RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-06_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 15.86 11.8625 0.191607
2 to 25 15.72 21.1824 0.781762
3 to 26 15.77 16.6200 0.519614
4 to 27 15.71 8.2416 0.038896
5 to 28 15.68 21.6062 0.799657
6 to 29 16.08 12.8332 0.252722
7 to 30 15.83 9.1434 0.064344
8 to 31 15.85 17.2853 0.564795
9 to 32 15.85 13.6930 0.311299
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.460837
Tough bday spacings test for dh-ranFile-2018-07-06_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 6 47 78 83 95 89 51 23 14 8 6
(O-E)^2/E 1.1 2.9 0.3 2.2 0.1 1.5 0.0 1.5 0.1 0.3 0.9
Birthday Spacings: Sum(O-E)^2/E= 10.943, p= 0.638
RESULTS OF GCD FOR dh-ranFile-2018-07-06_18:31
Euclid's algorithm:
p-value, steps to gcd: 0.384819
p-value, dist. of gcd's: 0.683817
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-06_18:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.250 0.774 0.784 0.559 0.752 0.872 0.519 0.093
Bits 8 to 15---> 0.458 0.091 0.941 0.424 0.523 0.381 0.616 0.639
Bits 16 to 23---> 0.150 0.485 0.238 0.233 0.857 0.192 0.655 0.962
Bits 24 to 31---> 0.080 0.812 0.817 0.245 0.249 0.809 0.076 0.165
KS test for the above 32 p values: 0.094
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-06_18:31,
p-values for 5 runs: 0.4411, 0.5318, 0.7270, 0.0050, 0.4185
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-06_18:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 216 211.4 0.099 0.099
r= 29 5123 5134.0 0.024 0.123
r= 30 23026 23103.0 0.257 0.380
r= 31 11635 11551.5 0.603 0.983
chi-square = 0.983 with df = 3; p-value = 0.195
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-06_18:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 202 211.4 0.420 0.420
r= 30 5143 5134.0 0.016 0.435
r= 31 23073 23103.0 0.039 0.474
r= 32 11582 11551.5 0.080 0.555
chi-square = 0.555 with df = 3; p-value = 0.093
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-06_18:31
b-rank test for bits 1 to 8, p=0.45976
b-rank test for bits 2 to 9, p=0.55178
b-rank test for bits 3 to 10, p=0.68555
b-rank test for bits 4 to 11, p=0.56806
b-rank test for bits 5 to 12, p=0.61984
b-rank test for bits 6 to 13, p=0.48573
b-rank test for bits 7 to 14, p=0.88359
b-rank test for bits 8 to 15, p=0.09088
b-rank test for bits 9 to 16, p=0.09028
b-rank test for bits 10 to 17, p=0.01732
b-rank test for bits 11 to 18, p=0.71988
b-rank test for bits 12 to 19, p=0.73009
b-rank test for bits 13 to 20, p=0.31481
b-rank test for bits 14 to 21, p=0.73929
b-rank test for bits 15 to 22, p=0.09028
b-rank test for bits 16 to 23, p=0.73294
b-rank test for bits 17 to 24, p=0.43176
b-rank test for bits 18 to 25, p=0.49215
b-rank test for bits 19 to 26, p=0.08207
b-rank test for bits 20 to 27, p=0.92899
b-rank test for bits 21 to 28, p=0.40221
b-rank test for bits 22 to 29, p=0.87902
b-rank test for bits 23 to 30, p=0.33080
b-rank test for bits 24 to 31, p=0.90941
b-rank test for bits 25 to 32, p=0.05168
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 = 0.767124
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-06_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 142292 0.89 0.814363
2 142064 0.36 0.641092
3 141616 -0.69 0.246561
4 141737 -0.40 0.343607
5 142019 0.26 0.601117
6 141447 -1.08 0.140024
7 141472 -1.02 0.153438
8 142764 2.00 0.977082
9 141940 0.07 0.528563
10 142535 1.46 0.928108
11 141615 -0.69 0.245825
12 142524 1.44 0.924519
13 141580 -0.77 0.220809
14 142691 1.83 0.966100
15 142189 0.65 0.743262
16 142124 0.50 0.692013
17 141306 -1.41 0.079322
18 141965 0.13 0.551745
19 141874 -0.08 0.467106
20 141420 -1.14 0.126458
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-06_18:31
Bits used No. missing words z-score p-value
23 to 32 142233 1.1161 0.867811
22 to 31 141895 -0.0494 0.480295
21 to 30 142233 1.1161 0.867811
20 to 29 141789 -0.4149 0.339096
19 to 28 141657 -0.8701 0.192122
18 to 27 141739 -0.5873 0.278486
17 to 26 142459 1.8954 0.970981
16 to 25 142273 1.2540 0.895085
15 to 24 141767 -0.4908 0.311786
14 to 23 142267 1.2333 0.891276
13 to 22 142207 1.0264 0.847660
12 to 21 142183 0.9437 0.827336
11 to 20 142110 0.6920 0.755521
10 to 19 141701 -0.7184 0.236262
9 to 18 142246 1.1609 0.877165
8 to 17 142159 0.8609 0.805362
7 to 16 142018 0.3747 0.646067
6 to 15 141608 -1.0391 0.149386
5 to 14 141972 0.2161 0.585547
4 to 13 142104 0.6713 0.748978
3 to 12 142066 0.5402 0.705485
2 to 11 141383 -1.8149 0.034767
1 to 10 141961 0.1782 0.570706
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-06_18:31
Bits used No. missing words z-score p-value
28 to 32 142069 0.5413 0.705834
27 to 31 141960 0.1718 0.568188
26 to 30 142038 0.4362 0.668643
25 to 29 141438 -1.5977 0.055052
24 to 28 141812 -0.3299 0.370726
23 to 27 142140 0.7819 0.782873
22 to 26 141727 -0.6181 0.268265
21 to 25 142446 1.8192 0.965561
20 to 24 141839 -0.2384 0.405783
19 to 23 141322 -1.9909 0.023243
18 to 22 141810 -0.3367 0.368167
17 to 21 142320 1.3921 0.918054
16 to 20 141743 -0.5638 0.286435
15 to 19 142155 0.8328 0.797516
14 to 18 141918 0.0294 0.511723
13 to 17 141971 0.2091 0.582796
12 to 16 141745 -0.5571 0.288746
11 to 15 141515 -1.3367 0.090658
10 to 14 141996 0.2938 0.615543
9 to 13 142072 0.5514 0.709328
8 to 12 141835 -0.2520 0.400534
7 to 11 141931 0.0735 0.529279
6 to 10 141783 -0.4282 0.334239
5 to 9 141940 0.1040 0.541402
4 to 8 142322 1.3989 0.919076
3 to 7 142009 0.3379 0.632267
2 to 6 141509 -1.3571 0.087383
1 to 5 141657 -0.8554 0.196177
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-06_18:31
Bits used No. missing words z-score p-value
31 to 32 141881 -0.0836 0.466699
30 to 31 142180 0.7984 0.787691
29 to 30 141913 0.0108 0.504319
28 to 29 142122 0.6273 0.734784
27 to 28 142235 0.9607 0.831643
26 to 27 141621 -0.8505 0.197515
25 to 26 141752 -0.4641 0.321288
24 to 25 141459 -1.3284 0.092022
23 to 24 141866 -0.1278 0.449147
22 to 23 142284 1.1052 0.865468
21 to 22 142079 0.5005 0.691639
20 to 21 141662 -0.7296 0.232821
19 to 20 141999 0.2645 0.604308
18 to 19 141315 -1.7532 0.039785
17 to 18 141459 -1.3284 0.092022
16 to 17 142171 0.7719 0.779910
15 to 16 141429 -1.4169 0.078256
14 to 15 142434 1.5477 0.939153
13 to 14 141843 -0.1957 0.422437
12 to 13 141922 0.0374 0.514907
11 to 12 142146 0.6981 0.757456
10 to 11 141688 -0.6529 0.256913
9 to 10 141712 -0.5821 0.280252
8 to 9 142064 0.4563 0.675896
7 to 8 141691 -0.6440 0.259774
6 to 7 141685 -0.6617 0.254069
5 to 6 141642 -0.7886 0.215178
4 to 5 141666 -0.7178 0.236444
3 to 4 141912 0.0079 0.503142
2 to 3 142058 0.4386 0.669508
1 to 2 141725 -0.5437 0.293308
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-06_18:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2555.58 0.786 0.784056
Test results for specific bytes for dh-ranFile-2018-07-06_18:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2478.53 -0.304 0.380719
2 to 9 2476.28 -0.335 0.368664
3 to 10 2463.53 -0.516 0.303025
4 to 11 2447.95 -0.736 0.230820
5 to 12 2317.39 -2.583 0.004904
6 to 13 2465.38 -0.490 0.312225
7 to 14 2468.80 -0.441 0.329543
8 to 15 2559.06 0.835 0.798222
9 to 16 2587.78 1.241 0.892772
10 to 17 2441.61 -0.826 0.204483
11 to 18 2515.36 0.217 0.586000
12 to 19 2458.01 -0.594 0.276329
13 to 20 2573.81 1.044 0.851732
14 to 21 2467.65 -0.458 0.323644
15 to 22 2514.40 0.204 0.580661
16 to 23 2498.55 -0.020 0.491839
17 to 24 2617.09 1.656 0.951125
18 to 25 2421.24 -1.114 0.132662
19 to 26 2539.26 0.555 0.710641
20 to 27 2530.60 0.433 0.667422
21 to 28 2364.37 -1.918 0.027552
22 to 29 2366.52 -1.888 0.029530
23 to 30 2502.17 0.031 0.512234
24 to 31 2396.41 -1.465 0.071468
25 to 32 2614.71 1.622 0.947622
CDPARK for dh-ranFile-2018-07-06_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
3556 1.5068 0.934075
3532 0.4110 0.659449
3495 -1.2785 0.100530
3538 0.6849 0.753306
3519 -0.1826 0.427537
3567 2.0091 0.977738
3528 0.2283 0.590298
3532 0.4110 0.659449
3483 -1.8265 0.033889
3554 1.4155 0.921543
Square side=100, avg. no. parked=3530.40 sample std.=25.00
p-value of the KSTEST for those 10 p-values: 0.287647
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-06_18:31
0.1100,0.9331,0.3256,0.2542,0.9753,0.6974,0.8746,0.5651,0.2667,0.5575,
The KS test for those 10 p-values: 0.781423
The 3DSPHERES test for dh-ranFile-2018-07-06_18:31
sample no r^3 equiv. uni.
1 1.933 0.062411
2 35.546 0.694216
3 7.554 0.222594
4 21.498 0.511593
5 1.929 0.062270
6 2.355 0.075487
7 25.178 0.567973
8 6.290 0.189141
9 0.919 0.030176
10 11.666 0.322186
11 21.580 0.512928
12 21.850 0.517280
13 9.314 0.266902
14 15.661 0.406683
15 30.274 0.635462
16 33.094 0.668171
17 17.331 0.438807
18 34.645 0.684890
19 12.205 0.334234
20 32.545 0.662047
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.097955
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-06_18:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -2.0 -1.3 1.8 1.4 -1.5
0.8 -0.3 1.1 0.6 -1.1 -1.5
-2.1 2.4 -0.2 0.2 -1.9 -0.2
0.9 0.8 1.3 -0.6 0.9 -0.7
-0.7 -0.1 0.2 0.2 -0.7 2.2
-0.3 -0.2 -0.0 -0.6 0.6 -0.5
1.4 0.2 0.5 1.0 1.6 0.0
-1.1
Chi-square with 42 degrees of freedom:51.288054
z-score=1.013410, p-value=0.845814
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-06_18:31
Test no p-value
1 0.709692
2 0.537441
3 0.898094
4 0.024799
5 0.010093
6 0.556630
7 0.153963
8 0.041161
9 0.640824
10 0.467521
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.184356
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-06_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 66547 0.21 66830 0.40
3 25000.00 25078 0.24 24988 0.01
4 6666.67 6659 0.01 6550 2.04
5 1388.89 1429 1.16 1373 0.18
6 238.10 242 0.06 220 1.38
7 34.72 41 1.14 37 0.15
8 4.96 3 0.77 1 3.16
p=0.26935 p=0.70740
Number of rngs required: 687582, p-value: 0.171
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-06_18:31
No. of wins: Observed Expected
98590 98585.9
z-score= 0.019, pvalue=0.50739
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66627 66666.7 0.024 0.024
2 37643 37654.3 0.003 0.027
3 26804 26954.7 0.843 0.870
4 19437 19313.5 0.790 1.660
5 13915 13851.4 0.292 1.952
6 10133 9943.5 3.610 5.562
7 7139 7145.0 0.005 5.567
8 5065 5139.1 1.068 6.634
9 3754 3699.9 0.792 7.427
10 2657 2666.3 0.032 7.459
11 1890 1923.3 0.578 8.037
12 1342 1388.7 1.573 9.610
13 975 1003.7 0.822 10.431
14 744 726.1 0.439 10.870
15 495 525.8 1.808 12.679
16 360 381.2 1.174 13.852
17 279 276.5 0.022 13.874
18 187 200.8 0.952 14.827
19 137 146.0 0.553 15.380
20 110 106.2 0.135 15.514
21 307 287.1 1.377 16.892
Chisq= 16.89 for 20 degrees of freedom, p= 0.34001
SUMMARY of craptest
p-value for no. of wins: 0.507389
p-value for throws/game: 0.340008
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-06_18:31
No. of wins: Observed Expected
98755 98585.9
z-score= 0.756, pvalue=0.77532
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66566 66666.7 0.152 0.152
2 37864 37654.3 1.168 1.320
3 26821 26954.7 0.663 1.983
4 19420 19313.5 0.588 2.571
5 13961 13851.4 0.867 3.438
6 9861 9943.5 0.685 4.123
7 7145 7145.0 0.000 4.123
8 5190 5139.1 0.505 4.628
9 3765 3699.9 1.147 5.774
10 2573 2666.3 3.265 9.039
11 1905 1923.3 0.175 9.214
12 1316 1388.7 3.810 13.024
13 1038 1003.7 1.171 14.195
14 730 726.1 0.021 14.215
15 509 525.8 0.539 14.754
16 375 381.2 0.099 14.853
17 272 276.5 0.075 14.928
18 195 200.8 0.169 15.097
19 106 146.0 10.952 26.049
20 108 106.2 0.030 26.079
21 280 287.1 0.176 26.255
Chisq= 26.26 for 20 degrees of freedom, p= 0.84245
SUMMARY of craptest
p-value for no. of wins: 0.775325
p-value for throws/game: 0.842447
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0049,0.0050,0.0101,0.0173,0.0232,0.0248,0.0276,0.0295,0.0302,0.0339,
0.0348,0.0389,0.0398,0.0412,0.0517,0.0551,0.0623,0.0624,0.0643,0.0715,
0.0755,0.0762,0.0783,0.0793,0.0804,0.0821,0.0874,0.0903,0.0903,0.0907,
0.0909,0.0912,0.0920,0.0920,0.0933,0.0933,0.0940,0.0980,0.1005,0.1100,
0.1265,0.1327,0.1400,0.1494,0.1497,0.1534,0.1540,0.1655,0.1709,0.1844,
0.1891,0.1916,0.1920,0.1921,0.1947,0.1962,0.1975,0.2045,0.2152,0.2208,
0.2226,0.2308,0.2326,0.2328,0.2363,0.2364,0.2376,0.2450,0.2458,0.2466,
0.2493,0.2497,0.2527,0.2541,0.2542,0.2569,0.2598,0.2667,0.2669,0.2683,
0.2694,0.2763,0.2785,0.2803,0.2864,0.2876,0.2887,0.2933,0.3030,0.3113,
0.3118,0.3122,0.3148,0.3213,0.3222,0.3236,0.3256,0.3295,0.3308,0.3342,
0.3342,0.3391,0.3400,0.3436,0.3682,0.3687,0.3707,0.3807,0.3807,0.3848,
0.4005,0.4022,0.4058,0.4067,0.4185,0.4224,0.4245,0.4275,0.4318,0.4388,
0.4411,0.4491,0.4581,0.4598,0.4608,0.4667,0.4671,0.4675,0.4803,0.4851,
0.4857,0.4918,0.4921,0.5031,0.5043,0.5074,0.5116,0.5117,0.5122,0.5129,
0.5149,0.5173,0.5186,0.5196,0.5228,0.5286,0.5293,0.5318,0.5374,0.5414,
0.5517,0.5518,0.5566,0.5575,0.5585,0.5648,0.5651,0.5680,0.5681,0.5682,
0.5707,0.5807,0.5828,0.5855,0.5860,0.5903,0.6011,0.6043,0.6155,0.6162,
0.6198,0.6323,0.6355,0.6380,0.6391,0.6408,0.6411,0.6461,0.6548,0.6594,
0.6594,0.6620,0.6674,0.6682,0.6686,0.6695,0.6759,0.6838,0.6849,0.6856,
0.6916,0.6920,0.6942,0.6974,0.7055,0.7058,0.7074,0.7093,0.7097,0.7106,
0.7199,0.7270,0.7301,0.7329,0.7348,0.7393,0.7433,0.7490,0.7518,0.7533,
0.7555,0.7575,0.7671,0.7735,0.7753,0.7799,0.7814,0.7818,0.7829,0.7841,
0.7842,0.7877,0.7975,0.7982,0.7997,0.8054,0.8090,0.8123,0.8144,0.8171,
0.8273,0.8316,0.8424,0.8458,0.8477,0.8517,0.8573,0.8655,0.8678,0.8678,
0.8716,0.8746,0.8772,0.8790,0.8836,0.8913,0.8928,0.8951,0.8981,0.9094,
0.9181,0.9191,0.9215,0.9245,0.9281,0.9290,0.9331,0.9341,0.9392,0.9413,
0.9476,0.9511,0.9618,0.9656,0.9661,0.9710,0.9753,0.9771,0.9777,
Overall p-value after applying KStest on 269 p-values = 0.445248
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.