RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-03_07:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 16.31 24.0960 0.883150
2 to 25 15.98 16.8766 0.537245
3 to 26 15.49 12.1571 0.209468
4 to 27 15.62 11.3419 0.161751
5 to 28 15.64 18.7588 0.657446
6 to 29 15.62 21.1631 0.780922
7 to 30 15.76 27.2662 0.945723
8 to 31 15.65 34.8235 0.993438
9 to 32 15.97 21.7797 0.806661
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.110146
Tough bday spacings test for dh-ranFile-2018-07-03_07:31: 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 43 71 89 98 78 56 26 20 6 2
(O-E)^2/E 0.4 1.1 0.1 0.8 0.0 0.0 0.3 0.5 1.8 0.1 1.0
Birthday Spacings: Sum(O-E)^2/E= 5.955, p= 0.181
RESULTS OF GCD FOR dh-ranFile-2018-07-03_07:31
Euclid's algorithm:
p-value, steps to gcd: 0.566035
p-value, dist. of gcd's: 0.245681
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-03_07:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.051 0.495 0.785 0.991 0.095 0.931 0.113 0.521
Bits 8 to 15---> 0.750 0.843 0.453 0.531 0.343 0.707 0.267 0.389
Bits 16 to 23---> 0.735 0.975 0.899 0.075 0.427 0.841 0.047 0.978
Bits 24 to 31---> 0.524 0.962 0.282 0.637 0.244 0.274 0.478 0.134
KS test for the above 32 p values: 0.312
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-03_07:31,
p-values for 5 runs: 0.4739, 0.1595, 0.1631, 0.1037, 0.5653
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-03_07:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 199 211.4 0.729 0.729
r= 29 5118 5134.0 0.050 0.779
r= 30 23036 23103.0 0.195 0.974
r= 31 11647 11551.5 0.789 1.763
chi-square = 1.763 with df = 3; p-value = 0.377
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-03_07:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 206 211.4 0.139 0.139
r= 30 5105 5134.0 0.164 0.303
r= 31 23107 23103.0 0.001 0.303
r= 32 11582 11551.5 0.080 0.384
chi-square = 0.384 with df = 3; p-value = 0.056
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-03_07:31
b-rank test for bits 1 to 8, p=0.15133
b-rank test for bits 2 to 9, p=0.53908
b-rank test for bits 3 to 10, p=0.14437
b-rank test for bits 4 to 11, p=0.09577
b-rank test for bits 5 to 12, p=0.42785
b-rank test for bits 6 to 13, p=0.69358
b-rank test for bits 7 to 14, p=0.88574
b-rank test for bits 8 to 15, p=0.31331
b-rank test for bits 9 to 16, p=0.37977
b-rank test for bits 10 to 17, p=0.26100
b-rank test for bits 11 to 18, p=0.02307
b-rank test for bits 12 to 19, p=0.70403
b-rank test for bits 13 to 20, p=0.71886
b-rank test for bits 14 to 21, p=0.07875
b-rank test for bits 15 to 22, p=0.25503
b-rank test for bits 16 to 23, p=0.35097
b-rank test for bits 17 to 24, p=0.49411
b-rank test for bits 18 to 25, p=0.96064
b-rank test for bits 19 to 26, p=0.98117
b-rank test for bits 20 to 27, p=0.78412
b-rank test for bits 21 to 28, p=0.58518
b-rank test for bits 22 to 29, p=0.24168
b-rank test for bits 23 to 30, p=0.27832
b-rank test for bits 24 to 31, p=0.21419
b-rank test for bits 25 to 32, p=0.41811
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 = 0.496522
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-03_07:31
(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 141878 -0.07 0.470823
2 141659 -0.58 0.279313
3 142256 0.81 0.791023
4 141498 -0.96 0.168263
5 142067 0.37 0.643708
6 142269 0.84 0.799644
7 142019 0.26 0.601117
8 141057 -1.99 0.023217
9 141973 0.15 0.559129
10 141903 -0.01 0.494100
11 140857 -2.46 0.006972
12 142062 0.36 0.639344
13 141873 -0.08 0.466177
14 142084 0.41 0.658403
15 142052 0.33 0.630562
16 141792 -0.27 0.391990
17 141838 -0.17 0.433819
18 142080 0.40 0.654966
19 141478 -1.01 0.156780
20 141132 -1.82 0.034671
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-03_07:31
Bits used No. missing words z-score p-value
23 to 32 141811 -0.3391 0.367279
22 to 31 141539 -1.2770 0.100801
21 to 30 141925 0.0540 0.521546
20 to 29 142155 0.8471 0.801541
19 to 28 141825 -0.2908 0.385605
18 to 27 141401 -1.7529 0.039813
17 to 26 141635 -0.9460 0.172083
16 to 25 142121 0.7299 0.767273
15 to 24 141946 0.1264 0.550312
14 to 23 141360 -1.8942 0.029096
13 to 22 141750 -0.5494 0.291361
12 to 21 141459 -1.5529 0.060228
11 to 20 141828 -0.2804 0.389567
10 to 19 141843 -0.2287 0.409542
9 to 18 142014 0.3609 0.640925
8 to 17 141785 -0.4287 0.334062
7 to 16 141875 -0.1184 0.452884
6 to 15 141859 -0.1736 0.431109
5 to 14 141771 -0.4770 0.316681
4 to 13 142010 0.3471 0.635756
3 to 12 141996 0.2989 0.617477
2 to 11 141655 -0.8770 0.190243
1 to 10 141418 -1.6942 0.045110
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-03_07:31
Bits used No. missing words z-score p-value
28 to 32 141556 -1.1977 0.115511
27 to 31 142424 1.7446 0.959477
26 to 30 142537 2.1277 0.983319
25 to 29 141861 -0.1638 0.434932
24 to 28 142777 2.9413 0.998366
23 to 27 141868 -0.1401 0.444290
22 to 26 141863 -0.1571 0.437602
21 to 25 141799 -0.3740 0.354202
20 to 24 141497 -1.3977 0.081097
19 to 23 141368 -1.8350 0.033252
18 to 22 142197 0.9752 0.835258
17 to 21 142154 0.8294 0.796558
16 to 20 141718 -0.6486 0.258306
15 to 19 141875 -0.1164 0.453679
14 to 18 142027 0.3989 0.655010
13 to 17 141665 -0.8282 0.203768
12 to 16 142062 0.5175 0.697605
11 to 15 142047 0.4667 0.679635
10 to 14 141929 0.0667 0.526581
9 to 13 142211 1.0226 0.846754
8 to 12 141231 -2.2994 0.010740
7 to 11 142055 0.4938 0.689275
6 to 10 141900 -0.0316 0.487385
5 to 9 142124 0.7277 0.766600
4 to 8 141994 0.2870 0.612950
3 to 7 141707 -0.6859 0.246399
2 to 6 141705 -0.6926 0.244267
1 to 5 141677 -0.7876 0.215477
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-03_07:31
Bits used No. missing words z-score p-value
31 to 32 141609 -0.8859 0.187828
30 to 31 142131 0.6539 0.743410
29 to 30 141841 -0.2016 0.420129
28 to 29 141496 -1.2193 0.111372
27 to 28 141682 -0.6706 0.251241
26 to 27 142196 0.8456 0.801122
25 to 26 141718 -0.5644 0.286243
24 to 25 141894 -0.0452 0.481966
23 to 24 141721 -0.5555 0.289261
22 to 23 141641 -0.7915 0.214316
21 to 22 142062 0.4504 0.673772
20 to 21 141783 -0.3727 0.354703
19 to 20 141805 -0.3078 0.379133
18 to 19 142366 1.3471 0.911027
17 to 18 141729 -0.5319 0.297381
16 to 17 141934 0.0728 0.529007
15 to 16 142370 1.3589 0.912912
14 to 15 141795 -0.3373 0.367962
13 to 14 141815 -0.2783 0.390407
12 to 13 142014 0.3088 0.621248
11 to 12 141906 -0.0098 0.496081
10 to 11 141837 -0.2134 0.415522
9 to 10 141853 -0.1662 0.434014
8 to 9 142239 0.9725 0.834594
7 to 8 142157 0.7306 0.767485
6 to 7 142101 0.5654 0.714099
5 to 6 141669 -0.7089 0.239182
4 to 5 141548 -1.0659 0.143241
3 to 4 142093 0.5418 0.706022
2 to 3 141512 -1.1721 0.120586
1 to 2 142177 0.7896 0.785116
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-03_07:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2450.90 -0.694 0.243706
Test results for specific bytes for dh-ranFile-2018-07-03_07:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2534.43 0.487 0.686854
2 to 9 2559.80 0.846 0.801131
3 to 10 2445.22 -0.775 0.219237
4 to 11 2455.63 -0.627 0.265192
5 to 12 2568.25 0.965 0.832790
6 to 13 2523.98 0.339 0.632727
7 to 14 2545.09 0.638 0.738155
8 to 15 2456.48 -0.615 0.269113
9 to 16 2406.53 -1.322 0.093112
10 to 17 2509.10 0.129 0.551186
11 to 18 2469.38 -0.433 0.332520
12 to 19 2691.75 2.712 0.996654
13 to 20 2403.15 -1.370 0.085388
14 to 21 2517.34 0.245 0.596873
15 to 22 2519.72 0.279 0.609841
16 to 23 2586.44 1.222 0.889218
17 to 24 2424.39 -1.069 0.142482
18 to 25 2487.77 -0.173 0.431368
19 to 26 2503.07 0.043 0.517317
20 to 27 2570.92 1.003 0.842063
21 to 28 2411.30 -1.254 0.104856
22 to 29 2494.30 -0.081 0.467856
23 to 30 2598.22 1.389 0.917593
24 to 31 2559.87 0.847 0.801402
25 to 32 2461.99 -0.538 0.295456
CDPARK for dh-ranFile-2018-07-03_07:31: 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
3516 -0.3196 0.374623
3525 0.0913 0.536383
3514 -0.4110 0.340551
3529 0.2740 0.607947
3543 0.9132 0.819442
3529 0.2740 0.607947
3526 0.1370 0.554479
3511 -0.5479 0.291865
3538 0.6849 0.753306
Square side=100, avg. no. parked=3524.10 sample std.=10.68
p-value of the KSTEST for those 10 p-values: 0.407650
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-03_07:31
0.3817,0.8008,0.5701,0.2059,0.2614,0.9873,0.0698,0.6367,0.3961,0.6481,
The KS test for those 10 p-values: 0.969535
The 3DSPHERES test for dh-ranFile-2018-07-03_07:31
sample no r^3 equiv. uni.
1 73.838 0.914672
2 30.026 0.632435
3 90.183 0.950515
4 41.454 0.748871
5 13.878 0.370364
6 13.543 0.363295
7 4.494 0.139118
8 13.250 0.357030
9 58.032 0.855491
10 23.253 0.539347
11 18.698 0.463803
12 37.278 0.711368
13 47.472 0.794521
14 58.479 0.857625
15 6.257 0.188254
16 12.611 0.343191
17 0.736 0.024226
18 6.948 0.206726
19 27.587 0.601306
20 175.160 0.997087
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.725303
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-03_07:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 0.1 -0.1 -0.1 0.0 -1.7
-0.2 -0.6 1.6 -1.1 -0.9 0.5
0.8 0.5 -0.1 1.1 -0.8 0.5
-0.4 -0.3 0.5 -0.8 -1.0 0.1
1.4 -0.2 0.2 -1.8 1.1 -0.2
-2.0 1.6 0.6 0.1 0.8 1.0
0.0 -0.1 0.1 0.4 -0.6 -1.0
-1.1
Chi-square with 42 degrees of freedom:31.738027
z-score=-1.119673, p-value=0.124627
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-03_07:31
Test no p-value
1 0.002045
2 0.575800
3 0.046344
4 0.906456
5 0.173060
6 0.643830
7 0.228329
8 0.330450
9 0.334735
10 0.001190
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.020258
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-03_07:31:
(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 66537 0.25 66787 0.22
3 25000.00 25111 0.49 24937 0.16
4 6666.67 6688 0.07 6611 0.46
5 1388.89 1373 0.18 1405 0.19
6 238.10 249 0.50 221 1.23
7 34.72 36 0.05 32 0.21
8 4.96 5 0.00 6 0.22
p=0.04335 p=0.15293
Number of rngs required: 688476, p-value: 0.533
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-03_07:31
No. of wins: Observed Expected
98790 98585.9
z-score= 0.913, pvalue=0.81939
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66716 66666.7 0.037 0.037
2 37538 37654.3 0.359 0.396
3 27137 26954.7 1.232 1.628
4 19452 19313.5 0.994 2.622
5 13802 13851.4 0.176 2.798
6 9906 9943.5 0.142 2.940
7 7118 7145.0 0.102 3.042
8 5078 5139.1 0.726 3.768
9 3647 3699.9 0.755 4.524
10 2648 2666.3 0.126 4.649
11 1986 1923.3 2.042 6.691
12 1341 1388.7 1.641 8.332
13 964 1003.7 1.571 9.904
14 742 726.1 0.346 10.250
15 557 525.8 1.847 12.097
16 368 381.2 0.454 12.551
17 276 276.5 0.001 12.552
18 176 200.8 3.070 15.622
19 132 146.0 1.340 16.961
20 110 106.2 0.135 17.096
21 306 287.1 1.242 18.339
Chisq= 18.34 for 20 degrees of freedom, p= 0.43488
SUMMARY of craptest
p-value for no. of wins: 0.819389
p-value for throws/game: 0.434884
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-03_07:31
No. of wins: Observed Expected
98226 98585.9
z-score=-1.609, pvalue=0.05375
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66630 66666.7 0.020 0.020
2 37847 37654.3 0.986 1.006
3 26949 26954.7 0.001 1.007
4 19342 19313.5 0.042 1.050
5 13666 13851.4 2.482 3.532
6 9795 9943.5 2.219 5.751
7 7253 7145.0 1.632 7.382
8 5146 5139.1 0.009 7.392
9 3735 3699.9 0.334 7.725
10 2653 2666.3 0.066 7.792
11 1958 1923.3 0.625 8.417
12 1329 1388.7 2.570 10.987
13 999 1003.7 0.022 11.009
14 737 726.1 0.162 11.171
15 532 525.8 0.072 11.243
16 395 381.2 0.503 11.747
17 291 276.5 0.756 12.503
18 207 200.8 0.190 12.692
19 150 146.0 0.110 12.803
20 103 106.2 0.097 12.900
21 283 287.1 0.059 12.959
Chisq= 12.96 for 20 degrees of freedom, p= 0.12086
SUMMARY of craptest
p-value for no. of wins: 0.053754
p-value for throws/game: 0.120864
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0012,0.0020,0.0070,0.0107,0.0203,0.0231,0.0232,0.0242,0.0291,0.0333,
0.0347,0.0398,0.0433,0.0451,0.0463,0.0472,0.0506,0.0538,0.0564,0.0602,
0.0698,0.0751,0.0788,0.0811,0.0854,0.0931,0.0950,0.0958,0.1008,0.1037,
0.1049,0.1101,0.1114,0.1129,0.1155,0.1206,0.1209,0.1246,0.1337,0.1391,
0.1425,0.1432,0.1444,0.1513,0.1529,0.1568,0.1595,0.1618,0.1631,0.1683,
0.1721,0.1731,0.1810,0.1878,0.1883,0.1902,0.2038,0.2059,0.2067,0.2095,
0.2142,0.2143,0.2155,0.2192,0.2283,0.2392,0.2417,0.2437,0.2438,0.2443,
0.2457,0.2464,0.2512,0.2550,0.2583,0.2610,0.2614,0.2652,0.2674,0.2691,
0.2740,0.2764,0.2783,0.2793,0.2816,0.2862,0.2893,0.2914,0.2919,0.2955,
0.2974,0.3117,0.3133,0.3167,0.3305,0.3325,0.3341,0.3347,0.3406,0.3427,
0.3432,0.3510,0.3542,0.3547,0.3570,0.3633,0.3673,0.3680,0.3704,0.3746,
0.3770,0.3791,0.3798,0.3817,0.3856,0.3892,0.3896,0.3904,0.3920,0.3961,
0.4077,0.4095,0.4155,0.4181,0.4201,0.4271,0.4278,0.4311,0.4314,0.4338,
0.4340,0.4349,0.4349,0.4376,0.4443,0.4526,0.4529,0.4537,0.4638,0.4662,
0.4679,0.4708,0.4739,0.4779,0.4820,0.4874,0.4941,0.4941,0.4950,0.4961,
0.4965,0.5173,0.5210,0.5215,0.5242,0.5266,0.5290,0.5309,0.5335,0.5364,
0.5372,0.5391,0.5393,0.5503,0.5512,0.5545,0.5591,0.5653,0.5660,0.5701,
0.5758,0.5852,0.5969,0.6011,0.6013,0.6079,0.6079,0.6098,0.6130,0.6175,
0.6212,0.6306,0.6324,0.6327,0.6358,0.6367,0.6368,0.6393,0.6409,0.6437,
0.6438,0.6481,0.6550,0.6550,0.6574,0.6584,0.6738,0.6796,0.6869,0.6893,
0.6936,0.6976,0.7040,0.7060,0.7075,0.7114,0.7141,0.7189,0.7253,0.7348,
0.7382,0.7434,0.7489,0.7501,0.7533,0.7666,0.7673,0.7675,0.7809,0.7841,
0.7845,0.7851,0.7910,0.7945,0.7966,0.7996,0.8008,0.8011,0.8011,0.8014,
0.8015,0.8067,0.8194,0.8194,0.8328,0.8346,0.8353,0.8407,0.8421,0.8435,
0.8468,0.8555,0.8576,0.8831,0.8857,0.8892,0.8989,0.9065,0.9110,0.9129,
0.9147,0.9176,0.9314,0.9457,0.9505,0.9595,0.9606,0.9623,0.9695,0.9754,
0.9783,0.9812,0.9833,0.9873,0.9915,0.9934,0.9967,0.9971,0.9984,
Overall p-value after applying KStest on 269 p-values = 0.105361
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.