RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-07_02:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.99 16.1370 0.485854
2 to 25 15.72 15.4235 0.434994
3 to 26 15.65 36.0093 0.995427
4 to 27 15.86 15.6139 0.448646
5 to 28 15.79 10.7142 0.128969
6 to 29 15.85 12.6752 0.242357
7 to 30 15.34 34.3769 0.992496
8 to 31 15.66 18.2552 0.627085
9 to 32 15.64 25.4513 0.914946
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.168335
Tough bday spacings test for dh-ranFile-2018-07-07_02:31: 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 7 43 66 103 88 74 42 44 21 9 3
(O-E)^2/E 0.5 1.1 0.7 0.3 1.0 0.2 2.0 6.8 2.5 0.9 0.3
Birthday Spacings: Sum(O-E)^2/E= 16.215, p= 0.906
RESULTS OF GCD FOR dh-ranFile-2018-07-07_02:31
Euclid's algorithm:
p-value, steps to gcd: 0.949147
p-value, dist. of gcd's: 0.758358
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-07_02:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.201 0.479 0.076 0.907 0.352 0.007 0.815 0.233
Bits 8 to 15---> 0.223 0.093 0.250 0.980 0.012 0.943 0.207 0.055
Bits 16 to 23---> 0.274 0.034 0.648 0.128 0.239 0.836 0.984 0.617
Bits 24 to 31---> 0.857 0.495 0.943 0.617 0.207 0.385 0.180 0.607
KS test for the above 32 p values: 0.882
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-07_02:31,
p-values for 5 runs: 0.1851, 0.6309, 0.1783, 0.9431, 0.5809
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-07_02:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 197 211.4 0.983 0.983
r= 29 5159 5134.0 0.122 1.105
r= 30 23078 23103.0 0.027 1.132
r= 31 11566 11551.5 0.018 1.150
chi-square = 1.150 with df = 3; p-value = 0.235
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-07_02:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 236 211.4 2.858 2.858
r= 30 5100 5134.0 0.225 3.084
r= 31 23190 23103.0 0.327 3.411
r= 32 11474 11551.5 0.520 3.931
chi-square = 3.931 with df = 3; p-value = 0.731
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-07_02:31
b-rank test for bits 1 to 8, p=0.78578
b-rank test for bits 2 to 9, p=0.87160
b-rank test for bits 3 to 10, p=0.81030
b-rank test for bits 4 to 11, p=0.67474
b-rank test for bits 5 to 12, p=0.85728
b-rank test for bits 6 to 13, p=0.96729
b-rank test for bits 7 to 14, p=0.89114
b-rank test for bits 8 to 15, p=0.92874
b-rank test for bits 9 to 16, p=0.17989
b-rank test for bits 10 to 17, p=0.34633
b-rank test for bits 11 to 18, p=0.56970
b-rank test for bits 12 to 19, p=0.04011
b-rank test for bits 13 to 20, p=0.15508
b-rank test for bits 14 to 21, p=0.84297
b-rank test for bits 15 to 22, p=0.17583
b-rank test for bits 16 to 23, p=0.04179
b-rank test for bits 17 to 24, p=0.05754
b-rank test for bits 18 to 25, p=0.42663
b-rank test for bits 19 to 26, p=0.89247
b-rank test for bits 20 to 27, p=0.47065
b-rank test for bits 21 to 28, p=0.84433
b-rank test for bits 22 to 29, p=0.94919
b-rank test for bits 23 to 30, p=0.88801
b-rank test for bits 24 to 31, p=0.47136
b-rank test for bits 25 to 32, p=0.17490
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 = 0.099899
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-07_02:31
(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 141401 -1.19 0.117478
2 141447 -1.08 0.140024
3 141950 0.10 0.537852
4 141806 -0.24 0.404613
5 142464 1.30 0.902505
6 142291 0.89 0.813737
7 142537 1.47 0.928746
8 142465 1.30 0.902907
9 142248 0.79 0.785611
10 141356 -1.29 0.098035
11 142215 0.71 0.762443
12 141386 -1.22 0.110715
13 142248 0.79 0.785611
14 141537 -0.87 0.192169
15 141535 -0.87 0.190895
16 141870 -0.09 0.463392
17 141744 -0.39 0.349643
18 141702 -0.48 0.314045
19 141999 0.21 0.582975
20 142911 2.34 0.990367
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-07_02:31
Bits used No. missing words z-score p-value
23 to 32 141476 -1.4942 0.067556
22 to 31 142004 0.3264 0.627957
21 to 30 141869 -0.1391 0.444698
20 to 29 142118 0.7196 0.764100
19 to 28 141874 -0.1218 0.451518
18 to 27 142218 1.0644 0.856422
17 to 26 141792 -0.4046 0.342891
16 to 25 141627 -0.9736 0.165140
15 to 24 141821 -0.3046 0.380341
14 to 23 141993 0.2885 0.613525
13 to 22 142032 0.4230 0.663852
12 to 21 142148 0.8230 0.794746
11 to 20 142658 2.5816 0.995083
10 to 19 141514 -1.3632 0.086409
9 to 18 141757 -0.5253 0.299696
8 to 17 141728 -0.6253 0.265895
7 to 16 141964 0.1885 0.574764
6 to 15 142210 1.0368 0.850084
5 to 14 141087 -2.8356 0.002287
4 to 13 141690 -0.7563 0.224732
3 to 12 141335 -1.9804 0.023827
2 to 11 141911 0.0058 0.502297
1 to 10 141758 -0.5218 0.300895
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-07_02:31
Bits used No. missing words z-score p-value
28 to 32 142297 1.3141 0.905600
27 to 31 142096 0.6328 0.736561
26 to 30 142012 0.3480 0.636093
25 to 29 141729 -0.6113 0.270504
24 to 28 141676 -0.7909 0.214487
23 to 27 142444 1.8124 0.965041
22 to 26 141810 -0.3367 0.368167
21 to 25 142279 1.2531 0.894919
20 to 24 141671 -0.8079 0.209575
19 to 23 141575 -1.1333 0.128540
18 to 22 141844 -0.2215 0.412368
17 to 21 142033 0.4192 0.662473
16 to 20 141812 -0.3299 0.370726
15 to 19 141421 -1.6554 0.048926
14 to 18 142267 1.2124 0.887328
13 to 17 141891 -0.0621 0.475227
12 to 16 142066 0.5311 0.702320
11 to 15 141734 -0.5943 0.276143
10 to 14 142020 0.3752 0.646227
9 to 13 142253 1.1650 0.877987
8 to 12 142121 0.7175 0.763475
7 to 11 141975 0.2226 0.588081
6 to 10 141211 -2.3672 0.008961
5 to 9 141500 -1.3876 0.082636
4 to 8 142010 0.3413 0.633544
3 to 7 141939 0.1006 0.540057
2 to 6 141970 0.2057 0.581472
1 to 5 142375 1.5785 0.942779
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-07_02:31
Bits used No. missing words z-score p-value
31 to 32 142386 1.4061 0.920154
30 to 31 142081 0.5064 0.693713
29 to 30 142090 0.5329 0.702966
28 to 29 142386 1.4061 0.920154
27 to 28 141866 -0.1278 0.449147
26 to 27 141642 -0.7886 0.215178
25 to 26 142359 1.3265 0.907656
24 to 25 142228 0.9400 0.826399
23 to 24 142009 0.2940 0.615626
22 to 23 141819 -0.2665 0.394942
21 to 22 142099 0.5595 0.712089
20 to 21 141778 -0.3874 0.349229
19 to 20 142601 2.0403 0.979341
18 to 19 142448 1.5890 0.943969
17 to 18 141673 -0.6971 0.242858
16 to 17 141984 0.2203 0.587168
15 to 16 141630 -0.8240 0.204975
14 to 15 141823 -0.2547 0.399493
13 to 14 141879 -0.0895 0.464355
12 to 13 141779 -0.3845 0.350321
11 to 12 142362 1.3353 0.909113
10 to 11 142311 1.1849 0.881965
9 to 10 142000 0.2675 0.605444
8 to 9 141405 -1.4877 0.068415
7 to 8 141525 -1.1337 0.128457
6 to 7 141638 -0.8004 0.211744
5 to 6 141651 -0.7620 0.223019
4 to 5 141979 0.2055 0.581416
3 to 4 142119 0.6185 0.731876
2 to 3 141669 -0.7089 0.239182
1 to 2 141587 -0.9508 0.170846
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-07_02:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2501.64 0.023 0.509252
Test results for specific bytes for dh-ranFile-2018-07-07_02:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2616.71 1.651 0.950584
2 to 9 2491.54 -0.120 0.452379
3 to 10 2500.69 0.010 0.503890
4 to 11 2395.93 -1.472 0.070533
5 to 12 2658.72 2.245 0.987603
6 to 13 2448.32 -0.731 0.232442
7 to 14 2564.80 0.916 0.820290
8 to 15 2527.34 0.387 0.650485
9 to 16 2452.38 -0.673 0.250345
10 to 17 2495.68 -0.061 0.475668
11 to 18 2486.87 -0.186 0.426346
12 to 19 2390.54 -1.548 0.060808
13 to 20 2528.04 0.397 0.654171
14 to 21 2490.09 -0.140 0.444272
15 to 22 2388.95 -1.570 0.058157
16 to 23 2478.24 -0.308 0.379124
17 to 24 2582.82 1.171 0.879241
18 to 25 2432.33 -0.957 0.169294
19 to 26 2527.76 0.393 0.652710
20 to 27 2551.69 0.731 0.767628
21 to 28 2407.22 -1.312 0.094746
22 to 29 2520.79 0.294 0.615614
23 to 30 2351.14 -2.105 0.017638
24 to 31 2413.32 -1.226 0.110128
25 to 32 2399.92 -1.415 0.078480
CDPARK for dh-ranFile-2018-07-07_02:31: 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
3537 0.6393 0.738676
3520 -0.1370 0.445521
3511 -0.5479 0.291865
3541 0.8219 0.794438
3529 0.2740 0.607947
3502 -0.9589 0.168804
3518 -0.2283 0.409702
3540 0.7763 0.781201
3498 -1.1416 0.126820
3505 -0.8219 0.205562
Square side=100, avg. no. parked=3520.10 sample std.=15.26
p-value of the KSTEST for those 10 p-values: 0.786837
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-07_02:31
0.0254,0.8443,0.9069,0.6901,0.2054,0.4823,0.5818,0.2254,0.6197,0.1329,
The KS test for those 10 p-values: 0.972595
The 3DSPHERES test for dh-ranFile-2018-07-07_02:31
sample no r^3 equiv. uni.
1 92.902 0.954803
2 4.343 0.134763
3 0.014 0.000464
4 26.793 0.590613
5 35.564 0.694398
6 3.708 0.116277
7 28.849 0.617731
8 11.749 0.324043
9 4.069 0.126836
10 37.157 0.710205
11 89.914 0.950070
12 17.606 0.443932
13 37.514 0.713633
14 92.544 0.954261
15 47.086 0.791859
16 3.856 0.120621
17 12.721 0.345588
18 28.756 0.616547
19 16.694 0.426777
20 13.441 0.361127
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.769282
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-07_02:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 -0.3 0.1 -0.3 0.3 0.5
-0.1 1.4 2.0 1.6 0.2 -0.3
-1.2 -0.5 -0.0 -0.8 0.4 0.7
-0.7 -0.6 -1.0 0.4 0.6 0.4
0.5 1.1 -1.1 -0.3 0.2 -1.1
0.9 -0.7 0.1 0.8 0.3 -1.6
0.5 0.5 0.9 -0.7 -0.6 1.0
-1.1
Chi-square with 42 degrees of freedom:29.152578
z-score=-1.401769, p-value=0.066492
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-07_02:31
Test no p-value
1 0.426589
2 0.259833
3 0.660179
4 0.029340
5 0.659704
6 0.074556
7 0.134494
8 0.138252
9 0.118939
10 0.518539
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.041911
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-07_02:31:
(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 66816 0.33 66591 0.09
3 25000.00 24899 0.41 25097 0.38
4 6666.67 6589 0.90 6610 0.48
5 1388.89 1392 0.01 1422 0.79
6 238.10 257 1.50 232 0.16
7 34.72 40 0.80 40 0.80
8 4.96 6 0.22 7 0.84
p=0.34719 p=0.26020
Number of rngs required: 689632, p-value: 0.924
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-07_02:31
No. of wins: Observed Expected
98452 98585.9
z-score=-0.599, pvalue=0.27469
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66756 66666.7 0.120 0.120
2 37766 37654.3 0.331 0.451
3 27058 26954.7 0.396 0.847
4 19193 19313.5 0.751 1.598
5 13788 13851.4 0.290 1.888
6 9880 9943.5 0.406 2.294
7 7237 7145.0 1.184 3.478
8 5162 5139.1 0.102 3.581
9 3668 3699.9 0.274 3.855
10 2658 2666.3 0.026 3.881
11 1890 1923.3 0.578 4.458
12 1331 1388.7 2.401 6.859
13 969 1003.7 1.201 8.060
14 735 726.1 0.108 8.168
15 564 525.8 2.770 10.938
16 345 381.2 3.429 14.366
17 276 276.5 0.001 14.368
18 194 200.8 0.232 14.600
19 132 146.0 1.340 15.939
20 104 106.2 0.046 15.986
21 294 287.1 0.165 16.151
Chisq= 16.15 for 20 degrees of freedom, p= 0.29277
SUMMARY of craptest
p-value for no. of wins: 0.274689
p-value for throws/game: 0.292772
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-07_02:31
No. of wins: Observed Expected
98216 98585.9
z-score=-1.654, pvalue=0.04904
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66697 66666.7 0.014 0.014
2 37642 37654.3 0.004 0.018
3 26851 26954.7 0.399 0.417
4 19446 19313.5 0.910 1.327
5 13766 13851.4 0.527 1.853
6 9890 9943.5 0.288 2.142
7 7125 7145.0 0.056 2.198
8 5100 5139.1 0.297 2.495
9 3715 3699.9 0.062 2.557
10 2663 2666.3 0.004 2.561
11 1988 1923.3 2.175 4.735
12 1445 1388.7 2.279 7.015
13 1023 1003.7 0.371 7.385
14 724 726.1 0.006 7.391
15 505 525.8 0.826 8.217
16 379 381.2 0.012 8.229
17 264 276.5 0.569 8.798
18 220 200.8 1.830 10.628
19 171 146.0 4.287 14.914
20 86 106.2 3.847 18.762
21 300 287.1 0.578 19.340
Chisq= 19.34 for 20 degrees of freedom, p= 0.50016
SUMMARY of craptest
p-value for no. of wins: 0.049041
p-value for throws/game: 0.500163
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0005,0.0023,0.0069,0.0090,0.0116,0.0176,0.0238,0.0254,0.0293,0.0335,
0.0401,0.0418,0.0419,0.0489,0.0490,0.0552,0.0575,0.0582,0.0608,0.0665,
0.0676,0.0684,0.0705,0.0746,0.0763,0.0785,0.0826,0.0864,0.0925,0.0947,
0.0980,0.0999,0.1101,0.1107,0.1163,0.1175,0.1189,0.1206,0.1268,0.1268,
0.1283,0.1285,0.1285,0.1290,0.1329,0.1345,0.1348,0.1383,0.1400,0.1551,
0.1651,0.1683,0.1688,0.1693,0.1708,0.1749,0.1758,0.1783,0.1798,0.1799,
0.1851,0.1909,0.1922,0.2008,0.2050,0.2054,0.2056,0.2070,0.2071,0.2096,
0.2117,0.2145,0.2152,0.2230,0.2232,0.2247,0.2254,0.2324,0.2329,0.2350,
0.2386,0.2392,0.2424,0.2429,0.2499,0.2503,0.2598,0.2602,0.2659,0.2705,
0.2741,0.2747,0.2761,0.2919,0.2928,0.2997,0.3009,0.3140,0.3240,0.3429,
0.3456,0.3463,0.3472,0.3492,0.3496,0.3503,0.3517,0.3611,0.3682,0.3707,
0.3791,0.3803,0.3855,0.3949,0.3995,0.4046,0.4097,0.4124,0.4263,0.4266,
0.4266,0.4268,0.4350,0.4439,0.4443,0.4447,0.4455,0.4486,0.4491,0.4515,
0.4524,0.4634,0.4644,0.4706,0.4714,0.4752,0.4757,0.4794,0.4823,0.4859,
0.4946,0.5002,0.5023,0.5039,0.5093,0.5185,0.5379,0.5401,0.5697,0.5748,
0.5809,0.5814,0.5815,0.5818,0.5830,0.5872,0.5881,0.5906,0.6054,0.6074,
0.6079,0.6135,0.6156,0.6156,0.6165,0.6166,0.6172,0.6177,0.6197,0.6271,
0.6280,0.6309,0.6335,0.6361,0.6462,0.6484,0.6505,0.6527,0.6542,0.6597,
0.6602,0.6625,0.6639,0.6747,0.6901,0.6937,0.6944,0.7023,0.7030,0.7102,
0.7121,0.7136,0.7310,0.7319,0.7366,0.7387,0.7584,0.7624,0.7635,0.7641,
0.7676,0.7693,0.7812,0.7856,0.7856,0.7858,0.7868,0.7919,0.7944,0.7947,
0.8103,0.8137,0.8148,0.8203,0.8264,0.8360,0.8430,0.8443,0.8443,0.8501,
0.8564,0.8573,0.8575,0.8716,0.8780,0.8792,0.8820,0.8822,0.8873,0.8880,
0.8911,0.8925,0.8949,0.9025,0.9029,0.9056,0.9064,0.9069,0.9075,0.9077,
0.9091,0.9149,0.9202,0.9202,0.9242,0.9287,0.9287,0.9427,0.9428,0.9431,
0.9432,0.9440,0.9491,0.9492,0.9501,0.9506,0.9543,0.9548,0.9650,0.9673,
0.9726,0.9793,0.9796,0.9837,0.9876,0.9904,0.9925,0.9951,0.9954,
Overall p-value after applying KStest on 269 p-values = 0.202666
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.