RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-07-28_17:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.62 14.7295 0.385045
2 to 25 15.87 27.2667 0.945729
3 to 26 15.75 21.3122 0.787365
4 to 27 15.45 25.1510 0.908619
5 to 28 15.61 16.5102 0.512004
6 to 29 15.82 10.6430 0.125492
7 to 30 15.88 19.1416 0.679532
8 to 31 15.77 12.1176 0.207036
9 to 32 15.62 16.9889 0.544883
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.878743
Tough bday spacings test for dh-ranFile-2016-07-28_17:31: 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 35 86 92 80 87 46 37 15 7 7
(O-E)^2/E 0.1 0.1 2.2 0.3 3.2 1.0 0.7 1.8 0.0 0.0 2.1
Birthday Spacings: Sum(O-E)^2/E= 11.578, p= 0.686
RESULTS OF GCD FOR dh-ranFile-2016-07-28_17:31
Euclid's algorithm:
p-value, steps to gcd: 0.737099
p-value, dist. of gcd's: 0.506365
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-07-28_17:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.520 0.409 0.131 0.037 0.207 0.715 0.669 0.473
Bits 8 to 15---> 0.950 0.677 0.470 0.196 0.379 0.663 0.407 0.061
Bits 16 to 23---> 0.262 0.714 0.905 0.327 0.665 0.292 0.989 0.720
Bits 24 to 31---> 0.804 0.073 0.556 0.434 0.331 0.881 0.904 0.688
KS test for the above 32 p values: 0.047
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-07-28_17:31,
p-values for 5 runs: 0.2731, 0.6830, 0.7260, 0.9288, 0.6078
Rank test for binary matrices (31x31) for dh-ranFile-2016-07-28_17:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 219 211.4 0.272 0.272
r= 29 5268 5134.0 3.497 3.769
r= 30 23093 23103.0 0.004 3.773
r= 31 11420 11551.5 1.498 5.271
chi-square = 5.271 with df = 3; p-value = 0.847
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2016-07-28_17:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 220 211.4 0.348 0.348
r= 30 5207 5134.0 1.038 1.386
r= 31 23118 23103.0 0.010 1.396
r= 32 11455 11551.5 0.807 2.202
chi-square = 2.202 with df = 3; p-value = 0.468
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2016-07-28_17:31
b-rank test for bits 1 to 8, p=0.33938
b-rank test for bits 2 to 9, p=0.21174
b-rank test for bits 3 to 10, p=0.47478
b-rank test for bits 4 to 11, p=0.23151
b-rank test for bits 5 to 12, p=0.25979
b-rank test for bits 6 to 13, p=0.10119
b-rank test for bits 7 to 14, p=0.59159
b-rank test for bits 8 to 15, p=0.28319
b-rank test for bits 9 to 16, p=0.05473
b-rank test for bits 10 to 17, p=0.81386
b-rank test for bits 11 to 18, p=0.90332
b-rank test for bits 12 to 19, p=0.97202
b-rank test for bits 13 to 20, p=0.50074
b-rank test for bits 14 to 21, p=0.54048
b-rank test for bits 15 to 22, p=0.54344
b-rank test for bits 16 to 23, p=0.50675
b-rank test for bits 17 to 24, p=0.05935
b-rank test for bits 18 to 25, p=0.44426
b-rank test for bits 19 to 26, p=0.57733
b-rank test for bits 20 to 27, p=0.57378
b-rank test for bits 21 to 28, p=0.46202
b-rank test for bits 22 to 29, p=0.05289
b-rank test for bits 23 to 30, p=0.16135
b-rank test for bits 24 to 31, p=0.77311
b-rank test for bits 25 to 32, p=0.98607
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 = 0.594389
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-07-28_17:31
(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 142067 0.37 0.643708
2 142743 1.95 0.974282
3 141570 -0.79 0.213939
4 141828 -0.19 0.424645
5 141570 -0.79 0.213939
6 141429 -1.12 0.130875
7 142344 1.02 0.845086
8 142340 1.01 0.842850
9 142114 0.48 0.683746
10 141592 -0.74 0.229218
11 141184 -1.69 0.045067
12 140825 -2.53 0.005647
13 141495 -0.97 0.166507
14 141167 -1.73 0.041422
15 142007 0.23 0.590255
16 142350 1.03 0.848402
17 141208 -1.64 0.050646
18 142019 0.26 0.601117
19 141212 -1.63 0.051627
20 141718 -0.45 0.327426
----------------------------------------------------------------
OPSO test for dh-ranFile-2016-07-28_17:31
Bits used No. missing words z-score p-value
23 to 32 141749 -0.5529 0.290179
22 to 31 142227 1.0954 0.863332
21 to 30 141721 -0.6494 0.258036
20 to 29 141449 -1.5873 0.056217
19 to 28 141192 -2.4736 0.006689
18 to 27 141740 -0.5839 0.279645
17 to 26 142266 1.2299 0.890632
16 to 25 141782 -0.4391 0.330306
15 to 24 141694 -0.7425 0.228887
14 to 23 141866 -0.1494 0.440614
13 to 22 142182 0.9402 0.826453
12 to 21 141688 -0.7632 0.222670
11 to 20 141855 -0.1873 0.425695
10 to 19 141998 0.3058 0.620106
9 to 18 141620 -0.9977 0.159215
8 to 17 141633 -0.9529 0.170330
7 to 16 141654 -0.8804 0.189308
6 to 15 142138 0.7885 0.784803
5 to 14 141715 -0.6701 0.251396
4 to 13 141338 -1.9701 0.024413
3 to 12 141575 -1.1529 0.124484
2 to 11 141879 -0.1046 0.458352
1 to 10 141993 0.2885 0.613525
-----------------------------------------------------------------
OQSO test for dh-ranFile-2016-07-28_17:31
Bits used No. missing words z-score p-value
28 to 32 142009 0.3379 0.632267
27 to 31 142042 0.4497 0.673547
26 to 30 142012 0.3480 0.636093
25 to 29 142149 0.8124 0.791731
24 to 28 141665 -0.8282 0.203768
23 to 27 142253 1.1650 0.877987
22 to 26 142470 1.9006 0.971321
21 to 25 141304 -2.0520 0.020086
20 to 24 142185 0.9345 0.824970
19 to 23 141746 -0.5537 0.289905
18 to 22 141703 -0.6994 0.242144
17 to 21 141610 -1.0147 0.155130
16 to 20 141764 -0.4926 0.311132
15 to 19 142130 0.7480 0.772780
14 to 18 141688 -0.7503 0.226546
13 to 17 142108 0.6735 0.749672
12 to 16 142261 1.1921 0.883389
11 to 15 142082 0.5853 0.720834
10 to 14 142104 0.6599 0.745341
9 to 13 141833 -0.2587 0.397916
8 to 12 142086 0.5989 0.725374
7 to 11 141946 0.1243 0.549463
6 to 10 142275 1.2396 0.892431
5 to 9 141688 -0.7503 0.226546
4 to 8 142023 0.3853 0.650001
3 to 7 141986 0.2599 0.602529
2 to 6 141723 -0.6316 0.263815
1 to 5 141969 0.2023 0.580148
-----------------------------------------------------------------
DNA test for dh-ranFile-2016-07-28_17:31
Bits used No. missing words z-score p-value
31 to 32 141889 -0.0600 0.476090
30 to 31 141810 -0.2930 0.384758
29 to 30 141706 -0.5998 0.274322
28 to 29 142350 1.2999 0.903184
27 to 28 141829 -0.2370 0.406343
26 to 27 141706 -0.5998 0.274322
25 to 26 141614 -0.8712 0.191828
24 to 25 142343 1.2793 0.899598
23 to 24 141702 -0.6116 0.270404
22 to 23 141868 -0.1219 0.451482
21 to 22 141647 -0.7738 0.219514
20 to 21 142256 1.0226 0.846758
19 to 20 141910 0.0020 0.500789
18 to 19 142065 0.4592 0.676956
17 to 18 141412 -1.4671 0.071181
16 to 17 141747 -0.4788 0.316023
15 to 16 141976 0.1967 0.577956
14 to 15 142476 1.6716 0.952698
13 to 14 141170 -2.1809 0.014595
12 to 13 142183 0.8073 0.790249
11 to 12 141700 -0.6175 0.268455
10 to 11 141790 -0.3520 0.362417
9 to 10 141360 -1.6204 0.052569
8 to 9 142003 0.2763 0.608846
7 to 8 142094 0.5447 0.707037
6 to 7 141493 -1.2281 0.109702
5 to 6 141712 -0.5821 0.280252
4 to 5 142127 0.6421 0.739594
3 to 4 141990 0.2380 0.594046
2 to 3 142548 1.8840 0.970216
1 to 2 141778 -0.3874 0.349229
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2016-07-28_17:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2418.24 -1.156 0.123794
Test results for specific bytes for dh-ranFile-2016-07-28_17:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2543.61 0.617 0.731306
2 to 9 2480.31 -0.278 0.390331
3 to 10 2387.60 -1.590 0.055963
4 to 11 2326.33 -2.456 0.007022
5 to 12 2338.02 -2.291 0.010988
6 to 13 2540.88 0.578 0.718406
7 to 14 2480.25 -0.279 0.390026
8 to 15 2365.49 -1.902 0.028566
9 to 16 2566.86 0.946 0.827812
10 to 17 2420.25 -1.128 0.129709
11 to 18 2439.50 -0.856 0.196098
12 to 19 2432.48 -0.955 0.169825
13 to 20 2470.69 -0.414 0.339254
14 to 21 2455.04 -0.636 0.262425
15 to 22 2514.16 0.200 0.579338
16 to 23 2470.17 -0.422 0.336581
17 to 24 2363.78 -1.926 0.027026
18 to 25 2678.48 2.524 0.994199
19 to 26 2574.04 1.047 0.852469
20 to 27 2435.10 -0.918 0.179368
21 to 28 2502.61 0.037 0.514742
22 to 29 2449.15 -0.719 0.236027
23 to 30 2525.23 0.357 0.639375
24 to 31 2446.99 -0.750 0.226704
25 to 32 2534.57 0.489 0.687549
CDPARK for dh-ranFile-2016-07-28_17:31: 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
3527 0.1826 0.572463
3527 0.1826 0.572463
3523 0.0000 0.500000
3536 0.5936 0.723613
3536 0.5936 0.723613
3507 -0.7306 0.232514
3542 0.8676 0.807188
3520 -0.1370 0.445521
3527 0.1826 0.572463
3518 -0.2283 0.409702
Square side=100, avg. no. parked=3526.30 sample std.=9.63
p-value of the KSTEST for those 10 p-values: 0.246308
Results for the MINIMUM DISTANCE test for dh-ranFile-2016-07-28_17:31
0.6930,0.9563,0.8125,0.8721,0.6935,0.0551,0.6017,0.9914,0.3684,0.2997,
The KS test for those 10 p-values: 0.206641
The 3DSPHERES test for dh-ranFile-2016-07-28_17:31
sample no r^3 equiv. uni.
1 0.548 0.018109
2 0.876 0.028767
3 0.718 0.023647
4 87.877 0.946562
5 39.002 0.727485
6 101.696 0.966286
7 9.732 0.277029
8 31.167 0.646159
9 15.491 0.403321
10 0.148 0.004909
11 91.982 0.953396
12 32.776 0.664629
13 26.922 0.592372
14 23.703 0.546206
15 3.367 0.106161
16 23.911 0.549341
17 25.177 0.567957
18 34.188 0.680050
19 10.328 0.291267
20 59.571 0.862714
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.300364
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-07-28_17:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -2.0 -1.6 0.6 0.5 -0.8
-0.9 0.3 -0.5 0.2 1.1 0.9
1.4 -1.1 -0.5 1.0 -0.2 0.1
-0.1 -0.9 -0.5 0.7 -1.0 0.5
-0.1 1.1 -2.3 -0.1 -0.6 -0.1
3.1 0.3 -1.7 2.0 0.1 0.6
0.0 -1.3 -1.6 -1.3 -1.3 -1.0
-0.1
Chi-square with 42 degrees of freedom:50.485921
z-score=0.925890, p-value=0.826816
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2016-07-28_17:31
Test no p-value
1 0.159143
2 0.110921
3 0.370163
4 0.084204
5 0.565049
6 0.666577
7 0.004759
8 0.426059
9 0.058525
10 0.503451
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.031090
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-07-28_17:31:
(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 66632 0.02 66536 0.26
3 25000.00 25064 0.16 25045 0.08
4 6666.67 6600 0.67 6773 1.70
5 1388.89 1398 0.06 1382 0.03
6 238.10 266 3.27 219 1.53
7 34.72 33 0.09 42 1.53
8 4.96 6 0.22 2 1.77
p=0.38827 p=0.66901
Number of rngs required: 688003, p-value: 0.322
RESULTS OF CRAPS TEST for dh-ranFile-2016-07-28_17:31
No. of wins: Observed Expected
99025 98585.9
z-score= 1.964, pvalue=0.97524
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66707 66666.7 0.024 0.024
2 37957 37654.3 2.433 2.457
3 26946 26954.7 0.003 2.460
4 19082 19313.5 2.774 5.234
5 13711 13851.4 1.424 6.658
6 9855 9943.5 0.788 7.446
7 7173 7145.0 0.110 7.556
8 5153 5139.1 0.038 7.593
9 3650 3699.9 0.672 8.266
10 2627 2666.3 0.579 8.845
11 1951 1923.3 0.398 9.243
12 1428 1388.7 1.110 10.353
13 993 1003.7 0.114 10.467
14 779 726.1 3.848 14.315
15 526 525.8 0.000 14.315
16 375 381.2 0.099 14.414
17 287 276.5 0.396 14.810
18 210 200.8 0.419 15.229
19 169 146.0 3.629 18.857
20 123 106.2 2.652 21.510
21 298 287.1 0.413 21.922
Chisq= 21.92 for 20 degrees of freedom, p= 0.65527
SUMMARY of craptest
p-value for no. of wins: 0.975241
p-value for throws/game: 0.655266
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2016-07-28_17:31
No. of wins: Observed Expected
98397 98585.9
z-score=-0.845, pvalue=0.19914
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66630 66666.7 0.020 0.020
2 37579 37654.3 0.151 0.171
3 27099 26954.7 0.772 0.943
4 19169 19313.5 1.081 2.024
5 13809 13851.4 0.130 2.153
6 10010 9943.5 0.444 2.598
7 7100 7145.0 0.284 2.881
8 5172 5139.1 0.211 3.092
9 3766 3699.9 1.182 4.274
10 2694 2666.3 0.288 4.562
11 1886 1923.3 0.725 5.287
12 1417 1388.7 0.575 5.862
13 1022 1003.7 0.333 6.195
14 688 726.1 2.003 8.198
15 531 525.8 0.051 8.249
16 397 381.2 0.659 8.908
17 278 276.5 0.008 8.916
18 196 200.8 0.116 9.032
19 149 146.0 0.062 9.094
20 99 106.2 0.490 9.584
21 309 287.1 1.668 11.253
Chisq= 11.25 for 20 degrees of freedom, p= 0.06060
SUMMARY of craptest
p-value for no. of wins: 0.199143
p-value for throws/game: 0.060597
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0048,0.0049,0.0056,0.0067,0.0070,0.0110,0.0146,0.0181,0.0201,0.0236,
0.0244,0.0270,0.0286,0.0288,0.0311,0.0370,0.0414,0.0451,0.0468,0.0506,
0.0516,0.0526,0.0529,0.0547,0.0551,0.0560,0.0562,0.0585,0.0594,0.0606,
0.0606,0.0712,0.0734,0.0842,0.1012,0.1062,0.1097,0.1109,0.1238,0.1245,
0.1255,0.1297,0.1309,0.1313,0.1551,0.1591,0.1592,0.1614,0.1665,0.1698,
0.1703,0.1794,0.1893,0.1918,0.1956,0.1961,0.1991,0.2038,0.2066,0.2070,
0.2072,0.2117,0.2139,0.2139,0.2195,0.2227,0.2265,0.2265,0.2267,0.2289,
0.2292,0.2315,0.2325,0.2360,0.2421,0.2463,0.2514,0.2580,0.2598,0.2620,
0.2624,0.2638,0.2685,0.2704,0.2731,0.2743,0.2743,0.2770,0.2796,0.2803,
0.2832,0.2899,0.2902,0.2913,0.2924,0.2997,0.3004,0.3111,0.3160,0.3225,
0.3274,0.3274,0.3303,0.3313,0.3366,0.3393,0.3394,0.3492,0.3624,0.3684,
0.3702,0.3791,0.3848,0.3850,0.3883,0.3900,0.3903,0.3979,0.4033,0.4063,
0.4073,0.4088,0.4097,0.4246,0.4257,0.4261,0.4338,0.4406,0.4443,0.4455,
0.4515,0.4584,0.4620,0.4685,0.4695,0.4732,0.4748,0.4761,0.5000,0.5007,
0.5008,0.5035,0.5064,0.5068,0.5120,0.5147,0.5201,0.5405,0.5434,0.5449,
0.5462,0.5493,0.5495,0.5557,0.5650,0.5680,0.5725,0.5725,0.5725,0.5738,
0.5773,0.5780,0.5793,0.5801,0.5903,0.5916,0.5924,0.5940,0.5944,0.6011,
0.6017,0.6025,0.6078,0.6088,0.6135,0.6201,0.6323,0.6361,0.6394,0.6437,
0.6462,0.6500,0.6553,0.6630,0.6646,0.6646,0.6666,0.6686,0.6690,0.6735,
0.6768,0.6770,0.6795,0.6801,0.6830,0.6837,0.6857,0.6875,0.6880,0.6930,
0.6935,0.7070,0.7142,0.7150,0.7184,0.7195,0.7208,0.7236,0.7236,0.7254,
0.7260,0.7275,0.7313,0.7371,0.7396,0.7453,0.7497,0.7728,0.7731,0.7848,
0.7874,0.7902,0.7917,0.8044,0.8072,0.8125,0.8139,0.8250,0.8265,0.8268,
0.8278,0.8428,0.8451,0.8468,0.8470,0.8484,0.8525,0.8627,0.8633,0.8721,
0.8780,0.8787,0.8806,0.8834,0.8906,0.8924,0.8996,0.9032,0.9033,0.9039,
0.9047,0.9086,0.9288,0.9457,0.9466,0.9501,0.9527,0.9534,0.9563,0.9663,
0.9702,0.9713,0.9720,0.9743,0.9752,0.9861,0.9888,0.9914,0.9942,
Overall p-value after applying KStest on 269 p-values = 0.122684
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.