RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-16_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 16.05 6.9326 0.015595
2 to 25 15.80 17.0422 0.548489
3 to 26 15.59 21.0910 0.777752
4 to 27 15.76 22.8681 0.846405
5 to 28 15.91 19.1039 0.677397
6 to 29 15.65 16.4521 0.507956
7 to 30 15.92 16.9475 0.542072
8 to 31 16.09 28.1368 0.956635
9 to 32 15.87 8.7331 0.051736
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.571878
Tough bday spacings test for dh-ranFile-2018-06-16_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 7 45 74 106 88 81 53 27 14 3 2
(O-E)^2/E 0.5 1.9 0.0 0.7 1.0 0.1 0.0 0.3 0.1 2.0 1.0
Birthday Spacings: Sum(O-E)^2/E= 7.552, p= 0.327
RESULTS OF GCD FOR dh-ranFile-2018-06-16_03:31
Euclid's algorithm:
p-value, steps to gcd: 0.671052
p-value, dist. of gcd's: 0.812980
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-16_03:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.361 0.879 0.509 0.697 0.495 0.882 0.619 0.320
Bits 8 to 15---> 0.481 0.690 0.444 0.188 0.036 0.713 0.197 0.056
Bits 16 to 23---> 0.613 0.342 0.899 0.109 0.297 0.693 0.095 0.892
Bits 24 to 31---> 0.708 0.438 0.892 0.582 0.175 0.374 0.472 0.811
KS test for the above 32 p values: 0.130
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-16_03:31,
p-values for 5 runs: 0.3997, 0.7953, 0.5720, 0.9603, 0.5566
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-16_03:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 208 211.4 0.055 0.055
r= 29 5196 5134.0 0.748 0.804
r= 30 23133 23103.0 0.039 0.843
r= 31 11463 11551.5 0.678 1.521
chi-square = 1.521 with df = 3; p-value = 0.323
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-16_03:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 210 211.4 0.010 0.010
r= 30 5149 5134.0 0.044 0.053
r= 31 23152 23103.0 0.104 0.157
r= 32 11489 11551.5 0.338 0.495
chi-square = 0.495 with df = 3; p-value = 0.080
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-16_03:31
b-rank test for bits 1 to 8, p=0.38192
b-rank test for bits 2 to 9, p=0.80395
b-rank test for bits 3 to 10, p=0.38365
b-rank test for bits 4 to 11, p=0.52308
b-rank test for bits 5 to 12, p=0.58353
b-rank test for bits 6 to 13, p=0.49086
b-rank test for bits 7 to 14, p=0.08374
b-rank test for bits 8 to 15, p=0.55803
b-rank test for bits 9 to 16, p=0.19380
b-rank test for bits 10 to 17, p=0.20208
b-rank test for bits 11 to 18, p=0.66627
b-rank test for bits 12 to 19, p=0.29412
b-rank test for bits 13 to 20, p=0.44553
b-rank test for bits 14 to 21, p=0.04562
b-rank test for bits 15 to 22, p=0.34966
b-rank test for bits 16 to 23, p=0.97147
b-rank test for bits 17 to 24, p=0.91743
b-rank test for bits 18 to 25, p=0.65840
b-rank test for bits 19 to 26, p=0.19497
b-rank test for bits 20 to 27, p=0.19678
b-rank test for bits 21 to 28, p=0.06324
b-rank test for bits 22 to 29, p=0.65464
b-rank test for bits 23 to 30, p=0.24254
b-rank test for bits 24 to 31, p=0.83453
b-rank test for bits 25 to 32, p=0.98697
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 = 0.865028
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-16_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 142086 0.41 0.660116
2 141448 -1.08 0.140545
3 141631 -0.65 0.257748
4 141663 -0.58 0.282464
5 142252 0.80 0.788327
6 141755 -0.36 0.359205
7 141364 -1.27 0.101308
8 141910 0.00 0.500625
9 142347 1.02 0.846750
10 142022 0.26 0.603820
11 142215 0.71 0.762443
12 142176 0.62 0.733378
13 142595 1.60 0.945426
14 141423 -1.14 0.127919
15 142305 0.92 0.822377
16 142128 0.51 0.695293
17 141732 -0.41 0.339319
18 141615 -0.69 0.245825
19 142265 0.83 0.797015
20 141832 -0.18 0.428310
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-16_03:31
Bits used No. missing words z-score p-value
23 to 32 141878 -0.1080 0.456984
22 to 31 141985 0.2609 0.602927
21 to 30 141651 -0.8908 0.186520
20 to 29 141472 -1.5080 0.065773
19 to 28 142133 0.7713 0.779728
18 to 27 141982 0.2506 0.598933
17 to 26 141660 -0.8598 0.194961
16 to 25 141853 -0.1942 0.422994
15 to 24 142349 1.5161 0.935253
14 to 23 142128 0.7540 0.774586
13 to 22 142034 0.4299 0.666365
12 to 21 142140 0.7954 0.786814
11 to 20 142114 0.7058 0.759831
10 to 19 141809 -0.3460 0.364684
9 to 18 141921 0.0402 0.516050
8 to 17 142009 0.3437 0.634460
7 to 16 141875 -0.1184 0.452884
6 to 15 142522 2.1127 0.982685
5 to 14 142228 1.0989 0.864086
4 to 13 141522 -1.3356 0.090837
3 to 12 142120 0.7264 0.766218
2 to 11 141511 -1.3736 0.084790
1 to 10 141781 -0.4425 0.329058
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-16_03:31
Bits used No. missing words z-score p-value
28 to 32 142582 2.2802 0.988703
27 to 31 141849 -0.2045 0.418978
26 to 30 141790 -0.4045 0.342919
25 to 29 141605 -1.0316 0.151123
24 to 28 141752 -0.5333 0.296905
23 to 27 141833 -0.2587 0.397916
22 to 26 141773 -0.4621 0.321992
21 to 25 141727 -0.6181 0.268265
20 to 24 141713 -0.6655 0.252857
19 to 23 141675 -0.7943 0.213499
18 to 22 141914 0.0158 0.506315
17 to 21 142388 1.6226 0.947664
16 to 20 142016 0.3616 0.641172
15 to 19 142342 1.4667 0.928768
14 to 18 141534 -1.2723 0.101632
13 to 17 141968 0.1989 0.578822
12 to 16 142160 0.8497 0.802262
11 to 15 141854 -0.1876 0.425611
10 to 14 141829 -0.2723 0.392694
9 to 13 141397 -1.7367 0.041219
8 to 12 142258 1.1819 0.881384
7 to 11 142105 0.6633 0.746427
6 to 10 141733 -0.5977 0.275010
5 to 9 141674 -0.7977 0.212514
4 to 8 141681 -0.7740 0.219465
3 to 7 142033 0.4192 0.662473
2 to 6 142036 0.4294 0.666180
1 to 5 142090 0.6124 0.729877
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-16_03:31
Bits used No. missing words z-score p-value
31 to 32 142170 0.7689 0.779035
30 to 31 142111 0.5949 0.724044
29 to 30 141641 -0.7915 0.214316
28 to 29 142291 1.1259 0.869890
27 to 28 141433 -1.4051 0.079995
26 to 27 141857 -0.1544 0.438661
25 to 26 141657 -0.7443 0.228337
24 to 25 141859 -0.1485 0.440988
23 to 24 141854 -0.1632 0.435174
22 to 23 141849 -0.1780 0.429375
21 to 22 142030 0.3560 0.639064
20 to 21 142227 0.9371 0.825641
19 to 20 141556 -1.0423 0.148643
18 to 19 141691 -0.6440 0.259774
17 to 18 141456 -1.3373 0.090569
16 to 17 141893 -0.0482 0.480790
15 to 16 142460 1.6244 0.947854
14 to 15 141365 -1.6057 0.054171
13 to 14 142623 2.1052 0.982364
12 to 13 142167 0.7601 0.776399
11 to 12 142429 1.5329 0.937356
10 to 11 142444 1.5772 0.942625
9 to 10 142476 1.6716 0.952698
8 to 9 141646 -0.7768 0.218643
7 to 8 141446 -1.3668 0.085851
6 to 7 141995 0.2527 0.599755
5 to 6 142179 0.7955 0.786835
4 to 5 141795 -0.3373 0.367962
3 to 4 142178 0.7925 0.785976
2 to 3 141751 -0.4671 0.320232
1 to 2 142502 1.7483 0.959793
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-16_03:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2577.28 1.093 0.862789
Test results for specific bytes for dh-ranFile-2018-06-16_03:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2464.31 -0.505 0.306889
2 to 9 2558.12 0.822 0.794441
3 to 10 2701.33 2.847 0.997795
4 to 11 2454.17 -0.648 0.258468
5 to 12 2523.24 0.329 0.628800
6 to 13 2442.57 -0.812 0.208331
7 to 14 2523.75 0.336 0.631536
8 to 15 2445.73 -0.768 0.221385
9 to 16 2525.94 0.367 0.643119
10 to 17 2459.48 -0.573 0.283309
11 to 18 2488.74 -0.159 0.436765
12 to 19 2520.57 0.291 0.614458
13 to 20 2565.85 0.931 0.824123
14 to 21 2594.92 1.342 0.910254
15 to 22 2475.70 -0.344 0.365576
16 to 23 2416.67 -1.178 0.119310
17 to 24 2514.34 0.203 0.580348
18 to 25 2428.21 -1.015 0.154980
19 to 26 2368.96 -1.853 0.031924
20 to 27 2615.52 1.634 0.948842
21 to 28 2508.15 0.115 0.545904
22 to 29 2419.90 -1.133 0.128648
23 to 30 2584.21 1.191 0.883151
24 to 31 2391.45 -1.535 0.062370
25 to 32 2369.56 -1.845 0.032539
CDPARK for dh-ranFile-2018-06-16_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
3497 -1.1872 0.117571
3554 1.4155 0.921543
3498 -1.1416 0.126820
3509 -0.6393 0.261324
3513 -0.4566 0.323972
3529 0.2740 0.607947
3531 0.3653 0.642555
3484 -1.7808 0.037471
3499 -1.0959 0.136563
3517 -0.2740 0.392053
Square side=100, avg. no. parked=3513.10 sample std.=19.52
p-value of the KSTEST for those 10 p-values: 0.186193
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-16_03:31
0.4448,0.8058,0.1187,0.9323,0.0768,0.3917,0.6242,0.9591,0.8682,0.5708,
The KS test for those 10 p-values: 0.627019
The 3DSPHERES test for dh-ranFile-2018-06-16_03:31
sample no r^3 equiv. uni.
1 20.413 0.493610
2 20.528 0.495540
3 0.995 0.032618
4 9.289 0.266290
5 21.280 0.508024
6 7.103 0.210832
7 42.496 0.757444
8 71.161 0.906709
9 41.572 0.749859
10 20.629 0.497232
11 3.408 0.107374
12 36.570 0.704471
13 9.144 0.262738
14 21.543 0.512317
15 46.863 0.790306
16 16.619 0.425339
17 80.100 0.930747
18 119.835 0.981584
19 56.928 0.850073
20 41.771 0.751513
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.588973
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-16_03:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 0.5 -0.8 0.3 -0.3 0.4
-0.4 0.0 0.2 -0.6 -1.0 -1.7
-1.0 0.0 0.4 1.4 0.1 1.1
1.4 -0.0 -0.3 -1.7 0.1 0.9
0.8 -2.0 0.4 -1.0 -0.2 -0.1
-0.1 1.4 2.4 0.2 1.3 -1.2
0.7 -1.3 0.1 -0.1 -1.3 0.0
-0.1
Chi-square with 42 degrees of freedom:38.476447
z-score=-0.384451, p-value=0.373567
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-16_03:31
Test no p-value
1 0.031920
2 0.784240
3 0.492343
4 0.292984
5 0.592169
6 0.007418
7 0.732126
8 0.033206
9 0.187753
10 0.040072
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.021229
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-16_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 66616 0.04 66636 0.01
3 25000.00 25158 1.00 25144 0.83
4 6666.67 6591 0.86 6523 3.10
5 1388.89 1385 0.01 1413 0.42
6 238.10 206 4.33 238 0.00
7 34.72 34 0.01 38 0.31
8 4.96 9 3.29 7 0.84
p=0.85454 p=0.51941
Number of rngs required: 687393, p-value: 0.120
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-16_03:31
No. of wins: Observed Expected
98825 98585.9
z-score= 1.070, pvalue=0.85760
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66659 66666.7 0.001 0.001
2 37860 37654.3 1.123 1.124
3 26842 26954.7 0.471 1.596
4 19377 19313.5 0.209 1.805
5 13657 13851.4 2.729 4.534
6 9899 9943.5 0.200 4.733
7 7125 7145.0 0.056 4.789
8 5111 5139.1 0.153 4.943
9 3792 3699.9 2.294 7.237
10 2745 2666.3 2.323 9.560
11 1887 1923.3 0.686 10.246
12 1345 1388.7 1.378 11.624
13 1062 1003.7 3.385 15.009
14 720 726.1 0.052 15.061
15 508 525.8 0.605 15.666
16 409 381.2 2.035 17.700
17 282 276.5 0.108 17.808
18 200 200.8 0.003 17.812
19 145 146.0 0.007 17.818
20 100 106.2 0.364 18.182
21 275 287.1 0.511 18.693
Chisq= 18.69 for 20 degrees of freedom, p= 0.45816
SUMMARY of craptest
p-value for no. of wins: 0.857596
p-value for throws/game: 0.458155
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-16_03:31
No. of wins: Observed Expected
99214 98585.9
z-score= 2.809, pvalue=0.99752
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66651 66666.7 0.004 0.004
2 37660 37654.3 0.001 0.005
3 27084 26954.7 0.620 0.624
4 19389 19313.5 0.295 0.920
5 13788 13851.4 0.290 1.210
6 9882 9943.5 0.381 1.591
7 7075 7145.0 0.686 2.277
8 5115 5139.1 0.113 2.390
9 3693 3699.9 0.013 2.403
10 2615 2666.3 0.987 3.390
11 1938 1923.3 0.112 3.502
12 1378 1388.7 0.083 3.585
13 1061 1003.7 3.269 6.854
14 737 726.1 0.162 7.017
15 533 525.8 0.098 7.114
16 356 381.2 1.660 8.774
17 278 276.5 0.008 8.782
18 220 200.8 1.830 10.611
19 144 146.0 0.027 10.638
20 111 106.2 0.216 10.854
21 292 287.1 0.083 10.937
Chisq= 10.94 for 20 degrees of freedom, p= 0.05216
SUMMARY of craptest
p-value for no. of wins: 0.997518
p-value for throws/game: 0.052163
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0074,0.0156,0.0212,0.0319,0.0319,0.0325,0.0326,0.0332,0.0359,0.0375,
0.0401,0.0412,0.0456,0.0517,0.0522,0.0542,0.0556,0.0624,0.0632,0.0658,
0.0768,0.0800,0.0801,0.0837,0.0848,0.0859,0.0906,0.0908,0.0947,0.1013,
0.1016,0.1074,0.1092,0.1176,0.1187,0.1193,0.1204,0.1268,0.1279,0.1286,
0.1300,0.1366,0.1405,0.1486,0.1511,0.1550,0.1749,0.1862,0.1865,0.1878,
0.1878,0.1938,0.1950,0.1950,0.1967,0.1968,0.2021,0.2083,0.2108,0.2125,
0.2135,0.2143,0.2186,0.2195,0.2214,0.2283,0.2425,0.2458,0.2529,0.2577,
0.2585,0.2598,0.2613,0.2627,0.2663,0.2683,0.2750,0.2825,0.2833,0.2930,
0.2941,0.2969,0.2971,0.3069,0.3197,0.3202,0.3220,0.3226,0.3240,0.3275,
0.3291,0.3393,0.3420,0.3429,0.3497,0.3592,0.3605,0.3647,0.3656,0.3680,
0.3736,0.3738,0.3819,0.3837,0.3917,0.3921,0.3927,0.3979,0.3997,0.4190,
0.4230,0.4253,0.4256,0.4283,0.4294,0.4352,0.4368,0.4382,0.4387,0.4410,
0.4438,0.4448,0.4455,0.4529,0.4570,0.4582,0.4715,0.4807,0.4808,0.4909,
0.4923,0.4936,0.4954,0.4955,0.4972,0.5006,0.5063,0.5080,0.5080,0.5092,
0.5123,0.5160,0.5194,0.5231,0.5421,0.5459,0.5485,0.5566,0.5580,0.5708,
0.5719,0.5720,0.5788,0.5803,0.5821,0.5835,0.5890,0.5922,0.5989,0.5998,
0.6029,0.6038,0.6079,0.6126,0.6145,0.6193,0.6242,0.6270,0.6288,0.6315,
0.6345,0.6391,0.6412,0.6426,0.6431,0.6546,0.6584,0.6601,0.6625,0.6662,
0.6663,0.6664,0.6711,0.6774,0.6896,0.6931,0.6953,0.6971,0.7045,0.7080,
0.7131,0.7240,0.7299,0.7321,0.7334,0.7464,0.7499,0.7515,0.7574,0.7598,
0.7624,0.7662,0.7746,0.7764,0.7778,0.7790,0.7797,0.7842,0.7860,0.7868,
0.7868,0.7883,0.7903,0.7944,0.7953,0.7970,0.8023,0.8039,0.8058,0.8107,
0.8130,0.8224,0.8241,0.8256,0.8345,0.8464,0.8467,0.8501,0.8545,0.8576,
0.8628,0.8641,0.8650,0.8682,0.8699,0.8788,0.8814,0.8817,0.8832,0.8920,
0.8924,0.8990,0.9067,0.9103,0.9174,0.9215,0.9288,0.9307,0.9323,0.9353,
0.9374,0.9426,0.9454,0.9477,0.9479,0.9488,0.9527,0.9566,0.9591,0.9598,
0.9603,0.9715,0.9816,0.9824,0.9827,0.9870,0.9887,0.9975,0.9978,
Overall p-value after applying KStest on 269 p-values = 0.995210
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.