RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-02_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 15.77 32.7104 0.987737
2 to 25 15.73 11.1361 0.150596
3 to 26 16.24 20.2525 0.738484
4 to 27 16.04 16.9235 0.540440
5 to 28 15.76 7.9834 0.033099
6 to 29 15.73 15.4220 0.434886
7 to 30 16.06 9.9229 0.093188
8 to 31 15.48 30.4911 0.976987
9 to 32 15.76 15.9596 0.473300
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.505797
Tough bday spacings test for dh-ranFile-2018-07-02_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 13 34 68 98 115 72 49 22 19 5 5
(O-E)^2/E 1.6 0.2 0.4 0.0 3.1 0.5 0.2 2.0 1.1 0.4 0.2
Birthday Spacings: Sum(O-E)^2/E= 9.692, p= 0.532
RESULTS OF GCD FOR dh-ranFile-2018-07-02_02:31
Euclid's algorithm:
p-value, steps to gcd: 0.679782
p-value, dist. of gcd's: 0.882054
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-02_02:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.154 0.819 0.139 0.094 0.882 0.139 0.343 0.067
Bits 8 to 15---> 0.017 0.350 0.975 0.828 0.558 0.955 0.791 0.787
Bits 16 to 23---> 0.793 0.748 0.249 0.301 0.774 0.932 0.616 0.804
Bits 24 to 31---> 0.144 0.872 0.525 0.520 0.658 0.037 0.637 0.545
KS test for the above 32 p values: 0.463
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-02_02:31,
p-values for 5 runs: 0.7860, 0.0154, 0.7239, 0.9215, 0.5243
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-02_02:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 184 211.4 3.556 3.556
r= 29 5128 5134.0 0.007 3.563
r= 30 22955 23103.0 0.949 4.511
r= 31 11733 11551.5 2.851 7.363
chi-square = 7.363 with df = 3; p-value = 0.939
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-02_02:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 205 211.4 0.195 0.195
r= 30 5185 5134.0 0.506 0.701
r= 31 23092 23103.0 0.005 0.707
r= 32 11518 11551.5 0.097 0.804
chi-square = 0.804 with df = 3; p-value = 0.151
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-02_02:31
b-rank test for bits 1 to 8, p=0.52794
b-rank test for bits 2 to 9, p=0.72643
b-rank test for bits 3 to 10, p=0.07958
b-rank test for bits 4 to 11, p=0.97753
b-rank test for bits 5 to 12, p=0.13694
b-rank test for bits 6 to 13, p=0.31697
b-rank test for bits 7 to 14, p=0.24416
b-rank test for bits 8 to 15, p=0.80374
b-rank test for bits 9 to 16, p=0.43421
b-rank test for bits 10 to 17, p=0.29774
b-rank test for bits 11 to 18, p=0.29465
b-rank test for bits 12 to 19, p=0.68668
b-rank test for bits 13 to 20, p=0.55788
b-rank test for bits 14 to 21, p=0.97731
b-rank test for bits 15 to 22, p=0.90132
b-rank test for bits 16 to 23, p=0.92153
b-rank test for bits 17 to 24, p=0.69863
b-rank test for bits 18 to 25, p=0.85164
b-rank test for bits 19 to 26, p=0.49010
b-rank test for bits 20 to 27, p=0.45389
b-rank test for bits 21 to 28, p=0.11472
b-rank test for bits 22 to 29, p=0.71000
b-rank test for bits 23 to 30, p=0.09767
b-rank test for bits 24 to 31, p=0.38813
b-rank test for bits 25 to 32, p=0.44837
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 = 0.922072
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-02_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 142125 0.50 0.692835
2 141830 -0.19 0.426477
3 141697 -0.50 0.309913
4 141282 -1.47 0.071362
5 141653 -0.60 0.274619
6 141597 -0.73 0.232774
7 142030 0.28 0.611005
8 141356 -1.29 0.098035
9 141913 0.01 0.503421
10 142058 0.35 0.635840
11 141261 -1.51 0.064913
12 141712 -0.46 0.322381
13 141250 -1.54 0.061720
14 142106 0.46 0.677066
15 141795 -0.27 0.394686
16 142223 0.73 0.768182
17 141717 -0.45 0.326583
18 142083 0.41 0.657545
19 141884 -0.06 0.476404
20 141837 -0.17 0.432900
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-02_02:31
Bits used No. missing words z-score p-value
23 to 32 141888 -0.0736 0.470684
22 to 31 141922 0.0437 0.517424
21 to 30 142222 1.0782 0.859522
20 to 29 141932 0.0782 0.531155
19 to 28 141908 -0.0046 0.498170
18 to 27 141754 -0.5356 0.296110
17 to 26 142037 0.4402 0.670119
16 to 25 142137 0.7851 0.783793
15 to 24 142300 1.3471 0.911032
14 to 23 142185 0.9506 0.829093
13 to 22 142125 0.7437 0.771468
12 to 21 142200 1.0023 0.841903
11 to 20 142573 2.2885 0.988946
10 to 19 141380 -1.8253 0.033980
9 to 18 142026 0.4023 0.656272
8 to 17 141817 -0.3184 0.375099
7 to 16 142034 0.4299 0.666365
6 to 15 142062 0.5264 0.700712
5 to 14 142433 1.8058 0.964522
4 to 13 142402 1.6989 0.955327
3 to 12 142263 1.2196 0.888683
2 to 11 141747 -0.5598 0.287822
1 to 10 141911 0.0058 0.502297
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-02_02:31
Bits used No. missing words z-score p-value
28 to 32 141755 -0.5232 0.300434
27 to 31 141907 -0.0079 0.496849
26 to 30 141972 0.2124 0.584118
25 to 29 141966 0.1921 0.576169
24 to 28 142200 0.9853 0.837767
23 to 27 141715 -0.6587 0.255030
22 to 26 141581 -1.1130 0.132858
21 to 25 141400 -1.7265 0.042125
20 to 24 141503 -1.3774 0.084196
19 to 23 142031 0.4124 0.659992
18 to 22 141969 0.2023 0.580148
17 to 21 141863 -0.1571 0.437602
16 to 20 142452 1.8396 0.967084
15 to 19 142008 0.3345 0.630989
14 to 18 141341 -1.9265 0.027018
13 to 17 141854 -0.1876 0.425611
12 to 16 141658 -0.8520 0.197116
11 to 15 141925 0.0531 0.521181
10 to 14 142107 0.6701 0.748593
9 to 13 141580 -1.1164 0.132131
8 to 12 141135 -2.6248 0.004334
7 to 11 141399 -1.7299 0.041821
6 to 10 142151 0.8192 0.793670
5 to 9 141920 0.0362 0.514426
4 to 8 141988 0.2667 0.605141
3 to 7 141811 -0.3333 0.369446
2 to 6 142069 0.5413 0.705834
1 to 5 141940 0.1040 0.541402
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-02_02:31
Bits used No. missing words z-score p-value
31 to 32 141642 -0.7886 0.215178
30 to 31 141573 -0.9921 0.160569
29 to 30 142163 0.7483 0.772857
28 to 29 142105 0.5772 0.718097
27 to 28 142344 1.2822 0.900116
26 to 27 141646 -0.7768 0.218643
25 to 26 141772 -0.4051 0.342701
24 to 25 141925 0.0462 0.518434
23 to 24 141536 -1.1013 0.135390
22 to 23 142458 1.6185 0.947222
21 to 22 141558 -1.0364 0.150014
20 to 21 141524 -1.1367 0.127839
19 to 20 141315 -1.7532 0.039785
18 to 19 142034 0.3678 0.643473
17 to 18 142365 1.3442 0.910552
16 to 17 142333 1.2498 0.894307
15 to 16 141914 0.0138 0.505496
14 to 15 141984 0.2203 0.587168
13 to 14 142312 1.1878 0.882547
12 to 13 141208 -2.0688 0.019281
11 to 12 142308 1.1760 0.880206
10 to 11 142019 0.3235 0.626846
9 to 10 141960 0.1495 0.559408
8 to 9 142275 1.0787 0.859633
7 to 8 141847 -0.1839 0.427060
6 to 7 141543 -1.0806 0.139933
5 to 6 141950 0.1200 0.547747
4 to 5 141727 -0.5378 0.295342
3 to 4 141665 -0.7207 0.235536
2 to 3 140937 -2.8682 0.002064
1 to 2 141740 -0.4995 0.308714
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-02_02:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2538.34 0.542 0.706166
Test results for specific bytes for dh-ranFile-2018-07-02_02:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2487.96 -0.170 0.432421
2 to 9 2434.79 -0.922 0.178208
3 to 10 2446.65 -0.754 0.225282
4 to 11 2541.70 0.590 0.722310
5 to 12 2564.82 0.917 0.820357
6 to 13 2471.73 -0.400 0.344660
7 to 14 2521.58 0.305 0.619905
8 to 15 2511.90 0.168 0.566796
9 to 16 2564.48 0.912 0.819075
10 to 17 2526.20 0.370 0.644490
11 to 18 2461.55 -0.544 0.293285
12 to 19 2487.68 -0.174 0.430829
13 to 20 2398.04 -1.442 0.074665
14 to 21 2551.37 0.727 0.766240
15 to 22 2532.77 0.463 0.678456
16 to 23 2584.82 1.200 0.884844
17 to 24 2433.24 -0.944 0.172559
18 to 25 2632.72 1.877 0.969741
19 to 26 2431.77 -0.965 0.167302
20 to 27 2378.92 -1.712 0.043424
21 to 28 2481.84 -0.257 0.398676
22 to 29 2531.05 0.439 0.669701
23 to 30 2388.80 -1.573 0.057912
24 to 31 2682.64 2.583 0.995101
25 to 32 2410.71 -1.263 0.103337
CDPARK for dh-ranFile-2018-07-02_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
3510 -0.5936 0.276387
3530 0.3196 0.625377
3512 -0.5023 0.307734
3512 -0.5023 0.307734
3559 1.6438 0.949895
3507 -0.7306 0.232514
3537 0.6393 0.738676
3535 0.5479 0.708135
3518 -0.2283 0.409702
3503 -0.9132 0.180558
Square side=100, avg. no. parked=3522.30 sample std.=16.65
p-value of the KSTEST for those 10 p-values: 0.711326
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-02_02:31
0.9861,0.0775,0.2967,0.4595,0.5319,0.0052,0.4208,0.8620,0.1231,0.0107,
The KS test for those 10 p-values: 0.098446
The 3DSPHERES test for dh-ranFile-2018-07-02_02:31
sample no r^3 equiv. uni.
1 12.368 0.337852
2 11.927 0.328049
3 11.073 0.308642
4 104.281 0.969070
5 41.381 0.748259
6 40.884 0.744060
7 20.896 0.501684
8 37.522 0.713701
9 34.739 0.685871
10 146.246 0.992364
11 28.064 0.607598
12 18.231 0.455402
13 54.050 0.834975
14 46.887 0.790473
15 6.149 0.185332
16 27.294 0.597398
17 107.439 0.972161
18 40.297 0.739002
19 45.797 0.782722
20 34.558 0.683974
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.025361
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-02_02:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -1.2 1.8 0.8 -2.4 -0.1
0.5 -0.0 -0.5 -0.8 0.6 1.2
-0.1 1.4 0.7 1.0 -0.3 -1.2
-1.3 -0.4 -0.3 0.1 -0.3 0.1
0.7 0.9 0.1 -0.8 -0.4 -0.1
0.1 -0.8 0.6 -0.5 -1.0 0.6
2.8 -0.7 -1.6 0.4 0.1 -1.0
-1.1
Chi-square with 42 degrees of freedom:38.902970
z-score=-0.337914, p-value=0.392304
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-02_02:31
Test no p-value
1 0.092536
2 0.140609
3 0.651644
4 0.006041
5 0.143788
6 0.663885
7 0.281992
8 0.305898
9 0.478330
10 0.145642
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.029856
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-02_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 66872 0.63 66766 0.15
3 25000.00 24774 2.04 25002 0.00
4 6666.67 6718 0.40 6648 0.05
5 1388.89 1360 0.60 1293 6.62
6 238.10 238 0.00 244 0.15
7 34.72 32 0.21 42 1.53
8 4.96 5 0.00 4 0.19
p=0.30777 p=0.80758
Number of rngs required: 687813, p-value: 0.248
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-02_02:31
No. of wins: Observed Expected
98661 98585.9
z-score= 0.336, pvalue=0.63159
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66783 66666.7 0.203 0.203
2 37879 37654.3 1.341 1.544
3 26922 26954.7 0.040 1.583
4 19385 19313.5 0.265 1.848
5 13938 13851.4 0.541 2.390
6 9843 9943.5 1.017 3.406
7 7018 7145.0 2.258 5.664
8 5031 5139.1 2.273 7.937
9 3626 3699.9 1.475 9.412
10 2672 2666.3 0.012 9.424
11 1928 1923.3 0.011 9.435
12 1357 1388.7 0.725 10.161
13 1044 1003.7 1.617 11.778
14 706 726.1 0.559 12.336
15 529 525.8 0.019 12.355
16 343 381.2 3.819 16.174
17 296 276.5 1.369 17.543
18 189 200.8 0.697 18.240
19 150 146.0 0.110 18.351
20 88 106.2 3.124 21.475
21 273 287.1 0.694 22.168
Chisq= 22.17 for 20 degrees of freedom, p= 0.66855
SUMMARY of craptest
p-value for no. of wins: 0.631593
p-value for throws/game: 0.668553
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-02_02:31
No. of wins: Observed Expected
98330 98585.9
z-score=-1.144, pvalue=0.12624
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66562 66666.7 0.164 0.164
2 37741 37654.3 0.200 0.364
3 27190 26954.7 2.053 2.417
4 19202 19313.5 0.643 3.061
5 13623 13851.4 3.767 6.827
6 9956 9943.5 0.016 6.843
7 7211 7145.0 0.609 7.452
8 5136 5139.1 0.002 7.454
9 3737 3699.9 0.373 7.827
10 2715 2666.3 0.890 8.716
11 1911 1923.3 0.079 8.795
12 1426 1388.7 1.000 9.795
13 962 1003.7 1.734 11.529
14 735 726.1 0.108 11.637
15 503 525.8 0.992 12.629
16 382 381.2 0.002 12.630
17 259 276.5 1.112 13.743
18 205 200.8 0.087 13.829
19 154 146.0 0.440 14.270
20 115 106.2 0.727 14.996
21 275 287.1 0.511 15.507
Chisq= 15.51 for 20 degrees of freedom, p= 0.25332
SUMMARY of craptest
p-value for no. of wins: 0.126240
p-value for throws/game: 0.253318
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0021,0.0043,0.0052,0.0060,0.0107,0.0154,0.0171,0.0193,0.0254,0.0270,
0.0299,0.0331,0.0340,0.0365,0.0398,0.0418,0.0421,0.0434,0.0579,0.0617,
0.0649,0.0671,0.0714,0.0747,0.0775,0.0796,0.0842,0.0925,0.0932,0.0935,
0.0977,0.0980,0.0984,0.1033,0.1147,0.1231,0.1262,0.1278,0.1321,0.1329,
0.1354,0.1369,0.1392,0.1394,0.1399,0.1406,0.1438,0.1439,0.1456,0.1500,
0.1506,0.1514,0.1542,0.1606,0.1673,0.1726,0.1782,0.1806,0.1853,0.1971,
0.2152,0.2186,0.2253,0.2325,0.2328,0.2355,0.2442,0.2479,0.2485,0.2533,
0.2550,0.2746,0.2764,0.2820,0.2878,0.2933,0.2946,0.2953,0.2961,0.2967,
0.2977,0.3004,0.3014,0.3059,0.3077,0.3077,0.3078,0.3086,0.3087,0.3099,
0.3170,0.3224,0.3266,0.3280,0.3379,0.3427,0.3434,0.3447,0.3504,0.3694,
0.3751,0.3881,0.3923,0.3947,0.3987,0.4097,0.4208,0.4256,0.4265,0.4271,
0.4308,0.4324,0.4329,0.4342,0.4349,0.4376,0.4484,0.4539,0.4554,0.4595,
0.4630,0.4707,0.4733,0.4764,0.4783,0.4901,0.4968,0.4982,0.5017,0.5023,
0.5034,0.5055,0.5058,0.5144,0.5174,0.5184,0.5198,0.5212,0.5243,0.5253,
0.5279,0.5312,0.5319,0.5321,0.5404,0.5414,0.5447,0.5477,0.5579,0.5582,
0.5594,0.5668,0.5762,0.5801,0.5841,0.5872,0.5974,0.6051,0.6076,0.6110,
0.6164,0.6199,0.6254,0.6268,0.6310,0.6316,0.6358,0.6373,0.6435,0.6445,
0.6516,0.6563,0.6575,0.6575,0.6600,0.6639,0.6664,0.6686,0.6697,0.6701,
0.6771,0.6785,0.6798,0.6840,0.6859,0.6867,0.6928,0.6986,0.7007,0.7058,
0.7062,0.7081,0.7100,0.7113,0.7137,0.7181,0.7223,0.7239,0.7264,0.7385,
0.7387,0.7390,0.7441,0.7479,0.7483,0.7486,0.7662,0.7682,0.7715,0.7729,
0.7741,0.7827,0.7838,0.7860,0.7868,0.7905,0.7914,0.7934,0.7937,0.8037,
0.8044,0.8076,0.8189,0.8191,0.8204,0.8279,0.8291,0.8350,0.8378,0.8419,
0.8516,0.8595,0.8596,0.8620,0.8722,0.8802,0.8819,0.8821,0.8825,0.8848,
0.8887,0.8943,0.9001,0.9013,0.9106,0.9110,0.9215,0.9215,0.9221,0.9318,
0.9388,0.9472,0.9499,0.9550,0.9553,0.9645,0.9671,0.9691,0.9697,0.9722,
0.9751,0.9770,0.9773,0.9775,0.9861,0.9877,0.9889,0.9924,0.9951,
Overall p-value after applying KStest on 269 p-values = 0.822274
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.