RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-05_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 15.93 11.4193 0.166045
2 to 25 15.78 13.3140 0.285074
3 to 26 15.60 23.1784 0.856468
4 to 27 15.74 18.4388 0.638325
5 to 28 15.88 8.2816 0.039852
6 to 29 16.08 12.2713 0.216563
7 to 30 15.29 27.6499 0.950800
8 to 31 15.90 16.0965 0.482994
9 to 32 15.82 20.3071 0.741176
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.996421
Tough bday spacings test for dh-ranFile-2018-07-05_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 9 39 72 113 97 72 48 28 11 10 1
(O-E)^2/E 0.0 0.2 0.0 2.4 0.0 0.5 0.3 0.1 1.0 1.7 2.3
Birthday Spacings: Sum(O-E)^2/E= 8.553, p= 0.425
RESULTS OF GCD FOR dh-ranFile-2018-07-05_06:31
Euclid's algorithm:
p-value, steps to gcd: 0.050421
p-value, dist. of gcd's: 0.077305
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-05_06:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.923 0.868 0.175 0.444 0.698 0.480 0.637 0.262
Bits 8 to 15---> 0.626 0.030 0.177 0.044 0.052 0.046 0.115 0.189
Bits 16 to 23---> 0.671 0.643 0.893 0.757 0.196 0.288 0.902 0.335
Bits 24 to 31---> 0.272 0.614 0.616 0.570 0.489 0.396 0.921 0.676
KS test for the above 32 p values: 0.248
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-05_06:31,
p-values for 5 runs: 0.9138, 0.4851, 0.7211, 0.8877, 0.2435
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-05_06:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 196 211.4 1.124 1.124
r= 29 5181 5134.0 0.430 1.554
r= 30 23178 23103.0 0.243 1.798
r= 31 11445 11551.5 0.982 2.780
chi-square = 2.780 with df = 3; p-value = 0.573
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-05_06:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 200 211.4 0.617 0.617
r= 30 5255 5134.0 2.851 3.468
r= 31 23033 23103.0 0.212 3.680
r= 32 11512 11551.5 0.135 3.816
chi-square = 3.816 with df = 3; p-value = 0.718
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-05_06:31
b-rank test for bits 1 to 8, p=0.87720
b-rank test for bits 2 to 9, p=0.96992
b-rank test for bits 3 to 10, p=0.35982
b-rank test for bits 4 to 11, p=0.57568
b-rank test for bits 5 to 12, p=0.00809
b-rank test for bits 6 to 13, p=0.64464
b-rank test for bits 7 to 14, p=0.89836
b-rank test for bits 8 to 15, p=0.44064
b-rank test for bits 9 to 16, p=0.22253
b-rank test for bits 10 to 17, p=0.55200
b-rank test for bits 11 to 18, p=0.73796
b-rank test for bits 12 to 19, p=0.75034
b-rank test for bits 13 to 20, p=0.57764
b-rank test for bits 14 to 21, p=0.25044
b-rank test for bits 15 to 22, p=0.05154
b-rank test for bits 16 to 23, p=0.14492
b-rank test for bits 17 to 24, p=0.65700
b-rank test for bits 18 to 25, p=0.60686
b-rank test for bits 19 to 26, p=0.04036
b-rank test for bits 20 to 27, p=0.20006
b-rank test for bits 21 to 28, p=0.45715
b-rank test for bits 22 to 29, p=0.71102
b-rank test for bits 23 to 30, p=0.54525
b-rank test for bits 24 to 31, p=0.04844
b-rank test for bits 25 to 32, p=0.82153
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 = 0.841531
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-05_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 141723 -0.44 0.331654
2 141412 -1.16 0.122621
3 142361 1.06 0.854357
4 141831 -0.18 0.427394
5 142263 0.83 0.795692
6 142067 0.37 0.643708
7 142478 1.33 0.908021
8 142448 1.26 0.895908
9 141078 -1.94 0.026047
10 141699 -0.49 0.311563
11 141776 -0.31 0.377703
12 141733 -0.41 0.340175
13 142231 0.75 0.773844
14 140998 -2.13 0.016616
15 141779 -0.30 0.380370
16 141993 0.20 0.577496
17 141976 0.16 0.561893
18 141332 -1.35 0.088684
19 142219 0.72 0.765322
20 141671 -0.56 0.288816
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-05_06:31
Bits used No. missing words z-score p-value
23 to 32 142089 0.6196 0.732224
22 to 31 142037 0.4402 0.670119
21 to 30 142124 0.7402 0.770423
20 to 29 141633 -0.9529 0.170330
19 to 28 141554 -1.2253 0.110236
18 to 27 141859 -0.1736 0.431109
17 to 26 141942 0.1127 0.544848
16 to 25 141937 0.0954 0.538007
15 to 24 142365 1.5713 0.941941
14 to 23 142090 0.6230 0.733358
13 to 22 141923 0.0471 0.518798
12 to 21 142403 1.7023 0.955651
11 to 20 141882 -0.0942 0.462459
10 to 19 141718 -0.6598 0.254704
9 to 18 141727 -0.6287 0.264765
8 to 17 142092 0.6299 0.735619
7 to 16 141562 -1.1977 0.115519
6 to 15 141647 -0.9046 0.182842
5 to 14 141893 -0.0563 0.477547
4 to 13 141967 0.1989 0.578815
3 to 12 141954 0.1540 0.561209
2 to 11 141827 -0.2839 0.388245
1 to 10 142244 1.1540 0.875757
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-05_06:31
Bits used No. missing words z-score p-value
28 to 32 141496 -1.4011 0.080589
27 to 31 141867 -0.1435 0.442951
26 to 30 141710 -0.6757 0.249617
25 to 29 141848 -0.2079 0.417654
24 to 28 141801 -0.3672 0.356727
23 to 27 141804 -0.3571 0.360527
22 to 26 142590 2.3074 0.989483
21 to 25 141889 -0.0689 0.472529
20 to 24 142006 0.3277 0.628429
19 to 23 141788 -0.4113 0.340431
18 to 22 142176 0.9040 0.816993
17 to 21 142081 0.5819 0.719694
16 to 20 142149 0.8124 0.791731
15 to 19 141987 0.2633 0.603836
14 to 18 141493 -1.4113 0.079080
13 to 17 141777 -0.4486 0.326869
12 to 16 141882 -0.0926 0.463093
11 to 15 141812 -0.3299 0.370726
10 to 14 142188 0.9446 0.827580
9 to 13 141667 -0.8215 0.205693
8 to 12 141952 0.1446 0.557504
7 to 11 141773 -0.4621 0.321992
6 to 10 142083 0.5887 0.721973
5 to 9 142042 0.4497 0.673547
4 to 8 141918 0.0294 0.511723
3 to 7 142014 0.3548 0.638635
2 to 6 141897 -0.0418 0.483330
1 to 5 141765 -0.4893 0.312331
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-05_06:31
Bits used No. missing words z-score p-value
31 to 32 141752 -0.4641 0.321288
30 to 31 141602 -0.9066 0.182315
29 to 30 141186 -2.1337 0.016433
28 to 29 141645 -0.7797 0.217774
27 to 28 142106 0.5801 0.719092
26 to 27 141812 -0.2871 0.387014
25 to 26 141809 -0.2960 0.383631
24 to 25 141680 -0.6765 0.249365
23 to 24 141950 0.1200 0.547747
22 to 23 141982 0.2144 0.584869
21 to 22 142052 0.4209 0.663070
20 to 21 142129 0.6480 0.741506
19 to 20 141964 0.1613 0.564059
18 to 19 141942 0.0964 0.538387
17 to 18 141757 -0.4494 0.326589
16 to 17 142249 1.0020 0.841823
15 to 16 142104 0.5742 0.717100
14 to 15 141975 0.1937 0.576801
13 to 14 141631 -0.8210 0.205814
12 to 13 142162 0.7453 0.771967
11 to 12 142225 0.9312 0.824120
10 to 11 141135 -2.2842 0.011181
9 to 10 141435 -1.3992 0.080876
8 to 9 141902 -0.0216 0.491375
7 to 8 142015 0.3117 0.622370
6 to 7 141437 -1.3933 0.081764
5 to 6 142252 1.0108 0.843950
4 to 5 141855 -0.1603 0.436336
3 to 4 142388 1.4120 0.921026
2 to 3 141587 -0.9508 0.170846
1 to 2 142412 1.4828 0.930937
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-05_06:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2434.17 -0.931 0.175943
Test results for specific bytes for dh-ranFile-2018-07-05_06:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2666.94 2.361 0.990883
2 to 9 2455.32 -0.632 0.263732
3 to 10 2551.98 0.735 0.768853
4 to 11 2473.14 -0.380 0.352040
5 to 12 2551.97 0.735 0.768806
6 to 13 2494.68 -0.075 0.470032
7 to 14 2484.31 -0.222 0.412223
8 to 15 2530.56 0.432 0.667196
9 to 16 2514.70 0.208 0.582336
10 to 17 2443.19 -0.803 0.210859
11 to 18 2511.12 0.157 0.562491
12 to 19 2526.47 0.374 0.645912
13 to 20 2566.83 0.945 0.827688
14 to 21 2518.00 0.255 0.600485
15 to 22 2578.07 1.104 0.865225
16 to 23 2532.42 0.459 0.676717
17 to 24 2516.48 0.233 0.592147
18 to 25 2493.86 -0.087 0.465390
19 to 26 2516.68 0.236 0.593217
20 to 27 2525.05 0.354 0.638416
21 to 28 2465.46 -0.489 0.312591
22 to 29 2557.02 0.806 0.790008
23 to 30 2476.27 -0.336 0.368602
24 to 31 2558.22 0.823 0.794830
25 to 32 2544.29 0.626 0.734477
CDPARK for dh-ranFile-2018-07-05_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
3540 0.7763 0.781201
3543 0.9132 0.819442
3541 0.8219 0.794438
3516 -0.3196 0.374623
3452 -3.2420 0.000593
3505 -0.8219 0.205562
3527 0.1826 0.572463
3550 1.2329 0.891189
3516 -0.3196 0.374623
3519 -0.1826 0.427537
Square side=100, avg. no. parked=3520.90 sample std.=26.82
p-value of the KSTEST for those 10 p-values: 0.581985
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-05_06:31
0.6147,0.7569,0.4396,0.1775,0.3900,0.5785,0.7530,0.5602,0.6228,0.4071,
The KS test for those 10 p-values: 0.307156
The 3DSPHERES test for dh-ranFile-2018-07-05_06:31
sample no r^3 equiv. uni.
1 11.492 0.318224
2 66.648 0.891565
3 20.624 0.497156
4 2.553 0.081586
5 9.407 0.269170
6 58.305 0.856798
7 12.614 0.343261
8 5.531 0.168373
9 122.202 0.982980
10 16.353 0.420212
11 18.048 0.452074
12 7.324 0.216613
13 39.863 0.735199
14 65.476 0.887244
15 3.233 0.102158
16 25.855 0.577608
17 17.422 0.440517
18 25.165 0.567790
19 14.477 0.382810
20 25.708 0.575533
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.859103
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-05_06:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
2.0 -1.6 2.0 0.8 0.3 0.7
-1.7 -0.6 0.5 0.1 0.1 1.2
1.2 -0.3 -1.0 0.2 0.6 -1.1
1.2 -0.6 -1.4 1.0 -1.0 -0.5
0.5 0.4 -0.8 -0.5 0.2 0.6
-0.9 0.8 -0.5 -0.3 2.4 0.4
2.4 -0.7 0.9 1.5 -0.6 1.0
-0.1
Chi-square with 42 degrees of freedom:47.268484
z-score=0.574839, p-value=0.733855
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-05_06:31
Test no p-value
1 0.103224
2 0.001410
3 0.762097
4 0.542627
5 0.155046
6 0.595174
7 0.980864
8 0.035549
9 0.066953
10 0.056759
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.015537
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-05_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 66703 0.02 66499 0.42
3 25000.00 24906 0.35 25122 0.60
4 6666.67 6672 0.00 6714 0.34
5 1388.89 1412 0.38 1369 0.28
6 238.10 258 1.66 253 0.93
7 34.72 43 1.97 37 0.15
8 4.96 5 0.00 5 0.00
p=0.37742 p=0.15704
Number of rngs required: 690242, p-value: 0.985
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-05_06:31
No. of wins: Observed Expected
98152 98585.9
z-score=-1.940, pvalue=0.02616
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66470 66666.7 0.580 0.580
2 37718 37654.3 0.108 0.688
3 26928 26954.7 0.027 0.714
4 19503 19313.5 1.860 2.574
5 13806 13851.4 0.149 2.723
6 9958 9943.5 0.021 2.744
7 7234 7145.0 1.108 3.852
8 5087 5139.1 0.528 4.380
9 3694 3699.9 0.009 4.389
10 2688 2666.3 0.177 4.566
11 1870 1923.3 1.479 6.045
12 1401 1388.7 0.108 6.153
13 987 1003.7 0.278 6.431
14 687 726.1 2.110 8.541
15 578 525.8 5.175 13.716
16 372 381.2 0.220 13.935
17 296 276.5 1.369 15.305
18 206 200.8 0.133 15.438
19 150 146.0 0.110 15.548
20 98 106.2 0.635 16.184
21 269 287.1 1.143 17.327
Chisq= 17.33 for 20 degrees of freedom, p= 0.36833
SUMMARY of craptest
p-value for no. of wins: 0.026161
p-value for throws/game: 0.368332
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-05_06:31
No. of wins: Observed Expected
98673 98585.9
z-score= 0.390, pvalue=0.65164
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66922 66666.7 0.978 0.978
2 37520 37654.3 0.479 1.457
3 27089 26954.7 0.669 2.126
4 19126 19313.5 1.820 3.945
5 13792 13851.4 0.255 4.200
6 10008 9943.5 0.418 4.618
7 7030 7145.0 1.852 6.470
8 5319 5139.1 6.300 12.770
9 3621 3699.9 1.681 14.451
10 2684 2666.3 0.118 14.568
11 1938 1923.3 0.112 14.680
12 1402 1388.7 0.127 14.807
13 992 1003.7 0.137 14.943
14 710 726.1 0.359 15.302
15 506 525.8 0.748 16.050
16 369 381.2 0.387 16.438
17 260 276.5 0.989 17.427
18 193 200.8 0.305 17.732
19 128 146.0 2.216 19.948
20 108 106.2 0.030 19.978
21 283 287.1 0.059 20.037
Chisq= 20.04 for 20 degrees of freedom, p= 0.54437
SUMMARY of craptest
p-value for no. of wins: 0.651638
p-value for throws/game: 0.544366
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0006,0.0014,0.0081,0.0112,0.0155,0.0164,0.0166,0.0260,0.0262,0.0296,
0.0355,0.0399,0.0404,0.0440,0.0455,0.0484,0.0504,0.0515,0.0519,0.0568,
0.0670,0.0773,0.0791,0.0806,0.0809,0.0816,0.0818,0.0887,0.1022,0.1032,
0.1102,0.1153,0.1155,0.1226,0.1449,0.1550,0.1570,0.1660,0.1684,0.1703,
0.1708,0.1748,0.1759,0.1766,0.1775,0.1823,0.1828,0.1895,0.1960,0.2001,
0.2056,0.2057,0.2058,0.2109,0.2166,0.2166,0.2178,0.2225,0.2435,0.2476,
0.2494,0.2496,0.2504,0.2547,0.2620,0.2637,0.2648,0.2692,0.2719,0.2851,
0.2878,0.2888,0.3072,0.3116,0.3123,0.3126,0.3182,0.3213,0.3220,0.3266,
0.3269,0.3317,0.3354,0.3402,0.3404,0.3433,0.3520,0.3567,0.3598,0.3605,
0.3683,0.3686,0.3707,0.3746,0.3746,0.3774,0.3777,0.3804,0.3828,0.3836,
0.3870,0.3882,0.3900,0.3956,0.4071,0.4122,0.4177,0.4202,0.4250,0.4274,
0.4275,0.4311,0.4363,0.4396,0.4405,0.4406,0.4430,0.4437,0.4521,0.4571,
0.4625,0.4631,0.4654,0.4700,0.4725,0.4775,0.4801,0.4830,0.4833,0.4851,
0.4894,0.4914,0.4972,0.5117,0.5188,0.5380,0.5384,0.5426,0.5444,0.5448,
0.5452,0.5477,0.5520,0.5575,0.5602,0.5612,0.5619,0.5625,0.5641,0.5678,
0.5703,0.5725,0.5732,0.5755,0.5757,0.5768,0.5775,0.5776,0.5776,0.5785,
0.5788,0.5820,0.5823,0.5849,0.5921,0.5932,0.5952,0.6005,0.6038,0.6069,
0.6138,0.6147,0.6155,0.6224,0.6228,0.6263,0.6284,0.6375,0.6383,0.6384,
0.6386,0.6426,0.6437,0.6446,0.6459,0.6516,0.6570,0.6631,0.6672,0.6701,
0.6711,0.6735,0.6759,0.6767,0.6980,0.7110,0.7171,0.7179,0.7191,0.7197,
0.7211,0.7220,0.7322,0.7334,0.7339,0.7345,0.7352,0.7356,0.7380,0.7412,
0.7415,0.7503,0.7530,0.7569,0.7571,0.7621,0.7653,0.7688,0.7689,0.7704,
0.7720,0.7738,0.7812,0.7900,0.7917,0.7944,0.7948,0.7957,0.8170,0.8194,
0.8215,0.8241,0.8276,0.8277,0.8415,0.8418,0.8440,0.8544,0.8565,0.8568,
0.8591,0.8652,0.8681,0.8758,0.8772,0.8872,0.8877,0.8912,0.8916,0.8930,
0.8959,0.8984,0.9021,0.9080,0.9138,0.9210,0.9211,0.9227,0.9309,0.9419,
0.9508,0.9557,0.9699,0.9809,0.9830,0.9853,0.9895,0.9909,0.9964,
Overall p-value after applying KStest on 269 p-values = 0.317757
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.