RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-03_00:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.96 25.2046 0.909777
2 to 25 16.02 26.3618 0.931883
3 to 26 15.98 14.2531 0.350887
4 to 27 15.35 27.5039 0.948920
5 to 28 15.71 23.7743 0.874303
6 to 29 15.92 10.7237 0.129439
7 to 30 15.87 13.4750 0.296147
8 to 31 15.59 13.6214 0.306305
9 to 32 15.52 28.2659 0.958075
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.062478
Tough bday spacings test for dh-ranFile-2018-07-03_00:31: 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 29 81 90 119 75 43 34 11 6 5
(O-E)^2/E 0.5 1.6 0.8 0.6 4.7 0.1 1.6 0.6 1.0 0.1 0.2
Birthday Spacings: Sum(O-E)^2/E= 11.774, p= 0.700
RESULTS OF GCD FOR dh-ranFile-2018-07-03_00:31
Euclid's algorithm:
p-value, steps to gcd: 0.885102
p-value, dist. of gcd's: 0.671101
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-03_00:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.550 0.364 0.335 0.316 0.108 0.779 0.222 0.786
Bits 8 to 15---> 0.529 0.647 0.556 0.712 0.986 0.106 0.426 0.541
Bits 16 to 23---> 0.944 0.960 0.716 0.886 0.578 0.677 0.669 0.986
Bits 24 to 31---> 0.183 0.203 0.790 0.793 0.720 0.407 0.410 0.922
KS test for the above 32 p values: 0.867
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-03_00:31,
p-values for 5 runs: 0.5652, 0.3399, 0.0010, 0.0847, 0.0808
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-03_00:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 203 211.4 0.335 0.335
r= 29 5047 5134.0 1.475 1.810
r= 30 23166 23103.0 0.172 1.981
r= 31 11584 11551.5 0.091 2.073
chi-square = 2.073 with df = 3; p-value = 0.443
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-03_00:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 209 211.4 0.028 0.028
r= 30 5107 5134.0 0.142 0.170
r= 31 23141 23103.0 0.062 0.232
r= 32 11543 11551.5 0.006 0.238
chi-square = 0.238 with df = 3; p-value = 0.029
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-03_00:31
b-rank test for bits 1 to 8, p=0.61242
b-rank test for bits 2 to 9, p=0.00141
b-rank test for bits 3 to 10, p=0.08589
b-rank test for bits 4 to 11, p=0.02813
b-rank test for bits 5 to 12, p=0.64958
b-rank test for bits 6 to 13, p=0.06057
b-rank test for bits 7 to 14, p=0.03682
b-rank test for bits 8 to 15, p=0.09846
b-rank test for bits 9 to 16, p=0.68525
b-rank test for bits 10 to 17, p=0.51733
b-rank test for bits 11 to 18, p=0.44893
b-rank test for bits 12 to 19, p=0.70098
b-rank test for bits 13 to 20, p=0.60222
b-rank test for bits 14 to 21, p=0.19231
b-rank test for bits 15 to 22, p=0.58416
b-rank test for bits 16 to 23, p=0.56743
b-rank test for bits 17 to 24, p=0.07618
b-rank test for bits 18 to 25, p=0.05820
b-rank test for bits 19 to 26, p=0.03796
b-rank test for bits 20 to 27, p=0.76624
b-rank test for bits 21 to 28, p=0.44658
b-rank test for bits 22 to 29, p=0.80052
b-rank test for bits 23 to 30, p=0.13363
b-rank test for bits 24 to 31, p=0.23103
b-rank test for bits 25 to 32, p=0.33965
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 = 0.005074
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-03_00:31
(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 142097 0.44 0.669481
2 142204 0.69 0.754425
3 141909 -0.00 0.499692
4 141619 -0.68 0.248778
5 142192 0.66 0.745516
6 142159 0.58 0.720168
7 142062 0.36 0.639344
8 141990 0.19 0.574750
9 142188 0.65 0.742508
10 141571 -0.79 0.214621
11 141905 -0.01 0.495964
12 141982 0.17 0.567412
13 142096 0.44 0.668634
14 142117 0.49 0.686236
15 142305 0.92 0.822377
16 141924 0.03 0.513671
17 141191 -1.68 0.046640
18 141673 -0.55 0.290415
19 141975 0.15 0.560972
20 141599 -0.73 0.234205
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-03_00:31
Bits used No. missing words z-score p-value
23 to 32 142202 1.0092 0.843562
22 to 31 141882 -0.0942 0.462459
21 to 30 141629 -0.9667 0.166858
20 to 29 142088 0.6161 0.731087
19 to 28 141725 -0.6356 0.262512
18 to 27 141926 0.0575 0.522920
17 to 26 142139 0.7920 0.785810
16 to 25 141471 -1.5115 0.065333
15 to 24 141878 -0.1080 0.456984
14 to 23 141957 0.1644 0.565284
13 to 22 141767 -0.4908 0.311786
12 to 21 142292 1.3196 0.906508
11 to 20 142029 0.4127 0.660070
10 to 19 142268 1.2368 0.891918
9 to 18 141425 -1.6701 0.047449
8 to 17 141499 -1.4149 0.078544
7 to 16 141952 0.1471 0.558488
6 to 15 141574 -1.1563 0.123777
5 to 14 141678 -0.7977 0.212525
4 to 13 142287 1.3023 0.903595
3 to 12 141833 -0.2632 0.396196
2 to 11 142373 1.5989 0.945074
1 to 10 142247 1.1644 0.877865
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-03_00:31
Bits used No. missing words z-score p-value
28 to 32 141638 -0.9198 0.178848
27 to 31 141993 0.2836 0.611652
26 to 30 141353 -1.8859 0.029657
25 to 29 142332 1.4328 0.924040
24 to 28 142002 0.3141 0.623291
23 to 27 141929 0.0667 0.526581
22 to 26 141783 -0.4282 0.334239
21 to 25 141930 0.0701 0.527930
20 to 24 142039 0.4396 0.669872
19 to 23 142258 1.1819 0.881384
18 to 22 142293 1.3006 0.903298
17 to 21 141713 -0.6655 0.252857
16 to 20 141806 -0.3503 0.363068
15 to 19 141965 0.1887 0.574841
14 to 18 141911 0.0057 0.502258
13 to 17 141806 -0.3503 0.363068
12 to 16 142139 0.7785 0.781875
11 to 15 142012 0.3480 0.636093
10 to 14 141477 -1.4655 0.071389
9 to 13 141872 -0.1265 0.449651
8 to 12 141960 0.1718 0.568188
7 to 11 141833 -0.2587 0.397916
6 to 10 142230 1.0870 0.861485
5 to 9 141996 0.2938 0.615543
4 to 8 141679 -0.7808 0.217466
3 to 7 141941 0.1074 0.542747
2 to 6 142228 1.0802 0.859982
1 to 5 141591 -1.0791 0.140275
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-03_00:31
Bits used No. missing words z-score p-value
31 to 32 141981 0.2114 0.583719
30 to 31 141617 -0.8623 0.194253
29 to 30 141977 0.1996 0.579110
28 to 29 143031 3.3088 0.999531
27 to 28 141337 -1.6883 0.045678
26 to 27 141009 -2.6558 0.003956
25 to 26 142193 0.8368 0.798643
24 to 25 141808 -0.2989 0.382505
23 to 24 142295 1.1377 0.872371
22 to 23 141782 -0.3756 0.353605
21 to 22 141732 -0.5231 0.300453
20 to 21 142153 0.7188 0.763865
19 to 20 141592 -0.9361 0.174617
18 to 19 141797 -0.3314 0.370187
17 to 18 142238 0.9695 0.833859
16 to 17 141527 -1.1278 0.129699
15 to 16 141694 -0.6352 0.262652
14 to 15 142298 1.1465 0.874210
13 to 14 141575 -0.9862 0.162012
12 to 13 142621 2.0993 0.982106
11 to 12 141213 -2.0541 0.019984
10 to 11 141791 -0.3491 0.363524
9 to 10 142185 0.8132 0.791944
8 to 9 141629 -0.8269 0.204138
7 to 8 142161 0.7424 0.771074
6 to 7 142090 0.5329 0.702966
5 to 6 142582 1.9843 0.976388
4 to 5 141954 0.1318 0.552417
3 to 4 141810 -0.2930 0.384758
2 to 3 142210 0.8869 0.812442
1 to 2 141843 -0.1957 0.422437
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-03_00:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2466.79 -0.470 0.319287
Test results for specific bytes for dh-ranFile-2018-07-03_00:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2454.96 -0.637 0.262081
2 to 9 2423.83 -1.077 0.140679
3 to 10 2563.99 0.905 0.817268
4 to 11 2454.80 -0.639 0.261347
5 to 12 2512.28 0.174 0.568939
6 to 13 2430.47 -0.983 0.162725
7 to 14 2516.25 0.230 0.590866
8 to 15 2453.30 -0.660 0.254481
9 to 16 2377.82 -1.728 0.042005
10 to 17 2528.99 0.410 0.659104
11 to 18 2587.88 1.243 0.893033
12 to 19 2473.08 -0.381 0.351726
13 to 20 2487.81 -0.172 0.431582
14 to 21 2521.24 0.300 0.618052
15 to 22 2651.75 2.146 0.984069
16 to 23 2528.26 0.400 0.655287
17 to 24 2599.53 1.408 0.920373
18 to 25 2482.70 -0.245 0.403354
19 to 26 2306.61 -2.735 0.003120
20 to 27 2539.71 0.562 0.712777
21 to 28 2435.98 -0.905 0.182639
22 to 29 2476.02 -0.339 0.367280
23 to 30 2574.13 1.048 0.852747
24 to 31 2575.86 1.073 0.858336
25 to 32 2450.92 -0.694 0.243819
CDPARK for dh-ranFile-2018-07-03_00:31: 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
3551 1.2785 0.899470
3519 -0.1826 0.427537
3546 1.0502 0.853193
3547 1.0959 0.863437
3519 -0.1826 0.427537
3561 1.7352 0.958644
3518 -0.2283 0.409702
3489 -1.5525 0.060270
3545 1.0046 0.842447
3520 -0.1370 0.445521
Square side=100, avg. no. parked=3531.50 sample std.=20.78
p-value of the KSTEST for those 10 p-values: 0.200569
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-03_00:31
0.5854,0.4542,0.9532,0.4461,0.4842,0.8587,0.4819,0.1847,0.0521,0.3515,
The KS test for those 10 p-values: 0.827942
The 3DSPHERES test for dh-ranFile-2018-07-03_00:31
sample no r^3 equiv. uni.
1 42.738 0.759393
2 48.437 0.801026
3 4.464 0.138246
4 21.333 0.508889
5 43.034 0.761755
6 10.971 0.306278
7 25.247 0.568959
8 17.817 0.447824
9 233.595 0.999585
10 0.065 0.002157
11 1.031 0.033779
12 4.117 0.128245
13 24.022 0.551000
14 30.627 0.639727
15 9.870 0.280364
16 54.752 0.838794
17 2.673 0.085241
18 22.185 0.522655
19 11.504 0.318502
20 24.014 0.550888
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.589192
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-03_00:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 0.1 -0.1 -0.1 -0.9 -0.4
0.7 2.0 -2.0 -0.4 -0.2 -0.1
1.1 -1.6 0.2 0.5 0.8 -0.2
-1.2 -0.8 0.5 0.5 0.0 0.9
0.1 -0.5 -0.6 1.2 0.3 1.2
1.4 0.2 0.0 -1.2 -1.3 -1.9
0.0 0.5 0.5 -0.1 -1.3 1.0
-1.1
Chi-square with 42 degrees of freedom:34.648325
z-score=-0.802134, p-value=0.217564
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-03_00:31
Test no p-value
1 0.089125
2 0.449159
3 0.152981
4 0.497389
5 0.088689
6 0.010566
7 0.218770
8 0.005817
9 0.166149
10 0.098083
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000242
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-03_00:31:
(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 66793 0.24 66497 0.43
3 25000.00 24876 0.62 25177 1.25
4 6666.67 6635 0.15 6707 0.24
5 1388.89 1387 0.00 1348 1.20
6 238.10 264 2.82 227 0.52
7 34.72 38 0.31 36 0.05
8 4.96 6 0.22 7 0.84
p=0.37109 p=0.39546
Number of rngs required: 687769, p-value: 0.232
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-03_00:31
No. of wins: Observed Expected
98483 98585.9
z-score=-0.460, pvalue=0.32274
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66771 66666.7 0.163 0.163
2 37930 37654.3 2.018 2.182
3 27083 26954.7 0.610 2.792
4 19220 19313.5 0.452 3.244
5 13765 13851.4 0.539 3.783
6 9813 9943.5 1.714 5.497
7 7137 7145.0 0.009 5.506
8 5087 5139.1 0.528 6.034
9 3683 3699.9 0.077 6.111
10 2646 2666.3 0.155 6.265
11 1896 1923.3 0.388 6.654
12 1370 1388.7 0.253 6.907
13 984 1003.7 0.387 7.294
14 652 726.1 7.570 14.864
15 532 525.8 0.072 14.936
16 392 381.2 0.309 15.245
17 256 276.5 1.526 16.770
18 210 200.8 0.419 17.189
19 150 146.0 0.110 17.299
20 123 106.2 2.652 19.952
21 300 287.1 0.578 20.530
Chisq= 20.53 for 20 degrees of freedom, p= 0.57477
SUMMARY of craptest
p-value for no. of wins: 0.322742
p-value for throws/game: 0.574771
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-03_00:31
No. of wins: Observed Expected
98594 98585.9
z-score= 0.036, pvalue=0.51452
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66617 66666.7 0.037 0.037
2 37770 37654.3 0.355 0.392
3 26761 26954.7 1.392 1.785
4 19302 19313.5 0.007 1.792
5 13771 13851.4 0.467 2.259
6 10125 9943.5 3.311 5.570
7 7248 7145.0 1.484 7.054
8 5089 5139.1 0.488 7.542
9 3692 3699.9 0.017 7.559
10 2659 2666.3 0.020 7.579
11 2008 1923.3 3.727 11.306
12 1293 1388.7 6.600 17.906
13 1007 1003.7 0.011 17.917
14 732 726.1 0.047 17.964
15 564 525.8 2.770 20.734
16 363 381.2 0.864 21.599
17 270 276.5 0.155 21.753
18 194 200.8 0.232 21.986
19 143 146.0 0.061 22.047
20 91 106.2 2.180 24.226
21 301 287.1 0.672 24.898
Chisq= 24.90 for 20 degrees of freedom, p= 0.79463
SUMMARY of craptest
p-value for no. of wins: 0.514524
p-value for throws/game: 0.794627
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0002,0.0010,0.0014,0.0022,0.0031,0.0040,0.0051,0.0058,0.0106,0.0200,
0.0281,0.0288,0.0297,0.0338,0.0368,0.0380,0.0420,0.0457,0.0466,0.0474,
0.0521,0.0582,0.0603,0.0606,0.0625,0.0653,0.0714,0.0762,0.0785,0.0808,
0.0847,0.0852,0.0859,0.0887,0.0891,0.0981,0.0985,0.1059,0.1081,0.1238,
0.1282,0.1294,0.1297,0.1336,0.1382,0.1403,0.1407,0.1530,0.1620,0.1627,
0.1661,0.1669,0.1746,0.1788,0.1826,0.1826,0.1847,0.1923,0.1943,0.2006,
0.2030,0.2041,0.2125,0.2146,0.2175,0.2176,0.2188,0.2223,0.2310,0.2320,
0.2342,0.2438,0.2488,0.2529,0.2545,0.2613,0.2621,0.2625,0.2627,0.2804,
0.2904,0.2961,0.3005,0.3063,0.3063,0.3118,0.3159,0.3185,0.3193,0.3227,
0.3342,0.3349,0.3397,0.3399,0.3509,0.3515,0.3517,0.3536,0.3631,0.3631,
0.3635,0.3639,0.3673,0.3702,0.3711,0.3825,0.3848,0.3955,0.3962,0.3979,
0.4034,0.4068,0.4097,0.4098,0.4224,0.4259,0.4275,0.4275,0.4316,0.4425,
0.4455,0.4461,0.4466,0.4478,0.4489,0.4492,0.4497,0.4542,0.4570,0.4625,
0.4819,0.4842,0.4960,0.4974,0.4997,0.5023,0.5089,0.5137,0.5145,0.5173,
0.5227,0.5229,0.5266,0.5279,0.5288,0.5414,0.5427,0.5497,0.5509,0.5510,
0.5524,0.5561,0.5585,0.5610,0.5652,0.5653,0.5674,0.5674,0.5682,0.5689,
0.5690,0.5748,0.5748,0.5748,0.5780,0.5791,0.5837,0.5842,0.5854,0.5892,
0.5909,0.6022,0.6117,0.6124,0.6155,0.6181,0.6233,0.6361,0.6393,0.6397,
0.6472,0.6496,0.6553,0.6591,0.6601,0.6686,0.6690,0.6695,0.6699,0.6711,
0.6772,0.6853,0.6862,0.6995,0.7010,0.7030,0.7121,0.7128,0.7162,0.7202,
0.7202,0.7311,0.7425,0.7455,0.7544,0.7594,0.7618,0.7639,0.7662,0.7711,
0.7792,0.7819,0.7858,0.7861,0.7897,0.7919,0.7926,0.7946,0.7986,0.8005,
0.8010,0.8124,0.8173,0.8224,0.8279,0.8339,0.8388,0.8424,0.8436,0.8527,
0.8532,0.8583,0.8587,0.8600,0.8615,0.8634,0.8672,0.8724,0.8742,0.8743,
0.8779,0.8814,0.8851,0.8864,0.8919,0.8930,0.8995,0.9033,0.9036,0.9065,
0.9098,0.9204,0.9221,0.9240,0.9319,0.9435,0.9451,0.9489,0.9532,0.9581,
0.9586,0.9600,0.9764,0.9821,0.9841,0.9857,0.9863,0.9995,0.9996,
Overall p-value after applying KStest on 269 p-values = 0.358758
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.