RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-04_00:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.70 34.8600 0.993510
2 to 25 16.10 16.1493 0.486723
3 to 26 15.95 11.0389 0.145467
4 to 27 15.80 17.1396 0.555051
5 to 28 16.05 12.5229 0.232509
6 to 29 15.96 15.2610 0.423315
7 to 30 15.81 12.6881 0.243200
8 to 31 15.82 21.2474 0.784580
9 to 32 15.91 17.4952 0.578664
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.785104
Tough bday spacings test for dh-ranFile-2018-07-04_00:31: 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 4 29 82 94 90 85 46 39 22 6 3
(O-E)^2/E 2.9 1.6 1.0 0.1 0.6 0.6 0.7 2.9 3.4 0.1 0.3
Birthday Spacings: Sum(O-E)^2/E= 14.194, p= 0.836
RESULTS OF GCD FOR dh-ranFile-2018-07-04_00:31
Euclid's algorithm:
p-value, steps to gcd: 0.274363
p-value, dist. of gcd's: 0.975427
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-04_00:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.637 0.034 0.284 0.958 0.185 0.194 0.554 0.379
Bits 8 to 15---> 0.701 0.694 0.878 0.467 0.520 0.110 0.993 0.488
Bits 16 to 23---> 0.725 0.499 0.703 0.372 0.980 0.622 0.733 0.456
Bits 24 to 31---> 0.163 0.967 0.715 0.049 0.041 0.682 0.230 0.589
KS test for the above 32 p values: 0.246
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-04_00:31,
p-values for 5 runs: 0.1401, 0.4298, 0.6835, 0.7885, 0.8273
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-04_00:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 225 211.4 0.873 0.873
r= 29 5172 5134.0 0.281 1.154
r= 30 22893 23103.0 1.910 3.063
r= 31 11710 11551.5 2.174 5.237
chi-square = 5.237 with df = 3; p-value = 0.845
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-04_00:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 200 211.4 0.617 0.617
r= 30 5176 5134.0 0.343 0.960
r= 31 23163 23103.0 0.156 1.116
r= 32 11461 11551.5 0.709 1.825
chi-square = 1.825 with df = 3; p-value = 0.390
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-04_00:31
b-rank test for bits 1 to 8, p=0.16301
b-rank test for bits 2 to 9, p=0.42440
b-rank test for bits 3 to 10, p=0.27071
b-rank test for bits 4 to 11, p=0.92359
b-rank test for bits 5 to 12, p=0.49504
b-rank test for bits 6 to 13, p=0.20078
b-rank test for bits 7 to 14, p=0.10566
b-rank test for bits 8 to 15, p=0.21919
b-rank test for bits 9 to 16, p=0.65766
b-rank test for bits 10 to 17, p=0.98107
b-rank test for bits 11 to 18, p=0.90729
b-rank test for bits 12 to 19, p=0.54252
b-rank test for bits 13 to 20, p=0.72856
b-rank test for bits 14 to 21, p=0.67981
b-rank test for bits 15 to 22, p=0.67851
b-rank test for bits 16 to 23, p=0.65637
b-rank test for bits 17 to 24, p=0.15013
b-rank test for bits 18 to 25, p=0.14662
b-rank test for bits 19 to 26, p=0.44837
b-rank test for bits 20 to 27, p=0.39235
b-rank test for bits 21 to 28, p=0.68651
b-rank test for bits 22 to 29, p=0.39950
b-rank test for bits 23 to 30, p=0.77366
b-rank test for bits 24 to 31, p=0.73991
b-rank test for bits 25 to 32, p=0.49205
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 = 0.775671
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-04_00:31
(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 141525 -0.90 0.184602
2 142022 0.26 0.603820
3 142143 0.55 0.707453
4 142361 1.06 0.854357
5 141470 -1.03 0.152335
6 142448 1.26 0.895908
7 141567 -0.80 0.211903
8 141759 -0.35 0.362705
9 141778 -0.31 0.379480
10 141281 -1.47 0.071044
11 141806 -0.24 0.404613
12 141800 -0.26 0.399190
13 141703 -0.48 0.314875
14 141610 -0.70 0.242161
15 141767 -0.33 0.369738
16 140688 -2.85 0.002162
17 142017 0.25 0.599312
18 141549 -0.84 0.199924
19 141320 -1.38 0.084266
20 142284 0.88 0.809321
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-04_00:31
Bits used No. missing words z-score p-value
23 to 32 141575 -1.1529 0.124484
22 to 31 141583 -1.1253 0.130236
21 to 30 142259 1.2058 0.886045
20 to 29 142260 1.2092 0.886708
19 to 28 142033 0.4264 0.665109
18 to 27 142423 1.7713 0.961743
17 to 26 142101 0.6609 0.745672
16 to 25 141903 -0.0218 0.491293
15 to 24 141550 -1.2391 0.107660
14 to 23 141739 -0.5873 0.278486
13 to 22 142354 1.5333 0.937405
12 to 21 141500 -1.4115 0.079051
11 to 20 141887 -0.0770 0.469312
10 to 19 141380 -1.8253 0.033980
9 to 18 141982 0.2506 0.598933
8 to 17 142402 1.6989 0.955327
7 to 16 141740 -0.5839 0.279645
6 to 15 141741 -0.5804 0.280806
5 to 14 141732 -0.6115 0.270440
4 to 13 141562 -1.1977 0.115519
3 to 12 142151 0.8333 0.797675
2 to 11 141133 -2.6770 0.003714
1 to 10 141830 -0.2736 0.392215
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-04_00:31
Bits used No. missing words z-score p-value
28 to 32 142112 0.6870 0.753964
27 to 31 141626 -0.9604 0.168417
26 to 30 141716 -0.6554 0.256119
25 to 29 142253 1.1650 0.877987
24 to 28 142377 1.5853 0.943553
23 to 27 141687 -0.7537 0.225526
22 to 26 141875 -0.1164 0.453679
21 to 25 141758 -0.5130 0.303982
20 to 24 142585 2.2904 0.989001
19 to 23 142270 1.2226 0.889262
18 to 22 142292 1.2972 0.902717
17 to 21 142206 1.0057 0.842711
16 to 20 142358 1.5209 0.935859
15 to 19 141924 0.0497 0.519831
14 to 18 142311 1.3616 0.913337
13 to 17 141995 0.2904 0.614248
12 to 16 141986 0.2599 0.602529
11 to 15 141950 0.1379 0.554826
10 to 14 141699 -0.7130 0.237928
9 to 13 141790 -0.4045 0.342919
8 to 12 142083 0.5887 0.721973
7 to 11 141669 -0.8147 0.207628
6 to 10 142079 0.5752 0.717406
5 to 9 142367 1.5514 0.939600
4 to 8 142013 0.3514 0.637365
3 to 7 141567 -1.1604 0.122935
2 to 6 141977 0.2294 0.590717
1 to 5 141398 -1.7333 0.041519
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-04_00:31
Bits used No. missing words z-score p-value
31 to 32 142139 0.6775 0.750953
30 to 31 141572 -0.9951 0.159850
29 to 30 141829 -0.2370 0.406343
28 to 29 141803 -0.3137 0.376891
27 to 28 141369 -1.5939 0.055480
26 to 27 142011 0.2999 0.617878
25 to 26 142219 0.9135 0.819505
24 to 25 142006 0.2852 0.612240
23 to 24 141575 -0.9862 0.162012
22 to 23 141683 -0.6676 0.252182
21 to 22 141957 0.1406 0.555915
20 to 21 142234 0.9577 0.830900
19 to 20 141956 0.1377 0.554749
18 to 19 141689 -0.6499 0.257865
17 to 18 141822 -0.2576 0.398354
16 to 17 142270 1.0639 0.856318
15 to 16 141997 0.2586 0.602033
14 to 15 141786 -0.3638 0.358002
13 to 14 141656 -0.7473 0.227445
12 to 13 141813 -0.2842 0.388144
11 to 12 142033 0.3648 0.642373
10 to 11 141836 -0.2163 0.414372
9 to 10 142106 0.5801 0.719092
8 to 9 141977 0.1996 0.579110
7 to 8 141801 -0.3196 0.374652
6 to 7 141644 -0.7827 0.216906
5 to 6 142124 0.6332 0.736713
4 to 5 142202 0.8633 0.806023
3 to 4 141374 -1.5791 0.057151
2 to 3 141939 0.0875 0.534872
1 to 2 142037 0.3766 0.646767
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-04_00:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2445.04 -0.777 0.218488
Test results for specific bytes for dh-ranFile-2018-07-04_00:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2486.92 -0.185 0.426634
2 to 9 2518.79 0.266 0.604801
3 to 10 2507.09 0.100 0.539924
4 to 11 2530.61 0.433 0.667451
5 to 12 2551.39 0.727 0.766330
6 to 13 2476.65 -0.330 0.370636
7 to 14 2538.55 0.545 0.707194
8 to 15 2573.26 1.036 0.849906
9 to 16 2535.91 0.508 0.694226
10 to 17 2364.16 -1.921 0.027364
11 to 18 2417.30 -1.170 0.121091
12 to 19 2488.40 -0.164 0.434835
13 to 20 2453.64 -0.656 0.256045
14 to 21 2497.87 -0.030 0.488009
15 to 22 2434.80 -0.922 0.178249
16 to 23 2552.91 0.748 0.772852
17 to 24 2506.32 0.089 0.535581
18 to 25 2557.04 0.807 0.790059
19 to 26 2605.22 1.488 0.931621
20 to 27 2455.23 -0.633 0.263303
21 to 28 2520.74 0.293 0.615367
22 to 29 2509.41 0.133 0.552944
23 to 30 2517.36 0.246 0.596981
24 to 31 2503.81 0.054 0.521464
25 to 32 2453.62 -0.656 0.255933
CDPARK for dh-ranFile-2018-07-04_00:31: 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
3527 0.1826 0.572463
3502 -0.9589 0.168804
3518 -0.2283 0.409702
3528 0.2283 0.590298
3518 -0.2283 0.409702
3554 1.4155 0.921543
3488 -1.5982 0.055002
3538 0.6849 0.753306
3535 0.5479 0.708135
3534 0.5023 0.692266
Square side=100, avg. no. parked=3524.20 sample std.=17.87
p-value of the KSTEST for those 10 p-values: 0.887568
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-04_00:31
0.8617,0.4109,0.7781,0.6517,0.3050,0.6762,0.7283,0.3426,0.5851,0.5532,
The KS test for those 10 p-values: 0.267800
The 3DSPHERES test for dh-ranFile-2018-07-04_00:31
sample no r^3 equiv. uni.
1 28.332 0.611086
2 27.632 0.601912
3 29.245 0.622741
4 19.451 0.477109
5 5.224 0.159806
6 92.595 0.954339
7 11.688 0.322680
8 35.530 0.694046
9 50.476 0.814098
10 0.052 0.001723
11 24.415 0.556838
12 114.337 0.977879
13 5.732 0.173915
14 44.949 0.776487
15 58.531 0.857871
16 52.701 0.827386
17 46.417 0.787162
18 37.617 0.714615
19 1.882 0.060800
20 11.102 0.309319
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.435138
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-04_00:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -0.7 1.3 -0.7 -1.4 1.4
2.5 -0.9 0.5 -0.3 -3.3 -0.6
-0.9 0.6 -0.1 1.7 0.2 0.8
-0.1 0.2 -2.8 1.1 -0.3 0.9
0.2 0.4 0.3 1.0 -0.9 -0.4
0.8 -0.1 0.5 0.2 0.5 0.1
0.5 0.8 0.5 1.0 0.1 1.0
-1.1
Chi-square with 42 degrees of freedom:48.149332
z-score=0.670947, p-value=0.761990
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-04_00:31
Test no p-value
1 0.339778
2 0.003856
3 0.309443
4 0.495071
5 0.347990
6 0.023590
7 0.000164
8 0.976788
9 0.534020
10 0.178751
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.011896
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-04_00:31:
(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 66577 0.12 66614 0.04
3 25000.00 25093 0.35 25108 0.47
4 6666.67 6694 0.11 6589 0.90
5 1388.89 1384 0.02 1418 0.61
6 238.10 213 2.65 234 0.07
7 34.72 36 0.05 32 0.21
8 4.96 2 1.77 4 0.19
p=0.46316 p=0.13070
Number of rngs required: 687730, p-value: 0.218
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-04_00:31
No. of wins: Observed Expected
98673 98585.9
z-score= 0.390, pvalue=0.65164
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66534 66666.7 0.264 0.264
2 37539 37654.3 0.353 0.617
3 26893 26954.7 0.141 0.759
4 19258 19313.5 0.159 0.918
5 13893 13851.4 0.125 1.043
6 10026 9943.5 0.684 1.726
7 7192 7145.0 0.309 2.035
8 5287 5139.1 4.258 6.293
9 3745 3699.9 0.551 6.844
10 2620 2666.3 0.804 7.648
11 1933 1923.3 0.049 7.696
12 1396 1388.7 0.038 7.734
13 1025 1003.7 0.451 8.186
14 702 726.1 0.803 8.988
15 516 525.8 0.184 9.172
16 389 381.2 0.162 9.334
17 272 276.5 0.075 9.409
18 216 200.8 1.146 10.554
19 141 146.0 0.170 10.725
20 103 106.2 0.097 10.822
21 320 287.1 3.767 14.589
Chisq= 14.59 for 20 degrees of freedom, p= 0.20056
SUMMARY of craptest
p-value for no. of wins: 0.651638
p-value for throws/game: 0.200561
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-04_00:31
No. of wins: Observed Expected
98438 98585.9
z-score=-0.661, pvalue=0.25421
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66785 66666.7 0.210 0.210
2 37497 37654.3 0.657 0.867
3 27069 26954.7 0.484 1.352
4 19392 19313.5 0.319 1.671
5 13731 13851.4 1.047 2.718
6 9927 9943.5 0.028 2.746
7 7135 7145.0 0.014 2.760
8 5215 5139.1 1.122 3.881
9 3645 3699.9 0.814 4.695
10 2639 2666.3 0.279 4.974
11 1921 1923.3 0.003 4.977
12 1422 1388.7 0.797 5.774
13 1031 1003.7 0.742 6.516
14 706 726.1 0.559 7.074
15 513 525.8 0.313 7.388
16 369 381.2 0.387 7.775
17 283 276.5 0.151 7.926
18 209 200.8 0.332 8.258
19 141 146.0 0.170 8.428
20 95 106.2 1.184 9.613
21 275 287.1 0.511 10.124
Chisq= 10.12 for 20 degrees of freedom, p= 0.03413
SUMMARY of craptest
p-value for no. of wins: 0.254207
p-value for throws/game: 0.034126
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0002,0.0017,0.0022,0.0037,0.0039,0.0119,0.0236,0.0274,0.0340,0.0341,
0.0341,0.0414,0.0415,0.0486,0.0550,0.0555,0.0572,0.0608,0.0710,0.0791,
0.0843,0.1057,0.1077,0.1104,0.1155,0.1211,0.1229,0.1245,0.1302,0.1307,
0.1401,0.1455,0.1466,0.1501,0.1523,0.1598,0.1599,0.1620,0.1629,0.1630,
0.1684,0.1688,0.1739,0.1782,0.1788,0.1846,0.1853,0.1944,0.1999,0.2006,
0.2008,0.2076,0.2119,0.2169,0.2184,0.2185,0.2192,0.2255,0.2274,0.2299,
0.2325,0.2379,0.2422,0.2432,0.2459,0.2522,0.2542,0.2559,0.2560,0.2561,
0.2579,0.2633,0.2678,0.2704,0.2707,0.2744,0.2785,0.2796,0.2808,0.2843,
0.3040,0.3050,0.3093,0.3094,0.3149,0.3227,0.3398,0.3426,0.3429,0.3480,
0.3580,0.3627,0.3697,0.3706,0.3720,0.3747,0.3769,0.3791,0.3795,0.3881,
0.3905,0.3922,0.3923,0.3984,0.3992,0.3995,0.4046,0.4063,0.4097,0.4097,
0.4109,0.4144,0.4233,0.4244,0.4266,0.4298,0.4348,0.4351,0.4484,0.4537,
0.4562,0.4632,0.4667,0.4693,0.4771,0.4867,0.4880,0.4884,0.4913,0.4920,
0.4950,0.4951,0.4987,0.5198,0.5198,0.5215,0.5340,0.5349,0.5356,0.5399,
0.5425,0.5529,0.5532,0.5544,0.5547,0.5548,0.5551,0.5559,0.5568,0.5725,
0.5787,0.5791,0.5851,0.5895,0.5903,0.5907,0.5970,0.5989,0.5993,0.6019,
0.6020,0.6025,0.6038,0.6048,0.6111,0.6122,0.6142,0.6154,0.6179,0.6217,
0.6227,0.6369,0.6374,0.6424,0.6468,0.6516,0.6517,0.6564,0.6577,0.6651,
0.6675,0.6762,0.6785,0.6798,0.6817,0.6835,0.6865,0.6923,0.6937,0.6940,
0.6942,0.7007,0.7033,0.7072,0.7075,0.7081,0.7146,0.7148,0.7174,0.7191,
0.7220,0.7251,0.7283,0.7286,0.7333,0.7367,0.7399,0.7457,0.7510,0.7533,
0.7540,0.7620,0.7663,0.7729,0.7737,0.7757,0.7765,0.7781,0.7846,0.7851,
0.7872,0.7885,0.7901,0.7977,0.8060,0.8093,0.8141,0.8195,0.8273,0.8274,
0.8309,0.8357,0.8427,0.8448,0.8499,0.8544,0.8563,0.8579,0.8617,0.8780,
0.8780,0.8860,0.8867,0.8876,0.8893,0.8959,0.9027,0.9073,0.9133,0.9215,
0.9236,0.9316,0.9359,0.9374,0.9396,0.9436,0.9543,0.9553,0.9582,0.9617,
0.9665,0.9754,0.9768,0.9779,0.9803,0.9811,0.9890,0.9934,0.9935,
Overall p-value after applying KStest on 269 p-values = 0.732693
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.