RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-08_20:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.90 13.3321 0.286316
2 to 25 15.60 41.0601 0.999085
3 to 26 15.54 17.5015 0.579080
4 to 27 15.52 23.0043 0.850888
5 to 28 15.69 26.5307 0.934681
6 to 29 15.76 17.4235 0.573953
7 to 30 15.85 23.4886 0.865992
8 to 31 15.83 13.8682 0.323590
9 to 32 15.95 23.3503 0.861810
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.037242
Tough bday spacings test for dh-ranFile-2018-07-08_20:31: 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 11 36 69 95 100 72 57 32 20 7 1
(O-E)^2/E 0.4 0.0 0.2 0.1 0.1 0.5 0.5 0.2 1.8 0.0 2.3
Birthday Spacings: Sum(O-E)^2/E= 5.962, p= 0.182
RESULTS OF GCD FOR dh-ranFile-2018-07-08_20:31
Euclid's algorithm:
p-value, steps to gcd: 0.426836
p-value, dist. of gcd's: 0.897119
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-08_20:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.423 0.323 0.451 0.614 0.385 0.039 0.922 0.765
Bits 8 to 15---> 0.993 0.403 0.356 0.948 0.320 0.679 0.353 0.546
Bits 16 to 23---> 0.050 0.949 0.147 0.719 0.743 0.291 0.785 0.876
Bits 24 to 31---> 0.319 0.053 0.762 0.270 0.893 0.051 0.964 0.741
KS test for the above 32 p values: 0.444
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-08_20:31,
p-values for 5 runs: 0.7423, 0.6247, 0.9301, 0.7563, 0.7407
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-08_20:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 216 211.4 0.099 0.099
r= 29 5182 5134.0 0.449 0.548
r= 30 23028 23103.0 0.244 0.792
r= 31 11574 11551.5 0.044 0.835
chi-square = 0.835 with df = 3; p-value = 0.159
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-08_20:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 221 211.4 0.434 0.434
r= 30 5141 5134.0 0.010 0.444
r= 31 23101 23103.0 0.000 0.444
r= 32 11537 11551.5 0.018 0.462
chi-square = 0.462 with df = 3; p-value = 0.073
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-08_20:31
b-rank test for bits 1 to 8, p=0.38187
b-rank test for bits 2 to 9, p=0.49763
b-rank test for bits 3 to 10, p=0.25981
b-rank test for bits 4 to 11, p=0.18910
b-rank test for bits 5 to 12, p=0.75961
b-rank test for bits 6 to 13, p=0.77501
b-rank test for bits 7 to 14, p=0.95630
b-rank test for bits 8 to 15, p=0.97383
b-rank test for bits 9 to 16, p=0.88849
b-rank test for bits 10 to 17, p=0.99822
b-rank test for bits 11 to 18, p=0.01034
b-rank test for bits 12 to 19, p=0.81086
b-rank test for bits 13 to 20, p=0.91714
b-rank test for bits 14 to 21, p=0.02111
b-rank test for bits 15 to 22, p=0.32586
b-rank test for bits 16 to 23, p=0.70632
b-rank test for bits 17 to 24, p=0.22407
b-rank test for bits 18 to 25, p=0.44270
b-rank test for bits 19 to 26, p=0.71579
b-rank test for bits 20 to 27, p=0.04845
b-rank test for bits 21 to 28, p=0.29840
b-rank test for bits 22 to 29, p=0.35942
b-rank test for bits 23 to 30, p=0.80237
b-rank test for bits 24 to 31, p=0.50783
b-rank test for bits 25 to 32, p=0.82934
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 = 0.414578
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-08_20:31
(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 141822 -0.20 0.419160
2 142060 0.35 0.637593
3 142019 0.26 0.601117
4 141834 -0.18 0.430145
5 141468 -1.03 0.151236
6 142573 1.55 0.939505
7 142847 2.19 0.985768
8 142000 0.21 0.583886
9 141820 -0.21 0.417335
10 142213 0.71 0.760996
11 141674 -0.55 0.291216
12 141289 -1.45 0.073617
13 142602 1.62 0.947210
14 142105 0.46 0.676227
15 141574 -0.78 0.216672
16 141754 -0.36 0.358332
17 141641 -0.63 0.265350
18 141111 -1.87 0.031073
19 142039 0.30 0.619043
20 142219 0.72 0.765322
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-08_20:31
Bits used No. missing words z-score p-value
23 to 32 141999 0.3092 0.621418
22 to 31 141827 -0.2839 0.388245
21 to 30 141558 -1.2115 0.112855
20 to 29 141392 -1.7839 0.037220
19 to 28 141534 -1.2942 0.097791
18 to 27 141745 -0.5667 0.285474
17 to 26 142056 0.5058 0.693487
16 to 25 141708 -0.6942 0.243765
15 to 24 141872 -0.1287 0.448788
14 to 23 141598 -1.0736 0.141512
13 to 22 141653 -0.8839 0.188376
12 to 21 141514 -1.3632 0.086409
11 to 20 142022 0.3885 0.651183
10 to 19 142066 0.5402 0.705485
9 to 18 141757 -0.5253 0.299696
8 to 17 142260 1.2092 0.886708
7 to 16 141835 -0.2563 0.398856
6 to 15 142182 0.9402 0.826453
5 to 14 141952 0.1471 0.558488
4 to 13 142547 2.1989 0.986056
3 to 12 142121 0.7299 0.767273
2 to 11 141913 0.0127 0.505049
1 to 10 141038 -3.0046 0.001330
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-08_20:31
Bits used No. missing words z-score p-value
28 to 32 142305 1.3413 0.910081
27 to 31 142118 0.7074 0.760327
26 to 30 141690 -0.7435 0.228592
25 to 29 141943 0.1141 0.545435
24 to 28 142176 0.9040 0.816993
23 to 27 142144 0.7955 0.786836
22 to 26 141928 0.0633 0.525232
21 to 25 141451 -1.5537 0.060133
20 to 24 141812 -0.3299 0.370726
19 to 23 141629 -0.9503 0.170987
18 to 22 142184 0.9311 0.824095
17 to 21 141391 -1.7571 0.039455
16 to 20 141796 -0.3842 0.350426
15 to 19 142476 1.9209 0.972629
14 to 18 142336 1.4463 0.925959
13 to 17 141813 -0.3265 0.372007
12 to 16 141936 0.0904 0.536018
11 to 15 141587 -1.0926 0.137275
10 to 14 141775 -0.4554 0.324427
9 to 13 142348 1.4870 0.931495
8 to 12 142222 1.0599 0.855405
7 to 11 141900 -0.0316 0.487385
6 to 10 142186 0.9379 0.825843
5 to 9 141899 -0.0350 0.486033
4 to 8 142146 0.8023 0.788802
3 to 7 141817 -0.3130 0.377147
2 to 6 142238 1.1141 0.867390
1 to 5 141589 -1.0859 0.138770
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-08_20:31
Bits used No. missing words z-score p-value
31 to 32 142068 0.4681 0.680127
30 to 31 142844 2.7571 0.997085
29 to 30 141576 -0.9833 0.162736
28 to 29 141748 -0.4759 0.317073
27 to 28 141595 -0.9272 0.176904
26 to 27 142418 1.5005 0.933258
25 to 26 141795 -0.3373 0.367962
24 to 25 141970 0.1790 0.571018
23 to 24 141633 -0.8151 0.207498
22 to 23 142143 0.6893 0.754680
21 to 22 142401 1.4504 0.926520
20 to 21 141816 -0.2753 0.391539
19 to 20 141819 -0.2665 0.394942
18 to 19 141844 -0.1927 0.423592
17 to 18 141764 -0.4287 0.334070
16 to 17 141670 -0.7060 0.240098
15 to 16 142017 0.3176 0.624610
14 to 15 142170 0.7689 0.779035
13 to 14 141907 -0.0069 0.497258
12 to 13 141235 -1.9892 0.023341
11 to 12 141097 -2.3963 0.008282
10 to 11 141609 -0.8859 0.187828
9 to 10 142084 0.5153 0.696811
8 to 9 141849 -0.1780 0.429375
7 to 8 141890 -0.0570 0.477264
6 to 7 142116 0.6096 0.728952
5 to 6 141536 -1.1013 0.135390
4 to 5 141769 -0.4140 0.339454
3 to 4 141834 -0.2222 0.412074
2 to 3 142464 1.6362 0.949101
1 to 2 142070 0.4740 0.682233
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-08_20:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2557.72 0.816 0.792849
Test results for specific bytes for dh-ranFile-2018-07-08_20:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2517.70 0.250 0.598825
2 to 9 2484.14 -0.224 0.411246
3 to 10 2545.93 0.650 0.742009
4 to 11 2544.42 0.628 0.735041
5 to 12 2526.38 0.373 0.645446
6 to 13 2520.89 0.295 0.616158
7 to 14 2449.77 -0.710 0.238750
8 to 15 2523.53 0.333 0.630362
9 to 16 2524.79 0.351 0.637048
10 to 17 2344.73 -2.196 0.014053
11 to 18 2463.74 -0.513 0.304041
12 to 19 2494.43 -0.079 0.468627
13 to 20 2489.67 -0.146 0.441950
14 to 21 2402.65 -1.377 0.084289
15 to 22 2379.71 -1.701 0.044450
16 to 23 2462.78 -0.526 0.299317
17 to 24 2507.54 0.107 0.542483
18 to 25 2615.82 1.638 0.949280
19 to 26 2583.50 1.181 0.881169
20 to 27 2657.55 2.228 0.987064
21 to 28 2643.27 2.026 0.978623
22 to 29 2584.39 1.194 0.883665
23 to 30 2501.98 0.028 0.511177
24 to 31 2538.80 0.549 0.708390
25 to 32 2477.60 -0.317 0.375706
CDPARK for dh-ranFile-2018-07-08_20:31: 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
3476 -2.1461 0.015932
3569 2.1005 0.982156
3507 -0.7306 0.232514
3529 0.2740 0.607947
3505 -0.8219 0.205562
3532 0.4110 0.659449
3499 -1.0959 0.136563
3516 -0.3196 0.374623
3483 -1.8265 0.033889
3547 1.0959 0.863437
Square side=100, avg. no. parked=3516.30 sample std.=27.16
p-value of the KSTEST for those 10 p-values: 0.359014
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-08_20:31
0.3177,0.8173,0.7741,0.3323,0.0442,0.9288,0.1025,0.5550,0.9116,0.9664,
The KS test for those 10 p-values: 0.429281
The 3DSPHERES test for dh-ranFile-2018-07-08_20:31
sample no r^3 equiv. uni.
1 34.127 0.679404
2 6.701 0.200168
3 51.840 0.822358
4 41.182 0.746586
5 14.512 0.383524
6 12.493 0.340611
7 14.792 0.389247
8 12.088 0.331646
9 1.854 0.059921
10 50.203 0.812398
11 39.927 0.735764
12 44.065 0.769803
13 54.524 0.837563
14 12.343 0.337309
15 4.511 0.139610
16 57.972 0.855202
17 95.369 0.958372
18 84.204 0.939602
19 2.908 0.092385
20 17.323 0.438665
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.663630
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-08_20:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 0.1 -0.6 1.5 0.4 0.4
1.2 -0.7 0.9 2.2 -0.8 -1.3
-0.4 -0.4 -0.0 0.9 -1.4 2.0
-1.2 0.5 -0.3 -1.7 1.1 0.0
1.0 -0.0 -0.3 -1.6 0.9 -0.2
0.3 0.4 2.0 0.0 1.7 -1.9
1.9 -1.3 0.9 -0.7 0.1 -1.0
-1.1
Chi-square with 42 degrees of freedom:50.059212
z-score=0.879332, p-value=0.816040
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-08_20:31
Test no p-value
1 0.027349
2 0.005173
3 0.049266
4 0.196728
5 0.601697
6 0.020040
7 0.071562
8 0.199754
9 0.814561
10 0.624038
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.002016
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-08_20:31:
(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 66596 0.07 66709 0.03
3 25000.00 25095 0.36 24908 0.34
4 6666.67 6683 0.04 6672 0.00
5 1388.89 1343 1.52 1447 2.43
6 238.10 249 0.50 234 0.07
7 34.72 28 1.30 23 3.96
8 4.96 5 0.00 6 0.22
p=0.29528 p=0.68335
Number of rngs required: 688350, p-value: 0.476
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-08_20:31
No. of wins: Observed Expected
98539 98585.9
z-score=-0.210, pvalue=0.41700
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66774 66666.7 0.173 0.173
2 37457 37654.3 1.034 1.207
3 26949 26954.7 0.001 1.208
4 19078 19313.5 2.871 4.079
5 13905 13851.4 0.207 4.286
6 9938 9943.5 0.003 4.289
7 7168 7145.0 0.074 4.363
8 5201 5139.1 0.746 5.109
9 3679 3699.9 0.118 5.227
10 2721 2666.3 1.122 6.349
11 1933 1923.3 0.049 6.398
12 1379 1388.7 0.068 6.466
13 1057 1003.7 2.829 9.295
14 759 726.1 1.487 10.782
15 548 525.8 0.934 11.716
16 395 381.2 0.503 12.219
17 305 276.5 2.929 15.148
18 202 200.8 0.007 15.155
19 150 146.0 0.110 15.266
20 104 106.2 0.046 15.312
21 298 287.1 0.413 15.725
Chisq= 15.72 for 20 degrees of freedom, p= 0.26644
SUMMARY of craptest
p-value for no. of wins: 0.416998
p-value for throws/game: 0.266442
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-08_20:31
No. of wins: Observed Expected
98774 98585.9
z-score= 0.841, pvalue=0.79996
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66689 66666.7 0.007 0.007
2 37639 37654.3 0.006 0.014
3 27058 26954.7 0.396 0.409
4 19155 19313.5 1.300 1.709
5 13726 13851.4 1.136 2.845
6 10012 9943.5 0.471 3.316
7 7209 7145.0 0.573 3.889
8 5130 5139.1 0.016 3.905
9 3692 3699.9 0.017 3.922
10 2688 2666.3 0.177 4.099
11 1930 1923.3 0.023 4.122
12 1445 1388.7 2.279 6.401
13 1029 1003.7 0.637 7.038
14 729 726.1 0.011 7.049
15 508 525.8 0.605 7.654
16 356 381.2 1.660 9.314
17 270 276.5 0.155 9.468
18 203 200.8 0.023 9.492
19 159 146.0 1.160 10.652
20 86 106.2 3.847 14.500
21 287 287.1 0.000 14.500
Chisq= 14.50 for 20 degrees of freedom, p= 0.19572
SUMMARY of craptest
p-value for no. of wins: 0.799960
p-value for throws/game: 0.195716
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0013,0.0020,0.0052,0.0083,0.0103,0.0141,0.0159,0.0200,0.0211,0.0233,
0.0273,0.0311,0.0339,0.0372,0.0372,0.0392,0.0395,0.0442,0.0445,0.0485,
0.0493,0.0500,0.0509,0.0528,0.0599,0.0601,0.0716,0.0729,0.0736,0.0843,
0.0864,0.0924,0.0978,0.1025,0.1129,0.1354,0.1366,0.1373,0.1388,0.1396,
0.1415,0.1465,0.1512,0.1590,0.1627,0.1710,0.1769,0.1815,0.1878,0.1884,
0.1891,0.1957,0.1967,0.1998,0.2002,0.2056,0.2075,0.2167,0.2241,0.2286,
0.2325,0.2388,0.2401,0.2438,0.2598,0.2653,0.2664,0.2704,0.2855,0.2863,
0.2909,0.2912,0.2953,0.2984,0.2993,0.2997,0.3040,0.3171,0.3177,0.3188,
0.3205,0.3231,0.3236,0.3244,0.3259,0.3316,0.3323,0.3341,0.3373,0.3395,
0.3406,0.3504,0.3534,0.3556,0.3583,0.3590,0.3594,0.3680,0.3707,0.3720,
0.3746,0.3757,0.3771,0.3819,0.3835,0.3851,0.3882,0.3892,0.3915,0.3949,
0.3989,0.4032,0.4112,0.4121,0.4146,0.4170,0.4173,0.4192,0.4232,0.4236,
0.4268,0.4293,0.4294,0.4301,0.4387,0.4420,0.4427,0.4439,0.4488,0.4512,
0.4686,0.4757,0.4773,0.4860,0.4874,0.4973,0.4976,0.5050,0.5078,0.5112,
0.5252,0.5360,0.5425,0.5454,0.5459,0.5550,0.5585,0.5710,0.5740,0.5791,
0.5839,0.5988,0.6011,0.6017,0.6079,0.6138,0.6162,0.6190,0.6214,0.6240,
0.6246,0.6247,0.6304,0.6370,0.6376,0.6454,0.6512,0.6594,0.6636,0.6762,
0.6794,0.6794,0.6801,0.6822,0.6834,0.6935,0.6968,0.7055,0.7063,0.7084,
0.7158,0.7190,0.7290,0.7350,0.7358,0.7407,0.7408,0.7420,0.7423,0.7428,
0.7466,0.7547,0.7563,0.7596,0.7603,0.7610,0.7624,0.7648,0.7653,0.7673,
0.7698,0.7741,0.7750,0.7790,0.7849,0.7868,0.7888,0.7928,0.8000,0.8024,
0.8109,0.8124,0.8146,0.8160,0.8170,0.8173,0.8224,0.8241,0.8258,0.8265,
0.8293,0.8376,0.8509,0.8552,0.8554,0.8618,0.8634,0.8660,0.8674,0.8761,
0.8812,0.8837,0.8867,0.8885,0.8928,0.8971,0.9101,0.9116,0.9171,0.9219,
0.9260,0.9265,0.9288,0.9301,0.9315,0.9333,0.9347,0.9395,0.9396,0.9472,
0.9483,0.9485,0.9491,0.9493,0.9563,0.9584,0.9641,0.9664,0.9726,0.9738,
0.9786,0.9822,0.9858,0.9861,0.9871,0.9931,0.9971,0.9982,0.9991,
Overall p-value after applying KStest on 269 p-values = 0.331731
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.