RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-23_08:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.70 14.3453 0.357470
2 to 25 15.91 23.8877 0.877482
3 to 26 15.99 34.3863 0.992518
4 to 27 15.69 19.9966 0.725599
5 to 28 15.41 20.4872 0.749928
6 to 29 15.51 18.2666 0.627788
7 to 30 15.65 14.3505 0.357848
8 to 31 15.88 14.6457 0.379014
9 to 32 15.76 14.3571 0.358321
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.312466
Tough bday spacings test for dh-ranFile-2018-06-23_08:31: 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 33 69 101 103 76 60 22 19 2 4
(O-E)^2/E 0.4 0.4 0.2 0.1 0.3 0.1 1.2 2.0 1.1 3.2 0.0
Birthday Spacings: Sum(O-E)^2/E= 9.025, p= 0.470
RESULTS OF GCD FOR dh-ranFile-2018-06-23_08:31
Euclid's algorithm:
p-value, steps to gcd: 0.001083
p-value, dist. of gcd's: 0.246800
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-23_08:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.128 0.667 0.893 0.033 0.571 0.611 0.576 0.815
Bits 8 to 15---> 0.909 0.647 0.864 0.913 0.208 0.347 0.818 0.521
Bits 16 to 23---> 0.660 0.246 0.994 0.524 0.048 0.654 0.306 0.279
Bits 24 to 31---> 0.674 0.528 0.144 0.704 0.727 0.108 0.120 0.450
KS test for the above 32 p values: 0.132
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-23_08:31,
p-values for 5 runs: 0.8440, 0.2156, 0.2217, 0.3631, 0.6097
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-23_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 212 211.4 0.002 0.002
r= 29 5095 5134.0 0.296 0.298
r= 30 23119 23103.0 0.011 0.309
r= 31 11574 11551.5 0.044 0.353
chi-square = 0.353 with df = 3; p-value = 0.050
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-23_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 226 211.4 1.006 1.006
r= 30 5130 5134.0 0.003 1.009
r= 31 23133 23103.0 0.039 1.048
r= 32 11511 11551.5 0.142 1.190
chi-square = 1.190 with df = 3; p-value = 0.245
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-23_08:31
b-rank test for bits 1 to 8, p=0.06594
b-rank test for bits 2 to 9, p=0.81687
b-rank test for bits 3 to 10, p=0.00961
b-rank test for bits 4 to 11, p=0.91741
b-rank test for bits 5 to 12, p=0.72580
b-rank test for bits 6 to 13, p=0.01503
b-rank test for bits 7 to 14, p=0.30372
b-rank test for bits 8 to 15, p=0.21383
b-rank test for bits 9 to 16, p=0.82422
b-rank test for bits 10 to 17, p=0.15301
b-rank test for bits 11 to 18, p=0.13591
b-rank test for bits 12 to 19, p=0.87663
b-rank test for bits 13 to 20, p=0.31583
b-rank test for bits 14 to 21, p=0.48540
b-rank test for bits 15 to 22, p=0.24066
b-rank test for bits 16 to 23, p=0.53458
b-rank test for bits 17 to 24, p=0.41603
b-rank test for bits 18 to 25, p=0.87404
b-rank test for bits 19 to 26, p=0.18065
b-rank test for bits 20 to 27, p=0.93483
b-rank test for bits 21 to 28, p=0.90786
b-rank test for bits 22 to 29, p=0.31125
b-rank test for bits 23 to 30, p=0.67056
b-rank test for bits 24 to 31, p=0.60944
b-rank test for bits 25 to 32, p=0.94409
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 = 0.662949
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-23_08:31
(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 141876 -0.08 0.468964
2 141559 -0.82 0.206528
3 141914 0.01 0.504353
4 141432 -1.12 0.132370
5 142238 0.77 0.778733
6 141978 0.16 0.563734
7 141792 -0.27 0.391990
8 140965 -2.21 0.013679
9 141919 0.02 0.509013
10 141834 -0.18 0.430145
11 142150 0.56 0.713049
12 142345 1.02 0.845642
13 142473 1.32 0.906078
14 142089 0.42 0.662681
15 141968 0.14 0.554516
16 142146 0.55 0.709857
17 142328 0.98 0.836013
18 141720 -0.44 0.329114
19 142404 1.16 0.876113
20 141603 -0.72 0.237081
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-23_08:31
Bits used No. missing words z-score p-value
23 to 32 141965 0.1920 0.576115
22 to 31 142349 1.5161 0.935253
21 to 30 141541 -1.2701 0.102024
20 to 29 142200 1.0023 0.841903
19 to 28 142165 0.8816 0.811009
18 to 27 142113 0.7023 0.758757
17 to 26 141925 0.0540 0.521546
16 to 25 142132 0.7678 0.778705
15 to 24 141732 -0.6115 0.270440
14 to 23 142211 1.0402 0.850886
13 to 22 142040 0.4506 0.673856
12 to 21 141797 -0.3873 0.349251
11 to 20 141526 -1.3218 0.093113
10 to 19 141511 -1.3736 0.084790
9 to 18 141629 -0.9667 0.166858
8 to 17 141182 -2.5080 0.006070
7 to 16 141853 -0.1942 0.422994
6 to 15 141998 0.3058 0.620106
5 to 14 141969 0.2058 0.581510
4 to 13 141954 0.1540 0.561209
3 to 12 142373 1.5989 0.945074
2 to 11 142382 1.6299 0.948438
1 to 10 142416 1.7471 0.959693
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-23_08:31
Bits used No. missing words z-score p-value
28 to 32 142881 3.2938 0.999506
27 to 31 141954 0.1514 0.560179
26 to 30 141928 0.0633 0.525232
25 to 29 141621 -0.9774 0.164188
24 to 28 142344 1.4735 0.929686
23 to 27 142146 0.8023 0.788802
22 to 26 142011 0.3446 0.634819
21 to 25 141501 -1.3842 0.083153
20 to 24 141856 -0.1808 0.428270
19 to 23 141846 -0.2147 0.415009
18 to 22 141470 -1.4893 0.068210
17 to 21 141882 -0.0926 0.463093
16 to 20 141522 -1.3130 0.094594
15 to 19 142315 1.3752 0.915458
14 to 18 141767 -0.4825 0.314734
13 to 17 142418 1.7243 0.957674
12 to 16 142234 1.1006 0.864459
11 to 15 141862 -0.1604 0.436267
10 to 14 142531 2.1074 0.982457
9 to 13 141595 -1.0655 0.143319
8 to 12 142058 0.5040 0.692857
7 to 11 141609 -1.0181 0.154323
6 to 10 141952 0.1446 0.557504
5 to 9 141493 -1.4113 0.079080
4 to 8 141752 -0.5333 0.296905
3 to 7 141708 -0.6825 0.247470
2 to 6 141576 -1.1299 0.129252
1 to 5 142127 0.7379 0.769702
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-23_08:31
Bits used No. missing words z-score p-value
31 to 32 142092 0.5388 0.705005
30 to 31 142276 1.0816 0.860290
29 to 30 141885 -0.0718 0.471393
28 to 29 142380 1.3884 0.917493
27 to 28 141957 0.1406 0.555915
26 to 27 141443 -1.3756 0.084472
25 to 26 142306 1.1701 0.879023
24 to 25 142070 0.4740 0.682233
23 to 24 141289 -1.8299 0.033634
22 to 23 141556 -1.0423 0.148643
21 to 22 141912 0.0079 0.503142
20 to 21 142689 2.2999 0.989273
19 to 20 141816 -0.2753 0.391539
18 to 19 141800 -0.3225 0.373534
17 to 18 141808 -0.2989 0.382505
16 to 17 141827 -0.2429 0.404056
15 to 16 142282 1.0993 0.864186
14 to 15 141984 0.2203 0.587168
13 to 14 142397 1.4386 0.924862
12 to 13 141987 0.2291 0.590610
11 to 12 141847 -0.1839 0.427060
10 to 11 141785 -0.3668 0.356901
9 to 10 142171 0.7719 0.779910
8 to 9 141778 -0.3874 0.349229
7 to 8 142144 0.6922 0.755607
6 to 7 140882 -3.0305 0.001221
5 to 6 142281 1.0964 0.863542
4 to 5 141880 -0.0865 0.465527
3 to 4 141943 0.0993 0.539559
2 to 3 142086 0.5212 0.698869
1 to 2 141415 -1.4582 0.072393
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-23_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2545.74 0.647 0.741130
Test results for specific bytes for dh-ranFile-2018-06-23_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2352.00 -2.093 0.018173
2 to 9 2479.25 -0.293 0.384577
3 to 10 2560.90 0.861 0.805445
4 to 11 2460.57 -0.558 0.288530
5 to 12 2507.11 0.101 0.540070
6 to 13 2553.14 0.751 0.773810
7 to 14 2628.11 1.812 0.964983
8 to 15 2429.24 -1.001 0.158479
9 to 16 2524.16 0.342 0.633714
10 to 17 2482.58 -0.246 0.402681
11 to 18 2494.49 -0.078 0.468931
12 to 19 2448.73 -0.725 0.234188
13 to 20 2588.10 1.246 0.893602
14 to 21 2466.16 -0.479 0.316139
15 to 22 2495.11 -0.069 0.472405
16 to 23 2451.87 -0.681 0.248031
17 to 24 2431.90 -0.963 0.167747
18 to 25 2478.49 -0.304 0.380515
19 to 26 2543.37 0.613 0.730164
20 to 27 2544.90 0.635 0.737295
21 to 28 2545.87 0.649 0.741717
22 to 29 2484.42 -0.220 0.412782
23 to 30 2644.76 2.047 0.979679
24 to 31 2498.79 -0.017 0.493188
25 to 32 2543.93 0.621 0.732809
CDPARK for dh-ranFile-2018-06-23_08:31: 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
3547 1.0959 0.863437
3569 2.1005 0.982156
3536 0.5936 0.723613
3528 0.2283 0.590298
3516 -0.3196 0.374623
3505 -0.8219 0.205562
3516 -0.3196 0.374623
3498 -1.1416 0.126820
3560 1.6895 0.954438
3518 -0.2283 0.409702
Square side=100, avg. no. parked=3529.30 sample std.=22.20
p-value of the KSTEST for those 10 p-values: 0.679177
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-23_08:31
0.2898,0.3405,0.3421,0.4270,0.4928,0.4100,0.1294,0.9398,0.8173,0.2702,
The KS test for those 10 p-values: 0.443489
The 3DSPHERES test for dh-ranFile-2018-06-23_08:31
sample no r^3 equiv. uni.
1 4.630 0.143021
2 1.539 0.050013
3 28.760 0.616590
4 90.450 0.950954
5 16.854 0.429812
6 3.471 0.109247
7 39.014 0.727597
8 36.253 0.701334
9 1.505 0.048933
10 3.442 0.108410
11 0.210 0.006981
12 51.101 0.817929
13 114.814 0.978228
14 77.864 0.925390
15 6.181 0.186198
16 4.450 0.137854
17 72.243 0.910014
18 8.627 0.249925
19 44.642 0.774194
20 27.148 0.595427
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.261736
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-23_08:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 0.5 1.5 0.9 -0.6 -1.7
1.1 -0.2 -1.9 1.1 -1.3 -0.2
0.1 0.2 -1.8 0.7 -0.2 -1.6
0.3 1.2 0.2 0.7 0.4 0.9
1.2 -0.6 0.3 0.5 -0.9 0.3
-0.3 0.6 0.1 0.7 -0.5 0.6
-0.9 1.5 -0.4 0.4 1.6 1.0
-1.1
Chi-square with 42 degrees of freedom:36.034326
z-score=-0.650908, p-value=0.270651
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-23_08:31
Test no p-value
1 0.014512
2 0.366619
3 0.726684
4 0.576902
5 0.310549
6 0.206385
7 0.458170
8 0.244795
9 0.756829
10 0.060536
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.282266
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-23_08:31:
(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 66675 0.00 66933 1.06
3 25000.00 24943 0.13 24750 2.50
4 6666.67 6715 0.35 6674 0.01
5 1388.89 1384 0.02 1358 0.69
6 238.10 240 0.02 244 0.15
7 34.72 36 0.05 37 0.15
8 4.96 6 0.22 3 0.77
p=0.00738 p=0.49773
Number of rngs required: 688322, p-value: 0.463
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-23_08:31
No. of wins: Observed Expected
98670 98585.9
z-score= 0.376, pvalue=0.64666
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66605 66666.7 0.057 0.057
2 37632 37654.3 0.013 0.070
3 26982 26954.7 0.028 0.098
4 19524 19313.5 2.295 2.393
5 13865 13851.4 0.013 2.406
6 9826 9943.5 1.389 3.796
7 7132 7145.0 0.024 3.819
8 5063 5139.1 1.126 4.946
9 3611 3699.9 2.134 7.080
10 2695 2666.3 0.309 7.389
11 1917 1923.3 0.021 7.410
12 1417 1388.7 0.575 7.985
13 974 1003.7 0.880 8.865
14 736 726.1 0.134 8.998
15 564 525.8 2.770 11.768
16 393 381.2 0.368 12.137
17 302 276.5 2.344 14.481
18 195 200.8 0.169 14.650
19 162 146.0 1.757 16.407
20 102 106.2 0.167 16.574
21 303 287.1 0.879 17.453
Chisq= 17.45 for 20 degrees of freedom, p= 0.37663
SUMMARY of craptest
p-value for no. of wins: 0.646664
p-value for throws/game: 0.376628
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-23_08:31
No. of wins: Observed Expected
98611 98585.9
z-score= 0.112, pvalue=0.54477
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66583 66666.7 0.105 0.105
2 37571 37654.3 0.184 0.289
3 26995 26954.7 0.060 0.350
4 19410 19313.5 0.483 0.832
5 13904 13851.4 0.200 1.032
6 9952 9943.5 0.007 1.039
7 7074 7145.0 0.706 1.745
8 5214 5139.1 1.092 2.837
9 3700 3699.9 0.000 2.837
10 2670 2666.3 0.005 2.842
11 1855 1923.3 2.427 5.270
12 1389 1388.7 0.000 5.270
13 982 1003.7 0.470 5.740
14 715 726.1 0.171 5.911
15 567 525.8 3.222 9.133
16 367 381.2 0.525 9.659
17 287 276.5 0.396 10.054
18 205 200.8 0.087 10.141
19 165 146.0 2.477 12.618
20 113 106.2 0.433 13.051
21 282 287.1 0.091 13.142
Chisq= 13.14 for 20 degrees of freedom, p= 0.12880
SUMMARY of craptest
p-value for no. of wins: 0.544766
p-value for throws/game: 0.128803
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0011,0.0012,0.0061,0.0070,0.0074,0.0096,0.0137,0.0145,0.0150,0.0182,
0.0326,0.0336,0.0482,0.0489,0.0500,0.0502,0.0605,0.0659,0.0682,0.0724,
0.0791,0.0832,0.0845,0.0848,0.0931,0.0946,0.1020,0.1083,0.1084,0.1092,
0.1198,0.1268,0.1277,0.1288,0.1293,0.1294,0.1320,0.1324,0.1359,0.1379,
0.1430,0.1433,0.1438,0.1486,0.1530,0.1543,0.1585,0.1642,0.1669,0.1677,
0.1807,0.1862,0.2056,0.2064,0.2065,0.2079,0.2138,0.2156,0.2217,0.2342,
0.2371,0.2407,0.2446,0.2448,0.2461,0.2468,0.2475,0.2480,0.2499,0.2617,
0.2702,0.2704,0.2707,0.2791,0.2823,0.2885,0.2898,0.2969,0.3037,0.3058,
0.3105,0.3113,0.3125,0.3147,0.3158,0.3161,0.3291,0.3405,0.3421,0.3473,
0.3492,0.3493,0.3569,0.3575,0.3578,0.3583,0.3631,0.3666,0.3735,0.3746,
0.3746,0.3766,0.3790,0.3805,0.3825,0.3846,0.3915,0.3920,0.4027,0.4041,
0.4097,0.4100,0.4128,0.4150,0.4160,0.4230,0.4270,0.4271,0.4283,0.4298,
0.4301,0.4363,0.4435,0.4502,0.4582,0.4629,0.4631,0.4655,0.4689,0.4690,
0.4703,0.4714,0.4724,0.4854,0.4928,0.4932,0.4977,0.5031,0.5044,0.5090,
0.5207,0.5215,0.5243,0.5252,0.5278,0.5346,0.5396,0.5401,0.5448,0.5545,
0.5559,0.5575,0.5602,0.5612,0.5637,0.5707,0.5759,0.5761,0.5769,0.5815,
0.5872,0.5903,0.5906,0.5954,0.6094,0.6097,0.6107,0.6166,0.6201,0.6278,
0.6337,0.6348,0.6466,0.6467,0.6541,0.6601,0.6627,0.6629,0.6673,0.6706,
0.6739,0.6743,0.6792,0.6822,0.6929,0.6989,0.7013,0.7038,0.7050,0.7099,
0.7130,0.7236,0.7256,0.7258,0.7267,0.7272,0.7276,0.7302,0.7328,0.7373,
0.7411,0.7417,0.7499,0.7556,0.7568,0.7588,0.7697,0.7738,0.7742,0.7787,
0.7787,0.7799,0.7888,0.8054,0.8110,0.8154,0.8169,0.8173,0.8179,0.8179,
0.8242,0.8360,0.8419,0.8440,0.8456,0.8509,0.8603,0.8634,0.8635,0.8642,
0.8642,0.8645,0.8740,0.8761,0.8766,0.8775,0.8790,0.8926,0.8936,0.9061,
0.9079,0.9086,0.9100,0.9129,0.9155,0.9174,0.9175,0.9249,0.9254,0.9297,
0.9348,0.9353,0.9398,0.9441,0.9451,0.9484,0.9510,0.9544,0.9577,0.9597,
0.9650,0.9782,0.9797,0.9822,0.9825,0.9893,0.9925,0.9941,0.9995,
Overall p-value after applying KStest on 269 p-values = 0.993488
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.