RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-19_15:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.93 11.6558 0.179483
2 to 25 15.78 19.0441 0.673993
3 to 26 15.57 21.4209 0.791974
4 to 27 15.43 21.6411 0.801081
5 to 28 16.09 19.5933 0.704444
6 to 29 16.00 23.7470 0.873525
7 to 30 15.74 13.9842 0.331781
8 to 31 15.80 9.9503 0.094318
9 to 32 15.85 24.6560 0.897322
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.421066
Tough bday spacings test for dh-ranFile-2018-06-19_15:31: 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 8 39 87 99 77 95 46 28 13 7 1
(O-E)^2/E 0.1 0.2 2.6 0.0 4.4 3.6 0.7 0.1 0.2 0.0 2.3
Birthday Spacings: Sum(O-E)^2/E= 14.299, p= 0.840
RESULTS OF GCD FOR dh-ranFile-2018-06-19_15:31
Euclid's algorithm:
p-value, steps to gcd: 0.339572
p-value, dist. of gcd's: 0.691579
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-19_15:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.750 0.619 0.232 0.443 0.475 0.100 0.991 0.940
Bits 8 to 15---> 0.836 0.925 0.747 0.574 0.271 0.960 0.073 0.835
Bits 16 to 23---> 0.878 0.039 0.367 0.857 0.713 0.925 0.947 0.169
Bits 24 to 31---> 0.540 0.097 0.434 0.619 0.696 0.917 0.397 0.814
KS test for the above 32 p values: 0.938
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-19_15:31,
p-values for 5 runs: 0.6551, 0.6643, 0.3651, 0.4482, 0.6407
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-19_15:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 205 211.4 0.195 0.195
r= 29 5134 5134.0 0.000 0.195
r= 30 23060 23103.0 0.080 0.275
r= 31 11601 11551.5 0.212 0.487
chi-square = 0.487 with df = 3; p-value = 0.078
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-19_15:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 239 211.4 3.598 3.598
r= 30 5204 5134.0 0.954 4.553
r= 31 22885 23103.0 2.058 6.610
r= 32 11672 11551.5 1.257 7.867
chi-square = 7.867 with df = 3; p-value = 0.951
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-19_15:31
b-rank test for bits 1 to 8, p=0.55815
b-rank test for bits 2 to 9, p=0.56989
b-rank test for bits 3 to 10, p=0.63096
b-rank test for bits 4 to 11, p=0.51696
b-rank test for bits 5 to 12, p=0.89928
b-rank test for bits 6 to 13, p=0.12752
b-rank test for bits 7 to 14, p=0.47954
b-rank test for bits 8 to 15, p=0.62173
b-rank test for bits 9 to 16, p=0.96612
b-rank test for bits 10 to 17, p=0.39761
b-rank test for bits 11 to 18, p=0.74824
b-rank test for bits 12 to 19, p=0.68603
b-rank test for bits 13 to 20, p=0.62221
b-rank test for bits 14 to 21, p=0.67509
b-rank test for bits 15 to 22, p=0.77660
b-rank test for bits 16 to 23, p=0.88995
b-rank test for bits 17 to 24, p=0.86822
b-rank test for bits 18 to 25, p=0.14411
b-rank test for bits 19 to 26, p=0.26033
b-rank test for bits 20 to 27, p=0.64561
b-rank test for bits 21 to 28, p=0.91861
b-rank test for bits 22 to 29, p=0.79815
b-rank test for bits 23 to 30, p=0.03149
b-rank test for bits 24 to 31, p=0.84886
b-rank test for bits 25 to 32, p=0.84120
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 = 0.046602
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-19_15:31
(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 141896 -0.03 0.487577
2 142387 1.12 0.867800
3 141478 -1.01 0.156780
4 142929 2.38 0.991400
5 141558 -0.82 0.205862
6 141718 -0.45 0.327426
7 141239 -1.57 0.058652
8 141856 -0.12 0.450419
9 142162 0.59 0.722522
10 141977 0.16 0.562814
11 142388 1.12 0.868299
12 141816 -0.22 0.413691
13 141803 -0.25 0.401899
14 141450 -1.07 0.141591
15 141930 0.05 0.519259
16 142403 1.15 0.875634
17 141500 -0.96 0.169441
18 142152 0.57 0.714638
19 142590 1.59 0.944122
20 141743 -0.39 0.348778
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-19_15:31
Bits used No. missing words z-score p-value
23 to 32 141694 -0.7425 0.228887
22 to 31 141850 -0.2046 0.418948
21 to 30 142224 1.0851 0.861054
20 to 29 141683 -0.7804 0.217564
19 to 28 141458 -1.5563 0.059817
18 to 27 142049 0.4816 0.684962
17 to 26 141887 -0.0770 0.469312
16 to 25 141828 -0.2804 0.389567
15 to 24 141692 -0.7494 0.226804
14 to 23 141893 -0.0563 0.477547
13 to 22 141621 -0.9942 0.160053
12 to 21 142288 1.3058 0.904183
11 to 20 141877 -0.1115 0.455617
10 to 19 142008 0.3402 0.633163
9 to 18 141527 -1.3184 0.093688
8 to 17 142002 0.3196 0.625346
7 to 16 141695 -0.7391 0.229933
6 to 15 141362 -1.8873 0.029557
5 to 14 142205 1.0196 0.846029
4 to 13 141422 -1.6804 0.046435
3 to 12 141719 -0.6563 0.255812
2 to 11 141728 -0.6253 0.265895
1 to 10 141508 -1.3839 0.083195
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-19_15:31
Bits used No. missing words z-score p-value
28 to 32 141740 -0.5740 0.282984
27 to 31 142263 1.1989 0.884713
26 to 30 141884 -0.0859 0.465787
25 to 29 142119 0.7107 0.761379
24 to 28 141998 0.3006 0.618131
23 to 27 141787 -0.4147 0.339189
22 to 26 141862 -0.1604 0.436267
21 to 25 141511 -1.3503 0.088465
20 to 24 141599 -1.0520 0.146408
19 to 23 141481 -1.4520 0.073256
18 to 22 142072 0.5514 0.709328
17 to 21 141936 0.0904 0.536018
16 to 20 142149 0.8124 0.791731
15 to 19 142061 0.5141 0.696421
14 to 18 142103 0.6565 0.744252
13 to 17 141848 -0.2079 0.417654
12 to 16 142242 1.1277 0.870276
11 to 15 142023 0.3853 0.650001
10 to 14 141668 -0.8181 0.206659
9 to 13 141833 -0.2587 0.397916
8 to 12 142180 0.9175 0.820566
7 to 11 141887 -0.0757 0.469831
6 to 10 142154 0.8294 0.796558
5 to 9 141585 -1.0994 0.135792
4 to 8 142068 0.5379 0.704665
3 to 7 141706 -0.6893 0.245332
2 to 6 142078 0.5718 0.716259
1 to 5 141690 -0.7435 0.228592
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-19_15:31
Bits used No. missing words z-score p-value
31 to 32 141639 -0.7974 0.212600
30 to 31 142362 1.3353 0.909113
29 to 30 142426 1.5241 0.936258
28 to 29 141942 0.0964 0.538387
27 to 28 141833 -0.2252 0.410927
26 to 27 141872 -0.1101 0.456158
25 to 26 141459 -1.3284 0.092022
24 to 25 141836 -0.2163 0.414372
23 to 24 142141 0.6834 0.752821
22 to 23 141461 -1.3225 0.093000
21 to 22 141693 -0.6381 0.261691
20 to 21 141998 0.2616 0.603171
19 to 20 142146 0.6981 0.757456
18 to 19 141749 -0.4729 0.318125
17 to 18 141974 0.1908 0.575646
16 to 17 142474 1.6657 0.952113
15 to 16 142135 0.6657 0.747196
14 to 15 141891 -0.0541 0.478439
13 to 14 141868 -0.1219 0.451482
12 to 13 141229 -2.0069 0.022382
11 to 12 141949 0.1170 0.546578
10 to 11 142126 0.6391 0.738636
9 to 10 142339 1.2675 0.897505
8 to 9 142063 0.4533 0.674835
7 to 8 141900 -0.0275 0.489022
6 to 7 142397 1.4386 0.924862
5 to 6 141924 0.0433 0.517259
4 to 5 141613 -0.8741 0.191024
3 to 4 142121 0.6244 0.733816
2 to 3 142242 0.9813 0.836784
1 to 2 142369 1.3560 0.912444
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-19_15:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2401.27 -1.396 0.081316
Test results for specific bytes for dh-ranFile-2018-06-19_15:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2466.89 -0.468 0.319819
2 to 9 2493.90 -0.086 0.465629
3 to 10 2604.62 1.479 0.930495
4 to 11 2511.76 0.166 0.566033
5 to 12 2476.77 -0.328 0.371277
6 to 13 2408.34 -1.296 0.097453
7 to 14 2494.18 -0.082 0.467194
8 to 15 2534.01 0.481 0.684756
9 to 16 2520.08 0.284 0.611770
10 to 17 2404.78 -1.347 0.089049
11 to 18 2500.37 0.005 0.502083
12 to 19 2504.60 0.065 0.525957
13 to 20 2501.51 0.021 0.508535
14 to 21 2581.80 1.157 0.876316
15 to 22 2590.05 1.273 0.898578
16 to 23 2448.86 -0.723 0.234756
17 to 24 2442.34 -0.815 0.207396
18 to 25 2403.68 -1.362 0.086563
19 to 26 2523.89 0.338 0.632260
20 to 27 2520.61 0.291 0.614660
21 to 28 2478.53 -0.304 0.380720
22 to 29 2482.80 -0.243 0.403881
23 to 30 2397.26 -1.453 0.073111
24 to 31 2519.13 0.271 0.606649
25 to 32 2406.96 -1.316 0.094119
CDPARK for dh-ranFile-2018-06-19_15:31: 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
3528 0.2283 0.590298
3522 -0.0457 0.481790
3530 0.3196 0.625377
3470 -2.4201 0.007758
3528 0.2283 0.590298
3532 0.4110 0.659449
3508 -0.6849 0.246694
3511 -0.5479 0.291865
3484 -1.7808 0.037471
3522 -0.0457 0.481790
Square side=100, avg. no. parked=3513.50 sample std.=19.95
p-value of the KSTEST for those 10 p-values: 0.232390
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-19_15:31
0.4518,0.7342,0.8654,0.0476,0.7289,0.8742,0.5464,0.3855,0.5575,0.3542,
The KS test for those 10 p-values: 0.698809
The 3DSPHERES test for dh-ranFile-2018-06-19_15:31
sample no r^3 equiv. uni.
1 0.843 0.027722
2 25.621 0.574308
3 83.961 0.939110
4 1.050 0.034390
5 44.824 0.775554
6 45.950 0.783822
7 63.537 0.879716
8 53.474 0.831775
9 7.916 0.231931
10 3.102 0.098230
11 208.582 0.999044
12 13.655 0.365651
13 38.667 0.724430
14 1.830 0.059166
15 18.198 0.454790
16 2.170 0.069788
17 40.281 0.738857
18 19.168 0.472149
19 110.464 0.974831
20 23.104 0.537042
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.355367
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-19_15:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 0.9 -1.6 -1.1 -0.1 -0.9
-0.7 -2.0 -1.1 -0.4 -1.4 -1.5
2.8 0.2 0.0 0.3 0.4 -1.2
-1.2 3.3 0.6 0.1 -0.8 0.4
-0.5 -0.7 -1.9 0.7 2.6 -0.3
0.5 0.2 0.0 -0.4 0.8 -1.9
-0.5 -0.4 -1.2 -0.1 0.9 -1.0
-0.1
Chi-square with 42 degrees of freedom:58.572933
z-score=1.808255, p-value=0.953934
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-19_15:31
Test no p-value
1 0.264413
2 0.468320
3 0.076270
4 0.886325
5 0.576500
6 0.362715
7 0.034747
8 0.360357
9 0.338644
10 0.179342
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.181532
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-19_15:31:
(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 66805 0.29 66640 0.01
3 25000.00 24738 2.75 24912 0.31
4 6666.67 6795 2.47 6736 0.72
5 1388.89 1376 0.12 1442 2.03
6 238.10 226 0.61 235 0.04
7 34.72 54 10.71 32 0.21
8 4.96 5 0.00 2 1.77
p=0.99051 p=0.46794
Number of rngs required: 688558, p-value: 0.571
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-19_15:31
No. of wins: Observed Expected
98837 98585.9
z-score= 1.123, pvalue=0.86933
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66782 66666.7 0.200 0.200
2 37581 37654.3 0.143 0.342
3 27158 26954.7 1.533 1.875
4 19241 19313.5 0.272 2.147
5 13777 13851.4 0.400 2.547
6 9857 9943.5 0.753 3.300
7 6956 7145.0 5.001 8.301
8 5247 5139.1 2.267 10.567
9 3672 3699.9 0.210 10.777
10 2694 2666.3 0.288 11.065
11 1928 1923.3 0.011 11.077
12 1441 1388.7 1.967 13.043
13 998 1003.7 0.033 13.076
14 725 726.1 0.002 13.077
15 559 525.8 2.092 15.169
16 368 381.2 0.454 15.623
17 278 276.5 0.008 15.631
18 199 200.8 0.017 15.647
19 135 146.0 0.827 16.474
20 116 106.2 0.901 17.375
21 288 287.1 0.003 17.378
Chisq= 17.38 for 20 degrees of freedom, p= 0.37168
SUMMARY of craptest
p-value for no. of wins: 0.869335
p-value for throws/game: 0.371680
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-19_15:31
No. of wins: Observed Expected
98308 98585.9
z-score=-1.243, pvalue=0.10698
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66454 66666.7 0.678 0.678
2 37558 37654.3 0.246 0.925
3 26960 26954.7 0.001 0.926
4 19332 19313.5 0.018 0.944
5 13735 13851.4 0.979 1.922
6 10119 9943.5 3.096 5.018
7 7245 7145.0 1.399 6.417
8 5194 5139.1 0.587 7.004
9 3715 3699.9 0.062 7.066
10 2693 2666.3 0.267 7.333
11 1861 1923.3 2.020 9.353
12 1449 1388.7 2.615 11.968
13 1087 1003.7 6.911 18.879
14 703 726.1 0.737 19.616
15 534 525.8 0.127 19.743
16 371 381.2 0.270 20.013
17 267 276.5 0.329 20.342
18 201 200.8 0.000 20.342
19 133 146.0 1.155 21.497
20 115 106.2 0.727 22.224
21 274 287.1 0.599 22.823
Chisq= 22.82 for 20 degrees of freedom, p= 0.70243
SUMMARY of craptest
p-value for no. of wins: 0.106981
p-value for throws/game: 0.702427
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0078,0.0224,0.0277,0.0296,0.0315,0.0344,0.0347,0.0375,0.0393,0.0464,
0.0466,0.0476,0.0587,0.0592,0.0598,0.0698,0.0729,0.0731,0.0733,0.0763,
0.0783,0.0813,0.0832,0.0866,0.0885,0.0890,0.0920,0.0930,0.0937,0.0941,
0.0943,0.0965,0.0975,0.0982,0.0996,0.1070,0.1275,0.1358,0.1416,0.1441,
0.1464,0.1568,0.1601,0.1690,0.1694,0.1793,0.1795,0.1815,0.1910,0.2059,
0.2067,0.2074,0.2126,0.2176,0.2268,0.2286,0.2289,0.2299,0.2319,0.2320,
0.2324,0.2348,0.2453,0.2467,0.2558,0.2603,0.2617,0.2644,0.2659,0.2708,
0.2830,0.2919,0.3181,0.3198,0.3274,0.3318,0.3386,0.3392,0.3396,0.3488,
0.3542,0.3554,0.3604,0.3627,0.3651,0.3657,0.3674,0.3713,0.3717,0.3807,
0.3855,0.3896,0.3974,0.3976,0.3979,0.4019,0.4039,0.4109,0.4137,0.4144,
0.4177,0.4189,0.4211,0.4345,0.4363,0.4426,0.4482,0.4504,0.4515,0.4518,
0.4548,0.4556,0.4562,0.4656,0.4658,0.4672,0.4679,0.4683,0.4693,0.4698,
0.4721,0.4748,0.4775,0.4784,0.4795,0.4818,0.4818,0.4876,0.4890,0.5021,
0.5085,0.5170,0.5173,0.5193,0.5260,0.5360,0.5370,0.5384,0.5399,0.5464,
0.5466,0.5575,0.5581,0.5628,0.5660,0.5699,0.5708,0.5736,0.5743,0.5756,
0.5765,0.5903,0.5903,0.6032,0.6066,0.6118,0.6147,0.6181,0.6189,0.6189,
0.6217,0.6222,0.6253,0.6254,0.6310,0.6323,0.6332,0.6407,0.6456,0.6500,
0.6551,0.6594,0.6643,0.6740,0.6748,0.6751,0.6848,0.6850,0.6860,0.6916,
0.6959,0.6964,0.6988,0.7024,0.7044,0.7047,0.7093,0.7126,0.7146,0.7163,
0.7225,0.7244,0.7289,0.7338,0.7342,0.7386,0.7389,0.7443,0.7472,0.7473,
0.7482,0.7505,0.7528,0.7575,0.7614,0.7756,0.7766,0.7838,0.7917,0.7920,
0.7966,0.7982,0.8011,0.8137,0.8206,0.8318,0.8351,0.8364,0.8368,0.8402,
0.8412,0.8460,0.8489,0.8565,0.8611,0.8654,0.8678,0.8682,0.8683,0.8693,
0.8703,0.8735,0.8742,0.8756,0.8763,0.8783,0.8797,0.8847,0.8863,0.8900,
0.8973,0.8975,0.8986,0.8993,0.9042,0.9091,0.9124,0.9171,0.9186,0.9248,
0.9249,0.9253,0.9305,0.9363,0.9375,0.9391,0.9399,0.9441,0.9473,0.9512,
0.9521,0.9539,0.9603,0.9661,0.9748,0.9905,0.9914,0.9914,0.9990,
Overall p-value after applying KStest on 269 p-values = 0.385338
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.