RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-07_15:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.76 15.8239 0.463652
2 to 25 15.86 24.3670 0.890199
3 to 26 15.95 13.4640 0.295384
4 to 27 15.72 16.3684 0.502118
5 to 28 16.01 11.9686 0.197963
6 to 29 15.54 20.7001 0.760007
7 to 30 15.82 17.0210 0.547054
8 to 31 15.79 24.1471 0.884508
9 to 32 16.12 14.8760 0.395587
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.740269
Tough bday spacings test for dh-ranFile-2018-07-07_15:31: 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 9 46 57 92 90 93 50 40 12 4 7
(O-E)^2/E 0.0 2.4 3.6 0.3 0.6 2.8 0.1 3.5 0.6 1.0 2.1
Birthday Spacings: Sum(O-E)^2/E= 17.077, p= 0.927
RESULTS OF GCD FOR dh-ranFile-2018-07-07_15:31
Euclid's algorithm:
p-value, steps to gcd: 0.701563
p-value, dist. of gcd's: 0.482518
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-07_15:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.625 0.215 0.152 0.007 0.464 0.344 0.674 0.148
Bits 8 to 15---> 0.976 0.542 0.221 0.734 0.220 0.895 0.734 0.544
Bits 16 to 23---> 0.883 0.378 0.520 0.181 0.655 0.054 0.723 0.913
Bits 24 to 31---> 0.599 0.704 0.983 0.504 0.191 0.378 0.845 0.993
KS test for the above 32 p values: 0.216
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-07_15:31,
p-values for 5 runs: 0.2346, 0.8177, 0.1226, 0.7862, 0.2337
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-07_15:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 181 211.4 4.376 4.376
r= 29 5252 5134.0 2.712 7.088
r= 30 23027 23103.0 0.250 7.338
r= 31 11540 11551.5 0.011 7.350
chi-square = 7.350 with df = 3; p-value = 0.938
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-07_15:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 226 211.4 1.006 1.006
r= 30 5147 5134.0 0.033 1.039
r= 31 23045 23103.0 0.146 1.184
r= 32 11582 11551.5 0.080 1.265
chi-square = 1.265 with df = 3; p-value = 0.263
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-07_15:31
b-rank test for bits 1 to 8, p=0.86864
b-rank test for bits 2 to 9, p=0.79392
b-rank test for bits 3 to 10, p=0.73750
b-rank test for bits 4 to 11, p=0.82685
b-rank test for bits 5 to 12, p=0.47538
b-rank test for bits 6 to 13, p=0.83783
b-rank test for bits 7 to 14, p=0.01383
b-rank test for bits 8 to 15, p=0.57989
b-rank test for bits 9 to 16, p=0.68290
b-rank test for bits 10 to 17, p=0.89331
b-rank test for bits 11 to 18, p=0.76055
b-rank test for bits 12 to 19, p=0.83328
b-rank test for bits 13 to 20, p=0.35285
b-rank test for bits 14 to 21, p=0.37263
b-rank test for bits 15 to 22, p=0.76522
b-rank test for bits 16 to 23, p=0.12488
b-rank test for bits 17 to 24, p=0.53752
b-rank test for bits 18 to 25, p=0.10203
b-rank test for bits 19 to 26, p=0.33774
b-rank test for bits 20 to 27, p=0.08004
b-rank test for bits 21 to 28, p=0.02847
b-rank test for bits 22 to 29, p=0.37696
b-rank test for bits 23 to 30, p=0.38819
b-rank test for bits 24 to 31, p=0.41009
b-rank test for bits 25 to 32, p=0.06444
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 = 0.657097
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-07_15:31
(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 142142 0.54 0.706649
2 141627 -0.66 0.254739
3 141593 -0.74 0.229927
4 141317 -1.38 0.083187
5 141436 -1.11 0.134382
6 141720 -0.44 0.329114
7 141751 -0.37 0.355717
8 141903 -0.01 0.494100
9 141584 -0.76 0.223592
10 141323 -1.37 0.085354
11 142185 0.64 0.740241
12 142521 1.43 0.923517
13 142128 0.51 0.695293
14 141973 0.15 0.559129
15 142247 0.79 0.784929
16 142032 0.29 0.612795
17 141654 -0.60 0.275399
18 142277 0.86 0.804841
19 142127 0.51 0.694475
20 142477 1.33 0.907635
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-07_15:31
Bits used No. missing words z-score p-value
23 to 32 142416 1.7471 0.959693
22 to 31 142001 0.3161 0.624038
21 to 30 142227 1.0954 0.863332
20 to 29 141845 -0.2218 0.412224
19 to 28 142170 0.8989 0.815637
18 to 27 141772 -0.4736 0.317910
17 to 26 141669 -0.8287 0.203630
16 to 25 141807 -0.3529 0.362096
15 to 24 141799 -0.3804 0.351806
14 to 23 142370 1.5885 0.943915
13 to 22 142250 1.1747 0.879947
12 to 21 142234 1.1196 0.868548
11 to 20 142165 0.8816 0.811009
10 to 19 141593 -1.0908 0.137682
9 to 18 141598 -1.0736 0.141512
8 to 17 141862 -0.1632 0.435178
7 to 16 141973 0.2196 0.586890
6 to 15 141889 -0.0701 0.472056
5 to 14 141947 0.1299 0.551676
4 to 13 141764 -0.5011 0.308137
3 to 12 141811 -0.3391 0.367279
2 to 11 142272 1.2506 0.894457
1 to 10 142420 1.7609 0.960875
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-07_15:31
Bits used No. missing words z-score p-value
28 to 32 141881 -0.0960 0.461747
27 to 31 142300 1.3243 0.907299
26 to 30 141850 -0.2011 0.420303
25 to 29 141818 -0.3096 0.378435
24 to 28 141812 -0.3299 0.370726
23 to 27 141832 -0.2621 0.396609
22 to 26 141462 -1.5164 0.064713
21 to 25 142111 0.6836 0.752895
20 to 24 141990 0.2735 0.607749
19 to 23 141958 0.1650 0.565521
18 to 22 141899 -0.0350 0.486033
17 to 21 142272 1.2294 0.890537
16 to 20 141770 -0.4723 0.318355
15 to 19 141738 -0.5808 0.280695
14 to 18 141396 -1.7401 0.040921
13 to 17 141889 -0.0689 0.472529
12 to 16 141920 0.0362 0.514426
11 to 15 142386 1.6158 0.946935
10 to 14 142063 0.5209 0.698787
9 to 13 142350 1.4938 0.932386
8 to 12 141722 -0.6350 0.262709
7 to 11 141597 -1.0587 0.144858
6 to 10 142103 0.6565 0.744252
5 to 9 141512 -1.3469 0.089009
4 to 8 141580 -1.1164 0.132131
3 to 7 142197 0.9752 0.835258
2 to 6 141923 0.0463 0.518480
1 to 5 141917 0.0260 0.510371
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-07_15:31
Bits used No. missing words z-score p-value
31 to 32 141772 -0.4051 0.342701
30 to 31 141830 -0.2340 0.407488
29 to 30 141597 -0.9213 0.178440
28 to 29 141906 -0.0098 0.496081
27 to 28 141369 -1.5939 0.055480
26 to 27 142339 1.2675 0.897505
25 to 26 141750 -0.4700 0.319178
24 to 25 141882 -0.0806 0.467872
23 to 24 141618 -0.8594 0.195065
22 to 23 142340 1.2704 0.898031
21 to 22 141506 -1.1898 0.117070
20 to 21 142014 0.3088 0.621248
19 to 20 142089 0.5300 0.701944
18 to 19 142145 0.6952 0.756532
17 to 18 142209 0.8840 0.811647
16 to 17 141859 -0.1485 0.440988
15 to 16 141739 -0.5024 0.307676
14 to 15 141798 -0.3284 0.371302
13 to 14 141930 0.0610 0.524310
12 to 13 141801 -0.3196 0.374652
11 to 12 141817 -0.2724 0.392673
10 to 11 141961 0.1524 0.560572
9 to 10 142154 0.7217 0.764773
8 to 9 141454 -1.3432 0.089611
7 to 8 141630 -0.8240 0.204975
6 to 7 142093 0.5418 0.706022
5 to 6 141876 -0.0983 0.460840
4 to 5 141808 -0.2989 0.382505
3 to 4 142007 0.2881 0.613370
2 to 3 141623 -0.8446 0.199158
1 to 2 141852 -0.1691 0.432853
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-07_15:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2488.42 -0.164 0.434967
Test results for specific bytes for dh-ranFile-2018-07-07_15:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2491.63 -0.118 0.452863
2 to 9 2491.47 -0.121 0.451987
3 to 10 2429.29 -1.000 0.158660
4 to 11 2469.88 -0.426 0.335047
5 to 12 2472.70 -0.386 0.349737
6 to 13 2408.77 -1.290 0.098491
7 to 14 2505.92 0.084 0.533372
8 to 15 2457.65 -0.599 0.274632
9 to 16 2516.63 0.235 0.592963
10 to 17 2614.83 1.624 0.947809
11 to 18 2592.01 1.301 0.903406
12 to 19 2565.74 0.930 0.823728
13 to 20 2503.92 0.055 0.522082
14 to 21 2541.77 0.591 0.722652
15 to 22 2530.40 0.430 0.666366
16 to 23 2371.16 -1.822 0.034227
17 to 24 2559.77 0.845 0.801013
18 to 25 2448.31 -0.731 0.232400
19 to 26 2450.28 -0.703 0.240986
20 to 27 2570.08 0.991 0.839172
21 to 28 2576.25 1.078 0.859549
22 to 29 2498.26 -0.025 0.490172
23 to 30 2501.51 0.021 0.508503
24 to 31 2551.69 0.731 0.767634
25 to 32 2461.27 -0.548 0.291962
CDPARK for dh-ranFile-2018-07-07_15:31: 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
3519 -0.1826 0.427537
3510 -0.5936 0.276387
3544 0.9589 0.831196
3507 -0.7306 0.232514
3510 -0.5936 0.276387
3488 -1.5982 0.055002
3502 -0.9589 0.168804
3534 0.5023 0.692266
3519 -0.1826 0.427537
3540 0.7763 0.781201
Square side=100, avg. no. parked=3517.30 sample std.=16.79
p-value of the KSTEST for those 10 p-values: 0.572779
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-07_15:31
0.9004,0.1063,0.6559,0.4521,0.3134,0.7176,0.7686,0.5411,0.6263,0.9294,
The KS test for those 10 p-values: 0.471995
The 3DSPHERES test for dh-ranFile-2018-07-07_15:31
sample no r^3 equiv. uni.
1 27.379 0.598536
2 14.720 0.387778
3 0.958 0.031421
4 17.313 0.438479
5 36.327 0.702070
6 14.656 0.386468
7 5.139 0.157428
8 91.662 0.952897
9 27.508 0.600256
10 0.237 0.007861
11 59.981 0.864579
12 21.124 0.505467
13 12.686 0.344823
14 4.701 0.145049
15 2.019 0.065080
16 60.646 0.867546
17 32.772 0.664587
18 1.535 0.049866
19 15.269 0.398877
20 0.055 0.001823
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.121309
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-07_15:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 -0.7 0.6 0.5 1.1 -0.2
-1.6 0.4 -0.3 0.0 0.3 -0.1
0.9 -1.0 0.3 0.1 -0.4 -0.8
1.1 1.2 0.7 0.4 -0.5 -0.1
-0.5 -1.9 -0.5 0.3 -1.2 0.5
-0.0 -1.1 -0.0 0.9 -0.4 -0.5
-0.9 0.2 -0.4 1.0 -0.6 -1.0
-1.1
Chi-square with 42 degrees of freedom:25.569873
z-score=-1.792674, p-value=0.021429
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-07_15:31
Test no p-value
1 0.390714
2 0.595579
3 0.007245
4 0.121766
5 0.289466
6 0.257648
7 0.108055
8 0.644261
9 0.385660
10 0.663499
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.139488
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-07_15:31:
(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 66676 0.00 66699 0.02
3 25000.00 24941 0.14 24850 0.90
4 6666.67 6750 1.04 6806 2.91
5 1388.89 1381 0.04 1390 0.00
6 238.10 211 3.08 222 1.09
7 34.72 35 0.00 27 1.72
8 4.96 5 0.00 5 0.00
p=0.36560 p=0.64392
Number of rngs required: 687401, p-value: 0.122
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-07_15:31
No. of wins: Observed Expected
98688 98585.9
z-score= 0.457, pvalue=0.67611
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66343 66666.7 1.571 1.571
2 37672 37654.3 0.008 1.580
3 27185 26954.7 1.967 3.547
4 19375 19313.5 0.196 3.743
5 13865 13851.4 0.013 3.756
6 9930 9943.5 0.018 3.775
7 7232 7145.0 1.059 4.833
8 5150 5139.1 0.023 4.857
9 3644 3699.9 0.844 5.700
10 2551 2666.3 4.986 10.686
11 1972 1923.3 1.232 11.918
12 1355 1388.7 0.820 12.737
13 1030 1003.7 0.688 13.426
14 726 726.1 0.000 13.426
15 528 525.8 0.009 13.435
16 391 381.2 0.255 13.689
17 272 276.5 0.075 13.764
18 218 200.8 1.468 15.232
19 158 146.0 0.989 16.221
20 104 106.2 0.046 16.267
21 299 287.1 0.492 16.759
Chisq= 16.76 for 20 degrees of freedom, p= 0.33142
SUMMARY of craptest
p-value for no. of wins: 0.676106
p-value for throws/game: 0.331422
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-07_15:31
No. of wins: Observed Expected
98330 98585.9
z-score=-1.144, pvalue=0.12624
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66684 66666.7 0.005 0.005
2 37670 37654.3 0.007 0.011
3 27265 26954.7 3.571 3.582
4 19129 19313.5 1.762 5.344
5 13844 13851.4 0.004 5.348
6 9852 9943.5 0.843 6.191
7 7128 7145.0 0.041 6.232
8 5094 5139.1 0.395 6.627
9 3665 3699.9 0.329 6.955
10 2698 2666.3 0.377 7.332
11 1879 1923.3 1.022 8.354
12 1397 1388.7 0.049 8.403
13 990 1003.7 0.187 8.591
14 769 726.1 2.530 11.120
15 546 525.8 0.773 11.894
16 376 381.2 0.070 11.963
17 301 276.5 2.164 14.127
18 179 200.8 2.373 16.500
19 155 146.0 0.557 17.056
20 114 106.2 0.571 17.627
21 265 287.1 1.703 19.330
Chisq= 19.33 for 20 degrees of freedom, p= 0.49953
SUMMARY of craptest
p-value for no. of wins: 0.126240
p-value for throws/game: 0.499533
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0018,0.0072,0.0074,0.0079,0.0138,0.0214,0.0285,0.0314,0.0342,0.0409,
0.0499,0.0538,0.0550,0.0555,0.0644,0.0647,0.0651,0.0800,0.0832,0.0854,
0.0890,0.0896,0.0985,0.1020,0.1063,0.1081,0.1171,0.1213,0.1218,0.1223,
0.1226,0.1249,0.1262,0.1321,0.1344,0.1377,0.1395,0.1415,0.1449,0.1450,
0.1481,0.1520,0.1574,0.1587,0.1688,0.1784,0.1808,0.1912,0.1951,0.1980,
0.1992,0.2036,0.2050,0.2147,0.2156,0.2201,0.2207,0.2236,0.2299,0.2324,
0.2325,0.2337,0.2346,0.2410,0.2547,0.2576,0.2625,0.2627,0.2746,0.2754,
0.2764,0.2764,0.2807,0.2895,0.2920,0.2954,0.3077,0.3081,0.3134,0.3179,
0.3184,0.3192,0.3291,0.3314,0.3350,0.3377,0.3427,0.3444,0.3448,0.3497,
0.3518,0.3529,0.3557,0.3621,0.3656,0.3673,0.3707,0.3713,0.3726,0.3747,
0.3770,0.3777,0.3783,0.3784,0.3825,0.3857,0.3865,0.3878,0.3882,0.3907,
0.3927,0.3956,0.3966,0.3989,0.4075,0.4101,0.4122,0.4203,0.4275,0.4275,
0.4329,0.4350,0.4352,0.4385,0.4410,0.4520,0.4521,0.4529,0.4608,0.4617,
0.4637,0.4644,0.4679,0.4720,0.4721,0.4725,0.4754,0.4825,0.4860,0.4902,
0.4941,0.4961,0.4995,0.5021,0.5045,0.5055,0.5085,0.5104,0.5144,0.5185,
0.5195,0.5221,0.5243,0.5334,0.5375,0.5411,0.5417,0.5443,0.5471,0.5517,
0.5591,0.5606,0.5655,0.5728,0.5799,0.5869,0.5930,0.5956,0.5985,0.5993,
0.6003,0.6077,0.6128,0.6134,0.6212,0.6240,0.6247,0.6263,0.6439,0.6443,
0.6547,0.6559,0.6571,0.6635,0.6646,0.6664,0.6739,0.6761,0.6829,0.6923,
0.6945,0.6953,0.6988,0.7016,0.7019,0.7021,0.7037,0.7060,0.7066,0.7176,
0.7227,0.7232,0.7336,0.7337,0.7375,0.7402,0.7403,0.7443,0.7529,0.7565,
0.7600,0.7605,0.7648,0.7652,0.7676,0.7686,0.7812,0.7849,0.7862,0.7939,
0.8010,0.8048,0.8110,0.8116,0.8156,0.8177,0.8237,0.8269,0.8312,0.8333,
0.8353,0.8378,0.8392,0.8454,0.8595,0.8633,0.8646,0.8675,0.8685,0.8686,
0.8799,0.8826,0.8845,0.8902,0.8905,0.8933,0.8945,0.8951,0.8975,0.8980,
0.9004,0.9034,0.9073,0.9076,0.9132,0.9235,0.9273,0.9294,0.9324,0.9385,
0.9439,0.9469,0.9478,0.9529,0.9597,0.9609,0.9758,0.9834,0.9926,
Overall p-value after applying KStest on 269 p-values = 0.439870
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.