RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-12_08:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.75 18.4980 0.641903
2 to 25 15.76 13.9286 0.327854
3 to 26 15.72 25.7231 0.920345
4 to 27 15.78 14.1849 0.346028
5 to 28 15.75 16.6775 0.523587
6 to 29 15.62 15.8046 0.462270
7 to 30 15.53 15.5527 0.444264
8 to 31 15.27 31.1720 0.980969
9 to 32 15.47 27.8586 0.953382
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.195035
Tough bday spacings test for dh-ranFile-2018-07-12_08:31: 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 10 33 65 94 92 93 58 32 11 6 6
(O-E)^2/E 0.1 0.4 0.9 0.1 0.3 2.8 0.7 0.2 1.0 0.1 0.9
Birthday Spacings: Sum(O-E)^2/E= 7.489, p= 0.321
RESULTS OF GCD FOR dh-ranFile-2018-07-12_08:31
Euclid's algorithm:
p-value, steps to gcd: 0.418442
p-value, dist. of gcd's: 0.983404
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-12_08:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.708 0.518 0.385 0.974 0.225 0.275 0.088 0.938
Bits 8 to 15---> 0.594 0.019 0.736 0.391 0.250 0.875 0.721 0.986
Bits 16 to 23---> 0.195 0.280 0.495 0.637 0.287 0.308 0.966 0.969
Bits 24 to 31---> 0.745 0.886 0.084 0.307 0.770 0.871 0.404 0.786
KS test for the above 32 p values: 0.625
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-12_08:31,
p-values for 5 runs: 0.6518, 0.4173, 0.5623, 0.3417, 0.6921
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-12_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 206 211.4 0.139 0.139
r= 29 5057 5134.0 1.155 1.294
r= 30 23062 23103.0 0.073 1.367
r= 31 11675 11551.5 1.320 2.687
chi-square = 2.687 with df = 3; p-value = 0.558
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-12_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 205 211.4 0.195 0.195
r= 30 5054 5134.0 1.247 1.442
r= 31 23118 23103.0 0.010 1.451
r= 32 11623 11551.5 0.442 1.894
chi-square = 1.894 with df = 3; p-value = 0.405
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-12_08:31
b-rank test for bits 1 to 8, p=0.53785
b-rank test for bits 2 to 9, p=0.17524
b-rank test for bits 3 to 10, p=0.27075
b-rank test for bits 4 to 11, p=0.72850
b-rank test for bits 5 to 12, p=0.46320
b-rank test for bits 6 to 13, p=0.90824
b-rank test for bits 7 to 14, p=0.89668
b-rank test for bits 8 to 15, p=0.75145
b-rank test for bits 9 to 16, p=0.22241
b-rank test for bits 10 to 17, p=0.99178
b-rank test for bits 11 to 18, p=0.97837
b-rank test for bits 12 to 19, p=0.53452
b-rank test for bits 13 to 20, p=0.58835
b-rank test for bits 14 to 21, p=0.89207
b-rank test for bits 15 to 22, p=0.83819
b-rank test for bits 16 to 23, p=0.71554
b-rank test for bits 17 to 24, p=0.15958
b-rank test for bits 18 to 25, p=0.03408
b-rank test for bits 19 to 26, p=0.20608
b-rank test for bits 20 to 27, p=0.11490
b-rank test for bits 21 to 28, p=0.29494
b-rank test for bits 22 to 29, p=0.56143
b-rank test for bits 23 to 30, p=0.03397
b-rank test for bits 24 to 31, p=0.40378
b-rank test for bits 25 to 32, p=0.29658
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 = 0.942906
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-12_08:31
(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 141877 -0.08 0.469894
2 141726 -0.43 0.334201
3 142030 0.28 0.611005
4 141074 -1.95 0.025487
5 142127 0.51 0.694475
6 141904 -0.01 0.495032
7 142072 0.38 0.648053
8 141578 -0.77 0.219425
9 142426 1.21 0.886317
10 142081 0.40 0.655826
11 141974 0.15 0.560051
12 141808 -0.24 0.406425
13 142617 1.65 0.950879
14 141379 -1.24 0.107656
15 141422 -1.14 0.127431
16 142033 0.29 0.613690
17 142161 0.59 0.721739
18 141247 -1.55 0.060871
19 141461 -1.05 0.147435
20 141915 0.01 0.505285
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-12_08:31
Bits used No. missing words z-score p-value
23 to 32 141936 0.0920 0.536637
22 to 31 141567 -1.1804 0.118911
21 to 30 142024 0.3954 0.653731
20 to 29 141776 -0.4598 0.322845
19 to 28 141740 -0.5839 0.279645
18 to 27 142098 0.6506 0.742343
17 to 26 141785 -0.4287 0.334062
16 to 25 141780 -0.4460 0.327811
15 to 24 141782 -0.4391 0.330306
14 to 23 141570 -1.1701 0.120980
13 to 22 142525 2.1230 0.983123
12 to 21 142061 0.5230 0.699513
11 to 20 142126 0.7471 0.772510
10 to 19 141922 0.0437 0.517424
9 to 18 142483 1.9782 0.976045
8 to 17 142185 0.9506 0.829093
7 to 16 142168 0.8920 0.813794
6 to 15 141942 0.1127 0.544848
5 to 14 141675 -0.8080 0.209535
4 to 13 142182 0.9402 0.826453
3 to 12 141993 0.2885 0.613525
2 to 11 141558 -1.2115 0.112855
1 to 10 141768 -0.4873 0.313007
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-12_08:31
Bits used No. missing words z-score p-value
28 to 32 141654 -0.8655 0.193375
27 to 31 141800 -0.3706 0.355464
26 to 30 141955 0.1548 0.561516
25 to 29 141740 -0.5740 0.282984
24 to 28 142034 0.4226 0.663710
23 to 27 141753 -0.5299 0.298080
22 to 26 141857 -0.1774 0.429601
21 to 25 141687 -0.7537 0.225526
20 to 24 141505 -1.3706 0.085248
19 to 23 141481 -1.4520 0.073256
18 to 22 141736 -0.5876 0.278414
17 to 21 141479 -1.4587 0.072318
16 to 20 142325 1.4091 0.920590
15 to 19 141646 -0.8926 0.186024
14 to 18 141801 -0.3672 0.356727
13 to 17 141652 -0.8723 0.191521
12 to 16 142322 1.3989 0.919076
11 to 15 141742 -0.5672 0.285282
10 to 14 141892 -0.0587 0.476577
9 to 13 141701 -0.7062 0.240031
8 to 12 141698 -0.7164 0.236881
7 to 11 141861 -0.1638 0.434932
6 to 10 141507 -1.3638 0.086310
5 to 9 142351 1.4972 0.932828
4 to 8 141811 -0.3333 0.369446
3 to 7 142253 1.1650 0.877987
2 to 6 141895 -0.0486 0.480629
1 to 5 142120 0.7141 0.762428
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-12_08:31
Bits used No. missing words z-score p-value
31 to 32 141735 -0.5142 0.303539
30 to 31 141369 -1.5939 0.055480
29 to 30 141729 -0.5319 0.297381
28 to 29 142324 1.2232 0.889376
27 to 28 142310 1.1819 0.881381
26 to 27 141399 -1.5054 0.066111
25 to 26 141448 -1.3609 0.086780
24 to 25 142530 1.8309 0.966441
23 to 24 141982 0.2144 0.584869
22 to 23 141812 -0.2871 0.387014
21 to 22 141707 -0.5968 0.275306
20 to 21 142124 0.6332 0.736713
19 to 20 141907 -0.0069 0.497258
18 to 19 141671 -0.7030 0.241016
17 to 18 142270 1.0639 0.856318
16 to 17 141649 -0.7679 0.221263
15 to 16 142337 1.2616 0.896447
14 to 15 142051 0.4179 0.661992
13 to 14 142173 0.7778 0.781653
12 to 13 141352 -1.6440 0.050084
11 to 12 141866 -0.1278 0.449147
10 to 11 142083 0.5123 0.695780
9 to 10 141743 -0.4906 0.311837
8 to 9 142250 1.0049 0.842534
7 to 8 141559 -1.0334 0.150703
6 to 7 142206 0.8751 0.809249
5 to 6 141538 -1.0954 0.136678
4 to 5 141483 -1.2576 0.104266
3 to 4 142143 0.6893 0.754680
2 to 3 141982 0.2144 0.584869
1 to 2 141599 -0.9154 0.179984
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-12_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2552.29 0.739 0.770186
Test results for specific bytes for dh-ranFile-2018-07-12_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2701.62 2.851 0.997823
2 to 9 2429.25 -1.001 0.158511
3 to 10 2382.84 -1.657 0.048764
4 to 11 2419.89 -1.133 0.128631
5 to 12 2588.52 1.252 0.894687
6 to 13 2416.09 -1.187 0.117688
7 to 14 2374.99 -1.768 0.038543
8 to 15 2420.69 -1.122 0.131022
9 to 16 2575.85 1.073 0.858285
10 to 17 2437.71 -0.881 0.189173
11 to 18 2482.38 -0.249 0.401616
12 to 19 2567.19 0.950 0.828985
13 to 20 2583.06 1.175 0.879933
14 to 21 2477.98 -0.311 0.377749
15 to 22 2465.33 -0.490 0.311951
16 to 23 2496.58 -0.048 0.480726
17 to 24 2535.13 0.497 0.690324
18 to 25 2552.10 0.737 0.769376
19 to 26 2486.10 -0.197 0.422062
20 to 27 2537.29 0.527 0.701004
21 to 28 2423.85 -1.077 0.140758
22 to 29 2553.35 0.754 0.774711
23 to 30 2462.88 -0.525 0.299796
24 to 31 2486.20 -0.195 0.422649
25 to 32 2470.81 -0.413 0.339898
CDPARK for dh-ranFile-2018-07-12_08:31: 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
3550 1.2329 0.891189
3530 0.3196 0.625377
3566 1.9635 0.975204
3477 -2.1005 0.017844
3493 -1.3699 0.085365
3482 -1.8721 0.030593
3561 1.7352 0.958644
3542 0.8676 0.807188
3482 -1.8721 0.030593
3532 0.4110 0.659449
Square side=100, avg. no. parked=3521.50 sample std.=32.97
p-value of the KSTEST for those 10 p-values: 0.067082
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-12_08:31
0.3716,0.3497,0.3291,0.6245,0.8872,0.5567,0.4453,0.8370,0.2400,0.8533,
The KS test for those 10 p-values: 0.593634
The 3DSPHERES test for dh-ranFile-2018-07-12_08:31
sample no r^3 equiv. uni.
1 23.261 0.539472
2 2.516 0.080459
3 15.391 0.401323
4 48.331 0.800318
5 31.639 0.651678
6 2.187 0.070302
7 70.506 0.904650
8 13.331 0.358769
9 21.584 0.512995
10 84.231 0.939656
11 54.484 0.837349
12 3.250 0.102685
13 53.735 0.833236
14 155.702 0.994428
15 27.304 0.597524
16 51.252 0.818843
17 9.673 0.275623
18 9.197 0.264029
19 15.073 0.394949
20 3.780 0.118397
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.887503
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-12_08:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -0.7 0.1 -1.7 -2.0 0.9
-0.6 0.2 -0.1 -1.2 0.9 1.0
0.4 -0.3 1.5 -0.6 -0.2 -0.8
-1.4 -0.3 -0.2 -0.5 1.7 0.7
0.1 0.2 0.9 0.4 -1.4 0.8
-0.3 -0.7 -0.1 0.1 -1.5 -0.1
-0.7 0.2 0.9 0.4 1.6 1.0
0.8
Chi-square with 42 degrees of freedom:32.798938
z-score=-1.003918, p-value=0.155274
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-12_08:31
Test no p-value
1 0.074673
2 0.073754
3 0.875913
4 0.313199
5 0.126477
6 0.212576
7 0.579742
8 0.131145
9 0.537002
10 0.068083
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.027673
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-12_08:31:
(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 66540 0.24 66653 0.00
3 25000.00 25060 0.14 25171 1.17
4 6666.67 6736 0.72 6531 2.76
5 1388.89 1372 0.21 1369 0.28
6 238.10 251 0.70 237 0.01
7 34.72 39 0.53 30 0.64
8 4.96 1 3.16 8 1.86
p=0.54235 p=0.65328
Number of rngs required: 687419, p-value: 0.127
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-12_08:31
No. of wins: Observed Expected
98683 98585.9
z-score= 0.434, pvalue=0.66803
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66362 66666.7 1.392 1.392
2 37961 37654.3 2.498 3.890
3 26859 26954.7 0.340 4.230
4 19330 19313.5 0.014 4.244
5 13701 13851.4 1.633 5.878
6 9961 9943.5 0.031 5.908
7 7119 7145.0 0.095 6.003
8 5139 5139.1 0.000 6.003
9 3701 3699.9 0.000 6.004
10 2729 2666.3 1.475 7.478
11 1971 1923.3 1.182 8.660
12 1491 1388.7 7.530 16.190
13 987 1003.7 0.278 16.468
14 714 726.1 0.203 16.671
15 546 525.8 0.773 17.444
16 409 381.2 2.035 19.479
17 278 276.5 0.008 19.487
18 209 200.8 0.332 19.819
19 135 146.0 0.827 20.646
20 108 106.2 0.030 20.676
21 290 287.1 0.029 20.705
Chisq= 20.70 for 20 degrees of freedom, p= 0.58530
SUMMARY of craptest
p-value for no. of wins: 0.668028
p-value for throws/game: 0.585299
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-12_08:31
No. of wins: Observed Expected
98527 98585.9
z-score=-0.263, pvalue=0.39618
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66436 66666.7 0.798 0.798
2 37572 37654.3 0.180 0.978
3 26948 26954.7 0.002 0.980
4 19472 19313.5 1.301 2.281
5 13985 13851.4 1.288 3.569
6 10042 9943.5 0.975 4.544
7 7265 7145.0 2.015 6.559
8 5097 5139.1 0.344 6.903
9 3696 3699.9 0.004 6.907
10 2613 2666.3 1.065 7.973
11 1855 1923.3 2.427 10.400
12 1334 1388.7 2.158 12.558
13 1063 1003.7 3.502 16.060
14 726 726.1 0.000 16.060
15 528 525.8 0.009 16.068
16 351 381.2 2.385 18.453
17 290 276.5 0.655 19.109
18 204 200.8 0.050 19.159
19 144 146.0 0.027 19.186
20 105 106.2 0.014 19.200
21 274 287.1 0.599 19.799
Chisq= 19.80 for 20 degrees of freedom, p= 0.52941
SUMMARY of craptest
p-value for no. of wins: 0.396179
p-value for throws/game: 0.529409
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0178,0.0195,0.0255,0.0277,0.0306,0.0306,0.0340,0.0341,0.0385,0.0488,
0.0501,0.0555,0.0609,0.0661,0.0671,0.0681,0.0703,0.0723,0.0733,0.0738,
0.0747,0.0805,0.0844,0.0852,0.0854,0.0863,0.0868,0.0880,0.1027,0.1043,
0.1077,0.1129,0.1149,0.1177,0.1184,0.1189,0.1210,0.1265,0.1266,0.1274,
0.1286,0.1310,0.1311,0.1367,0.1408,0.1474,0.1507,0.1553,0.1585,0.1596,
0.1752,0.1800,0.1860,0.1892,0.1915,0.1934,0.1949,0.1950,0.2061,0.2095,
0.2126,0.2194,0.2213,0.2224,0.2253,0.2255,0.2369,0.2400,0.2400,0.2410,
0.2498,0.2640,0.2707,0.2753,0.2754,0.2756,0.2784,0.2796,0.2804,0.2830,
0.2853,0.2872,0.2949,0.2966,0.2974,0.2981,0.2998,0.3035,0.3070,0.3080,
0.3118,0.3120,0.3130,0.3132,0.3214,0.3228,0.3278,0.3279,0.3291,0.3303,
0.3341,0.3342,0.3399,0.3417,0.3460,0.3497,0.3555,0.3567,0.3588,0.3694,
0.3716,0.3777,0.3848,0.3870,0.3905,0.3949,0.3962,0.4013,0.4016,0.4038,
0.4038,0.4052,0.4064,0.4173,0.4184,0.4221,0.4226,0.4296,0.4349,0.4443,
0.4453,0.4491,0.4623,0.4632,0.4699,0.4766,0.4806,0.4807,0.4950,0.4954,
0.4973,0.5053,0.5130,0.5174,0.5181,0.5236,0.5294,0.5345,0.5366,0.5370,
0.5378,0.5395,0.5423,0.5448,0.5567,0.5575,0.5601,0.5614,0.5615,0.5623,
0.5797,0.5849,0.5849,0.5853,0.5883,0.5936,0.5944,0.5975,0.6110,0.6135,
0.6137,0.6245,0.6253,0.6254,0.6368,0.6419,0.6481,0.6517,0.6518,0.6533,
0.6537,0.6558,0.6594,0.6620,0.6637,0.6680,0.6903,0.6921,0.6945,0.6958,
0.6995,0.7010,0.7083,0.7155,0.7211,0.7217,0.7285,0.7364,0.7367,0.7423,
0.7447,0.7514,0.7547,0.7624,0.7694,0.7702,0.7704,0.7725,0.7747,0.7817,
0.7858,0.8003,0.8072,0.8092,0.8138,0.8188,0.8265,0.8290,0.8291,0.8332,
0.8370,0.8373,0.8382,0.8425,0.8533,0.8563,0.8583,0.8707,0.8746,0.8759,
0.8780,0.8799,0.8814,0.8863,0.8863,0.8872,0.8875,0.8894,0.8912,0.8921,
0.8947,0.8964,0.8967,0.9046,0.9082,0.9191,0.9203,0.9206,0.9328,0.9380,
0.9397,0.9429,0.9509,0.9534,0.9586,0.9661,0.9664,0.9690,0.9735,0.9752,
0.9760,0.9784,0.9810,0.9831,0.9834,0.9863,0.9918,0.9944,0.9978,
Overall p-value after applying KStest on 269 p-values = 0.562411
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.