RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-04_04:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.86 14.0219 0.334449
2 to 25 16.06 14.6063 0.376187
3 to 26 15.76 15.9686 0.473940
4 to 27 15.70 7.8968 0.031297
5 to 28 15.77 18.0595 0.614903
6 to 29 15.60 16.7736 0.530193
7 to 30 16.00 9.6581 0.082668
8 to 31 15.73 12.1522 0.209166
9 to 32 15.70 16.0996 0.483215
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.156149
Tough bday spacings test for dh-ranFile-2018-07-04_04:31: 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 35 74 98 99 75 62 20 18 4 5
(O-E)^2/E 0.1 0.1 0.0 0.0 0.0 0.1 1.9 3.2 0.7 1.0 0.2
Birthday Spacings: Sum(O-E)^2/E= 7.292, p= 0.302
RESULTS OF GCD FOR dh-ranFile-2018-07-04_04:31
Euclid's algorithm:
p-value, steps to gcd: 0.005190
p-value, dist. of gcd's: 0.661038
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-04_04:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.753 0.202 0.674 0.640 0.529 0.567 0.556 0.496
Bits 8 to 15---> 0.750 0.258 0.543 0.876 0.778 0.713 0.488 0.639
Bits 16 to 23---> 0.820 0.062 0.763 0.584 0.140 0.329 0.705 0.939
Bits 24 to 31---> 0.468 0.317 0.167 0.233 0.657 0.172 0.480 0.862
KS test for the above 32 p values: 0.710
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-04_04:31,
p-values for 5 runs: 0.8959, 0.4913, 0.3708, 0.7441, 0.7334
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-04_04:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 230 211.4 1.633 1.633
r= 29 5092 5134.0 0.344 1.977
r= 30 23007 23103.0 0.399 2.376
r= 31 11671 11551.5 1.236 3.612
chi-square = 3.612 with df = 3; p-value = 0.693
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-04_04:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 210 211.4 0.010 0.010
r= 30 5118 5134.0 0.050 0.059
r= 31 23121 23103.0 0.014 0.073
r= 32 11551 11551.5 0.000 0.073
chi-square = 0.073 with df = 3; p-value = 0.005
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-04_04:31
b-rank test for bits 1 to 8, p=0.20641
b-rank test for bits 2 to 9, p=0.33806
b-rank test for bits 3 to 10, p=0.51524
b-rank test for bits 4 to 11, p=0.23247
b-rank test for bits 5 to 12, p=0.22672
b-rank test for bits 6 to 13, p=0.50621
b-rank test for bits 7 to 14, p=0.02823
b-rank test for bits 8 to 15, p=0.27040
b-rank test for bits 9 to 16, p=0.62771
b-rank test for bits 10 to 17, p=0.19170
b-rank test for bits 11 to 18, p=0.28889
b-rank test for bits 12 to 19, p=0.77522
b-rank test for bits 13 to 20, p=0.45842
b-rank test for bits 14 to 21, p=0.80558
b-rank test for bits 15 to 22, p=0.75305
b-rank test for bits 16 to 23, p=0.50983
b-rank test for bits 17 to 24, p=0.99300
b-rank test for bits 18 to 25, p=0.32717
b-rank test for bits 19 to 26, p=0.88772
b-rank test for bits 20 to 27, p=0.65663
b-rank test for bits 21 to 28, p=0.55356
b-rank test for bits 22 to 29, p=0.61284
b-rank test for bits 23 to 30, p=0.69965
b-rank test for bits 24 to 31, p=0.15942
b-rank test for bits 25 to 32, p=0.38318
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 = 0.669345
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-04_04:31
(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 142308 0.93 0.824195
2 141847 -0.15 0.442106
3 142369 1.07 0.858588
4 142270 0.84 0.800298
5 141965 0.13 0.551745
6 141223 -1.60 0.054404
7 141173 -1.72 0.042680
8 142308 0.93 0.824195
9 142137 0.53 0.702616
10 141973 0.15 0.559129
11 141955 0.11 0.542489
12 141770 -0.33 0.372387
13 142630 1.68 0.953891
14 142790 2.06 0.980188
15 141840 -0.16 0.435658
16 142113 0.48 0.682915
17 141770 -0.33 0.372387
18 142128 0.51 0.695293
19 142081 0.40 0.655826
20 141431 -1.12 0.131870
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-04_04:31
Bits used No. missing words z-score p-value
23 to 32 142055 0.5023 0.692275
22 to 31 141859 -0.1736 0.431109
21 to 30 142107 0.6816 0.752261
20 to 29 142051 0.4885 0.687408
19 to 28 141663 -0.8494 0.197826
18 to 27 141941 0.1092 0.543481
17 to 26 142006 0.3333 0.630563
16 to 25 141363 -1.8839 0.029789
15 to 24 142197 0.9920 0.839393
14 to 23 141586 -1.1149 0.132440
13 to 22 141728 -0.6253 0.265895
12 to 21 141348 -1.9356 0.026457
11 to 20 141795 -0.3942 0.346701
10 to 19 141656 -0.8736 0.191181
9 to 18 141855 -0.1873 0.425695
8 to 17 141697 -0.7322 0.232032
7 to 16 141337 -1.9736 0.024216
6 to 15 141583 -1.1253 0.130236
5 to 14 141419 -1.6908 0.045438
4 to 13 141903 -0.0218 0.491293
3 to 12 142084 0.6023 0.726516
2 to 11 141660 -0.8598 0.194961
1 to 10 141973 0.2196 0.586890
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-04_04:31
Bits used No. missing words z-score p-value
28 to 32 141759 -0.5096 0.305168
27 to 31 142067 0.5345 0.703493
26 to 30 142004 0.3209 0.625863
25 to 29 142027 0.3989 0.655010
24 to 28 141634 -0.9333 0.175327
23 to 27 141908 -0.0045 0.498201
22 to 26 141939 0.1006 0.540057
21 to 25 141994 0.2870 0.612950
20 to 24 141849 -0.2045 0.418978
19 to 23 141394 -1.7469 0.040329
18 to 22 141873 -0.1232 0.450993
17 to 21 142209 1.0158 0.845145
16 to 20 142253 1.1650 0.877987
15 to 19 141802 -0.3638 0.357992
14 to 18 141726 -0.6215 0.267149
13 to 17 141958 0.1650 0.565521
12 to 16 142344 1.4735 0.929686
11 to 15 141932 0.0768 0.530628
10 to 14 141769 -0.4757 0.317146
9 to 13 141750 -0.5401 0.294564
8 to 12 141646 -0.8926 0.186024
7 to 11 141972 0.2124 0.584118
6 to 10 141966 0.1921 0.576169
5 to 9 142016 0.3616 0.641172
4 to 8 141610 -1.0147 0.155130
3 to 7 142142 0.7887 0.784860
2 to 6 141977 0.2294 0.590717
1 to 5 141912 0.0091 0.503611
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-04_04:31
Bits used No. missing words z-score p-value
31 to 32 141776 -0.3933 0.347048
30 to 31 141967 0.1701 0.567541
29 to 30 141704 -0.6057 0.272359
28 to 29 142287 1.1141 0.867376
27 to 28 141768 -0.4169 0.338375
26 to 27 141970 0.1790 0.571018
25 to 26 141790 -0.3520 0.362417
24 to 25 142037 0.3766 0.646767
23 to 24 141768 -0.4169 0.338375
22 to 23 142229 0.9430 0.827154
21 to 22 142332 1.2468 0.893767
20 to 21 142352 1.3058 0.904192
19 to 20 142126 0.6391 0.738636
18 to 19 141436 -1.3963 0.081319
17 to 18 141772 -0.4051 0.342701
16 to 17 142130 0.6509 0.742459
15 to 16 141643 -0.7856 0.216041
14 to 15 142168 0.7630 0.777280
13 to 14 141992 0.2439 0.596332
12 to 13 141652 -0.7591 0.223901
11 to 12 141642 -0.7886 0.215178
10 to 11 142198 0.8515 0.802764
9 to 10 142068 0.4681 0.680127
8 to 9 141817 -0.2724 0.392673
7 to 8 141832 -0.2281 0.409780
6 to 7 141328 -1.7148 0.043188
5 to 6 141754 -0.4582 0.323404
4 to 5 142280 1.0934 0.862896
3 to 4 141426 -1.4258 0.076970
2 to 3 141741 -0.4965 0.309754
1 to 2 141714 -0.5762 0.282242
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-04_04:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2478.90 -0.298 0.382720
Test results for specific bytes for dh-ranFile-2018-07-04_04:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2577.78 1.100 0.864331
2 to 9 2448.44 -0.729 0.232955
3 to 10 2529.82 0.422 0.663368
4 to 11 2507.90 0.112 0.544486
5 to 12 2395.44 -1.479 0.069611
6 to 13 2462.84 -0.526 0.299604
7 to 14 2592.32 1.306 0.904146
8 to 15 2586.36 1.221 0.889022
9 to 16 2588.28 1.248 0.894069
10 to 17 2470.30 -0.420 0.337229
11 to 18 2484.25 -0.223 0.411890
12 to 19 2615.32 1.631 0.948534
13 to 20 2562.54 0.884 0.811770
14 to 21 2468.97 -0.439 0.330404
15 to 22 2647.83 2.091 0.981719
16 to 23 2442.51 -0.813 0.208105
17 to 24 2592.87 1.313 0.905478
18 to 25 2500.02 0.000 0.500116
19 to 26 2442.51 -0.813 0.208099
20 to 27 2426.76 -1.036 0.150165
21 to 28 2584.60 1.196 0.884232
22 to 29 2492.59 -0.105 0.458287
23 to 30 2565.39 0.925 0.822451
24 to 31 2594.70 1.339 0.909753
25 to 32 2457.36 -0.603 0.273258
CDPARK for dh-ranFile-2018-07-04_04:31: 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
3515 -0.3653 0.357445
3520 -0.1370 0.445521
3528 0.2283 0.590298
3547 1.0959 0.863437
3547 1.0959 0.863437
3556 1.5068 0.934075
3520 -0.1370 0.445521
3507 -0.7306 0.232514
3509 -0.6393 0.261324
3489 -1.5525 0.060270
Square side=100, avg. no. parked=3523.80 sample std.=19.87
p-value of the KSTEST for those 10 p-values: 0.954026
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-04_04:31
0.4760,0.8427,0.1508,0.2052,0.2765,0.1797,0.4237,0.8126,0.7111,0.7334,
The KS test for those 10 p-values: 0.859197
The 3DSPHERES test for dh-ranFile-2018-07-04_04:31
sample no r^3 equiv. uni.
1 1.296 0.042273
2 42.396 0.756635
3 39.456 0.731576
4 19.164 0.472076
5 74.648 0.916945
6 22.365 0.525508
7 98.568 0.962582
8 30.727 0.640931
9 13.081 0.353405
10 2.120 0.068225
11 33.740 0.675238
12 20.145 0.489057
13 32.541 0.661992
14 19.131 0.471485
15 2.565 0.081944
16 8.795 0.254111
17 16.748 0.427798
18 0.568 0.018739
19 29.443 0.625227
20 36.914 0.707847
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.734591
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-04_04:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 0.9 -0.8 1.5 -0.7 -0.6
0.1 0.2 -0.3 -1.7 0.6 0.1
0.4 -0.4 -0.1 -1.1 0.7 0.6
-0.2 1.4 -0.6 0.2 -0.1 -0.5
0.5 1.5 -1.3 -1.7 -0.5 1.4
1.8 -0.5 -0.0 -1.6 0.5 -1.6
1.2 -1.0 -1.2 -0.1 -0.6 0.0
-1.1
Chi-square with 42 degrees of freedom:39.006463
z-score=-0.326622, p-value=0.396869
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-04_04:31
Test no p-value
1 0.924537
2 0.106155
3 0.224656
4 0.745464
5 0.038981
6 0.063076
7 0.047535
8 0.249470
9 0.350053
10 0.809729
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.085551
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-04_04:31:
(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 66730 0.06 66380 1.23
3 25000.00 24908 0.34 25139 0.77
4 6666.67 6712 0.31 6724 0.49
5 1388.89 1353 0.93 1467 4.39
6 238.10 252 0.81 242 0.06
7 34.72 38 0.31 40 0.80
8 4.96 6 0.22 7 0.84
p=0.18794 p=0.80248
Number of rngs required: 689766, p-value: 0.945
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-04_04:31
No. of wins: Observed Expected
98695 98585.9
z-score= 0.488, pvalue=0.68728
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66737 66666.7 0.074 0.074
2 37510 37654.3 0.553 0.627
3 27125 26954.7 1.076 1.703
4 19434 19313.5 0.752 2.455
5 13684 13851.4 2.024 4.479
6 10056 9943.5 1.272 5.751
7 7160 7145.0 0.031 5.782
8 5166 5139.1 0.141 5.923
9 3684 3699.9 0.068 5.991
10 2642 2666.3 0.221 6.213
11 1868 1923.3 1.592 7.804
12 1354 1388.7 0.869 8.673
13 1027 1003.7 0.540 9.213
14 714 726.1 0.203 9.416
15 530 525.8 0.033 9.449
16 363 381.2 0.864 10.314
17 266 276.5 0.402 10.715
18 165 200.8 6.392 17.108
19 130 146.0 1.750 18.858
20 93 106.2 1.644 20.502
21 292 287.1 0.083 20.585
Chisq= 20.59 for 20 degrees of freedom, p= 0.57811
SUMMARY of craptest
p-value for no. of wins: 0.687276
p-value for throws/game: 0.578112
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-04_04:31
No. of wins: Observed Expected
98749 98585.9
z-score= 0.730, pvalue=0.76720
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66726 66666.7 0.053 0.053
2 37533 37654.3 0.391 0.444
3 27096 26954.7 0.740 1.184
4 19345 19313.5 0.051 1.236
5 13899 13851.4 0.163 1.399
6 9936 9943.5 0.006 1.405
7 7138 7145.0 0.007 1.412
8 5096 5139.1 0.361 1.773
9 3630 3699.9 1.319 3.092
10 2686 2666.3 0.146 3.237
11 1892 1923.3 0.510 3.748
12 1383 1388.7 0.024 3.772
13 1023 1003.7 0.371 4.142
14 708 726.1 0.453 4.595
15 523 525.8 0.015 4.611
16 377 381.2 0.045 4.656
17 282 276.5 0.108 4.764
18 187 200.8 0.952 5.716
19 168 146.0 3.320 9.036
20 112 106.2 0.315 9.351
21 260 287.1 2.561 11.912
Chisq= 11.91 for 20 degrees of freedom, p= 0.08092
SUMMARY of craptest
p-value for no. of wins: 0.767202
p-value for throws/game: 0.080918
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0052,0.0052,0.0187,0.0242,0.0265,0.0282,0.0298,0.0313,0.0390,0.0403,
0.0423,0.0427,0.0432,0.0454,0.0475,0.0544,0.0603,0.0621,0.0631,0.0682,
0.0696,0.0770,0.0809,0.0813,0.0819,0.0827,0.0856,0.1062,0.1302,0.1319,
0.1324,0.1403,0.1502,0.1508,0.1551,0.1561,0.1594,0.1671,0.1724,0.1753,
0.1797,0.1860,0.1879,0.1912,0.1917,0.1950,0.1978,0.2019,0.2052,0.2064,
0.2081,0.2081,0.2092,0.2152,0.2160,0.2239,0.2247,0.2267,0.2320,0.2325,
0.2325,0.2329,0.2330,0.2495,0.2541,0.2580,0.2613,0.2659,0.2671,0.2704,
0.2724,0.2733,0.2765,0.2822,0.2889,0.2946,0.2996,0.3024,0.3052,0.3098,
0.3171,0.3175,0.3234,0.3272,0.3294,0.3304,0.3344,0.3372,0.3381,0.3384,
0.3384,0.3427,0.3467,0.3470,0.3501,0.3534,0.3574,0.3580,0.3624,0.3708,
0.3724,0.3724,0.3762,0.3827,0.3832,0.3927,0.3969,0.4098,0.4119,0.4190,
0.4237,0.4257,0.4278,0.4311,0.4357,0.4421,0.4455,0.4455,0.4510,0.4583,
0.4584,0.4684,0.4715,0.4721,0.4739,0.4760,0.4804,0.4832,0.4883,0.4891,
0.4913,0.4913,0.4959,0.4982,0.5001,0.5036,0.5062,0.5098,0.5152,0.5255,
0.5287,0.5302,0.5306,0.5401,0.5425,0.5430,0.5435,0.5445,0.5517,0.5536,
0.5564,0.5591,0.5655,0.5672,0.5675,0.5710,0.5762,0.5781,0.5841,0.5841,
0.5869,0.5903,0.5907,0.5963,0.6128,0.6130,0.6149,0.6252,0.6259,0.6277,
0.6306,0.6393,0.6404,0.6409,0.6412,0.6468,0.6550,0.6558,0.6566,0.6574,
0.6610,0.6620,0.6634,0.6693,0.6745,0.6752,0.6801,0.6829,0.6873,0.6874,
0.6923,0.6935,0.6953,0.6996,0.7026,0.7035,0.7053,0.7078,0.7095,0.7111,
0.7133,0.7265,0.7316,0.7334,0.7334,0.7346,0.7386,0.7425,0.7441,0.7455,
0.7502,0.7523,0.7531,0.7533,0.7566,0.7628,0.7672,0.7752,0.7773,0.7778,
0.7849,0.8003,0.8025,0.8028,0.8056,0.8097,0.8118,0.8126,0.8199,0.8225,
0.8242,0.8242,0.8272,0.8394,0.8427,0.8451,0.8586,0.8592,0.8615,0.8629,
0.8634,0.8634,0.8643,0.8674,0.8763,0.8780,0.8842,0.8877,0.8890,0.8938,
0.8941,0.8959,0.9041,0.9042,0.9055,0.9098,0.9169,0.9245,0.9297,0.9341,
0.9395,0.9447,0.9485,0.9539,0.9540,0.9626,0.9802,0.9817,0.9930,
Overall p-value after applying KStest on 269 p-values = 0.388505
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.