RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-09_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 15.77 8.9824 0.059188
2 to 25 15.68 23.7976 0.874960
3 to 26 15.73 22.0399 0.816810
4 to 27 15.75 22.8323 0.845209
5 to 28 15.79 8.1858 0.037588
6 to 29 16.06 35.1679 0.994087
7 to 30 15.94 15.0442 0.407702
8 to 31 15.98 12.1617 0.209753
9 to 32 15.82 17.0466 0.548783
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.505949
Tough bday spacings test for dh-ranFile-2018-07-09_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 12 42 80 89 104 79 44 30 10 5 5
(O-E)^2/E 0.9 0.8 0.6 0.8 0.4 0.0 1.3 0.0 1.6 0.4 0.2
Birthday Spacings: Sum(O-E)^2/E= 6.951, p= 0.270
RESULTS OF GCD FOR dh-ranFile-2018-07-09_21:31
Euclid's algorithm:
p-value, steps to gcd: 0.351191
p-value, dist. of gcd's: 0.332458
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-09_21:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.901 0.448 0.226 0.725 0.226 0.830 0.025 0.868
Bits 8 to 15---> 0.182 0.157 0.265 0.226 0.891 0.469 0.489 0.943
Bits 16 to 23---> 0.488 0.043 0.149 0.642 0.096 0.314 0.692 0.316
Bits 24 to 31---> 0.484 0.844 0.675 0.677 0.719 0.051 0.345 0.271
KS test for the above 32 p values: 0.299
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-09_21:31,
p-values for 5 runs: 0.7596, 0.0753, 0.4172, 0.7281, 0.4860
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-09_21:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 204 211.4 0.260 0.260
r= 29 5108 5134.0 0.132 0.392
r= 30 23206 23103.0 0.459 0.851
r= 31 11482 11551.5 0.418 1.269
chi-square = 1.269 with df = 3; p-value = 0.264
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-09_21:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 181 211.4 4.376 4.376
r= 30 5133 5134.0 0.000 4.377
r= 31 22908 23103.0 1.647 6.023
r= 32 11778 11551.5 4.440 10.464
chi-square = 10.464 with df = 3; p-value = 0.985
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-09_21:31
b-rank test for bits 1 to 8, p=0.51618
b-rank test for bits 2 to 9, p=0.21655
b-rank test for bits 3 to 10, p=0.14419
b-rank test for bits 4 to 11, p=0.37750
b-rank test for bits 5 to 12, p=0.75882
b-rank test for bits 6 to 13, p=0.70705
b-rank test for bits 7 to 14, p=0.14112
b-rank test for bits 8 to 15, p=0.67841
b-rank test for bits 9 to 16, p=0.60713
b-rank test for bits 10 to 17, p=0.35578
b-rank test for bits 11 to 18, p=0.90510
b-rank test for bits 12 to 19, p=0.96766
b-rank test for bits 13 to 20, p=0.87029
b-rank test for bits 14 to 21, p=0.91492
b-rank test for bits 15 to 22, p=0.80032
b-rank test for bits 16 to 23, p=0.50269
b-rank test for bits 17 to 24, p=0.42564
b-rank test for bits 18 to 25, p=0.47690
b-rank test for bits 19 to 26, p=0.53737
b-rank test for bits 20 to 27, p=0.86728
b-rank test for bits 21 to 28, p=0.56754
b-rank test for bits 22 to 29, p=0.48699
b-rank test for bits 23 to 30, p=0.48907
b-rank test for bits 24 to 31, p=0.13183
b-rank test for bits 25 to 32, p=0.30899
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 = 0.470033
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-09_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 142172 0.61 0.730298
2 141788 -0.28 0.388404
3 141151 -1.77 0.038214
4 142040 0.31 0.619933
5 141432 -1.12 0.132370
6 142003 0.22 0.586619
7 141576 -0.78 0.218046
8 141388 -1.22 0.111600
9 141410 -1.17 0.121674
10 141730 -0.42 0.337610
11 142344 1.02 0.845086
12 142185 0.64 0.740241
13 142501 1.38 0.916577
14 141646 -0.62 0.269193
15 141719 -0.44 0.328270
16 142113 0.48 0.682915
17 142348 1.02 0.847302
18 142308 0.93 0.824195
19 142700 1.85 0.967653
20 141503 -0.95 0.171216
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-09_21:31
Bits used No. missing words z-score p-value
23 to 32 141770 -0.4804 0.315454
22 to 31 141945 0.1230 0.548947
21 to 30 141445 -1.6011 0.054673
20 to 29 142070 0.5540 0.710222
19 to 28 141762 -0.5080 0.305715
18 to 27 141857 -0.1804 0.428400
17 to 26 141867 -0.1460 0.441974
16 to 25 141740 -0.5839 0.279645
15 to 24 141844 -0.2253 0.410882
14 to 23 141865 -0.1529 0.439254
13 to 22 142027 0.4058 0.657540
12 to 21 142225 1.0885 0.861817
11 to 20 141891 -0.0632 0.474801
10 to 19 142022 0.3885 0.651183
9 to 18 141873 -0.1253 0.450153
8 to 17 141685 -0.7736 0.219598
7 to 16 142357 1.5437 0.938668
6 to 15 142051 0.4885 0.687408
5 to 14 141878 -0.1080 0.456984
4 to 13 141827 -0.2839 0.388245
3 to 12 142338 1.4782 0.930319
2 to 11 142235 1.1230 0.869281
1 to 10 142029 0.4127 0.660070
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-09_21:31
Bits used No. missing words z-score p-value
28 to 32 141476 -1.4689 0.070928
27 to 31 141861 -0.1638 0.434932
26 to 30 141995 0.2904 0.614248
25 to 29 141690 -0.7435 0.228592
24 to 28 142576 2.2599 0.988086
23 to 27 142577 2.2633 0.988191
22 to 26 141925 0.0531 0.521181
21 to 25 142084 0.5921 0.723109
20 to 24 142104 0.6599 0.745341
19 to 23 142062 0.5175 0.697605
18 to 22 142575 2.2565 0.987981
17 to 21 141982 0.2463 0.597290
16 to 20 141948 0.1311 0.552146
15 to 19 142393 1.6396 0.949452
14 to 18 141872 -0.1265 0.449651
13 to 17 141263 -2.1909 0.014228
12 to 16 141329 -1.9672 0.024579
11 to 15 141635 -0.9299 0.176203
10 to 14 142014 0.3548 0.638635
9 to 13 142437 1.7887 0.963169
8 to 12 141545 -1.2350 0.108412
7 to 11 141899 -0.0350 0.486033
6 to 10 142108 0.6735 0.749672
5 to 9 141760 -0.5062 0.306357
4 to 8 142238 1.1141 0.867390
3 to 7 141886 -0.0791 0.468483
2 to 6 141871 -0.1299 0.448310
1 to 5 141718 -0.6486 0.258306
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-09_21:31
Bits used No. missing words z-score p-value
31 to 32 142098 0.5565 0.711082
30 to 31 142331 1.2439 0.893225
29 to 30 141896 -0.0393 0.484317
28 to 29 142218 0.9105 0.818729
27 to 28 142132 0.6568 0.744359
26 to 27 141758 -0.4464 0.327654
25 to 26 142020 0.3265 0.627962
24 to 25 141931 0.0639 0.525484
23 to 24 141325 -1.7237 0.042382
22 to 23 141329 -1.7119 0.043459
21 to 22 142450 1.5949 0.944632
20 to 21 141858 -0.1514 0.439824
19 to 20 142745 2.4651 0.993151
18 to 19 141747 -0.4788 0.316023
17 to 18 142094 0.5447 0.707037
16 to 17 141319 -1.7414 0.040808
15 to 16 142416 1.4946 0.932491
14 to 15 141859 -0.1485 0.440988
13 to 14 141428 -1.4199 0.077825
12 to 13 141946 0.1082 0.543070
11 to 12 141959 0.1465 0.558244
10 to 11 141628 -0.8299 0.203303
9 to 10 141733 -0.5201 0.301480
8 to 9 141406 -1.4847 0.068805
7 to 8 141395 -1.5172 0.064608
6 to 7 141982 0.2144 0.584869
5 to 6 141030 -2.5939 0.004745
4 to 5 142323 1.2203 0.888818
3 to 4 141750 -0.4700 0.319178
2 to 3 142124 0.6332 0.736713
1 to 2 142250 1.0049 0.842534
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-09_21:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2455.95 -0.623 0.266651
Test results for specific bytes for dh-ranFile-2018-07-09_21:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2421.99 -1.103 0.134958
2 to 9 2453.64 -0.656 0.256018
3 to 10 2508.49 0.120 0.547773
4 to 11 2486.54 -0.190 0.424536
5 to 12 2394.12 -1.497 0.067140
6 to 13 2449.82 -0.710 0.238939
7 to 14 2529.08 0.411 0.659536
8 to 15 2423.13 -1.087 0.138487
9 to 16 2644.01 2.037 0.979158
10 to 17 2460.24 -0.562 0.286966
11 to 18 2472.65 -0.387 0.349471
12 to 19 2561.79 0.874 0.808882
13 to 20 2482.74 -0.244 0.403585
14 to 21 2396.22 -1.468 0.071105
15 to 22 2446.93 -0.751 0.226469
16 to 23 2491.44 -0.121 0.451826
17 to 24 2440.74 -0.838 0.201009
18 to 25 2502.10 0.030 0.511867
19 to 26 2592.29 1.305 0.904083
20 to 27 2493.07 -0.098 0.460943
21 to 28 2697.76 2.797 0.997419
22 to 29 2462.02 -0.537 0.295613
23 to 30 2534.75 0.492 0.688465
24 to 31 2524.13 0.341 0.633533
25 to 32 2551.80 0.733 0.768075
CDPARK for dh-ranFile-2018-07-09_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
3499 -1.0959 0.136563
3546 1.0502 0.853193
3550 1.2329 0.891189
3520 -0.1370 0.445521
3505 -0.8219 0.205562
3559 1.6438 0.949895
3517 -0.2740 0.392053
3516 -0.3196 0.374623
3508 -0.6849 0.246694
3518 -0.2283 0.409702
Square side=100, avg. no. parked=3523.80 sample std.=19.47
p-value of the KSTEST for those 10 p-values: 0.714446
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-09_21:31
0.4031,0.2787,0.0913,0.0743,0.9759,0.0854,0.6293,0.1260,0.4594,0.8793,
The KS test for those 10 p-values: 0.291501
The 3DSPHERES test for dh-ranFile-2018-07-09_21:31
sample no r^3 equiv. uni.
1 43.724 0.767171
2 21.385 0.509741
3 71.757 0.908543
4 32.776 0.664633
5 9.798 0.278624
6 16.648 0.425885
7 25.902 0.578270
8 18.484 0.459979
9 53.639 0.832699
10 57.446 0.852637
11 8.568 0.248445
12 88.566 0.947775
13 55.782 0.844235
14 37.360 0.712155
15 54.616 0.838058
16 63.928 0.881274
17 28.782 0.616880
18 17.664 0.445005
19 37.116 0.709801
20 67.532 0.894713
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.010511
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-09_21:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 -0.3 0.1 -1.1 0.5 -0.8
1.1 0.1 0.7 0.5 1.2 0.5
0.4 -0.6 -1.7 -0.1 -0.9 -0.9
-1.4 0.6 0.9 1.8 0.1 1.5
-0.7 -1.5 1.0 -0.3 -0.1 0.4
-0.4 0.4 1.3 0.1 0.3 -1.4
1.0 -1.0 1.7 -0.7 -0.6 -1.0
-1.1
Chi-square with 42 degrees of freedom:36.131559
z-score=-0.640299, p-value=0.274548
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-09_21:31
Test no p-value
1 0.218754
2 0.196153
3 0.000438
4 0.000878
5 0.146596
6 0.004109
7 0.016308
8 0.395529
9 0.000868
10 0.359639
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000000
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-09_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 66368 1.34 66744 0.09
3 25000.00 25160 1.02 24923 0.24
4 6666.67 6787 2.17 6712 0.31
5 1388.89 1416 0.53 1376 0.12
6 238.10 232 0.16 208 3.80
7 34.72 32 0.21 30 0.64
8 4.96 4 0.19 6 0.22
p=0.53269 p=0.50863
Number of rngs required: 688389, p-value: 0.494
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-09_21:31
No. of wins: Observed Expected
98687 98585.9
z-score= 0.452, pvalue=0.67450
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66792 66666.7 0.236 0.236
2 37419 37654.3 1.471 1.706
3 26914 26954.7 0.062 1.768
4 19109 19313.5 2.165 3.932
5 13859 13851.4 0.004 3.937
6 9983 9943.5 0.157 4.093
7 7196 7145.0 0.364 4.457
8 5214 5139.1 1.092 5.549
9 3696 3699.9 0.004 5.553
10 2626 2666.3 0.609 6.162
11 2027 1923.3 5.588 11.750
12 1395 1388.7 0.028 11.779
13 998 1003.7 0.033 11.811
14 746 726.1 0.543 12.354
15 535 525.8 0.160 12.514
16 394 381.2 0.433 12.947
17 313 276.5 4.807 17.754
18 227 200.8 3.410 21.164
19 155 146.0 0.557 21.721
20 116 106.2 0.901 22.623
21 286 287.1 0.004 22.627
Chisq= 22.63 for 20 degrees of freedom, p= 0.69252
SUMMARY of craptest
p-value for no. of wins: 0.674496
p-value for throws/game: 0.692520
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-09_21:31
No. of wins: Observed Expected
98347 98585.9
z-score=-1.068, pvalue=0.14269
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66936 66666.7 1.088 1.088
2 37360 37654.3 2.301 3.389
3 26883 26954.7 0.191 3.580
4 19465 19313.5 1.189 4.769
5 13943 13851.4 0.605 5.374
6 9851 9943.5 0.861 6.235
7 7132 7145.0 0.024 6.259
8 5070 5139.1 0.928 7.187
9 3671 3699.9 0.225 7.413
10 2669 2666.3 0.003 7.415
11 1939 1923.3 0.128 7.543
12 1364 1388.7 0.441 7.984
13 1024 1003.7 0.410 8.394
14 746 726.1 0.543 8.937
15 527 525.8 0.003 8.939
16 381 381.2 0.000 8.940
17 291 276.5 0.756 9.696
18 225 200.8 2.909 12.605
19 157 146.0 0.831 13.436
20 98 106.2 0.635 14.071
21 268 287.1 1.272 15.344
Chisq= 15.34 for 20 degrees of freedom, p= 0.24358
SUMMARY of craptest
p-value for no. of wins: 0.142689
p-value for throws/game: 0.243583
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0000,0.0004,0.0009,0.0009,0.0041,0.0047,0.0105,0.0142,0.0163,0.0246,
0.0247,0.0376,0.0382,0.0408,0.0424,0.0426,0.0435,0.0513,0.0547,0.0592,
0.0646,0.0671,0.0688,0.0709,0.0711,0.0743,0.0753,0.0778,0.0854,0.0913,
0.0961,0.1084,0.1116,0.1217,0.1260,0.1318,0.1324,0.1350,0.1366,0.1385,
0.1411,0.1427,0.1442,0.1466,0.1490,0.1565,0.1712,0.1762,0.1817,0.1962,
0.2010,0.2033,0.2056,0.2098,0.2166,0.2180,0.2188,0.2196,0.2257,0.2262,
0.2264,0.2265,0.2286,0.2389,0.2436,0.2467,0.2484,0.2560,0.2583,0.2636,
0.2648,0.2667,0.2692,0.2699,0.2714,0.2745,0.2786,0.2787,0.2796,0.2870,
0.2915,0.2956,0.2989,0.3015,0.3057,0.3064,0.3090,0.3143,0.3155,0.3155,
0.3160,0.3192,0.3277,0.3283,0.3325,0.3376,0.3447,0.3495,0.3512,0.3558,
0.3596,0.3746,0.3775,0.3882,0.3884,0.3921,0.3955,0.4031,0.4036,0.4077,
0.4097,0.4109,0.4172,0.4245,0.4256,0.4259,0.4284,0.4349,0.4393,0.4398,
0.4410,0.4420,0.4450,0.4455,0.4477,0.4483,0.4497,0.4502,0.4518,0.4570,
0.4594,0.4600,0.4609,0.4685,0.4691,0.4700,0.4748,0.4769,0.4843,0.4845,
0.4860,0.4860,0.4870,0.4879,0.4890,0.4891,0.4936,0.5027,0.5059,0.5086,
0.5097,0.5119,0.5162,0.5212,0.5255,0.5327,0.5374,0.5431,0.5478,0.5488,
0.5489,0.5521,0.5582,0.5675,0.5783,0.5849,0.5866,0.5973,0.6071,0.6142,
0.6169,0.6199,0.6280,0.6293,0.6335,0.6386,0.6417,0.6512,0.6575,0.6595,
0.6601,0.6646,0.6745,0.6755,0.6767,0.6784,0.6829,0.6874,0.6885,0.6915,
0.6925,0.6976,0.7070,0.7070,0.7098,0.7102,0.7111,0.7122,0.7144,0.7187,
0.7231,0.7247,0.7281,0.7303,0.7367,0.7402,0.7444,0.7453,0.7497,0.7588,
0.7596,0.7672,0.7681,0.8003,0.8089,0.8168,0.8187,0.8242,0.8304,0.8327,
0.8381,0.8425,0.8442,0.8444,0.8451,0.8452,0.8473,0.8526,0.8532,0.8618,
0.8673,0.8674,0.8675,0.8693,0.8703,0.8750,0.8793,0.8813,0.8888,0.8910,
0.8912,0.8932,0.8947,0.9007,0.9041,0.9051,0.9085,0.9149,0.9166,0.9303,
0.9325,0.9387,0.9427,0.9446,0.9478,0.9495,0.9499,0.9632,0.9677,0.9677,
0.9759,0.9792,0.9850,0.9880,0.9881,0.9882,0.9932,0.9941,0.9974,
Overall p-value after applying KStest on 269 p-values = 0.529332
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.