RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-21_06:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.78 17.9393 0.607321
2 to 25 15.59 23.1099 0.854292
3 to 26 15.79 21.6594 0.801824
4 to 27 15.50 30.4537 0.976747
5 to 28 15.71 15.4363 0.435910
6 to 29 15.66 12.7395 0.246556
7 to 30 15.84 21.9634 0.813870
8 to 31 15.78 14.5705 0.373610
9 to 32 15.82 14.2554 0.351054
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.421045
Tough bday spacings test for dh-ranFile-2018-06-21_06:31: 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 8 34 69 100 110 77 48 31 11 8 4
(O-E)^2/E 0.1 0.2 0.2 0.1 1.6 0.0 0.3 0.1 1.0 0.3 0.0
Birthday Spacings: Sum(O-E)^2/E= 3.886, p= 0.048
RESULTS OF GCD FOR dh-ranFile-2018-06-21_06:31
Euclid's algorithm:
p-value, steps to gcd: 0.701101
p-value, dist. of gcd's: 0.671018
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-21_06:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.793 0.384 0.042 0.673 0.339 0.667 0.352 0.676
Bits 8 to 15---> 0.405 0.194 0.677 0.321 0.565 0.558 0.438 0.554
Bits 16 to 23---> 0.669 0.738 0.268 0.370 0.749 0.540 0.829 0.463
Bits 24 to 31---> 0.661 0.053 0.755 0.684 0.577 0.487 0.448 0.539
KS test for the above 32 p values: 0.931
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-21_06:31,
p-values for 5 runs: 0.8454, 0.5502, 0.1264, 0.9676, 0.5523
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-21_06:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 209 211.4 0.028 0.028
r= 29 5149 5134.0 0.044 0.071
r= 30 23244 23103.0 0.860 0.931
r= 31 11398 11551.5 2.040 2.972
chi-square = 2.972 with df = 3; p-value = 0.604
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-21_06:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 231 211.4 1.814 1.814
r= 30 5057 5134.0 1.155 2.969
r= 31 23082 23103.0 0.019 2.988
r= 32 11630 11551.5 0.533 3.521
chi-square = 3.521 with df = 3; p-value = 0.682
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-21_06:31
b-rank test for bits 1 to 8, p=0.21311
b-rank test for bits 2 to 9, p=0.63785
b-rank test for bits 3 to 10, p=0.22905
b-rank test for bits 4 to 11, p=0.72688
b-rank test for bits 5 to 12, p=0.87460
b-rank test for bits 6 to 13, p=0.68169
b-rank test for bits 7 to 14, p=0.00733
b-rank test for bits 8 to 15, p=0.75800
b-rank test for bits 9 to 16, p=0.53261
b-rank test for bits 10 to 17, p=0.47884
b-rank test for bits 11 to 18, p=0.11329
b-rank test for bits 12 to 19, p=0.34127
b-rank test for bits 13 to 20, p=0.79779
b-rank test for bits 14 to 21, p=0.76391
b-rank test for bits 15 to 22, p=0.48818
b-rank test for bits 16 to 23, p=0.43417
b-rank test for bits 17 to 24, p=0.96238
b-rank test for bits 18 to 25, p=0.76997
b-rank test for bits 19 to 26, p=0.23470
b-rank test for bits 20 to 27, p=0.79093
b-rank test for bits 21 to 28, p=0.96513
b-rank test for bits 22 to 29, p=0.85046
b-rank test for bits 23 to 30, p=0.90363
b-rank test for bits 24 to 31, p=0.68779
b-rank test for bits 25 to 32, p=0.09767
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 = 0.311410
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-21_06:31
(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 141728 -0.42 0.335904
2 141999 0.21 0.582975
3 141190 -1.68 0.046413
4 141230 -1.59 0.056231
5 142365 1.06 0.856483
6 142345 1.02 0.845642
7 141543 -0.86 0.196023
8 141802 -0.25 0.400996
9 142030 0.28 0.611005
10 141460 -1.05 0.146897
11 142097 0.44 0.669481
12 142669 1.77 0.962045
13 141366 -1.27 0.102138
14 141254 -1.53 0.062867
15 141993 0.20 0.577496
16 142081 0.40 0.655826
17 141653 -0.60 0.274619
18 141692 -0.51 0.305804
19 142219 0.72 0.765322
20 142143 0.55 0.707453
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-21_06:31
Bits used No. missing words z-score p-value
23 to 32 141980 0.2437 0.596264
22 to 31 141709 -0.6908 0.244848
21 to 30 142251 1.1782 0.880636
20 to 29 142872 3.3196 0.999549
19 to 28 142489 1.9989 0.977188
18 to 27 141998 0.3058 0.620106
17 to 26 141811 -0.3391 0.367279
16 to 25 141887 -0.0770 0.469312
15 to 24 141868 -0.1425 0.443336
14 to 23 141881 -0.0977 0.461089
13 to 22 142119 0.7230 0.765160
12 to 21 142581 2.3161 0.989724
11 to 20 142155 0.8471 0.801541
10 to 19 142269 1.2402 0.892557
9 to 18 142119 0.7230 0.765160
8 to 17 142003 0.3230 0.626652
7 to 16 142490 2.0023 0.977374
6 to 15 142198 0.9954 0.840233
5 to 14 141415 -1.7046 0.044136
4 to 13 141306 -2.0804 0.018742
3 to 12 142080 0.5885 0.721907
2 to 11 141810 -0.3425 0.365981
1 to 10 141916 0.0230 0.509175
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-21_06:31
Bits used No. missing words z-score p-value
28 to 32 142113 0.6904 0.755031
27 to 31 142465 1.8836 0.970192
26 to 30 141935 0.0870 0.534671
25 to 29 142102 0.6531 0.743160
24 to 28 142188 0.9446 0.827580
23 to 27 141973 0.2158 0.585440
22 to 26 141716 -0.6554 0.256119
21 to 25 142108 0.6735 0.749672
20 to 24 142002 0.3141 0.623291
19 to 23 142158 0.8429 0.800372
18 to 22 142127 0.7379 0.769702
17 to 21 141900 -0.0316 0.487385
16 to 20 142136 0.7684 0.778867
15 to 19 141770 -0.4723 0.318355
14 to 18 141595 -1.0655 0.143319
13 to 17 142097 0.6362 0.737667
12 to 16 141938 0.0972 0.538711
11 to 15 142327 1.4158 0.921587
10 to 14 141752 -0.5333 0.296905
9 to 13 142296 1.3107 0.905028
8 to 12 142233 1.0972 0.863720
7 to 11 141323 -1.9876 0.023430
6 to 10 141859 -0.1706 0.432265
5 to 9 141561 -1.1808 0.118845
4 to 8 141978 0.2328 0.592034
3 to 7 141429 -1.6282 0.051737
2 to 6 141874 -0.1198 0.452336
1 to 5 141763 -0.4960 0.309935
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-21_06:31
Bits used No. missing words z-score p-value
31 to 32 142347 1.2911 0.901659
30 to 31 142335 1.2557 0.895381
29 to 30 141989 0.2350 0.592901
28 to 29 141943 0.0993 0.539559
27 to 28 142033 0.3648 0.642373
26 to 27 141630 -0.8240 0.204975
25 to 26 141927 0.0521 0.520785
24 to 25 142654 2.1967 0.985978
23 to 24 141779 -0.3845 0.350321
22 to 23 141313 -1.7591 0.039282
21 to 22 142261 1.0374 0.850219
20 to 21 142053 0.4238 0.664146
19 to 20 141377 -1.5703 0.058173
18 to 19 141771 -0.4081 0.341617
17 to 18 141930 0.0610 0.524310
16 to 17 141880 -0.0865 0.465527
15 to 16 142039 0.3825 0.648958
14 to 15 142352 1.3058 0.904192
13 to 14 141786 -0.3638 0.358002
12 to 13 141631 -0.8210 0.205814
11 to 12 141871 -0.1131 0.454988
10 to 11 141606 -0.8948 0.185453
9 to 10 141807 -0.3019 0.381380
8 to 9 142085 0.5182 0.697841
7 to 8 141932 0.0669 0.526659
6 to 7 142112 0.5978 0.725029
5 to 6 141701 -0.6145 0.269428
4 to 5 141411 -1.4700 0.070781
3 to 4 141661 -0.7325 0.231921
2 to 3 142069 0.4710 0.681181
1 to 2 141859 -0.1485 0.440988
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-21_06:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2459.09 -0.579 0.281450
Test results for specific bytes for dh-ranFile-2018-06-21_06:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2560.30 0.853 0.803095
2 to 9 2334.80 -2.336 0.009739
3 to 10 2469.90 -0.426 0.335180
4 to 11 2489.28 -0.152 0.439767
5 to 12 2317.60 -2.580 0.004946
6 to 13 2471.70 -0.400 0.344508
7 to 14 2484.90 -0.214 0.415428
8 to 15 2419.28 -1.142 0.126808
9 to 16 2515.24 0.215 0.585301
10 to 17 2510.49 0.148 0.558974
11 to 18 2492.86 -0.101 0.459811
12 to 19 2503.42 0.048 0.519282
13 to 20 2512.34 0.174 0.569255
14 to 21 2537.44 0.530 0.701774
15 to 22 2662.88 2.303 0.989372
16 to 23 2478.10 -0.310 0.378386
17 to 24 2401.87 -1.388 0.082596
18 to 25 2382.64 -1.660 0.048491
19 to 26 2350.29 -2.117 0.017123
20 to 27 2489.35 -0.151 0.440130
21 to 28 2524.34 0.344 0.634670
22 to 29 2274.57 -3.188 0.000716
23 to 30 2509.17 0.130 0.551612
24 to 31 2510.11 0.143 0.556846
25 to 32 2580.97 1.145 0.873919
CDPARK for dh-ranFile-2018-06-21_06:31: 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
3479 -2.0091 0.022262
3506 -0.7763 0.218799
3512 -0.5023 0.307734
3536 0.5936 0.723613
3526 0.1370 0.554479
3530 0.3196 0.625377
3515 -0.3653 0.357445
3549 1.1872 0.882429
3474 -2.2374 0.012629
3535 0.5479 0.708135
Square side=100, avg. no. parked=3516.20 sample std.=23.23
p-value of the KSTEST for those 10 p-values: 0.574413
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-21_06:31
0.4225,0.6237,0.6705,0.9236,0.5763,0.5458,0.7934,0.6473,0.5857,0.4391,
The KS test for those 10 p-values: 0.101177
The 3DSPHERES test for dh-ranFile-2018-06-21_06:31
sample no r^3 equiv. uni.
1 64.445 0.883301
2 41.349 0.747990
3 0.373 0.012364
4 20.719 0.498734
5 15.131 0.396119
6 11.681 0.322525
7 158.218 0.994877
8 39.570 0.732600
9 17.394 0.439991
10 5.712 0.173383
11 0.327 0.010840
12 236.336 0.999621
13 5.564 0.169287
14 18.784 0.465336
15 1.056 0.034586
16 10.353 0.291857
17 7.052 0.209482
18 42.653 0.758709
19 0.030 0.001010
20 19.287 0.474243
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.090417
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-21_06:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -1.2 0.6 -0.5 -0.4 0.5
-1.0 -1.7 1.5 0.5 -1.3 -0.7
-0.1 1.7 1.5 -0.4 1.1 -1.0
-0.2 -1.2 0.5 -1.2 -1.6 1.3
1.0 -0.8 0.4 -0.3 0.4 2.0
1.0 -0.5 -1.0 -0.6 0.9 1.5
-0.7 1.1 2.1 0.4 -1.3 0.0
2.7
Chi-square with 42 degrees of freedom:54.068736
z-score=1.316807, p-value=0.899652
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-21_06:31
Test no p-value
1 0.065950
2 0.702761
3 0.668722
4 0.221556
5 0.007309
6 0.275683
7 0.674154
8 0.007604
9 0.899446
10 0.052043
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.038284
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-21_06:31:
(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 66544 0.23 66924 0.99
3 25000.00 25093 0.35 24744 2.62
4 6666.67 6633 0.17 6670 0.00
5 1388.89 1432 1.34 1429 1.16
6 238.10 265 3.04 188 10.54
7 34.72 27 1.72 39 0.53
8 4.96 5 0.00 5 0.00
p=0.66381 p=0.98538
Number of rngs required: 687804, p-value: 0.245
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-21_06:31
No. of wins: Observed Expected
98410 98585.9
z-score=-0.787, pvalue=0.21577
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66500 66666.7 0.417 0.417
2 37803 37654.3 0.587 1.004
3 27015 26954.7 0.135 1.138
4 19228 19313.5 0.378 1.517
5 13973 13851.4 1.067 2.584
6 9897 9943.5 0.218 2.802
7 7210 7145.0 0.591 3.393
8 5140 5139.1 0.000 3.393
9 3655 3699.9 0.544 3.937
10 2628 2666.3 0.550 4.487
11 1881 1923.3 0.932 5.418
12 1389 1388.7 0.000 5.418
13 1027 1003.7 0.540 5.959
14 713 726.1 0.238 6.196
15 522 525.8 0.028 6.224
16 371 381.2 0.270 6.495
17 285 276.5 0.259 6.754
18 201 200.8 0.000 6.754
19 133 146.0 1.155 7.909
20 107 106.2 0.006 7.914
21 322 287.1 4.239 12.153
Chisq= 12.15 for 20 degrees of freedom, p= 0.08930
SUMMARY of craptest
p-value for no. of wins: 0.215775
p-value for throws/game: 0.089300
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-21_06:31
No. of wins: Observed Expected
98688 98585.9
z-score= 0.457, pvalue=0.67611
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66975 66666.7 1.426 1.426
2 38003 37654.3 3.229 4.655
3 26396 26954.7 11.582 16.237
4 19230 19313.5 0.361 16.597
5 13791 13851.4 0.264 16.861
6 9864 9943.5 0.636 17.497
7 7186 7145.0 0.235 17.732
8 5146 5139.1 0.009 17.741
9 3691 3699.9 0.021 17.763
10 2692 2666.3 0.248 18.010
11 1957 1923.3 0.589 18.600
12 1489 1388.7 7.238 25.838
13 1007 1003.7 0.011 25.849
14 702 726.1 0.803 26.651
15 524 525.8 0.006 26.658
16 378 381.2 0.026 26.684
17 282 276.5 0.108 26.792
18 188 200.8 0.820 27.611
19 130 146.0 1.750 29.361
20 108 106.2 0.030 29.391
21 261 287.1 2.375 31.767
Chisq= 31.77 for 20 degrees of freedom, p= 0.95415
SUMMARY of craptest
p-value for no. of wins: 0.676106
p-value for throws/game: 0.954150
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0007,0.0010,0.0049,0.0073,0.0073,0.0076,0.0097,0.0108,0.0124,0.0126,
0.0171,0.0187,0.0223,0.0234,0.0346,0.0383,0.0393,0.0424,0.0441,0.0464,
0.0477,0.0485,0.0517,0.0520,0.0529,0.0562,0.0582,0.0629,0.0659,0.0708,
0.0826,0.0893,0.0904,0.0977,0.1012,0.1021,0.1133,0.1188,0.1264,0.1268,
0.1433,0.1469,0.1693,0.1734,0.1855,0.1943,0.1960,0.2050,0.2058,0.2095,
0.2131,0.2158,0.2188,0.2216,0.2290,0.2319,0.2347,0.2446,0.2448,0.2466,
0.2561,0.2675,0.2694,0.2746,0.2757,0.2815,0.2919,0.2969,0.3058,0.3077,
0.3099,0.3114,0.3184,0.3211,0.3225,0.3352,0.3359,0.3385,0.3413,0.3416,
0.3445,0.3503,0.3511,0.3525,0.3574,0.3580,0.3660,0.3673,0.3704,0.3736,
0.3784,0.3814,0.3845,0.3961,0.4010,0.4053,0.4154,0.4210,0.4225,0.4323,
0.4342,0.4359,0.4377,0.4391,0.4398,0.4400,0.4401,0.4410,0.4433,0.4483,
0.4523,0.4550,0.4598,0.4611,0.4628,0.4653,0.4655,0.4693,0.4742,0.4788,
0.4873,0.4874,0.4882,0.4987,0.5092,0.5193,0.5208,0.5243,0.5267,0.5326,
0.5347,0.5385,0.5387,0.5396,0.5402,0.5458,0.5502,0.5516,0.5523,0.5539,
0.5545,0.5568,0.5577,0.5590,0.5646,0.5693,0.5744,0.5763,0.5766,0.5775,
0.5830,0.5853,0.5854,0.5857,0.5920,0.5929,0.5963,0.6040,0.6073,0.6110,
0.6201,0.6233,0.6237,0.6254,0.6267,0.6347,0.6379,0.6424,0.6473,0.6490,
0.6558,0.6612,0.6638,0.6641,0.6667,0.6687,0.6693,0.6695,0.6705,0.6710,
0.6734,0.6742,0.6757,0.6761,0.6773,0.6812,0.6817,0.6820,0.6836,0.6878,
0.6978,0.7011,0.7018,0.7028,0.7075,0.7081,0.7219,0.7236,0.7250,0.7269,
0.7326,0.7377,0.7377,0.7432,0.7480,0.7486,0.7497,0.7546,0.7550,0.7580,
0.7587,0.7639,0.7652,0.7652,0.7653,0.7697,0.7700,0.7789,0.7909,0.7928,
0.7934,0.7978,0.8004,0.8015,0.8018,0.8031,0.8139,0.8276,0.8289,0.8402,
0.8454,0.8456,0.8502,0.8505,0.8543,0.8565,0.8637,0.8739,0.8746,0.8806,
0.8824,0.8833,0.8926,0.8954,0.8994,0.8997,0.9017,0.9036,0.9042,0.9050,
0.9216,0.9236,0.9310,0.9542,0.9620,0.9624,0.9651,0.9676,0.9702,0.9767,
0.9772,0.9774,0.9854,0.9860,0.9894,0.9897,0.9949,0.9995,0.9996,
Overall p-value after applying KStest on 269 p-values = 0.145991
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.