RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-27_12:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.78 20.8447 0.766687
2 to 25 15.79 20.8792 0.768258
3 to 26 15.59 12.8135 0.251421
4 to 27 15.74 11.6442 0.178811
5 to 28 15.95 16.3874 0.503446
6 to 29 15.92 8.7295 0.051632
7 to 30 15.70 23.5260 0.867103
8 to 31 16.04 8.1367 0.036464
9 to 32 16.13 21.5229 0.796228
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.626718
Tough bday spacings test for dh-ranFile-2018-06-27_12:31: 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 7 41 80 111 80 80 46 31 16 4 4
(O-E)^2/E 0.5 0.5 0.6 1.8 3.2 0.0 0.7 0.1 0.1 1.0 0.0
Birthday Spacings: Sum(O-E)^2/E= 8.593, p= 0.429
RESULTS OF GCD FOR dh-ranFile-2018-06-27_12:31
Euclid's algorithm:
p-value, steps to gcd: 0.949852
p-value, dist. of gcd's: 0.461410
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-27_12:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.873 0.690 0.342 0.460 0.599 0.760 0.839 0.239
Bits 8 to 15---> 0.674 0.391 0.333 0.619 0.928 0.026 0.764 0.694
Bits 16 to 23---> 0.390 0.174 0.556 0.912 0.107 0.697 0.956 0.228
Bits 24 to 31---> 0.594 0.500 0.414 0.502 0.653 0.174 0.156 0.026
KS test for the above 32 p values: 0.050
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-27_12:31,
p-values for 5 runs: 0.3403, 0.4559, 0.1921, 0.5187, 0.6306
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-27_12:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 218 211.4 0.205 0.205
r= 29 5091 5134.0 0.360 0.565
r= 30 23110 23103.0 0.002 0.567
r= 31 11581 11551.5 0.075 0.643
chi-square = 0.643 with df = 3; p-value = 0.113
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-27_12:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 194 211.4 1.435 1.435
r= 30 4966 5134.0 5.498 6.933
r= 31 23053 23103.0 0.108 7.042
r= 32 11787 11551.5 4.800 11.842
chi-square = 11.842 with df = 3; p-value = 0.992
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-27_12:31
b-rank test for bits 1 to 8, p=0.10062
b-rank test for bits 2 to 9, p=0.81034
b-rank test for bits 3 to 10, p=0.58108
b-rank test for bits 4 to 11, p=0.19218
b-rank test for bits 5 to 12, p=0.18712
b-rank test for bits 6 to 13, p=0.39838
b-rank test for bits 7 to 14, p=0.53510
b-rank test for bits 8 to 15, p=0.87658
b-rank test for bits 9 to 16, p=0.82307
b-rank test for bits 10 to 17, p=0.12508
b-rank test for bits 11 to 18, p=0.11829
b-rank test for bits 12 to 19, p=0.09389
b-rank test for bits 13 to 20, p=0.67657
b-rank test for bits 14 to 21, p=0.71325
b-rank test for bits 15 to 22, p=0.88070
b-rank test for bits 16 to 23, p=0.33192
b-rank test for bits 17 to 24, p=0.26041
b-rank test for bits 18 to 25, p=0.55391
b-rank test for bits 19 to 26, p=0.87429
b-rank test for bits 20 to 27, p=0.43260
b-rank test for bits 21 to 28, p=0.95502
b-rank test for bits 22 to 29, p=0.97226
b-rank test for bits 23 to 30, p=0.93922
b-rank test for bits 24 to 31, p=0.32929
b-rank test for bits 25 to 32, p=0.07428
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 = 0.774549
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-27_12:31
(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 141819 -0.21 0.416424
2 141505 -0.94 0.172407
3 141118 -1.85 0.032236
4 141907 -0.01 0.497828
5 142651 1.73 0.958441
6 141193 -1.67 0.047098
7 141686 -0.52 0.300905
8 142047 0.32 0.626144
9 141658 -0.59 0.278528
10 142376 1.09 0.862221
11 141686 -0.52 0.300905
12 141961 0.12 0.548045
13 141814 -0.22 0.411871
14 141999 0.21 0.582975
15 142220 0.73 0.766039
16 142206 0.69 0.755894
17 141473 -1.02 0.153992
18 141718 -0.45 0.327426
19 141659 -0.58 0.279313
20 142173 0.62 0.731070
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-27_12:31
Bits used No. missing words z-score p-value
23 to 32 141653 -0.8839 0.188376
22 to 31 142036 0.4368 0.668869
21 to 30 141883 -0.0908 0.463829
20 to 29 141823 -0.2977 0.382970
19 to 28 141842 -0.2322 0.408202
18 to 27 141794 -0.3977 0.345430
17 to 26 141807 -0.3529 0.362096
16 to 25 141628 -0.9701 0.165998
15 to 24 141796 -0.3908 0.347975
14 to 23 142051 0.4885 0.687408
13 to 22 141786 -0.4253 0.335318
12 to 21 142220 1.0713 0.857977
11 to 20 142059 0.5161 0.697109
10 to 19 141548 -1.2460 0.106389
9 to 18 142092 0.6299 0.735619
8 to 17 141920 0.0368 0.514675
7 to 16 142133 0.7713 0.779728
6 to 15 141871 -0.1322 0.447424
5 to 14 141886 -0.0804 0.467940
4 to 13 142120 0.7264 0.766218
3 to 12 141598 -1.0736 0.141512
2 to 11 141743 -0.5736 0.283136
1 to 10 141749 -0.5529 0.290179
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-27_12:31
Bits used No. missing words z-score p-value
28 to 32 141703 -0.6994 0.242144
27 to 31 142115 0.6972 0.757157
26 to 30 141832 -0.2621 0.396609
25 to 29 142192 0.9582 0.831020
24 to 28 142047 0.4667 0.679635
23 to 27 142264 1.2023 0.885371
22 to 26 142258 1.1819 0.881384
21 to 25 141812 -0.3299 0.370726
20 to 24 141837 -0.2452 0.403156
19 to 23 141573 -1.1401 0.127122
18 to 22 142359 1.5243 0.936284
17 to 21 141933 0.0802 0.531976
16 to 20 142357 1.5175 0.935433
15 to 19 141669 -0.8147 0.207628
14 to 18 141855 -0.1842 0.426940
13 to 17 141490 -1.4215 0.077592
12 to 16 142043 0.4531 0.674768
11 to 15 141498 -1.3943 0.081608
10 to 14 141638 -0.9198 0.178848
9 to 13 141811 -0.3333 0.369446
8 to 12 141828 -0.2757 0.391391
7 to 11 141751 -0.5367 0.295733
6 to 10 141714 -0.6621 0.253942
5 to 9 141978 0.2328 0.592034
4 to 8 141589 -1.0859 0.138770
3 to 7 141440 -1.5909 0.055811
2 to 6 141852 -0.1943 0.422955
1 to 5 141824 -0.2893 0.386193
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-27_12:31
Bits used No. missing words z-score p-value
31 to 32 142161 0.7424 0.771074
30 to 31 142081 0.5064 0.693713
29 to 30 141365 -1.6057 0.054171
28 to 29 142269 1.0610 0.855649
27 to 28 141498 -1.2134 0.112496
26 to 27 141995 0.2527 0.599755
25 to 26 142214 0.8987 0.815602
24 to 25 140898 -2.9833 0.001426
23 to 24 142069 0.4710 0.681181
22 to 23 142218 0.9105 0.818729
21 to 22 141912 0.0079 0.503142
20 to 21 141736 -0.5113 0.304571
19 to 20 141994 0.2498 0.598615
18 to 19 142233 0.9548 0.830155
17 to 18 142243 0.9843 0.837510
16 to 17 142607 2.0580 0.980206
15 to 16 142287 1.1141 0.867376
14 to 15 141634 -0.8122 0.208343
13 to 14 142179 0.7955 0.786835
12 to 13 141849 -0.1780 0.429375
11 to 12 141406 -1.4847 0.068805
10 to 11 142040 0.3855 0.650051
9 to 10 141890 -0.0570 0.477264
8 to 9 141729 -0.5319 0.297381
7 to 8 142383 1.3973 0.918832
6 to 7 141684 -0.6647 0.253124
5 to 6 142204 0.8692 0.807640
4 to 5 141966 0.1672 0.566381
3 to 4 142083 0.5123 0.695780
2 to 3 141612 -0.8771 0.190222
1 to 2 142403 1.4563 0.927339
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-27_12:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2551.91 0.734 0.768569
Test results for specific bytes for dh-ranFile-2018-06-27_12:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2471.34 -0.405 0.342610
2 to 9 2418.21 -1.157 0.123708
3 to 10 2485.02 -0.212 0.416138
4 to 11 2566.67 0.943 0.827109
5 to 12 2489.56 -0.148 0.441306
6 to 13 2476.67 -0.330 0.370718
7 to 14 2522.74 0.322 0.626106
8 to 15 2582.17 1.162 0.877394
9 to 16 2359.78 -1.983 0.023685
10 to 17 2490.67 -0.132 0.447486
11 to 18 2541.57 0.588 0.721720
12 to 19 2454.61 -0.642 0.260447
13 to 20 2593.71 1.325 0.907449
14 to 21 2502.97 0.042 0.516735
15 to 22 2530.88 0.437 0.668857
16 to 23 2432.48 -0.955 0.169819
17 to 24 2496.31 -0.052 0.479186
18 to 25 2507.21 0.102 0.540582
19 to 26 2494.93 -0.072 0.471397
20 to 27 2567.50 0.955 0.830096
21 to 28 2463.32 -0.519 0.301953
22 to 29 2563.88 0.903 0.816841
23 to 30 2530.08 0.425 0.664723
24 to 31 2557.87 0.818 0.793427
25 to 32 2397.39 -1.451 0.073382
CDPARK for dh-ranFile-2018-06-27_12:31: 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
3520 -0.1370 0.445521
3496 -1.2329 0.108811
3504 -0.8676 0.192812
3507 -0.7306 0.232514
3534 0.5023 0.692266
3522 -0.0457 0.481790
3535 0.5479 0.708135
3515 -0.3653 0.357445
3552 1.3242 0.907282
3512 -0.5023 0.307734
Square side=100, avg. no. parked=3519.70 sample std.=15.93
p-value of the KSTEST for those 10 p-values: 0.757117
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-27_12:31
0.2252,0.6644,0.4315,0.0566,0.5392,0.4187,0.7045,0.4504,0.9361,0.7208,
The KS test for those 10 p-values: 0.874098
The 3DSPHERES test for dh-ranFile-2018-06-27_12:31
sample no r^3 equiv. uni.
1 3.410 0.107442
2 8.544 0.247833
3 48.266 0.799886
4 28.884 0.618172
5 112.724 0.976657
6 60.113 0.865174
7 2.369 0.075925
8 53.188 0.830168
9 126.203 0.985106
10 37.068 0.709340
11 10.344 0.291649
12 21.203 0.506764
13 11.436 0.316950
14 0.327 0.010845
15 10.022 0.283982
16 4.398 0.136358
17 24.983 0.565154
18 19.666 0.480829
19 7.884 0.231092
20 11.670 0.322263
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.838625
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-27_12:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 1.3 0.8 1.5 1.4 -2.1
-1.2 0.5 0.4 -0.1 0.5 -1.0
-0.4 1.5 -0.2 -0.5 0.2 0.3
-1.9 1.8 -1.7 0.6 0.9 -0.8
1.8 -0.7 0.6 -0.4 -0.3 -0.5
-2.3 0.8 1.7 0.0 2.7 -0.1
-1.6 0.2 -0.4 0.4 0.1 0.0
0.8
Chi-square with 42 degrees of freedom:53.180784
z-score=1.219924, p-value=0.884390
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-27_12:31
Test no p-value
1 0.462103
2 0.292874
3 0.774109
4 0.646748
5 0.982668
6 0.082650
7 0.332009
8 0.058674
9 0.716139
10 0.996424
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.498682
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-27_12:31:
(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 66771 0.16 66587 0.10
3 25000.00 24936 0.16 24999 0.00
4 6666.67 6624 0.27 6786 2.14
5 1388.89 1394 0.02 1358 0.69
6 238.10 236 0.02 235 0.04
7 34.72 31 0.40 29 0.94
8 4.96 7 0.84 5 0.00
p=0.06918 p=0.30994
Number of rngs required: 687618, p-value: 0.182
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-27_12:31
No. of wins: Observed Expected
98630 98585.9
z-score= 0.197, pvalue=0.57825
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66716 66666.7 0.037 0.037
2 37567 37654.3 0.202 0.239
3 26995 26954.7 0.060 0.299
4 19204 19313.5 0.620 0.920
5 13857 13851.4 0.002 0.922
6 10018 9943.5 0.558 1.479
7 7148 7145.0 0.001 1.481
8 5132 5139.1 0.010 1.490
9 3749 3699.9 0.653 2.143
10 2648 2666.3 0.126 2.268
11 1910 1923.3 0.092 2.361
12 1358 1388.7 0.680 3.041
13 1036 1003.7 1.038 4.080
14 747 726.1 0.599 4.679
15 514 525.8 0.266 4.945
16 357 381.2 1.530 6.476
17 273 276.5 0.045 6.521
18 222 200.8 2.232 8.752
19 172 146.0 4.636 13.389
20 92 106.2 1.902 15.291
21 285 287.1 0.016 15.307
Chisq= 15.31 for 20 degrees of freedom, p= 0.24140
SUMMARY of craptest
p-value for no. of wins: 0.578253
p-value for throws/game: 0.241402
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-27_12:31
No. of wins: Observed Expected
98468 98585.9
z-score=-0.527, pvalue=0.29905
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66618 66666.7 0.036 0.036
2 37884 37654.3 1.401 1.436
3 26699 26954.7 2.426 3.863
4 19219 19313.5 0.462 4.325
5 13957 13851.4 0.805 5.130
6 10066 9943.5 1.508 6.638
7 7043 7145.0 1.457 8.094
8 5120 5139.1 0.071 8.165
9 3715 3699.9 0.062 8.227
10 2763 2666.3 3.507 11.734
11 1924 1923.3 0.000 11.735
12 1400 1388.7 0.091 11.826
13 984 1003.7 0.387 12.213
14 724 726.1 0.006 12.220
15 497 525.8 1.581 13.801
16 355 381.2 1.794 15.595
17 288 276.5 0.475 16.070
18 202 200.8 0.007 16.077
19 149 146.0 0.062 16.139
20 104 106.2 0.046 16.185
21 289 287.1 0.012 16.198
Chisq= 16.20 for 20 degrees of freedom, p= 0.29571
SUMMARY of craptest
p-value for no. of wins: 0.299051
p-value for throws/game: 0.295711
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0014,0.0108,0.0237,0.0257,0.0259,0.0322,0.0365,0.0471,0.0500,0.0516,
0.0542,0.0558,0.0566,0.0587,0.0688,0.0692,0.0734,0.0743,0.0759,0.0776,
0.0816,0.0827,0.0939,0.1006,0.1064,0.1074,0.1075,0.1088,0.1125,0.1134,
0.1183,0.1237,0.1251,0.1271,0.1364,0.1388,0.1415,0.1540,0.1555,0.1660,
0.1698,0.1724,0.1736,0.1740,0.1788,0.1788,0.1818,0.1871,0.1884,0.1902,
0.1921,0.1922,0.1928,0.2076,0.2083,0.2252,0.2276,0.2311,0.2325,0.2389,
0.2414,0.2421,0.2478,0.2514,0.2531,0.2539,0.2604,0.2604,0.2785,0.2793,
0.2831,0.2840,0.2902,0.2916,0.2929,0.2957,0.2957,0.2974,0.2991,0.3009,
0.3009,0.3020,0.3046,0.3077,0.3099,0.3170,0.3223,0.3274,0.3293,0.3319,
0.3320,0.3331,0.3353,0.3403,0.3423,0.3426,0.3454,0.3480,0.3574,0.3621,
0.3694,0.3707,0.3707,0.3830,0.3862,0.3896,0.3908,0.3914,0.3966,0.3984,
0.4032,0.4082,0.4119,0.4142,0.4161,0.4164,0.4187,0.4230,0.4269,0.4289,
0.4294,0.4315,0.4326,0.4413,0.4455,0.4474,0.4475,0.4504,0.4559,0.4599,
0.4614,0.4621,0.4638,0.4679,0.4714,0.4773,0.4792,0.4808,0.4818,0.4978,
0.4987,0.4996,0.5018,0.5031,0.5034,0.5068,0.5147,0.5167,0.5187,0.5320,
0.5351,0.5392,0.5406,0.5480,0.5539,0.5558,0.5652,0.5664,0.5783,0.5811,
0.5830,0.5920,0.5942,0.5986,0.5989,0.5998,0.6182,0.6193,0.6261,0.6261,
0.6267,0.6306,0.6467,0.6501,0.6528,0.6644,0.6647,0.6689,0.6689,0.6744,
0.6748,0.6766,0.6796,0.6812,0.6874,0.6904,0.6923,0.6937,0.6941,0.6958,
0.6971,0.6973,0.7045,0.7081,0.7093,0.7133,0.7161,0.7208,0.7217,0.7311,
0.7356,0.7559,0.7571,0.7572,0.7596,0.7643,0.7660,0.7662,0.7667,0.7683,
0.7686,0.7711,0.7741,0.7745,0.7797,0.7868,0.7934,0.7962,0.7999,0.8076,
0.8103,0.8156,0.8168,0.8187,0.8231,0.8271,0.8301,0.8302,0.8302,0.8310,
0.8375,0.8386,0.8387,0.8556,0.8580,0.8622,0.8652,0.8671,0.8674,0.8729,
0.8741,0.8743,0.8766,0.8774,0.8807,0.8814,0.8844,0.8854,0.9073,0.9074,
0.9119,0.9188,0.9273,0.9276,0.9354,0.9361,0.9363,0.9392,0.9499,0.9550,
0.9563,0.9584,0.9723,0.9767,0.9802,0.9827,0.9851,0.9921,0.9964,
Overall p-value after applying KStest on 269 p-values = 0.789235
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.