RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-11_03:31
(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 10.8679 0.136652
2 to 25 15.99 9.8556 0.090444
3 to 26 15.94 10.1425 0.102472
4 to 27 15.88 17.0983 0.552276
5 to 28 16.04 21.7549 0.805671
6 to 29 15.98 17.7319 0.594061
7 to 30 15.67 15.8160 0.463087
8 to 31 15.69 22.1083 0.819411
9 to 32 15.85 9.9496 0.094290
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.349026
Tough bday spacings test for dh-ranFile-2018-07-11_03:31: 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 36 68 99 94 86 60 27 12 6 2
(O-E)^2/E 0.1 0.0 0.4 0.0 0.1 0.8 1.2 0.3 0.6 0.1 1.0
Birthday Spacings: Sum(O-E)^2/E= 4.535, p= 0.080
RESULTS OF GCD FOR dh-ranFile-2018-07-11_03:31
Euclid's algorithm:
p-value, steps to gcd: 0.456886
p-value, dist. of gcd's: 0.944212
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-11_03:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.915 0.677 0.285 0.118 0.148 0.351 0.604 0.605
Bits 8 to 15---> 0.885 0.598 0.731 0.664 0.268 0.664 0.990 0.507
Bits 16 to 23---> 0.884 0.218 0.591 0.411 0.033 0.481 0.664 0.602
Bits 24 to 31---> 0.816 0.425 0.665 0.917 0.587 0.414 0.946 0.900
KS test for the above 32 p values: 0.852
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-11_03:31,
p-values for 5 runs: 0.2544, 0.5378, 0.9498, 0.3982, 0.3731
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-11_03:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 195 211.4 1.275 1.275
r= 29 5159 5134.0 0.122 1.397
r= 30 22993 23103.0 0.524 1.921
r= 31 11653 11551.5 0.891 2.812
chi-square = 2.812 with df = 3; p-value = 0.579
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-11_03:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 195 211.4 1.275 1.275
r= 30 5173 5134.0 0.296 1.571
r= 31 23006 23103.0 0.408 1.979
r= 32 11626 11551.5 0.480 2.459
chi-square = 2.459 with df = 3; p-value = 0.517
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-11_03:31
b-rank test for bits 1 to 8, p=0.59182
b-rank test for bits 2 to 9, p=0.49253
b-rank test for bits 3 to 10, p=0.32131
b-rank test for bits 4 to 11, p=0.15057
b-rank test for bits 5 to 12, p=0.83016
b-rank test for bits 6 to 13, p=0.36384
b-rank test for bits 7 to 14, p=0.18799
b-rank test for bits 8 to 15, p=0.61949
b-rank test for bits 9 to 16, p=0.83422
b-rank test for bits 10 to 17, p=0.22908
b-rank test for bits 11 to 18, p=0.68520
b-rank test for bits 12 to 19, p=0.05436
b-rank test for bits 13 to 20, p=0.19329
b-rank test for bits 14 to 21, p=0.12499
b-rank test for bits 15 to 22, p=0.94475
b-rank test for bits 16 to 23, p=0.91772
b-rank test for bits 17 to 24, p=0.03620
b-rank test for bits 18 to 25, p=0.47346
b-rank test for bits 19 to 26, p=0.97843
b-rank test for bits 20 to 27, p=0.89211
b-rank test for bits 21 to 28, p=0.34289
b-rank test for bits 22 to 29, p=0.10930
b-rank test for bits 23 to 30, p=0.58174
b-rank test for bits 24 to 31, p=0.59044
b-rank test for bits 25 to 32, p=0.76788
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 = 0.992262
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-11_03:31
(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 142069 0.37 0.645448
2 142021 0.26 0.602920
3 141778 -0.31 0.379480
4 141442 -1.09 0.137440
5 141528 -0.89 0.186476
6 142046 0.32 0.625259
7 140882 -2.40 0.008191
8 141535 -0.87 0.190895
9 142501 1.38 0.916577
10 141951 0.10 0.538780
11 141451 -1.07 0.142115
12 141901 -0.02 0.492236
13 141635 -0.64 0.260775
14 141797 -0.26 0.396486
15 142300 0.91 0.819321
16 141571 -0.79 0.214621
17 142347 1.02 0.846750
18 142453 1.27 0.898003
19 141203 -1.65 0.049440
20 142481 1.34 0.909173
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-11_03:31
Bits used No. missing words z-score p-value
23 to 32 141522 -1.3356 0.090837
22 to 31 142172 0.9058 0.817468
21 to 30 142121 0.7299 0.767273
20 to 29 141994 0.2920 0.614844
19 to 28 141738 -0.5908 0.277330
18 to 27 141911 0.0058 0.502297
17 to 26 141438 -1.6253 0.052052
16 to 25 142160 0.8644 0.806310
15 to 24 141827 -0.2839 0.388245
14 to 23 142182 0.9402 0.826453
13 to 22 142331 1.4540 0.927032
12 to 21 142000 0.3127 0.622729
11 to 20 141831 -0.2701 0.393540
10 to 19 141690 -0.7563 0.224732
9 to 18 142508 2.0644 0.980509
8 to 17 141541 -1.2701 0.102024
7 to 16 141608 -1.0391 0.149386
6 to 15 141868 -0.1425 0.443336
5 to 14 142028 0.4092 0.658806
4 to 13 141996 0.2989 0.617477
3 to 12 141592 -1.0942 0.136925
2 to 11 141734 -0.6046 0.272727
1 to 10 142245 1.1575 0.876462
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-11_03:31
Bits used No. missing words z-score p-value
28 to 32 142287 1.2802 0.899769
27 to 31 142166 0.8701 0.807868
26 to 30 142058 0.5040 0.692857
25 to 29 141110 -2.7096 0.003368
24 to 28 142088 0.6057 0.727630
23 to 27 142098 0.6396 0.738770
22 to 26 141462 -1.5164 0.064713
21 to 25 141884 -0.0859 0.465787
20 to 24 142439 1.7955 0.963712
19 to 23 141767 -0.4825 0.314734
18 to 22 141703 -0.6994 0.242144
17 to 21 141920 0.0362 0.514426
16 to 20 141676 -0.7909 0.214487
15 to 19 141971 0.2091 0.582796
14 to 18 141639 -0.9164 0.179736
13 to 17 141807 -0.3469 0.364340
12 to 16 142388 1.6226 0.947664
11 to 15 141861 -0.1638 0.434932
10 to 14 142016 0.3616 0.641172
9 to 13 142038 0.4362 0.668643
8 to 12 141922 0.0429 0.517129
7 to 11 141190 -2.4384 0.007376
6 to 10 141724 -0.6282 0.264924
5 to 9 141805 -0.3537 0.361797
4 to 8 142074 0.5582 0.711647
3 to 7 141815 -0.3198 0.374574
2 to 6 140891 -3.4520 0.000278
1 to 5 141688 -0.7503 0.226546
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-11_03:31
Bits used No. missing words z-score p-value
31 to 32 141757 -0.4494 0.326589
30 to 31 142149 0.7070 0.760214
29 to 30 141970 0.1790 0.571018
28 to 29 142553 1.8987 0.971200
27 to 28 142027 0.3471 0.635745
26 to 27 142076 0.4917 0.688517
25 to 26 141839 -0.2075 0.417824
24 to 25 142259 1.0315 0.848841
23 to 24 141890 -0.0570 0.477264
22 to 23 141748 -0.4759 0.317073
21 to 22 141639 -0.7974 0.212600
20 to 21 141575 -0.9862 0.162012
19 to 20 141723 -0.5496 0.291281
18 to 19 141843 -0.1957 0.422437
17 to 18 141556 -1.0423 0.148643
16 to 17 141426 -1.4258 0.076970
15 to 16 142116 0.6096 0.728952
14 to 15 142147 0.7011 0.758377
13 to 14 141551 -1.0570 0.145251
12 to 13 141941 0.0934 0.537216
11 to 12 141472 -1.2901 0.098515
10 to 11 142000 0.2675 0.605444
9 to 10 141385 -1.5467 0.060968
8 to 9 141851 -0.1721 0.431693
7 to 8 141780 -0.3815 0.351415
6 to 7 142429 1.5329 0.937356
5 to 6 141383 -1.5526 0.060260
4 to 5 141993 0.2468 0.597474
3 to 4 141659 -0.7384 0.230125
2 to 3 141836 -0.2163 0.414372
1 to 2 141827 -0.2429 0.404056
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-11_03:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2559.22 0.838 0.798856
Test results for specific bytes for dh-ranFile-2018-07-11_03:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2564.92 0.918 0.820716
2 to 9 2429.90 -0.991 0.160763
3 to 10 2647.25 2.082 0.981346
4 to 11 2504.03 0.057 0.522750
5 to 12 2516.62 0.235 0.592893
6 to 13 2315.17 -2.614 0.004476
7 to 14 2541.41 0.586 0.720947
8 to 15 2598.18 1.388 0.917500
9 to 16 2490.55 -0.134 0.446821
10 to 17 2535.69 0.505 0.693119
11 to 18 2401.95 -1.387 0.082782
12 to 19 2466.73 -0.471 0.318983
13 to 20 2473.82 -0.370 0.355620
14 to 21 2673.04 2.447 0.992800
15 to 22 2596.83 1.369 0.914553
16 to 23 2408.63 -1.292 0.098153
17 to 24 2458.66 -0.585 0.279387
18 to 25 2429.57 -0.996 0.159631
19 to 26 2484.41 -0.221 0.412737
20 to 27 2594.17 1.332 0.908526
21 to 28 2493.85 -0.087 0.465364
22 to 29 2533.05 0.467 0.679909
23 to 30 2388.66 -1.575 0.057671
24 to 31 2529.37 0.415 0.661041
25 to 32 2424.16 -1.073 0.141736
CDPARK for dh-ranFile-2018-07-11_03:31: 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
3520 -0.1370 0.445521
3498 -1.1416 0.126820
3547 1.0959 0.863437
3500 -1.0502 0.146807
3526 0.1370 0.554479
3538 0.6849 0.753306
3507 -0.7306 0.232514
3492 -1.4155 0.078457
3533 0.4566 0.676028
3534 0.5023 0.692266
Square side=100, avg. no. parked=3519.50 sample std.=18.13
p-value of the KSTEST for those 10 p-values: 0.855028
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-11_03:31
0.8858,0.9167,0.0552,0.0943,0.3099,0.0206,0.3830,0.1550,0.4171,0.1560,
The KS test for those 10 p-values: 0.074623
The 3DSPHERES test for dh-ranFile-2018-07-11_03:31
sample no r^3 equiv. uni.
1 18.931 0.467951
2 2.838 0.090252
3 14.787 0.389145
4 13.093 0.353663
5 10.189 0.287968
6 6.407 0.192312
7 4.808 0.148089
8 18.173 0.454347
9 46.915 0.790668
10 38.038 0.718588
11 51.321 0.819259
12 37.836 0.716685
13 57.401 0.852418
14 0.731 0.024070
15 131.287 0.987427
16 37.127 0.709910
17 2.590 0.082703
18 8.812 0.254519
19 2.417 0.077401
20 138.928 0.990254
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.641772
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-11_03:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 0.1 1.1 -1.0 -0.2 1.6
-1.4 0.4 0.4 0.7 -1.2 -0.5
2.0 0.3 0.1 -0.3 -1.5 -0.0
0.8 0.4 0.4 1.8 -1.6 0.1
-0.7 -0.1 -0.3 -2.7 0.8 -0.0
-0.7 -0.2 -0.5 0.1 1.0 1.5
0.3 -0.1 0.9 -1.8 1.6 0.0
-0.1
Chi-square with 42 degrees of freedom:44.032211
z-score=0.221732, p-value=0.614393
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-11_03:31
Test no p-value
1 0.517262
2 0.576415
3 0.085204
4 0.748974
5 0.175306
6 0.571751
7 0.211516
8 0.011371
9 0.714625
10 0.233022
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.304227
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-11_03:31:
(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 66532 0.27 66495 0.44
3 25000.00 24949 0.10 25160 1.02
4 6666.67 6858 5.49 6690 0.08
5 1388.89 1376 0.12 1371 0.23
6 238.10 257 1.50 246 0.26
7 34.72 24 3.31 31 0.40
8 4.96 3 0.77 6 0.22
p=0.92778 p=0.14953
Number of rngs required: 690033, p-value: 0.973
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-11_03:31
No. of wins: Observed Expected
98686 98585.9
z-score= 0.448, pvalue=0.67288
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66717 66666.7 0.038 0.038
2 37625 37654.3 0.023 0.061
3 27091 26954.7 0.689 0.750
4 19264 19313.5 0.127 0.876
5 13804 13851.4 0.162 1.039
6 9967 9943.5 0.055 1.094
7 7040 7145.0 1.544 2.638
8 5163 5139.1 0.111 2.749
9 3693 3699.9 0.013 2.762
10 2685 2666.3 0.131 2.893
11 1948 1923.3 0.316 3.210
12 1409 1388.7 0.296 3.505
13 998 1003.7 0.033 3.538
14 712 726.1 0.275 3.813
15 512 525.8 0.364 4.177
16 408 381.2 1.891 6.069
17 250 276.5 2.547 8.616
18 172 200.8 4.139 12.754
19 139 146.0 0.334 13.088
20 114 106.2 0.571 13.659
21 289 287.1 0.012 13.671
Chisq= 13.67 for 20 degrees of freedom, p= 0.15324
SUMMARY of craptest
p-value for no. of wins: 0.672884
p-value for throws/game: 0.153235
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-11_03:31
No. of wins: Observed Expected
98903 98585.9
z-score= 1.418, pvalue=0.92197
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66552 66666.7 0.197 0.197
2 37593 37654.3 0.100 0.297
3 26865 26954.7 0.299 0.596
4 19529 19313.5 2.405 3.001
5 13870 13851.4 0.025 3.026
6 10085 9943.5 2.012 5.039
7 7080 7145.0 0.592 5.630
8 5103 5139.1 0.253 5.883
9 3752 3699.9 0.735 6.618
10 2565 2666.3 3.848 10.467
11 1972 1923.3 1.232 11.698
12 1363 1388.7 0.477 12.175
13 1048 1003.7 1.954 14.129
14 714 726.1 0.203 14.332
15 552 525.8 1.302 15.634
16 376 381.2 0.070 15.704
17 256 276.5 1.526 17.229
18 181 200.8 1.958 19.187
19 154 146.0 0.440 19.627
20 93 106.2 1.644 21.272
21 297 287.1 0.340 21.612
Chisq= 21.61 for 20 degrees of freedom, p= 0.63807
SUMMARY of craptest
p-value for no. of wins: 0.921969
p-value for throws/game: 0.638067
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0003,0.0034,0.0045,0.0074,0.0082,0.0114,0.0206,0.0241,0.0331,0.0362,
0.0494,0.0521,0.0544,0.0552,0.0577,0.0603,0.0610,0.0647,0.0746,0.0770,
0.0774,0.0785,0.0800,0.0827,0.0828,0.0852,0.0903,0.0904,0.0908,0.0943,
0.0943,0.0982,0.0985,0.1020,0.1025,0.1093,0.1184,0.1250,0.1268,0.1367,
0.1369,0.1374,0.1417,0.1421,0.1453,0.1468,0.1475,0.1481,0.1486,0.1494,
0.1495,0.1506,0.1532,0.1550,0.1560,0.1596,0.1608,0.1620,0.1753,0.1797,
0.1865,0.1880,0.1909,0.1923,0.1933,0.2115,0.2126,0.2145,0.2146,0.2180,
0.2247,0.2265,0.2291,0.2301,0.2325,0.2330,0.2421,0.2544,0.2545,0.2608,
0.2649,0.2682,0.2727,0.2773,0.2794,0.2852,0.2880,0.2913,0.3042,0.3099,
0.3147,0.3171,0.3190,0.3213,0.3266,0.3429,0.3490,0.3514,0.3514,0.3537,
0.3556,0.3618,0.3638,0.3643,0.3731,0.3746,0.3795,0.3830,0.3882,0.3891,
0.3935,0.3965,0.3982,0.4041,0.4106,0.4127,0.4143,0.4144,0.4171,0.4178,
0.4224,0.4254,0.4317,0.4349,0.4433,0.4455,0.4468,0.4543,0.4569,0.4631,
0.4654,0.4658,0.4680,0.4735,0.4773,0.4809,0.4922,0.4925,0.5023,0.5071,
0.5144,0.5171,0.5172,0.5173,0.5228,0.5372,0.5378,0.5388,0.5523,0.5545,
0.5710,0.5718,0.5764,0.5785,0.5817,0.5828,0.5868,0.5904,0.5909,0.5918,
0.5929,0.5941,0.5975,0.5981,0.6022,0.6029,0.6043,0.6050,0.6054,0.6144,
0.6148,0.6175,0.6195,0.6227,0.6253,0.6357,0.6381,0.6412,0.6418,0.6454,
0.6588,0.6610,0.6636,0.6638,0.6645,0.6650,0.6686,0.6729,0.6760,0.6765,
0.6799,0.6852,0.6885,0.6923,0.6929,0.6931,0.7099,0.7116,0.7146,0.7167,
0.7186,0.7209,0.7276,0.7290,0.7313,0.7388,0.7490,0.7533,0.7584,0.7602,
0.7673,0.7679,0.7907,0.7989,0.8057,0.8063,0.8079,0.8159,0.8175,0.8193,
0.8193,0.8194,0.8207,0.8265,0.8302,0.8342,0.8467,0.8488,0.8518,0.8524,
0.8550,0.8634,0.8765,0.8836,0.8854,0.8858,0.8921,0.8980,0.8998,0.9003,
0.9085,0.9092,0.9146,0.9150,0.9166,0.9166,0.9167,0.9175,0.9177,0.9220,
0.9270,0.9278,0.9374,0.9442,0.9447,0.9461,0.9477,0.9498,0.9637,0.9712,
0.9726,0.9784,0.9805,0.9813,0.9874,0.9899,0.9903,0.9923,0.9928,
Overall p-value after applying KStest on 269 p-values = 0.525852
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.