RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-27_03:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.98 29.7851 0.972063
2 to 25 15.84 24.5133 0.893853
3 to 26 15.68 19.5583 0.702558
4 to 27 15.61 15.4610 0.437684
5 to 28 15.28 34.4988 0.992765
6 to 29 15.56 17.0969 0.552182
7 to 30 15.70 17.5788 0.584136
8 to 31 15.95 15.4241 0.435034
9 to 32 15.74 22.5806 0.836590
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.035084
Tough bday spacings test for dh-ranFile-2018-06-27_03:31: 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 13 27 72 93 96 86 60 26 16 9 2
(O-E)^2/E 1.6 2.5 0.0 0.2 0.0 0.8 1.2 0.5 0.1 0.9 1.0
Birthday Spacings: Sum(O-E)^2/E= 8.878, p= 0.456
RESULTS OF GCD FOR dh-ranFile-2018-06-27_03:31
Euclid's algorithm:
p-value, steps to gcd: 0.709909
p-value, dist. of gcd's: 0.959321
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-27_03:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.045 0.632 0.886 0.413 0.557 0.479 0.460 0.587
Bits 8 to 15---> 0.139 0.249 0.324 0.753 0.390 0.147 0.228 0.850
Bits 16 to 23---> 0.683 0.005 0.197 0.443 0.706 0.575 0.522 0.742
Bits 24 to 31---> 0.070 0.934 0.992 0.433 0.507 0.604 0.395 0.648
KS test for the above 32 p values: 0.235
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-27_03:31,
p-values for 5 runs: 0.9826, 0.5203, 0.3681, 0.3113, 0.7661
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-27_03:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 200 211.4 0.617 0.617
r= 29 5127 5134.0 0.010 0.626
r= 30 23257 23103.0 1.026 1.652
r= 31 11416 11551.5 1.590 3.242
chi-square = 3.242 with df = 3; p-value = 0.644
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-27_03:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 208 211.4 0.055 0.055
r= 30 5075 5134.0 0.678 0.734
r= 31 23242 23103.0 0.836 1.569
r= 32 11475 11551.5 0.507 2.076
chi-square = 2.076 with df = 3; p-value = 0.443
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-27_03:31
b-rank test for bits 1 to 8, p=0.71511
b-rank test for bits 2 to 9, p=0.93657
b-rank test for bits 3 to 10, p=0.66116
b-rank test for bits 4 to 11, p=0.06832
b-rank test for bits 5 to 12, p=0.51744
b-rank test for bits 6 to 13, p=0.04926
b-rank test for bits 7 to 14, p=0.00740
b-rank test for bits 8 to 15, p=0.38295
b-rank test for bits 9 to 16, p=0.31784
b-rank test for bits 10 to 17, p=0.76075
b-rank test for bits 11 to 18, p=0.34456
b-rank test for bits 12 to 19, p=0.65956
b-rank test for bits 13 to 20, p=0.42883
b-rank test for bits 14 to 21, p=0.41221
b-rank test for bits 15 to 22, p=0.56423
b-rank test for bits 16 to 23, p=0.35572
b-rank test for bits 17 to 24, p=0.97794
b-rank test for bits 18 to 25, p=0.74038
b-rank test for bits 19 to 26, p=0.01502
b-rank test for bits 20 to 27, p=0.88737
b-rank test for bits 21 to 28, p=0.84762
b-rank test for bits 22 to 29, p=0.25069
b-rank test for bits 23 to 30, p=0.32865
b-rank test for bits 24 to 31, p=0.40607
b-rank test for bits 25 to 32, p=0.87093
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 = 0.852194
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-27_03:31
(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 141210 -1.63 0.051135
2 141900 -0.02 0.491304
3 141942 0.08 0.530422
4 142157 0.58 0.718594
5 142317 0.95 0.829578
6 142109 0.47 0.679578
7 141760 -0.35 0.363582
8 141758 -0.35 0.361829
9 142003 0.22 0.586619
10 141308 -1.40 0.080014
11 141955 0.11 0.542489
12 142674 1.79 0.963000
13 140940 -2.26 0.011763
14 142117 0.49 0.686236
15 141499 -0.96 0.168851
16 142243 0.78 0.782188
17 141320 -1.38 0.084266
18 141295 -1.44 0.075594
19 141786 -0.29 0.386614
20 142174 0.62 0.731840
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-27_03:31
Bits used No. missing words z-score p-value
23 to 32 141708 -0.6942 0.243765
22 to 31 142015 0.3644 0.642213
21 to 30 141824 -0.2942 0.384287
20 to 29 141990 0.2782 0.609560
19 to 28 141619 -1.0011 0.158380
18 to 27 141578 -1.1425 0.126620
17 to 26 142305 1.3644 0.913776
16 to 25 142071 0.5575 0.711401
15 to 24 141794 -0.3977 0.345430
14 to 23 141982 0.2506 0.598933
13 to 22 142269 1.2402 0.892557
12 to 21 142217 1.0609 0.855639
11 to 20 141943 0.1161 0.546215
10 to 19 141594 -1.0873 0.138442
9 to 18 141930 0.0713 0.528411
8 to 17 141973 0.2196 0.586890
7 to 16 141923 0.0471 0.518798
6 to 15 141860 -0.1701 0.432464
5 to 14 141788 -0.4184 0.337835
4 to 13 142256 1.1954 0.884037
3 to 12 142363 1.5644 0.941136
2 to 11 141682 -0.7839 0.216550
1 to 10 141709 -0.6908 0.244848
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-27_03:31
Bits used No. missing words z-score p-value
28 to 32 141684 -0.7638 0.222484
27 to 31 141843 -0.2248 0.411049
26 to 30 141904 -0.0181 0.492792
25 to 29 142167 0.8735 0.808793
24 to 28 141736 -0.5876 0.278414
23 to 27 142513 2.0463 0.979638
22 to 26 142071 0.5480 0.708166
21 to 25 142033 0.4192 0.662473
20 to 24 142273 1.2328 0.891171
19 to 23 142016 0.3616 0.641172
18 to 22 142237 1.1107 0.866661
17 to 21 141974 0.2192 0.586761
16 to 20 141906 -0.0113 0.495497
15 to 19 141924 0.0497 0.519831
14 to 18 141196 -2.4181 0.007802
13 to 17 141739 -0.5774 0.281838
12 to 16 142284 1.2701 0.897970
11 to 15 141575 -1.1333 0.128540
10 to 14 142389 1.6260 0.948025
9 to 13 141994 0.2870 0.612950
8 to 12 141837 -0.2452 0.403156
7 to 11 142205 1.0023 0.841894
6 to 10 141798 -0.3774 0.352942
5 to 9 141868 -0.1401 0.444290
4 to 8 141582 -1.1096 0.133587
3 to 7 141791 -0.4011 0.344166
2 to 6 141944 0.1175 0.546778
1 to 5 141664 -0.8316 0.202810
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-27_03:31
Bits used No. missing words z-score p-value
31 to 32 141750 -0.4700 0.319178
30 to 31 141864 -0.1337 0.446813
29 to 30 141188 -2.1278 0.016676
28 to 29 141548 -1.0659 0.143241
27 to 28 142171 0.7719 0.779910
26 to 27 142162 0.7453 0.771967
25 to 26 142073 0.4828 0.685382
24 to 25 141563 -1.0216 0.153480
23 to 24 142160 0.7394 0.770180
22 to 23 142151 0.7129 0.762043
21 to 22 141576 -0.9833 0.162736
20 to 21 141401 -1.4995 0.066872
19 to 20 142046 0.4032 0.656583
18 to 19 141549 -1.0629 0.143909
17 to 18 141767 -0.4199 0.337297
16 to 17 142353 1.3088 0.904692
15 to 16 142040 0.3855 0.650051
14 to 15 142324 1.2232 0.889376
13 to 14 141960 0.1495 0.559408
12 to 13 142015 0.3117 0.622370
11 to 12 142658 2.2085 0.986394
10 to 11 141647 -0.7738 0.219514
9 to 10 141627 -0.8328 0.202470
8 to 9 142314 1.1937 0.883706
7 to 8 141861 -0.1426 0.443316
6 to 7 140833 -3.1750 0.000749
5 to 6 142091 0.5359 0.703986
4 to 5 142317 1.2026 0.885428
3 to 4 141230 -2.0039 0.022539
2 to 3 142324 1.2232 0.889376
1 to 2 141871 -0.1131 0.454988
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-27_03:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2484.79 -0.215 0.414848
Test results for specific bytes for dh-ranFile-2018-06-27_03:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2363.20 -1.935 0.026514
2 to 9 2707.66 2.937 0.998341
3 to 10 2497.64 -0.033 0.486681
4 to 11 2567.89 0.960 0.831503
5 to 12 2333.31 -2.357 0.009203
6 to 13 2536.28 0.513 0.696043
7 to 14 2449.01 -0.721 0.235407
8 to 15 2535.95 0.508 0.694439
9 to 16 2668.22 2.379 0.991321
10 to 17 2569.29 0.980 0.836425
11 to 18 2356.78 -2.026 0.021408
12 to 19 2445.58 -0.770 0.220766
13 to 20 2463.44 -0.517 0.302550
14 to 21 2599.54 1.408 0.920401
15 to 22 2663.86 2.317 0.989757
16 to 23 2524.40 0.345 0.634989
17 to 24 2484.00 -0.226 0.410485
18 to 25 2457.14 -0.606 0.272206
19 to 26 2467.33 -0.462 0.322038
20 to 27 2536.06 0.510 0.694975
21 to 28 2480.29 -0.279 0.390206
22 to 29 2444.33 -0.787 0.215548
23 to 30 2448.32 -0.731 0.232421
24 to 31 2460.14 -0.564 0.286469
25 to 32 2550.56 0.715 0.762714
CDPARK for dh-ranFile-2018-06-27_03:31: 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
3557 1.5525 0.939730
3554 1.4155 0.921543
3508 -0.6849 0.246694
3526 0.1370 0.554479
3531 0.3653 0.642555
3525 0.0913 0.536383
3514 -0.4110 0.340551
3480 -1.9635 0.024796
3506 -0.7763 0.218799
3519 -0.1826 0.427537
Square side=100, avg. no. parked=3522.00 sample std.=21.55
p-value of the KSTEST for those 10 p-values: 0.952145
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-27_03:31
0.2877,0.5789,0.8996,0.2354,0.1863,0.1968,0.6692,0.8322,0.2600,0.4288,
The KS test for those 10 p-values: 0.686113
The 3DSPHERES test for dh-ranFile-2018-06-27_03:31
sample no r^3 equiv. uni.
1 6.690 0.199884
2 37.152 0.710156
3 17.834 0.448134
4 20.796 0.500033
5 25.889 0.578097
6 7.382 0.218122
7 69.274 0.900653
8 10.700 0.299993
9 0.885 0.029069
10 22.792 0.532208
11 21.494 0.511525
12 36.894 0.707651
13 4.945 0.151963
14 13.665 0.365862
15 72.402 0.910490
16 58.645 0.858413
17 5.442 0.165910
18 13.916 0.371160
19 9.145 0.262752
20 36.241 0.701213
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.843651
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-27_03:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
2.0 0.1 -1.8 0.0 -0.8 0.6
1.0 0.4 -0.6 0.4 0.3 -1.2
-1.0 -0.3 -0.6 0.3 -1.3 1.3
-0.3 0.2 1.9 -0.6 0.4 3.6
-1.3 -1.3 0.7 -0.6 -0.8 0.2
-0.4 -1.5 0.8 0.1 -1.9 -0.5
0.3 -0.1 -2.0 1.5 1.6 -1.0
-0.1
Chi-square with 42 degrees of freedom:55.917721
z-score=1.518548, p-value=0.926227
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-27_03:31
Test no p-value
1 0.920159
2 0.690392
3 0.024399
4 0.099377
5 0.012051
6 0.016801
7 0.142104
8 0.040692
9 0.222490
10 0.418874
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.001692
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-27_03:31:
(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 66870 0.62 66856 0.54
3 25000.00 24928 0.21 24905 0.36
4 6666.67 6548 2.11 6609 0.50
5 1388.89 1373 0.18 1388 0.00
6 238.10 239 0.00 212 2.86
7 34.72 37 0.15 26 2.19
8 4.96 4 0.19 3 0.77
p=0.25080 p=0.69926
Number of rngs required: 687141, p-value: 0.070
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-27_03:31
No. of wins: Observed Expected
98601 98585.9
z-score= 0.068, pvalue=0.52700
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66506 66666.7 0.387 0.387
2 37576 37654.3 0.163 0.550
3 26945 26954.7 0.004 0.554
4 19163 19313.5 1.172 1.726
5 14011 13851.4 1.838 3.564
6 10084 9943.5 1.984 5.548
7 7066 7145.0 0.874 6.422
8 5191 5139.1 0.525 6.947
9 3812 3699.9 3.399 10.346
10 2671 2666.3 0.008 10.354
11 1939 1923.3 0.128 10.482
12 1380 1388.7 0.055 10.537
13 1003 1003.7 0.001 10.537
14 753 726.1 0.994 11.531
15 500 525.8 1.269 12.800
16 385 381.2 0.039 12.839
17 282 276.5 0.108 12.947
18 192 200.8 0.388 13.335
19 135 146.0 0.827 14.161
20 112 106.2 0.315 14.477
21 294 287.1 0.165 14.642
Chisq= 14.64 for 20 degrees of freedom, p= 0.20347
SUMMARY of craptest
p-value for no. of wins: 0.526996
p-value for throws/game: 0.203469
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-27_03:31
No. of wins: Observed Expected
98531 98585.9
z-score=-0.245, pvalue=0.40309
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66525 66666.7 0.301 0.301
2 37715 37654.3 0.098 0.399
3 26858 26954.7 0.347 0.746
4 19417 19313.5 0.555 1.301
5 13794 13851.4 0.238 1.539
6 10000 9943.5 0.321 1.860
7 7203 7145.0 0.470 2.330
8 5218 5139.1 1.212 3.542
9 3718 3699.9 0.089 3.631
10 2708 2666.3 0.652 4.283
11 1810 1923.3 6.678 10.961
12 1375 1388.7 0.136 11.097
13 1012 1003.7 0.068 11.165
14 699 726.1 1.014 12.180
15 563 525.8 2.627 14.806
16 374 381.2 0.134 14.941
17 277 276.5 0.001 14.941
18 201 200.8 0.000 14.942
19 141 146.0 0.170 15.112
20 123 106.2 2.652 17.764
21 269 287.1 1.143 18.907
Chisq= 18.91 for 20 degrees of freedom, p= 0.47212
SUMMARY of craptest
p-value for no. of wins: 0.403089
p-value for throws/game: 0.472119
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0007,0.0017,0.0052,0.0074,0.0078,0.0092,0.0118,0.0121,0.0150,0.0167,
0.0168,0.0214,0.0225,0.0244,0.0248,0.0265,0.0291,0.0351,0.0407,0.0448,
0.0493,0.0511,0.0669,0.0683,0.0695,0.0703,0.0756,0.0800,0.0843,0.0994,
0.1266,0.1285,0.1336,0.1384,0.1386,0.1421,0.1432,0.1439,0.1467,0.1520,
0.1535,0.1584,0.1627,0.1659,0.1689,0.1863,0.1968,0.1970,0.1999,0.2025,
0.2028,0.2035,0.2155,0.2166,0.2181,0.2188,0.2195,0.2208,0.2225,0.2225,
0.2279,0.2324,0.2354,0.2354,0.2354,0.2438,0.2448,0.2467,0.2492,0.2507,
0.2508,0.2600,0.2628,0.2722,0.2784,0.2818,0.2865,0.2877,0.3000,0.3025,
0.3113,0.3178,0.3192,0.3220,0.3236,0.3287,0.3373,0.3378,0.3406,0.3442,
0.3446,0.3454,0.3529,0.3557,0.3618,0.3636,0.3659,0.3681,0.3712,0.3830,
0.3843,0.3866,0.3898,0.3902,0.3954,0.4031,0.4032,0.4061,0.4105,0.4110,
0.4122,0.4130,0.4148,0.4189,0.4275,0.4288,0.4288,0.4325,0.4329,0.4350,
0.4377,0.4429,0.4433,0.4433,0.4443,0.4468,0.4481,0.4550,0.4562,0.4604,
0.4721,0.4790,0.4867,0.4913,0.4928,0.4955,0.5000,0.5067,0.5115,0.5174,
0.5188,0.5198,0.5203,0.5222,0.5270,0.5284,0.5304,0.5322,0.5364,0.5425,
0.5462,0.5468,0.5522,0.5545,0.5567,0.5594,0.5642,0.5749,0.5781,0.5789,
0.5841,0.5866,0.5866,0.5868,0.5869,0.5989,0.6040,0.6096,0.6130,0.6224,
0.6315,0.6350,0.6412,0.6422,0.6426,0.6442,0.6484,0.6501,0.6566,0.6596,
0.6612,0.6625,0.6692,0.6796,0.6834,0.6854,0.6861,0.6862,0.6904,0.6944,
0.6950,0.6960,0.6993,0.7012,0.7026,0.7040,0.7064,0.7077,0.7082,0.7099,
0.7102,0.7114,0.7151,0.7186,0.7318,0.7404,0.7420,0.7526,0.7608,0.7620,
0.7627,0.7661,0.7702,0.7720,0.7799,0.7822,0.8088,0.8296,0.8315,0.8322,
0.8364,0.8366,0.8419,0.8437,0.8476,0.8496,0.8522,0.8556,0.8584,0.8667,
0.8709,0.8837,0.8840,0.8854,0.8864,0.8874,0.8894,0.8894,0.8912,0.8926,
0.8939,0.8980,0.8996,0.9007,0.9047,0.9105,0.9138,0.9202,0.9204,0.9215,
0.9262,0.9338,0.9366,0.9397,0.9411,0.9480,0.9521,0.9593,0.9630,0.9721,
0.9779,0.9796,0.9826,0.9864,0.9898,0.9913,0.9919,0.9928,0.9983,
Overall p-value after applying KStest on 269 p-values = 0.632755
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.