RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-08_18:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.94 12.1079 0.206443
2 to 25 15.92 17.8541 0.601898
3 to 26 15.69 13.0480 0.267034
4 to 27 15.79 21.7777 0.806582
5 to 28 16.16 13.5687 0.302637
6 to 29 16.03 17.7569 0.595671
7 to 30 15.98 15.2672 0.423759
8 to 31 15.60 16.2511 0.493894
9 to 32 15.70 18.0233 0.612630
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.490866
Tough bday spacings test for dh-ranFile-2018-07-08_18:31: 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 2 35 57 98 101 89 57 32 17 6 6
(O-E)^2/E 5.6 0.1 3.6 0.0 0.1 1.5 0.5 0.2 0.3 0.1 0.9
Birthday Spacings: Sum(O-E)^2/E= 12.804, p= 0.765
RESULTS OF GCD FOR dh-ranFile-2018-07-08_18:31
Euclid's algorithm:
p-value, steps to gcd: 0.905129
p-value, dist. of gcd's: 0.611984
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-08_18:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.134 0.038 0.360 0.839 0.544 0.794 0.726 0.895
Bits 8 to 15---> 0.597 0.885 0.320 0.395 0.220 0.616 0.112 0.806
Bits 16 to 23---> 0.472 0.838 0.039 0.734 0.460 0.344 0.837 0.164
Bits 24 to 31---> 0.205 0.144 0.843 0.722 0.797 0.810 0.178 0.806
KS test for the above 32 p values: 0.521
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-08_18:31,
p-values for 5 runs: 0.7832, 0.2157, 0.9942, 0.9229, 0.5587
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-08_18:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 240 211.4 3.864 3.864
r= 29 5059 5134.0 1.096 4.960
r= 30 23232 23103.0 0.720 5.680
r= 31 11469 11551.5 0.590 6.269
chi-square = 6.269 with df = 3; p-value = 0.901
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-08_18:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 227 211.4 1.148 1.148
r= 30 5070 5134.0 0.798 1.947
r= 31 23217 23103.0 0.562 2.509
r= 32 11486 11551.5 0.372 2.880
chi-square = 2.880 with df = 3; p-value = 0.590
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-08_18:31
b-rank test for bits 1 to 8, p=0.21514
b-rank test for bits 2 to 9, p=0.41355
b-rank test for bits 3 to 10, p=0.92058
b-rank test for bits 4 to 11, p=0.22333
b-rank test for bits 5 to 12, p=0.29279
b-rank test for bits 6 to 13, p=0.02318
b-rank test for bits 7 to 14, p=0.03520
b-rank test for bits 8 to 15, p=0.23411
b-rank test for bits 9 to 16, p=0.52447
b-rank test for bits 10 to 17, p=0.41196
b-rank test for bits 11 to 18, p=0.19033
b-rank test for bits 12 to 19, p=0.98256
b-rank test for bits 13 to 20, p=0.18996
b-rank test for bits 14 to 21, p=0.23067
b-rank test for bits 15 to 22, p=0.43627
b-rank test for bits 16 to 23, p=0.99630
b-rank test for bits 17 to 24, p=0.28319
b-rank test for bits 18 to 25, p=0.04022
b-rank test for bits 19 to 26, p=0.00643
b-rank test for bits 20 to 27, p=0.72071
b-rank test for bits 21 to 28, p=0.29095
b-rank test for bits 22 to 29, p=0.74184
b-rank test for bits 23 to 30, p=0.25911
b-rank test for bits 24 to 31, p=0.34487
b-rank test for bits 25 to 32, p=0.57522
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 = 0.033210
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-08_18:31
(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 142018 0.25 0.600214
2 141989 0.19 0.573834
3 142106 0.46 0.677066
4 142179 0.63 0.735676
5 141494 -0.97 0.165924
6 141690 -0.51 0.304167
7 141189 -1.68 0.046186
8 141806 -0.24 0.404613
9 142226 0.74 0.770315
10 142289 0.89 0.812482
11 141611 -0.70 0.242891
12 142444 1.25 0.894209
13 141214 -1.62 0.052124
14 141786 -0.29 0.386614
15 141727 -0.43 0.335052
16 142135 0.53 0.700996
17 142213 0.71 0.760996
18 142397 1.14 0.872735
19 141970 0.14 0.556362
20 141911 0.00 0.501557
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-08_18:31
Bits used No. missing words z-score p-value
23 to 32 141675 -0.8080 0.209535
22 to 31 141455 -1.5667 0.058598
21 to 30 142029 0.4127 0.660070
20 to 29 142037 0.4402 0.670119
19 to 28 141451 -1.5804 0.057002
18 to 27 141868 -0.1425 0.443336
17 to 26 141859 -0.1736 0.431109
16 to 25 142100 0.6575 0.744565
15 to 24 141960 0.1747 0.569352
14 to 23 141505 -1.3942 0.081622
13 to 22 141696 -0.7356 0.230981
12 to 21 142199 0.9989 0.841069
11 to 20 142154 0.8437 0.800579
10 to 19 141816 -0.3218 0.373792
9 to 18 141777 -0.4563 0.324083
8 to 17 141933 0.0816 0.532526
7 to 16 142101 0.6609 0.745672
6 to 15 142052 0.4920 0.688628
5 to 14 142175 0.9161 0.820194
4 to 13 141994 0.2920 0.614844
3 to 12 141490 -1.4460 0.074093
2 to 11 141925 0.0540 0.521546
1 to 10 141198 -2.4529 0.007086
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-08_18:31
Bits used No. missing words z-score p-value
28 to 32 141628 -0.9537 0.170128
27 to 31 141802 -0.3638 0.357992
26 to 30 141991 0.2768 0.609051
25 to 29 142150 0.8158 0.792702
24 to 28 142174 0.8972 0.815190
23 to 27 141982 0.2463 0.597290
22 to 26 141513 -1.3435 0.089556
21 to 25 142119 0.7107 0.761379
20 to 24 141893 -0.0554 0.477928
19 to 23 141977 0.2294 0.590717
18 to 22 142018 0.3684 0.643702
17 to 21 142276 1.2429 0.893057
16 to 20 142249 1.1514 0.875221
15 to 19 142348 1.4870 0.931495
14 to 18 141972 0.2124 0.584118
13 to 17 141444 -1.5774 0.057353
12 to 16 141885 -0.0825 0.467135
11 to 15 142225 1.0701 0.857706
10 to 14 141913 0.0124 0.504963
9 to 13 141962 0.1785 0.570852
8 to 12 141861 -0.1638 0.434932
7 to 11 141509 -1.3571 0.087383
6 to 10 142057 0.5006 0.691665
5 to 9 142272 1.2294 0.890537
4 to 8 142172 0.8904 0.813376
3 to 7 141547 -1.2282 0.109679
2 to 6 142039 0.4396 0.669872
1 to 5 141693 -0.7333 0.231681
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-08_18:31
Bits used No. missing words z-score p-value
31 to 32 141682 -0.6706 0.251241
30 to 31 141948 0.1141 0.545409
29 to 30 141665 -0.7207 0.235536
28 to 29 142031 0.3589 0.640168
27 to 28 141945 0.1052 0.541900
26 to 27 142192 0.8338 0.797813
25 to 26 141822 -0.2576 0.398354
24 to 25 141985 0.2232 0.588316
23 to 24 142188 0.8220 0.794472
22 to 23 141795 -0.3373 0.367962
21 to 22 142116 0.6096 0.728952
20 to 21 141982 0.2144 0.584869
19 to 20 141927 0.0521 0.520785
18 to 19 142263 1.0433 0.851589
17 to 18 142538 1.8545 0.968165
16 to 17 142058 0.4386 0.669508
15 to 16 142220 0.9164 0.820280
14 to 15 141261 -1.9125 0.027907
13 to 14 141979 0.2055 0.581416
12 to 13 141859 -0.1485 0.440988
11 to 12 141698 -0.6234 0.266513
10 to 11 141554 -1.0482 0.147280
9 to 10 142013 0.3058 0.620126
8 to 9 141661 -0.7325 0.231921
7 to 8 141900 -0.0275 0.489022
6 to 7 142143 0.6893 0.754680
5 to 6 141946 0.1082 0.543070
4 to 5 141625 -0.8387 0.200810
3 to 4 142068 0.4681 0.680127
2 to 3 142041 0.3884 0.651143
1 to 2 142243 0.9843 0.837510
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-08_18:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2534.25 0.484 0.685921
Test results for specific bytes for dh-ranFile-2018-07-08_18:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2548.00 0.679 0.751372
2 to 9 2442.02 -0.820 0.206112
3 to 10 2462.56 -0.530 0.298218
4 to 11 2415.13 -1.200 0.115016
5 to 12 2514.46 0.204 0.581016
6 to 13 2633.84 1.893 0.970809
7 to 14 2587.25 1.234 0.891373
8 to 15 2566.39 0.939 0.826106
9 to 16 2549.77 0.704 0.759223
10 to 17 2418.09 -1.158 0.123368
11 to 18 2525.48 0.360 0.640719
12 to 19 2521.92 0.310 0.621728
13 to 20 2554.14 0.766 0.778057
14 to 21 2479.91 -0.284 0.388155
15 to 22 2504.73 0.067 0.526678
16 to 23 2555.72 0.788 0.784672
17 to 24 2545.70 0.646 0.740977
18 to 25 2425.12 -1.059 0.144793
19 to 26 2391.17 -1.539 0.061890
20 to 27 2466.87 -0.469 0.319705
21 to 28 2471.86 -0.398 0.345343
22 to 29 2641.26 1.998 0.977126
23 to 30 2470.48 -0.417 0.338165
24 to 31 2481.47 -0.262 0.396657
25 to 32 2454.64 -0.641 0.260612
CDPARK for dh-ranFile-2018-07-08_18:31: 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
3456 -3.0594 0.001109
3519 -0.1826 0.427537
3496 -1.2329 0.108811
3503 -0.9132 0.180558
3506 -0.7763 0.218799
3529 0.2740 0.607947
3462 -2.7854 0.002673
3531 0.3653 0.642555
3530 0.3196 0.625377
3540 0.7763 0.781201
Square side=100, avg. no. parked=3507.20 sample std.=27.54
p-value of the KSTEST for those 10 p-values: 0.052105
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-08_18:31
0.6869,0.8776,0.2652,0.3910,0.8663,0.6333,0.6551,0.9116,0.2220,0.4308,
The KS test for those 10 p-values: 0.469421
The 3DSPHERES test for dh-ranFile-2018-07-08_18:31
sample no r^3 equiv. uni.
1 0.510 0.016843
2 34.153 0.679678
3 3.715 0.116459
4 7.861 0.230511
5 10.627 0.298287
6 53.301 0.830806
7 17.902 0.449401
8 58.484 0.857650
9 10.098 0.285816
10 6.514 0.195186
11 3.890 0.121610
12 59.724 0.863415
13 104.120 0.968904
14 21.137 0.505682
15 43.881 0.768389
16 25.201 0.568304
17 31.118 0.645578
18 39.905 0.735564
19 133.275 0.988233
20 19.382 0.475905
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.960018
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-08_18:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
2.0 -0.7 -1.1 0.0 0.0 0.6
1.5 -1.7 0.6 0.5 0.4 -1.3
-0.7 1.4 1.4 -1.2 -1.5 1.8
1.5 -0.7 1.4 -1.3 -0.5 1.1
-1.8 0.1 -0.8 -0.7 0.2 -0.9
0.2 -1.1 1.2 -1.0 -0.1 0.1
-0.9 -0.1 0.1 -1.3 -0.6 0.0
-0.1
Chi-square with 42 degrees of freedom:44.589323
z-score=0.282518, p-value=0.636594
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-08_18:31
Test no p-value
1 0.005105
2 0.067469
3 0.955613
4 0.000858
5 0.644076
6 0.143694
7 0.036125
8 0.394182
9 0.126337
10 0.696664
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.005670
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-08_18:31:
(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 66338 1.62 66732 0.06
3 25000.00 25171 1.17 24985 0.01
4 6666.67 6804 2.83 6673 0.01
5 1388.89 1414 0.45 1343 1.52
6 238.10 235 0.04 229 0.35
7 34.72 34 0.01 31 0.40
8 4.96 3 0.77 6 0.22
p=0.67005 p=0.13823
Number of rngs required: 688918, p-value: 0.724
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-08_18:31
No. of wins: Observed Expected
98488 98585.9
z-score=-0.438, pvalue=0.33081
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66787 66666.7 0.217 0.217
2 37432 37654.3 1.313 1.530
3 27330 26954.7 5.225 6.754
4 19233 19313.5 0.335 7.090
5 13918 13851.4 0.320 7.410
6 9927 9943.5 0.028 7.437
7 7146 7145.0 0.000 7.437
8 5066 5139.1 1.039 8.476
9 3686 3699.9 0.052 8.528
10 2601 2666.3 1.599 10.127
11 1825 1923.3 5.027 15.154
12 1322 1388.7 3.207 18.362
13 1017 1003.7 0.176 18.538
14 713 726.1 0.238 18.775
15 568 525.8 3.381 22.156
16 398 381.2 0.745 22.901
17 274 276.5 0.023 22.925
18 214 200.8 0.864 23.788
19 139 146.0 0.334 24.122
20 97 106.2 0.800 24.922
21 307 287.1 1.377 26.299
Chisq= 26.30 for 20 degrees of freedom, p= 0.84384
SUMMARY of craptest
p-value for no. of wins: 0.330809
p-value for throws/game: 0.843845
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-08_18:31
No. of wins: Observed Expected
98429 98585.9
z-score=-0.702, pvalue=0.24148
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66702 66666.7 0.019 0.019
2 37688 37654.3 0.030 0.049
3 27119 26954.7 1.001 1.050
4 18988 19313.5 5.485 6.534
5 13971 13851.4 1.032 7.567
6 10056 9943.5 1.272 8.839
7 7117 7145.0 0.110 8.949
8 5124 5139.1 0.044 8.993
9 3660 3699.9 0.430 9.422
10 2556 2666.3 4.563 13.985
11 1983 1923.3 1.851 15.836
12 1442 1388.7 2.043 17.879
13 954 1003.7 2.462 20.341
14 751 726.1 0.851 21.192
15 487 525.8 2.868 24.061
16 391 381.2 0.255 24.315
17 275 276.5 0.009 24.324
18 192 200.8 0.388 24.712
19 154 146.0 0.440 25.152
20 110 106.2 0.135 25.287
21 280 287.1 0.176 25.463
Chisq= 25.46 for 20 degrees of freedom, p= 0.81572
SUMMARY of craptest
p-value for no. of wins: 0.241476
p-value for throws/game: 0.815718
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0009,0.0011,0.0027,0.0051,0.0057,0.0064,0.0071,0.0168,0.0232,0.0279,
0.0332,0.0352,0.0361,0.0378,0.0386,0.0402,0.0462,0.0521,0.0521,0.0570,
0.0574,0.0586,0.0619,0.0675,0.0741,0.0816,0.0874,0.0896,0.1088,0.1097,
0.1122,0.1150,0.1165,0.1216,0.1234,0.1263,0.1342,0.1382,0.1437,0.1437,
0.1448,0.1473,0.1638,0.1659,0.1701,0.1776,0.1806,0.1900,0.1903,0.1952,
0.2008,0.2054,0.2061,0.2064,0.2095,0.2151,0.2157,0.2188,0.2197,0.2220,
0.2233,0.2305,0.2307,0.2310,0.2317,0.2319,0.2341,0.2355,0.2415,0.2429,
0.2512,0.2591,0.2606,0.2652,0.2665,0.2670,0.2832,0.2858,0.2910,0.2928,
0.2982,0.2983,0.3026,0.3042,0.3197,0.3198,0.3241,0.3308,0.3351,0.3382,
0.3443,0.3449,0.3453,0.3580,0.3603,0.3680,0.3738,0.3866,0.3882,0.3910,
0.3942,0.3953,0.3967,0.3984,0.4046,0.4120,0.4135,0.4238,0.4275,0.4308,
0.4311,0.4349,0.4363,0.4410,0.4433,0.4494,0.4601,0.4671,0.4694,0.4720,
0.4759,0.4779,0.4890,0.4909,0.4939,0.5016,0.5050,0.5057,0.5207,0.5208,
0.5215,0.5245,0.5267,0.5325,0.5419,0.5431,0.5442,0.5454,0.5564,0.5587,
0.5683,0.5694,0.5709,0.5738,0.5752,0.5810,0.5814,0.5841,0.5849,0.5883,
0.5895,0.5907,0.5957,0.5972,0.5973,0.6002,0.6019,0.6079,0.6091,0.6120,
0.6126,0.6148,0.6159,0.6201,0.6217,0.6254,0.6333,0.6366,0.6402,0.6407,
0.6426,0.6437,0.6441,0.6456,0.6511,0.6551,0.6601,0.6695,0.6699,0.6700,
0.6701,0.6771,0.6797,0.6801,0.6859,0.6869,0.6886,0.6917,0.6967,0.7010,
0.7207,0.7222,0.7237,0.7256,0.7290,0.7341,0.7356,0.7357,0.7410,0.7418,
0.7446,0.7457,0.7514,0.7547,0.7592,0.7610,0.7614,0.7652,0.7684,0.7703,
0.7781,0.7812,0.7832,0.7847,0.7927,0.7945,0.7945,0.7970,0.7978,0.8006,
0.8056,0.8063,0.8066,0.8100,0.8125,0.8134,0.8152,0.8157,0.8202,0.8203,
0.8261,0.8308,0.8368,0.8375,0.8378,0.8391,0.8411,0.8435,0.8438,0.8516,
0.8577,0.8577,0.8634,0.8663,0.8727,0.8752,0.8776,0.8851,0.8905,0.8914,
0.8931,0.8942,0.8947,0.9008,0.9051,0.9116,0.9206,0.9229,0.9315,0.9556,
0.9600,0.9682,0.9689,0.9708,0.9771,0.9826,0.9882,0.9942,0.9963,
Overall p-value after applying KStest on 269 p-values = 0.399055
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.