RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-06_04:31
(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 16.5759 0.516565
2 to 25 15.71 18.8115 0.660544
3 to 26 15.63 28.9152 0.964684
4 to 27 15.81 13.9446 0.328982
5 to 28 16.02 8.4358 0.043680
6 to 29 15.89 12.9413 0.259896
7 to 30 15.90 15.8603 0.466242
8 to 31 15.57 22.7834 0.843566
9 to 32 15.59 15.6988 0.454724
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.977680
Tough bday spacings test for dh-ranFile-2018-07-06_04:31: 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 38 68 96 107 74 51 35 14 3 3
(O-E)^2/E 0.4 0.1 0.4 0.0 0.9 0.2 0.0 0.9 0.1 2.0 0.3
Birthday Spacings: Sum(O-E)^2/E= 5.187, p= 0.122
RESULTS OF GCD FOR dh-ranFile-2018-07-06_04:31
Euclid's algorithm:
p-value, steps to gcd: 0.572369
p-value, dist. of gcd's: 0.070551
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-06_04:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.875 0.222 0.177 0.098 0.477 0.980 0.604 0.419
Bits 8 to 15---> 0.243 0.881 0.100 0.792 0.608 0.256 0.944 0.697
Bits 16 to 23---> 0.246 0.662 0.895 0.400 0.835 0.437 0.932 0.773
Bits 24 to 31---> 0.509 0.963 0.137 0.041 0.171 0.621 0.293 0.426
KS test for the above 32 p values: 0.109
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-06_04:31,
p-values for 5 runs: 0.6321, 0.2093, 0.5940, 0.6304, 0.8837
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-06_04:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 215 211.4 0.061 0.061
r= 29 5145 5134.0 0.024 0.084
r= 30 23000 23103.0 0.460 0.544
r= 31 11640 11551.5 0.678 1.222
chi-square = 1.222 with df = 3; p-value = 0.252
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-06_04:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 243 211.4 4.718 4.718
r= 30 5049 5134.0 1.408 6.125
r= 31 23110 23103.0 0.002 6.127
r= 32 11598 11551.5 0.187 6.314
chi-square = 6.314 with df = 3; p-value = 0.903
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-06_04:31
b-rank test for bits 1 to 8, p=0.88788
b-rank test for bits 2 to 9, p=0.43537
b-rank test for bits 3 to 10, p=0.29945
b-rank test for bits 4 to 11, p=0.84725
b-rank test for bits 5 to 12, p=0.66966
b-rank test for bits 6 to 13, p=0.25885
b-rank test for bits 7 to 14, p=0.67450
b-rank test for bits 8 to 15, p=0.91231
b-rank test for bits 9 to 16, p=0.46544
b-rank test for bits 10 to 17, p=0.85716
b-rank test for bits 11 to 18, p=0.63992
b-rank test for bits 12 to 19, p=0.87842
b-rank test for bits 13 to 20, p=0.55147
b-rank test for bits 14 to 21, p=0.73303
b-rank test for bits 15 to 22, p=0.55451
b-rank test for bits 16 to 23, p=0.31767
b-rank test for bits 17 to 24, p=0.60238
b-rank test for bits 18 to 25, p=0.66498
b-rank test for bits 19 to 26, p=0.05141
b-rank test for bits 20 to 27, p=0.55656
b-rank test for bits 21 to 28, p=0.93598
b-rank test for bits 22 to 29, p=0.33111
b-rank test for bits 23 to 30, p=0.11611
b-rank test for bits 24 to 31, p=0.12492
b-rank test for bits 25 to 32, p=0.96899
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 = 0.356940
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-06_04:31
(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 142439 1.24 0.892058
2 142352 1.03 0.849496
3 142192 0.66 0.745516
4 142299 0.91 0.818706
5 141929 0.05 0.518328
6 141968 0.14 0.554516
7 141916 0.02 0.506217
8 142300 0.91 0.819321
9 141582 -0.76 0.222198
10 141994 0.20 0.578410
11 141872 -0.09 0.465249
12 141982 0.17 0.567412
13 141685 -0.52 0.300092
14 142450 1.26 0.896750
15 142348 1.02 0.847302
16 141294 -1.44 0.075261
17 142222 0.73 0.767469
18 142089 0.42 0.662681
19 142496 1.37 0.914770
20 141573 -0.79 0.215987
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-06_04:31
Bits used No. missing words z-score p-value
23 to 32 142342 1.4920 0.932146
22 to 31 142293 1.3230 0.907082
21 to 30 142161 0.8678 0.807256
20 to 29 141915 0.0196 0.507800
19 to 28 142312 1.3885 0.917510
18 to 27 141991 0.2816 0.610883
17 to 26 141924 0.0506 0.520172
16 to 25 142269 1.2402 0.892557
15 to 24 142093 0.6333 0.736746
14 to 23 142298 1.3402 0.909917
13 to 22 141815 -0.3253 0.372486
12 to 21 141873 -0.1253 0.450153
11 to 20 141948 0.1333 0.553040
10 to 19 142114 0.7058 0.759831
9 to 18 142055 0.5023 0.692275
8 to 17 141842 -0.2322 0.408202
7 to 16 141685 -0.7736 0.219598
6 to 15 141467 -1.5253 0.063595
5 to 14 141558 -1.2115 0.112855
4 to 13 141974 0.2230 0.588232
3 to 12 141848 -0.2115 0.416255
2 to 11 141548 -1.2460 0.106389
1 to 10 142128 0.7540 0.774586
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-06_04:31
Bits used No. missing words z-score p-value
28 to 32 142091 0.6158 0.730997
27 to 31 142382 1.6023 0.945452
26 to 30 142144 0.7955 0.786836
25 to 29 141975 0.2226 0.588081
24 to 28 141959 0.1684 0.566855
23 to 27 141960 0.1718 0.568188
22 to 26 141924 0.0497 0.519831
21 to 25 142077 0.5684 0.715109
20 to 24 141887 -0.0757 0.469831
19 to 23 141635 -0.9299 0.176203
18 to 22 141832 -0.2621 0.396609
17 to 21 141391 -1.7571 0.039455
16 to 20 141913 0.0124 0.504963
15 to 19 142692 2.6531 0.996012
14 to 18 141890 -0.0655 0.473878
13 to 17 141973 0.2158 0.585440
12 to 16 141837 -0.2452 0.403156
11 to 15 141985 0.2565 0.601221
10 to 14 142009 0.3379 0.632267
9 to 13 141876 -0.1130 0.455022
8 to 12 142169 0.8802 0.810635
7 to 11 141952 0.1446 0.557504
6 to 10 141925 0.0531 0.521181
5 to 9 141703 -0.6994 0.242144
4 to 8 141992 0.2802 0.610352
3 to 7 141367 -1.8384 0.033001
2 to 6 142409 1.6938 0.954848
1 to 5 142017 0.3650 0.642438
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-06_04:31
Bits used No. missing words z-score p-value
31 to 32 141725 -0.5437 0.293308
30 to 31 142190 0.8279 0.796146
29 to 30 142149 0.7070 0.760214
28 to 29 141367 -1.5998 0.054822
27 to 28 141862 -0.1396 0.444482
26 to 27 142121 0.6244 0.733816
25 to 26 142387 1.4091 0.920591
24 to 25 141505 -1.1927 0.116491
23 to 24 141972 0.1849 0.573333
22 to 23 141971 0.1819 0.572176
21 to 22 141305 -1.7827 0.037319
20 to 21 141653 -0.7561 0.224784
19 to 20 141965 0.1642 0.565220
18 to 19 141997 0.2586 0.602033
17 to 18 141594 -0.9302 0.176140
16 to 17 142056 0.4327 0.667367
15 to 16 141106 -2.3697 0.008901
14 to 15 141951 0.1229 0.548915
13 to 14 142000 0.2675 0.605444
12 to 13 142108 0.5860 0.721078
11 to 12 142013 0.3058 0.620126
10 to 11 142381 1.3914 0.917941
9 to 10 141689 -0.6499 0.257865
8 to 9 141500 -1.2075 0.113627
7 to 8 141451 -1.3520 0.088187
6 to 7 141935 0.0757 0.530180
5 to 6 142404 1.4592 0.927745
4 to 5 142261 1.0374 0.850219
3 to 4 142140 0.6804 0.751888
2 to 3 141841 -0.2016 0.420129
1 to 2 142443 1.5742 0.942285
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-06_04:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2404.84 -1.346 0.089182
Test results for specific bytes for dh-ranFile-2018-07-06_04:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2349.00 -2.135 0.016364
2 to 9 2523.29 0.329 0.629067
3 to 10 2523.07 0.326 0.627895
4 to 11 2495.11 -0.069 0.472459
5 to 12 2529.23 0.413 0.660321
6 to 13 2553.24 0.753 0.774236
7 to 14 2474.04 -0.367 0.356756
8 to 15 2346.43 -2.172 0.014936
9 to 16 2531.04 0.439 0.669682
10 to 17 2455.75 -0.626 0.265710
11 to 18 2508.35 0.118 0.547005
12 to 19 2530.66 0.434 0.667701
13 to 20 2426.89 -1.034 0.150572
14 to 21 2417.42 -1.168 0.121424
15 to 22 2507.98 0.113 0.544937
16 to 23 2504.74 0.067 0.526704
17 to 24 2446.91 -0.751 0.226395
18 to 25 2529.93 0.423 0.663976
19 to 26 2454.19 -0.648 0.258550
20 to 27 2604.34 1.476 0.929973
21 to 28 2529.09 0.411 0.659614
22 to 29 2502.42 0.034 0.513661
23 to 30 2362.86 -1.939 0.026225
24 to 31 2509.21 0.130 0.551811
25 to 32 2407.97 -1.301 0.096549
CDPARK for dh-ranFile-2018-07-06_04:31: 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
3522 -0.0457 0.481790
3519 -0.1826 0.427537
3519 -0.1826 0.427537
3496 -1.2329 0.108811
3538 0.6849 0.753306
3535 0.5479 0.708135
3541 0.8219 0.794438
3521 -0.0913 0.463617
3508 -0.6849 0.246694
3516 -0.3196 0.374623
Square side=100, avg. no. parked=3521.50 sample std.=13.08
p-value of the KSTEST for those 10 p-values: 0.574472
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-06_04:31
0.5642,0.1638,0.4849,0.9636,0.2749,0.4694,0.3839,0.9855,0.0127,0.1834,
The KS test for those 10 p-values: 0.507027
The 3DSPHERES test for dh-ranFile-2018-07-06_04:31
sample no r^3 equiv. uni.
1 0.212 0.007043
2 9.717 0.276667
3 2.408 0.077133
4 51.476 0.820193
5 21.304 0.508416
6 67.373 0.894154
7 4.516 0.139755
8 16.650 0.425925
9 16.059 0.414516
10 27.816 0.604339
11 1.240 0.040506
12 21.947 0.518849
13 11.388 0.315875
14 2.537 0.081091
15 21.071 0.504591
16 21.745 0.515597
17 1.750 0.056678
18 62.553 0.875705
19 45.261 0.778805
20 30.917 0.643192
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.312219
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-06_04:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -0.3 -0.4 -1.6 0.4 0.1
-0.4 -0.9 -0.5 -0.2 -0.2 0.9
0.0 1.5 -0.1 -0.0 -0.3 0.8
0.8 -0.7 -0.3 -0.3 -0.5 -0.5
-0.3 1.3 -1.2 -2.0 1.1 -0.5
-0.6 0.6 0.8 1.7 -1.2 0.4
0.5 0.8 0.1 -0.7 1.6 0.0
-0.1
Chi-square with 42 degrees of freedom:28.950205
z-score=-1.423849, p-value=0.062917
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-06_04:31
Test no p-value
1 0.112250
2 0.000356
3 0.189638
4 0.567663
5 0.695355
6 0.401050
7 0.095514
8 0.085887
9 0.973080
10 0.020733
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.016267
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-06_04:31:
(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 66578 0.12 66623 0.03
3 25000.00 24903 0.38 25048 0.09
4 6666.67 6768 1.54 6696 0.13
5 1388.89 1457 3.34 1367 0.35
6 238.10 247 0.33 228 0.43
7 34.72 44 2.48 33 0.09
8 4.96 2 1.77 4 0.19
p=0.87341 p=0.02800
Number of rngs required: 688653, p-value: 0.613
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-06_04:31
No. of wins: Observed Expected
98455 98585.9
z-score=-0.585, pvalue=0.27918
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66634 66666.7 0.016 0.016
2 37670 37654.3 0.007 0.023
3 26814 26954.7 0.735 0.757
4 19393 19313.5 0.328 1.085
5 13956 13851.4 0.790 1.874
6 9907 9943.5 0.134 2.009
7 7149 7145.0 0.002 2.011
8 5236 5139.1 1.828 3.839
9 3696 3699.9 0.004 3.843
10 2663 2666.3 0.004 3.847
11 1934 1923.3 0.059 3.906
12 1322 1388.7 3.207 7.114
13 1023 1003.7 0.371 7.484
14 755 726.1 1.147 8.631
15 501 525.8 1.173 9.804
16 373 381.2 0.174 9.979
17 275 276.5 0.009 9.987
18 185 200.8 1.248 11.235
19 129 146.0 1.976 13.211
20 99 106.2 0.490 13.701
21 286 287.1 0.004 13.705
Chisq= 13.71 for 20 degrees of freedom, p= 0.15489
SUMMARY of craptest
p-value for no. of wins: 0.279181
p-value for throws/game: 0.154891
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-06_04:31
No. of wins: Observed Expected
98300 98585.9
z-score=-1.279, pvalue=0.10053
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66596 66666.7 0.075 0.075
2 37734 37654.3 0.169 0.244
3 27124 26954.7 1.063 1.306
4 19301 19313.5 0.008 1.315
5 13865 13851.4 0.013 1.328
6 9912 9943.5 0.100 1.428
7 7055 7145.0 1.134 2.562
8 5038 5139.1 1.988 4.550
9 3771 3699.9 1.368 5.918
10 2662 2666.3 0.007 5.925
11 1855 1923.3 2.427 8.352
12 1447 1388.7 2.444 10.796
13 1026 1003.7 0.495 11.291
14 733 726.1 0.065 11.356
15 500 525.8 1.269 12.625
16 376 381.2 0.070 12.695
17 258 276.5 1.243 13.938
18 211 200.8 0.515 14.453
19 127 146.0 2.469 16.921
20 110 106.2 0.135 17.056
21 299 287.1 0.492 17.548
Chisq= 17.55 for 20 degrees of freedom, p= 0.38287
SUMMARY of craptest
p-value for no. of wins: 0.100532
p-value for throws/game: 0.382869
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0004,0.0070,0.0089,0.0127,0.0149,0.0163,0.0164,0.0207,0.0262,0.0280,
0.0330,0.0373,0.0395,0.0405,0.0408,0.0437,0.0514,0.0548,0.0567,0.0629,
0.0636,0.0706,0.0753,0.0771,0.0811,0.0859,0.0882,0.0892,0.0955,0.0965,
0.0977,0.0995,0.1005,0.1064,0.1088,0.1093,0.1122,0.1129,0.1136,0.1161,
0.1165,0.1214,0.1217,0.1249,0.1375,0.1398,0.1506,0.1549,0.1638,0.1707,
0.1761,0.1762,0.1767,0.1834,0.1896,0.2093,0.2160,0.2196,0.2219,0.2222,
0.2248,0.2264,0.2421,0.2430,0.2455,0.2467,0.2521,0.2563,0.2579,0.2585,
0.2589,0.2599,0.2657,0.2749,0.2767,0.2792,0.2930,0.2933,0.2995,0.3001,
0.3122,0.3159,0.3177,0.3290,0.3311,0.3568,0.3569,0.3725,0.3746,0.3829,
0.3839,0.3966,0.4004,0.4010,0.4032,0.4082,0.4145,0.4163,0.4189,0.4201,
0.4259,0.4261,0.4275,0.4275,0.4354,0.4375,0.4445,0.4502,0.4547,0.4550,
0.4636,0.4652,0.4654,0.4662,0.4694,0.4698,0.4725,0.4739,0.4773,0.4818,
0.4849,0.5046,0.5050,0.5062,0.5070,0.5078,0.5084,0.5095,0.5137,0.5156,
0.5166,0.5183,0.5188,0.5198,0.5202,0.5212,0.5267,0.5302,0.5449,0.5470,
0.5489,0.5515,0.5518,0.5530,0.5545,0.5545,0.5566,0.5575,0.5642,0.5652,
0.5669,0.5674,0.5677,0.5682,0.5722,0.5724,0.5733,0.5745,0.5784,0.5854,
0.5881,0.5882,0.5940,0.6012,0.6020,0.6024,0.6042,0.6043,0.6054,0.6084,
0.6104,0.6109,0.6132,0.6201,0.6206,0.6279,0.6291,0.6304,0.6321,0.6323,
0.6399,0.6424,0.6432,0.6596,0.6603,0.6605,0.6622,0.6627,0.6640,0.6650,
0.6674,0.6677,0.6697,0.6697,0.6745,0.6923,0.6954,0.6974,0.7081,0.7151,
0.7211,0.7310,0.7330,0.7338,0.7367,0.7455,0.7519,0.7533,0.7598,0.7602,
0.7675,0.7727,0.7742,0.7746,0.7788,0.7868,0.7919,0.7944,0.7961,0.8073,
0.8106,0.8187,0.8193,0.8202,0.8346,0.8436,0.8472,0.8473,0.8495,0.8502,
0.8572,0.8734,0.8754,0.8757,0.8784,0.8812,0.8837,0.8879,0.8921,0.8926,
0.8942,0.8946,0.8967,0.9027,0.9071,0.9099,0.9123,0.9148,0.9175,0.9179,
0.9206,0.9277,0.9300,0.9321,0.9321,0.9360,0.9423,0.9436,0.9455,0.9548,
0.9632,0.9636,0.9647,0.9690,0.9731,0.9777,0.9799,0.9855,0.9960,
Overall p-value after applying KStest on 269 p-values = 0.413613
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.