RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-09_10:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.91 22.6689 0.839658
2 to 25 15.64 24.5405 0.894522
3 to 26 15.71 18.3582 0.633414
4 to 27 15.77 14.6949 0.382554
5 to 28 15.66 15.1874 0.418012
6 to 29 15.67 23.8200 0.875592
7 to 30 15.84 23.9448 0.879059
8 to 31 15.60 19.4495 0.696652
9 to 32 15.59 29.9033 0.972949
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.021947
Tough bday spacings test for dh-ranFile-2018-07-09_10:31: 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 8 38 66 115 104 64 56 27 14 5 3
(O-E)^2/E 0.1 0.1 0.7 3.1 0.4 2.6 0.3 0.3 0.1 0.4 0.3
Birthday Spacings: Sum(O-E)^2/E= 8.233, p= 0.394
RESULTS OF GCD FOR dh-ranFile-2018-07-09_10:31
Euclid's algorithm:
p-value, steps to gcd: 0.050905
p-value, dist. of gcd's: 0.365559
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-09_10:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.633 0.470 0.885 0.496 0.255 0.624 0.930 0.700
Bits 8 to 15---> 0.278 0.420 0.359 0.221 0.979 0.209 0.685 0.192
Bits 16 to 23---> 0.007 0.894 0.648 0.099 0.622 0.997 0.668 0.573
Bits 24 to 31---> 0.718 0.835 0.829 0.613 0.733 0.508 0.325 0.516
KS test for the above 32 p values: 0.670
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-09_10:31,
p-values for 5 runs: 0.3424, 0.2184, 0.6962, 0.7768, 0.4005
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-09_10:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 222 211.4 0.530 0.530
r= 29 5163 5134.0 0.164 0.693
r= 30 23036 23103.0 0.195 0.888
r= 31 11579 11551.5 0.065 0.953
chi-square = 0.953 with df = 3; p-value = 0.187
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-09_10:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 192 211.4 1.783 1.783
r= 30 5196 5134.0 0.748 2.532
r= 31 23176 23103.0 0.230 2.762
r= 32 11436 11551.5 1.155 3.918
chi-square = 3.918 with df = 3; p-value = 0.730
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-09_10:31
b-rank test for bits 1 to 8, p=0.88564
b-rank test for bits 2 to 9, p=0.92004
b-rank test for bits 3 to 10, p=0.87192
b-rank test for bits 4 to 11, p=0.89280
b-rank test for bits 5 to 12, p=0.57979
b-rank test for bits 6 to 13, p=0.54324
b-rank test for bits 7 to 14, p=0.75549
b-rank test for bits 8 to 15, p=0.67482
b-rank test for bits 9 to 16, p=0.53018
b-rank test for bits 10 to 17, p=0.49807
b-rank test for bits 11 to 18, p=0.43322
b-rank test for bits 12 to 19, p=0.18051
b-rank test for bits 13 to 20, p=0.28796
b-rank test for bits 14 to 21, p=0.67671
b-rank test for bits 15 to 22, p=0.40807
b-rank test for bits 16 to 23, p=0.36730
b-rank test for bits 17 to 24, p=0.33871
b-rank test for bits 18 to 25, p=0.22207
b-rank test for bits 19 to 26, p=0.79956
b-rank test for bits 20 to 27, p=0.74466
b-rank test for bits 21 to 28, p=0.65464
b-rank test for bits 22 to 29, p=0.43330
b-rank test for bits 23 to 30, p=0.30045
b-rank test for bits 24 to 31, p=0.44675
b-rank test for bits 25 to 32, p=0.81043
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 = 0.173677
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-09_10:31
(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 141710 -0.47 0.320706
2 142165 0.60 0.724866
3 141729 -0.42 0.336756
4 141917 0.02 0.507149
5 142072 0.38 0.648053
6 141519 -0.91 0.180888
7 142005 0.22 0.588438
8 141451 -1.07 0.142115
9 142152 0.57 0.714638
10 142934 2.39 0.991669
11 142101 0.45 0.672861
12 142444 1.25 0.894209
13 142180 0.63 0.736439
14 142008 0.23 0.591163
15 142832 2.16 0.984449
16 141604 -0.71 0.237803
17 142218 0.72 0.764604
18 141954 0.10 0.541562
19 142147 0.56 0.710657
20 142341 1.01 0.843411
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-09_10:31
Bits used No. missing words z-score p-value
23 to 32 142172 0.9058 0.817468
22 to 31 142237 1.1299 0.870740
21 to 30 141547 -1.2494 0.105757
20 to 29 141589 -1.1046 0.134669
19 to 28 142018 0.3747 0.646067
18 to 27 141792 -0.4046 0.342891
17 to 26 141207 -2.4218 0.007721
16 to 25 141842 -0.2322 0.408202
15 to 24 142111 0.6954 0.756602
14 to 23 141730 -0.6184 0.268163
13 to 22 141718 -0.6598 0.254704
12 to 21 141927 0.0609 0.524293
11 to 20 142180 0.9333 0.824679
10 to 19 142383 1.6333 0.948802
9 to 18 141954 0.1540 0.561209
8 to 17 141834 -0.2598 0.397525
7 to 16 141673 -0.8149 0.207556
6 to 15 141708 -0.6942 0.243765
5 to 14 142080 0.5885 0.721907
4 to 13 141635 -0.9460 0.172083
3 to 12 141441 -1.6149 0.053163
2 to 11 142098 0.6506 0.742343
1 to 10 141770 -0.4804 0.315454
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-09_10:31
Bits used No. missing words z-score p-value
28 to 32 141778 -0.4452 0.328093
27 to 31 141898 -0.0384 0.484682
26 to 30 142419 1.7277 0.957979
25 to 29 142126 0.7345 0.768670
24 to 28 141562 -1.1774 0.119520
23 to 27 141301 -2.0621 0.019597
22 to 26 142169 0.8802 0.810635
21 to 25 142006 0.3277 0.628429
20 to 24 141980 0.2396 0.594664
19 to 23 142048 0.4701 0.680847
18 to 22 142395 1.6463 0.950153
17 to 21 141653 -0.8689 0.192447
16 to 20 141911 0.0057 0.502258
15 to 19 141790 -0.4045 0.342919
14 to 18 141735 -0.5909 0.277277
13 to 17 141992 0.2802 0.610352
12 to 16 142001 0.3107 0.622003
11 to 15 141892 -0.0587 0.476577
10 to 14 141830 -0.2689 0.393998
9 to 13 142196 0.9718 0.834416
8 to 12 141594 -1.0689 0.142554
7 to 11 142237 1.1107 0.866661
6 to 10 141833 -0.2587 0.397916
5 to 9 142264 1.2023 0.885371
4 to 8 141114 -2.6960 0.003509
3 to 7 141852 -0.1943 0.422955
2 to 6 141394 -1.7469 0.040329
1 to 5 142318 1.3853 0.917023
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-09_10:31
Bits used No. missing words z-score p-value
31 to 32 141877 -0.0954 0.462011
30 to 31 141567 -1.0098 0.156290
29 to 30 141867 -0.1249 0.450314
28 to 29 141822 -0.2576 0.398354
27 to 28 141329 -1.7119 0.043459
26 to 27 140864 -3.0836 0.001023
25 to 26 141594 -0.9302 0.176140
24 to 25 142104 0.5742 0.717100
23 to 24 142211 0.8899 0.813235
22 to 23 141949 0.1170 0.546578
21 to 22 141911 0.0049 0.501965
20 to 21 141604 -0.9007 0.183880
19 to 20 142489 1.7099 0.956362
18 to 19 142087 0.5241 0.699896
17 to 18 141747 -0.4788 0.316023
16 to 17 142199 0.8545 0.803582
15 to 16 142218 0.9105 0.818729
14 to 15 141666 -0.7178 0.236444
13 to 14 141980 0.2085 0.582568
12 to 13 141775 -0.3963 0.345959
11 to 12 142333 1.2498 0.894307
10 to 11 142137 0.6716 0.749079
9 to 10 141701 -0.6145 0.269428
8 to 9 141584 -0.9597 0.168609
7 to 8 142656 2.2026 0.986187
6 to 7 141397 -1.5113 0.065356
5 to 6 142321 1.2144 0.887696
4 to 5 141832 -0.2281 0.409780
3 to 4 141331 -1.7060 0.044005
2 to 3 141446 -1.3668 0.085851
1 to 2 141974 0.1908 0.575646
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-09_10:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2566.17 0.936 0.825295
Test results for specific bytes for dh-ranFile-2018-07-09_10:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2517.38 0.246 0.597071
2 to 9 2453.60 -0.656 0.255830
3 to 10 2469.99 -0.424 0.335652
4 to 11 2433.76 -0.937 0.174445
5 to 12 2307.37 -2.724 0.003222
6 to 13 2479.64 -0.288 0.386691
7 to 14 2323.90 -2.490 0.006379
8 to 15 2614.59 1.621 0.947443
9 to 16 2368.85 -1.855 0.031816
10 to 17 2535.22 0.498 0.690811
11 to 18 2484.93 -0.213 0.415640
12 to 19 2519.60 0.277 0.609176
13 to 20 2580.83 1.143 0.873506
14 to 21 2573.23 1.036 0.849805
15 to 22 2643.51 2.030 0.978797
16 to 23 2528.64 0.405 0.657252
17 to 24 2514.67 0.207 0.582162
18 to 25 2599.17 1.402 0.919604
19 to 26 2579.40 1.123 0.869261
20 to 27 2468.86 -0.440 0.329828
21 to 28 2534.43 0.487 0.686862
22 to 29 2407.18 -1.313 0.094657
23 to 30 2360.86 -1.968 0.024548
24 to 31 2514.80 0.209 0.582914
25 to 32 2451.66 -0.684 0.247124
CDPARK for dh-ranFile-2018-07-09_10:31: 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
3506 -0.7763 0.218799
3539 0.7306 0.767486
3528 0.2283 0.590298
3525 0.0913 0.536383
3536 0.5936 0.723613
3558 1.5982 0.944998
3534 0.5023 0.692266
3521 -0.0913 0.463617
3536 0.5936 0.723613
Square side=100, avg. no. parked=3528.60 sample std.=15.32
p-value of the KSTEST for those 10 p-values: 0.456779
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-09_10:31
0.6538,0.3519,0.0603,0.9070,0.1911,0.3354,0.0742,0.2442,0.3514,0.4490,
The KS test for those 10 p-values: 0.201157
The 3DSPHERES test for dh-ranFile-2018-07-09_10:31
sample no r^3 equiv. uni.
1 26.090 0.580912
2 0.964 0.031614
3 7.264 0.215052
4 1.465 0.047674
5 53.150 0.829951
6 0.898 0.029475
7 24.421 0.556926
8 11.530 0.319101
9 27.340 0.598007
10 7.362 0.217598
11 20.052 0.487477
12 51.734 0.821731
13 23.294 0.539978
14 24.865 0.563444
15 4.755 0.146590
16 48.457 0.801154
17 14.874 0.390923
18 45.286 0.778989
19 14.369 0.380581
20 28.537 0.613742
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.469716
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-09_10:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 0.1 0.3 1.1 -0.5 -0.5
-0.5 -0.4 -0.6 1.3 1.6 0.4
-2.1 -1.8 0.5 -1.0 0.6 1.0
0.7 -0.1 0.1 0.0 2.2 -1.5
0.1 0.8 -0.8 1.6 -1.2 -0.8
-1.6 -0.5 -0.5 -1.0 -0.1 -1.2
-0.9 -0.1 0.1 1.0 -0.6 -1.0
-0.1
Chi-square with 42 degrees of freedom:39.638309
z-score=-0.257682, p-value=0.424846
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-09_10:31
Test no p-value
1 0.213412
2 0.669380
3 0.281780
4 0.881636
5 0.552320
6 0.136559
7 0.291649
8 0.981760
9 0.001757
10 0.151490
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.348250
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-09_10:31:
(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 66596 0.07 66707 0.02
3 25000.00 25044 0.08 24959 0.07
4 6666.67 6695 0.12 6711 0.29
5 1388.89 1385 0.01 1349 1.15
6 238.10 235 0.04 242 0.06
7 34.72 40 0.80 26 2.19
8 4.96 4 0.19 5 0.00
p=0.02904 p=0.29446
Number of rngs required: 689305, p-value: 0.852
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-09_10:31
No. of wins: Observed Expected
98465 98585.9
z-score=-0.541, pvalue=0.29441
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66542 66666.7 0.233 0.233
2 37582 37654.3 0.139 0.372
3 26712 26954.7 2.186 2.558
4 19420 19313.5 0.588 3.146
5 13965 13851.4 0.931 4.077
6 9897 9943.5 0.218 4.295
7 7302 7145.0 3.449 7.743
8 5119 5139.1 0.078 7.822
9 3738 3699.9 0.393 8.215
10 2722 2666.3 1.164 9.379
11 1964 1923.3 0.860 10.239
12 1414 1388.7 0.459 10.698
13 977 1003.7 0.711 11.409
14 734 726.1 0.085 11.494
15 520 525.8 0.065 11.559
16 377 381.2 0.045 11.604
17 269 276.5 0.206 11.810
18 216 200.8 1.146 12.956
19 141 146.0 0.170 13.126
20 117 106.2 1.095 14.221
21 272 287.1 0.796 15.017
Chisq= 15.02 for 20 degrees of freedom, p= 0.22454
SUMMARY of craptest
p-value for no. of wins: 0.294409
p-value for throws/game: 0.224537
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-09_10:31
No. of wins: Observed Expected
98731 98585.9
z-score= 0.649, pvalue=0.74188
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66709 66666.7 0.027 0.027
2 37584 37654.3 0.131 0.158
3 26907 26954.7 0.085 0.243
4 19401 19313.5 0.397 0.639
5 13916 13851.4 0.301 0.941
6 10021 9943.5 0.603 1.544
7 7106 7145.0 0.213 1.757
8 5008 5139.1 3.343 5.100
9 3741 3699.9 0.457 5.557
10 2611 2666.3 1.147 6.704
11 1919 1923.3 0.010 6.714
12 1433 1388.7 1.411 8.125
13 1047 1003.7 1.867 9.991
14 745 726.1 0.490 10.481
15 500 525.8 1.269 11.750
16 347 381.2 3.060 14.810
17 283 276.5 0.151 14.961
18 196 200.8 0.116 15.077
19 129 146.0 1.976 17.053
20 119 106.2 1.539 18.592
21 278 287.1 0.289 18.882
Chisq= 18.88 for 20 degrees of freedom, p= 0.47047
SUMMARY of craptest
p-value for no. of wins: 0.741882
p-value for throws/game: 0.470466
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0010,0.0018,0.0032,0.0035,0.0064,0.0070,0.0077,0.0196,0.0219,0.0245,
0.0290,0.0295,0.0316,0.0318,0.0403,0.0435,0.0440,0.0477,0.0509,0.0532,
0.0603,0.0654,0.0742,0.0859,0.0947,0.0991,0.1058,0.1195,0.1347,0.1366,
0.1421,0.1426,0.1466,0.1515,0.1563,0.1686,0.1721,0.1737,0.1744,0.1761,
0.1805,0.1806,0.1809,0.1839,0.1874,0.1911,0.1919,0.1924,0.2012,0.2076,
0.2087,0.2134,0.2151,0.2176,0.2184,0.2188,0.2207,0.2221,0.2245,0.2364,
0.2378,0.2438,0.2442,0.2471,0.2547,0.2548,0.2558,0.2682,0.2694,0.2773,
0.2775,0.2818,0.2880,0.2916,0.2944,0.2945,0.3005,0.3155,0.3160,0.3191,
0.3207,0.3248,0.3281,0.3298,0.3354,0.3357,0.3368,0.3387,0.3424,0.3429,
0.3429,0.3460,0.3483,0.3514,0.3519,0.3590,0.3656,0.3673,0.3806,0.3826,
0.3867,0.3909,0.3939,0.3940,0.3975,0.3979,0.3984,0.4005,0.4081,0.4082,
0.4098,0.4156,0.4180,0.4197,0.4230,0.4248,0.4332,0.4333,0.4468,0.4490,
0.4503,0.4568,0.4620,0.4636,0.4695,0.4697,0.4705,0.4766,0.4847,0.4875,
0.4964,0.4981,0.5020,0.5023,0.5071,0.5083,0.5164,0.5243,0.5302,0.5364,
0.5400,0.5416,0.5432,0.5466,0.5523,0.5569,0.5612,0.5634,0.5727,0.5756,
0.5798,0.5809,0.5822,0.5826,0.5829,0.5884,0.5903,0.5912,0.5947,0.5971,
0.5980,0.6092,0.6104,0.6131,0.6137,0.6220,0.6221,0.6237,0.6284,0.6325,
0.6334,0.6461,0.6481,0.6481,0.6538,0.6546,0.6573,0.6678,0.6694,0.6703,
0.6729,0.6748,0.6767,0.6808,0.6853,0.6869,0.6908,0.6923,0.6962,0.6967,
0.6999,0.7000,0.7107,0.7146,0.7171,0.7177,0.7219,0.7236,0.7236,0.7249,
0.7295,0.7326,0.7364,0.7419,0.7423,0.7447,0.7491,0.7555,0.7566,0.7646,
0.7675,0.7687,0.7768,0.7790,0.7996,0.8012,0.8036,0.8104,0.8106,0.8132,
0.8175,0.8187,0.8217,0.8247,0.8253,0.8290,0.8300,0.8344,0.8354,0.8397,
0.8434,0.8498,0.8522,0.8667,0.8693,0.8707,0.8719,0.8735,0.8756,0.8791,
0.8816,0.8848,0.8854,0.8856,0.8877,0.8928,0.8937,0.8942,0.8943,0.8945,
0.9070,0.9170,0.9196,0.9200,0.9304,0.9450,0.9474,0.9488,0.9502,0.9564,
0.9580,0.9729,0.9787,0.9788,0.9818,0.9844,0.9862,0.9917,0.9972,
Overall p-value after applying KStest on 269 p-values = 0.728944
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.