RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-06_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 19.7590 0.713261
2 to 25 15.51 15.8559 0.465929
3 to 26 16.00 19.7685 0.713757
4 to 27 15.94 7.1782 0.018879
5 to 28 15.66 17.4718 0.577128
6 to 29 15.86 24.4027 0.891101
7 to 30 15.73 21.4679 0.793944
8 to 31 15.76 13.1518 0.274031
9 to 32 15.65 17.4379 0.574899
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.647042
Tough bday spacings test for dh-ranFile-2018-07-06_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 11 31 76 106 75 87 41 38 16 12 7
(O-E)^2/E 0.4 0.9 0.1 0.7 5.3 1.0 2.4 2.3 0.1 4.4 2.1
Birthday Spacings: Sum(O-E)^2/E= 19.539, p= 0.966
RESULTS OF GCD FOR dh-ranFile-2018-07-06_06:31
Euclid's algorithm:
p-value, steps to gcd: 0.737804
p-value, dist. of gcd's: 0.086154
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-06_06:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.612 0.905 0.032 0.566 0.135 0.245 0.884 0.910
Bits 8 to 15---> 0.233 0.034 0.544 0.025 0.665 0.472 0.573 0.023
Bits 16 to 23---> 0.295 0.636 0.812 0.246 0.397 0.976 0.304 0.524
Bits 24 to 31---> 0.858 0.148 0.973 0.613 0.946 0.468 0.107 0.907
KS test for the above 32 p values: 0.349
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-06_06:31,
p-values for 5 runs: 0.0865, 0.9993, 0.1759, 0.6099, 0.8134
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-06_06:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 184 211.4 3.556 3.556
r= 29 5112 5134.0 0.094 3.650
r= 30 23105 23103.0 0.000 3.650
r= 31 11599 11551.5 0.195 3.845
chi-square = 3.845 with df = 3; p-value = 0.721
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-06_06:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 194 211.4 1.435 1.435
r= 30 5184 5134.0 0.487 1.922
r= 31 23170 23103.0 0.194 2.116
r= 32 11452 11551.5 0.857 2.973
chi-square = 2.973 with df = 3; p-value = 0.604
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-06_06:31
b-rank test for bits 1 to 8, p=0.80964
b-rank test for bits 2 to 9, p=0.93351
b-rank test for bits 3 to 10, p=0.89792
b-rank test for bits 4 to 11, p=0.68462
b-rank test for bits 5 to 12, p=0.64140
b-rank test for bits 6 to 13, p=0.17162
b-rank test for bits 7 to 14, p=0.38314
b-rank test for bits 8 to 15, p=0.07348
b-rank test for bits 9 to 16, p=0.21014
b-rank test for bits 10 to 17, p=0.64197
b-rank test for bits 11 to 18, p=0.46989
b-rank test for bits 12 to 19, p=0.63295
b-rank test for bits 13 to 20, p=0.41765
b-rank test for bits 14 to 21, p=0.53511
b-rank test for bits 15 to 22, p=0.04844
b-rank test for bits 16 to 23, p=0.61701
b-rank test for bits 17 to 24, p=0.54362
b-rank test for bits 18 to 25, p=0.45578
b-rank test for bits 19 to 26, p=0.78847
b-rank test for bits 20 to 27, p=0.22379
b-rank test for bits 21 to 28, p=0.87036
b-rank test for bits 22 to 29, p=0.76391
b-rank test for bits 23 to 30, p=0.80993
b-rank test for bits 24 to 31, p=0.14399
b-rank test for bits 25 to 32, p=0.84756
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 = 0.627311
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-06_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 142166 0.60 0.725646
2 141730 -0.42 0.337610
3 141493 -0.97 0.165343
4 141804 -0.25 0.402803
5 141918 0.02 0.508081
6 141794 -0.27 0.393787
7 142263 0.83 0.795692
8 141183 -1.70 0.044845
9 142051 0.33 0.629680
10 141755 -0.36 0.359205
11 142346 1.02 0.846197
12 141711 -0.46 0.321543
13 142461 1.29 0.901292
14 142303 0.92 0.821159
15 142037 0.30 0.617261
16 141765 -0.34 0.367976
17 141977 0.16 0.562814
18 141792 -0.27 0.391990
19 141770 -0.33 0.372387
20 140828 -2.53 0.005761
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-06_06:31
Bits used No. missing words z-score p-value
23 to 32 142018 0.3747 0.646067
22 to 31 141922 0.0437 0.517424
21 to 30 142098 0.6506 0.742343
20 to 29 141992 0.2851 0.612204
19 to 28 141827 -0.2839 0.388245
18 to 27 141284 -2.1563 0.015530
17 to 26 142138 0.7885 0.784803
16 to 25 142353 1.5299 0.936979
15 to 24 141376 -1.8391 0.032953
14 to 23 141946 0.1264 0.550312
13 to 22 141222 -2.3701 0.008892
12 to 21 141584 -1.1218 0.130968
11 to 20 142035 0.4333 0.667618
10 to 19 141774 -0.4667 0.320373
9 to 18 142099 0.6540 0.743455
8 to 17 142440 1.8299 0.966367
7 to 16 141984 0.2575 0.601597
6 to 15 141999 0.3092 0.621418
5 to 14 142095 0.6402 0.738992
4 to 13 141912 0.0092 0.503673
3 to 12 141679 -0.7942 0.213528
2 to 11 141395 -1.7736 0.038069
1 to 10 141979 0.2402 0.594928
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-06_06:31
Bits used No. missing words z-score p-value
28 to 32 142002 0.3141 0.623291
27 to 31 141898 -0.0384 0.484682
26 to 30 141817 -0.3130 0.377147
25 to 29 141947 0.1277 0.550805
24 to 28 141884 -0.0859 0.465787
23 to 27 141897 -0.0418 0.483330
22 to 26 142002 0.3141 0.623291
21 to 25 141434 -1.6113 0.053558
20 to 24 141729 -0.6113 0.270504
19 to 23 141981 0.2429 0.595978
18 to 22 141759 -0.5096 0.305168
17 to 21 141586 -1.0960 0.136532
16 to 20 142058 0.5040 0.692857
15 to 19 142124 0.7277 0.766600
14 to 18 141405 -1.7096 0.043671
13 to 17 141664 -0.8316 0.202810
12 to 16 141590 -1.0825 0.139521
11 to 15 142129 0.7446 0.771757
10 to 14 141583 -1.1062 0.134319
9 to 13 141737 -0.5842 0.279553
8 to 12 142060 0.5107 0.695236
7 to 11 142055 0.4938 0.689275
6 to 10 141428 -1.6316 0.051379
5 to 9 141260 -2.2011 0.013864
4 to 8 142526 2.0904 0.981709
3 to 7 142156 0.8362 0.798470
2 to 6 142048 0.4701 0.680847
1 to 5 142078 0.5718 0.716259
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-06_06:31
Bits used No. missing words z-score p-value
31 to 32 142378 1.3825 0.916592
30 to 31 141897 -0.0364 0.485493
29 to 30 141959 0.1465 0.558244
28 to 29 142211 0.8899 0.813235
27 to 28 141616 -0.8653 0.193443
26 to 27 141689 -0.6499 0.257865
25 to 26 142158 0.7335 0.768385
24 to 25 141548 -1.0659 0.143241
23 to 24 141827 -0.2429 0.404056
22 to 23 141954 0.1318 0.552417
21 to 22 142009 0.2940 0.615626
20 to 21 141882 -0.0806 0.467872
19 to 20 141611 -0.8800 0.189422
18 to 19 141722 -0.5526 0.290270
17 to 18 141937 0.0816 0.532527
16 to 17 142092 0.5388 0.705005
15 to 16 141910 0.0020 0.500789
14 to 15 141845 -0.1898 0.424747
13 to 14 142633 2.1347 0.983608
12 to 13 141829 -0.2370 0.406343
11 to 12 142161 0.7424 0.771074
10 to 11 141840 -0.2045 0.418976
9 to 10 141819 -0.2665 0.394942
8 to 9 141812 -0.2871 0.387014
7 to 8 141971 0.1819 0.572176
6 to 7 141311 -1.7650 0.038783
5 to 6 142513 1.7807 0.962522
4 to 5 141894 -0.0452 0.481966
3 to 4 141104 -2.3756 0.008760
2 to 3 141450 -1.3550 0.087716
1 to 2 141752 -0.4641 0.321288
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-06_06:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2412.50 -1.237 0.107962
Test results for specific bytes for dh-ranFile-2018-07-06_06:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2511.94 0.169 0.567031
2 to 9 2532.04 0.453 0.674779
3 to 10 2581.58 1.154 0.875699
4 to 11 2397.58 -1.448 0.073755
5 to 12 2526.89 0.380 0.648121
6 to 13 2517.83 0.252 0.599542
7 to 14 2516.70 0.236 0.593364
8 to 15 2555.10 0.779 0.782079
9 to 16 2432.05 -0.961 0.168285
10 to 17 2482.50 -0.247 0.402285
11 to 18 2314.23 -2.627 0.004305
12 to 19 2548.69 0.689 0.754450
13 to 20 2523.89 0.338 0.632244
14 to 21 2535.71 0.505 0.693228
15 to 22 2475.78 -0.342 0.366000
16 to 23 2542.77 0.605 0.727376
17 to 24 2589.58 1.267 0.897384
18 to 25 2512.05 0.170 0.567664
19 to 26 2555.58 0.786 0.784089
20 to 27 2509.04 0.128 0.550854
21 to 28 2504.59 0.065 0.525855
22 to 29 2403.45 -1.365 0.086061
23 to 30 2559.08 0.836 0.798285
24 to 31 2549.50 0.700 0.758056
25 to 32 2486.06 -0.197 0.421853
CDPARK for dh-ranFile-2018-07-06_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
3559 1.6438 0.949895
3572 2.2374 0.987371
3553 1.3699 0.914635
3496 -1.2329 0.108811
3490 -1.5068 0.065925
3506 -0.7763 0.218799
3531 0.3653 0.642555
3523 0.0000 0.500000
3511 -0.5479 0.291865
3513 -0.4566 0.323972
Square side=100, avg. no. parked=3525.40 sample std.=26.37
p-value of the KSTEST for those 10 p-values: 0.609858
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-06_06:31
0.7746,0.0345,0.6924,0.8206,0.7073,0.1802,0.7825,0.7229,0.9449,0.6469,
The KS test for those 10 p-values: 0.125667
The 3DSPHERES test for dh-ranFile-2018-07-06_06:31
sample no r^3 equiv. uni.
1 1.538 0.049969
2 50.660 0.815231
3 16.588 0.424744
4 44.624 0.774053
5 52.899 0.828523
6 17.604 0.443905
7 1.268 0.041381
8 41.539 0.749588
9 20.375 0.492963
10 10.680 0.299529
11 37.164 0.710264
12 37.129 0.709931
13 14.498 0.383239
14 26.176 0.582106
15 8.382 0.243760
16 6.145 0.185221
17 15.519 0.403863
18 15.218 0.397859
19 98.419 0.962396
20 8.444 0.245333
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.896712
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-06_06:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -1.6 -0.4 -0.4 2.5 0.3
0.0 1.9 -1.0 0.7 1.2 0.2
-0.3 -0.8 -0.2 -0.2 -0.2 1.1
-0.6 0.9 0.6 -1.5 1.0 -0.1
-1.9 -1.2 -0.7 -0.8 -1.1 1.4
3.2 -0.4 1.0 1.1 -0.8 2.4
-0.7 0.2 1.3 0.4 0.9 -1.0
-1.1
Chi-square with 42 degrees of freedom:56.879999
z-score=1.623541, p-value=0.937560
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-06_06:31
Test no p-value
1 0.949309
2 0.029509
3 0.197999
4 0.765926
5 0.699642
6 0.701060
7 0.307084
8 0.627193
9 0.117705
10 0.027353
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.484853
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-06_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 66725 0.05 66791 0.23
3 25000.00 25002 0.00 25044 0.08
4 6666.67 6617 0.37 6548 2.11
5 1388.89 1382 0.03 1351 1.03
6 238.10 240 0.02 221 1.23
7 34.72 32 0.21 40 0.80
8 4.96 1 3.16 4 0.19
p=0.30241 p=0.53903
Number of rngs required: 687664, p-value: 0.196
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-06_06:31
No. of wins: Observed Expected
98280 98585.9
z-score=-1.368, pvalue=0.08566
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66708 66666.7 0.026 0.026
2 37709 37654.3 0.079 0.105
3 26921 26954.7 0.042 0.147
4 19297 19313.5 0.014 0.161
5 13777 13851.4 0.400 0.561
6 9992 9943.5 0.236 0.797
7 7252 7145.0 1.602 2.399
8 5154 5139.1 0.043 2.442
9 3665 3699.9 0.329 2.771
10 2624 2666.3 0.671 3.442
11 1911 1923.3 0.079 3.521
12 1424 1388.7 0.895 4.416
13 1000 1003.7 0.014 4.430
14 704 726.1 0.675 5.105
15 490 525.8 2.442 7.547
16 372 381.2 0.220 7.767
17 261 276.5 0.873 8.640
18 203 200.8 0.023 8.663
19 136 146.0 0.683 9.346
20 106 106.2 0.000 9.347
21 294 287.1 0.165 9.512
Chisq= 9.51 for 20 degrees of freedom, p= 0.02382
SUMMARY of craptest
p-value for no. of wins: 0.085659
p-value for throws/game: 0.023815
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-06_06:31
No. of wins: Observed Expected
98550 98585.9
z-score=-0.160, pvalue=0.43629
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66880 66666.7 0.683 0.683
2 37872 37654.3 1.258 1.941
3 26885 26954.7 0.180 2.121
4 18961 19313.5 6.432 8.554
5 13826 13851.4 0.047 8.600
6 9957 9943.5 0.018 8.619
7 7152 7145.0 0.007 8.625
8 5058 5139.1 1.279 9.904
9 3737 3699.9 0.373 10.277
10 2672 2666.3 0.012 10.289
11 1924 1923.3 0.000 10.290
12 1378 1388.7 0.083 10.373
13 1071 1003.7 4.511 14.883
14 712 726.1 0.275 15.158
15 557 525.8 1.847 17.005
16 387 381.2 0.090 17.095
17 263 276.5 0.663 17.758
18 187 200.8 0.952 18.710
19 123 146.0 3.619 22.329
20 99 106.2 0.490 22.819
21 299 287.1 0.492 23.311
Chisq= 23.31 for 20 degrees of freedom, p= 0.72624
SUMMARY of craptest
p-value for no. of wins: 0.436291
p-value for throws/game: 0.726237
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0043,0.0058,0.0088,0.0089,0.0139,0.0155,0.0189,0.0235,0.0238,0.0245,
0.0274,0.0295,0.0321,0.0330,0.0335,0.0345,0.0381,0.0388,0.0414,0.0437,
0.0448,0.0484,0.0500,0.0514,0.0536,0.0659,0.0735,0.0738,0.0857,0.0861,
0.0862,0.0865,0.0877,0.1068,0.1080,0.1088,0.1177,0.1257,0.1310,0.1343,
0.1348,0.1365,0.1395,0.1432,0.1440,0.1475,0.1653,0.1683,0.1716,0.1759,
0.1802,0.1852,0.1894,0.1934,0.1964,0.1980,0.2028,0.2101,0.2135,0.2188,
0.2238,0.2332,0.2438,0.2448,0.2453,0.2456,0.2579,0.2705,0.2740,0.2796,
0.2903,0.2919,0.2949,0.2995,0.3024,0.3043,0.3052,0.3071,0.3204,0.3213,
0.3215,0.3240,0.3376,0.3491,0.3592,0.3660,0.3680,0.3724,0.3771,0.3831,
0.3832,0.3870,0.3882,0.3920,0.3938,0.3949,0.3974,0.3979,0.4023,0.4028,
0.4039,0.4041,0.4063,0.4176,0.4190,0.4219,0.4247,0.4247,0.4363,0.4439,
0.4558,0.4658,0.4659,0.4679,0.4682,0.4699,0.4722,0.4820,0.4833,0.4847,
0.4849,0.4855,0.4930,0.5000,0.5008,0.5037,0.5081,0.5174,0.5237,0.5259,
0.5325,0.5351,0.5390,0.5436,0.5442,0.5503,0.5508,0.5509,0.5524,0.5582,
0.5628,0.5663,0.5670,0.5677,0.5722,0.5731,0.5749,0.5771,0.5821,0.5934,
0.5949,0.5960,0.5995,0.6016,0.6042,0.6099,0.6099,0.6118,0.6122,0.6126,
0.6156,0.6170,0.6173,0.6214,0.6233,0.6233,0.6272,0.6273,0.6297,0.6322,
0.6330,0.6364,0.6414,0.6420,0.6426,0.6461,0.6469,0.6470,0.6481,0.6650,
0.6676,0.6748,0.6808,0.6846,0.6893,0.6924,0.6929,0.6932,0.6952,0.6996,
0.7011,0.7050,0.7073,0.7099,0.7103,0.7133,0.7138,0.7163,0.7213,0.7229,
0.7256,0.7262,0.7274,0.7378,0.7390,0.7423,0.7435,0.7496,0.7544,0.7581,
0.7639,0.7659,0.7666,0.7684,0.7711,0.7718,0.7741,0.7746,0.7821,0.7825,
0.7841,0.7848,0.7885,0.7939,0.7957,0.7983,0.7985,0.8096,0.8099,0.8122,
0.8132,0.8134,0.8152,0.8206,0.8212,0.8285,0.8462,0.8476,0.8577,0.8704,
0.8757,0.8838,0.8911,0.8967,0.8974,0.8979,0.9013,0.9046,0.9068,0.9103,
0.9146,0.9166,0.9335,0.9370,0.9376,0.9449,0.9461,0.9493,0.9499,0.9624,
0.9625,0.9661,0.9664,0.9728,0.9765,0.9817,0.9836,0.9874,0.9993,
Overall p-value after applying KStest on 269 p-values = 0.248508
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.