RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-02_06:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.74 8.0310 0.034120
2 to 25 16.02 24.8772 0.902507
3 to 26 15.76 17.5330 0.581143
4 to 27 15.68 9.9824 0.095652
5 to 28 15.65 41.8448 0.999294
6 to 29 15.66 15.5469 0.443850
7 to 30 15.62 25.0023 0.905342
8 to 31 15.93 12.3747 0.223061
9 to 32 15.98 26.1732 0.928637
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.164624
Tough bday spacings test for dh-ranFile-2018-07-02_06:31: 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 14 48 86 87 95 78 44 28 10 4 6
(O-E)^2/E 2.6 3.5 2.2 1.2 0.1 0.0 1.3 0.1 1.6 1.0 0.9
Birthday Spacings: Sum(O-E)^2/E= 14.467, p= 0.847
RESULTS OF GCD FOR dh-ranFile-2018-07-02_06:31
Euclid's algorithm:
p-value, steps to gcd: 0.411933
p-value, dist. of gcd's: 0.991812
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-02_06:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.393 0.010 0.836 0.801 0.589 0.852 0.241 0.047
Bits 8 to 15---> 0.343 0.571 0.633 0.608 0.690 0.188 0.792 0.905
Bits 16 to 23---> 0.124 0.306 0.459 0.306 0.904 0.083 0.972 0.047
Bits 24 to 31---> 0.952 0.250 0.222 0.716 0.548 0.163 0.202 0.971
KS test for the above 32 p values: 0.082
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-02_06:31,
p-values for 5 runs: 0.5450, 0.3488, 0.5175, 0.1795, 0.1010
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-02_06:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 198 211.4 0.852 0.852
r= 29 5100 5134.0 0.225 1.077
r= 30 23017 23103.0 0.320 1.397
r= 31 11685 11551.5 1.542 2.940
chi-square = 2.940 with df = 3; p-value = 0.599
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-02_06:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 198 211.4 0.852 0.852
r= 30 5149 5134.0 0.044 0.895
r= 31 23135 23103.0 0.044 0.940
r= 32 11518 11551.5 0.097 1.037
chi-square = 1.037 with df = 3; p-value = 0.208
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-02_06:31
b-rank test for bits 1 to 8, p=0.78771
b-rank test for bits 2 to 9, p=0.33552
b-rank test for bits 3 to 10, p=0.18890
b-rank test for bits 4 to 11, p=0.98127
b-rank test for bits 5 to 12, p=0.88111
b-rank test for bits 6 to 13, p=0.59188
b-rank test for bits 7 to 14, p=0.59770
b-rank test for bits 8 to 15, p=0.93774
b-rank test for bits 9 to 16, p=0.00458
b-rank test for bits 10 to 17, p=0.19166
b-rank test for bits 11 to 18, p=0.55722
b-rank test for bits 12 to 19, p=0.70368
b-rank test for bits 13 to 20, p=0.80963
b-rank test for bits 14 to 21, p=0.47545
b-rank test for bits 15 to 22, p=0.77416
b-rank test for bits 16 to 23, p=0.47882
b-rank test for bits 17 to 24, p=0.64807
b-rank test for bits 18 to 25, p=0.92137
b-rank test for bits 19 to 26, p=0.85215
b-rank test for bits 20 to 27, p=0.49756
b-rank test for bits 21 to 28, p=0.35896
b-rank test for bits 22 to 29, p=0.88387
b-rank test for bits 23 to 30, p=0.62445
b-rank test for bits 24 to 31, p=0.16390
b-rank test for bits 25 to 32, p=0.02895
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 = 0.357471
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-02_06:31
(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 142126 0.51 0.693655
2 141844 -0.15 0.439341
3 142961 2.46 0.992998
4 142243 0.78 0.782188
5 142316 0.95 0.828985
6 141635 -0.64 0.260775
7 141675 -0.55 0.292018
8 142020 0.26 0.602018
9 141889 -0.05 0.481057
10 142064 0.36 0.641092
11 141649 -0.61 0.271512
12 141697 -0.50 0.309913
13 140720 -2.78 0.002728
14 141683 -0.53 0.298469
15 141478 -1.01 0.156780
16 141912 0.01 0.502489
17 141830 -0.19 0.426477
18 141881 -0.07 0.473613
19 142056 0.34 0.634083
20 142428 1.21 0.887214
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-02_06:31
Bits used No. missing words z-score p-value
23 to 32 142007 0.3368 0.631864
22 to 31 141541 -1.2701 0.102024
21 to 30 142057 0.5092 0.694696
20 to 29 141272 -2.1977 0.013986
19 to 28 141745 -0.5667 0.285474
18 to 27 142318 1.4092 0.920613
17 to 26 141653 -0.8839 0.188376
16 to 25 142306 1.3678 0.914317
15 to 24 142052 0.4920 0.688628
14 to 23 141803 -0.3667 0.356938
13 to 22 141820 -0.3080 0.379028
12 to 21 141531 -1.3046 0.096017
11 to 20 141452 -1.5770 0.057398
10 to 19 142344 1.4989 0.933045
9 to 18 141757 -0.5253 0.299696
8 to 17 141701 -0.7184 0.236262
7 to 16 141874 -0.1218 0.451518
6 to 15 141975 0.2264 0.589574
5 to 14 141795 -0.3942 0.346701
4 to 13 141770 -0.4804 0.315454
3 to 12 142063 0.5299 0.701908
2 to 11 141297 -2.1115 0.017365
1 to 10 141382 -1.8184 0.034503
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-02_06:31
Bits used No. missing words z-score p-value
28 to 32 142432 1.7718 0.961783
27 to 31 141502 -1.3808 0.083673
26 to 30 141653 -0.8689 0.192447
25 to 29 142274 1.2362 0.891802
24 to 28 141848 -0.2079 0.417654
23 to 27 141794 -0.3909 0.347917
22 to 26 141764 -0.4926 0.311132
21 to 25 141873 -0.1232 0.450993
20 to 24 142011 0.3446 0.634819
19 to 23 141927 0.0599 0.523882
18 to 22 141958 0.1650 0.565521
17 to 21 141611 -1.0113 0.155939
16 to 20 142252 1.1616 0.877300
15 to 19 142175 0.9006 0.816093
14 to 18 142047 0.4667 0.679635
13 to 17 141869 -0.1367 0.445629
12 to 16 142179 0.9141 0.819677
11 to 15 141895 -0.0486 0.480629
10 to 14 142566 2.2260 0.986993
9 to 13 142158 0.8429 0.800372
8 to 12 142231 1.0904 0.862233
7 to 11 142011 0.3446 0.634819
6 to 10 141985 0.2565 0.601221
5 to 9 142048 0.4701 0.680847
4 to 8 141690 -0.7435 0.228592
3 to 7 141808 -0.3435 0.365614
2 to 6 141966 0.1921 0.576169
1 to 5 142199 0.9819 0.836933
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-02_06:31
Bits used No. missing words z-score p-value
31 to 32 142289 1.1200 0.868637
30 to 31 141991 0.2409 0.595189
29 to 30 142059 0.4415 0.670576
28 to 29 142263 1.0433 0.851589
27 to 28 142468 1.6480 0.950323
26 to 27 142073 0.4828 0.685382
25 to 26 141771 -0.4081 0.341617
24 to 25 142742 2.4563 0.992980
23 to 24 140765 -3.3756 0.000368
22 to 23 142020 0.3265 0.627962
21 to 22 141669 -0.7089 0.239182
20 to 21 141658 -0.7414 0.229230
19 to 20 141937 0.0816 0.532527
18 to 19 141725 -0.5437 0.293308
17 to 18 141908 -0.0039 0.498435
16 to 17 142241 0.9784 0.836056
15 to 16 141754 -0.4582 0.323404
14 to 15 141601 -0.9095 0.181536
13 to 14 141657 -0.7443 0.228337
12 to 13 142194 0.8397 0.799471
11 to 12 142546 1.8781 0.969815
10 to 11 141959 0.1465 0.558244
9 to 10 141779 -0.3845 0.350321
8 to 9 141925 0.0462 0.518434
7 to 8 142000 0.2675 0.605444
6 to 7 141817 -0.2724 0.392673
5 to 6 141583 -0.9626 0.167868
4 to 5 141620 -0.8535 0.196696
3 to 4 141765 -0.4258 0.335144
2 to 3 142000 0.2675 0.605444
1 to 2 141980 0.2085 0.582568
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-02_06:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2548.39 0.684 0.753134
Test results for specific bytes for dh-ranFile-2018-07-02_06:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2471.43 -0.404 0.343091
2 to 9 2530.79 0.435 0.668359
3 to 10 2495.84 -0.059 0.476555
4 to 11 2602.85 1.455 0.927096
5 to 12 2501.98 0.028 0.511181
6 to 13 2549.23 0.696 0.756872
7 to 14 2533.45 0.473 0.681926
8 to 15 2540.55 0.573 0.716817
9 to 16 2516.01 0.226 0.589563
10 to 17 2560.00 0.848 0.801917
11 to 18 2558.53 0.828 0.796111
12 to 19 2535.35 0.500 0.691417
13 to 20 2429.56 -0.996 0.159590
14 to 21 2498.31 -0.024 0.490451
15 to 22 2407.46 -1.309 0.095321
16 to 23 2491.39 -0.122 0.451544
17 to 24 2567.48 0.954 0.830024
18 to 25 2444.44 -0.786 0.216003
19 to 26 2524.11 0.341 0.633453
20 to 27 2609.39 1.547 0.939077
21 to 28 2456.80 -0.611 0.270640
22 to 29 2456.09 -0.621 0.267312
23 to 30 2585.77 1.213 0.887432
24 to 31 2517.44 0.247 0.597402
25 to 32 2509.53 0.135 0.553628
CDPARK for dh-ranFile-2018-07-02_06:31: 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
3518 -0.2283 0.409702
3557 1.5525 0.939730
3520 -0.1370 0.445521
3523 0.0000 0.500000
3516 -0.3196 0.374623
3510 -0.5936 0.276387
3529 0.2740 0.607947
3505 -0.8219 0.205562
3523 0.0000 0.500000
Square side=100, avg. no. parked=3523.80 sample std.=13.99
p-value of the KSTEST for those 10 p-values: 0.545352
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-02_06:31
0.9565,0.6607,0.0916,0.2603,0.1735,0.1142,0.3541,0.8920,0.2009,0.5176,
The KS test for those 10 p-values: 0.540568
The 3DSPHERES test for dh-ranFile-2018-07-02_06:31
sample no r^3 equiv. uni.
1 36.603 0.704799
2 1.396 0.045465
3 55.839 0.844531
4 9.964 0.282619
5 11.022 0.307470
6 22.486 0.527415
7 10.591 0.297450
8 20.806 0.500187
9 7.271 0.215227
10 32.617 0.662849
11 12.117 0.332289
12 61.965 0.873244
13 38.241 0.720487
14 16.049 0.414303
15 58.562 0.858019
16 23.565 0.544102
17 5.027 0.154275
18 12.637 0.343756
19 0.119 0.003945
20 79.923 0.930337
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.913342
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-02_06:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 0.5 -1.3 -1.4 0.7 1.2
-0.4 1.8 -0.6 0.5 0.0 0.2
-0.7 -0.1 0.9 0.1 -0.5 0.2
-0.8 -0.1 1.3 -0.8 -0.8 -0.4
-0.4 -0.5 0.8 1.3 -0.5 -1.9
2.0 1.3 0.2 1.3 -0.5 -0.1
-0.9 -1.0 -0.4 1.5 0.1 0.0
-0.1
Chi-square with 42 degrees of freedom:35.066563
z-score=-0.756500, p-value=0.233064
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-02_06:31
Test no p-value
1 0.191301
2 0.980792
3 0.285364
4 0.002145
5 0.509431
6 0.298655
7 0.789810
8 0.038048
9 0.018830
10 0.159788
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.029445
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-02_06:31:
(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 66590 0.09 66722 0.05
3 25000.00 24923 0.24 24890 0.48
4 6666.67 6682 0.04 6663 0.00
5 1388.89 1537 15.79 1460 3.64
6 238.10 228 0.43 236 0.02
7 34.72 33 0.09 26 2.19
8 4.96 6 0.22 2 1.77
p=0.99029 p=0.77252
Number of rngs required: 688233, p-value: 0.422
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-02_06:31
No. of wins: Observed Expected
98632 98585.9
z-score= 0.206, pvalue=0.58175
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66601 66666.7 0.065 0.065
2 37839 37654.3 0.906 0.970
3 26894 26954.7 0.137 1.107
4 19247 19313.5 0.229 1.336
5 13829 13851.4 0.036 1.372
6 9901 9943.5 0.182 1.554
7 7128 7145.0 0.041 1.595
8 5210 5139.1 0.979 2.574
9 3766 3699.9 1.182 3.756
10 2601 2666.3 1.599 5.355
11 1928 1923.3 0.011 5.366
12 1382 1388.7 0.033 5.399
13 1033 1003.7 0.854 6.254
14 728 726.1 0.005 6.258
15 527 525.8 0.003 6.261
16 383 381.2 0.009 6.270
17 267 276.5 0.329 6.599
18 189 200.8 0.697 7.296
19 128 146.0 2.216 9.511
20 113 106.2 0.433 9.945
21 306 287.1 1.242 11.187
Chisq= 11.19 for 20 degrees of freedom, p= 0.05877
SUMMARY of craptest
p-value for no. of wins: 0.581750
p-value for throws/game: 0.058774
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-02_06:31
No. of wins: Observed Expected
98638 98585.9
z-score= 0.233, pvalue=0.59220
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66898 66666.7 0.803 0.803
2 37722 37654.3 0.122 0.924
3 26902 26954.7 0.103 1.028
4 19173 19313.5 1.022 2.049
5 13659 13851.4 2.673 4.722
6 10040 9943.5 0.936 5.658
7 7066 7145.0 0.874 6.532
8 5014 5139.1 3.044 9.576
9 3665 3699.9 0.329 9.904
10 2732 2666.3 1.619 11.523
11 2022 1923.3 5.062 16.585
12 1384 1388.7 0.016 16.602
13 1004 1003.7 0.000 16.602
14 726 726.1 0.000 16.602
15 491 525.8 2.308 18.910
16 413 381.2 2.661 21.571
17 306 276.5 3.139 24.709
18 222 200.8 2.232 26.941
19 174 146.0 5.376 32.317
20 115 106.2 0.727 33.044
21 272 287.1 0.796 33.840
Chisq= 33.84 for 20 degrees of freedom, p= 0.97277
SUMMARY of craptest
p-value for no. of wins: 0.592200
p-value for throws/game: 0.972770
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0004,0.0021,0.0027,0.0039,0.0046,0.0096,0.0140,0.0174,0.0188,0.0289,
0.0294,0.0341,0.0345,0.0380,0.0455,0.0468,0.0472,0.0574,0.0588,0.0816,
0.0826,0.0837,0.0916,0.0953,0.0957,0.0960,0.1010,0.1020,0.1142,0.1242,
0.1543,0.1559,0.1568,0.1596,0.1598,0.1625,0.1639,0.1646,0.1679,0.1735,
0.1795,0.1815,0.1882,0.1884,0.1889,0.1913,0.1917,0.1924,0.1967,0.2009,
0.2024,0.2056,0.2077,0.2152,0.2160,0.2218,0.2231,0.2283,0.2286,0.2292,
0.2331,0.2363,0.2392,0.2414,0.2497,0.2603,0.2608,0.2673,0.2706,0.2715,
0.2764,0.2826,0.2854,0.2855,0.2920,0.2933,0.2974,0.2985,0.2987,0.2997,
0.3062,0.3063,0.3075,0.3099,0.3111,0.3155,0.3234,0.3323,0.3351,0.3355,
0.3416,0.3430,0.3431,0.3438,0.3467,0.3479,0.3488,0.3503,0.3541,0.3569,
0.3575,0.3590,0.3656,0.3746,0.3790,0.3926,0.3927,0.4097,0.4119,0.4143,
0.4177,0.4225,0.4265,0.4393,0.4439,0.4455,0.4456,0.4510,0.4515,0.4515,
0.4587,0.4736,0.4755,0.4766,0.4788,0.4806,0.4811,0.4905,0.4976,0.4984,
0.5000,0.5000,0.5002,0.5025,0.5094,0.5112,0.5175,0.5176,0.5184,0.5239,
0.5274,0.5325,0.5406,0.5441,0.5450,0.5454,0.5476,0.5536,0.5572,0.5582,
0.5655,0.5705,0.5762,0.5811,0.5817,0.5826,0.5894,0.5896,0.5896,0.5919,
0.5922,0.5952,0.5974,0.5977,0.5990,0.6012,0.6020,0.6054,0.6054,0.6079,
0.6085,0.6245,0.6280,0.6319,0.6332,0.6335,0.6341,0.6348,0.6348,0.6411,
0.6481,0.6607,0.6628,0.6684,0.6706,0.6796,0.6808,0.6819,0.6854,0.6886,
0.6904,0.6914,0.6937,0.6947,0.7019,0.7037,0.7048,0.7159,0.7168,0.7205,
0.7387,0.7531,0.7569,0.7725,0.7742,0.7822,0.7877,0.7898,0.7919,0.7961,
0.7995,0.8004,0.8010,0.8019,0.8096,0.8161,0.8197,0.8290,0.8300,0.8361,
0.8363,0.8369,0.8445,0.8472,0.8516,0.8522,0.8524,0.8580,0.8622,0.8686,
0.8732,0.8773,0.8811,0.8839,0.8872,0.8874,0.8918,0.8920,0.9025,0.9043,
0.9045,0.9053,0.9133,0.9143,0.9206,0.9214,0.9271,0.9286,0.9303,0.9330,
0.9377,0.9391,0.9397,0.9503,0.9520,0.9565,0.9618,0.9698,0.9709,0.9723,
0.9728,0.9808,0.9813,0.9870,0.9903,0.9918,0.9930,0.9930,0.9993,
Overall p-value after applying KStest on 269 p-values = 0.782521
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.