RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-03-24_01:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.73 12.3359 0.220613
2 to 25 15.62 27.4542 0.948266
3 to 26 15.71 9.4076 0.073399
4 to 27 15.85 15.1234 0.413408
5 to 28 15.66 18.9874 0.670744
6 to 29 15.82 20.7537 0.762497
7 to 30 15.91 16.9909 0.545017
8 to 31 15.89 9.7824 0.087512
9 to 32 15.67 22.4666 0.832564
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.989005
Tough bday spacings test for dh-ranFile-2017-03-24_01:31: 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 40 78 87 85 95 44 35 16 12 1
(O-E)^2/E 0.5 0.3 0.3 1.2 1.6 3.6 1.3 0.9 0.1 4.4 2.3
Birthday Spacings: Sum(O-E)^2/E= 16.530, p= 0.915
RESULTS OF GCD FOR dh-ranFile-2017-03-24_01:31
Euclid's algorithm:
p-value, steps to gcd: 0.763344
p-value, dist. of gcd's: 0.659425
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-03-24_01:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.947 0.420 0.843 0.006 0.905 0.672 0.830 0.409
Bits 8 to 15---> 0.533 0.353 0.522 0.944 0.871 0.190 0.020 0.802
Bits 16 to 23---> 0.880 0.661 0.012 0.195 0.141 0.239 0.196 0.154
Bits 24 to 31---> 0.519 0.782 0.542 0.068 0.482 0.365 0.930 0.052
KS test for the above 32 p values: 0.428
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-03-24_01:31,
p-values for 5 runs: 0.5950, 0.6055, 0.5451, 0.7561, 0.3661
Rank test for binary matrices (31x31) for dh-ranFile-2017-03-24_01:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 182 211.4 4.093 4.093
r= 29 5061 5134.0 1.038 5.132
r= 30 23295 23103.0 1.595 6.727
r= 31 11462 11551.5 0.694 7.420
chi-square = 7.420 with df = 3; p-value = 0.940
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2017-03-24_01:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 222 211.4 0.530 0.530
r= 30 5124 5134.0 0.020 0.549
r= 31 23119 23103.0 0.011 0.560
r= 32 11535 11551.5 0.024 0.584
chi-square = 0.584 with df = 3; p-value = 0.100
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2017-03-24_01:31
b-rank test for bits 1 to 8, p=0.60270
b-rank test for bits 2 to 9, p=0.38505
b-rank test for bits 3 to 10, p=0.65964
b-rank test for bits 4 to 11, p=0.15581
b-rank test for bits 5 to 12, p=0.74887
b-rank test for bits 6 to 13, p=0.76761
b-rank test for bits 7 to 14, p=0.11483
b-rank test for bits 8 to 15, p=0.39686
b-rank test for bits 9 to 16, p=0.42426
b-rank test for bits 10 to 17, p=0.86518
b-rank test for bits 11 to 18, p=0.89335
b-rank test for bits 12 to 19, p=0.61517
b-rank test for bits 13 to 20, p=0.11865
b-rank test for bits 14 to 21, p=0.36215
b-rank test for bits 15 to 22, p=0.97886
b-rank test for bits 16 to 23, p=0.97451
b-rank test for bits 17 to 24, p=0.82741
b-rank test for bits 18 to 25, p=0.60265
b-rank test for bits 19 to 26, p=0.08114
b-rank test for bits 20 to 27, p=0.02980
b-rank test for bits 21 to 28, p=0.90004
b-rank test for bits 22 to 29, p=0.62706
b-rank test for bits 23 to 30, p=0.63360
b-rank test for bits 24 to 31, p=0.81118
b-rank test for bits 25 to 32, p=0.44897
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 = 0.476895
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-03-24_01:31
(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 141786 -0.29 0.386614
2 142113 0.48 0.682915
3 141608 -0.70 0.240703
4 140862 -2.45 0.007202
5 141771 -0.32 0.373272
6 141425 -1.13 0.128899
7 141869 -0.09 0.462464
8 141802 -0.25 0.400996
9 142265 0.83 0.797015
10 142137 0.53 0.702616
11 141444 -1.09 0.138470
12 141270 -1.49 0.067619
13 142106 0.46 0.677066
14 142236 0.76 0.777342
15 141206 -1.64 0.050161
16 142381 1.10 0.864776
17 141546 -0.85 0.197968
18 142454 1.27 0.898419
19 142033 0.29 0.613690
20 141330 -1.35 0.087936
----------------------------------------------------------------
OPSO test for dh-ranFile-2017-03-24_01:31
Bits used No. missing words z-score p-value
23 to 32 141897 -0.0425 0.483043
22 to 31 141955 0.1575 0.562568
21 to 30 141999 0.3092 0.621418
20 to 29 141946 0.1264 0.550312
19 to 28 141881 -0.0977 0.461089
18 to 27 141656 -0.8736 0.191181
17 to 26 141929 0.0678 0.527039
16 to 25 142073 0.5644 0.713752
15 to 24 142134 0.7747 0.780749
14 to 23 141863 -0.1598 0.436536
13 to 22 142144 0.8092 0.790802
12 to 21 141673 -0.8149 0.207556
11 to 20 141966 0.1954 0.577466
10 to 19 141641 -0.9253 0.177411
9 to 18 141448 -1.5908 0.055828
8 to 17 141815 -0.3253 0.372486
7 to 16 141941 0.1092 0.543481
6 to 15 141669 -0.8287 0.203630
5 to 14 142451 1.8678 0.969107
4 to 13 142660 2.5885 0.995180
3 to 12 142406 1.7127 0.956612
2 to 11 141916 0.0230 0.509175
1 to 10 141998 0.3058 0.620106
-----------------------------------------------------------------
OQSO test for dh-ranFile-2017-03-24_01:31
Bits used No. missing words z-score p-value
28 to 32 141483 -1.4452 0.074203
27 to 31 141710 -0.6757 0.249617
26 to 30 141726 -0.6215 0.267149
25 to 29 141887 -0.0757 0.469831
24 to 28 141609 -1.0181 0.154323
23 to 27 141755 -0.5232 0.300434
22 to 26 141735 -0.5909 0.277277
21 to 25 141873 -0.1232 0.450993
20 to 24 141929 0.0667 0.526581
19 to 23 141823 -0.2926 0.384897
18 to 22 142213 1.0294 0.848352
17 to 21 141930 0.0701 0.527930
16 to 20 142154 0.8294 0.796558
15 to 19 141638 -0.9198 0.178848
14 to 18 141749 -0.5435 0.293396
13 to 17 141798 -0.3774 0.352942
12 to 16 142077 0.5684 0.715109
11 to 15 142187 0.9413 0.826713
10 to 14 141846 -0.2147 0.415009
9 to 13 141994 0.2870 0.612950
8 to 12 141991 0.2768 0.609051
7 to 11 141842 -0.2282 0.409731
6 to 10 141923 0.0463 0.518480
5 to 9 141897 -0.0418 0.483330
4 to 8 142006 0.3277 0.628429
3 to 7 141669 -0.8147 0.207628
2 to 6 142072 0.5514 0.709328
1 to 5 142353 1.5040 0.933705
-----------------------------------------------------------------
DNA test for dh-ranFile-2017-03-24_01:31
Bits used No. missing words z-score p-value
31 to 32 142389 1.4150 0.921459
30 to 31 141982 0.2144 0.584869
29 to 30 141651 -0.7620 0.223019
28 to 29 141794 -0.3402 0.366851
27 to 28 141542 -1.0836 0.139278
26 to 27 142452 1.6008 0.945289
25 to 26 141732 -0.5231 0.300453
24 to 25 142126 0.6391 0.738636
23 to 24 142342 1.2763 0.899078
22 to 23 141591 -0.9390 0.173859
21 to 22 141749 -0.4729 0.318125
20 to 21 141928 0.0551 0.521960
19 to 20 142111 0.5949 0.724044
18 to 19 142568 1.9430 0.973991
17 to 18 141340 -1.6794 0.046533
16 to 17 141490 -1.2370 0.108051
15 to 16 142121 0.6244 0.733816
14 to 15 141655 -0.7502 0.226556
13 to 14 141674 -0.6942 0.243782
12 to 13 142139 0.6775 0.750953
11 to 12 141375 -1.5762 0.057490
10 to 11 141892 -0.0511 0.479615
9 to 10 141716 -0.5703 0.284239
8 to 9 141788 -0.3579 0.360207
7 to 8 142380 1.3884 0.917493
6 to 7 141505 -1.1927 0.116491
5 to 6 141865 -0.1308 0.447980
4 to 5 142000 0.2675 0.605444
3 to 4 142092 0.5388 0.705005
2 to 3 142089 0.5300 0.701944
1 to 2 141487 -1.2458 0.106417
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2017-03-24_01:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2608.60 1.536 0.937717
Test results for specific bytes for dh-ranFile-2017-03-24_01:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2443.44 -0.800 0.211911
2 to 9 2450.80 -0.696 0.243265
3 to 10 2590.51 1.280 0.899726
4 to 11 2628.70 1.820 0.965632
5 to 12 2512.77 0.181 0.571639
6 to 13 2463.03 -0.523 0.300532
7 to 14 2468.38 -0.447 0.327381
8 to 15 2517.20 0.243 0.596085
9 to 16 2564.39 0.911 0.818734
10 to 17 2468.89 -0.440 0.329977
11 to 18 2484.66 -0.217 0.414133
12 to 19 2460.78 -0.555 0.289581
13 to 20 2558.17 0.823 0.794627
14 to 21 2530.97 0.438 0.669302
15 to 22 2557.78 0.817 0.793081
16 to 23 2454.09 -0.649 0.258099
17 to 24 2496.01 -0.056 0.477490
18 to 25 2474.75 -0.357 0.360507
19 to 26 2522.17 0.314 0.623056
20 to 27 2503.48 0.049 0.519606
21 to 28 2441.76 -0.824 0.205078
22 to 29 2525.56 0.361 0.641103
23 to 30 2563.20 0.894 0.814271
24 to 31 2538.44 0.544 0.706630
25 to 32 2524.72 0.350 0.636695
CDPARK for dh-ranFile-2017-03-24_01:31: 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
3526 0.1370 0.554479
3498 -1.1416 0.126820
3544 0.9589 0.831196
3527 0.1826 0.572463
3520 -0.1370 0.445521
3566 1.9635 0.975204
3510 -0.5936 0.276387
3535 0.5479 0.708135
3545 1.0046 0.842447
3505 -0.8219 0.205562
Square side=100, avg. no. parked=3527.60 sample std.=19.64
p-value of the KSTEST for those 10 p-values: 0.913995
Results for the MINIMUM DISTANCE test for dh-ranFile-2017-03-24_01:31
0.1010,0.0115,0.9469,0.6546,0.3145,0.7129,0.2947,0.8982,0.6413,0.0304,
The KS test for those 10 p-values: 0.523386
The 3DSPHERES test for dh-ranFile-2017-03-24_01:31
sample no r^3 equiv. uni.
1 6.337 0.190412
2 73.715 0.914323
3 51.093 0.817882
4 7.466 0.220327
5 64.741 0.884448
6 9.621 0.274361
7 32.695 0.663724
8 6.158 0.185564
9 8.633 0.250060
10 12.566 0.342211
11 22.132 0.521798
12 13.857 0.369924
13 10.201 0.288260
14 53.553 0.832220
15 46.436 0.787300
16 58.985 0.860007
17 17.947 0.450210
18 12.560 0.342085
19 18.435 0.459096
20 23.700 0.546148
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.557583
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-03-24_01:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
2.0 -0.7 0.3 -1.4 0.1 3.2
-0.6 -0.5 0.6 -1.0 -0.4 1.8
0.6 1.0 -0.6 0.2 -1.8 0.7
0.2 -1.1 -0.6 0.0 0.3 -0.9
-0.6 0.3 1.1 1.4 -0.6 1.9
0.3 -1.7 0.7 -0.6 -0.8 0.2
3.3 -1.0 -0.4 0.4 -1.3 0.0
-0.1
Chi-square with 42 degrees of freedom:57.069120
z-score=1.644176, p-value=0.939605
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2017-03-24_01:31
Test no p-value
1 0.912379
2 0.679432
3 0.762723
4 0.597387
5 0.584664
6 0.216299
7 0.185621
8 0.323952
9 0.195316
10 0.315305
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.807727
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-03-24_01:31:
(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 66811 0.31 66671 0.00
3 25000.00 24840 1.02 24890 0.48
4 6666.67 6697 0.14 6785 2.10
5 1388.89 1399 0.07 1377 0.10
6 238.10 221 1.23 235 0.04
7 34.72 28 1.30 37 0.15
8 4.96 3 0.77 4 0.19
p=0.43689 p=0.19899
Number of rngs required: 687987, p-value: 0.316
RESULTS OF CRAPS TEST for dh-ranFile-2017-03-24_01:31
No. of wins: Observed Expected
98460 98585.9
z-score=-0.563, pvalue=0.28675
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66478 66666.7 0.534 0.534
2 37855 37654.3 1.070 1.603
3 27110 26954.7 0.894 2.498
4 19331 19313.5 0.016 2.514
5 13797 13851.4 0.214 2.728
6 9810 9943.5 1.793 4.521
7 7106 7145.0 0.213 4.734
8 5204 5139.1 0.820 5.555
9 3664 3699.9 0.348 5.902
10 2665 2666.3 0.001 5.903
11 1997 1923.3 2.822 8.725
12 1386 1388.7 0.005 8.730
13 976 1003.7 0.765 9.495
14 742 726.1 0.346 9.842
15 499 525.8 1.370 11.211
16 376 381.2 0.070 11.281
17 268 276.5 0.264 11.545
18 192 200.8 0.388 11.933
19 147 146.0 0.007 11.940
20 111 106.2 0.216 12.155
21 286 287.1 0.004 12.160
Chisq= 12.16 for 20 degrees of freedom, p= 0.08953
SUMMARY of craptest
p-value for no. of wins: 0.286747
p-value for throws/game: 0.089534
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2017-03-24_01:31
No. of wins: Observed Expected
98311 98585.9
z-score=-1.229, pvalue=0.10947
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66057 66666.7 5.575 5.575
2 37911 37654.3 1.750 7.325
3 27254 26954.7 3.323 10.648
4 19307 19313.5 0.002 10.650
5 13845 13851.4 0.003 10.653
6 9976 9943.5 0.106 10.759
7 7188 7145.0 0.258 11.017
8 5112 5139.1 0.143 11.160
9 3802 3699.9 2.819 13.979
10 2623 2666.3 0.703 14.682
11 1899 1923.3 0.308 14.990
12 1421 1388.7 0.749 15.740
13 995 1003.7 0.076 15.815
14 715 726.1 0.171 15.986
15 513 525.8 0.313 16.300
16 377 381.2 0.045 16.345
17 290 276.5 0.655 17.000
18 181 200.8 1.958 18.958
19 131 146.0 1.538 20.496
20 121 106.2 2.058 22.554
21 282 287.1 0.091 22.645
Chisq= 22.65 for 20 degrees of freedom, p= 0.69344
SUMMARY of craptest
p-value for no. of wins: 0.109474
p-value for throws/game: 0.693442
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0061,0.0072,0.0115,0.0123,0.0198,0.0298,0.0304,0.0465,0.0502,0.0518,
0.0558,0.0575,0.0676,0.0681,0.0734,0.0742,0.0811,0.0875,0.0879,0.0895,
0.0999,0.1010,0.1064,0.1081,0.1095,0.1148,0.1165,0.1187,0.1268,0.1289,
0.1385,0.1393,0.1414,0.1538,0.1543,0.1558,0.1739,0.1774,0.1788,0.1856,
0.1856,0.1898,0.1904,0.1912,0.1950,0.1953,0.1965,0.1980,0.1990,0.2036,
0.2051,0.2056,0.2076,0.2076,0.2119,0.2163,0.2203,0.2206,0.2230,0.2266,
0.2388,0.2407,0.2433,0.2438,0.2496,0.2501,0.2581,0.2671,0.2744,0.2764,
0.2773,0.2842,0.2867,0.2883,0.2896,0.2934,0.2947,0.3004,0.3005,0.3005,
0.3145,0.3153,0.3158,0.3181,0.3240,0.3274,0.3300,0.3421,0.3422,0.3527,
0.3529,0.3602,0.3605,0.3621,0.3647,0.3661,0.3669,0.3699,0.3725,0.3733,
0.3849,0.3851,0.3866,0.3969,0.4010,0.4086,0.4097,0.4134,0.4141,0.4150,
0.4199,0.4243,0.4279,0.4365,0.4369,0.4455,0.4480,0.4490,0.4502,0.4510,
0.4591,0.4611,0.4625,0.4698,0.4769,0.4775,0.4796,0.4818,0.4830,0.4833,
0.5092,0.5185,0.5186,0.5196,0.5218,0.5220,0.5222,0.5234,0.5266,0.5270,
0.5279,0.5332,0.5419,0.5435,0.5450,0.5451,0.5461,0.5503,0.5545,0.5576,
0.5626,0.5716,0.5725,0.5775,0.5847,0.5849,0.5950,0.5961,0.5974,0.6026,
0.6027,0.6054,0.6055,0.6091,0.6130,0.6137,0.6152,0.6201,0.6214,0.6231,
0.6271,0.6284,0.6336,0.6367,0.6411,0.6413,0.6546,0.6594,0.6596,0.6606,
0.6637,0.6693,0.6707,0.6719,0.6771,0.6794,0.6829,0.6934,0.7019,0.7026,
0.7050,0.7066,0.7081,0.7093,0.7129,0.7138,0.7151,0.7240,0.7338,0.7386,
0.7489,0.7510,0.7561,0.7625,0.7627,0.7633,0.7676,0.7773,0.7807,0.7823,
0.7873,0.7908,0.7931,0.7946,0.7966,0.7970,0.8022,0.8077,0.8112,0.8143,
0.8179,0.8187,0.8267,0.8274,0.8297,0.8312,0.8322,0.8326,0.8424,0.8427,
0.8484,0.8600,0.8648,0.8652,0.8707,0.8795,0.8844,0.8933,0.8982,0.8984,
0.8991,0.8997,0.9000,0.9054,0.9124,0.9140,0.9143,0.9146,0.9175,0.9215,
0.9299,0.9337,0.9377,0.9396,0.9404,0.9439,0.9453,0.9469,0.9473,0.9483,
0.9566,0.9656,0.9691,0.9740,0.9745,0.9752,0.9789,0.9890,0.9952,
Overall p-value after applying KStest on 269 p-values = 0.842661
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.