RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-10_16:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.61 15.9789 0.474670
2 to 25 15.90 13.2295 0.279309
3 to 26 15.42 39.0234 0.998226
4 to 27 16.08 15.6819 0.453513
5 to 28 16.01 14.4988 0.368470
6 to 29 15.42 31.7401 0.983794
7 to 30 15.58 15.6574 0.451758
8 to 31 15.55 26.5621 0.935189
9 to 32 15.59 14.9713 0.402451
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.092361
Tough bday spacings test for dh-ranFile-2018-07-10_16:31: 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 52 63 94 110 81 42 22 17 7 2
(O-E)^2/E 0.1 6.4 1.4 0.1 1.6 0.1 2.0 2.0 0.3 0.0 1.0
Birthday Spacings: Sum(O-E)^2/E= 15.117, p= 0.872
RESULTS OF GCD FOR dh-ranFile-2018-07-10_16:31
Euclid's algorithm:
p-value, steps to gcd: 0.171691
p-value, dist. of gcd's: 0.702141
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-10_16:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.826 0.620 0.307 0.279 0.888 0.081 0.435 0.085
Bits 8 to 15---> 0.131 0.151 0.031 0.790 0.373 0.627 0.491 0.590
Bits 16 to 23---> 0.815 0.702 0.232 0.252 0.729 0.345 0.474 0.932
Bits 24 to 31---> 0.259 0.193 0.411 0.748 0.246 0.508 0.166 0.694
KS test for the above 32 p values: 0.491
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-10_16:31,
p-values for 5 runs: 0.0980, 0.0058, 0.4224, 0.3013, 0.2002
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-10_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 212 211.4 0.002 0.002
r= 29 5069 5134.0 0.823 0.825
r= 30 23254 23103.0 0.986 1.811
r= 31 11465 11551.5 0.648 2.459
chi-square = 2.459 with df = 3; p-value = 0.517
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-10_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 184 211.4 3.556 3.556
r= 30 5176 5134.0 0.343 3.899
r= 31 23107 23103.0 0.001 3.900
r= 32 11533 11551.5 0.030 3.930
chi-square = 3.930 with df = 3; p-value = 0.731
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-10_16:31
b-rank test for bits 1 to 8, p=0.18786
b-rank test for bits 2 to 9, p=0.07960
b-rank test for bits 3 to 10, p=0.90988
b-rank test for bits 4 to 11, p=0.92547
b-rank test for bits 5 to 12, p=0.53084
b-rank test for bits 6 to 13, p=0.48724
b-rank test for bits 7 to 14, p=0.94743
b-rank test for bits 8 to 15, p=0.82040
b-rank test for bits 9 to 16, p=0.10325
b-rank test for bits 10 to 17, p=0.09806
b-rank test for bits 11 to 18, p=0.29985
b-rank test for bits 12 to 19, p=0.37525
b-rank test for bits 13 to 20, p=0.03681
b-rank test for bits 14 to 21, p=0.16076
b-rank test for bits 15 to 22, p=0.93101
b-rank test for bits 16 to 23, p=0.27644
b-rank test for bits 17 to 24, p=0.92894
b-rank test for bits 18 to 25, p=0.09639
b-rank test for bits 19 to 26, p=0.03831
b-rank test for bits 20 to 27, p=0.28437
b-rank test for bits 21 to 28, p=0.08218
b-rank test for bits 22 to 29, p=0.20556
b-rank test for bits 23 to 30, p=0.38112
b-rank test for bits 24 to 31, p=0.15766
b-rank test for bits 25 to 32, p=0.28122
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 = 0.018359
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-10_16:31
(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 141764 -0.34 0.367095
2 141686 -0.52 0.300905
3 142345 1.02 0.845642
4 141828 -0.19 0.424645
5 142364 1.06 0.855953
6 142578 1.56 0.940893
7 142502 1.38 0.916934
8 141722 -0.44 0.330807
9 143105 2.79 0.997394
10 141441 -1.09 0.136927
11 141922 0.03 0.511808
12 141784 -0.29 0.384827
13 142443 1.25 0.893782
14 141994 0.20 0.578410
15 142213 0.71 0.760996
16 141276 -1.48 0.069471
17 140989 -2.15 0.015766
18 141336 -1.34 0.090195
19 141312 -1.40 0.081413
20 141805 -0.24 0.403708
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-10_16:31
Bits used No. missing words z-score p-value
23 to 32 141944 0.1196 0.547581
22 to 31 142276 1.2644 0.896953
21 to 30 142393 1.6678 0.952325
20 to 29 141811 -0.3391 0.367279
19 to 28 141710 -0.6873 0.245933
18 to 27 141758 -0.5218 0.300895
17 to 26 142190 0.9678 0.833435
16 to 25 142286 1.2989 0.903004
15 to 24 142187 0.9575 0.830838
14 to 23 142451 1.8678 0.969107
13 to 22 142449 1.8609 0.968623
12 to 21 141945 0.1230 0.548947
11 to 20 141867 -0.1460 0.441974
10 to 19 141543 -1.2632 0.103257
9 to 18 141622 -0.9908 0.160893
8 to 17 142088 0.6161 0.731087
7 to 16 141824 -0.2942 0.384287
6 to 15 141922 0.0437 0.517424
5 to 14 141909 -0.0011 0.499546
4 to 13 142463 1.9092 0.971882
3 to 12 142355 1.5368 0.937828
2 to 11 141929 0.0678 0.527039
1 to 10 141946 0.1264 0.550312
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-10_16:31
Bits used No. missing words z-score p-value
28 to 32 141937 0.0938 0.537365
27 to 31 142394 1.6429 0.949803
26 to 30 141868 -0.1401 0.444290
25 to 29 142356 1.5141 0.935004
24 to 28 141943 0.1141 0.545435
23 to 27 142088 0.6057 0.727630
22 to 26 141391 -1.7571 0.039455
21 to 25 141616 -0.9943 0.160029
20 to 24 141843 -0.2248 0.411049
19 to 23 142010 0.3413 0.633544
18 to 22 141971 0.2091 0.582796
17 to 21 142169 0.8802 0.810635
16 to 20 141260 -2.2011 0.013864
15 to 19 141505 -1.3706 0.085248
14 to 18 142270 1.2226 0.889262
13 to 17 142048 0.4701 0.680847
12 to 16 141710 -0.6757 0.249617
11 to 15 141970 0.2057 0.581472
10 to 14 141673 -0.8011 0.211532
9 to 13 141847 -0.2113 0.416331
8 to 12 142071 0.5480 0.708166
7 to 11 142121 0.7175 0.763475
6 to 10 142432 1.7718 0.961783
5 to 9 141562 -1.1774 0.119520
4 to 8 142118 0.7074 0.760327
3 to 7 141883 -0.0893 0.464440
2 to 6 142274 1.2362 0.891802
1 to 5 141498 -1.3943 0.081608
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-10_16:31
Bits used No. missing words z-score p-value
31 to 32 142418 1.5005 0.933258
30 to 31 142015 0.3117 0.622370
29 to 30 141303 -1.7886 0.036841
28 to 29 142144 0.6922 0.755607
27 to 28 142244 0.9872 0.838234
26 to 27 142026 0.3442 0.634637
25 to 26 142269 1.0610 0.855649
24 to 25 141901 -0.0246 0.490198
23 to 24 142002 0.2734 0.607713
22 to 23 142090 0.5329 0.702966
21 to 22 141771 -0.4081 0.341617
20 to 21 141796 -0.3343 0.369074
19 to 20 141405 -1.4877 0.068415
18 to 19 142162 0.7453 0.771967
17 to 18 141798 -0.3284 0.371302
16 to 17 142458 1.6185 0.947222
15 to 16 142056 0.4327 0.667367
14 to 15 142153 0.7188 0.763865
13 to 14 141978 0.2026 0.580263
12 to 13 142249 1.0020 0.841823
11 to 12 142062 0.4504 0.673772
10 to 11 141615 -0.8682 0.192634
9 to 10 142987 3.1790 0.999261
8 to 9 141387 -1.5408 0.061683
7 to 8 141980 0.2085 0.582568
6 to 7 141820 -0.2635 0.396079
5 to 6 141834 -0.2222 0.412074
4 to 5 141550 -1.0600 0.144579
3 to 4 142037 0.3766 0.646767
2 to 3 141301 -1.7945 0.036368
1 to 2 141414 -1.4612 0.071987
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-10_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2515.91 0.225 0.588998
Test results for specific bytes for dh-ranFile-2018-07-10_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2497.52 -0.035 0.485994
2 to 9 2382.12 -1.667 0.047754
3 to 10 2587.39 1.236 0.891762
4 to 11 2514.82 0.210 0.583014
5 to 12 2487.19 -0.181 0.428118
6 to 13 2342.64 -2.225 0.013026
7 to 14 2601.63 1.437 0.924681
8 to 15 2595.41 1.349 0.911373
9 to 16 2475.94 -0.340 0.366804
10 to 17 2557.14 0.808 0.790480
11 to 18 2507.25 0.103 0.540839
12 to 19 2522.26 0.315 0.623552
13 to 20 2352.91 -2.080 0.018753
14 to 21 2462.34 -0.533 0.297167
15 to 22 2500.15 0.002 0.500838
16 to 23 2446.28 -0.760 0.223694
17 to 24 2483.53 -0.233 0.407886
18 to 25 2423.73 -1.079 0.140365
19 to 26 2619.98 1.697 0.955134
20 to 27 2448.83 -0.724 0.234645
21 to 28 2506.82 0.096 0.538411
22 to 29 2518.03 0.255 0.600650
23 to 30 2500.53 0.008 0.502996
24 to 31 2578.56 1.111 0.866723
25 to 32 2451.00 -0.693 0.244171
CDPARK for dh-ranFile-2018-07-10_16:31: 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
3569 2.1005 0.982156
3524 0.0457 0.518210
3494 -1.3242 0.092718
3515 -0.3653 0.357445
3548 1.1416 0.873180
3553 1.3699 0.914635
3502 -0.9589 0.168804
3524 0.0457 0.518210
3532 0.4110 0.659449
3554 1.4155 0.921543
Square side=100, avg. no. parked=3531.50 sample std.=23.04
p-value of the KSTEST for those 10 p-values: 0.354200
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-10_16:31
0.6220,0.4555,0.7594,0.3254,0.3308,0.2991,0.9297,0.1705,0.7715,0.7030,
The KS test for those 10 p-values: 0.806221
The 3DSPHERES test for dh-ranFile-2018-07-10_16:31
sample no r^3 equiv. uni.
1 29.493 0.625848
2 39.863 0.735198
3 59.300 0.861471
4 16.074 0.414789
5 39.979 0.736215
6 66.225 0.890025
7 78.771 0.927611
8 62.581 0.875821
9 33.492 0.672548
10 73.482 0.913655
11 1.861 0.060156
12 17.275 0.437757
13 5.437 0.165772
14 24.161 0.553082
15 31.811 0.653667
16 6.157 0.185549
17 7.215 0.213759
18 46.096 0.784876
19 12.012 0.329959
20 87.522 0.945926
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.198382
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-10_16:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 -1.2 -0.6 -2.3 -0.3 0.2
-1.3 0.4 -1.1 1.1 0.2 -0.5
-1.6 -0.2 0.5 -0.7 -0.0 1.0
1.1 0.9 0.5 -0.3 1.0 0.3
-0.8 -0.1 -1.0 0.1 -0.8 -1.4
-0.4 -0.6 -0.8 -0.3 0.5 1.0
-0.5 -1.3 0.5 2.6 -0.6 0.0
-0.1
Chi-square with 42 degrees of freedom:37.508016
z-score=-0.490116, p-value=0.331680
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-10_16:31
Test no p-value
1 0.124934
2 0.923533
3 0.262684
4 0.687879
5 0.000342
6 0.340767
7 0.115528
8 0.566028
9 0.240481
10 0.406405
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.165283
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-10_16:31:
(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 66617 0.04 66682 0.00
3 25000.00 25104 0.43 24959 0.07
4 6666.67 6611 0.46 6702 0.19
5 1388.89 1415 0.49 1394 0.02
6 238.10 213 2.65 224 0.83
7 34.72 33 0.09 33 0.09
8 4.96 6 0.22 5 0.00
p=0.37375 p=0.02296
Number of rngs required: 688341, p-value: 0.472
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-10_16:31
No. of wins: Observed Expected
98479 98585.9
z-score=-0.478, pvalue=0.31635
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66673 66666.7 0.001 0.001
2 37762 37654.3 0.308 0.309
3 26976 26954.7 0.017 0.325
4 19221 19313.5 0.443 0.768
5 13915 13851.4 0.292 1.060
6 9873 9943.5 0.500 1.560
7 7005 7145.0 2.744 4.304
8 5231 5139.1 1.644 5.949
9 3652 3699.9 0.619 6.568
10 2706 2666.3 0.591 7.159
11 1978 1923.3 1.554 8.713
12 1432 1388.7 1.348 10.061
13 976 1003.7 0.765 10.826
14 732 726.1 0.047 10.873
15 503 525.8 0.992 11.865
16 386 381.2 0.062 11.927
17 284 276.5 0.201 12.128
18 185 200.8 1.248 13.376
19 129 146.0 1.976 15.352
20 97 106.2 0.800 16.151
21 284 287.1 0.034 16.185
Chisq= 16.19 for 20 degrees of freedom, p= 0.29493
SUMMARY of craptest
p-value for no. of wins: 0.316349
p-value for throws/game: 0.294927
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-10_16:31
No. of wins: Observed Expected
98625 98585.9
z-score= 0.175, pvalue=0.56949
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66738 66666.7 0.076 0.076
2 37828 37654.3 0.801 0.877
3 27027 26954.7 0.194 1.071
4 18984 19313.5 5.620 6.691
5 14059 13851.4 3.111 9.802
6 9857 9943.5 0.753 10.555
7 7193 7145.0 0.322 10.878
8 5178 5139.1 0.295 11.172
9 3557 3699.9 5.517 16.689
10 2641 2666.3 0.240 16.929
11 1913 1923.3 0.055 16.984
12 1361 1388.7 0.554 17.539
13 1019 1003.7 0.233 17.771
14 699 726.1 1.014 18.786
15 579 525.8 5.375 24.161
16 384 381.2 0.021 24.182
17 263 276.5 0.663 24.845
18 201 200.8 0.000 24.845
19 148 146.0 0.028 24.873
20 99 106.2 0.490 25.363
21 272 287.1 0.796 26.159
Chisq= 26.16 for 20 degrees of freedom, p= 0.83937
SUMMARY of craptest
p-value for no. of wins: 0.569485
p-value for throws/game: 0.839367
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0003,0.0058,0.0130,0.0139,0.0158,0.0184,0.0188,0.0230,0.0305,0.0364,
0.0368,0.0368,0.0383,0.0395,0.0478,0.0602,0.0617,0.0684,0.0695,0.0720,
0.0796,0.0812,0.0814,0.0816,0.0822,0.0852,0.0852,0.0902,0.0924,0.0927,
0.0964,0.0980,0.0981,0.1033,0.1033,0.1155,0.1195,0.1249,0.1307,0.1369,
0.1404,0.1446,0.1511,0.1577,0.1600,0.1608,0.1609,0.1653,0.1658,0.1658,
0.1688,0.1705,0.1717,0.1855,0.1879,0.1926,0.1929,0.1984,0.2002,0.2056,
0.2115,0.2138,0.2237,0.2324,0.2346,0.2405,0.2442,0.2459,0.2463,0.2496,
0.2516,0.2587,0.2627,0.2764,0.2792,0.2793,0.2812,0.2844,0.2949,0.2972,
0.2991,0.2998,0.3009,0.3009,0.3013,0.3072,0.3163,0.3254,0.3300,0.3308,
0.3308,0.3317,0.3408,0.3416,0.3451,0.3542,0.3574,0.3668,0.3671,0.3673,
0.3685,0.3691,0.3713,0.3733,0.3738,0.3752,0.3811,0.3843,0.3848,0.3961,
0.4025,0.4037,0.4064,0.4079,0.4110,0.4110,0.4121,0.4148,0.4163,0.4224,
0.4246,0.4281,0.4352,0.4378,0.4420,0.4443,0.4518,0.4535,0.4555,0.4644,
0.4716,0.4742,0.4747,0.4860,0.4872,0.4902,0.4906,0.4907,0.4995,0.5008,
0.5030,0.5077,0.5118,0.5173,0.5174,0.5182,0.5182,0.5270,0.5308,0.5374,
0.5384,0.5408,0.5454,0.5476,0.5489,0.5503,0.5531,0.5660,0.5695,0.5784,
0.5803,0.5815,0.5826,0.5828,0.5830,0.5890,0.5897,0.6007,0.6077,0.6199,
0.6220,0.6224,0.6236,0.6258,0.6269,0.6335,0.6346,0.6468,0.6537,0.6594,
0.6674,0.6725,0.6738,0.6808,0.6879,0.6936,0.7021,0.7023,0.7030,0.7030,
0.7082,0.7276,0.7285,0.7308,0.7311,0.7352,0.7362,0.7481,0.7556,0.7594,
0.7603,0.7610,0.7635,0.7639,0.7715,0.7720,0.7849,0.7901,0.7905,0.8062,
0.8106,0.8153,0.8204,0.8262,0.8308,0.8334,0.8382,0.8394,0.8418,0.8456,
0.8556,0.8560,0.8615,0.8667,0.8721,0.8732,0.8758,0.8885,0.8893,0.8900,
0.8918,0.8918,0.8938,0.8970,0.9030,0.9099,0.9114,0.9137,0.9146,0.9169,
0.9215,0.9235,0.9247,0.9255,0.9276,0.9289,0.9297,0.9310,0.9319,0.9333,
0.9350,0.9352,0.9378,0.9409,0.9459,0.9472,0.9474,0.9498,0.9523,0.9551,
0.9618,0.9686,0.9691,0.9719,0.9822,0.9838,0.9974,0.9982,0.9993,
Overall p-value after applying KStest on 269 p-values = 0.652777
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.