RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-03_16:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.89 11.7151 0.182927
2 to 25 16.02 14.4739 0.366679
3 to 26 15.62 32.0856 0.985316
4 to 27 15.65 37.4015 0.997032
5 to 28 16.04 18.4105 0.636605
6 to 29 15.83 18.1741 0.622065
7 to 30 15.81 21.2535 0.784846
8 to 31 15.89 14.7425 0.385974
9 to 32 15.60 24.9404 0.903949
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.098317
Tough bday spacings test for dh-ranFile-2018-07-03_16:31: 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 40 86 87 106 78 45 24 10 9 4
(O-E)^2/E 0.4 0.3 2.2 1.2 0.7 0.0 1.0 1.1 1.6 0.9 0.0
Birthday Spacings: Sum(O-E)^2/E= 9.321, p= 0.498
RESULTS OF GCD FOR dh-ranFile-2018-07-03_16:31
Euclid's algorithm:
p-value, steps to gcd: 0.697548
p-value, dist. of gcd's: 0.949010
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-03_16:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.127 0.979 0.240 0.645 0.115 0.458 0.834 0.954
Bits 8 to 15---> 0.208 0.487 0.205 0.385 0.175 0.207 0.192 0.914
Bits 16 to 23---> 0.578 0.324 0.858 0.079 0.766 0.928 0.106 0.935
Bits 24 to 31---> 0.040 0.193 0.124 0.338 0.754 0.449 0.368 0.649
KS test for the above 32 p values: 0.639
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-03_16:31,
p-values for 5 runs: 0.7009, 0.5218, 0.8351, 0.8332, 0.6464
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-03_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 234 211.4 2.412 2.412
r= 29 5150 5134.0 0.050 2.462
r= 30 23099 23103.0 0.001 2.463
r= 31 11517 11551.5 0.103 2.566
chi-square = 2.566 with df = 3; p-value = 0.536
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-03_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 214 211.4 0.032 0.032
r= 30 5225 5134.0 1.613 1.644
r= 31 23011 23103.0 0.367 2.011
r= 32 11550 11551.5 0.000 2.011
chi-square = 2.011 with df = 3; p-value = 0.430
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-03_16:31
b-rank test for bits 1 to 8, p=0.18203
b-rank test for bits 2 to 9, p=0.83446
b-rank test for bits 3 to 10, p=0.77025
b-rank test for bits 4 to 11, p=0.53971
b-rank test for bits 5 to 12, p=0.82434
b-rank test for bits 6 to 13, p=0.82581
b-rank test for bits 7 to 14, p=0.06745
b-rank test for bits 8 to 15, p=0.85580
b-rank test for bits 9 to 16, p=0.42903
b-rank test for bits 10 to 17, p=0.45317
b-rank test for bits 11 to 18, p=0.13812
b-rank test for bits 12 to 19, p=0.04524
b-rank test for bits 13 to 20, p=0.88715
b-rank test for bits 14 to 21, p=0.73640
b-rank test for bits 15 to 22, p=0.88737
b-rank test for bits 16 to 23, p=0.23049
b-rank test for bits 17 to 24, p=0.29339
b-rank test for bits 18 to 25, p=0.86872
b-rank test for bits 19 to 26, p=0.84846
b-rank test for bits 20 to 27, p=0.79113
b-rank test for bits 21 to 28, p=0.34071
b-rank test for bits 22 to 29, p=0.93619
b-rank test for bits 23 to 30, p=0.37567
b-rank test for bits 24 to 31, p=0.32856
b-rank test for bits 25 to 32, p=0.34539
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 = 0.309919
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-03_16:31
(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 142153 0.57 0.715431
2 142074 0.38 0.649786
3 141519 -0.91 0.180888
4 141796 -0.26 0.395586
5 142656 1.74 0.959469
6 142337 1.00 0.841158
7 142208 0.70 0.757357
8 141809 -0.23 0.407331
9 141799 -0.26 0.398288
10 142122 0.50 0.690368
11 141541 -0.86 0.194734
12 141844 -0.15 0.439341
13 142108 0.46 0.678741
14 141986 0.18 0.571084
15 141972 0.15 0.558207
16 141500 -0.96 0.169441
17 142189 0.65 0.743262
18 142005 0.22 0.588438
19 141759 -0.35 0.362705
20 142186 0.65 0.740998
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-03_16:31
Bits used No. missing words z-score p-value
23 to 32 142063 0.5299 0.701908
22 to 31 141862 -0.1632 0.435178
21 to 30 141889 -0.0701 0.472056
20 to 29 141770 -0.4804 0.315454
19 to 28 141952 0.1471 0.558488
18 to 27 141990 0.2782 0.609560
17 to 26 142030 0.4161 0.661333
16 to 25 142020 0.3816 0.648629
15 to 24 141934 0.0851 0.533897
14 to 23 142225 1.0885 0.861817
13 to 22 142197 0.9920 0.839393
12 to 21 141804 -0.3632 0.358225
11 to 20 141536 -1.2873 0.098987
10 to 19 141734 -0.6046 0.272727
9 to 18 141882 -0.0942 0.462459
8 to 17 141703 -0.7115 0.238393
7 to 16 141822 -0.3011 0.381655
6 to 15 141968 0.2023 0.580163
5 to 14 141865 -0.1529 0.439254
4 to 13 142515 2.0885 0.981624
3 to 12 142261 1.2127 0.887369
2 to 11 142008 0.3402 0.633163
1 to 10 141545 -1.2563 0.104502
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-03_16:31
Bits used No. missing words z-score p-value
28 to 32 141804 -0.3571 0.360527
27 to 31 141919 0.0328 0.513075
26 to 30 141674 -0.7977 0.212514
25 to 29 142135 0.7650 0.777859
24 to 28 142150 0.8158 0.792702
23 to 27 141885 -0.0825 0.467135
22 to 26 142341 1.4633 0.928306
21 to 25 142161 0.8531 0.803203
20 to 24 142213 1.0294 0.848352
19 to 23 142368 1.5548 0.940005
18 to 22 142212 1.0260 0.847554
17 to 21 142205 1.0023 0.841894
16 to 20 142151 0.8192 0.793670
15 to 19 142028 0.4023 0.656258
14 to 18 141697 -0.7198 0.235836
13 to 17 141615 -0.9977 0.159205
12 to 16 142061 0.5141 0.696421
11 to 15 142586 2.2938 0.989099
10 to 14 142545 2.1548 0.984412
9 to 13 141656 -0.8587 0.195240
8 to 12 142118 0.7074 0.760327
7 to 11 141654 -0.8655 0.193375
6 to 10 142272 1.2294 0.890537
5 to 9 141602 -1.0418 0.148753
4 to 8 141831 -0.2655 0.395302
3 to 7 141671 -0.8079 0.209575
2 to 6 141408 -1.6994 0.044620
1 to 5 141708 -0.6825 0.247470
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-03_16:31
Bits used No. missing words z-score p-value
31 to 32 142162 0.7453 0.771967
30 to 31 141651 -0.7620 0.223019
29 to 30 141813 -0.2842 0.388144
28 to 29 141793 -0.3432 0.365740
27 to 28 141799 -0.3255 0.372418
26 to 27 142189 0.8250 0.795310
25 to 26 141686 -0.6588 0.255015
24 to 25 141883 -0.0777 0.469045
23 to 24 142455 1.6096 0.946262
22 to 23 142078 0.4976 0.690600
21 to 22 141946 0.1082 0.543070
20 to 21 141780 -0.3815 0.351415
19 to 20 141864 -0.1337 0.446813
18 to 19 141872 -0.1101 0.456158
17 to 18 142194 0.8397 0.799471
16 to 17 141986 0.2262 0.589464
15 to 16 142252 1.0108 0.843950
14 to 15 141538 -1.0954 0.136678
13 to 14 141758 -0.4464 0.327654
12 to 13 141682 -0.6706 0.251241
11 to 12 141928 0.0551 0.521960
10 to 11 141775 -0.3963 0.345959
9 to 10 142281 1.0964 0.863542
8 to 9 141880 -0.0865 0.465527
7 to 8 141756 -0.4523 0.325526
6 to 7 141747 -0.4788 0.316023
5 to 6 141338 -1.6853 0.045962
4 to 5 141289 -1.8299 0.033634
3 to 4 141606 -0.8948 0.185453
2 to 3 142314 1.1937 0.883706
1 to 2 142278 1.0875 0.861597
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-03_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2568.04 0.962 0.832037
Test results for specific bytes for dh-ranFile-2018-07-03_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2566.21 0.936 0.825442
2 to 9 2568.67 0.971 0.834260
3 to 10 2528.26 0.400 0.655289
4 to 11 2446.04 -0.763 0.222702
5 to 12 2523.04 0.326 0.627728
6 to 13 2365.32 -1.905 0.028411
7 to 14 2528.31 0.400 0.655573
8 to 15 2417.46 -1.167 0.121540
9 to 16 2492.58 -0.105 0.458199
10 to 17 2473.06 -0.381 0.351612
11 to 18 2364.69 -1.914 0.027833
12 to 19 2493.64 -0.090 0.464147
13 to 20 2431.96 -0.962 0.167971
14 to 21 2517.28 0.244 0.596530
15 to 22 2514.40 0.204 0.580686
16 to 23 2573.35 1.037 0.850217
17 to 24 2594.68 1.339 0.909718
18 to 25 2517.45 0.247 0.597439
19 to 26 2573.29 1.036 0.850004
20 to 27 2556.24 0.795 0.786792
21 to 28 2504.45 0.063 0.525110
22 to 29 2489.57 -0.147 0.441380
23 to 30 2563.05 0.892 0.813698
24 to 31 2554.82 0.775 0.780907
25 to 32 2463.31 -0.519 0.301940
CDPARK for dh-ranFile-2018-07-03_16:31: 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
3501 -1.0046 0.157553
3520 -0.1370 0.445521
3553 1.3699 0.914635
3512 -0.5023 0.307734
3498 -1.1416 0.126820
3533 0.4566 0.676028
3507 -0.7306 0.232514
3530 0.3196 0.625377
3553 1.3699 0.914635
3551 1.2785 0.899470
Square side=100, avg. no. parked=3525.80 sample std.=20.37
p-value of the KSTEST for those 10 p-values: 0.821677
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-03_16:31
0.6480,0.1660,0.8116,0.2728,0.8464,0.9576,0.0194,0.0032,0.2833,0.7806,
The KS test for those 10 p-values: 0.366179
The 3DSPHERES test for dh-ranFile-2018-07-03_16:31
sample no r^3 equiv. uni.
1 19.438 0.476878
2 6.158 0.185557
3 10.802 0.302378
4 6.954 0.206896
5 16.089 0.415085
6 40.845 0.743722
7 46.021 0.784337
8 39.123 0.728581
9 81.469 0.933837
10 9.753 0.277539
11 10.021 0.283964
12 117.295 0.979956
13 25.425 0.571516
14 2.331 0.074757
15 6.758 0.201685
16 4.477 0.138632
17 22.255 0.523753
18 70.221 0.903740
19 28.941 0.618909
20 103.131 0.967862
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.885467
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-03_16:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 2.2 -0.6 -0.5 -0.4 1.2
0.3 -0.1 0.7 0.1 1.1 -0.5
0.7 -1.8 -0.6 0.1 0.0 -1.3
-0.2 -0.3 -1.0 1.2 1.8 -1.4
-0.3 1.8 0.5 0.8 -0.6 0.8
0.0 1.5 1.4 0.9 0.1 1.9
1.2 -0.4 0.5 -0.7 0.9 1.0
-1.1
Chi-square with 42 degrees of freedom:41.379063
z-score=-0.067750, p-value=0.501924
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-03_16:31
Test no p-value
1 0.446645
2 0.255067
3 0.604227
4 0.887068
5 0.108498
6 0.544418
7 0.035459
8 0.136074
9 0.104984
10 0.753878
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.349069
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-03_16:31:
(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 66705 0.02 66784 0.21
3 25000.00 24890 0.48 25018 0.01
4 6666.67 6646 0.06 6527 2.93
5 1388.89 1448 2.52 1370 0.26
6 238.10 254 1.06 266 3.27
7 34.72 46 3.66 29 0.94
8 4.96 10 5.12 5 0.00
p=0.95591 p=0.73236
Number of rngs required: 688169, p-value: 0.394
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-03_16:31
No. of wins: Observed Expected
99027 98585.9
z-score= 1.973, pvalue=0.97575
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67000 66666.7 1.667 1.667
2 37754 37654.3 0.264 1.931
3 27019 26954.7 0.153 2.084
4 19128 19313.5 1.781 3.865
5 13806 13851.4 0.149 4.014
6 9925 9943.5 0.035 4.048
7 6933 7145.0 6.292 10.340
8 5091 5139.1 0.450 10.790
9 3681 3699.9 0.096 10.886
10 2660 2666.3 0.015 10.901
11 1907 1923.3 0.139 11.039
12 1377 1388.7 0.099 11.139
13 996 1003.7 0.059 11.198
14 753 726.1 0.994 12.191
15 522 525.8 0.028 12.219
16 378 381.2 0.026 12.245
17 279 276.5 0.022 12.267
18 218 200.8 1.468 13.735
19 146 146.0 0.000 13.735
20 128 106.2 4.468 18.203
21 299 287.1 0.492 18.695
Chisq= 18.70 for 20 degrees of freedom, p= 0.45831
SUMMARY of craptest
p-value for no. of wins: 0.975755
p-value for throws/game: 0.458306
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-03_16:31
No. of wins: Observed Expected
98534 98585.9
z-score=-0.232, pvalue=0.40829
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66972 66666.7 1.398 1.398
2 37496 37654.3 0.666 2.064
3 26875 26954.7 0.236 2.300
4 19290 19313.5 0.029 2.328
5 13860 13851.4 0.005 2.334
6 9866 9943.5 0.605 2.938
7 7199 7145.0 0.408 3.346
8 5050 5139.1 1.544 4.890
9 3729 3699.9 0.229 5.119
10 2693 2666.3 0.267 5.387
11 1987 1923.3 2.108 7.495
12 1407 1388.7 0.240 7.735
13 974 1003.7 0.880 8.614
14 699 726.1 1.014 9.629
15 517 525.8 0.148 9.777
16 368 381.2 0.454 10.231
17 291 276.5 0.756 10.987
18 202 200.8 0.007 10.994
19 142 146.0 0.109 11.103
20 94 106.2 1.405 12.508
21 289 287.1 0.012 12.520
Chisq= 12.52 for 20 degrees of freedom, p= 0.10298
SUMMARY of craptest
p-value for no. of wins: 0.408292
p-value for throws/game: 0.102984
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0032,0.0194,0.0278,0.0284,0.0336,0.0355,0.0405,0.0446,0.0452,0.0460,
0.0675,0.0748,0.0786,0.0983,0.0990,0.1030,0.1045,0.1050,0.1058,0.1085,
0.1151,0.1215,0.1243,0.1268,0.1274,0.1361,0.1367,0.1381,0.1386,0.1488,
0.1576,0.1592,0.1660,0.1680,0.1694,0.1754,0.1809,0.1820,0.1829,0.1855,
0.1856,0.1917,0.1928,0.1934,0.1947,0.1952,0.2017,0.2050,0.2066,0.2069,
0.2075,0.2096,0.2125,0.2227,0.2230,0.2305,0.2325,0.2358,0.2384,0.2399,
0.2475,0.2512,0.2550,0.2551,0.2727,0.2728,0.2775,0.2833,0.2840,0.2934,
0.3019,0.3024,0.3077,0.3099,0.3155,0.3160,0.3238,0.3255,0.3277,0.3286,
0.3383,0.3407,0.3454,0.3460,0.3491,0.3514,0.3516,0.3582,0.3605,0.3627,
0.3657,0.3662,0.3667,0.3679,0.3724,0.3757,0.3817,0.3850,0.3860,0.3881,
0.3938,0.3953,0.3956,0.3983,0.4073,0.4083,0.4151,0.4290,0.4299,0.4352,
0.4393,0.4393,0.4414,0.4455,0.4466,0.4468,0.4493,0.4532,0.4562,0.4577,
0.4582,0.4583,0.4625,0.4641,0.4655,0.4671,0.4690,0.4721,0.4769,0.4867,
0.4980,0.5019,0.5131,0.5218,0.5220,0.5238,0.5251,0.5339,0.5365,0.5397,
0.5431,0.5444,0.5582,0.5585,0.5711,0.5715,0.5781,0.5802,0.5807,0.5884,
0.5895,0.5965,0.5974,0.6042,0.6096,0.6189,0.6221,0.6254,0.6277,0.6332,
0.6366,0.6390,0.6448,0.6464,0.6480,0.6486,0.6486,0.6498,0.6553,0.6556,
0.6563,0.6613,0.6760,0.6787,0.6904,0.6906,0.6964,0.6975,0.7009,0.7019,
0.7154,0.7286,0.7324,0.7364,0.7410,0.7433,0.7437,0.7539,0.7542,0.7574,
0.7603,0.7665,0.7703,0.7720,0.7779,0.7806,0.7809,0.7843,0.7848,0.7868,
0.7911,0.7927,0.7937,0.7953,0.7995,0.8032,0.8116,0.8137,0.8217,0.8243,
0.8254,0.8258,0.8320,0.8332,0.8335,0.8343,0.8345,0.8351,0.8394,0.8412,
0.8419,0.8440,0.8464,0.8476,0.8484,0.8485,0.8500,0.8502,0.8558,0.8584,
0.8616,0.8618,0.8635,0.8687,0.8837,0.8855,0.8871,0.8872,0.8874,0.8874,
0.8905,0.8995,0.9037,0.9039,0.9097,0.9144,0.9146,0.9146,0.9283,0.9284,
0.9338,0.9347,0.9362,0.9400,0.9463,0.9490,0.9542,0.9559,0.9576,0.9595,
0.9679,0.9758,0.9793,0.9800,0.9816,0.9844,0.9853,0.9891,0.9970,
Overall p-value after applying KStest on 269 p-values = 0.153536
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.