RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-30_11:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.88 8.6216 0.048608
2 to 25 15.85 14.9237 0.399019
3 to 26 15.81 20.5792 0.754321
4 to 27 15.65 14.1127 0.340890
5 to 28 15.61 17.6675 0.589898
6 to 29 15.90 13.8140 0.319780
7 to 30 15.56 29.2281 0.967521
8 to 31 15.64 15.3573 0.430234
9 to 32 15.46 32.7263 0.987794
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.619202
Tough bday spacings test for dh-ranFile-2018-06-30_11:31: 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 37 70 108 92 78 53 30 9 5 5
(O-E)^2/E 1.6 0.0 0.1 1.1 0.3 0.0 0.0 0.0 2.3 0.4 0.2
Birthday Spacings: Sum(O-E)^2/E= 6.135, p= 0.196
RESULTS OF GCD FOR dh-ranFile-2018-06-30_11:31
Euclid's algorithm:
p-value, steps to gcd: 0.697698
p-value, dist. of gcd's: 0.852722
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-30_11:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.959 0.409 0.070 0.840 0.985 0.474 0.671 0.149
Bits 8 to 15---> 0.310 0.168 0.040 0.686 0.082 0.442 0.644 0.842
Bits 16 to 23---> 0.249 0.776 0.347 0.064 0.201 0.545 0.477 0.160
Bits 24 to 31---> 0.298 0.149 0.280 0.140 0.736 0.515 0.792 0.025
KS test for the above 32 p values: 0.781
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-30_11:31,
p-values for 5 runs: 0.3212, 0.8379, 0.3297, 0.9639, 0.5944
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-30_11:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 209 211.4 0.028 0.028
r= 29 5220 5134.0 1.440 1.468
r= 30 23068 23103.0 0.053 1.521
r= 31 11503 11551.5 0.204 1.725
chi-square = 1.725 with df = 3; p-value = 0.369
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-30_11:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 205 211.4 0.195 0.195
r= 30 5261 5134.0 3.141 3.336
r= 31 22966 23103.0 0.813 4.149
r= 32 11568 11551.5 0.024 4.172
chi-square = 4.172 with df = 3; p-value = 0.757
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-30_11:31
b-rank test for bits 1 to 8, p=0.26576
b-rank test for bits 2 to 9, p=0.85387
b-rank test for bits 3 to 10, p=0.99926
b-rank test for bits 4 to 11, p=0.72190
b-rank test for bits 5 to 12, p=0.45595
b-rank test for bits 6 to 13, p=0.23664
b-rank test for bits 7 to 14, p=0.76775
b-rank test for bits 8 to 15, p=0.93273
b-rank test for bits 9 to 16, p=0.54261
b-rank test for bits 10 to 17, p=0.33589
b-rank test for bits 11 to 18, p=0.90906
b-rank test for bits 12 to 19, p=0.68646
b-rank test for bits 13 to 20, p=0.12743
b-rank test for bits 14 to 21, p=0.15269
b-rank test for bits 15 to 22, p=0.10966
b-rank test for bits 16 to 23, p=0.18749
b-rank test for bits 17 to 24, p=0.73823
b-rank test for bits 18 to 25, p=0.09547
b-rank test for bits 19 to 26, p=0.87540
b-rank test for bits 20 to 27, p=0.28092
b-rank test for bits 21 to 28, p=0.21844
b-rank test for bits 22 to 29, p=0.52477
b-rank test for bits 23 to 30, p=0.02819
b-rank test for bits 24 to 31, p=0.99397
b-rank test for bits 25 to 32, p=0.06427
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 = 0.430441
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-30_11:31
(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 142585 1.58 0.942794
2 142328 0.98 0.836013
3 141985 0.18 0.570167
4 141963 0.13 0.549895
5 141097 -1.90 0.028850
6 142674 1.79 0.963000
7 142025 0.27 0.606519
8 142130 0.52 0.696928
9 142548 1.49 0.932179
10 141961 0.12 0.548045
11 141685 -0.52 0.300092
12 142058 0.35 0.635840
13 141938 0.07 0.526704
14 142166 0.60 0.725646
15 141983 0.17 0.568331
16 142472 1.31 0.905686
17 142193 0.66 0.746264
18 142377 1.09 0.862734
19 141421 -1.14 0.126944
20 141771 -0.32 0.373272
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-30_11:31
Bits used No. missing words z-score p-value
23 to 32 141389 -1.7942 0.036387
22 to 31 141517 -1.3529 0.088050
21 to 30 141851 -0.2011 0.420295
20 to 29 142150 0.8299 0.796701
19 to 28 141838 -0.2460 0.402855
18 to 27 141803 -0.3667 0.356938
17 to 26 141466 -1.5287 0.063166
16 to 25 141584 -1.1218 0.130968
15 to 24 141836 -0.2529 0.400187
14 to 23 141632 -0.9563 0.169458
13 to 22 141882 -0.0942 0.462459
12 to 21 141926 0.0575 0.522920
11 to 20 141752 -0.5425 0.293731
10 to 19 141857 -0.1804 0.428400
9 to 18 141640 -0.9287 0.176516
8 to 17 142160 0.8644 0.806310
7 to 16 141373 -1.8494 0.032199
6 to 15 141696 -0.7356 0.230981
5 to 14 141405 -1.7391 0.041011
4 to 13 141504 -1.3977 0.081103
3 to 12 141927 0.0609 0.524293
2 to 11 141803 -0.3667 0.356938
1 to 10 141968 0.2023 0.580163
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-30_11:31
Bits used No. missing words z-score p-value
28 to 32 142870 3.2565 0.999436
27 to 31 142065 0.5277 0.701145
26 to 30 141678 -0.7842 0.216470
25 to 29 141518 -1.3265 0.092330
24 to 28 142343 1.4701 0.929228
23 to 27 141809 -0.3401 0.366890
22 to 26 141942 0.1107 0.544091
21 to 25 142042 0.4497 0.673547
20 to 24 141548 -1.2248 0.110316
19 to 23 141720 -0.6418 0.260503
18 to 22 141861 -0.1638 0.434932
17 to 21 142731 2.7853 0.997326
16 to 20 141699 -0.7130 0.237928
15 to 19 142071 0.5480 0.708166
14 to 18 141772 -0.4655 0.320778
13 to 17 141707 -0.6859 0.246399
12 to 16 142150 0.8158 0.792702
11 to 15 141553 -1.2079 0.113543
10 to 14 141968 0.1989 0.578822
9 to 13 141707 -0.6859 0.246399
8 to 12 141796 -0.3842 0.350426
7 to 11 141868 -0.1401 0.444290
6 to 10 141993 0.2836 0.611652
5 to 9 141749 -0.5435 0.293396
4 to 8 142255 1.1718 0.879354
3 to 7 141941 0.1074 0.542747
2 to 6 141750 -0.5401 0.294564
1 to 5 141334 -1.9503 0.025572
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-30_11:31
Bits used No. missing words z-score p-value
31 to 32 142671 2.2468 0.987674
30 to 31 141785 -0.3668 0.356901
29 to 30 141974 0.1908 0.575646
28 to 29 141931 0.0639 0.525484
27 to 28 141559 -1.0334 0.150703
26 to 27 142270 1.0639 0.856318
25 to 26 142004 0.2793 0.609978
24 to 25 141994 0.2498 0.598615
23 to 24 141934 0.0728 0.529007
22 to 23 141642 -0.7886 0.215178
21 to 22 141491 -1.2340 0.108599
20 to 21 141987 0.2291 0.590610
19 to 20 141915 0.0167 0.506672
18 to 19 141472 -1.2901 0.098515
17 to 18 140606 -3.8446 0.000060
16 to 17 142359 1.3265 0.907656
15 to 16 141788 -0.3579 0.360207
14 to 15 141360 -1.6204 0.052569
13 to 14 142371 1.3619 0.913379
12 to 13 141534 -1.1072 0.134111
11 to 12 141613 -0.8741 0.191024
10 to 11 141914 0.0138 0.505496
9 to 10 142161 0.7424 0.771074
8 to 9 141662 -0.7296 0.232821
7 to 8 142145 0.6952 0.756532
6 to 7 141712 -0.5821 0.280252
5 to 6 141865 -0.1308 0.447980
4 to 5 142087 0.5241 0.699896
3 to 4 141889 -0.0600 0.476090
2 to 3 141980 0.2085 0.582568
1 to 2 142326 1.2291 0.890486
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-30_11:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2319.26 -2.556 0.005293
Test results for specific bytes for dh-ranFile-2018-06-30_11:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2460.03 -0.565 0.285943
2 to 9 2505.29 0.075 0.529793
3 to 10 2326.78 -2.450 0.007148
4 to 11 2342.37 -2.229 0.012902
5 to 12 2573.08 1.033 0.849309
6 to 13 2496.72 -0.046 0.481493
7 to 14 2270.56 -3.245 0.000588
8 to 15 2519.51 0.276 0.608671
9 to 16 2461.73 -0.541 0.294156
10 to 17 2777.64 3.926 0.999957
11 to 18 2545.66 0.646 0.740765
12 to 19 2503.45 0.049 0.519444
13 to 20 2503.24 0.046 0.518287
14 to 21 2441.90 -0.822 0.205625
15 to 22 2557.68 0.816 0.792664
16 to 23 2505.60 0.079 0.531536
17 to 24 2449.13 -0.719 0.235927
18 to 25 2668.00 2.376 0.991245
19 to 26 2412.92 -1.232 0.109061
20 to 27 2505.02 0.071 0.528276
21 to 28 2526.96 0.381 0.648507
22 to 29 2375.35 -1.763 0.038961
23 to 30 2447.96 -0.736 0.230900
24 to 31 2534.10 0.482 0.685190
25 to 32 2485.20 -0.209 0.417120
CDPARK for dh-ranFile-2018-06-30_11:31: 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
3530 0.3196 0.625377
3520 -0.1370 0.445521
3535 0.5479 0.708135
3525 0.0913 0.536383
3542 0.8676 0.807188
3516 -0.3196 0.374623
3524 0.0457 0.518210
3520 -0.1370 0.445521
3518 -0.2283 0.409702
3507 -0.7306 0.232514
Square side=100, avg. no. parked=3523.70 sample std.=9.50
p-value of the KSTEST for those 10 p-values: 0.292264
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-30_11:31
0.0409,0.6359,0.8961,0.8161,0.9585,0.9248,0.2999,0.6052,0.1027,0.2312,
The KS test for those 10 p-values: 0.615603
The 3DSPHERES test for dh-ranFile-2018-06-30_11:31
sample no r^3 equiv. uni.
1 28.907 0.618475
2 14.262 0.378360
3 8.959 0.258161
4 26.145 0.581680
5 25.081 0.566567
6 15.197 0.397440
7 7.457 0.220084
8 40.198 0.738136
9 57.271 0.851775
10 4.651 0.143624
11 22.091 0.521148
12 6.389 0.191819
13 24.404 0.556680
14 47.722 0.796227
15 31.159 0.646064
16 28.423 0.612269
17 48.808 0.803466
18 34.931 0.687877
19 9.440 0.269975
20 2.637 0.084144
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.523871
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-30_11:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 0.5 -0.8 1.4 1.3 0.1
-1.4 0.4 -1.9 2.4 -0.2 0.4
1.1 0.1 -1.1 -2.2 -0.5 -0.3
0.2 0.1 0.5 0.3 1.0 -0.6
-0.0 0.2 1.2 1.0 -0.8 0.2
1.0 0.4 0.0 -0.9 -1.0 1.9
0.3 -0.7 0.1 -0.7 -1.3 0.0
1.8
Chi-square with 42 degrees of freedom:43.593910
z-score=0.173910, p-value=0.596521
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-30_11:31
Test no p-value
1 0.578352
2 0.296728
3 0.008832
4 0.140254
5 0.065133
6 0.004057
7 0.451826
8 0.597472
9 0.990448
10 0.391783
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.061076
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-30_11:31:
(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 66891 0.75 66511 0.36
3 25000.00 24827 1.20 25151 0.91
4 6666.67 6617 0.37 6625 0.26
5 1388.89 1387 0.00 1436 1.60
6 238.10 233 0.11 236 0.02
7 34.72 42 1.53 37 0.15
8 4.96 2 1.77 3 0.77
p=0.54550 p=0.33369
Number of rngs required: 689383, p-value: 0.872
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-30_11:31
No. of wins: Observed Expected
98458 98585.9
z-score=-0.572, pvalue=0.28371
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66417 66666.7 0.935 0.935
2 37695 37654.3 0.044 0.979
3 27083 26954.7 0.610 1.589
4 19243 19313.5 0.257 1.846
5 13940 13851.4 0.566 2.413
6 10085 9943.5 2.012 4.425
7 7056 7145.0 1.109 5.534
8 5058 5139.1 1.279 6.813
9 3714 3699.9 0.054 6.867
10 2764 2666.3 3.580 10.448
11 1846 1923.3 3.109 13.557
12 1426 1388.7 1.000 14.556
13 998 1003.7 0.033 14.589
14 712 726.1 0.275 14.864
15 565 525.8 2.917 17.781
16 386 381.2 0.062 17.843
17 267 276.5 0.329 18.172
18 188 200.8 0.820 18.992
19 148 146.0 0.028 19.019
20 114 106.2 0.571 19.590
21 295 287.1 0.217 19.807
Chisq= 19.81 for 20 degrees of freedom, p= 0.52992
SUMMARY of craptest
p-value for no. of wins: 0.283709
p-value for throws/game: 0.529916
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-30_11:31
No. of wins: Observed Expected
98713 98585.9
z-score= 0.569, pvalue=0.71520
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66658 66666.7 0.001 0.001
2 37468 37654.3 0.922 0.923
3 26749 26954.7 1.570 2.493
4 19653 19313.5 5.969 8.463
5 13722 13851.4 1.209 9.672
6 10078 9943.5 1.818 11.490
7 7118 7145.0 0.102 11.592
8 5191 5139.1 0.525 12.117
9 3718 3699.9 0.089 12.206
10 2643 2666.3 0.204 12.409
11 1931 1923.3 0.031 12.440
12 1380 1388.7 0.055 12.495
13 978 1003.7 0.659 13.154
14 771 726.1 2.771 15.925
15 541 525.8 0.437 16.362
16 392 381.2 0.309 16.671
17 270 276.5 0.155 16.826
18 192 200.8 0.388 17.214
19 149 146.0 0.062 17.276
20 110 106.2 0.135 17.411
21 288 287.1 0.003 17.414
Chisq= 17.41 for 20 degrees of freedom, p= 0.37404
SUMMARY of craptest
p-value for no. of wins: 0.715203
p-value for throws/game: 0.374044
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0001,0.0006,0.0041,0.0053,0.0071,0.0088,0.0129,0.0252,0.0256,0.0282,
0.0289,0.0322,0.0364,0.0390,0.0403,0.0409,0.0410,0.0486,0.0526,0.0611,
0.0632,0.0642,0.0643,0.0651,0.0704,0.0811,0.0817,0.0841,0.0880,0.0923,
0.0955,0.0985,0.1027,0.1086,0.1091,0.1097,0.1103,0.1135,0.1269,0.1274,
0.1310,0.1341,0.1402,0.1403,0.1436,0.1486,0.1492,0.1507,0.1527,0.1596,
0.1680,0.1695,0.1765,0.1875,0.1910,0.1918,0.1962,0.2010,0.2056,0.2152,
0.2165,0.2184,0.2201,0.2309,0.2310,0.2312,0.2325,0.2328,0.2359,0.2366,
0.2379,0.2464,0.2464,0.2487,0.2582,0.2605,0.2658,0.2700,0.2798,0.2803,
0.2809,0.2837,0.2859,0.2923,0.2934,0.2937,0.2942,0.2946,0.2967,0.2977,
0.2999,0.3001,0.3101,0.3198,0.3208,0.3212,0.3297,0.3337,0.3359,0.3409,
0.3473,0.3504,0.3569,0.3569,0.3569,0.3602,0.3669,0.3686,0.3733,0.3740,
0.3746,0.3784,0.3918,0.3974,0.3990,0.4002,0.4029,0.4086,0.4097,0.4171,
0.4203,0.4284,0.4302,0.4304,0.4349,0.4424,0.4443,0.4455,0.4455,0.4480,
0.4518,0.4560,0.4625,0.4741,0.4761,0.4772,0.4815,0.5055,0.5067,0.5154,
0.5182,0.5183,0.5194,0.5211,0.5229,0.5239,0.5243,0.5248,0.5255,0.5267,
0.5283,0.5290,0.5298,0.5299,0.5315,0.5364,0.5426,0.5427,0.5441,0.5455,
0.5455,0.5480,0.5499,0.5567,0.5666,0.5683,0.5702,0.5756,0.5784,0.5788,
0.5802,0.5817,0.5826,0.5899,0.5906,0.5944,0.5965,0.5975,0.5986,0.6052,
0.6065,0.6087,0.6100,0.6117,0.6123,0.6156,0.6185,0.6192,0.6254,0.6358,
0.6359,0.6444,0.6461,0.6485,0.6709,0.6735,0.6852,0.6859,0.6865,0.6879,
0.6969,0.6977,0.6999,0.7011,0.7081,0.7082,0.7152,0.7219,0.7256,0.7358,
0.7381,0.7382,0.7408,0.7463,0.7543,0.7565,0.7566,0.7677,0.7711,0.7759,
0.7814,0.7915,0.7927,0.7927,0.7962,0.7967,0.8035,0.8063,0.8072,0.8161,
0.8360,0.8379,0.8402,0.8425,0.8493,0.8518,0.8527,0.8539,0.8563,0.8627,
0.8724,0.8754,0.8794,0.8905,0.8961,0.9057,0.9077,0.9091,0.9134,0.9248,
0.9292,0.9322,0.9327,0.9428,0.9585,0.9588,0.9630,0.9639,0.9675,0.9851,
0.9877,0.9878,0.9904,0.9912,0.9940,0.9973,0.9993,0.9994,1.0000,
Overall p-value after applying KStest on 269 p-values = 0.117753
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.