RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-29_18:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.51 16.3087 0.497938
2 to 25 15.55 24.8611 0.902137
3 to 26 15.74 20.1871 0.735227
4 to 27 15.67 20.7765 0.763553
5 to 28 15.77 19.7581 0.713212
6 to 29 15.65 14.7890 0.389326
7 to 30 15.77 21.4065 0.791368
8 to 31 15.68 21.8982 0.811335
9 to 32 15.86 12.7418 0.246711
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.143716
Tough bday spacings test for dh-ranFile-2018-06-29_18:31: 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 13 38 67 109 91 74 60 25 15 4 4
(O-E)^2/E 1.6 0.1 0.5 1.3 0.5 0.2 1.2 0.8 0.0 1.0 0.0
Birthday Spacings: Sum(O-E)^2/E= 7.186, p= 0.292
RESULTS OF GCD FOR dh-ranFile-2018-06-29_18:31
Euclid's algorithm:
p-value, steps to gcd: 0.220003
p-value, dist. of gcd's: 0.854034
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-29_18:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.406 0.920 0.371 0.856 0.378 0.319 0.573 0.970
Bits 8 to 15---> 0.137 0.518 0.227 0.590 0.745 0.822 0.240 0.392
Bits 16 to 23---> 0.133 0.581 0.098 0.526 0.562 0.569 0.645 0.983
Bits 24 to 31---> 0.489 0.767 0.073 0.901 0.252 0.277 0.313 0.213
KS test for the above 32 p values: 0.175
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-29_18:31,
p-values for 5 runs: 0.9033, 0.9576, 0.7891, 0.7850, 0.4735
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-29_18:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 194 211.4 1.435 1.435
r= 29 5192 5134.0 0.655 2.090
r= 30 23034 23103.0 0.206 2.296
r= 31 11580 11551.5 0.070 2.367
chi-square = 2.367 with df = 3; p-value = 0.500
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-29_18:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 203 211.4 0.335 0.335
r= 30 5279 5134.0 4.095 4.430
r= 31 22995 23103.0 0.505 4.935
r= 32 11523 11551.5 0.070 5.006
chi-square = 5.006 with df = 3; p-value = 0.829
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-29_18:31
b-rank test for bits 1 to 8, p=0.88887
b-rank test for bits 2 to 9, p=0.02202
b-rank test for bits 3 to 10, p=0.87337
b-rank test for bits 4 to 11, p=0.08074
b-rank test for bits 5 to 12, p=0.47317
b-rank test for bits 6 to 13, p=0.30224
b-rank test for bits 7 to 14, p=0.99644
b-rank test for bits 8 to 15, p=0.86267
b-rank test for bits 9 to 16, p=0.24826
b-rank test for bits 10 to 17, p=0.35678
b-rank test for bits 11 to 18, p=0.84889
b-rank test for bits 12 to 19, p=0.18825
b-rank test for bits 13 to 20, p=0.44879
b-rank test for bits 14 to 21, p=0.09217
b-rank test for bits 15 to 22, p=0.96459
b-rank test for bits 16 to 23, p=0.07643
b-rank test for bits 17 to 24, p=0.32540
b-rank test for bits 18 to 25, p=0.12492
b-rank test for bits 19 to 26, p=0.72759
b-rank test for bits 20 to 27, p=0.50681
b-rank test for bits 21 to 28, p=0.07764
b-rank test for bits 22 to 29, p=0.73672
b-rank test for bits 23 to 30, p=0.54869
b-rank test for bits 24 to 31, p=0.28423
b-rank test for bits 25 to 32, p=0.14108
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 = 0.358184
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-29_18:31
(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 141827 -0.19 0.423730
2 142369 1.07 0.858588
3 141889 -0.05 0.481057
4 141996 0.20 0.580237
5 141872 -0.09 0.465249
6 141945 0.08 0.533210
7 141766 -0.33 0.368857
8 142311 0.94 0.826001
9 141611 -0.70 0.242891
10 141873 -0.08 0.466177
11 142333 0.99 0.838884
12 141621 -0.67 0.250261
13 142059 0.35 0.636717
14 142129 0.51 0.696111
15 141895 -0.03 0.486645
16 142022 0.26 0.603820
17 141477 -1.01 0.156220
18 141646 -0.62 0.269193
19 141984 0.17 0.569249
20 142439 1.24 0.892058
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-29_18:31
Bits used No. missing words z-score p-value
23 to 32 141832 -0.2667 0.394867
22 to 31 141973 0.2196 0.586890
21 to 30 141404 -1.7425 0.040709
20 to 29 141916 0.0230 0.509175
19 to 28 141457 -1.5598 0.059408
18 to 27 142078 0.5816 0.719589
17 to 26 141961 0.1782 0.570706
16 to 25 142443 1.8402 0.967134
15 to 24 141859 -0.1736 0.431109
14 to 23 142325 1.4333 0.924120
13 to 22 141873 -0.1253 0.450153
12 to 21 142429 1.7920 0.963431
11 to 20 142322 1.4230 0.922632
10 to 19 141854 -0.1908 0.424344
9 to 18 142157 0.8540 0.803457
8 to 17 142293 1.3230 0.907082
7 to 16 142044 0.4644 0.678812
6 to 15 141619 -1.0011 0.158380
5 to 14 141650 -0.8942 0.185596
4 to 13 141607 -1.0425 0.148586
3 to 12 141844 -0.2253 0.410882
2 to 11 141739 -0.5873 0.278486
1 to 10 141673 -0.8149 0.207556
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-29_18:31
Bits used No. missing words z-score p-value
28 to 32 141613 -1.0045 0.157567
27 to 31 141806 -0.3503 0.363068
26 to 30 141696 -0.7232 0.234793
25 to 29 142232 1.0938 0.862978
24 to 28 141804 -0.3571 0.360527
23 to 27 142150 0.8158 0.792702
22 to 26 142022 0.3819 0.648744
21 to 25 141552 -1.2113 0.112893
20 to 24 142220 1.0531 0.853857
19 to 23 141998 0.3006 0.618131
18 to 22 142406 1.6836 0.953873
17 to 21 141796 -0.3842 0.350426
16 to 20 142009 0.3379 0.632267
15 to 19 141522 -1.3130 0.094594
14 to 18 142022 0.3819 0.648744
13 to 17 141678 -0.7842 0.216470
12 to 16 142120 0.7141 0.762428
11 to 15 141688 -0.7503 0.226546
10 to 14 141505 -1.3706 0.085248
9 to 13 142014 0.3548 0.638635
8 to 12 141787 -0.4147 0.339189
7 to 11 142089 0.6091 0.728755
6 to 10 141936 0.0904 0.536018
5 to 9 141858 -0.1740 0.430933
4 to 8 141530 -1.2859 0.099245
3 to 7 142611 2.3785 0.991309
2 to 6 141849 -0.2045 0.418978
1 to 5 141894 -0.0520 0.479278
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-29_18:31
Bits used No. missing words z-score p-value
31 to 32 141767 -0.4199 0.337297
30 to 31 141912 0.0079 0.503142
29 to 30 142289 1.1200 0.868637
28 to 29 142104 0.5742 0.717100
27 to 28 142987 3.1790 0.999261
26 to 27 142061 0.4474 0.672708
25 to 26 142320 1.2114 0.887132
24 to 25 141906 -0.0098 0.496081
23 to 24 142260 1.0344 0.849531
22 to 23 141746 -0.4818 0.314974
21 to 22 142256 1.0226 0.846758
20 to 21 142671 2.2468 0.987674
19 to 20 142043 0.3943 0.653323
18 to 19 142619 2.0934 0.981844
17 to 18 141739 -0.5024 0.307676
16 to 17 141936 0.0787 0.531354
15 to 16 141844 -0.1927 0.423592
14 to 15 142095 0.5477 0.708051
13 to 14 142100 0.5624 0.713095
12 to 13 141730 -0.5290 0.298404
11 to 12 142278 1.0875 0.861597
10 to 11 141235 -1.9892 0.023341
9 to 10 141845 -0.1898 0.424747
8 to 9 141623 -0.8446 0.199158
7 to 8 141666 -0.7178 0.236444
6 to 7 141610 -0.8830 0.188624
5 to 6 142113 0.6008 0.726012
4 to 5 142246 0.9931 0.839676
3 to 4 142110 0.5919 0.723057
2 to 3 142203 0.8663 0.806833
1 to 2 142060 0.4445 0.671643
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-29_18:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2456.63 -0.613 0.269830
Test results for specific bytes for dh-ranFile-2018-06-29_18:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2510.68 0.151 0.560006
2 to 9 2478.83 -0.299 0.382318
3 to 10 2453.03 -0.664 0.253264
4 to 11 2517.92 0.253 0.600038
5 to 12 2556.27 0.796 0.786929
6 to 13 2446.13 -0.762 0.223065
7 to 14 2453.83 -0.653 0.256881
8 to 15 2569.07 0.977 0.835682
9 to 16 2484.90 -0.214 0.415462
10 to 17 2483.38 -0.235 0.407108
11 to 18 2448.38 -0.730 0.232701
12 to 19 2490.19 -0.139 0.444855
13 to 20 2549.75 0.704 0.759168
14 to 21 2471.68 -0.400 0.344400
15 to 22 2622.88 1.738 0.958879
16 to 23 2457.79 -0.597 0.275290
17 to 24 2602.64 1.451 0.926678
18 to 25 2581.49 1.152 0.875417
19 to 26 2569.82 0.987 0.838291
20 to 27 2467.10 -0.465 0.320878
21 to 28 2387.72 -1.588 0.056154
22 to 29 2489.71 -0.145 0.442166
23 to 30 2512.76 0.180 0.571595
24 to 31 2500.49 0.007 0.502743
25 to 32 2621.87 1.723 0.957600
CDPARK for dh-ranFile-2018-06-29_18:31: 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
3507 -0.7306 0.232514
3516 -0.3196 0.374623
3537 0.6393 0.738676
3558 1.5982 0.944998
3552 1.3242 0.907282
3504 -0.8676 0.192812
3505 -0.8219 0.205562
3488 -1.5982 0.055002
3528 0.2283 0.590298
3507 -0.7306 0.232514
Square side=100, avg. no. parked=3520.20 sample std.=21.63
p-value of the KSTEST for those 10 p-values: 0.671901
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-29_18:31
0.1587,0.5715,0.4358,0.3162,0.7738,0.8693,0.9897,0.6009,0.8128,0.1878,
The KS test for those 10 p-values: 0.736285
The 3DSPHERES test for dh-ranFile-2018-06-29_18:31
sample no r^3 equiv. uni.
1 11.713 0.323227
2 60.618 0.867422
3 9.346 0.267665
4 29.647 0.627761
5 11.168 0.310825
6 26.791 0.590585
7 8.817 0.254651
8 10.136 0.286701
9 16.481 0.422691
10 29.599 0.627172
11 66.361 0.890522
12 50.182 0.812268
13 35.284 0.691526
14 0.409 0.013548
15 100.464 0.964874
16 0.579 0.019109
17 47.836 0.796996
18 50.616 0.814963
19 29.503 0.625980
20 9.597 0.273784
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.756116
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-29_18:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -0.7 1.8 0.3 -0.8 -1.6
-1.9 1.0 -0.3 1.2 -0.2 -0.1
0.6 0.5 0.1 0.9 -0.2 0.2
-0.9 -2.1 0.5 -0.4 1.3 0.2
1.2 -0.6 -0.3 -1.7 0.9 -0.6
0.5 -0.9 0.6 0.4 -0.2 -0.7
2.4 -0.1 0.5 2.1 0.1 0.0
0.8
Chi-square with 42 degrees of freedom:41.718038
z-score=-0.030765, p-value=0.516762
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-29_18:31
Test no p-value
1 0.761229
2 0.363934
3 0.087058
4 0.107884
5 0.016461
6 0.732753
7 0.043701
8 0.409886
9 0.000106
10 0.192864
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.004534
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-29_18:31:
(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 66543 0.23 66453 0.68
3 25000.00 25011 0.00 25114 0.52
4 6666.67 6762 1.36 6707 0.24
5 1388.89 1395 0.03 1433 1.40
6 238.10 256 1.35 258 1.66
7 34.72 27 1.72 30 0.64
8 4.96 5 0.00 4 0.19
p=0.41554 p=0.49913
Number of rngs required: 688161, p-value: 0.390
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-29_18:31
No. of wins: Observed Expected
98373 98585.9
z-score=-0.952, pvalue=0.17054
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66556 66666.7 0.184 0.184
2 37931 37654.3 2.033 2.217
3 26771 26954.7 1.252 3.469
4 19375 19313.5 0.196 3.665
5 13903 13851.4 0.192 3.857
6 10089 9943.5 2.128 5.985
7 6999 7145.0 2.984 8.969
8 5063 5139.1 1.126 10.095
9 3730 3699.9 0.245 10.341
10 2688 2666.3 0.177 10.518
11 1918 1923.3 0.015 10.532
12 1398 1388.7 0.062 10.594
13 975 1003.7 0.822 11.416
14 723 726.1 0.014 11.429
15 509 525.8 0.539 11.968
16 386 381.2 0.062 12.030
17 244 276.5 3.829 15.859
18 207 200.8 0.190 16.048
19 138 146.0 0.437 16.485
20 126 106.2 3.685 20.170
21 271 287.1 0.904 21.075
Chisq= 21.07 for 20 degrees of freedom, p= 0.60725
SUMMARY of craptest
p-value for no. of wins: 0.170541
p-value for throws/game: 0.607252
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-29_18:31
No. of wins: Observed Expected
98464 98585.9
z-score=-0.545, pvalue=0.29287
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66552 66666.7 0.197 0.197
2 37725 37654.3 0.133 0.330
3 26926 26954.7 0.031 0.361
4 19313 19313.5 0.000 0.361
5 13896 13851.4 0.143 0.504
6 9974 9943.5 0.093 0.597
7 7207 7145.0 0.538 1.135
8 5053 5139.1 1.442 2.576
9 3797 3699.9 2.550 5.127
10 2705 2666.3 0.562 5.688
11 1870 1923.3 1.479 7.167
12 1378 1388.7 0.083 7.250
13 998 1003.7 0.033 7.283
14 747 726.1 0.599 7.882
15 471 525.8 5.718 13.600
16 394 381.2 0.433 14.034
17 256 276.5 1.526 15.559
18 187 200.8 0.952 16.511
19 151 146.0 0.172 16.684
20 110 106.2 0.135 16.819
21 290 287.1 0.029 16.848
Chisq= 16.85 for 20 degrees of freedom, p= 0.33716
SUMMARY of craptest
p-value for no. of wins: 0.292869
p-value for throws/game: 0.337156
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0001,0.0045,0.0135,0.0165,0.0191,0.0220,0.0233,0.0407,0.0437,0.0550,
0.0562,0.0594,0.0727,0.0764,0.0776,0.0807,0.0852,0.0871,0.0922,0.0946,
0.0977,0.0992,0.1079,0.1129,0.1249,0.1331,0.1368,0.1411,0.1437,0.1486,
0.1562,0.1576,0.1584,0.1587,0.1705,0.1751,0.1856,0.1878,0.1882,0.1886,
0.1928,0.1929,0.1992,0.2056,0.2076,0.2128,0.2165,0.2200,0.2231,0.2265,
0.2265,0.2325,0.2325,0.2327,0.2348,0.2364,0.2403,0.2429,0.2467,0.2483,
0.2503,0.2516,0.2533,0.2547,0.2569,0.2677,0.2692,0.2698,0.2738,0.2753,
0.2767,0.2785,0.2842,0.2867,0.2922,0.2929,0.2984,0.3022,0.3077,0.3108,
0.3135,0.3150,0.3162,0.3189,0.3209,0.3232,0.3254,0.3372,0.3373,0.3392,
0.3444,0.3504,0.3568,0.3582,0.3605,0.3631,0.3639,0.3689,0.3705,0.3746,
0.3779,0.3823,0.3893,0.3903,0.3923,0.3949,0.4060,0.4071,0.4099,0.4109,
0.4155,0.4155,0.4190,0.4227,0.4236,0.4237,0.4243,0.4247,0.4309,0.4311,
0.4358,0.4422,0.4449,0.4488,0.4502,0.4652,0.4662,0.4732,0.4735,0.4793,
0.4811,0.4866,0.4889,0.4961,0.4979,0.4991,0.5001,0.5027,0.5031,0.5068,
0.5092,0.5168,0.5181,0.5258,0.5314,0.5332,0.5360,0.5487,0.5600,0.5619,
0.5688,0.5692,0.5707,0.5715,0.5716,0.5731,0.5802,0.5810,0.5869,0.5900,
0.5903,0.5906,0.6000,0.6009,0.6038,0.6073,0.6181,0.6260,0.6272,0.6278,
0.6323,0.6367,0.6386,0.6454,0.6487,0.6487,0.6533,0.6716,0.6719,0.6727,
0.6788,0.6915,0.6961,0.7081,0.7131,0.7132,0.7171,0.7196,0.7231,0.7260,
0.7276,0.7288,0.7328,0.7352,0.7363,0.7367,0.7387,0.7450,0.7561,0.7592,
0.7612,0.7624,0.7636,0.7666,0.7738,0.7850,0.7869,0.7891,0.7914,0.7927,
0.7970,0.8035,0.8068,0.8113,0.8123,0.8128,0.8150,0.8224,0.8260,0.8286,
0.8357,0.8383,0.8389,0.8397,0.8468,0.8489,0.8495,0.8539,0.8540,0.8557,
0.8586,0.8616,0.8627,0.8630,0.8674,0.8686,0.8693,0.8734,0.8754,0.8871,
0.8889,0.8905,0.8921,0.9005,0.9021,0.9033,0.9071,0.9073,0.9201,0.9226,
0.9241,0.9267,0.9450,0.9539,0.9576,0.9576,0.9589,0.9634,0.9646,0.9649,
0.9671,0.9703,0.9818,0.9834,0.9877,0.9897,0.9913,0.9964,0.9993,
Overall p-value after applying KStest on 269 p-values = 0.573454
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.