RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-11_17:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.64 16.1067 0.483717
2 to 25 15.73 24.0841 0.882831
3 to 26 15.77 21.4022 0.791187
4 to 27 15.77 21.5870 0.798872
5 to 28 15.67 12.6083 0.238015
6 to 29 15.86 22.2010 0.822889
7 to 30 15.83 9.4611 0.075322
8 to 31 15.65 16.3881 0.503491
9 to 32 15.71 12.7104 0.244655
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.839894
Tough bday spacings test for dh-ranFile-2018-07-11_17:31: 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 12 34 66 100 97 85 53 28 14 6 5
(O-E)^2/E 0.9 0.2 0.7 0.1 0.0 0.6 0.0 0.1 0.1 0.1 0.2
Birthday Spacings: Sum(O-E)^2/E= 2.897, p= 0.016
RESULTS OF GCD FOR dh-ranFile-2018-07-11_17:31
Euclid's algorithm:
p-value, steps to gcd: 0.588169
p-value, dist. of gcd's: 0.455608
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-11_17:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.141 0.569 0.810 0.180 0.354 0.607 0.497 0.455
Bits 8 to 15---> 0.238 0.215 0.169 0.557 0.854 0.995 0.649 0.724
Bits 16 to 23---> 0.393 0.969 0.722 0.992 0.012 0.794 0.863 0.236
Bits 24 to 31---> 0.902 0.565 0.386 0.806 0.507 0.301 0.464 0.642
KS test for the above 32 p values: 0.491
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-11_17:31,
p-values for 5 runs: 0.3112, 0.7523, 0.5592, 0.5663, 0.2350
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-11_17:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 215 211.4 0.061 0.061
r= 29 5081 5134.0 0.547 0.608
r= 30 23252 23103.0 0.960 1.568
r= 31 11452 11551.5 0.857 2.426
chi-square = 2.426 with df = 3; p-value = 0.511
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-11_17:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 210 211.4 0.010 0.010
r= 30 5172 5134.0 0.281 0.291
r= 31 23050 23103.0 0.122 0.412
r= 32 11568 11551.5 0.024 0.436
chi-square = 0.436 with df = 3; p-value = 0.067
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-11_17:31
b-rank test for bits 1 to 8, p=0.82543
b-rank test for bits 2 to 9, p=0.19706
b-rank test for bits 3 to 10, p=0.64987
b-rank test for bits 4 to 11, p=0.33143
b-rank test for bits 5 to 12, p=0.79799
b-rank test for bits 6 to 13, p=0.16842
b-rank test for bits 7 to 14, p=0.28873
b-rank test for bits 8 to 15, p=0.91535
b-rank test for bits 9 to 16, p=0.22207
b-rank test for bits 10 to 17, p=0.31836
b-rank test for bits 11 to 18, p=0.24076
b-rank test for bits 12 to 19, p=0.66171
b-rank test for bits 13 to 20, p=0.61259
b-rank test for bits 14 to 21, p=0.91050
b-rank test for bits 15 to 22, p=0.57401
b-rank test for bits 16 to 23, p=0.27882
b-rank test for bits 17 to 24, p=0.84084
b-rank test for bits 18 to 25, p=0.23411
b-rank test for bits 19 to 26, p=0.60804
b-rank test for bits 20 to 27, p=0.84479
b-rank test for bits 21 to 28, p=0.78446
b-rank test for bits 22 to 29, p=0.53357
b-rank test for bits 23 to 30, p=0.84876
b-rank test for bits 24 to 31, p=0.87295
b-rank test for bits 25 to 32, p=0.87484
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 = 0.159141
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-11_17:31
(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 141531 -0.88 0.188362
2 142207 0.70 0.756626
3 141941 0.07 0.529493
4 142303 0.92 0.821159
5 141117 -1.85 0.032068
6 141603 -0.72 0.237081
7 141538 -0.87 0.192808
8 141851 -0.14 0.445798
9 141771 -0.32 0.373272
10 142077 0.39 0.652379
11 142398 1.14 0.873222
12 142648 1.73 0.957814
13 142061 0.35 0.638469
14 141572 -0.79 0.215303
15 141693 -0.51 0.306624
16 141657 -0.59 0.277744
17 141709 -0.47 0.319871
18 142482 1.34 0.909554
19 142578 1.56 0.940893
20 142153 0.57 0.715431
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-11_17:31
Bits used No. missing words z-score p-value
23 to 32 141931 0.0747 0.529783
22 to 31 142354 1.5333 0.937405
21 to 30 141401 -1.7529 0.039813
20 to 29 141580 -1.1356 0.128058
19 to 28 141501 -1.4080 0.079560
18 to 27 141638 -0.9356 0.174734
17 to 26 142535 2.1575 0.984516
16 to 25 142251 1.1782 0.880636
15 to 24 142254 1.1885 0.882685
14 to 23 142109 0.6885 0.754436
13 to 22 142228 1.0989 0.864086
12 to 21 141913 0.0127 0.505049
11 to 20 141870 -0.1356 0.446061
10 to 19 142015 0.3644 0.642213
9 to 18 142206 1.0230 0.846846
8 to 17 141991 0.2816 0.610883
7 to 16 141758 -0.5218 0.300895
6 to 15 141968 0.2023 0.580163
5 to 14 141937 0.0954 0.538007
4 to 13 142010 0.3471 0.635756
3 to 12 141680 -0.7908 0.214532
2 to 11 142270 1.2437 0.893193
1 to 10 141863 -0.1598 0.436536
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-11_17:31
Bits used No. missing words z-score p-value
28 to 32 142003 0.3175 0.624578
27 to 31 142081 0.5819 0.719694
26 to 30 141405 -1.7096 0.043671
25 to 29 141958 0.1650 0.565521
24 to 28 142005 0.3243 0.627147
23 to 27 141320 -1.9977 0.022873
22 to 26 141718 -0.6486 0.258306
21 to 25 141903 -0.0215 0.491440
20 to 24 142173 0.8938 0.814285
19 to 23 142353 1.5040 0.933705
18 to 22 141670 -0.8113 0.208600
17 to 21 141749 -0.5435 0.293396
16 to 20 141918 0.0294 0.511723
15 to 19 142109 0.6768 0.750749
14 to 18 142065 0.5277 0.701145
13 to 17 142475 1.9175 0.972414
12 to 16 141789 -0.4079 0.341674
11 to 15 142053 0.4870 0.686877
10 to 14 141828 -0.2757 0.391391
9 to 13 142312 1.3650 0.913871
8 to 12 141860 -0.1672 0.433598
7 to 11 142585 2.2904 0.989001
6 to 10 141963 0.1819 0.572182
5 to 9 142172 0.8904 0.813376
4 to 8 141702 -0.7028 0.241086
3 to 7 141764 -0.4926 0.311132
2 to 6 141512 -1.3469 0.089009
1 to 5 142578 2.2667 0.988295
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-11_17:31
Bits used No. missing words z-score p-value
31 to 32 141857 -0.1544 0.438661
30 to 31 141554 -1.0482 0.147280
29 to 30 142313 1.1908 0.883127
28 to 29 141749 -0.4729 0.318125
27 to 28 141858 -0.1514 0.439824
26 to 27 142484 1.6952 0.954980
25 to 26 141145 -2.2547 0.012077
24 to 25 142049 0.4120 0.659832
23 to 24 141937 0.0816 0.532527
22 to 23 141603 -0.9036 0.183096
21 to 22 141879 -0.0895 0.464355
20 to 21 142237 0.9666 0.833123
19 to 20 141699 -0.6204 0.267483
18 to 19 141514 -1.1662 0.121774
17 to 18 142029 0.3530 0.637959
16 to 17 142023 0.3353 0.631304
15 to 16 141715 -0.5732 0.283240
14 to 15 142003 0.2763 0.608846
13 to 14 141466 -1.3078 0.095478
12 to 13 142019 0.3235 0.626846
11 to 12 141824 -0.2517 0.400632
10 to 11 142464 1.6362 0.949101
9 to 10 142320 1.2114 0.887132
8 to 9 142086 0.5212 0.698869
7 to 8 141582 -0.9656 0.167128
6 to 7 141865 -0.1308 0.447980
5 to 6 142345 1.2852 0.900632
4 to 5 142109 0.5890 0.722068
3 to 4 142147 0.7011 0.758377
2 to 3 142096 0.5506 0.709063
1 to 2 142065 0.4592 0.676956
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-11_17:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2514.40 0.204 0.580681
Test results for specific bytes for dh-ranFile-2018-07-11_17:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2523.92 0.338 0.632447
2 to 9 2540.50 0.573 0.716594
3 to 10 2526.90 0.380 0.648201
4 to 11 2305.59 -2.749 0.002985
5 to 12 2588.44 1.251 0.894493
6 to 13 2392.84 -1.516 0.064823
7 to 14 2482.41 -0.249 0.401797
8 to 15 2568.18 0.964 0.832519
9 to 16 2483.76 -0.230 0.409188
10 to 17 2462.79 -0.526 0.299385
11 to 18 2441.84 -0.823 0.205379
12 to 19 2525.07 0.355 0.638519
13 to 20 2479.31 -0.293 0.384893
14 to 21 2453.37 -0.659 0.254820
15 to 22 2490.61 -0.133 0.447179
16 to 23 2420.28 -1.127 0.129789
17 to 24 2538.47 0.544 0.706818
18 to 25 2572.15 1.020 0.846222
19 to 26 2691.30 2.705 0.996588
20 to 27 2520.45 0.289 0.613777
21 to 28 2438.55 -0.869 0.192421
22 to 29 2510.01 0.142 0.556286
23 to 30 2511.89 0.168 0.566790
24 to 31 2436.66 -0.896 0.185201
25 to 32 2491.34 -0.122 0.451254
CDPARK for dh-ranFile-2018-07-11_17:31: 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
3483 -1.8265 0.033889
3531 0.3653 0.642555
3525 0.0913 0.536383
3516 -0.3196 0.374623
3536 0.5936 0.723613
3538 0.6849 0.753306
3518 -0.2283 0.409702
3535 0.5479 0.708135
3492 -1.4155 0.078457
3527 0.1826 0.572463
Square side=100, avg. no. parked=3520.10 sample std.=17.81
p-value of the KSTEST for those 10 p-values: 0.612442
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-11_17:31
0.3849,0.3555,0.4211,0.4987,0.5418,0.0798,0.0279,0.6803,0.3420,0.6926,
The KS test for those 10 p-values: 0.300702
The 3DSPHERES test for dh-ranFile-2018-07-11_17:31
sample no r^3 equiv. uni.
1 31.091 0.645259
2 26.023 0.579978
3 20.515 0.495317
4 41.697 0.750897
5 21.871 0.517617
6 45.985 0.784075
7 34.431 0.682631
8 8.928 0.257411
9 2.234 0.071765
10 16.984 0.432280
11 51.364 0.819519
12 5.246 0.160418
13 61.525 0.871374
14 0.989 0.032443
15 82.966 0.937056
16 2.997 0.095078
17 17.699 0.445653
18 38.375 0.721735
19 6.863 0.204494
20 0.111 0.003684
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.816218
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-11_17:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -1.2 1.1 -0.7 -0.1 1.2
1.5 0.8 0.7 -1.1 1.7 -0.4
-1.9 0.3 -0.0 0.7 1.1 -0.7
-0.6 0.5 0.7 -0.1 -1.9 1.0
1.7 -1.9 -0.6 -0.4 -0.8 -1.1
0.1 -0.3 -0.5 1.0 -0.1 -1.2
0.7 3.3 -1.6 -0.7 -0.6 0.0
-1.1
Chi-square with 42 degrees of freedom:51.988368
z-score=1.089820, p-value=0.861087
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-11_17:31
Test no p-value
1 0.045254
2 0.077235
3 0.187619
4 0.153121
5 0.818859
6 0.642212
7 0.240150
8 0.103929
9 0.657424
10 0.237358
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.049612
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-11_17:31:
(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 66519 0.33 66824 0.37
3 25000.00 25084 0.28 24898 0.42
4 6666.67 6717 0.38 6685 0.05
5 1388.89 1409 0.29 1323 3.13
6 238.10 226 0.61 234 0.07
7 34.72 40 0.80 29 0.94
8 4.96 4 0.19 6 0.22
p=0.17670 p=0.48089
Number of rngs required: 688657, p-value: 0.615
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-11_17:31
No. of wins: Observed Expected
98576 98585.9
z-score=-0.044, pvalue=0.48241
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66892 66666.7 0.762 0.762
2 37771 37654.3 0.362 1.123
3 26940 26954.7 0.008 1.131
4 19088 19313.5 2.632 3.763
5 13789 13851.4 0.281 4.045
6 9844 9943.5 0.997 5.041
7 7131 7145.0 0.028 5.069
8 5255 5139.1 2.615 7.684
9 3586 3699.9 3.504 11.188
10 2680 2666.3 0.070 11.258
11 1902 1923.3 0.237 11.495
12 1312 1388.7 4.241 15.735
13 1072 1003.7 4.646 20.381
14 770 726.1 2.649 23.030
15 540 525.8 0.382 23.412
16 345 381.2 3.429 26.840
17 291 276.5 0.756 27.597
18 213 200.8 0.737 28.334
19 157 146.0 0.831 29.165
20 113 106.2 0.433 29.599
21 309 287.1 1.668 31.267
Chisq= 31.27 for 20 degrees of freedom, p= 0.94824
SUMMARY of craptest
p-value for no. of wins: 0.482415
p-value for throws/game: 0.948237
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-11_17:31
No. of wins: Observed Expected
98081 98585.9
z-score=-2.258, pvalue=0.01197
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66209 66666.7 3.142 3.142
2 37346 37654.3 2.525 5.666
3 27143 26954.7 1.315 6.981
4 19353 19313.5 0.081 7.062
5 13865 13851.4 0.013 7.076
6 10109 9943.5 2.753 9.829
7 7336 7145.0 5.104 14.933
8 5211 5139.1 1.007 15.940
9 3745 3699.9 0.551 16.491
10 2673 2666.3 0.017 16.507
11 1977 1923.3 1.498 18.005
12 1371 1388.7 0.227 18.232
13 993 1003.7 0.114 18.346
14 735 726.1 0.108 18.454
15 530 525.8 0.033 18.487
16 354 381.2 1.934 20.421
17 305 276.5 2.929 23.350
18 205 200.8 0.087 23.437
19 157 146.0 0.831 24.268
20 98 106.2 0.635 24.904
21 285 287.1 0.016 24.919
Chisq= 24.92 for 20 degrees of freedom, p= 0.79546
SUMMARY of craptest
p-value for no. of wins: 0.011972
p-value for throws/game: 0.795455
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0030,0.0037,0.0119,0.0120,0.0121,0.0163,0.0229,0.0279,0.0321,0.0324,
0.0339,0.0398,0.0437,0.0453,0.0496,0.0648,0.0673,0.0718,0.0753,0.0772,
0.0785,0.0796,0.0798,0.0890,0.0951,0.0955,0.1039,0.1218,0.1281,0.1298,
0.1414,0.1473,0.1531,0.1591,0.1604,0.1671,0.1684,0.1690,0.1747,0.1767,
0.1803,0.1831,0.1852,0.1876,0.1884,0.1924,0.1928,0.1971,0.2045,0.2054,
0.2086,0.2145,0.2151,0.2153,0.2221,0.2341,0.2350,0.2356,0.2371,0.2374,
0.2380,0.2382,0.2401,0.2408,0.2411,0.2447,0.2548,0.2574,0.2583,0.2675,
0.2777,0.2788,0.2832,0.2887,0.2934,0.2994,0.3007,0.3007,0.3009,0.3066,
0.3111,0.3112,0.3181,0.3184,0.3199,0.3314,0.3417,0.3420,0.3536,0.3555,
0.3733,0.3746,0.3849,0.3849,0.3863,0.3914,0.3929,0.4006,0.4018,0.4092,
0.4097,0.4211,0.4323,0.4336,0.4365,0.4387,0.4398,0.4457,0.4458,0.4461,
0.4472,0.4480,0.4513,0.4548,0.4556,0.4637,0.4644,0.4809,0.4824,0.4837,
0.4914,0.4914,0.4953,0.4970,0.4987,0.5035,0.5050,0.5072,0.5112,0.5117,
0.5176,0.5295,0.5298,0.5325,0.5336,0.5364,0.5380,0.5418,0.5563,0.5567,
0.5592,0.5651,0.5655,0.5663,0.5668,0.5695,0.5722,0.5725,0.5740,0.5800,
0.5802,0.5807,0.5882,0.6065,0.6080,0.6088,0.6109,0.6124,0.6126,0.6138,
0.6150,0.6246,0.6268,0.6271,0.6313,0.6324,0.6358,0.6380,0.6385,0.6385,
0.6416,0.6422,0.6422,0.6426,0.6453,0.6482,0.6490,0.6499,0.6524,0.6574,
0.6598,0.6617,0.6770,0.6803,0.6826,0.6869,0.6926,0.6989,0.7011,0.7068,
0.7081,0.7091,0.7154,0.7166,0.7197,0.7217,0.7221,0.7223,0.7236,0.7239,
0.7507,0.7509,0.7523,0.7533,0.7544,0.7566,0.7584,0.7841,0.7845,0.7912,
0.7936,0.7955,0.7980,0.7989,0.8061,0.8100,0.8134,0.8143,0.8162,0.8189,
0.8195,0.8212,0.8229,0.8254,0.8325,0.8331,0.8399,0.8408,0.8448,0.8462,
0.8468,0.8488,0.8537,0.8611,0.8627,0.8641,0.8714,0.8729,0.8732,0.8748,
0.8806,0.8827,0.8828,0.8831,0.8871,0.8932,0.8945,0.9006,0.9018,0.9096,
0.9105,0.9139,0.9153,0.9337,0.9371,0.9374,0.9409,0.9482,0.9491,0.9550,
0.9578,0.9693,0.9724,0.9845,0.9883,0.9890,0.9923,0.9952,0.9966,
Overall p-value after applying KStest on 269 p-values = 0.567594
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.