RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-03_13:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.62 22.0485 0.817139
2 to 25 15.66 14.8215 0.391664
3 to 26 15.58 18.3851 0.635054
4 to 27 15.85 20.5781 0.754269
5 to 28 15.90 11.6402 0.178585
6 to 29 15.77 8.0414 0.034347
7 to 30 15.80 13.1870 0.276422
8 to 31 16.05 13.6607 0.309042
9 to 32 15.96 14.0488 0.336355
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.606157
Tough bday spacings test for dh-ranFile-2018-07-03_13:31: 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 27 88 87 105 66 47 37 20 6 6
(O-E)^2/E 0.4 2.5 3.0 1.2 0.5 1.9 0.5 1.8 1.8 0.1 0.9
Birthday Spacings: Sum(O-E)^2/E= 14.461, p= 0.847
RESULTS OF GCD FOR dh-ranFile-2018-07-03_13:31
Euclid's algorithm:
p-value, steps to gcd: 0.174656
p-value, dist. of gcd's: 0.194898
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-03_13:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.462 0.227 0.791 0.615 0.390 0.503 0.935 0.221
Bits 8 to 15---> 0.127 0.819 0.968 0.996 0.838 0.997 0.829 0.117
Bits 16 to 23---> 0.822 0.324 0.204 0.132 0.587 0.610 0.477 0.764
Bits 24 to 31---> 0.316 0.599 0.318 0.395 0.040 0.632 0.658 0.377
KS test for the above 32 p values: 0.358
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-03_13:31,
p-values for 5 runs: 0.1248, 0.9406, 0.4423, 0.6873, 0.6724
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-03_13:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 205 211.4 0.195 0.195
r= 29 5064 5134.0 0.955 1.150
r= 30 23083 23103.0 0.017 1.167
r= 31 11648 11551.5 0.806 1.973
chi-square = 1.973 with df = 3; p-value = 0.422
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-03_13:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 240 211.4 3.864 3.864
r= 30 5144 5134.0 0.019 3.883
r= 31 23207 23103.0 0.468 4.351
r= 32 11409 11551.5 1.758 6.110
chi-square = 6.110 with df = 3; p-value = 0.894
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-03_13:31
b-rank test for bits 1 to 8, p=0.17988
b-rank test for bits 2 to 9, p=0.00278
b-rank test for bits 3 to 10, p=0.04982
b-rank test for bits 4 to 11, p=0.89179
b-rank test for bits 5 to 12, p=0.89758
b-rank test for bits 6 to 13, p=0.61723
b-rank test for bits 7 to 14, p=0.86535
b-rank test for bits 8 to 15, p=0.57257
b-rank test for bits 9 to 16, p=0.70843
b-rank test for bits 10 to 17, p=0.59334
b-rank test for bits 11 to 18, p=0.93967
b-rank test for bits 12 to 19, p=0.66659
b-rank test for bits 13 to 20, p=0.50189
b-rank test for bits 14 to 21, p=0.92054
b-rank test for bits 15 to 22, p=0.99332
b-rank test for bits 16 to 23, p=0.27760
b-rank test for bits 17 to 24, p=0.01270
b-rank test for bits 18 to 25, p=0.48841
b-rank test for bits 19 to 26, p=0.88316
b-rank test for bits 20 to 27, p=0.00283
b-rank test for bits 21 to 28, p=0.26196
b-rank test for bits 22 to 29, p=0.72365
b-rank test for bits 23 to 30, p=0.51986
b-rank test for bits 24 to 31, p=0.44356
b-rank test for bits 25 to 32, p=0.46266
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 = 0.235877
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-03_13:31
(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 142962 2.46 0.993044
2 142155 0.57 0.717015
3 141271 -1.49 0.067925
4 141493 -0.97 0.165343
5 142322 0.96 0.832523
6 141279 -1.47 0.070411
7 142064 0.36 0.641092
8 142276 0.86 0.804196
9 141598 -0.73 0.233489
10 141807 -0.24 0.405518
11 141635 -0.64 0.260775
12 142397 1.14 0.872735
13 142205 0.69 0.755160
14 141765 -0.34 0.367976
15 141880 -0.07 0.472683
16 141701 -0.49 0.313217
17 142398 1.14 0.873222
18 141400 -1.19 0.117019
19 141856 -0.12 0.450419
20 141948 0.09 0.535996
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-03_13:31
Bits used No. missing words z-score p-value
23 to 32 142433 1.8058 0.964522
22 to 31 142270 1.2437 0.893193
21 to 30 141945 0.1230 0.548947
20 to 29 142290 1.3127 0.905350
19 to 28 142463 1.9092 0.971882
18 to 27 141470 -1.5149 0.064895
17 to 26 141875 -0.1184 0.452884
16 to 25 141764 -0.5011 0.308137
15 to 24 141689 -0.7598 0.223699
14 to 23 141644 -0.9149 0.180114
13 to 22 141695 -0.7391 0.229933
12 to 21 142212 1.0437 0.851686
11 to 20 141924 0.0506 0.520172
10 to 19 141499 -1.4149 0.078544
9 to 18 142045 0.4678 0.680046
8 to 17 142267 1.2333 0.891276
7 to 16 142323 1.4264 0.923131
6 to 15 142133 0.7713 0.779728
5 to 14 141726 -0.6322 0.263637
4 to 13 141874 -0.1218 0.451518
3 to 12 142107 0.6816 0.752261
2 to 11 142480 1.9678 0.975456
1 to 10 141836 -0.2529 0.400187
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-03_13:31
Bits used No. missing words z-score p-value
28 to 32 141924 0.0497 0.519831
27 to 31 142053 0.4870 0.686877
26 to 30 141917 0.0260 0.510371
25 to 29 141963 0.1819 0.572182
24 to 28 141696 -0.7232 0.234793
23 to 27 141836 -0.2486 0.401844
22 to 26 141199 -2.4079 0.008022
21 to 25 142273 1.2328 0.891171
20 to 24 141599 -1.0520 0.146408
19 to 23 141657 -0.8554 0.196177
18 to 22 142150 0.8158 0.792702
17 to 21 142211 1.0226 0.846754
16 to 20 142027 0.3989 0.655010
15 to 19 141864 -0.1537 0.438939
14 to 18 142267 1.2124 0.887328
13 to 17 141716 -0.6554 0.256119
12 to 16 142087 0.6023 0.726503
11 to 15 141478 -1.4621 0.071852
10 to 14 142238 1.1141 0.867390
9 to 13 142222 1.0599 0.855405
8 to 12 142546 2.1582 0.984544
7 to 11 142254 1.1684 0.878672
6 to 10 142173 0.8938 0.814285
5 to 9 142145 0.7989 0.787820
4 to 8 141312 -2.0248 0.021442
3 to 7 141466 -1.5028 0.066444
2 to 6 141909 -0.0011 0.499554
1 to 5 141110 -2.7096 0.003368
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-03_13:31
Bits used No. missing words z-score p-value
31 to 32 142028 0.3501 0.636853
30 to 31 141542 -1.0836 0.139278
29 to 30 142043 0.3943 0.653323
28 to 29 142009 0.2940 0.615626
27 to 28 142165 0.7542 0.774632
26 to 27 141866 -0.1278 0.449147
25 to 26 142632 2.1318 0.983487
24 to 25 141695 -0.6322 0.263614
23 to 24 141889 -0.0600 0.476090
22 to 23 141772 -0.4051 0.342701
21 to 22 141291 -1.8240 0.034077
20 to 21 141883 -0.0777 0.469045
19 to 20 142037 0.3766 0.646767
18 to 19 141556 -1.0423 0.148643
17 to 18 141891 -0.0541 0.478439
16 to 17 141858 -0.1514 0.439824
15 to 16 142112 0.5978 0.725029
14 to 15 142601 2.0403 0.979341
13 to 14 142215 0.9017 0.816387
12 to 13 141934 0.0728 0.529007
11 to 12 142110 0.5919 0.723057
10 to 11 142628 2.1200 0.982996
9 to 10 141979 0.2055 0.581416
8 to 9 142131 0.6539 0.743410
7 to 8 141812 -0.2871 0.387014
6 to 7 142339 1.2675 0.897505
5 to 6 141815 -0.2783 0.390407
4 to 5 141886 -0.0688 0.472566
3 to 4 141610 -0.8830 0.188624
2 to 3 141127 -2.3078 0.010506
1 to 2 142402 1.4533 0.926930
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-03_13:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2513.01 0.184 0.573006
Test results for specific bytes for dh-ranFile-2018-07-03_13:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2469.63 -0.429 0.333781
2 to 9 2445.13 -0.776 0.218882
3 to 10 2516.91 0.239 0.594523
4 to 11 2436.82 -0.894 0.185786
5 to 12 2548.01 0.679 0.751423
6 to 13 2477.30 -0.321 0.374091
7 to 14 2599.49 1.407 0.920286
8 to 15 2453.59 -0.656 0.255807
9 to 16 2471.42 -0.404 0.343044
10 to 17 2496.56 -0.049 0.480599
11 to 18 2445.99 -0.764 0.222486
12 to 19 2409.71 -1.277 0.100813
13 to 20 2494.45 -0.078 0.468717
14 to 21 2587.96 1.244 0.893237
15 to 22 2444.67 -0.783 0.216950
16 to 23 2505.37 0.076 0.530268
17 to 24 2490.12 -0.140 0.444431
18 to 25 2454.84 -0.639 0.261531
19 to 26 2470.44 -0.418 0.337983
20 to 27 2447.47 -0.743 0.228769
21 to 28 2394.59 -1.491 0.068017
22 to 29 2473.94 -0.369 0.356245
23 to 30 2394.64 -1.490 0.068101
24 to 31 2386.24 -1.609 0.053830
25 to 32 2528.98 0.410 0.659057
CDPARK for dh-ranFile-2018-07-03_13:31: 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
3536 0.5936 0.723613
3524 0.0457 0.518210
3493 -1.3699 0.085365
3507 -0.7306 0.232514
3532 0.4110 0.659449
3540 0.7763 0.781201
3517 -0.2740 0.392053
3539 0.7306 0.767486
3538 0.6849 0.753306
3520 -0.1370 0.445521
Square side=100, avg. no. parked=3524.60 sample std.=14.82
p-value of the KSTEST for those 10 p-values: 0.622900
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-03_13:31
0.5325,0.6415,0.3519,0.9743,0.2490,0.5948,0.5905,0.8227,0.8099,0.8765,
The KS test for those 10 p-values: 0.188140
The 3DSPHERES test for dh-ranFile-2018-07-03_13:31
sample no r^3 equiv. uni.
1 72.613 0.911116
2 18.330 0.457193
3 21.410 0.510154
4 53.169 0.830056
5 16.322 0.419607
6 30.697 0.640571
7 26.574 0.587612
8 9.968 0.282695
9 61.044 0.869295
10 11.888 0.327169
11 2.675 0.085311
12 29.864 0.630447
13 63.387 0.879114
14 87.320 0.945561
15 67.789 0.895611
16 9.192 0.263916
17 54.123 0.835377
18 83.891 0.938969
19 7.657 0.225260
20 6.201 0.186726
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.243547
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-03_13:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 -1.6 1.1 -0.4 1.1 -0.1
-0.5 1.1 0.5 0.5 0.2 -0.0
-0.2 -0.4 2.1 0.0 0.0 -0.4
-0.4 -0.5 0.2 -0.2 -0.8 -0.4
0.1 -1.4 0.9 -0.1 0.7 -1.0
0.9 0.4 -1.7 0.9 -1.2 0.2
0.7 -1.3 -1.2 -1.8 1.6 0.0
0.8
Chi-square with 42 degrees of freedom:33.873026
z-score=-0.886726, p-value=0.190153
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-03_13:31
Test no p-value
1 0.012442
2 0.260931
3 0.245684
4 0.023968
5 0.520643
6 0.113872
7 0.694225
8 0.195086
9 0.210447
10 0.010388
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.001936
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-03_13:31:
(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 66309 1.92 66575 0.13
3 25000.00 25328 4.30 25075 0.23
4 6666.67 6724 0.49 6735 0.70
5 1388.89 1362 0.52 1333 2.25
6 238.10 242 0.06 233 0.11
7 34.72 30 0.64 39 0.53
8 4.96 4 0.19 9 3.29
p=0.77108 p=0.69970
Number of rngs required: 688335, p-value: 0.469
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-03_13:31
No. of wins: Observed Expected
98637 98585.9
z-score= 0.229, pvalue=0.59046
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66585 66666.7 0.100 0.100
2 38040 37654.3 3.950 4.050
3 26715 26954.7 2.132 6.183
4 19419 19313.5 0.577 6.759
5 13594 13851.4 4.784 11.543
6 10024 9943.5 0.651 12.194
7 7216 7145.0 0.705 12.899
8 5219 5139.1 1.243 14.142
9 3666 3699.9 0.310 14.452
10 2686 2666.3 0.146 14.598
11 1912 1923.3 0.067 14.665
12 1364 1388.7 0.441 15.105
13 1017 1003.7 0.176 15.281
14 688 726.1 2.003 17.285
15 510 525.8 0.477 17.762
16 362 381.2 0.962 18.724
17 278 276.5 0.008 18.731
18 182 200.8 1.765 20.497
19 142 146.0 0.109 20.606
20 103 106.2 0.097 20.703
21 278 287.1 0.289 20.992
Chisq= 20.99 for 20 degrees of freedom, p= 0.60242
SUMMARY of craptest
p-value for no. of wins: 0.590462
p-value for throws/game: 0.602416
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-03_13:31
No. of wins: Observed Expected
98234 98585.9
z-score=-1.574, pvalue=0.05778
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66174 66666.7 3.641 3.641
2 37854 37654.3 1.059 4.700
3 26947 26954.7 0.002 4.702
4 19276 19313.5 0.073 4.775
5 13962 13851.4 0.883 5.657
6 9940 9943.5 0.001 5.659
7 7152 7145.0 0.007 5.665
8 5224 5139.1 1.404 7.069
9 3665 3699.9 0.329 7.397
10 2665 2666.3 0.001 7.398
11 1937 1923.3 0.097 7.495
12 1398 1388.7 0.062 7.557
13 1029 1003.7 0.637 8.194
14 748 726.1 0.658 8.852
15 589 525.8 7.587 16.439
16 394 381.2 0.433 16.873
17 303 276.5 2.532 19.404
18 193 200.8 0.305 19.710
19 157 146.0 0.831 20.541
20 94 106.2 1.405 21.946
21 299 287.1 0.492 22.438
Chisq= 22.44 for 20 degrees of freedom, p= 0.68276
SUMMARY of craptest
p-value for no. of wins: 0.057776
p-value for throws/game: 0.682765
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0019,0.0028,0.0028,0.0034,0.0080,0.0104,0.0105,0.0124,0.0127,0.0214,
0.0240,0.0341,0.0343,0.0398,0.0498,0.0538,0.0578,0.0649,0.0664,0.0679,
0.0680,0.0681,0.0704,0.0719,0.0785,0.0853,0.0854,0.1008,0.1139,0.1169,
0.1170,0.1248,0.1272,0.1322,0.1393,0.1464,0.1486,0.1653,0.1747,0.1786,
0.1799,0.1801,0.1858,0.1867,0.1881,0.1886,0.1902,0.1949,0.1951,0.1962,
0.2042,0.2104,0.2170,0.2189,0.2211,0.2225,0.2237,0.2253,0.2269,0.2288,
0.2299,0.2325,0.2335,0.2348,0.2359,0.2435,0.2457,0.2490,0.2558,0.2561,
0.2608,0.2609,0.2615,0.2620,0.2636,0.2636,0.2639,0.2764,0.2776,0.2827,
0.3081,0.3090,0.3132,0.3155,0.3180,0.3241,0.3272,0.3338,0.3364,0.3380,
0.3427,0.3430,0.3519,0.3562,0.3582,0.3680,0.3741,0.3769,0.3870,0.3904,
0.3904,0.3917,0.3921,0.3948,0.4002,0.4018,0.4055,0.4196,0.4219,0.4389,
0.4398,0.4423,0.4436,0.4444,0.4455,0.4491,0.4504,0.4515,0.4529,0.4572,
0.4621,0.4627,0.4687,0.4688,0.4690,0.4726,0.4727,0.4761,0.4772,0.4784,
0.4806,0.4884,0.4996,0.5019,0.5034,0.5102,0.5104,0.5182,0.5198,0.5199,
0.5202,0.5206,0.5290,0.5303,0.5325,0.5360,0.5489,0.5722,0.5726,0.5730,
0.5814,0.5875,0.5876,0.5905,0.5905,0.5933,0.5945,0.5948,0.5988,0.6024,
0.6062,0.6103,0.6148,0.6156,0.6172,0.6229,0.6304,0.6320,0.6351,0.6369,
0.6406,0.6411,0.6415,0.6468,0.6533,0.6550,0.6580,0.6591,0.6594,0.6666,
0.6724,0.6800,0.6828,0.6869,0.6873,0.6942,0.6997,0.7084,0.7170,0.7231,
0.7236,0.7236,0.7250,0.7265,0.7434,0.7514,0.7523,0.7533,0.7543,0.7552,
0.7638,0.7675,0.7711,0.7746,0.7797,0.7812,0.7878,0.7906,0.7927,0.8042,
0.8099,0.8143,0.8164,0.8171,0.8194,0.8223,0.8227,0.8291,0.8301,0.8325,
0.8354,0.8384,0.8468,0.8470,0.8517,0.8554,0.8653,0.8674,0.8693,0.8727,
0.8732,0.8765,0.8787,0.8791,0.8832,0.8873,0.8912,0.8913,0.8918,0.8932,
0.8932,0.8936,0.8956,0.8975,0.8976,0.9054,0.9111,0.9203,0.9205,0.9231,
0.9269,0.9350,0.9390,0.9397,0.9406,0.9456,0.9645,0.9678,0.9719,0.9743,
0.9755,0.9793,0.9830,0.9835,0.9845,0.9930,0.9933,0.9956,0.9974,
Overall p-value after applying KStest on 269 p-values = 0.819792
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.