RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-16_23:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.32 34.9763 0.993734
2 to 25 15.63 23.1702 0.856208
3 to 26 15.75 12.3968 0.224465
4 to 27 15.81 19.2431 0.685244
5 to 28 15.97 17.7014 0.592095
6 to 29 15.62 20.8374 0.766352
7 to 30 15.81 28.0996 0.956212
8 to 31 15.95 13.8673 0.323528
9 to 32 15.84 24.3027 0.888560
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.051515
Tough bday spacings test for dh-ranFile-2018-06-16_23:31: 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 36 88 118 80 74 51 21 18 5 2
(O-E)^2/E 0.5 0.0 3.0 4.2 3.2 0.2 0.0 2.6 0.7 0.4 1.0
Birthday Spacings: Sum(O-E)^2/E= 15.834, p= 0.896
RESULTS OF GCD FOR dh-ranFile-2018-06-16_23:31
Euclid's algorithm:
p-value, steps to gcd: 0.444365
p-value, dist. of gcd's: 0.773925
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-16_23:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.284 0.054 0.602 0.082 0.392 0.277 0.611 0.749
Bits 8 to 15---> 0.948 0.166 0.974 0.132 0.795 0.501 0.172 0.378
Bits 16 to 23---> 0.373 0.495 0.422 0.699 0.818 0.432 0.742 0.654
Bits 24 to 31---> 0.494 0.876 0.450 0.971 0.116 0.396 0.091 0.257
KS test for the above 32 p values: 0.092
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-16_23:31,
p-values for 5 runs: 0.5445, 0.8013, 0.0768, 0.0541, 0.2158
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-16_23:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 202 211.4 0.420 0.420
r= 29 5223 5134.0 1.542 1.962
r= 30 23078 23103.0 0.027 1.989
r= 31 11497 11551.5 0.257 2.247
chi-square = 2.247 with df = 3; p-value = 0.477
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-16_23:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 225 211.4 0.873 0.873
r= 30 5058 5134.0 1.125 1.998
r= 31 23148 23103.0 0.087 2.085
r= 32 11569 11551.5 0.026 2.112
chi-square = 2.112 with df = 3; p-value = 0.450
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-16_23:31
b-rank test for bits 1 to 8, p=0.07565
b-rank test for bits 2 to 9, p=0.62366
b-rank test for bits 3 to 10, p=0.90445
b-rank test for bits 4 to 11, p=0.28092
b-rank test for bits 5 to 12, p=0.02052
b-rank test for bits 6 to 13, p=0.28227
b-rank test for bits 7 to 14, p=0.82418
b-rank test for bits 8 to 15, p=0.13715
b-rank test for bits 9 to 16, p=0.38333
b-rank test for bits 10 to 17, p=0.45688
b-rank test for bits 11 to 18, p=0.45164
b-rank test for bits 12 to 19, p=0.49379
b-rank test for bits 13 to 20, p=0.00394
b-rank test for bits 14 to 21, p=0.33760
b-rank test for bits 15 to 22, p=0.81222
b-rank test for bits 16 to 23, p=0.78759
b-rank test for bits 17 to 24, p=0.92509
b-rank test for bits 18 to 25, p=0.95900
b-rank test for bits 19 to 26, p=0.11999
b-rank test for bits 20 to 27, p=0.65374
b-rank test for bits 21 to 28, p=0.90753
b-rank test for bits 22 to 29, p=0.75446
b-rank test for bits 23 to 30, p=0.82942
b-rank test for bits 24 to 31, p=0.27296
b-rank test for bits 25 to 32, p=0.07246
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 = 0.755759
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-16_23:31
(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 141766 -0.33 0.368857
2 142239 0.77 0.779426
3 141790 -0.28 0.390196
4 141722 -0.44 0.330807
5 142110 0.47 0.680413
6 141783 -0.30 0.383935
7 141366 -1.27 0.102138
8 141389 -1.22 0.112045
9 141192 -1.68 0.046869
10 142023 0.27 0.604720
11 142254 0.81 0.789678
12 142349 1.03 0.847852
13 141821 -0.21 0.418248
14 142180 0.63 0.736439
15 142294 0.90 0.815610
16 142104 0.45 0.675387
17 142073 0.38 0.648920
18 141787 -0.29 0.387509
19 142050 0.33 0.628797
20 141687 -0.52 0.301719
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-16_23:31
Bits used No. missing words z-score p-value
23 to 32 142219 1.0678 0.857201
22 to 31 141769 -0.4839 0.314230
21 to 30 141604 -1.0529 0.146202
20 to 29 142099 0.6540 0.743455
19 to 28 141970 0.2092 0.582857
18 to 27 141630 -0.9632 0.167722
17 to 26 141799 -0.3804 0.351806
16 to 25 142386 1.6437 0.949880
15 to 24 141691 -0.7529 0.225766
14 to 23 141698 -0.7287 0.233085
13 to 22 141785 -0.4287 0.334062
12 to 21 141799 -0.3804 0.351806
11 to 20 142233 1.1161 0.867811
10 to 19 142043 0.4609 0.677576
9 to 18 142059 0.5161 0.697109
8 to 17 142112 0.6989 0.757681
7 to 16 142235 1.1230 0.869281
6 to 15 142417 1.7506 0.959991
5 to 14 142408 1.7196 0.957243
4 to 13 141823 -0.2977 0.382970
3 to 12 141812 -0.3356 0.368579
2 to 11 141828 -0.2804 0.389567
1 to 10 142092 0.6299 0.735619
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-16_23:31
Bits used No. missing words z-score p-value
28 to 32 142050 0.4768 0.683265
27 to 31 141755 -0.5232 0.300434
26 to 30 141323 -1.9876 0.023430
25 to 29 141628 -0.9537 0.170128
24 to 28 142428 1.7582 0.960644
23 to 27 142127 0.7379 0.769702
22 to 26 142122 0.7209 0.764519
21 to 25 141956 0.1582 0.562852
20 to 24 142063 0.5209 0.698787
19 to 23 141950 0.1379 0.554826
18 to 22 141973 0.2158 0.585440
17 to 21 142070 0.5446 0.707001
16 to 20 141367 -1.8384 0.033001
15 to 19 141729 -0.6113 0.270504
14 to 18 141975 0.2226 0.588081
13 to 17 141749 -0.5435 0.293396
12 to 16 141922 0.0429 0.517129
11 to 15 141959 0.1684 0.566855
10 to 14 141980 0.2396 0.594664
9 to 13 142459 1.8633 0.968789
8 to 12 142326 1.4124 0.921090
7 to 11 141926 0.0565 0.522532
6 to 10 141681 -0.7740 0.219465
5 to 9 141816 -0.3164 0.375860
4 to 8 141785 -0.4215 0.336711
3 to 7 141692 -0.7367 0.230649
2 to 6 142158 0.8429 0.800372
1 to 5 141886 -0.0791 0.468483
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-16_23:31
Bits used No. missing words z-score p-value
31 to 32 141814 -0.2812 0.389275
30 to 31 142049 0.4120 0.659832
29 to 30 141935 0.0757 0.530180
28 to 29 141543 -1.0806 0.139933
27 to 28 142437 1.5565 0.940211
26 to 27 142427 1.5271 0.936626
25 to 26 141819 -0.2665 0.394942
24 to 25 141926 0.0492 0.519610
23 to 24 141902 -0.0216 0.491375
22 to 23 141821 -0.2606 0.397216
21 to 22 141918 0.0256 0.510202
20 to 21 141480 -1.2665 0.102674
19 to 20 141104 -2.3756 0.008760
18 to 19 141861 -0.1426 0.443316
17 to 18 141927 0.0521 0.520785
16 to 17 141884 -0.0747 0.470219
15 to 16 142045 0.4002 0.655498
14 to 15 141492 -1.2311 0.109150
13 to 14 141687 -0.6558 0.255963
12 to 13 142042 0.3914 0.652233
11 to 12 142033 0.3648 0.642373
10 to 11 142189 0.8250 0.795310
9 to 10 141841 -0.2016 0.420129
8 to 9 142407 1.4681 0.928955
7 to 8 142149 0.7070 0.760214
6 to 7 141946 0.1082 0.543070
5 to 6 141496 -1.2193 0.111372
4 to 5 142265 1.0492 0.852951
3 to 4 142206 0.8751 0.809249
2 to 3 141687 -0.6558 0.255963
1 to 2 141913 0.0108 0.504319
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-16_23:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2489.39 -0.150 0.440345
Test results for specific bytes for dh-ranFile-2018-06-16_23:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2448.02 -0.735 0.231123
2 to 9 2449.11 -0.720 0.235857
3 to 10 2371.53 -1.817 0.034623
4 to 11 2484.90 -0.213 0.415474
5 to 12 2327.07 -2.446 0.007232
6 to 13 2651.59 2.144 0.983976
7 to 14 2466.71 -0.471 0.318874
8 to 15 2452.55 -0.671 0.251117
9 to 16 2590.76 1.283 0.900340
10 to 17 2418.47 -1.153 0.124445
11 to 18 2496.22 -0.054 0.478656
12 to 19 2430.03 -0.990 0.161192
13 to 20 2536.00 0.509 0.694685
14 to 21 2556.68 0.802 0.788585
15 to 22 2496.57 -0.048 0.480680
16 to 23 2384.52 -1.633 0.051221
17 to 24 2681.02 2.560 0.994766
18 to 25 2390.03 -1.555 0.059944
19 to 26 2449.43 -0.715 0.237258
20 to 27 2672.44 2.439 0.992629
21 to 28 2428.93 -1.005 0.157428
22 to 29 2586.51 1.224 0.889430
23 to 30 2506.61 0.093 0.537220
24 to 31 2581.22 1.149 0.874633
25 to 32 2525.50 0.361 0.640791
CDPARK for dh-ranFile-2018-06-16_23:31: 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
3554 1.4155 0.921543
3546 1.0502 0.853193
3492 -1.4155 0.078457
3488 -1.5982 0.055002
3512 -0.5023 0.307734
3518 -0.2283 0.409702
3515 -0.3653 0.357445
3531 0.3653 0.642555
3557 1.5525 0.939730
3532 0.4110 0.659449
Square side=100, avg. no. parked=3524.50 sample std.=22.73
p-value of the KSTEST for those 10 p-values: 0.917710
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-16_23:31
0.9140,0.2757,0.8939,0.8011,0.1288,0.5067,0.2044,0.8744,0.5342,0.1732,
The KS test for those 10 p-values: 0.769221
The 3DSPHERES test for dh-ranFile-2018-06-16_23:31
sample no r^3 equiv. uni.
1 19.956 0.485836
2 9.746 0.277382
3 66.647 0.891560
4 18.559 0.461328
5 16.404 0.421206
6 33.242 0.669798
7 12.123 0.332430
8 164.163 0.995798
9 4.373 0.135636
10 4.892 0.150464
11 64.741 0.884447
12 108.247 0.972900
13 45.500 0.780554
14 0.321 0.010654
15 25.253 0.569047
16 47.111 0.792033
17 0.241 0.008012
18 56.271 0.846754
19 13.726 0.367164
20 54.073 0.835100
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.487631
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-16_23:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 0.5 0.6 -0.7 0.3 -0.2
1.0 -0.8 -0.1 -0.5 0.4 0.6
-0.3 -1.6 -0.1 0.3 0.6 -0.5
-0.4 1.4 0.3 -0.4 2.2 -3.0
0.2 0.6 -1.1 0.4 -1.3 1.3
0.7 1.2 -0.5 1.0 -0.2 1.0
-0.7 0.2 0.5 -0.7 -1.3 1.0
-1.1
Chi-square with 42 degrees of freedom:38.231610
z-score=-0.411165, p-value=0.362880
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-16_23:31
Test no p-value
1 0.026408
2 0.812852
3 0.546704
4 0.607970
5 0.002349
6 0.039944
7 0.964891
8 0.098951
9 0.036934
10 0.127860
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.007354
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-16_23:31:
(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 67023 1.90 66750 0.10
3 25000.00 24682 4.04 24976 0.02
4 6666.67 6652 0.03 6532 2.72
5 1388.89 1368 0.31 1466 4.28
6 238.10 248 0.41 249 0.50
7 34.72 21 5.42 25 2.72
8 4.96 5 0.00 1 3.16
p=0.94087 p=0.96440
Number of rngs required: 688238, p-value: 0.425
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-16_23:31
No. of wins: Observed Expected
98651 98585.9
z-score= 0.291, pvalue=0.61461
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66511 66666.7 0.363 0.363
2 37639 37654.3 0.006 0.370
3 27104 26954.7 0.827 1.196
4 19379 19313.5 0.222 1.419
5 13837 13851.4 0.015 1.434
6 10018 9943.5 0.558 1.991
7 7064 7145.0 0.919 2.910
8 5139 5139.1 0.000 2.910
9 3736 3699.9 0.353 3.263
10 2668 2666.3 0.001 3.264
11 1888 1923.3 0.649 3.913
12 1334 1388.7 2.158 6.071
13 1064 1003.7 3.621 9.692
14 699 726.1 1.014 10.706
15 509 525.8 0.539 11.245
16 378 381.2 0.026 11.271
17 266 276.5 0.402 11.673
18 207 200.8 0.190 11.862
19 141 146.0 0.170 12.033
20 117 106.2 1.095 13.128
21 302 287.1 0.772 13.899
Chisq= 13.90 for 20 degrees of freedom, p= 0.16444
SUMMARY of craptest
p-value for no. of wins: 0.614608
p-value for throws/game: 0.164439
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-16_23:31
No. of wins: Observed Expected
98674 98585.9
z-score= 0.394, pvalue=0.65329
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66815 66666.7 0.330 0.330
2 37644 37654.3 0.003 0.333
3 26654 26954.7 3.355 3.688
4 19491 19313.5 1.632 5.320
5 13735 13851.4 0.979 6.299
6 9938 9943.5 0.003 6.302
7 7142 7145.0 0.001 6.303
8 5160 5139.1 0.085 6.388
9 3678 3699.9 0.129 6.517
10 2733 2666.3 1.669 8.186
11 1911 1923.3 0.079 8.265
12 1398 1388.7 0.062 8.327
13 1033 1003.7 0.854 9.181
14 768 726.1 2.413 11.594
15 556 525.8 1.730 13.325
16 351 381.2 2.385 15.710
17 281 276.5 0.072 15.782
18 178 200.8 2.595 18.377
19 141 146.0 0.170 18.547
20 120 106.2 1.789 20.336
21 273 287.1 0.694 21.030
Chisq= 21.03 for 20 degrees of freedom, p= 0.60463
SUMMARY of craptest
p-value for no. of wins: 0.653291
p-value for throws/game: 0.604630
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0023,0.0039,0.0072,0.0074,0.0080,0.0088,0.0107,0.0205,0.0234,0.0264,
0.0330,0.0346,0.0369,0.0399,0.0469,0.0512,0.0515,0.0539,0.0541,0.0550,
0.0599,0.0725,0.0756,0.0768,0.0785,0.0823,0.0906,0.0924,0.0990,0.1021,
0.1027,0.1091,0.1114,0.1120,0.1163,0.1200,0.1244,0.1279,0.1288,0.1324,
0.1356,0.1371,0.1399,0.1462,0.1505,0.1574,0.1612,0.1644,0.1656,0.1677,
0.1701,0.1722,0.1732,0.2044,0.2158,0.2195,0.2245,0.2258,0.2306,0.2311,
0.2331,0.2359,0.2373,0.2511,0.2560,0.2560,0.2570,0.2705,0.2730,0.2757,
0.2772,0.2774,0.2809,0.2823,0.2835,0.2934,0.3004,0.3017,0.3077,0.3142,
0.3189,0.3235,0.3308,0.3324,0.3341,0.3367,0.3376,0.3518,0.3518,0.3574,
0.3629,0.3672,0.3686,0.3689,0.3729,0.3759,0.3779,0.3830,0.3833,0.3839,
0.3875,0.3893,0.3896,0.3902,0.3917,0.3949,0.3960,0.3972,0.4097,0.4155,
0.4182,0.4201,0.4212,0.4219,0.4247,0.4325,0.4403,0.4433,0.4444,0.4504,
0.4505,0.4516,0.4569,0.4613,0.4685,0.4702,0.4772,0.4787,0.4807,0.4858,
0.4876,0.4914,0.4938,0.4944,0.4951,0.5007,0.5043,0.5067,0.5102,0.5171,
0.5196,0.5208,0.5225,0.5302,0.5342,0.5372,0.5431,0.5445,0.5467,0.5548,
0.5629,0.5669,0.5690,0.5829,0.5854,0.5881,0.5921,0.5947,0.6022,0.6046,
0.6047,0.6080,0.6106,0.6146,0.6237,0.6288,0.6408,0.6424,0.6426,0.6489,
0.6522,0.6533,0.6537,0.6544,0.6555,0.6594,0.6598,0.6698,0.6754,0.6776,
0.6804,0.6833,0.6852,0.6947,0.6971,0.6985,0.6988,0.7070,0.7356,0.7364,
0.7424,0.7435,0.7488,0.7545,0.7558,0.7577,0.7602,0.7645,0.7664,0.7692,
0.7697,0.7739,0.7794,0.7806,0.7876,0.7886,0.7897,0.7920,0.7949,0.7953,
0.8004,0.8011,0.8013,0.8092,0.8122,0.8129,0.8156,0.8181,0.8242,0.8294,
0.8351,0.8468,0.8479,0.8530,0.8532,0.8562,0.8572,0.8678,0.8693,0.8744,
0.8746,0.8765,0.8844,0.8886,0.8894,0.8916,0.8939,0.8955,0.9003,0.9045,
0.9075,0.9140,0.9177,0.9211,0.9215,0.9251,0.9290,0.9366,0.9397,0.9402,
0.9409,0.9479,0.9499,0.9562,0.9572,0.9590,0.9600,0.9606,0.9644,0.9649,
0.9688,0.9708,0.9729,0.9740,0.9840,0.9926,0.9937,0.9948,0.9958,
Overall p-value after applying KStest on 269 p-values = 0.811962
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.