RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-12_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 15.70 14.9588 0.401553
2 to 25 15.98 13.6297 0.306878
3 to 26 16.03 17.4453 0.575389
4 to 27 15.40 26.5894 0.935629
5 to 28 16.24 23.5967 0.869185
6 to 29 15.89 13.7954 0.318470
7 to 30 15.71 16.5057 0.511687
8 to 31 15.93 13.7110 0.312558
9 to 32 15.87 13.5614 0.302135
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.494258
Tough bday spacings test for dh-ranFile-2018-07-12_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 6 27 82 99 104 75 52 32 10 6 7
(O-E)^2/E 1.1 2.5 1.0 0.0 0.4 0.1 0.0 0.2 1.6 0.1 2.1
Birthday Spacings: Sum(O-E)^2/E= 9.161, p= 0.483
RESULTS OF GCD FOR dh-ranFile-2018-07-12_12:31
Euclid's algorithm:
p-value, steps to gcd: 0.798583
p-value, dist. of gcd's: 0.442684
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-12_12:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.150 0.797 0.961 0.116 0.351 0.725 0.679 0.454
Bits 8 to 15---> 0.305 0.064 0.750 0.119 0.480 0.779 0.899 0.280
Bits 16 to 23---> 0.553 0.495 0.202 0.980 0.966 0.254 0.568 0.992
Bits 24 to 31---> 0.020 0.406 0.607 0.202 0.786 0.900 0.339 0.533
KS test for the above 32 p values: 0.104
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-12_12:31,
p-values for 5 runs: 0.9236, 0.6347, 0.4765, 0.2904, 0.4730
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-12_12:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 208 211.4 0.055 0.055
r= 29 5071 5134.0 0.773 0.829
r= 30 23194 23103.0 0.358 1.187
r= 31 11527 11551.5 0.052 1.239
chi-square = 1.239 with df = 3; p-value = 0.256
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-12_12:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 214 211.4 0.032 0.032
r= 30 5085 5134.0 0.468 0.499
r= 31 23184 23103.0 0.284 0.783
r= 32 11517 11551.5 0.103 0.886
chi-square = 0.886 with df = 3; p-value = 0.171
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-12_12:31
b-rank test for bits 1 to 8, p=0.13724
b-rank test for bits 2 to 9, p=0.65138
b-rank test for bits 3 to 10, p=0.14094
b-rank test for bits 4 to 11, p=0.29494
b-rank test for bits 5 to 12, p=0.08947
b-rank test for bits 6 to 13, p=0.91150
b-rank test for bits 7 to 14, p=0.20837
b-rank test for bits 8 to 15, p=0.61655
b-rank test for bits 9 to 16, p=0.49691
b-rank test for bits 10 to 17, p=0.16813
b-rank test for bits 11 to 18, p=0.62758
b-rank test for bits 12 to 19, p=0.01923
b-rank test for bits 13 to 20, p=0.40542
b-rank test for bits 14 to 21, p=0.01912
b-rank test for bits 15 to 22, p=0.79727
b-rank test for bits 16 to 23, p=0.90251
b-rank test for bits 17 to 24, p=0.21035
b-rank test for bits 18 to 25, p=0.14694
b-rank test for bits 19 to 26, p=0.42988
b-rank test for bits 20 to 27, p=0.18202
b-rank test for bits 21 to 28, p=0.55413
b-rank test for bits 22 to 29, p=0.73897
b-rank test for bits 23 to 30, p=0.76616
b-rank test for bits 24 to 31, p=0.68497
b-rank test for bits 25 to 32, p=0.85452
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 = 0.455245
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-12_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 141751 -0.37 0.355717
2 141949 0.09 0.536924
3 141887 -0.05 0.479196
4 141731 -0.42 0.338464
5 140901 -2.36 0.009239
6 142207 0.70 0.756626
7 141168 -1.73 0.041630
8 141966 0.13 0.552669
9 141497 -0.96 0.167676
10 142579 1.56 0.941167
11 142298 0.91 0.818089
12 142738 1.94 0.973575
13 141972 0.15 0.558207
14 140584 -3.10 0.000979
15 141679 -0.54 0.295235
16 142743 1.95 0.974282
17 141680 -0.54 0.296042
18 142371 1.08 0.859632
19 141307 -1.41 0.079667
20 142039 0.30 0.619043
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-12_12:31
Bits used No. missing words z-score p-value
23 to 32 142077 0.5782 0.718426
22 to 31 141622 -0.9908 0.160893
21 to 30 141693 -0.7460 0.227844
20 to 29 141912 0.0092 0.503673
19 to 28 142452 1.8713 0.969347
18 to 27 141816 -0.3218 0.373792
17 to 26 141871 -0.1322 0.447424
16 to 25 141540 -1.2736 0.101411
15 to 24 142022 0.3885 0.651183
14 to 23 141912 0.0092 0.503673
13 to 22 141964 0.1885 0.574764
12 to 21 142735 2.8471 0.997794
11 to 20 141854 -0.1908 0.424344
10 to 19 141940 0.1058 0.542113
9 to 18 142434 1.8092 0.964791
8 to 17 141519 -1.3460 0.089157
7 to 16 141886 -0.0804 0.467940
6 to 15 142311 1.3851 0.916984
5 to 14 141894 -0.0529 0.478921
4 to 13 141856 -0.1839 0.427047
3 to 12 141462 -1.5425 0.061474
2 to 11 142014 0.3609 0.640925
1 to 10 142118 0.7196 0.764100
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-12_12:31
Bits used No. missing words z-score p-value
28 to 32 141418 -1.6655 0.047904
27 to 31 142131 0.7514 0.773801
26 to 30 141616 -0.9943 0.160029
25 to 29 141772 -0.4655 0.320778
24 to 28 142231 1.0904 0.862233
23 to 27 142176 0.9040 0.816993
22 to 26 141966 0.1921 0.576169
21 to 25 141560 -1.1842 0.118173
20 to 24 141660 -0.8452 0.199003
19 to 23 142163 0.8599 0.805077
18 to 22 142198 0.9785 0.836097
17 to 21 141921 0.0396 0.515778
16 to 20 142196 0.9718 0.834416
15 to 19 141764 -0.4926 0.311132
14 to 18 142007 0.3311 0.629710
13 to 17 142589 2.3040 0.989388
12 to 16 141984 0.2531 0.599912
11 to 15 141640 -0.9130 0.180626
10 to 14 141760 -0.5062 0.306357
9 to 13 141882 -0.0926 0.463093
8 to 12 141859 -0.1706 0.432265
7 to 11 141515 -1.3367 0.090658
6 to 10 142435 1.7819 0.962620
5 to 9 142023 0.3853 0.650001
4 to 8 141777 -0.4486 0.326869
3 to 7 142058 0.5040 0.692857
2 to 6 141730 -0.6079 0.271628
1 to 5 141824 -0.2893 0.386193
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-12_12:31
Bits used No. missing words z-score p-value
31 to 32 141974 0.1908 0.575646
30 to 31 141894 -0.0452 0.481966
29 to 30 141641 -0.7915 0.214316
28 to 29 141487 -1.2458 0.106417
27 to 28 141531 -1.1160 0.132207
26 to 27 142404 1.4592 0.927745
25 to 26 142035 0.3707 0.644573
24 to 25 141518 -1.1544 0.124175
23 to 24 141875 -0.1013 0.459669
22 to 23 142393 1.4268 0.923175
21 to 22 142053 0.4238 0.664146
20 to 21 141269 -1.8889 0.029454
19 to 20 142150 0.7099 0.761130
18 to 19 141761 -0.4376 0.330856
17 to 18 142113 0.6008 0.726012
16 to 17 142199 0.8545 0.803582
15 to 16 142180 0.7984 0.787691
14 to 15 141950 0.1200 0.547747
13 to 14 142361 1.3324 0.908629
12 to 13 141716 -0.5703 0.284239
11 to 12 142256 1.0226 0.846758
10 to 11 141543 -1.0806 0.139933
9 to 10 142216 0.9046 0.817170
8 to 9 142263 1.0433 0.851589
7 to 8 142129 0.6480 0.741506
6 to 7 142182 0.8043 0.789399
5 to 6 141229 -2.0069 0.022382
4 to 5 141605 -0.8977 0.184665
3 to 4 140786 -3.3137 0.000460
2 to 3 141612 -0.8771 0.190222
1 to 2 141546 -1.0718 0.141912
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-12_12:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2463.07 -0.522 0.300728
Test results for specific bytes for dh-ranFile-2018-07-12_12:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2542.98 0.608 0.728347
2 to 9 2417.79 -1.163 0.122490
3 to 10 2490.86 -0.129 0.448567
4 to 11 2468.98 -0.439 0.330443
5 to 12 2597.36 1.377 0.915724
6 to 13 2471.67 -0.401 0.344323
7 to 14 2399.74 -1.418 0.078104
8 to 15 2504.05 0.057 0.522861
9 to 16 2394.04 -1.499 0.066993
10 to 17 2569.96 0.989 0.838764
11 to 18 2495.12 -0.069 0.472499
12 to 19 2548.24 0.682 0.752433
13 to 20 2624.47 1.760 0.960817
14 to 21 2334.65 -2.338 0.009681
15 to 22 2550.06 0.708 0.760497
16 to 23 2494.46 -0.078 0.468750
17 to 24 2495.10 -0.069 0.472353
18 to 25 2438.21 -0.874 0.191116
19 to 26 2377.13 -1.738 0.041134
20 to 27 2435.62 -0.910 0.181287
21 to 28 2444.85 -0.780 0.217716
22 to 29 2504.26 0.060 0.524029
23 to 30 2572.25 1.022 0.846545
24 to 31 2486.09 -0.197 0.422012
25 to 32 2398.99 -1.429 0.076568
CDPARK for dh-ranFile-2018-07-12_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
3499 -1.0959 0.136563
3498 -1.1416 0.126820
3531 0.3653 0.642555
3502 -0.9589 0.168804
3563 1.8265 0.966111
3524 0.0457 0.518210
3547 1.0959 0.863437
3498 -1.1416 0.126820
3538 0.6849 0.753306
3567 2.0091 0.977738
Square side=100, avg. no. parked=3526.70 sample std.=25.56
p-value of the KSTEST for those 10 p-values: 0.424176
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-12_12:31
0.6412,0.7143,0.9271,0.8281,0.1259,0.5714,0.5946,0.5672,0.6865,0.2298,
The KS test for those 10 p-values: 0.390481
The 3DSPHERES test for dh-ranFile-2018-07-12_12:31
sample no r^3 equiv. uni.
1 82.694 0.936485
2 30.262 0.635319
3 26.031 0.580090
4 13.596 0.364404
5 19.746 0.482214
6 9.724 0.276852
7 7.562 0.222798
8 21.955 0.518966
9 7.525 0.221856
10 35.420 0.692926
11 11.537 0.319256
12 26.934 0.592541
13 8.518 0.247188
14 117.830 0.980310
15 40.155 0.737757
16 36.955 0.708241
17 24.057 0.551520
18 95.713 0.958846
19 19.662 0.480762
20 34.002 0.678067
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.296594
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-12_12:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 1.3 -0.4 1.4 0.1 -1.3
-2.5 -0.3 2.2 -0.7 -0.1 -0.7
-1.0 1.8 -0.6 1.0 -0.7 -0.3
0.7 -1.6 -1.1 0.8 1.4 0.5
-0.1 0.1 0.4 0.0 0.5 0.3
-0.3 -1.0 -1.1 0.1 1.7 0.4
1.7 0.2 0.1 -0.7 0.9 3.0
-0.1
Chi-square with 42 degrees of freedom:50.049364
z-score=0.878258, p-value=0.815786
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-12_12:31
Test no p-value
1 0.354317
2 0.398757
3 0.780706
4 0.094494
5 0.489382
6 0.024434
7 0.195661
8 0.022725
9 0.397542
10 0.234565
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.039389
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-12_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 66504 0.40 66820 0.35
3 25000.00 25196 1.54 24839 1.04
4 6666.67 6667 0.00 6633 0.17
5 1388.89 1346 1.32 1412 0.38
6 238.10 241 0.04 250 0.60
7 34.72 38 0.31 35 0.00
8 4.96 7 0.84 10 5.12
p=0.38296 p=0.73614
Number of rngs required: 688922, p-value: 0.725
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-12_12:31
No. of wins: Observed Expected
98358 98585.9
z-score=-1.019, pvalue=0.15407
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66453 66666.7 0.685 0.685
2 37721 37654.3 0.118 0.803
3 26901 26954.7 0.107 0.910
4 19464 19313.5 1.173 2.083
5 14034 13851.4 2.407 4.490
6 9949 9943.5 0.003 4.493
7 7051 7145.0 1.237 5.730
8 5095 5139.1 0.378 6.108
9 3821 3699.9 3.966 10.074
10 2569 2666.3 3.551 13.625
11 1930 1923.3 0.023 13.648
12 1351 1388.7 1.026 14.674
13 1022 1003.7 0.333 15.007
14 733 726.1 0.065 15.071
15 527 525.8 0.003 15.074
16 398 381.2 0.745 15.819
17 273 276.5 0.045 15.864
18 178 200.8 2.595 18.459
19 143 146.0 0.061 18.520
20 106 106.2 0.000 18.521
21 281 287.1 0.130 18.651
Chisq= 18.65 for 20 degrees of freedom, p= 0.45540
SUMMARY of craptest
p-value for no. of wins: 0.154074
p-value for throws/game: 0.455404
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-12_12:31
No. of wins: Observed Expected
98587 98585.9
z-score= 0.005, pvalue=0.50204
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66699 66666.7 0.016 0.016
2 37480 37654.3 0.807 0.823
3 26906 26954.7 0.088 0.911
4 19373 19313.5 0.184 1.094
5 13723 13851.4 1.191 2.285
6 10127 9943.5 3.385 5.670
7 7245 7145.0 1.399 7.069
8 5199 5139.1 0.699 7.767
9 3686 3699.9 0.052 7.819
10 2710 2666.3 0.716 8.536
11 1867 1923.3 1.650 10.185
12 1418 1388.7 0.616 10.802
13 975 1003.7 0.822 11.623
14 717 726.1 0.115 11.738
15 504 525.8 0.907 12.645
16 370 381.2 0.326 12.971
17 264 276.5 0.569 13.540
18 174 200.8 3.584 17.124
19 152 146.0 0.248 17.372
20 107 106.2 0.006 17.378
21 304 287.1 0.993 18.371
Chisq= 18.37 for 20 degrees of freedom, p= 0.43703
SUMMARY of craptest
p-value for no. of wins: 0.502037
p-value for throws/game: 0.437027
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0005,0.0010,0.0092,0.0097,0.0191,0.0192,0.0204,0.0224,0.0227,0.0244,
0.0295,0.0394,0.0411,0.0416,0.0479,0.0615,0.0641,0.0670,0.0766,0.0781,
0.0797,0.0892,0.0895,0.0907,0.0945,0.1014,0.1044,0.1064,0.1156,0.1182,
0.1186,0.1225,0.1242,0.1259,0.1268,0.1268,0.1322,0.1366,0.1372,0.1399,
0.1409,0.1419,0.1469,0.1503,0.1541,0.1600,0.1609,0.1677,0.1681,0.1688,
0.1713,0.1806,0.1813,0.1820,0.1847,0.1902,0.1911,0.1957,0.1990,0.2016,
0.2020,0.2084,0.2103,0.2143,0.2177,0.2219,0.2228,0.2278,0.2298,0.2346,
0.2472,0.2540,0.2563,0.2716,0.2769,0.2799,0.2842,0.2904,0.2949,0.2952,
0.2960,0.2966,0.3007,0.3021,0.3048,0.3064,0.3069,0.3111,0.3126,0.3185,
0.3193,0.3208,0.3269,0.3304,0.3309,0.3385,0.3395,0.3443,0.3511,0.3543,
0.3557,0.3644,0.3738,0.3830,0.3862,0.3905,0.3975,0.3988,0.4016,0.4054,
0.4062,0.4220,0.4242,0.4243,0.4270,0.4299,0.4323,0.4370,0.4427,0.4474,
0.4486,0.4545,0.4552,0.4554,0.4597,0.4631,0.4679,0.4687,0.4724,0.4725,
0.4730,0.4765,0.4789,0.4792,0.4803,0.4808,0.4820,0.4822,0.4831,0.4894,
0.4943,0.4952,0.4969,0.5020,0.5037,0.5037,0.5117,0.5158,0.5182,0.5190,
0.5229,0.5240,0.5330,0.5369,0.5421,0.5477,0.5515,0.5527,0.5527,0.5541,
0.5582,0.5672,0.5684,0.5714,0.5748,0.5754,0.5756,0.5762,0.5801,0.5925,
0.5946,0.5999,0.6074,0.6166,0.6190,0.6276,0.6297,0.6347,0.6353,0.6409,
0.6412,0.6426,0.6446,0.6500,0.6512,0.6514,0.6641,0.6781,0.6788,0.6850,
0.6865,0.6929,0.6929,0.7082,0.7143,0.7184,0.7253,0.7253,0.7260,0.7283,
0.7361,0.7378,0.7390,0.7415,0.7496,0.7524,0.7533,0.7566,0.7605,0.7611,
0.7641,0.7662,0.7738,0.7791,0.7807,0.7857,0.7877,0.7894,0.7973,0.7973,
0.7986,0.8036,0.8051,0.8158,0.8170,0.8172,0.8181,0.8281,0.8344,0.8361,
0.8388,0.8465,0.8468,0.8516,0.8545,0.8596,0.8622,0.8634,0.8692,0.8988,
0.9001,0.9025,0.9086,0.9115,0.9157,0.9170,0.9232,0.9236,0.9271,0.9277,
0.9356,0.9365,0.9412,0.9588,0.9608,0.9613,0.9626,0.9648,0.9661,0.9662,
0.9693,0.9736,0.9743,0.9777,0.9800,0.9803,0.9894,0.9921,0.9978,
Overall p-value after applying KStest on 269 p-values = 0.749996
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.