank test for bits 22 to 29, p=0.57314
b-rank test for bits 23 to 30, p=0.67995
b-rank test for bits 24 to 31, p=0.20175
b-rank test for bits 25 to 32, p=0.74652
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 = 0.582892
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-03-26_21:31
(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 141946 0.09 0.534139
2 141566 -0.80 0.211227
3 141506 -0.94 0.173004
4 141767 -0.33 0.369738
5 141615 -0.69 0.245825
6 141680 -0.54 0.296042
7 141791 -0.28 0.391093
8 141842 -0.16 0.437499
9 141898 -0.03 0.489440
10 142258 0.81 0.792364
11 142798 2.08 0.981068
12 142387 1.12 0.867800
13 141558 -0.82 0.205862
14 141988 0.18 0.572918
15 142362 1.06 0.854890
16 141721 -0.44 0.329960
17 141798 -0.26 0.397387
18 142243 0.78 0.782188
19 142010 0.24 0.592977
20 141893 -0.04 0.484782
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-03-26_21:31
Bits used No. missing words z-score p-value
23 to 32 142237 1.1299 0.870740
22 to 31 141533 -1.2977 0.097197
21 to 30 141615 -1.0149 0.155069
20 to 29 141706 -0.7011 0.241609
19 to 28 141644 -0.9149 0.180114
18 to 27 141680 -0.7908 0.214532
17 to 26 141835 -0.2563 0.398856
16 to 25 141872 -0.1287 0.448788
15 to 24 141972 0.2161 0.585547
14 to 23 141990 0.2782 0.609560
13 to 22 141928 0.0644 0.525666
12 to 21 141745 -0.5667 0.285474
11 to 20 141928 0.0644 0.525666
10 to 19 142160 0.8644 0.806310
9 to 18 141588 -1.1080 0.133923
8 to 17 142451 1.8678 0.969107
7 to 16 142120 0.7264 0.766218
6 to 15 142135 0.7782 0.781766
5 to 14 141876 -0.1149 0.454250
4 to 13 142472 1.9402 0.973825
3 to 12 142339 1.4816 0.930779
2 to 11 142037 0.4402 0.670119
1 to 10 141996 0.2989 0.617477
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-03-26_21:31
Bits used No. missing words z-score p-value
28 to 32 141988 0.2667 0.605141
27 to 31 141625 -0.9638 0.167565
26 to 30 141813 -0.3265 0.372007
25 to 29 142090 0.6124 0.729877
24 to 28 141863 -0.1571 0.437602
23 to 27 142218 1.0463 0.852298
22 to 26 141574 -1.1367 0.127829
21 to 25 141713 -0.6655 0.252857
20 to 24 142213 1.0294 0.848352
19 to 23 141623 -0.9706 0.165871
18 to 22 142007 0.3311 0.629710
17 to 21 142049 0.4735 0.682057
16 to 20 142204 0.9989 0.841074
15 to 19 141406 -1.7062 0.043985
14 to 18 141884 -0.0859 0.465787
13 to 17 141874 -0.1198 0.452336
12 to 16 142343 1.4701 0.929228
11 to 15 142193 0.9616 0.831873
10 to 14 141880 -0.0994 0.460401
9 to 13 141937 0.0938 0.537365
8 to 12 141972 0.2124 0.584118
7 to 11 141957 0.1616 0.564187
6 to 10 142266 1.2091 0.886678
5 to 9 141701 -0.7062 0.240031
4 to 8 141675 -0.7943 0.213499
3 to 7 141444 -1.5774 0.057353
2 to 6 142010 0.3413 0.633544
1 to 5 142068 0.5379 0.704665
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-03-26_21:31
Bits used No. missing words z-score p-value
31 to 32 141858 -0.1514 0.439824
30 to 31 141409 -1.4759 0.069985
29 to 30 142515 1.7866 0.963002
28 to 29 142035 0.3707 0.644573
27 to 28 142151 0.7129 0.762043
26 to 27 141876 -0.0983 0.460840
25 to 26 141629 -0.8269 0.204138
24 to 25 141799 -0.3255 0.372418
23 to 24 142170 0.7689 0.779035
22 to 23 141692 -0.6411 0.260732
21 to 22 142033 0.3648 0.642373
20 to 21 142096 0.5506 0.709063
19 to 20 141881 -0.0836 0.466699
18 to 19 141770 -0.4110 0.340535
17 to 18 141358 -1.6263 0.051938
16 to 17 142825 2.7011 0.996544
15 to 16 141733 -0.5201 0.301480
14 to 15 142241 0.9784 0.836056
13 to 14 141858 -0.1514 0.439824
12 to 13 141444 -1.3727 0.084930
11 to 12 141994 0.2498 0.598615
10 to 11 142235 0.9607 0.831643
9 to 10 142422 1.5123 0.934771
8 to 9 141733 -0.5201 0.301480
7 to 8 141954 0.1318 0.552417
6 to 7 141536 -1.1013 0.135390
5 to 6 142448 1.5890 0.943969
4 to 5 141308 -1.7738 0.038045
3 to 4 141899 -0.0305 0.487845
2 to 3 142131 0.6539 0.743410
1 to 2 141593 -0.9331 0.175377
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-03-26_21:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2573.54 1.040 0.850846
Test results for specific bytes for dh-ranFile-2018-03-26_21:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2401.81 -1.389 0.082467
2 to 9 2475.31 -0.349 0.363492
3 to 10 2544.03 0.623 0.733239
4 to 11 2600.15 1.416 0.921669
5 to 12 2503.34 0.047 0.518854
6 to 13 2453.46 -0.658 0.255225
7 to 14 2442.89 -0.808 0.209629
8 to 15 2528.22 0.399 0.655103
9 to 16 2487.46 -0.177 0.429597
10 to 17 2559.85 0.846 0.801334
11 to 18 2558.23 0.823 0.794888
12 to 19 2490.55 -0.134 0.446854
13 to 20 2608.01 1.527 0.936675
14 to 21 2427.22 -1.029 0.151669
15 to 22 2470.68 -0.415 0.339209
16 to 23 2433.10 -0.946 0.172062
17 to 24 2581.29 1.150 0.874863
18 to 25 2449.32 -0.717 0.236767
19 to 26 2534.58 0.489 0.687607
20 to 27 2549.47 0.700 0.757936
21 to 28 2496.72 -0.046 0.481484
22 to 29 2524.30 0.344 0.634424
23 to 30 2528.63 0.405 0.657206
24 to 31 2573.01 1.032 0.849080
25 to 32 2562.15 0.879 0.810276
CDPARK for dh-ranFile-2018-03-26_21:31: 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
3568 2.0548 0.980051
3564 1.8721 0.969407
3516 -0.3196 0.374623
3491 -1.4612 0.071982
3552 1.3242 0.907282
3530 0.3196 0.625377
3489 -1.5525 0.060270
3531 0.3653 0.642555
3562 1.7808 0.962529
3541 0.8219 0.794438
Square side=100, avg. no. parked=3534.40 sample std.=27.27
p-value of the KSTEST for those 10 p-values: 0.060094
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-03-26_21:31
0.8018,0.3514,0.3551,0.1092,0.6163,0.4708,0.2611,0.4608,0.0751,0.6337,
The KS test for those 10 p-values: 0.481668
The 3DSPHERES test for dh-ranFile-2018-03-26_21:31
sample no r^3 equiv. uni.
1 36.180 0.700609
2 32.548 0.662077
3 5.703 0.173127
4 9.950 0.282278
5 89.533 0.949433
6 7.519 0.221691
7 8.303 0.241779
8 29.855 0.630335
9 58.421 0.857353
10 1.212 0.039597
11 61.087 0.869479
12 5.148 0.157682
13 9.847 0.279809
14 1.321 0.043065
15 31.443 0.649392
16 19.915 0.485130
17 13.076 0.353286
18 7.731 0.227186
19 58.797 0.859126
20 5.327 0.162706
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.498247
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-03-26_21:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -0.7 0.3 -0.7 -0.5 -1.0
-1.3 -0.8 0.4 -0.3 -1.3 1.3
0.2 0.2 -0.2 0.2 2.0 -0.7
-0.9 1.0 -0.2 -0.9 0.1 -0.1
-0.4 -1.0 -0.9 2.1 0.6 1.7
-1.3 -1.4 0.6 -0.6 2.6 0.6
-0.5 0.5 -1.2 -0.1 0.1 0.0
-0.1
Chi-square with 42 degrees of freedom:39.329967
z-score=-0.291324, p-value=0.411174
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-03-26_21:31
Test no p-value
1 0.651148
2 0.083192
3 0.773267
4 0.201541
5 0.819839
6 0.225230
7 0.524829
8 0.077294
9 0.804745
10 0.080210
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.397756
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-03-26_21:31:
(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 66725 0.05 66667 0.00
3 25000.00 24923 0.24 24819 1.31
4 6666.67 6671 0.00 6766 1.48
5 1388.89 1408 0.26 1452 2.87
6 238.10 230 0.28 262 2.40
7 34.72 32 0.21 29 0.94
8 4.96 10 5.12 4 0.19
p=0.59488 p=0.83663
Number of rngs required: 687995, p-value: 0.319
RESULTS OF CRAPS TEST for dh-ranFile-2018-03-26_21:31
No. of wins: Observed Expected
98865 98585.9
z-score= 1.248, pvalue=0.89407
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66544 66666.7 0.226 0.226
2 37722 37654.3 0.122 0.347
3 27001 26954.7 0.079 0.427
4 19376 19313.5 0.203 0.629
5 13744 13851.4 0.833 1.462
6 10062 9943.5 1.411 2.874
7 7164 7145.0 0.050 2.924
8 5120 5139.1 0.071 2.995
9 3698 3699.9 0.001 2.996
10 2665 2666.3 0.001 2.996
11 1854 1923.3 2.499 5.495
12 1404 1388.7 0.168 5.663
13 1022 1003.7 0.333 5.996
14 708 726.1 0.453 6.449
15 527 525.8 0.003 6.452
16 408 381.2 1.891 8.343
17 293 276.5 0.980 9.323
18 193 200.8 0.305 9.628
19 156 146.0 0.687 10.315
20 89 106.2 2.790 13.106
21 250 287.1 4.798 17.903
Chisq= 17.90 for 20 degrees of freedom, p= 0.40621
SUMMARY of craptest
p-value for no. of wins: 0.894073
p-value for throws/game: 0.406215
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-03-26_21:31
No. of wins: Observed Expected
98344 98585.9
z-score=-1.082, pvalue=0.13969
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66544 66666.7 0.226 0.226
2 37772 37654.3 0.368 0.593
3 26730 26954.7 1.874 2.467
4 19397 19313.5 0.361 2.829
5 13676 13851.4 2.222 5.050
6 10071 9943.5 1.634 6.684
7 7187 7145.0 0.247 6.930
8 5120 5139.1 0.071 7.001
9 3763 3699.9 1.077 8.079
10 2761 2666.3 3.364 11.442
11 1909 1923.3 0.107 11.549
12 1432 1388.7 1.348 12.897
13 967 1003.7 1.343 14.240
14 757 726.1 1.311 15.551
15 502 525.8 1.080 16.631
16 377 381.2 0.045 16.677
17 261 276.5 0.873 17.550
18 197 200.8 0.073 17.623
19 166 146.0 2.744 20.367
20 116 106.2 0.901 21.269
21 295 287.1 0.217 21.485
Chisq= 21.49 for 20 degrees of freedom, p= 0.63092
SUMMARY of craptest
p-value for no. of wins: 0.139686
p-value for throws/game: 0.630916
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0183,0.0380,0.0395,0.0396,0.0408,0.0431,0.0440,0.0441,0.0519,0.0574,
0.0601,0.0603,0.0677,0.0700,0.0720,0.0751,0.0773,0.0802,0.0825,0.0832,
0.0849,0.0891,0.0972,0.1092,0.1259,0.1262,0.1278,0.1322,0.1323,0.1339,
0.1354,0.1397,0.1455,0.1469,0.1517,0.1551,0.1577,0.1589,0.1627,0.1659,
0.1676,0.1679,0.1721,0.1730,0.1731,0.1754,0.1801,0.2015,0.2017,0.2020,
0.2041,0.2059,0.2096,0.2112,0.2128,0.2135,0.2145,0.2217,0.2252,0.2272,
0.2277,0.2301,0.2368,0.2400,0.2416,0.2418,0.2458,0.2529,0.2537,0.2552,
0.2607,0.2611,0.2731,0.2798,0.2823,0.2832,0.2855,0.2960,0.2980,0.3015,
0.3015,0.3078,0.3115,0.3191,0.3300,0.3377,0.3389,0.3392,0.3405,0.3514,
0.3533,0.3551,0.3635,0.3675,0.3697,0.3720,0.3724,0.3746,0.3767,0.3911,
0.3974,0.3978,0.3989,0.4062,0.4112,0.4296,0.4300,0.4375,0.4376,0.4398,
0.4398,0.4469,0.4488,0.4523,0.4542,0.4558,0.4604,0.4608,0.4608,0.4630,
0.4658,0.4667,0.4708,0.4792,0.4815,0.4817,0.4848,0.4851,0.4878,0.4894,
0.4982,0.5121,0.5189,0.5244,0.5248,0.5257,0.5257,0.5258,0.5273,0.5341,
0.5374,0.5465,0.5472,0.5524,0.5642,0.5660,0.5729,0.5731,0.5776,0.5829,
0.5841,0.5855,0.5930,0.5949,0.5986,0.6051,0.6090,0.6096,0.6141,0.6150,
0.6151,0.6163,0.6172,0.6175,0.6254,0.6297,0.6303,0.6309,0.6335,0.6337,
0.6344,0.6421,0.6424,0.6426,0.6446,0.6494,0.6511,0.6551,0.6571,0.6572,
0.6577,0.6621,0.6627,0.6701,0.6799,0.6821,0.6835,0.6876,0.6944,0.7006,
0.7047,0.7091,0.7217,0.7276,0.7281,0.7299,0.7332,0.7376,0.7406,0.7434,
0.7465,0.7579,0.7620,0.7662,0.7684,0.7733,0.7790,0.7818,0.7822,0.7916,
0.7924,0.7934,0.7943,0.7944,0.7949,0.8013,0.8018,0.8047,0.8063,0.8103,
0.8198,0.8201,0.8227,0.8277,0.8309,0.8316,0.8319,0.8361,0.8366,0.8411,
0.8484,0.8491,0.8508,0.8523,0.8549,0.8574,0.8591,0.8678,0.8695,0.8707,
0.8749,0.8800,0.8867,0.8889,0.8941,0.8997,0.9073,0.9152,0.9177,0.9217,
0.9292,0.9308,0.9348,0.9367,0.9440,0.9494,0.9560,0.9602,0.9625,0.9630,
0.9691,0.9694,0.9738,0.9752,0.9801,0.9811,0.9835,0.9940,0.9965,
Overall p-value after applying KStest on 269 p-values = 0.634390
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.