RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-06_23:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.50 35.9557 0.995351
2 to 25 15.55 17.4835 0.577897
3 to 26 15.56 13.7543 0.315588
4 to 27 15.58 27.9457 0.954423
5 to 28 15.71 24.1928 0.885709
6 to 29 15.64 14.5208 0.370042
7 to 30 15.83 15.4471 0.436690
8 to 31 15.85 21.1709 0.781260
9 to 32 15.59 20.8927 0.768874
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.089502
Tough bday spacings test for dh-ranFile-2018-07-06_23:31: 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 27 85 96 109 75 48 27 18 4 2
(O-E)^2/E 0.0 2.5 1.9 0.0 1.3 0.1 0.3 0.3 0.7 1.0 1.0
Birthday Spacings: Sum(O-E)^2/E= 9.198, p= 0.487
RESULTS OF GCD FOR dh-ranFile-2018-07-06_23:31
Euclid's algorithm:
p-value, steps to gcd: 0.681631
p-value, dist. of gcd's: 0.473546
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-06_23:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.967 0.928 0.205 0.573 0.209 0.620 0.626 0.167
Bits 8 to 15---> 0.107 0.718 0.154 0.310 0.093 0.775 0.514 0.878
Bits 16 to 23---> 0.357 0.657 0.376 0.906 0.737 0.963 0.007 0.293
Bits 24 to 31---> 0.919 0.464 0.739 0.581 0.756 0.396 0.775 0.168
KS test for the above 32 p values: 0.109
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-06_23:31,
p-values for 5 runs: 0.9231, 0.7535, 0.0005, 0.8811, 0.1476
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-06_23:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 201 211.4 0.513 0.513
r= 29 5099 5134.0 0.239 0.752
r= 30 23246 23103.0 0.885 1.637
r= 31 11454 11551.5 0.823 2.460
chi-square = 2.460 with df = 3; p-value = 0.517
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-06_23:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 205 211.4 0.195 0.195
r= 30 5142 5134.0 0.012 0.207
r= 31 22903 23103.0 1.732 1.939
r= 32 11750 11551.5 3.410 5.350
chi-square = 5.350 with df = 3; p-value = 0.852
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-06_23:31
b-rank test for bits 1 to 8, p=0.35819
b-rank test for bits 2 to 9, p=0.19241
b-rank test for bits 3 to 10, p=0.49890
b-rank test for bits 4 to 11, p=0.39462
b-rank test for bits 5 to 12, p=0.71496
b-rank test for bits 6 to 13, p=0.61645
b-rank test for bits 7 to 14, p=0.28018
b-rank test for bits 8 to 15, p=0.60574
b-rank test for bits 9 to 16, p=0.32768
b-rank test for bits 10 to 17, p=0.87861
b-rank test for bits 11 to 18, p=0.15567
b-rank test for bits 12 to 19, p=0.32434
b-rank test for bits 13 to 20, p=0.15289
b-rank test for bits 14 to 21, p=0.94895
b-rank test for bits 15 to 22, p=0.59200
b-rank test for bits 16 to 23, p=0.10576
b-rank test for bits 17 to 24, p=0.20744
b-rank test for bits 18 to 25, p=0.53647
b-rank test for bits 19 to 26, p=0.02983
b-rank test for bits 20 to 27, p=0.32024
b-rank test for bits 21 to 28, p=0.71812
b-rank test for bits 22 to 29, p=0.77984
b-rank test for bits 23 to 30, p=0.91035
b-rank test for bits 24 to 31, p=0.38873
b-rank test for bits 25 to 32, p=0.68018
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 = 0.814701
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-06_23:31
(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 141692 -0.51 0.305804
2 142100 0.45 0.672017
3 141594 -0.74 0.230637
4 142283 0.87 0.808685
5 142413 1.18 0.880362
6 141386 -1.22 0.110715
7 142267 0.84 0.798332
8 142244 0.78 0.782875
9 141383 -1.23 0.109397
10 141214 -1.62 0.052124
11 142019 0.26 0.601117
12 140793 -2.61 0.004550
13 142105 0.46 0.676227
14 141309 -1.40 0.080362
15 142678 1.80 0.963749
16 140967 -2.20 0.013843
17 141729 -0.42 0.336756
18 142067 0.37 0.643708
19 141525 -0.90 0.184602
20 141840 -0.16 0.435658
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-06_23:31
Bits used No. missing words z-score p-value
23 to 32 142267 1.2333 0.891276
22 to 31 141889 -0.0701 0.472056
21 to 30 141852 -0.1977 0.421644
20 to 29 141834 -0.2598 0.397525
19 to 28 142264 1.2230 0.889335
18 to 27 141826 -0.2873 0.386924
17 to 26 141867 -0.1460 0.441974
16 to 25 142064 0.5333 0.703103
15 to 24 141858 -0.1770 0.429754
14 to 23 142501 2.0402 0.979337
13 to 22 142357 1.5437 0.938668
12 to 21 141804 -0.3632 0.358225
11 to 20 141752 -0.5425 0.293731
10 to 19 142325 1.4333 0.924120
9 to 18 142301 1.3506 0.911586
8 to 17 141976 0.2299 0.590914
7 to 16 141990 0.2782 0.609560
6 to 15 142201 1.0058 0.842734
5 to 14 142096 0.6437 0.740112
4 to 13 142256 1.1954 0.884037
3 to 12 142143 0.8058 0.789809
2 to 11 141725 -0.6356 0.262512
1 to 10 141490 -1.4460 0.074093
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-06_23:31
Bits used No. missing words z-score p-value
28 to 32 141725 -0.6248 0.266036
27 to 31 141985 0.2565 0.601221
26 to 30 142108 0.6735 0.749672
25 to 29 142245 1.1379 0.872411
24 to 28 141780 -0.4384 0.330546
23 to 27 141999 0.3040 0.619423
22 to 26 142584 2.2870 0.988903
21 to 25 141724 -0.6282 0.264924
20 to 24 142134 0.7616 0.776849
19 to 23 141466 -1.5028 0.066444
18 to 22 141540 -1.2520 0.105291
17 to 21 141920 0.0362 0.514426
16 to 20 141720 -0.6418 0.260503
15 to 19 141791 -0.4011 0.344166
14 to 18 141960 0.1718 0.568188
13 to 17 141865 -0.1503 0.440275
12 to 16 141463 -1.5130 0.065142
11 to 15 142297 1.3141 0.905600
10 to 14 141653 -0.8689 0.192447
9 to 13 141699 -0.7130 0.237928
8 to 12 141910 0.0023 0.500906
7 to 11 141698 -0.7164 0.236881
6 to 10 142226 1.0735 0.858467
5 to 9 141784 -0.4248 0.335474
4 to 8 142194 0.9650 0.832723
3 to 7 141820 -0.3028 0.381016
2 to 6 141902 -0.0248 0.490088
1 to 5 141537 -1.2621 0.103450
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-06_23:31
Bits used No. missing words z-score p-value
31 to 32 141667 -0.7148 0.237355
30 to 31 141717 -0.5673 0.285240
29 to 30 142218 0.9105 0.818729
28 to 29 141560 -1.0305 0.151394
27 to 28 142251 1.0079 0.843243
26 to 27 141767 -0.4199 0.337297
25 to 26 142013 0.3058 0.620126
24 to 25 141663 -0.7266 0.233724
23 to 24 142349 1.2970 0.902678
22 to 23 142500 1.7424 0.959280
21 to 22 141702 -0.6116 0.270404
20 to 21 142430 1.5359 0.937719
19 to 20 141810 -0.2930 0.384758
18 to 19 141687 -0.6558 0.255963
17 to 18 141953 0.1288 0.551250
16 to 17 141451 -1.3520 0.088187
15 to 16 141738 -0.5054 0.306640
14 to 15 141753 -0.4612 0.322345
13 to 14 142186 0.8161 0.792789
12 to 13 141372 -1.5850 0.056478
11 to 12 141946 0.1082 0.543070
10 to 11 142137 0.6716 0.749079
9 to 10 141964 0.1613 0.564059
8 to 9 142206 0.8751 0.809249
7 to 8 142109 0.5890 0.722068
6 to 7 141565 -1.0157 0.154881
5 to 6 141879 -0.0895 0.464355
4 to 5 141693 -0.6381 0.261691
3 to 4 141736 -0.5113 0.304571
2 to 3 142469 1.6509 0.950625
1 to 2 142825 2.7011 0.996544
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-06_23:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2506.05 0.086 0.534119
Test results for specific bytes for dh-ranFile-2018-07-06_23:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2417.91 -1.161 0.122837
2 to 9 2573.60 1.041 0.851043
3 to 10 2382.38 -1.663 0.048113
4 to 11 2444.84 -0.780 0.217674
5 to 12 2464.81 -0.498 0.309383
6 to 13 2341.81 -2.237 0.012637
7 to 14 2425.48 -1.054 0.145964
8 to 15 2475.14 -0.352 0.362591
9 to 16 2557.10 0.808 0.790329
10 to 17 2586.31 1.221 0.888879
11 to 18 2360.24 -1.976 0.024050
12 to 19 2511.78 0.167 0.566141
13 to 20 2614.72 1.622 0.947642
14 to 21 2309.39 -2.696 0.003513
15 to 22 2576.55 1.083 0.860492
16 to 23 2384.29 -1.636 0.050884
17 to 24 2328.80 -2.421 0.007735
18 to 25 2462.41 -0.532 0.297482
19 to 26 2431.28 -0.972 0.165580
20 to 27 2490.21 -0.138 0.444930
21 to 28 2585.08 1.203 0.885566
22 to 29 2577.97 1.103 0.864925
23 to 30 2446.43 -0.758 0.224340
24 to 31 2563.90 0.904 0.816933
25 to 32 2553.01 0.750 0.773293
CDPARK for dh-ranFile-2018-07-06_23:31: 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
3569 2.1005 0.982156
3571 2.1918 0.985802
3533 0.4566 0.676028
3501 -1.0046 0.157553
3546 1.0502 0.853193
3533 0.4566 0.676028
3542 0.8676 0.807188
3513 -0.4566 0.323972
3525 0.0913 0.536383
3505 -0.8219 0.205562
Square side=100, avg. no. parked=3533.80 sample std.=22.93
p-value of the KSTEST for those 10 p-values: 0.226182
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-06_23:31
0.3430,0.4771,0.4243,0.8463,0.2587,0.3265,0.8934,0.7853,0.7462,0.5120,
The KS test for those 10 p-values: 0.548930
The 3DSPHERES test for dh-ranFile-2018-07-06_23:31
sample no r^3 equiv. uni.
1 47.679 0.795932
2 19.806 0.483259
3 45.891 0.783402
4 45.908 0.783520
5 5.936 0.179527
6 0.312 0.010351
7 35.171 0.690372
8 12.997 0.351593
9 0.239 0.007931
10 7.906 0.231660
11 17.388 0.439878
12 18.593 0.461923
13 52.068 0.823703
14 21.926 0.518502
15 6.429 0.192888
16 6.006 0.181428
17 40.008 0.736477
18 15.746 0.408363
19 13.895 0.370719
20 1.812 0.058627
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.294662
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-06_23:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 -0.3 -0.4 -0.3 1.1 0.3
1.8 1.3 0.3 1.2 -1.3 -1.0
0.1 1.3 -0.8 0.8 -1.1 -0.2
-0.1 1.9 0.1 0.3 0.5 -2.6
-1.6 1.4 -0.2 -0.7 -0.7 -0.2
-0.9 -2.4 0.9 0.2 0.6 -1.4
2.6 1.1 1.7 -0.7 2.4 1.0
-0.1
Chi-square with 42 degrees of freedom:60.160455
z-score=1.981468, p-value=0.965777
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-06_23:31
Test no p-value
1 0.158446
2 0.016149
3 0.106237
4 0.004819
5 0.091501
6 0.057418
7 0.186975
8 0.035948
9 0.811518
10 0.363812
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000116
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-06_23:31:
(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 66357 1.44 66748 0.10
3 25000.00 25174 1.21 24837 1.06
4 6666.67 6753 1.12 6695 0.12
5 1388.89 1423 0.84 1437 1.67
6 238.10 239 0.00 240 0.02
7 34.72 43 1.97 33 0.09
8 4.96 10 5.12 9 3.29
p=0.93110 p=0.61379
Number of rngs required: 688248, p-value: 0.429
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-06_23:31
No. of wins: Observed Expected
98231 98585.9
z-score=-1.587, pvalue=0.05624
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66632 66666.7 0.018 0.018
2 37553 37654.3 0.273 0.291
3 26873 26954.7 0.248 0.538
4 19410 19313.5 0.483 1.021
5 13825 13851.4 0.050 1.071
6 10047 9943.5 1.076 2.148
7 7273 7145.0 2.292 4.440
8 5094 5139.1 0.395 4.835
9 3668 3699.9 0.274 5.110
10 2706 2666.3 0.591 5.701
11 1909 1923.3 0.107 5.808
12 1363 1388.7 0.477 6.285
13 1030 1003.7 0.688 6.973
14 743 726.1 0.391 7.365
15 523 525.8 0.015 7.380
16 350 381.2 2.546 9.926
17 282 276.5 0.108 10.034
18 212 200.8 0.621 10.655
19 141 146.0 0.170 10.825
20 86 106.2 3.847 14.672
21 280 287.1 0.176 14.849
Chisq= 14.85 for 20 degrees of freedom, p= 0.21500
SUMMARY of craptest
p-value for no. of wins: 0.056241
p-value for throws/game: 0.215001
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-06_23:31
No. of wins: Observed Expected
98326 98585.9
z-score=-1.162, pvalue=0.12257
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66470 66666.7 0.580 0.580
2 37798 37654.3 0.548 1.128
3 27162 26954.7 1.594 2.722
4 19085 19313.5 2.703 5.425
5 13979 13851.4 1.175 6.600
6 9797 9943.5 2.160 8.759
7 7225 7145.0 0.895 9.655
8 5204 5139.1 0.820 10.475
9 3732 3699.9 0.279 10.754
10 2587 2666.3 2.358 13.112
11 1963 1923.3 0.818 13.931
12 1453 1388.7 2.973 16.904
13 920 1003.7 6.982 23.886
14 687 726.1 2.110 25.996
15 541 525.8 0.437 26.433
16 373 381.2 0.174 26.608
17 291 276.5 0.756 27.364
18 193 200.8 0.305 27.669
19 142 146.0 0.109 27.778
20 96 106.2 0.982 28.760
21 302 287.1 0.772 29.532
Chisq= 29.53 for 20 degrees of freedom, p= 0.92220
SUMMARY of craptest
p-value for no. of wins: 0.122569
p-value for throws/game: 0.922202
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0001,0.0005,0.0035,0.0046,0.0048,0.0071,0.0077,0.0079,0.0104,0.0126,
0.0138,0.0161,0.0240,0.0298,0.0359,0.0481,0.0509,0.0521,0.0562,0.0565,
0.0574,0.0586,0.0651,0.0664,0.0741,0.0804,0.0882,0.0895,0.0915,0.0935,
0.1035,0.1053,0.1058,0.1062,0.1074,0.1092,0.1094,0.1107,0.1226,0.1228,
0.1460,0.1476,0.1514,0.1529,0.1539,0.1549,0.1557,0.1576,0.1584,0.1656,
0.1668,0.1678,0.1795,0.1814,0.1846,0.1870,0.1924,0.1924,0.1929,0.2049,
0.2056,0.2074,0.2093,0.2150,0.2177,0.2243,0.2262,0.2306,0.2317,0.2337,
0.2369,0.2374,0.2379,0.2560,0.2587,0.2605,0.2617,0.2625,0.2649,0.2660,
0.2704,0.2802,0.2852,0.2927,0.2937,0.2947,0.2975,0.3046,0.3058,0.3066,
0.3094,0.3104,0.3156,0.3202,0.3223,0.3240,0.3243,0.3265,0.3277,0.3305,
0.3355,0.3368,0.3373,0.3430,0.3442,0.3516,0.3572,0.3582,0.3582,0.3626,
0.3638,0.3700,0.3707,0.3759,0.3810,0.3848,0.3869,0.3887,0.3946,0.3957,
0.3975,0.4084,0.4216,0.4243,0.4292,0.4298,0.4357,0.4367,0.4399,0.4403,
0.4420,0.4449,0.4619,0.4636,0.4644,0.4721,0.4735,0.4771,0.4833,0.4866,
0.4901,0.4989,0.5009,0.5120,0.5141,0.5144,0.5174,0.5185,0.5341,0.5364,
0.5365,0.5431,0.5489,0.5513,0.5641,0.5661,0.5682,0.5731,0.5779,0.5814,
0.5909,0.5920,0.6011,0.6012,0.6057,0.6096,0.6138,0.6165,0.6194,0.6201,
0.6203,0.6258,0.6437,0.6573,0.6720,0.6760,0.6760,0.6762,0.6802,0.6816,
0.6904,0.7031,0.7150,0.7181,0.7185,0.7221,0.7365,0.7371,0.7391,0.7401,
0.7462,0.7491,0.7497,0.7535,0.7559,0.7689,0.7733,0.7751,0.7751,0.7768,
0.7798,0.7813,0.7829,0.7834,0.7835,0.7853,0.7898,0.7903,0.7928,0.7959,
0.7983,0.8072,0.8087,0.8092,0.8115,0.8147,0.8169,0.8187,0.8237,0.8327,
0.8427,0.8432,0.8463,0.8510,0.8521,0.8532,0.8585,0.8605,0.8649,0.8724,
0.8776,0.8786,0.8804,0.8811,0.8840,0.8856,0.8857,0.8889,0.8893,0.8913,
0.8934,0.9027,0.9056,0.9056,0.9104,0.9116,0.9189,0.9222,0.9231,0.9241,
0.9277,0.9311,0.9377,0.9387,0.9476,0.9489,0.9506,0.9544,0.9593,0.9634,
0.9637,0.9658,0.9673,0.9793,0.9822,0.9858,0.9889,0.9954,0.9965,
Overall p-value after applying KStest on 269 p-values = 0.301110
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.