RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-11_21:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.71 14.9429 0.400403
2 to 25 15.70 22.0327 0.816536
3 to 26 15.39 36.2982 0.995816
4 to 27 15.78 10.7438 0.130432
5 to 28 15.80 17.8378 0.600856
6 to 29 15.83 8.7109 0.051102
7 to 30 15.93 10.8604 0.136271
8 to 31 15.66 19.5296 0.701006
9 to 32 15.59 18.5743 0.646491
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.777091
Tough bday spacings test for dh-ranFile-2018-07-11_21:31: 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 10 35 74 105 98 82 51 22 11 5 7
(O-E)^2/E 0.1 0.1 0.0 0.5 0.0 0.2 0.0 2.0 1.0 0.4 2.1
Birthday Spacings: Sum(O-E)^2/E= 6.473, p= 0.226
RESULTS OF GCD FOR dh-ranFile-2018-07-11_21:31
Euclid's algorithm:
p-value, steps to gcd: 0.496645
p-value, dist. of gcd's: 0.264838
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-11_21:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.310 0.160 0.944 0.825 0.644 0.510 0.937 0.726
Bits 8 to 15---> 0.217 0.918 0.053 0.415 0.457 0.961 0.896 0.993
Bits 16 to 23---> 0.652 0.216 0.232 0.026 0.263 0.628 0.615 0.421
Bits 24 to 31---> 0.572 0.186 0.682 0.872 0.249 0.098 0.119 0.878
KS test for the above 32 p values: 0.226
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-11_21:31,
p-values for 5 runs: 0.2927, 0.4215, 0.8603, 0.4117, 0.6736
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-11_21:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 212 211.4 0.002 0.002
r= 29 5044 5134.0 1.578 1.580
r= 30 23152 23103.0 0.104 1.683
r= 31 11592 11551.5 0.142 1.825
chi-square = 1.825 with df = 3; p-value = 0.391
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-11_21:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 216 211.4 0.099 0.099
r= 30 5118 5134.0 0.050 0.149
r= 31 23209 23103.0 0.486 0.635
r= 32 11457 11551.5 0.773 1.409
chi-square = 1.409 with df = 3; p-value = 0.296
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-11_21:31
b-rank test for bits 1 to 8, p=0.68802
b-rank test for bits 2 to 9, p=0.55590
b-rank test for bits 3 to 10, p=0.54072
b-rank test for bits 4 to 11, p=0.43101
b-rank test for bits 5 to 12, p=0.27637
b-rank test for bits 6 to 13, p=0.48151
b-rank test for bits 7 to 14, p=0.45384
b-rank test for bits 8 to 15, p=0.75963
b-rank test for bits 9 to 16, p=0.54726
b-rank test for bits 10 to 17, p=0.19353
b-rank test for bits 11 to 18, p=0.92318
b-rank test for bits 12 to 19, p=0.10587
b-rank test for bits 13 to 20, p=0.23259
b-rank test for bits 14 to 21, p=0.77172
b-rank test for bits 15 to 22, p=0.44289
b-rank test for bits 16 to 23, p=0.04074
b-rank test for bits 17 to 24, p=0.04695
b-rank test for bits 18 to 25, p=0.33643
b-rank test for bits 19 to 26, p=0.07523
b-rank test for bits 20 to 27, p=0.03867
b-rank test for bits 21 to 28, p=0.70805
b-rank test for bits 22 to 29, p=0.90740
b-rank test for bits 23 to 30, p=0.47982
b-rank test for bits 24 to 31, p=0.60617
b-rank test for bits 25 to 32, p=0.67916
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 = 0.533455
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-11_21:31
(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 142301 0.92 0.819935
2 141854 -0.13 0.448570
3 142066 0.37 0.642837
4 141969 0.14 0.555439
5 141329 -1.36 0.087564
6 141834 -0.18 0.430145
7 142420 1.19 0.883596
8 141676 -0.55 0.292821
9 141249 -1.54 0.061436
10 142147 0.56 0.710657
11 142865 2.23 0.987221
12 141545 -0.85 0.197319
13 142892 2.30 0.989161
14 142090 0.42 0.663534
15 141411 -1.16 0.122147
16 141868 -0.10 0.461536
17 142365 1.06 0.856483
18 141594 -0.74 0.230637
19 141340 -1.33 0.091725
20 141866 -0.10 0.459681
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-11_21:31
Bits used No. missing words z-score p-value
23 to 32 142039 0.4471 0.672612
22 to 31 142157 0.8540 0.803457
21 to 30 142076 0.5747 0.717261
20 to 29 142285 1.2954 0.902411
19 to 28 142069 0.5506 0.709041
18 to 27 141837 -0.2494 0.401520
17 to 26 141784 -0.4322 0.332808
16 to 25 141499 -1.4149 0.078544
15 to 24 142210 1.0368 0.850084
14 to 23 142208 1.0299 0.848471
13 to 22 141890 -0.0667 0.473428
12 to 21 141926 0.0575 0.522920
11 to 20 141995 0.2954 0.616161
10 to 19 141686 -0.7701 0.220619
9 to 18 141774 -0.4667 0.320373
8 to 17 141865 -0.1529 0.439254
7 to 16 141918 0.0299 0.511925
6 to 15 141443 -1.6080 0.053914
5 to 14 141773 -0.4701 0.319141
4 to 13 142612 2.4230 0.992304
3 to 12 141670 -0.8253 0.204608
2 to 11 141456 -1.5632 0.059002
1 to 10 142019 0.3782 0.647349
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-11_21:31
Bits used No. missing words z-score p-value
28 to 32 141394 -1.7469 0.040329
27 to 31 142221 1.0565 0.854632
26 to 30 141698 -0.7164 0.236881
25 to 29 142286 1.2768 0.899172
24 to 28 142100 0.6463 0.740970
23 to 27 141788 -0.4113 0.340431
22 to 26 140736 -3.9774 0.000035
21 to 25 141514 -1.3401 0.090106
20 to 24 141201 -2.4011 0.008173
19 to 23 142121 0.7175 0.763475
18 to 22 142310 1.3582 0.912800
17 to 21 141882 -0.0926 0.463093
16 to 20 142213 1.0294 0.848352
15 to 19 141955 0.1548 0.561516
14 to 18 141554 -1.2045 0.114197
13 to 17 141960 0.1718 0.568188
12 to 16 142339 1.4565 0.927374
11 to 15 141748 -0.5469 0.292230
10 to 14 141866 -0.1469 0.441613
9 to 13 142180 0.9175 0.820566
8 to 12 141622 -0.9740 0.165028
7 to 11 142199 0.9819 0.836933
6 to 10 142024 0.3887 0.651255
5 to 9 142322 1.3989 0.919076
4 to 8 142176 0.9040 0.816993
3 to 7 141967 0.1955 0.577496
2 to 6 141997 0.2972 0.616838
1 to 5 142097 0.6362 0.737667
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-11_21:31
Bits used No. missing words z-score p-value
31 to 32 142047 0.4061 0.657668
30 to 31 141996 0.2557 0.600895
29 to 30 141986 0.2262 0.589464
28 to 29 141548 -1.0659 0.143241
27 to 28 141970 0.1790 0.571018
26 to 27 142024 0.3383 0.632416
25 to 26 141695 -0.6322 0.263614
24 to 25 141505 -1.1927 0.116491
23 to 24 141863 -0.1367 0.445647
22 to 23 141862 -0.1396 0.444482
21 to 22 141666 -0.7178 0.236444
20 to 21 141690 -0.6470 0.258819
19 to 20 142021 0.3294 0.629077
18 to 19 142104 0.5742 0.717100
17 to 18 141753 -0.4612 0.322345
16 to 17 142170 0.7689 0.779035
15 to 16 141982 0.2144 0.584869
14 to 15 142039 0.3825 0.648958
13 to 14 142192 0.8338 0.797813
12 to 13 142263 1.0433 0.851589
11 to 12 142126 0.6391 0.738636
10 to 11 141666 -0.7178 0.236444
9 to 10 141741 -0.4965 0.309754
8 to 9 141771 -0.4081 0.341617
7 to 8 141721 -0.5555 0.289261
6 to 7 142328 1.2350 0.891588
5 to 6 141986 0.2262 0.589464
4 to 5 141719 -0.5614 0.287247
3 to 4 142534 1.8427 0.967312
2 to 3 142218 0.9105 0.818729
1 to 2 141946 0.1082 0.543070
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-11_21:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2554.82 0.775 0.780919
Test results for specific bytes for dh-ranFile-2018-07-11_21:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2517.08 0.242 0.595429
2 to 9 2546.15 0.653 0.743025
3 to 10 2612.25 1.587 0.943791
4 to 11 2592.17 1.303 0.903790
5 to 12 2509.59 0.136 0.553917
6 to 13 2418.33 -1.155 0.124049
7 to 14 2529.89 0.423 0.663724
8 to 15 2479.25 -0.293 0.384576
9 to 16 2476.60 -0.331 0.370349
10 to 17 2559.17 0.837 0.798657
11 to 18 2496.65 -0.047 0.481116
12 to 19 2623.03 1.740 0.959062
13 to 20 2578.95 1.117 0.867912
14 to 21 2492.11 -0.112 0.455564
15 to 22 2522.94 0.324 0.627191
16 to 23 2554.30 0.768 0.778750
17 to 24 2382.69 -1.659 0.048554
18 to 25 2502.89 0.041 0.516318
19 to 26 2619.55 1.691 0.954557
20 to 27 2561.64 0.872 0.808310
21 to 28 2546.92 0.663 0.746490
22 to 29 2474.26 -0.364 0.357922
23 to 30 2559.78 0.845 0.801080
24 to 31 2621.21 1.714 0.956751
25 to 32 2585.22 1.205 0.885930
CDPARK for dh-ranFile-2018-07-11_21:31: 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
3521 -0.0913 0.463617
3499 -1.0959 0.136563
3516 -0.3196 0.374623
3511 -0.5479 0.291865
3552 1.3242 0.907282
3523 0.0000 0.500000
3567 2.0091 0.977738
3549 1.1872 0.882429
3516 -0.3196 0.374623
3510 -0.5936 0.276387
Square side=100, avg. no. parked=3526.40 sample std.=20.80
p-value of the KSTEST for those 10 p-values: 0.650487
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-11_21:31
0.1978,0.0876,0.9173,0.1750,0.2349,0.9342,0.0154,0.2331,0.6154,0.5365,
The KS test for those 10 p-values: 0.267193
The 3DSPHERES test for dh-ranFile-2018-07-11_21:31
sample no r^3 equiv. uni.
1 12.504 0.340841
2 22.121 0.521633
3 4.389 0.136114
4 4.070 0.126864
5 58.121 0.855916
6 7.251 0.214712
7 16.413 0.421379
8 11.091 0.309048
9 1.929 0.062279
10 22.666 0.530242
11 7.297 0.215901
12 31.913 0.654849
13 136.804 0.989539
14 8.526 0.247381
15 6.541 0.195908
16 12.513 0.341055
17 4.170 0.129770
18 11.475 0.317855
19 12.135 0.332683
20 72.675 0.911302
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.089219
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-11_21:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 0.1 0.3 -0.7 1.3 -1.3
0.4 -0.1 -0.7 0.0 -1.9 -1.2
0.4 -0.0 0.5 0.6 0.4 0.1
0.7 -0.0 0.2 0.3 0.7 0.6
-2.0 0.4 0.2 -0.0 -0.4 -0.8
0.2 -2.2 0.3 -0.8 -0.2 -0.7
-1.2 0.8 -0.8 0.4 -0.6 2.0
-1.1
Chi-square with 42 degrees of freedom:31.724720
z-score=-1.121125, p-value=0.124268
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-11_21:31
Test no p-value
1 0.520730
2 0.003256
3 0.099271
4 0.356746
5 0.019337
6 0.221277
7 0.568695
8 0.826909
9 0.410123
10 0.269216
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.074366
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-11_21:31:
(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 66745 0.09 66725 0.05
3 25000.00 24850 0.90 24880 0.58
4 6666.67 6796 2.51 6692 0.10
5 1388.89 1345 1.39 1399 0.07
6 238.10 231 0.21 263 2.61
7 34.72 29 0.94 33 0.09
8 4.96 3 0.77 7 0.84
p=0.66182 p=0.36737
Number of rngs required: 687683, p-value: 0.203
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-11_21:31
No. of wins: Observed Expected
98867 98585.9
z-score= 1.257, pvalue=0.89570
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66715 66666.7 0.035 0.035
2 37733 37654.3 0.164 0.199
3 26778 26954.7 1.159 1.358
4 19372 19313.5 0.177 1.536
5 13860 13851.4 0.005 1.541
6 9734 9943.5 4.416 5.957
7 7278 7145.0 2.475 8.431
8 5224 5139.1 1.404 9.835
9 3699 3699.9 0.000 9.835
10 2636 2666.3 0.344 10.179
11 1948 1923.3 0.316 10.496
12 1367 1388.7 0.340 10.836
13 998 1003.7 0.033 10.869
14 718 726.1 0.091 10.960
15 526 525.8 0.000 10.960
16 368 381.2 0.454 11.414
17 273 276.5 0.045 11.459
18 205 200.8 0.087 11.546
19 158 146.0 0.989 12.535
20 107 106.2 0.006 12.540
21 303 287.1 0.879 13.419
Chisq= 13.42 for 20 degrees of freedom, p= 0.14133
SUMMARY of craptest
p-value for no. of wins: 0.895701
p-value for throws/game: 0.141330
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-11_21:31
No. of wins: Observed Expected
98492 98585.9
z-score=-0.420, pvalue=0.33732
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66816 66666.7 0.335 0.335
2 37628 37654.3 0.018 0.353
3 26813 26954.7 0.745 1.098
4 19363 19313.5 0.127 1.225
5 13911 13851.4 0.256 1.481
6 10036 9943.5 0.860 2.341
7 7077 7145.0 0.648 2.989
8 5114 5139.1 0.122 3.111
9 3718 3699.9 0.089 3.200
10 2614 2666.3 1.026 4.226
11 1836 1923.3 3.965 8.191
12 1374 1388.7 0.156 8.347
13 1022 1003.7 0.333 8.681
14 705 726.1 0.615 9.296
15 544 525.8 0.627 9.923
16 388 381.2 0.123 10.047
17 267 276.5 0.329 10.376
18 203 200.8 0.023 10.399
19 141 146.0 0.170 10.569
20 124 106.2 2.978 13.547
21 306 287.1 1.242 14.789
Chisq= 14.79 for 20 degrees of freedom, p= 0.21168
SUMMARY of craptest
p-value for no. of wins: 0.337319
p-value for throws/game: 0.211676
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0000,0.0033,0.0082,0.0154,0.0193,0.0256,0.0387,0.0403,0.0407,0.0470,
0.0486,0.0511,0.0528,0.0539,0.0590,0.0614,0.0623,0.0744,0.0752,0.0785,
0.0876,0.0876,0.0892,0.0901,0.0917,0.0977,0.0993,0.1059,0.1142,0.1165,
0.1190,0.1221,0.1240,0.1243,0.1269,0.1298,0.1304,0.1361,0.1363,0.1366,
0.1413,0.1432,0.1596,0.1650,0.1750,0.1855,0.1935,0.1959,0.1973,0.1978,
0.2026,0.2046,0.2117,0.2147,0.2156,0.2159,0.2168,0.2206,0.2213,0.2259,
0.2260,0.2306,0.2316,0.2326,0.2331,0.2349,0.2364,0.2364,0.2369,0.2474,
0.2488,0.2588,0.2627,0.2636,0.2648,0.2672,0.2692,0.2764,0.2764,0.2872,
0.2893,0.2919,0.2922,0.2927,0.2928,0.2965,0.3090,0.3098,0.3104,0.3179,
0.3191,0.3204,0.3223,0.3327,0.3328,0.3364,0.3373,0.3404,0.3408,0.3411,
0.3416,0.3567,0.3579,0.3674,0.3703,0.3746,0.3746,0.3846,0.3905,0.4004,
0.4015,0.4101,0.4117,0.4150,0.4208,0.4214,0.4215,0.4301,0.4310,0.4393,
0.4416,0.4429,0.4445,0.4456,0.4486,0.4538,0.4556,0.4565,0.4597,0.4615,
0.4631,0.4636,0.4734,0.4798,0.4811,0.4815,0.4966,0.5000,0.5104,0.5119,
0.5163,0.5207,0.5216,0.5229,0.5302,0.5335,0.5365,0.5407,0.5431,0.5473,
0.5539,0.5554,0.5559,0.5615,0.5682,0.5687,0.5710,0.5722,0.5775,0.5849,
0.5895,0.5895,0.5954,0.6009,0.6009,0.6062,0.6147,0.6154,0.6162,0.6168,
0.6272,0.6277,0.6291,0.6324,0.6428,0.6443,0.6465,0.6473,0.6490,0.6505,
0.6513,0.6523,0.6548,0.6577,0.6618,0.6635,0.6637,0.6726,0.6736,0.6792,
0.6822,0.6880,0.7010,0.7080,0.7090,0.7107,0.7171,0.7173,0.7261,0.7377,
0.7386,0.7410,0.7430,0.7465,0.7596,0.7635,0.7717,0.7771,0.7788,0.7790,
0.7809,0.7978,0.7987,0.8011,0.8035,0.8083,0.8165,0.8170,0.8187,0.8199,
0.8206,0.8253,0.8269,0.8369,0.8484,0.8485,0.8501,0.8516,0.8546,0.8559,
0.8565,0.8603,0.8679,0.8724,0.8782,0.8824,0.8836,0.8859,0.8916,0.8957,
0.8962,0.8992,0.9024,0.9038,0.9073,0.9074,0.9113,0.9128,0.9173,0.9177,
0.9191,0.9232,0.9274,0.9342,0.9368,0.9438,0.9439,0.9546,0.9568,0.9591,
0.9607,0.9673,0.9777,0.9872,0.9892,0.9895,0.9923,0.9934,0.9958,
Overall p-value after applying KStest on 269 p-values = 0.970522
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.