RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-21_14:31
(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 12.7615 0.247998
2 to 25 15.63 20.8862 0.768576
3 to 26 15.55 23.7047 0.872317
4 to 27 15.73 21.3731 0.789956
5 to 28 15.87 21.5070 0.795573
6 to 29 15.83 19.9405 0.722718
7 to 30 15.70 14.0428 0.335928
8 to 31 15.83 11.3561 0.162537
9 to 32 15.75 14.0711 0.337939
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.563887
Tough bday spacings test for dh-ranFile-2018-06-21_14:31: 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 26 90 91 107 71 55 24 18 9 3
(O-E)^2/E 1.1 3.1 3.8 0.5 0.9 0.7 0.2 1.1 0.7 0.9 0.3
Birthday Spacings: Sum(O-E)^2/E= 13.068, p= 0.780
RESULTS OF GCD FOR dh-ranFile-2018-06-21_14:31
Euclid's algorithm:
p-value, steps to gcd: 0.666145
p-value, dist. of gcd's: 0.567324
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-21_14:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.298 0.483 0.183 0.837 0.526 0.183 0.085 0.912
Bits 8 to 15---> 0.088 0.370 0.422 0.200 0.470 0.219 0.983 0.690
Bits 16 to 23---> 0.309 0.916 0.583 0.443 0.553 0.585 0.916 0.674
Bits 24 to 31---> 0.000 0.033 0.661 0.830 0.357 0.139 0.575 0.501
KS test for the above 32 p values: 0.207
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-21_14:31,
p-values for 5 runs: 0.2705, 0.0818, 0.7988, 0.2787, 0.5141
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-21_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 201 211.4 0.513 0.513
r= 29 5131 5134.0 0.002 0.515
r= 30 22975 23103.0 0.710 1.225
r= 31 11693 11551.5 1.733 2.958
chi-square = 2.958 with df = 3; p-value = 0.602
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-21_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 185 211.4 3.301 3.301
r= 30 5138 5134.0 0.003 3.304
r= 31 23132 23103.0 0.036 3.340
r= 32 11545 11551.5 0.004 3.344
chi-square = 3.344 with df = 3; p-value = 0.658
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-21_14:31
b-rank test for bits 1 to 8, p=0.12188
b-rank test for bits 2 to 9, p=0.75832
b-rank test for bits 3 to 10, p=0.66523
b-rank test for bits 4 to 11, p=0.43748
b-rank test for bits 5 to 12, p=0.14019
b-rank test for bits 6 to 13, p=0.21443
b-rank test for bits 7 to 14, p=0.21246
b-rank test for bits 8 to 15, p=0.78223
b-rank test for bits 9 to 16, p=0.74692
b-rank test for bits 10 to 17, p=0.80974
b-rank test for bits 11 to 18, p=0.22411
b-rank test for bits 12 to 19, p=0.02511
b-rank test for bits 13 to 20, p=0.62518
b-rank test for bits 14 to 21, p=0.92668
b-rank test for bits 15 to 22, p=0.98068
b-rank test for bits 16 to 23, p=0.21249
b-rank test for bits 17 to 24, p=0.79109
b-rank test for bits 18 to 25, p=0.15199
b-rank test for bits 19 to 26, p=0.83963
b-rank test for bits 20 to 27, p=0.07917
b-rank test for bits 21 to 28, p=0.05971
b-rank test for bits 22 to 29, p=0.18466
b-rank test for bits 23 to 30, p=0.23689
b-rank test for bits 24 to 31, p=0.58913
b-rank test for bits 25 to 32, p=0.38142
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 = 0.361212
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-21_14:31
(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 141772 -0.32 0.374157
2 141740 -0.40 0.346189
3 142022 0.26 0.603820
4 142187 0.65 0.741754
5 141721 -0.44 0.329960
6 141835 -0.17 0.431063
7 142219 0.72 0.765322
8 141908 -0.00 0.498760
9 141760 -0.35 0.363582
10 142746 1.95 0.974699
11 142656 1.74 0.959469
12 141525 -0.90 0.184602
13 141455 -1.06 0.144227
14 141400 -1.19 0.117019
15 141676 -0.55 0.292821
16 142101 0.45 0.672861
17 142187 0.65 0.741754
18 141903 -0.01 0.494100
19 141577 -0.78 0.218735
20 142165 0.60 0.724866
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-21_14:31
Bits used No. missing words z-score p-value
23 to 32 141940 0.1058 0.542113
22 to 31 141997 0.3023 0.618792
21 to 30 142107 0.6816 0.752261
20 to 29 142739 2.8609 0.997888
19 to 28 141866 -0.1494 0.440614
18 to 27 141991 0.2816 0.610883
17 to 26 141873 -0.1253 0.450153
16 to 25 141865 -0.1529 0.439254
15 to 24 142127 0.7506 0.773549
14 to 23 142089 0.6196 0.732224
13 to 22 142104 0.6713 0.748978
12 to 21 142258 1.2023 0.885378
11 to 20 141722 -0.6460 0.259151
10 to 19 142497 2.0264 0.978641
9 to 18 141664 -0.8460 0.198786
8 to 17 141927 0.0609 0.524293
7 to 16 141598 -1.0736 0.141512
6 to 15 141678 -0.7977 0.212525
5 to 14 142220 1.0713 0.857977
4 to 13 142409 1.7230 0.957556
3 to 12 142074 0.5678 0.714924
2 to 11 142099 0.6540 0.743455
1 to 10 141945 0.1230 0.548947
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-21_14:31
Bits used No. missing words z-score p-value
28 to 32 141894 -0.0520 0.479278
27 to 31 142031 0.4124 0.659992
26 to 30 142255 1.1718 0.879354
25 to 29 142103 0.6565 0.744252
24 to 28 142164 0.8633 0.806011
23 to 27 142192 0.9582 0.831020
22 to 26 141911 0.0057 0.502258
21 to 25 142262 1.1955 0.884053
20 to 24 141864 -0.1537 0.438939
19 to 23 141785 -0.4215 0.336711
18 to 22 142143 0.7921 0.785849
17 to 21 141636 -0.9265 0.177082
16 to 20 142239 1.1175 0.868115
15 to 19 141315 -2.0147 0.021969
14 to 18 141477 -1.4655 0.071389
13 to 17 141605 -1.0316 0.151123
12 to 16 142361 1.5311 0.937126
11 to 15 142195 0.9684 0.833571
10 to 14 142299 1.3209 0.906735
9 to 13 141900 -0.0316 0.487385
8 to 12 141692 -0.7367 0.230649
7 to 11 141956 0.1582 0.562852
6 to 10 141937 0.0938 0.537365
5 to 9 141699 -0.7130 0.237928
4 to 8 142379 1.5921 0.944319
3 to 7 141683 -0.7672 0.221475
2 to 6 141977 0.2294 0.590717
1 to 5 142516 2.0565 0.980133
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-21_14:31
Bits used No. missing words z-score p-value
31 to 32 141876 -0.0983 0.460840
30 to 31 142108 0.5860 0.721078
29 to 30 142302 1.1583 0.876633
28 to 29 142558 1.9135 0.972157
27 to 28 141999 0.2645 0.604308
26 to 27 142159 0.7365 0.769284
25 to 26 142188 0.8220 0.794472
24 to 25 141631 -0.8210 0.205814
23 to 24 142671 2.2468 0.987674
22 to 23 141924 0.0433 0.517259
21 to 22 141995 0.2527 0.599755
20 to 21 141702 -0.6116 0.270404
19 to 20 142390 1.4179 0.921891
18 to 19 141815 -0.2783 0.390407
17 to 18 141659 -0.7384 0.230125
16 to 17 142068 0.4681 0.680127
15 to 16 141983 0.2173 0.586019
14 to 15 141663 -0.7266 0.233724
13 to 14 141966 0.1672 0.566381
12 to 13 141624 -0.8417 0.199983
11 to 12 141991 0.2409 0.595189
10 to 11 141855 -0.1603 0.436336
9 to 10 142062 0.4504 0.673772
8 to 9 141310 -1.7679 0.038536
7 to 8 141361 -1.6175 0.052886
6 to 7 141998 0.2616 0.603171
5 to 6 141283 -1.8476 0.032331
4 to 5 142680 2.2734 0.988498
3 to 4 142025 0.3412 0.633527
2 to 3 141796 -0.3343 0.369074
1 to 2 142355 1.3147 0.905688
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-21_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2567.19 0.950 0.828990
Test results for specific bytes for dh-ranFile-2018-06-21_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2522.07 0.312 0.622519
2 to 9 2499.79 -0.003 0.498797
3 to 10 2472.41 -0.390 0.348215
4 to 11 2443.19 -0.803 0.210857
5 to 12 2497.40 -0.037 0.485315
6 to 13 2562.24 0.880 0.810626
7 to 14 2535.31 0.499 0.691213
8 to 15 2506.27 0.089 0.535337
9 to 16 2601.94 1.442 0.925309
10 to 17 2375.21 -1.765 0.038800
11 to 18 2548.84 0.691 0.755128
12 to 19 2459.01 -0.580 0.281042
13 to 20 2580.40 1.137 0.872247
14 to 21 2498.62 -0.020 0.492218
15 to 22 2413.81 -1.219 0.111444
16 to 23 2479.19 -0.294 0.384253
17 to 24 2528.42 0.402 0.656147
18 to 25 2607.25 1.517 0.935337
19 to 26 2531.62 0.447 0.672625
20 to 27 2574.00 1.047 0.852350
21 to 28 2540.64 0.575 0.717287
22 to 29 2400.46 -1.408 0.079609
23 to 30 2461.45 -0.545 0.292802
24 to 31 2587.50 1.237 0.892038
25 to 32 2293.76 -2.917 0.001769
CDPARK for dh-ranFile-2018-06-21_14:31: 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
3540 0.7763 0.781201
3530 0.3196 0.625377
3497 -1.1872 0.117571
3532 0.4110 0.659449
3538 0.6849 0.753306
3539 0.7306 0.767486
3515 -0.3653 0.357445
3551 1.2785 0.899470
3549 1.1872 0.882429
3529 0.2740 0.607947
Square side=100, avg. no. parked=3532.00 sample std.=15.25
p-value of the KSTEST for those 10 p-values: 0.138120
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-21_14:31
0.4398,0.6096,0.1161,0.8229,0.2368,0.7521,0.3427,0.6495,0.1338,0.1873,
The KS test for those 10 p-values: 0.671198
The 3DSPHERES test for dh-ranFile-2018-06-21_14:31
sample no r^3 equiv. uni.
1 130.817 0.987229
2 13.090 0.353606
3 44.458 0.772801
4 7.017 0.208552
5 10.929 0.305323
6 11.827 0.325795
7 60.337 0.866176
8 24.039 0.551247
9 16.286 0.418922
10 7.522 0.221780
11 46.806 0.789903
12 5.360 0.163617
13 138.059 0.989968
14 0.659 0.021731
15 5.006 0.153678
16 13.416 0.360575
17 37.686 0.715268
18 30.870 0.642632
19 0.223 0.007410
20 13.613 0.364760
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.586459
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-21_14:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 -0.7 1.1 0.3 0.9 -1.5
0.4 0.8 0.2 -1.7 1.4 -0.2
-0.6 1.0 -1.1 -0.6 0.8 0.0
-0.8 2.4 0.4 -0.3 -1.9 1.1
-0.3 -0.1 -0.5 1.1 0.0 -0.9
-0.5 0.6 0.0 -1.0 -0.9 0.1
0.5 -0.7 -0.8 1.0 0.1 -1.0
-0.1
Chi-square with 42 degrees of freedom:33.917928
z-score=-0.881826, p-value=0.191692
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-21_14:31
Test no p-value
1 0.972600
2 0.028976
3 0.047993
4 0.034502
5 0.154416
6 0.042826
7 0.511589
8 0.502424
9 0.015589
10 0.358778
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.001978
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-21_14:31:
(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 66699 0.02 66629 0.02
3 25000.00 24859 0.80 24987 0.01
4 6666.67 6740 0.81 6780 1.93
5 1388.89 1417 0.57 1317 3.72
6 238.10 232 0.16 234 0.07
7 34.72 44 2.48 44 2.48
8 4.96 8 1.86 8 1.86
p=0.64914 p=0.87908
Number of rngs required: 690347, p-value: 0.990
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-21_14:31
No. of wins: Observed Expected
98459 98585.9
z-score=-0.567, pvalue=0.28523
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66726 66666.7 0.053 0.053
2 37491 37654.3 0.708 0.761
3 27117 26954.7 0.977 1.738
4 19445 19313.5 0.896 2.634
5 13866 13851.4 0.015 2.649
6 9895 9943.5 0.237 2.886
7 7087 7145.0 0.471 3.357
8 5262 5139.1 2.940 6.298
9 3469 3699.9 14.406 20.703
10 2682 2666.3 0.092 20.796
11 1917 1923.3 0.021 20.817
12 1341 1388.7 1.641 22.458
13 1001 1003.7 0.007 22.465
14 738 726.1 0.194 22.659
15 572 525.8 4.053 26.712
16 362 381.2 0.962 27.674
17 273 276.5 0.045 27.719
18 194 200.8 0.232 27.952
19 139 146.0 0.334 28.286
20 105 106.2 0.014 28.300
21 318 287.1 3.323 31.622
Chisq= 31.62 for 20 degrees of freedom, p= 0.95251
SUMMARY of craptest
p-value for no. of wins: 0.285226
p-value for throws/game: 0.952506
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-21_14:31
No. of wins: Observed Expected
98481 98585.9
z-score=-0.469, pvalue=0.31954
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66924 66666.7 0.993 0.993
2 37640 37654.3 0.005 0.999
3 26695 26954.7 2.503 3.502
4 19208 19313.5 0.576 4.077
5 13978 13851.4 1.157 5.234
6 9893 9943.5 0.257 5.491
7 7088 7145.0 0.455 5.946
8 5169 5139.1 0.174 6.120
9 3754 3699.9 0.792 6.913
10 2657 2666.3 0.032 6.945
11 1989 1923.3 2.242 9.187
12 1323 1388.7 3.112 12.299
13 1017 1003.7 0.176 12.475
14 685 726.1 2.331 14.806
15 523 525.8 0.015 14.821
16 381 381.2 0.000 14.821
17 293 276.5 0.980 15.801
18 200 200.8 0.003 15.805
19 160 146.0 1.346 17.150
20 125 106.2 3.322 20.472
21 298 287.1 0.413 20.885
Chisq= 20.89 for 20 degrees of freedom, p= 0.59608
SUMMARY of craptest
p-value for no. of wins: 0.319539
p-value for throws/game: 0.596077
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0004,0.0018,0.0020,0.0074,0.0156,0.0217,0.0220,0.0251,0.0290,0.0323,
0.0331,0.0345,0.0385,0.0388,0.0428,0.0480,0.0529,0.0597,0.0714,0.0792,
0.0796,0.0818,0.0852,0.0875,0.1114,0.1161,0.1170,0.1176,0.1219,0.1338,
0.1381,0.1388,0.1402,0.1415,0.1442,0.1511,0.1520,0.1537,0.1544,0.1625,
0.1636,0.1771,0.1831,0.1832,0.1846,0.1847,0.1873,0.1917,0.1988,0.1998,
0.2000,0.2058,0.2066,0.2086,0.2109,0.2125,0.2125,0.2125,0.2144,0.2187,
0.2194,0.2215,0.2218,0.2241,0.2301,0.2306,0.2337,0.2368,0.2369,0.2379,
0.2480,0.2592,0.2704,0.2705,0.2787,0.2810,0.2852,0.2928,0.2928,0.2981,
0.3053,0.3095,0.3195,0.3258,0.3300,0.3359,0.3367,0.3379,0.3427,0.3462,
0.3482,0.3536,0.3568,0.3574,0.3588,0.3606,0.3612,0.3636,0.3648,0.3691,
0.3704,0.3742,0.3814,0.3843,0.3904,0.4189,0.4220,0.4311,0.4363,0.4375,
0.4389,0.4393,0.4398,0.4406,0.4434,0.4502,0.4608,0.4702,0.4793,0.4830,
0.4853,0.4874,0.4922,0.4941,0.4988,0.4988,0.5007,0.5023,0.5024,0.5116,
0.5141,0.5173,0.5243,0.5265,0.5353,0.5374,0.5421,0.5489,0.5512,0.5531,
0.5629,0.5639,0.5664,0.5673,0.5751,0.5827,0.5854,0.5860,0.5865,0.5891,
0.5907,0.5952,0.5961,0.5998,0.6018,0.6032,0.6038,0.6043,0.6079,0.6096,
0.6109,0.6188,0.6225,0.6252,0.6254,0.6335,0.6426,0.6491,0.6495,0.6561,
0.6585,0.6594,0.6600,0.6614,0.6652,0.6661,0.6712,0.6726,0.6729,0.6737,
0.6738,0.6801,0.6902,0.6912,0.7149,0.7153,0.7173,0.7211,0.7227,0.7249,
0.7322,0.7418,0.7418,0.7435,0.7443,0.7469,0.7490,0.7521,0.7523,0.7533,
0.7551,0.7583,0.7653,0.7675,0.7686,0.7693,0.7728,0.7735,0.7801,0.7812,
0.7822,0.7858,0.7899,0.7900,0.7911,0.7945,0.7956,0.7988,0.8060,0.8097,
0.8106,0.8229,0.8290,0.8304,0.8310,0.8336,0.8374,0.8396,0.8523,0.8580,
0.8662,0.8681,0.8722,0.8723,0.8766,0.8791,0.8794,0.8824,0.8841,0.8854,
0.8920,0.8995,0.9057,0.9067,0.9121,0.9160,0.9162,0.9219,0.9253,0.9267,
0.9353,0.9371,0.9443,0.9525,0.9576,0.9595,0.9722,0.9726,0.9747,0.9786,
0.9801,0.9807,0.9829,0.9872,0.9877,0.9885,0.9895,0.9900,0.9979,
Overall p-value after applying KStest on 269 p-values = 0.733949
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.