RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-30_22:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.52 25.2050 0.909786
2 to 25 15.83 17.3233 0.567319
3 to 26 15.84 38.1692 0.997670
4 to 27 15.79 25.7892 0.921613
5 to 28 15.80 17.3133 0.566655
6 to 29 15.73 24.7261 0.898990
7 to 30 15.78 25.1000 0.907507
8 to 31 15.63 16.5699 0.516148
9 to 32 15.51 27.6594 0.950922
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.000779
Tough bday spacings test for dh-ranFile-2018-06-30_22:31: 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 5 34 64 85 121 85 51 31 15 7 2
(O-E)^2/E 1.9 0.2 1.2 1.6 5.6 0.6 0.0 0.1 0.0 0.0 1.0
Birthday Spacings: Sum(O-E)^2/E= 12.208, p= 0.729
RESULTS OF GCD FOR dh-ranFile-2018-06-30_22:31
Euclid's algorithm:
p-value, steps to gcd: 0.058172
p-value, dist. of gcd's: 0.549439
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-30_22:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.934 0.771 0.316 0.495 0.497 0.922 0.885 0.659
Bits 8 to 15---> 0.295 0.078 0.154 0.340 0.546 0.058 0.249 0.540
Bits 16 to 23---> 0.418 0.496 0.138 0.230 0.099 0.750 0.512 0.368
Bits 24 to 31---> 0.602 0.498 0.059 0.815 0.835 0.525 0.320 0.283
KS test for the above 32 p values: 0.458
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-30_22:31,
p-values for 5 runs: 0.3958, 0.5727, 0.3607, 0.5759, 0.5280
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-30_22:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 228 211.4 1.301 1.301
r= 29 5099 5134.0 0.239 1.539
r= 30 23104 23103.0 0.000 1.539
r= 31 11569 11551.5 0.026 1.566
chi-square = 1.566 with df = 3; p-value = 0.333
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-30_22:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 238 211.4 3.342 3.342
r= 30 5031 5134.0 2.067 5.409
r= 31 23080 23103.0 0.023 5.432
r= 32 11651 11551.5 0.857 6.289
chi-square = 6.289 with df = 3; p-value = 0.902
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-30_22:31
b-rank test for bits 1 to 8, p=0.03325
b-rank test for bits 2 to 9, p=0.67250
b-rank test for bits 3 to 10, p=0.03737
b-rank test for bits 4 to 11, p=0.38570
b-rank test for bits 5 to 12, p=0.32434
b-rank test for bits 6 to 13, p=0.84408
b-rank test for bits 7 to 14, p=0.26916
b-rank test for bits 8 to 15, p=0.12264
b-rank test for bits 9 to 16, p=0.72208
b-rank test for bits 10 to 17, p=0.50678
b-rank test for bits 11 to 18, p=0.07356
b-rank test for bits 12 to 19, p=0.54449
b-rank test for bits 13 to 20, p=0.64734
b-rank test for bits 14 to 21, p=0.44191
b-rank test for bits 15 to 22, p=0.47707
b-rank test for bits 16 to 23, p=0.66093
b-rank test for bits 17 to 24, p=0.95926
b-rank test for bits 18 to 25, p=0.40405
b-rank test for bits 19 to 26, p=0.01908
b-rank test for bits 20 to 27, p=0.13245
b-rank test for bits 21 to 28, p=0.03667
b-rank test for bits 22 to 29, p=0.17238
b-rank test for bits 23 to 30, p=0.15166
b-rank test for bits 24 to 31, p=0.64152
b-rank test for bits 25 to 32, p=0.01383
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 = 0.025083
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-30_22:31
(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 143109 2.80 0.997468
2 141572 -0.79 0.215303
3 142496 1.37 0.914770
4 142279 0.86 0.806128
5 141445 -1.08 0.138987
6 142529 1.45 0.926167
7 141472 -1.02 0.153438
8 141875 -0.08 0.468035
9 141808 -0.24 0.406425
10 141889 -0.05 0.481057
11 142196 0.67 0.748504
12 141176 -1.71 0.043321
13 142049 0.33 0.627913
14 141855 -0.13 0.449494
15 142042 0.31 0.621711
16 142043 0.31 0.622599
17 141920 0.02 0.509945
18 141624 -0.67 0.252495
19 141570 -0.79 0.213939
20 141352 -1.30 0.096429
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-30_22:31
Bits used No. missing words z-score p-value
23 to 32 141224 -2.3632 0.009059
22 to 31 141748 -0.5563 0.288999
21 to 30 141359 -1.8977 0.028868
20 to 29 141865 -0.1529 0.439254
19 to 28 142010 0.3471 0.635756
18 to 27 141898 -0.0391 0.484418
17 to 26 141686 -0.7701 0.220619
16 to 25 141310 -2.0667 0.019383
15 to 24 141690 -0.7563 0.224732
14 to 23 141881 -0.0977 0.461089
13 to 22 141805 -0.3598 0.359514
12 to 21 141782 -0.4391 0.330306
11 to 20 141837 -0.2494 0.401520
10 to 19 141807 -0.3529 0.362096
9 to 18 142094 0.6368 0.737870
8 to 17 142380 1.6230 0.947705
7 to 16 141562 -1.1977 0.115519
6 to 15 141969 0.2058 0.581510
5 to 14 141299 -2.1046 0.017664
4 to 13 142299 1.3437 0.910476
3 to 12 141935 0.0885 0.535267
2 to 11 141226 -2.3563 0.009229
1 to 10 142443 1.8402 0.967134
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-30_22:31
Bits used No. missing words z-score p-value
28 to 32 141948 0.1311 0.552146
27 to 31 141979 0.2362 0.593349
26 to 30 141851 -0.1977 0.421629
25 to 29 142244 1.1345 0.871702
24 to 28 141940 0.1040 0.541402
23 to 27 142231 1.0904 0.862233
22 to 26 141495 -1.4045 0.080084
21 to 25 142010 0.3413 0.633544
20 to 24 141583 -1.1062 0.134319
19 to 23 141112 -2.7028 0.003438
18 to 22 141636 -0.9265 0.177082
17 to 21 142339 1.4565 0.927374
16 to 20 141763 -0.4960 0.309935
15 to 19 141725 -0.6248 0.266036
14 to 18 142486 1.9548 0.974697
13 to 17 142100 0.6463 0.740970
12 to 16 142080 0.5785 0.718551
11 to 15 141855 -0.1842 0.426940
10 to 14 141670 -0.8113 0.208600
9 to 13 141688 -0.7503 0.226546
8 to 12 142190 0.9514 0.829305
7 to 11 141308 -2.0384 0.020755
6 to 10 142120 0.7141 0.762428
5 to 9 141370 -1.8282 0.033757
4 to 8 142141 0.7853 0.783868
3 to 7 141639 -0.9164 0.179736
2 to 6 142487 1.9582 0.974897
1 to 5 142003 0.3175 0.624578
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-30_22:31
Bits used No. missing words z-score p-value
31 to 32 141317 -1.7473 0.040294
30 to 31 141558 -1.0364 0.150014
29 to 30 142069 0.4710 0.681181
28 to 29 141871 -0.1131 0.454988
27 to 28 142482 1.6893 0.954418
26 to 27 142571 1.9518 0.974521
25 to 26 141702 -0.6116 0.270404
24 to 25 141597 -0.9213 0.178440
23 to 24 141531 -1.1160 0.132207
22 to 23 142143 0.6893 0.754680
21 to 22 141982 0.2144 0.584869
20 to 21 141227 -2.0128 0.022069
19 to 20 142095 0.5477 0.708051
18 to 19 142275 1.0787 0.859633
17 to 18 141367 -1.5998 0.054822
16 to 17 142005 0.2822 0.611110
15 to 16 142012 0.3029 0.619002
14 to 15 141808 -0.2989 0.382505
13 to 14 141728 -0.5349 0.296361
12 to 13 142308 1.1760 0.880206
11 to 12 142365 1.3442 0.910552
10 to 11 141214 -2.0511 0.020128
9 to 10 142004 0.2793 0.609978
8 to 9 141917 0.0226 0.509025
7 to 8 141701 -0.6145 0.269428
6 to 7 141621 -0.8505 0.197515
5 to 6 142117 0.6126 0.729928
4 to 5 142007 0.2881 0.613370
3 to 4 141552 -1.0541 0.145925
2 to 3 142143 0.6893 0.754680
1 to 2 141664 -0.7237 0.234629
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-30_22:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2517.10 0.242 0.595557
Test results for specific bytes for dh-ranFile-2018-06-30_22:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2488.20 -0.167 0.433722
2 to 9 2428.82 -1.007 0.157057
3 to 10 2518.88 0.267 0.605273
4 to 11 2629.60 1.833 0.966588
5 to 12 2402.39 -1.380 0.083721
6 to 13 2457.67 -0.599 0.274695
7 to 14 2428.54 -1.011 0.156089
8 to 15 2581.88 1.158 0.876561
9 to 16 2558.88 0.833 0.797494
10 to 17 2572.12 1.020 0.846119
11 to 18 2373.27 -1.792 0.036543
12 to 19 2494.97 -0.071 0.471659
13 to 20 2596.91 1.371 0.914744
14 to 21 2474.30 -0.363 0.358148
15 to 22 2453.26 -0.661 0.254287
16 to 23 2430.85 -0.978 0.164061
17 to 24 2524.07 0.340 0.633231
18 to 25 2511.63 0.165 0.565344
19 to 26 2468.62 -0.444 0.328617
20 to 27 2578.41 1.109 0.866246
21 to 28 2452.38 -0.674 0.250311
22 to 29 2554.57 0.772 0.779858
23 to 30 2485.49 -0.205 0.418727
24 to 31 2534.56 0.489 0.687506
25 to 32 2537.12 0.525 0.700178
CDPARK for dh-ranFile-2018-06-30_22:31: 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
3503 -0.9132 0.180558
3551 1.2785 0.899470
3507 -0.7306 0.232514
3510 -0.5936 0.276387
3522 -0.0457 0.481790
3557 1.5525 0.939730
3529 0.2740 0.607947
3513 -0.4566 0.323972
3514 -0.4110 0.340551
3522 -0.0457 0.481790
Square side=100, avg. no. parked=3522.80 sample std.=17.27
p-value of the KSTEST for those 10 p-values: 0.668938
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-30_22:31
0.1926,0.1582,0.2013,0.1440,0.4143,0.1238,0.7143,0.6377,0.2749,0.6285,
The KS test for those 10 p-values: 0.109223
The 3DSPHERES test for dh-ranFile-2018-06-30_22:31
sample no r^3 equiv. uni.
1 24.174 0.553264
2 12.806 0.347446
3 14.662 0.386599
4 89.709 0.949728
5 1.148 0.037539
6 30.779 0.641546
7 17.833 0.448119
8 14.584 0.384992
9 27.919 0.605691
10 56.887 0.849865
11 7.202 0.213426
12 74.113 0.915451
13 6.074 0.183284
14 17.349 0.439157
15 7.061 0.209721
16 35.791 0.696696
17 35.987 0.698678
18 5.534 0.168462
19 16.600 0.424968
20 19.817 0.483434
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.776052
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-30_22:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 2.6 -0.8 -0.7 0.0 0.5
-1.0 -0.1 -0.1 -1.3 -0.6 -0.4
1.5 0.7 1.1 -0.6 1.4 -0.7
-1.8 0.5 1.0 -1.3 0.2 0.2
1.2 -0.7 0.2 0.7 -0.6 -1.7
0.9 -0.6 0.5 -2.6 0.5 -0.7
-0.2 -0.4 -0.8 -0.1 -1.3 0.0
-0.1
Chi-square with 42 degrees of freedom:43.950086
z-score=0.212772, p-value=0.611070
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-30_22:31
Test no p-value
1 0.013381
2 0.098216
3 0.157963
4 0.697757
5 0.101513
6 0.049430
7 0.005746
8 0.611894
9 0.661031
10 0.928101
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.017575
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-30_22:31:
(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 66799 0.26 66818 0.34
3 25000.00 24833 1.12 24878 0.60
4 6666.67 6702 0.19 6625 0.26
5 1388.89 1375 0.14 1395 0.03
6 238.10 261 2.20 250 0.60
7 34.72 26 2.19 29 0.94
8 4.96 3 0.77 4 0.19
p=0.66719 p=0.18486
Number of rngs required: 687685, p-value: 0.203
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-30_22:31
No. of wins: Observed Expected
98548 98585.9
z-score=-0.169, pvalue=0.43277
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66502 66666.7 0.407 0.407
2 37843 37654.3 0.945 1.352
3 26906 26954.7 0.088 1.440
4 19290 19313.5 0.029 1.469
5 14036 13851.4 2.460 3.928
6 9927 9943.5 0.028 3.956
7 7166 7145.0 0.062 4.018
8 5076 5139.1 0.774 4.792
9 3768 3699.9 1.255 6.046
10 2602 2666.3 1.551 7.597
11 1922 1923.3 0.001 7.598
12 1310 1388.7 4.465 12.062
13 973 1003.7 0.940 13.002
14 757 726.1 1.311 14.314
15 538 525.8 0.281 14.595
16 363 381.2 0.864 15.459
17 275 276.5 0.009 15.468
18 195 200.8 0.169 15.637
19 130 146.0 1.750 17.387
20 105 106.2 0.014 17.401
21 316 287.1 2.906 20.307
Chisq= 20.31 for 20 degrees of freedom, p= 0.56115
SUMMARY of craptest
p-value for no. of wins: 0.432770
p-value for throws/game: 0.561151
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-30_22:31
No. of wins: Observed Expected
98545 98585.9
z-score=-0.183, pvalue=0.42750
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66555 66666.7 0.187 0.187
2 37674 37654.3 0.010 0.197
3 26747 26954.7 1.601 1.798
4 19269 19313.5 0.102 1.901
5 13881 13851.4 0.063 1.964
6 10078 9943.5 1.818 3.782
7 7160 7145.0 0.031 3.813
8 5188 5139.1 0.466 4.279
9 3780 3699.9 1.736 6.015
10 2688 2666.3 0.177 6.191
11 1941 1923.3 0.162 6.354
12 1410 1388.7 0.325 6.679
13 984 1003.7 0.387 7.066
14 735 726.1 0.108 7.175
15 524 525.8 0.006 7.181
16 372 381.2 0.220 7.401
17 275 276.5 0.009 7.409
18 203 200.8 0.023 7.433
19 123 146.0 3.619 11.051
20 100 106.2 0.364 11.415
21 313 287.1 2.334 13.749
Chisq= 13.75 for 20 degrees of freedom, p= 0.15701
SUMMARY of craptest
p-value for no. of wins: 0.427500
p-value for throws/game: 0.157009
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0008,0.0034,0.0057,0.0091,0.0092,0.0134,0.0138,0.0176,0.0177,0.0191,
0.0194,0.0201,0.0208,0.0221,0.0251,0.0289,0.0332,0.0338,0.0365,0.0367,
0.0374,0.0375,0.0403,0.0433,0.0494,0.0548,0.0580,0.0582,0.0589,0.0736,
0.0775,0.0801,0.0837,0.0964,0.0982,0.0995,0.1015,0.1092,0.1155,0.1226,
0.1238,0.1322,0.1325,0.1343,0.1385,0.1390,0.1440,0.1459,0.1500,0.1517,
0.1534,0.1544,0.1561,0.1570,0.1571,0.1580,0.1582,0.1641,0.1685,0.1724,
0.1771,0.1784,0.1797,0.1806,0.1833,0.1849,0.1926,0.1975,0.2013,0.2032,
0.2086,0.2097,0.2134,0.2139,0.2153,0.2206,0.2247,0.2265,0.2302,0.2325,
0.2346,0.2494,0.2503,0.2525,0.2543,0.2660,0.2692,0.2694,0.2704,0.2747,
0.2749,0.2764,0.2830,0.2890,0.2948,0.2964,0.3099,0.3163,0.3203,0.3240,
0.3243,0.3286,0.3303,0.3328,0.3403,0.3406,0.3474,0.3581,0.3595,0.3607,
0.3621,0.3683,0.3825,0.3850,0.3857,0.3866,0.3958,0.4015,0.4040,0.4064,
0.4143,0.4182,0.4187,0.4216,0.4250,0.4269,0.4275,0.4328,0.4337,0.4392,
0.4393,0.4419,0.4481,0.4495,0.4550,0.4585,0.4611,0.4680,0.4717,0.4771,
0.4811,0.4818,0.4818,0.4834,0.4844,0.4949,0.4963,0.4974,0.4977,0.5068,
0.5090,0.5099,0.5117,0.5161,0.5252,0.5280,0.5353,0.5404,0.5414,0.5445,
0.5459,0.5494,0.5521,0.5533,0.5612,0.5653,0.5667,0.5673,0.5727,0.5759,
0.5815,0.5849,0.5933,0.5956,0.6025,0.6053,0.6057,0.6079,0.6100,0.6111,
0.6111,0.6119,0.6134,0.6190,0.6217,0.6226,0.6246,0.6279,0.6285,0.6332,
0.6335,0.6358,0.6377,0.6415,0.6415,0.6473,0.6589,0.6609,0.6610,0.6672,
0.6689,0.6725,0.6812,0.6875,0.6967,0.6978,0.6987,0.7002,0.7081,0.7143,
0.7186,0.7221,0.7286,0.7299,0.7379,0.7410,0.7485,0.7502,0.7547,0.7547,
0.7624,0.7714,0.7761,0.7799,0.7839,0.7975,0.8061,0.8145,0.8293,0.8346,
0.8441,0.8461,0.8499,0.8596,0.8622,0.8662,0.8717,0.8766,0.8802,0.8851,
0.8990,0.8995,0.9016,0.9075,0.9098,0.9105,0.9106,0.9147,0.9148,0.9155,
0.9216,0.9222,0.9262,0.9274,0.9281,0.9345,0.9397,0.9477,0.9497,0.9509,
0.9544,0.9593,0.9666,0.9671,0.9745,0.9747,0.9749,0.9975,0.9977,
Overall p-value after applying KStest on 269 p-values = 0.017057
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.