RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-19_19:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.86 19.5831 0.703896
2 to 25 15.79 11.3096 0.159975
3 to 26 15.79 23.1837 0.856635
4 to 27 15.59 17.0968 0.552177
5 to 28 16.01 20.9233 0.770262
6 to 29 15.74 10.7988 0.133168
7 to 30 15.93 14.0635 0.337396
8 to 31 15.58 11.0632 0.146742
9 to 32 15.74 10.0465 0.098353
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.508494
Tough bday spacings test for dh-ranFile-2018-06-19_19:31: 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 16 42 81 100 101 71 47 20 14 5 3
(O-E)^2/E 5.1 0.8 0.8 0.1 0.1 0.7 0.5 3.2 0.1 0.4 0.3
Birthday Spacings: Sum(O-E)^2/E= 11.969, p= 0.713
RESULTS OF GCD FOR dh-ranFile-2018-06-19_19:31
Euclid's algorithm:
p-value, steps to gcd: 0.451245
p-value, dist. of gcd's: 0.831820
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-19_19:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.475 0.512 0.803 0.787 0.635 0.764 0.295 0.625
Bits 8 to 15---> 0.553 0.650 0.409 0.116 0.246 0.495 0.184 0.360
Bits 16 to 23---> 0.425 0.808 0.692 0.485 0.902 0.989 0.896 0.508
Bits 24 to 31---> 0.367 0.361 0.576 0.670 0.747 0.079 0.033 0.119
KS test for the above 32 p values: 0.308
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-19_19:31,
p-values for 5 runs: 0.7999, 0.0651, 0.6115, 0.5109, 0.4147
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-19_19:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 220 211.4 0.348 0.348
r= 29 5183 5134.0 0.467 0.816
r= 30 23079 23103.0 0.025 0.841
r= 31 11518 11551.5 0.097 0.938
chi-square = 0.938 with df = 3; p-value = 0.184
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-19_19:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 227 211.4 1.148 1.148
r= 30 5170 5134.0 0.252 1.401
r= 31 23217 23103.0 0.562 1.963
r= 32 11386 11551.5 2.372 4.335
chi-square = 4.335 with df = 3; p-value = 0.772
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-19_19:31
b-rank test for bits 1 to 8, p=0.00120
b-rank test for bits 2 to 9, p=0.56936
b-rank test for bits 3 to 10, p=0.38431
b-rank test for bits 4 to 11, p=0.00302
b-rank test for bits 5 to 12, p=0.59982
b-rank test for bits 6 to 13, p=0.52196
b-rank test for bits 7 to 14, p=0.36983
b-rank test for bits 8 to 15, p=0.85792
b-rank test for bits 9 to 16, p=0.00619
b-rank test for bits 10 to 17, p=0.37754
b-rank test for bits 11 to 18, p=0.98164
b-rank test for bits 12 to 19, p=0.91422
b-rank test for bits 13 to 20, p=0.06773
b-rank test for bits 14 to 21, p=0.59867
b-rank test for bits 15 to 22, p=0.64624
b-rank test for bits 16 to 23, p=0.73128
b-rank test for bits 17 to 24, p=0.96506
b-rank test for bits 18 to 25, p=0.55501
b-rank test for bits 19 to 26, p=0.16833
b-rank test for bits 20 to 27, p=0.96502
b-rank test for bits 21 to 28, p=0.18057
b-rank test for bits 22 to 29, p=0.31292
b-rank test for bits 23 to 30, p=0.13247
b-rank test for bits 24 to 31, p=0.41678
b-rank test for bits 25 to 32, p=0.92467
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 = 0.263805
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-19_19:31
(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 142208 0.70 0.757357
2 142091 0.42 0.664386
3 141178 -1.71 0.043752
4 142084 0.41 0.658403
5 142433 1.22 0.889435
6 141548 -0.84 0.199271
7 141732 -0.41 0.339319
8 141709 -0.47 0.319871
9 142113 0.48 0.682915
10 142312 0.94 0.826601
11 142127 0.51 0.694475
12 141786 -0.29 0.386614
13 141852 -0.13 0.446722
14 141821 -0.21 0.418248
15 141931 0.05 0.520190
16 141523 -0.90 0.183358
17 141845 -0.15 0.440263
18 142141 0.54 0.705844
19 141713 -0.46 0.323219
20 141915 0.01 0.505285
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-19_19:31
Bits used No. missing words z-score p-value
23 to 32 141557 -1.2149 0.112196
22 to 31 142203 1.0127 0.844388
21 to 30 141713 -0.6770 0.249203
20 to 29 141841 -0.2356 0.406864
19 to 28 142234 1.1196 0.868548
18 to 27 142291 1.3161 0.905930
17 to 26 142053 0.4954 0.689846
16 to 25 141981 0.2471 0.597599
15 to 24 141697 -0.7322 0.232032
14 to 23 142265 1.2264 0.889985
13 to 22 141945 0.1230 0.548947
12 to 21 141805 -0.3598 0.359514
11 to 20 141787 -0.4218 0.336575
10 to 19 142368 1.5816 0.943132
9 to 18 141555 -1.2218 0.110886
8 to 17 141937 0.0954 0.538007
7 to 16 142154 0.8437 0.800579
6 to 15 142491 2.0058 0.977559
5 to 14 142203 1.0127 0.844388
4 to 13 141927 0.0609 0.524293
3 to 12 142401 1.6954 0.955002
2 to 11 141974 0.2230 0.588232
1 to 10 142291 1.3161 0.905930
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-19_19:31
Bits used No. missing words z-score p-value
28 to 32 141562 -1.1774 0.119520
27 to 31 141538 -1.2587 0.104061
26 to 30 141672 -0.8045 0.210552
25 to 29 142143 0.7921 0.785849
24 to 28 141972 0.2124 0.584118
23 to 27 142223 1.0633 0.856174
22 to 26 141575 -1.1333 0.128540
21 to 25 141893 -0.0554 0.477928
20 to 24 141647 -0.8893 0.186933
19 to 23 141763 -0.4960 0.309935
18 to 22 142085 0.5955 0.724243
17 to 21 142203 0.9955 0.840251
16 to 20 141460 -1.5232 0.063860
15 to 19 141883 -0.0893 0.464440
14 to 18 141765 -0.4893 0.312331
13 to 17 141635 -0.9299 0.176203
12 to 16 141962 0.1785 0.570852
11 to 15 142204 0.9989 0.841074
10 to 14 141657 -0.8554 0.196177
9 to 13 141953 0.1480 0.558842
8 to 12 141901 -0.0282 0.488737
7 to 11 142105 0.6633 0.746427
6 to 10 141925 0.0531 0.521181
5 to 9 141748 -0.5469 0.292230
4 to 8 142160 0.8497 0.802262
3 to 7 141720 -0.6418 0.260503
2 to 6 142427 1.7548 0.960354
1 to 5 142127 0.7379 0.769702
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-19_19:31
Bits used No. missing words z-score p-value
31 to 32 141768 -0.4169 0.338375
30 to 31 142323 1.2203 0.888818
29 to 30 141578 -0.9774 0.164192
28 to 29 142258 1.0285 0.848149
27 to 28 141341 -1.6765 0.046821
26 to 27 142356 1.3176 0.906183
25 to 26 141910 0.0020 0.500789
24 to 25 141801 -0.3196 0.374652
23 to 24 141581 -0.9685 0.166391
22 to 23 141871 -0.1131 0.454988
21 to 22 142310 1.1819 0.881381
20 to 21 141510 -1.1780 0.119405
19 to 20 142320 1.2114 0.887132
18 to 19 141763 -0.4317 0.332997
17 to 18 141766 -0.4228 0.336220
16 to 17 141445 -1.3697 0.085390
15 to 16 141803 -0.3137 0.376891
14 to 15 141676 -0.6883 0.245635
13 to 14 142381 1.3914 0.917941
12 to 13 141850 -0.1750 0.430534
11 to 12 142038 0.3796 0.647863
10 to 11 141956 0.1377 0.554749
9 to 10 142413 1.4858 0.931328
8 to 9 142036 0.3737 0.645671
7 to 8 141658 -0.7414 0.229230
6 to 7 142451 1.5978 0.944961
5 to 6 141871 -0.1131 0.454988
4 to 5 141665 -0.7207 0.235536
3 to 4 141099 -2.3904 0.008416
2 to 3 141366 -1.6027 0.054496
1 to 2 141901 -0.0246 0.490198
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-19_19:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2531.07 0.439 0.669832
Test results for specific bytes for dh-ranFile-2018-06-19_19:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2468.14 -0.451 0.326142
2 to 9 2498.42 -0.022 0.491068
3 to 10 2539.92 0.565 0.713822
4 to 11 2486.88 -0.186 0.426405
5 to 12 2404.89 -1.345 0.089307
6 to 13 2716.32 3.059 0.998890
7 to 14 2397.62 -1.448 0.073834
8 to 15 2478.82 -0.299 0.382280
9 to 16 2438.05 -0.876 0.190487
10 to 17 2474.23 -0.365 0.357741
11 to 18 2564.75 0.916 0.820077
12 to 19 2389.10 -1.568 0.058395
13 to 20 2528.42 0.402 0.656112
14 to 21 2451.64 -0.684 0.247010
15 to 22 2602.79 1.454 0.926972
16 to 23 2513.55 0.192 0.575964
17 to 24 2544.76 0.633 0.736617
18 to 25 2520.42 0.289 0.613614
19 to 26 2598.38 1.391 0.917924
20 to 27 2433.14 -0.946 0.172196
21 to 28 2583.14 1.176 0.880154
22 to 29 2512.27 0.173 0.568856
23 to 30 2648.24 2.096 0.981979
24 to 31 2648.78 2.104 0.982316
25 to 32 2476.37 -0.334 0.369103
CDPARK for dh-ranFile-2018-06-19_19:31: 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
3520 -0.1370 0.445521
3533 0.4566 0.676028
3523 0.0000 0.500000
3514 -0.4110 0.340551
3516 -0.3196 0.374623
3560 1.6895 0.954438
3529 0.2740 0.607947
3543 0.9132 0.819442
3511 -0.5479 0.291865
3497 -1.1872 0.117571
Square side=100, avg. no. parked=3524.60 sample std.=16.85
p-value of the KSTEST for those 10 p-values: 0.910684
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-19_19:31
0.5085,0.1484,0.0310,0.4461,0.4878,0.7338,0.9002,0.5289,0.4488,0.3896,
The KS test for those 10 p-values: 0.622729
The 3DSPHERES test for dh-ranFile-2018-06-19_19:31
sample no r^3 equiv. uni.
1 21.268 0.507833
2 128.505 0.986206
3 16.674 0.426394
4 2.172 0.069827
5 19.963 0.485949
6 20.116 0.488558
7 19.109 0.471114
8 10.599 0.297639
9 71.173 0.906747
10 22.266 0.523939
11 7.575 0.223133
12 12.712 0.345398
13 31.954 0.655319
14 35.743 0.696215
15 4.244 0.131913
16 56.735 0.849107
17 41.648 0.750495
18 22.855 0.533195
19 10.661 0.299077
20 13.973 0.372349
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.656570
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-19_19:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 0.1 -1.6 0.5 0.1 -0.6
0.1 -0.9 -0.2 -1.5 0.4 1.3
0.9 -0.5 -2.2 1.3 0.7 0.5
-1.8 -0.3 0.2 -0.4 -0.4 2.5
1.3 -0.5 -0.6 0.2 0.9 -0.7
-1.3 -1.2 1.4 -0.9 0.1 0.1
0.3 -1.0 1.7 0.4 1.6 0.0
0.8
Chi-square with 42 degrees of freedom:43.377650
z-score=0.150314, p-value=0.587581
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-19_19:31
Test no p-value
1 0.228533
2 0.077400
3 0.746720
4 0.760866
5 0.709884
6 0.100584
7 0.092986
8 0.807351
9 0.936006
10 0.996346
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.267942
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-19_19:31:
(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 66642 0.01 66726 0.05
3 25000.00 24977 0.02 24938 0.15
4 6666.67 6749 1.02 6692 0.10
5 1388.89 1347 1.26 1348 1.20
6 238.10 248 0.41 256 1.35
7 34.72 34 0.01 37 0.15
8 4.96 2 1.77 2 1.77
p=0.39118 p=0.42627
Number of rngs required: 688541, p-value: 0.563
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-19_19:31
No. of wins: Observed Expected
98704 98585.9
z-score= 0.528, pvalue=0.70139
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66520 66666.7 0.323 0.323
2 37792 37654.3 0.503 0.826
3 26955 26954.7 0.000 0.826
4 19180 19313.5 0.922 1.748
5 13973 13851.4 1.067 2.816
6 10039 9943.5 0.916 3.732
7 7118 7145.0 0.102 3.834
8 5114 5139.1 0.122 3.956
9 3787 3699.9 2.052 6.009
10 2616 2666.3 0.949 6.957
11 1978 1923.3 1.554 8.511
12 1298 1388.7 5.929 14.440
13 976 1003.7 0.765 15.206
14 711 726.1 0.316 15.521
15 561 525.8 2.352 17.873
16 375 381.2 0.099 17.972
17 271 276.5 0.111 18.083
18 185 200.8 1.248 19.331
19 149 146.0 0.062 19.393
20 98 106.2 0.635 20.029
21 304 287.1 0.993 21.022
Chisq= 21.02 for 20 degrees of freedom, p= 0.60414
SUMMARY of craptest
p-value for no. of wins: 0.701388
p-value for throws/game: 0.604140
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-19_19:31
No. of wins: Observed Expected
98634 98585.9
z-score= 0.215, pvalue=0.58524
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66840 66666.7 0.451 0.451
2 37792 37654.3 0.503 0.954
3 26817 26954.7 0.704 1.658
4 19074 19313.5 2.969 4.627
5 13837 13851.4 0.015 4.642
6 9914 9943.5 0.088 4.730
7 7158 7145.0 0.024 4.753
8 5120 5139.1 0.071 4.824
9 3773 3699.9 1.446 6.270
10 2631 2666.3 0.467 6.737
11 1945 1923.3 0.244 6.981
12 1469 1388.7 4.638 11.620
13 1023 1003.7 0.371 11.990
14 778 726.1 3.704 15.694
15 519 525.8 0.089 15.783
16 357 381.2 1.530 17.313
17 257 276.5 1.381 18.694
18 189 200.8 0.697 19.390
19 154 146.0 0.440 19.830
20 94 106.2 1.405 21.235
21 259 287.1 2.753 23.988
Chisq= 23.99 for 20 degrees of freedom, p= 0.75709
SUMMARY of craptest
p-value for no. of wins: 0.585240
p-value for throws/game: 0.757091
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0012,0.0030,0.0062,0.0084,0.0310,0.0330,0.0438,0.0468,0.0545,0.0584,
0.0639,0.0651,0.0677,0.0698,0.0738,0.0774,0.0795,0.0854,0.0893,0.0930,
0.0984,0.1006,0.1041,0.1109,0.1122,0.1160,0.1176,0.1192,0.1194,0.1195,
0.1285,0.1319,0.1325,0.1332,0.1467,0.1484,0.1600,0.1642,0.1664,0.1683,
0.1722,0.1762,0.1806,0.1834,0.1837,0.1838,0.1869,0.1905,0.1962,0.1993,
0.2106,0.2231,0.2285,0.2292,0.2320,0.2355,0.2456,0.2458,0.2470,0.2492,
0.2605,0.2638,0.2679,0.2919,0.2922,0.2949,0.2976,0.2991,0.3077,0.3099,
0.3123,0.3129,0.3199,0.3232,0.3261,0.3330,0.3362,0.3366,0.3374,0.3384,
0.3393,0.3406,0.3454,0.3577,0.3595,0.3597,0.3611,0.3671,0.3691,0.3698,
0.3723,0.3746,0.3747,0.3769,0.3775,0.3823,0.3843,0.3866,0.3896,0.3912,
0.4069,0.4091,0.4147,0.4168,0.4182,0.4251,0.4263,0.4264,0.4264,0.4305,
0.4403,0.4455,0.4461,0.4467,0.4488,0.4512,0.4550,0.4550,0.4644,0.4711,
0.4748,0.4779,0.4849,0.4859,0.4878,0.4886,0.4887,0.4902,0.4911,0.4947,
0.5000,0.5008,0.5053,0.5078,0.5081,0.5085,0.5085,0.5109,0.5122,0.5202,
0.5212,0.5220,0.5239,0.5243,0.5289,0.5332,0.5380,0.5489,0.5522,0.5533,
0.5547,0.5550,0.5588,0.5631,0.5689,0.5694,0.5709,0.5758,0.5760,0.5841,
0.5852,0.5876,0.5882,0.5976,0.5987,0.5998,0.6041,0.6079,0.6115,0.6136,
0.6227,0.6251,0.6347,0.6457,0.6462,0.6479,0.6505,0.6553,0.6561,0.6566,
0.6584,0.6644,0.6698,0.6701,0.6760,0.6829,0.6898,0.6925,0.6945,0.6962,
0.7014,0.7039,0.7058,0.7099,0.7129,0.7138,0.7242,0.7313,0.7338,0.7366,
0.7464,0.7466,0.7467,0.7505,0.7571,0.7574,0.7609,0.7637,0.7697,0.7703,
0.7725,0.7858,0.7870,0.7999,0.8006,0.8023,0.8029,0.8074,0.8083,0.8194,
0.8201,0.8266,0.8318,0.8403,0.8411,0.8444,0.8444,0.8481,0.8491,0.8562,
0.8566,0.8579,0.8685,0.8802,0.8814,0.8871,0.8888,0.8894,0.8900,0.8965,
0.9002,0.9021,0.9059,0.9059,0.9062,0.9067,0.9107,0.9142,0.9179,0.9179,
0.9247,0.9270,0.9313,0.9360,0.9431,0.9450,0.9544,0.9550,0.9604,0.9650,
0.9651,0.9776,0.9816,0.9820,0.9823,0.9862,0.9894,0.9963,0.9989,
Overall p-value after applying KStest on 269 p-values = 0.520769
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.