RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-16_00:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.47 20.3735 0.744426
2 to 25 15.66 15.7782 0.460394
3 to 26 15.73 19.9716 0.724314
4 to 27 15.95 17.0920 0.551853
5 to 28 15.94 12.0270 0.201501
6 to 29 16.03 16.7729 0.530145
7 to 30 15.60 23.6037 0.869391
8 to 31 15.96 17.3048 0.566094
9 to 32 15.74 13.9676 0.330606
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.525805
Tough bday spacings test for dh-ranFile-2018-06-16_00:31: 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 11 37 75 84 122 69 49 29 12 6 6
(O-E)^2/E 0.4 0.0 0.0 1.9 6.1 1.1 0.2 0.0 0.6 0.1 0.9
Birthday Spacings: Sum(O-E)^2/E= 11.196, p= 0.658
RESULTS OF GCD FOR dh-ranFile-2018-06-16_00:31
Euclid's algorithm:
p-value, steps to gcd: 0.734493
p-value, dist. of gcd's: 0.949810
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-16_00:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.129 0.453 0.083 0.149 0.278 0.360 0.528 0.933
Bits 8 to 15---> 0.683 0.601 0.744 0.394 0.721 0.409 0.097 0.058
Bits 16 to 23---> 0.922 0.418 0.199 0.328 0.921 0.854 0.704 0.598
Bits 24 to 31---> 0.540 0.741 0.770 0.571 0.818 0.692 0.379 0.640
KS test for the above 32 p values: 0.254
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-16_00:31,
p-values for 5 runs: 0.8304, 0.5279, 0.1603, 0.1053, 0.0136
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-16_00:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 202 211.4 0.420 0.420
r= 29 5185 5134.0 0.506 0.926
r= 30 23056 23103.0 0.096 1.022
r= 31 11557 11551.5 0.003 1.024
chi-square = 1.024 with df = 3; p-value = 0.205
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-16_00:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 218 211.4 0.205 0.205
r= 30 5190 5134.0 0.611 0.816
r= 31 23151 23103.0 0.100 0.915
r= 32 11441 11551.5 1.057 1.973
chi-square = 1.973 with df = 3; p-value = 0.422
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-16_00:31
b-rank test for bits 1 to 8, p=0.06892
b-rank test for bits 2 to 9, p=0.21199
b-rank test for bits 3 to 10, p=0.72902
b-rank test for bits 4 to 11, p=0.41900
b-rank test for bits 5 to 12, p=0.16703
b-rank test for bits 6 to 13, p=0.47873
b-rank test for bits 7 to 14, p=0.05000
b-rank test for bits 8 to 15, p=0.13101
b-rank test for bits 9 to 16, p=0.54804
b-rank test for bits 10 to 17, p=0.42442
b-rank test for bits 11 to 18, p=0.03936
b-rank test for bits 12 to 19, p=0.27907
b-rank test for bits 13 to 20, p=0.52213
b-rank test for bits 14 to 21, p=0.30345
b-rank test for bits 15 to 22, p=0.46343
b-rank test for bits 16 to 23, p=0.57252
b-rank test for bits 17 to 24, p=0.04879
b-rank test for bits 18 to 25, p=0.32213
b-rank test for bits 19 to 26, p=0.69049
b-rank test for bits 20 to 27, p=0.13525
b-rank test for bits 21 to 28, p=0.85731
b-rank test for bits 22 to 29, p=0.61514
b-rank test for bits 23 to 30, p=0.87130
b-rank test for bits 24 to 31, p=0.23519
b-rank test for bits 25 to 32, p=0.54241
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 = 0.083763
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-16_00:31
(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 141906 -0.01 0.496896
2 141906 -0.01 0.496896
3 141380 -1.24 0.108090
4 141930 0.05 0.519259
5 142012 0.24 0.594790
6 142157 0.58 0.718594
7 141986 0.18 0.571084
8 142067 0.37 0.643708
9 141360 -1.28 0.099662
10 142043 0.31 0.622599
11 142270 0.84 0.800298
12 141766 -0.33 0.368857
13 142673 1.78 0.962811
14 141219 -1.61 0.053381
15 142349 1.03 0.847852
16 141155 -1.76 0.038996
17 142145 0.55 0.709057
18 142142 0.54 0.706649
19 141751 -0.37 0.355717
20 141006 -2.11 0.017404
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-16_00:31
Bits used No. missing words z-score p-value
23 to 32 142281 1.2816 0.900012
22 to 31 141457 -1.5598 0.059408
21 to 30 141959 0.1713 0.567997
20 to 29 142090 0.6230 0.733358
19 to 28 142151 0.8333 0.797675
18 to 27 141738 -0.5908 0.277330
17 to 26 141839 -0.2425 0.404190
16 to 25 141781 -0.4425 0.329058
15 to 24 141726 -0.6322 0.263637
14 to 23 141446 -1.5977 0.055056
13 to 22 141759 -0.5184 0.302097
12 to 21 142250 1.1747 0.879947
11 to 20 141869 -0.1391 0.444698
10 to 19 142543 2.1851 0.985558
9 to 18 141869 -0.1391 0.444698
8 to 17 141885 -0.0839 0.466569
7 to 16 141871 -0.1322 0.447424
6 to 15 142323 1.4264 0.923131
5 to 14 142022 0.3885 0.651183
4 to 13 142371 1.5920 0.944304
3 to 12 141431 -1.6494 0.049531
2 to 11 142055 0.5023 0.692275
1 to 10 142178 0.9264 0.822894
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-16_00:31
Bits used No. missing words z-score p-value
28 to 32 141535 -1.2689 0.102236
27 to 31 141760 -0.5062 0.306357
26 to 30 141982 0.2463 0.597290
25 to 29 141833 -0.2587 0.397916
24 to 28 142094 0.6260 0.734343
23 to 27 142177 0.9074 0.817891
22 to 26 141695 -0.7265 0.233753
21 to 25 141601 -1.0452 0.147968
20 to 24 141412 -1.6859 0.045911
19 to 23 142390 1.6294 0.948385
18 to 22 142265 1.2057 0.886026
17 to 21 142240 1.1209 0.868838
16 to 20 142181 0.9209 0.821453
15 to 19 141775 -0.4554 0.324427
14 to 18 142258 1.1819 0.881384
13 to 17 142254 1.1684 0.878672
12 to 16 142068 0.5379 0.704665
11 to 15 141822 -0.2960 0.383602
10 to 14 141898 -0.0384 0.484682
9 to 13 141784 -0.4248 0.335474
8 to 12 141737 -0.5842 0.279553
7 to 11 142008 0.3345 0.630989
6 to 10 141967 0.1955 0.577496
5 to 9 142179 0.9141 0.819677
4 to 8 141410 -1.6926 0.045262
3 to 7 142399 1.6599 0.951533
2 to 6 142218 1.0463 0.852298
1 to 5 141665 -0.8282 0.203768
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-16_00:31
Bits used No. missing words z-score p-value
31 to 32 141879 -0.0895 0.464355
30 to 31 141832 -0.2281 0.409780
29 to 30 142101 0.5654 0.714099
28 to 29 141742 -0.4936 0.310795
27 to 28 141448 -1.3609 0.086780
26 to 27 141496 -1.2193 0.111372
25 to 26 142512 1.7778 0.962281
24 to 25 142134 0.6627 0.746253
23 to 24 141680 -0.6765 0.249365
22 to 23 142036 0.3737 0.645671
21 to 22 141634 -0.8122 0.208343
20 to 21 141853 -0.1662 0.434014
19 to 20 141733 -0.5201 0.301480
18 to 19 141669 -0.7089 0.239182
17 to 18 141771 -0.4081 0.341617
16 to 17 141977 0.1996 0.579110
15 to 16 141514 -1.1662 0.121774
14 to 15 142100 0.5624 0.713095
13 to 14 142087 0.5241 0.699896
12 to 13 141759 -0.4435 0.328720
11 to 12 142067 0.4651 0.679071
10 to 11 141906 -0.0098 0.496081
9 to 10 141800 -0.3225 0.373534
8 to 9 141344 -1.6676 0.047694
7 to 8 141755 -0.4553 0.324464
6 to 7 141391 -1.5290 0.063133
5 to 6 141676 -0.6883 0.245635
4 to 5 141566 -1.0128 0.155584
3 to 4 142603 2.0462 0.979633
2 to 3 142320 1.2114 0.887132
1 to 2 142433 1.5447 0.938797
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-16_00:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2453.18 -0.662 0.253935
Test results for specific bytes for dh-ranFile-2018-06-16_00:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2612.04 1.585 0.943466
2 to 9 2423.11 -1.087 0.138447
3 to 10 2581.93 1.159 0.876692
4 to 11 2563.12 0.893 0.813983
5 to 12 2510.86 0.154 0.561034
6 to 13 2472.38 -0.391 0.348053
7 to 14 2533.91 0.480 0.684223
8 to 15 2400.16 -1.412 0.078992
9 to 16 2514.77 0.209 0.582745
10 to 17 2328.83 -2.421 0.007746
11 to 18 2513.62 0.193 0.576354
12 to 19 2448.86 -0.723 0.234791
13 to 20 2472.88 -0.384 0.350662
14 to 21 2498.08 -0.027 0.489188
15 to 22 2428.17 -1.016 0.154842
16 to 23 2439.42 -0.857 0.195802
17 to 24 2490.59 -0.133 0.447057
18 to 25 2530.57 0.432 0.667223
19 to 26 2598.99 1.400 0.919235
20 to 27 2456.18 -0.620 0.267715
21 to 28 2434.36 -0.928 0.176620
22 to 29 2469.36 -0.433 0.332378
23 to 30 2588.98 1.258 0.895861
24 to 31 2464.61 -0.500 0.308372
25 to 32 2442.49 -0.813 0.208028
CDPARK for dh-ranFile-2018-06-16_00:31: 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
3541 0.8219 0.794438
3539 0.7306 0.767486
3511 -0.5479 0.291865
3519 -0.1826 0.427537
3533 0.4566 0.676028
3510 -0.5936 0.276387
3506 -0.7763 0.218799
3555 1.4612 0.928018
3561 1.7352 0.958644
3537 0.6393 0.738676
Square side=100, avg. no. parked=3531.20 sample std.=18.14
p-value of the KSTEST for those 10 p-values: 0.378914
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-16_00:31
0.8883,0.4096,0.2086,0.5241,0.6971,0.5484,0.8731,0.1071,0.8240,0.9959,
The KS test for those 10 p-values: 0.374866
The 3DSPHERES test for dh-ranFile-2018-06-16_00:31
sample no r^3 equiv. uni.
1 13.589 0.364266
2 9.804 0.278771
3 2.971 0.094274
4 4.580 0.141591
5 35.822 0.697008
6 31.547 0.650613
7 75.776 0.920011
8 34.203 0.680216
9 27.886 0.605259
10 22.481 0.527332
11 3.631 0.113995
12 61.523 0.871363
13 35.203 0.690692
14 24.841 0.563089
15 53.716 0.833128
16 31.919 0.654914
17 11.876 0.326908
18 21.584 0.512992
19 3.442 0.108402
20 41.662 0.750608
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.696694
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-16_00:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 0.1 0.1 0.3 -0.2 0.7
-1.2 -0.6 0.2 1.5 0.3 1.5
1.0 -0.3 0.6 -0.6 -0.3 0.2
0.1 -0.1 -0.6 -0.2 -0.7 -1.3
0.1 0.2 -0.3 -0.5 0.5 -0.5
2.0 -0.3 -0.1 -1.3 -1.2 1.1
-0.5 -1.0 -2.4 -0.1 -0.6 0.0
0.8
Chi-square with 42 degrees of freedom:30.740696
z-score=-1.228491, p-value=0.099418
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-16_00:31
Test no p-value
1 0.086584
2 0.072612
3 0.781943
4 0.514570
5 0.070194
6 0.047508
7 0.684078
8 0.193316
9 0.038921
10 0.109820
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.003353
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-16_00:31:
(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 66694 0.01 66626 0.02
3 25000.00 24985 0.01 24961 0.06
4 6666.67 6677 0.02 6717 0.38
5 1388.89 1355 0.83 1434 1.47
6 238.10 243 0.10 221 1.23
7 34.72 39 0.53 35 0.00
8 4.96 6 0.22 5 0.00
p=0.05564 p=0.21158
Number of rngs required: 690008, p-value: 0.971
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-16_00:31
No. of wins: Observed Expected
98524 98585.9
z-score=-0.277, pvalue=0.39102
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66385 66666.7 1.190 1.190
2 37679 37654.3 0.016 1.206
3 26975 26954.7 0.015 1.221
4 19224 19313.5 0.414 1.636
5 13950 13851.4 0.702 2.337
6 9985 9943.5 0.173 2.510
7 7135 7145.0 0.014 2.524
8 5172 5139.1 0.211 2.735
9 3779 3699.9 1.693 4.428
10 2708 2666.3 0.652 5.080
11 1952 1923.3 0.427 5.508
12 1370 1388.7 0.253 5.760
13 1019 1003.7 0.233 5.993
14 768 726.1 2.413 8.406
15 529 525.8 0.019 8.425
16 379 381.2 0.012 8.437
17 277 276.5 0.001 8.438
18 206 200.8 0.133 8.571
19 146 146.0 0.000 8.571
20 102 106.2 0.167 8.739
21 260 287.1 2.561 11.299
Chisq= 11.30 for 20 degrees of freedom, p= 0.06191
SUMMARY of craptest
p-value for no. of wins: 0.391018
p-value for throws/game: 0.061907
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-16_00:31
No. of wins: Observed Expected
98786 98585.9
z-score= 0.895, pvalue=0.81465
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66944 66666.7 1.154 1.154
2 37579 37654.3 0.151 1.304
3 27096 26954.7 0.740 2.045
4 19276 19313.5 0.073 2.117
5 13841 13851.4 0.008 2.125
6 9828 9943.5 1.343 3.468
7 7114 7145.0 0.135 3.603
8 5091 5139.1 0.450 4.052
9 3606 3699.9 2.381 6.434
10 2713 2666.3 0.818 7.252
11 1922 1923.3 0.001 7.253
12 1360 1388.7 0.595 7.847
13 1005 1003.7 0.002 7.849
14 714 726.1 0.203 8.052
15 514 525.8 0.266 8.318
16 387 381.2 0.090 8.408
17 279 276.5 0.022 8.430
18 205 200.8 0.087 8.517
19 141 146.0 0.170 8.687
20 107 106.2 0.006 8.693
21 278 287.1 0.289 8.982
Chisq= 8.98 for 20 degrees of freedom, p= 0.01688
SUMMARY of craptest
p-value for no. of wins: 0.814646
p-value for throws/game: 0.016884
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0034,0.0077,0.0136,0.0169,0.0174,0.0389,0.0390,0.0394,0.0453,0.0459,
0.0475,0.0477,0.0488,0.0495,0.0500,0.0534,0.0551,0.0556,0.0577,0.0594,
0.0619,0.0631,0.0689,0.0702,0.0726,0.0790,0.0834,0.0838,0.0866,0.0868,
0.0943,0.0970,0.0994,0.0997,0.1022,0.1053,0.1071,0.1081,0.1084,0.1098,
0.1114,0.1140,0.1218,0.1290,0.1310,0.1352,0.1384,0.1416,0.1480,0.1490,
0.1548,0.1556,0.1603,0.1670,0.1766,0.1933,0.1958,0.1988,0.2015,0.2038,
0.2046,0.2080,0.2083,0.2086,0.2116,0.2120,0.2188,0.2338,0.2348,0.2352,
0.2392,0.2456,0.2494,0.2539,0.2541,0.2636,0.2677,0.2764,0.2773,0.2777,
0.2788,0.2791,0.2796,0.2919,0.3015,0.3021,0.3035,0.3064,0.3084,0.3108,
0.3221,0.3244,0.3245,0.3269,0.3280,0.3287,0.3291,0.3306,0.3324,0.3355,
0.3416,0.3481,0.3507,0.3557,0.3595,0.3643,0.3689,0.3735,0.3749,0.3789,
0.3794,0.3836,0.3910,0.3941,0.3979,0.4042,0.4088,0.4096,0.4098,0.4183,
0.4190,0.4219,0.4244,0.4275,0.4340,0.4447,0.4447,0.4471,0.4474,0.4531,
0.4604,0.4634,0.4644,0.4666,0.4787,0.4847,0.4892,0.4961,0.4969,0.4969,
0.5130,0.5146,0.5193,0.5221,0.5241,0.5258,0.5273,0.5279,0.5283,0.5301,
0.5403,0.5424,0.5480,0.5484,0.5519,0.5610,0.5631,0.5661,0.5680,0.5710,
0.5711,0.5725,0.5764,0.5775,0.5791,0.5827,0.5948,0.5973,0.5977,0.6013,
0.6053,0.6151,0.6226,0.6310,0.6401,0.6437,0.6457,0.6506,0.6512,0.6549,
0.6576,0.6672,0.6760,0.6791,0.6802,0.6830,0.6841,0.6842,0.6905,0.6907,
0.6923,0.6925,0.6967,0.6970,0.6971,0.6999,0.7037,0.7047,0.7066,0.7091,
0.7131,0.7141,0.7186,0.7207,0.7243,0.7290,0.7334,0.7343,0.7345,0.7387,
0.7413,0.7442,0.7444,0.7463,0.7506,0.7675,0.7703,0.7819,0.7944,0.7977,
0.8003,0.8140,0.8146,0.8179,0.8180,0.8197,0.8215,0.8229,0.8240,0.8304,
0.8331,0.8479,0.8523,0.8543,0.8573,0.8688,0.8694,0.8713,0.8714,0.8731,
0.8767,0.8787,0.8799,0.8814,0.8860,0.8871,0.8883,0.8959,0.9000,0.9192,
0.9200,0.9208,0.9220,0.9231,0.9280,0.9333,0.9388,0.9435,0.9443,0.9484,
0.9498,0.9515,0.9586,0.9623,0.9628,0.9706,0.9796,0.9856,0.9959,
Overall p-value after applying KStest on 269 p-values = 0.353224
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.