RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-23_09:31
(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 11.5687 0.174480
2 to 25 15.54 22.2724 0.825531
3 to 26 15.50 27.9394 0.954349
4 to 27 15.44 22.4720 0.832760
5 to 28 15.44 24.9594 0.904377
6 to 29 15.71 20.2836 0.740020
7 to 30 15.83 15.3447 0.429334
8 to 31 15.69 33.8089 0.991114
9 to 32 15.43 31.6451 0.983350
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.003557
Tough bday spacings test for dh-ranFile-2018-06-23_09:31: 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 6 35 74 114 89 71 54 26 16 7 8
(O-E)^2/E 1.1 0.1 0.0 2.7 0.8 0.7 0.1 0.5 0.1 0.0 3.8
Birthday Spacings: Sum(O-E)^2/E= 9.779, p= 0.540
RESULTS OF GCD FOR dh-ranFile-2018-06-23_09:31
Euclid's algorithm:
p-value, steps to gcd: 0.352192
p-value, dist. of gcd's: 0.335850
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-23_09:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.978 0.849 0.799 0.351 0.159 0.610 0.342 0.101
Bits 8 to 15---> 0.227 0.372 0.632 0.976 0.548 0.028 0.178 0.042
Bits 16 to 23---> 0.658 0.148 0.171 0.850 0.009 0.704 0.931 0.068
Bits 24 to 31---> 0.022 0.894 0.601 0.509 0.378 0.941 0.600 0.741
KS test for the above 32 p values: 0.455
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-23_09:31,
p-values for 5 runs: 0.9970, 0.4327, 0.7373, 0.1760, 0.9856
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-23_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 214 211.4 0.032 0.032
r= 29 5121 5134.0 0.033 0.065
r= 30 23163 23103.0 0.156 0.220
r= 31 11502 11551.5 0.212 0.432
chi-square = 0.432 with df = 3; p-value = 0.067
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-23_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 229 211.4 1.462 1.462
r= 30 5183 5134.0 0.467 1.930
r= 31 23059 23103.0 0.084 2.014
r= 32 11529 11551.5 0.044 2.058
chi-square = 2.058 with df = 3; p-value = 0.439
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-23_09:31
b-rank test for bits 1 to 8, p=0.48643
b-rank test for bits 2 to 9, p=0.62419
b-rank test for bits 3 to 10, p=0.58644
b-rank test for bits 4 to 11, p=0.34367
b-rank test for bits 5 to 12, p=0.31030
b-rank test for bits 6 to 13, p=0.70403
b-rank test for bits 7 to 14, p=0.77833
b-rank test for bits 8 to 15, p=0.02310
b-rank test for bits 9 to 16, p=0.90644
b-rank test for bits 10 to 17, p=0.60152
b-rank test for bits 11 to 18, p=0.26898
b-rank test for bits 12 to 19, p=0.63818
b-rank test for bits 13 to 20, p=0.54668
b-rank test for bits 14 to 21, p=0.73823
b-rank test for bits 15 to 22, p=0.99666
b-rank test for bits 16 to 23, p=0.45917
b-rank test for bits 17 to 24, p=0.23190
b-rank test for bits 18 to 25, p=0.31574
b-rank test for bits 19 to 26, p=0.47292
b-rank test for bits 20 to 27, p=0.18332
b-rank test for bits 21 to 28, p=0.58797
b-rank test for bits 22 to 29, p=0.55598
b-rank test for bits 23 to 30, p=0.33768
b-rank test for bits 24 to 31, p=0.74087
b-rank test for bits 25 to 32, p=0.00028
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 = 0.432400
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-23_09:31
(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 142440 1.24 0.892491
2 141914 0.01 0.504353
3 141453 -1.07 0.143169
4 141588 -0.75 0.226395
5 141526 -0.90 0.185225
6 142806 2.10 0.981916
7 141765 -0.34 0.367976
8 141631 -0.65 0.257748
9 140743 -2.73 0.003214
10 142094 0.43 0.666937
11 142171 0.61 0.729526
12 141702 -0.48 0.314045
13 141716 -0.45 0.325741
14 141521 -0.91 0.182121
15 141850 -0.14 0.444875
16 141219 -1.61 0.053381
17 141649 -0.61 0.271512
18 141845 -0.15 0.440263
19 142758 1.98 0.976309
20 142033 0.29 0.613690
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-23_09:31
Bits used No. missing words z-score p-value
23 to 32 142318 1.4092 0.920613
22 to 31 142438 1.8230 0.965848
21 to 30 141884 -0.0873 0.465199
20 to 29 142193 0.9782 0.836006
19 to 28 141966 0.1954 0.577466
18 to 27 142079 0.5851 0.720749
17 to 26 141959 0.1713 0.567997
16 to 25 142226 1.0920 0.862576
15 to 24 141642 -0.9218 0.178309
14 to 23 141585 -1.1184 0.131703
13 to 22 142068 0.5471 0.707858
12 to 21 141945 0.1230 0.548947
11 to 20 141535 -1.2908 0.098388
10 to 19 141429 -1.6563 0.048830
9 to 18 141977 0.2333 0.592253
8 to 17 141843 -0.2287 0.409542
7 to 16 141472 -1.5080 0.065773
6 to 15 141728 -0.6253 0.265895
5 to 14 142259 1.2058 0.886045
4 to 13 141599 -1.0701 0.142286
3 to 12 141568 -1.1770 0.119598
2 to 11 141351 -1.9253 0.027097
1 to 10 141716 -0.6667 0.252496
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-23_09:31
Bits used No. missing words z-score p-value
28 to 32 141918 0.0294 0.511723
27 to 31 142246 1.1413 0.873118
26 to 30 141443 -1.5808 0.056964
25 to 29 142160 0.8497 0.802262
24 to 28 142153 0.8260 0.795598
23 to 27 141090 -2.7774 0.002740
22 to 26 141915 0.0192 0.507667
21 to 25 141921 0.0396 0.515778
20 to 24 142200 0.9853 0.837767
19 to 23 141581 -1.1130 0.132858
18 to 22 141804 -0.3571 0.360527
17 to 21 142139 0.7785 0.781875
16 to 20 141596 -1.0621 0.144087
15 to 19 141941 0.1074 0.542747
14 to 18 141868 -0.1401 0.444290
13 to 17 142283 1.2667 0.897365
12 to 16 142037 0.4328 0.667413
11 to 15 142057 0.5006 0.691665
10 to 14 141903 -0.0215 0.491440
9 to 13 141744 -0.5604 0.287589
8 to 12 141926 0.0565 0.522532
7 to 11 142082 0.5853 0.720834
6 to 10 142116 0.7006 0.758216
5 to 9 141546 -1.2316 0.109044
4 to 8 142009 0.3379 0.632267
3 to 7 142286 1.2768 0.899172
2 to 6 142414 1.7107 0.956436
1 to 5 141588 -1.0893 0.138021
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-23_09:31
Bits used No. missing words z-score p-value
31 to 32 142554 1.9017 0.971394
30 to 31 141847 -0.1839 0.427060
29 to 30 142448 1.5890 0.943969
28 to 29 141916 0.0197 0.507849
27 to 28 142414 1.4887 0.931717
26 to 27 141759 -0.4435 0.328720
25 to 26 142415 1.4917 0.932105
24 to 25 141763 -0.4317 0.332997
23 to 24 141969 0.1760 0.569860
22 to 23 141881 -0.0836 0.466699
21 to 22 141962 0.1554 0.561735
20 to 21 142184 0.8102 0.791098
19 to 20 141191 -2.1190 0.017047
18 to 19 142568 1.9430 0.973991
17 to 18 142130 0.6509 0.742459
16 to 17 141545 -1.0747 0.141250
15 to 16 142550 1.8899 0.970613
14 to 15 141618 -0.8594 0.195065
13 to 14 141697 -0.6263 0.265545
12 to 13 141851 -0.1721 0.431693
11 to 12 141712 -0.5821 0.280252
10 to 11 141671 -0.7030 0.241016
9 to 10 142012 0.3029 0.619002
8 to 9 141841 -0.2016 0.420129
7 to 8 141973 0.1878 0.574490
6 to 7 141785 -0.3668 0.356901
5 to 6 141780 -0.3815 0.351415
4 to 5 141547 -1.0688 0.142575
3 to 4 142122 0.6273 0.734784
2 to 3 141803 -0.3137 0.376891
1 to 2 141455 -1.3402 0.090089
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-23_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2456.63 -0.613 0.269821
Test results for specific bytes for dh-ranFile-2018-06-23_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2431.40 -0.970 0.165975
2 to 9 2578.05 1.104 0.865146
3 to 10 2452.81 -0.667 0.252271
4 to 11 2524.10 0.341 0.633405
5 to 12 2601.39 1.434 0.924205
6 to 13 2467.33 -0.462 0.322051
7 to 14 2508.60 0.122 0.548383
8 to 15 2577.99 1.103 0.864960
9 to 16 2560.97 0.862 0.805740
10 to 17 2479.90 -0.284 0.388129
11 to 18 2477.26 -0.322 0.373898
12 to 19 2542.67 0.603 0.726907
13 to 20 2500.71 0.010 0.504023
14 to 21 2521.53 0.304 0.619613
15 to 22 2558.23 0.824 0.794891
16 to 23 2575.08 1.062 0.855829
17 to 24 2513.06 0.185 0.573252
18 to 25 2626.09 1.783 0.962717
19 to 26 2482.06 -0.254 0.399865
20 to 27 2496.50 -0.050 0.480235
21 to 28 2443.10 -0.805 0.210503
22 to 29 2559.19 0.837 0.798744
23 to 30 2532.11 0.454 0.675126
24 to 31 2575.67 1.070 0.857733
25 to 32 2472.94 -0.383 0.350977
CDPARK for dh-ranFile-2018-06-23_09:31: 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
3536 0.5936 0.723613
3519 -0.1826 0.427537
3506 -0.7763 0.218799
3498 -1.1416 0.126820
3514 -0.4110 0.340551
3503 -0.9132 0.180558
3499 -1.0959 0.136563
3534 0.5023 0.692266
3522 -0.0457 0.481790
3529 0.2740 0.607947
Square side=100, avg. no. parked=3516.00 sample std.=13.51
p-value of the KSTEST for those 10 p-values: 0.326835
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-23_09:31
0.0462,0.6284,0.4092,0.3255,0.1537,0.2697,0.0669,0.2555,0.7324,0.4442,
The KS test for those 10 p-values: 0.115821
The 3DSPHERES test for dh-ranFile-2018-06-23_09:31
sample no r^3 equiv. uni.
1 21.792 0.516354
2 0.513 0.016944
3 57.831 0.854520
4 30.841 0.642292
5 14.671 0.386776
6 12.992 0.351482
7 24.533 0.558588
8 2.152 0.069227
9 104.768 0.969569
10 8.257 0.240614
11 5.261 0.160850
12 20.309 0.491838
13 2.160 0.069454
14 4.912 0.151030
15 18.873 0.466924
16 61.395 0.870813
17 1.817 0.058764
18 51.169 0.818340
19 23.661 0.545568
20 25.042 0.566015
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.551654
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-23_09:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 0.9 -0.6 1.4 -2.0 1.1
-0.7 -0.2 0.7 -0.4 0.6 -0.0
-1.7 0.4 1.4 -0.9 0.2 -1.1
-0.7 2.1 -1.4 0.1 -0.7 0.2
-0.3 0.8 2.3 1.6 -0.1 -1.5
0.7 -0.7 0.5 0.5 -0.8 0.1
-0.2 -0.1 0.5 -0.7 0.9 -1.0
-0.1
Chi-square with 42 degrees of freedom:39.638902
z-score=-0.257617, p-value=0.424873
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-23_09:31
Test no p-value
1 0.797128
2 0.009650
3 0.046878
4 0.001720
5 0.127136
6 0.276697
7 0.016673
8 0.003063
9 0.572503
10 0.214370
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000046
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-23_09:31:
(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 66785 0.21 66782 0.20
3 25000.00 24930 0.20 24848 0.92
4 6666.67 6577 1.21 6747 0.97
5 1388.89 1437 1.67 1347 1.26
6 238.10 224 0.83 236 0.02
7 34.72 44 2.48 34 0.01
8 4.96 2 1.77 5 0.00
p=0.78709 p=0.24129
Number of rngs required: 687843, p-value: 0.259
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-23_09:31
No. of wins: Observed Expected
98820 98585.9
z-score= 1.047, pvalue=0.85250
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66454 66666.7 0.678 0.678
2 37600 37654.3 0.078 0.757
3 27044 26954.7 0.296 1.052
4 19509 19313.5 1.980 3.032
5 13799 13851.4 0.198 3.230
6 10032 9943.5 0.787 4.017
7 7078 7145.0 0.629 4.646
8 5236 5139.1 1.828 6.474
9 3690 3699.9 0.026 6.501
10 2592 2666.3 2.070 8.571
11 1928 1923.3 0.011 8.582
12 1359 1388.7 0.637 9.219
13 1007 1003.7 0.011 9.230
14 718 726.1 0.091 9.321
15 576 525.8 4.786 14.107
16 395 381.2 0.503 14.610
17 235 276.5 6.240 20.850
18 223 200.8 2.447 23.297
19 154 146.0 0.440 23.737
20 103 106.2 0.097 23.835
21 268 287.1 1.272 25.107
Chisq= 25.11 for 20 degrees of freedom, p= 0.80263
SUMMARY of craptest
p-value for no. of wins: 0.852500
p-value for throws/game: 0.802634
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-23_09:31
No. of wins: Observed Expected
98707 98585.9
z-score= 0.542, pvalue=0.70603
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66860 66666.7 0.561 0.561
2 37598 37654.3 0.084 0.645
3 26876 26954.7 0.230 0.875
4 19396 19313.5 0.353 1.228
5 13752 13851.4 0.714 1.941
6 10017 9943.5 0.543 2.484
7 7064 7145.0 0.919 3.403
8 5050 5139.1 1.544 4.947
9 3744 3699.9 0.526 5.473
10 2711 2666.3 0.749 6.222
11 1912 1923.3 0.067 6.289
12 1336 1388.7 2.003 8.292
13 995 1003.7 0.076 8.368
14 742 726.1 0.346 8.714
15 510 525.8 0.477 9.191
16 387 381.2 0.090 9.281
17 316 276.5 5.631 14.912
18 214 200.8 0.864 15.775
19 135 146.0 0.827 16.602
20 94 106.2 1.405 18.007
21 291 287.1 0.053 18.059
Chisq= 18.06 for 20 degrees of freedom, p= 0.41649
SUMMARY of craptest
p-value for no. of wins: 0.706027
p-value for throws/game: 0.416494
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0000,0.0003,0.0017,0.0027,0.0031,0.0032,0.0036,0.0095,0.0096,0.0167,
0.0169,0.0170,0.0221,0.0231,0.0271,0.0277,0.0422,0.0462,0.0469,0.0488,
0.0534,0.0570,0.0588,0.0658,0.0665,0.0669,0.0679,0.0692,0.0695,0.0901,
0.0984,0.1010,0.1090,0.1158,0.1196,0.1268,0.1271,0.1317,0.1329,0.1366,
0.1380,0.1413,0.1423,0.1426,0.1432,0.1441,0.1477,0.1510,0.1537,0.1592,
0.1609,0.1660,0.1710,0.1745,0.1760,0.1781,0.1783,0.1806,0.1821,0.1833,
0.1852,0.1951,0.2105,0.2144,0.2188,0.2264,0.2265,0.2319,0.2406,0.2410,
0.2413,0.2523,0.2525,0.2555,0.2577,0.2591,0.2655,0.2659,0.2690,0.2697,
0.2698,0.2715,0.2767,0.2803,0.2876,0.3103,0.3140,0.3157,0.3221,0.3255,
0.3257,0.3268,0.3287,0.3330,0.3359,0.3377,0.3406,0.3423,0.3437,0.3510,
0.3510,0.3514,0.3515,0.3522,0.3569,0.3605,0.3680,0.3720,0.3739,0.3769,
0.3779,0.3868,0.3881,0.3999,0.4092,0.4095,0.4165,0.4201,0.4249,0.4271,
0.4275,0.4293,0.4317,0.4324,0.4327,0.4394,0.4403,0.4442,0.4443,0.4449,
0.4551,0.4592,0.4652,0.4667,0.4669,0.4729,0.4802,0.4818,0.4864,0.4914,
0.4918,0.5040,0.5044,0.5077,0.5078,0.5092,0.5117,0.5158,0.5164,0.5225,
0.5399,0.5427,0.5456,0.5467,0.5479,0.5484,0.5489,0.5517,0.5560,0.5586,
0.5617,0.5660,0.5680,0.5699,0.5725,0.5733,0.5745,0.5775,0.5864,0.5880,
0.5923,0.5997,0.6008,0.6015,0.6079,0.6099,0.6137,0.6190,0.6196,0.6242,
0.6284,0.6321,0.6323,0.6334,0.6382,0.6423,0.6583,0.6669,0.6674,0.6751,
0.6917,0.6923,0.7037,0.7040,0.7060,0.7079,0.7207,0.7208,0.7236,0.7269,
0.7295,0.7324,0.7348,0.7373,0.7382,0.7400,0.7409,0.7412,0.7425,0.7582,
0.7783,0.7819,0.7871,0.7911,0.7949,0.7956,0.7971,0.7987,0.7992,0.8023,
0.8026,0.8057,0.8183,0.8255,0.8328,0.8360,0.8378,0.8492,0.8496,0.8525,
0.8545,0.8558,0.8577,0.8626,0.8650,0.8651,0.8708,0.8731,0.8860,0.8925,
0.8937,0.8974,0.8992,0.9044,0.9064,0.9206,0.9242,0.9306,0.9317,0.9321,
0.9414,0.9440,0.9543,0.9564,0.9627,0.9658,0.9696,0.9706,0.9714,0.9740,
0.9758,0.9763,0.9785,0.9819,0.9833,0.9856,0.9911,0.9967,0.9970,
Overall p-value after applying KStest on 269 p-values = 0.245231
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.