RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-15_22:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.83 16.7154 0.526194
2 to 25 15.94 24.0751 0.882591
3 to 26 15.90 17.7040 0.592258
4 to 27 15.81 16.2365 0.492863
5 to 28 15.79 14.1284 0.342004
6 to 29 16.01 19.1572 0.680415
7 to 30 15.53 28.0328 0.955443
8 to 31 15.70 36.9435 0.996575
9 to 32 15.78 19.7853 0.714641
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.067292
Tough bday spacings test for dh-ranFile-2018-06-15_22:31: 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 8 38 73 87 112 80 46 31 15 5 5
(O-E)^2/E 0.1 0.1 0.0 1.2 2.1 0.0 0.7 0.1 0.0 0.4 0.2
Birthday Spacings: Sum(O-E)^2/E= 4.884, p= 0.101
RESULTS OF GCD FOR dh-ranFile-2018-06-15_22:31
Euclid's algorithm:
p-value, steps to gcd: 0.768696
p-value, dist. of gcd's: 0.687180
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-15_22:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.292 0.356 0.905 0.561 0.624 0.090 0.241 0.947
Bits 8 to 15---> 0.651 0.948 0.652 0.058 0.287 0.006 0.104 0.314
Bits 16 to 23---> 0.367 0.858 0.119 0.685 0.710 0.089 0.836 0.130
Bits 24 to 31---> 0.503 0.332 0.539 0.364 0.283 0.527 0.385 0.372
KS test for the above 32 p values: 0.599
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-15_22:31,
p-values for 5 runs: 0.3708, 0.5083, 0.1759, 0.4445, 0.6334
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-15_22:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 230 211.4 1.633 1.633
r= 29 5121 5134.0 0.033 1.666
r= 30 23047 23103.0 0.136 1.802
r= 31 11602 11551.5 0.221 2.023
chi-square = 2.023 with df = 3; p-value = 0.432
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-15_22:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 219 211.4 0.272 0.272
r= 30 5126 5134.0 0.012 0.284
r= 31 23109 23103.0 0.002 0.286
r= 32 11546 11551.5 0.003 0.289
chi-square = 0.289 with df = 3; p-value = 0.038
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-15_22:31
b-rank test for bits 1 to 8, p=0.91127
b-rank test for bits 2 to 9, p=0.55623
b-rank test for bits 3 to 10, p=0.66097
b-rank test for bits 4 to 11, p=0.60400
b-rank test for bits 5 to 12, p=0.86032
b-rank test for bits 6 to 13, p=0.33349
b-rank test for bits 7 to 14, p=0.65832
b-rank test for bits 8 to 15, p=0.07652
b-rank test for bits 9 to 16, p=0.69033
b-rank test for bits 10 to 17, p=0.84225
b-rank test for bits 11 to 18, p=0.35793
b-rank test for bits 12 to 19, p=0.83869
b-rank test for bits 13 to 20, p=0.08012
b-rank test for bits 14 to 21, p=0.37088
b-rank test for bits 15 to 22, p=0.43804
b-rank test for bits 16 to 23, p=0.47595
b-rank test for bits 17 to 24, p=0.70018
b-rank test for bits 18 to 25, p=0.07592
b-rank test for bits 19 to 26, p=0.39218
b-rank test for bits 20 to 27, p=0.86166
b-rank test for bits 21 to 28, p=0.28074
b-rank test for bits 22 to 29, p=0.50516
b-rank test for bits 23 to 30, p=0.18462
b-rank test for bits 24 to 31, p=0.57305
b-rank test for bits 25 to 32, p=0.14916
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 = 0.854398
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-15_22:31
(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 141832 -0.18 0.428310
2 141683 -0.53 0.298469
3 141415 -1.15 0.124050
4 141324 -1.37 0.085720
5 141854 -0.13 0.448570
6 141963 0.13 0.549895
7 141411 -1.16 0.122147
8 141769 -0.33 0.371504
9 142280 0.87 0.806769
10 141859 -0.12 0.453195
11 142075 0.39 0.650651
12 141560 -0.82 0.207195
13 141520 -0.91 0.181504
14 141720 -0.44 0.329114
15 142015 0.25 0.597504
16 141710 -0.47 0.320706
17 141784 -0.29 0.384827
18 141800 -0.26 0.399190
19 141588 -0.75 0.226395
20 141530 -0.89 0.187732
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-15_22:31
Bits used No. missing words z-score p-value
23 to 32 142245 1.1575 0.876462
22 to 31 142120 0.7264 0.766218
21 to 30 142274 1.2575 0.895711
20 to 29 142125 0.7437 0.771468
19 to 28 141777 -0.4563 0.324083
18 to 27 142021 0.3851 0.649907
17 to 26 142000 0.3127 0.622729
16 to 25 141371 -1.8563 0.031705
15 to 24 141519 -1.3460 0.089157
14 to 23 142277 1.2678 0.897570
13 to 22 141437 -1.6287 0.051686
12 to 21 141358 -1.9011 0.028642
11 to 20 141468 -1.5218 0.064026
10 to 19 141334 -1.9839 0.023634
9 to 18 141611 -1.0287 0.151805
8 to 17 142056 0.5058 0.693487
7 to 16 141824 -0.2942 0.384287
6 to 15 142597 2.3713 0.991137
5 to 14 141877 -0.1115 0.455617
4 to 13 141789 -0.4149 0.339096
3 to 12 141794 -0.3977 0.345430
2 to 11 142078 0.5816 0.719589
1 to 10 141774 -0.4667 0.320373
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-15_22:31
Bits used No. missing words z-score p-value
28 to 32 141549 -1.2215 0.110956
27 to 31 141712 -0.6689 0.251775
26 to 30 142367 1.5514 0.939600
25 to 29 141667 -0.8215 0.205693
24 to 28 142108 0.6735 0.749672
23 to 27 141841 -0.2316 0.408414
22 to 26 142287 1.2802 0.899769
21 to 25 141969 0.2023 0.580148
20 to 24 141435 -1.6079 0.053929
19 to 23 141434 -1.6113 0.053558
18 to 22 142403 1.6735 0.952881
17 to 21 141838 -0.2418 0.404469
16 to 20 142277 1.2463 0.893680
15 to 19 141687 -0.7537 0.225526
14 to 18 141979 0.2362 0.593349
13 to 17 142191 0.9548 0.830164
12 to 16 141982 0.2463 0.597290
11 to 15 141835 -0.2520 0.400534
10 to 14 142104 0.6599 0.745341
9 to 13 142106 0.6667 0.747511
8 to 12 141760 -0.5062 0.306357
7 to 11 142076 0.5650 0.713957
6 to 10 142106 0.6667 0.747511
5 to 9 141719 -0.6452 0.259403
4 to 8 142007 0.3311 0.629710
3 to 7 142025 0.3921 0.652509
2 to 6 141900 -0.0316 0.487385
1 to 5 141377 -1.8045 0.035576
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-15_22:31
Bits used No. missing words z-score p-value
31 to 32 142136 0.6686 0.748138
30 to 31 142176 0.7866 0.784253
29 to 30 142240 0.9754 0.835326
28 to 29 142027 0.3471 0.635745
27 to 28 141898 -0.0334 0.486669
26 to 27 142179 0.7955 0.786835
25 to 26 141433 -1.4051 0.079995
24 to 25 142038 0.3796 0.647863
23 to 24 142352 1.3058 0.904192
22 to 23 142183 0.8073 0.790249
21 to 22 141980 0.2085 0.582568
20 to 21 141329 -1.7119 0.043459
19 to 20 142533 1.8397 0.967096
18 to 19 142220 0.9164 0.820280
17 to 18 142470 1.6539 0.950925
16 to 17 141327 -1.7178 0.042918
15 to 16 141827 -0.2429 0.404056
14 to 15 142216 0.9046 0.817170
13 to 14 142031 0.3589 0.640168
12 to 13 141840 -0.2045 0.418976
11 to 12 142005 0.2822 0.611110
10 to 11 141833 -0.2252 0.410927
9 to 10 142230 0.9459 0.827908
8 to 9 142320 1.2114 0.887132
7 to 8 142010 0.2970 0.616752
6 to 7 142296 1.1406 0.872986
5 to 6 141759 -0.4435 0.328720
4 to 5 141854 -0.1632 0.435174
3 to 4 142355 1.3147 0.905688
2 to 3 141971 0.1819 0.572176
1 to 2 141907 -0.0069 0.497258
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-15_22:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2641.64 2.003 0.977414
Test results for specific bytes for dh-ranFile-2018-06-15_22:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2445.66 -0.769 0.221095
2 to 9 2534.04 0.481 0.684878
3 to 10 2459.38 -0.574 0.282844
4 to 11 2536.98 0.523 0.699513
5 to 12 2450.82 -0.695 0.243380
6 to 13 2478.31 -0.307 0.379503
7 to 14 2511.09 0.157 0.562320
8 to 15 2459.63 -0.571 0.284032
9 to 16 2341.63 -2.240 0.012555
10 to 17 2448.68 -0.726 0.233979
11 to 18 2466.27 -0.477 0.316697
12 to 19 2535.74 0.505 0.693357
13 to 20 2607.75 1.524 0.936230
14 to 21 2440.16 -0.846 0.198697
15 to 22 2572.04 1.019 0.845859
16 to 23 2531.34 0.443 0.671179
17 to 24 2339.88 -2.264 0.011774
18 to 25 2519.13 0.271 0.606643
19 to 26 2504.83 0.068 0.527203
20 to 27 2512.61 0.178 0.570764
21 to 28 2453.13 -0.663 0.253712
22 to 29 2378.65 -1.716 0.043064
23 to 30 2471.61 -0.401 0.344034
24 to 31 2590.12 1.275 0.898760
25 to 32 2503.98 0.056 0.522432
CDPARK for dh-ranFile-2018-06-15_22:31: 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
3527 0.1826 0.572463
3537 0.6393 0.738676
3497 -1.1872 0.117571
3525 0.0913 0.536383
3543 0.9132 0.819442
3550 1.2329 0.891189
3521 -0.0913 0.463617
3506 -0.7763 0.218799
3515 -0.3653 0.357445
3546 1.0502 0.853193
Square side=100, avg. no. parked=3526.70 sample std.=16.64
p-value of the KSTEST for those 10 p-values: 0.837236
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-15_22:31
0.5545,0.6382,0.4617,0.5512,0.3377,0.2732,0.5105,0.2276,0.3183,0.2726,
The KS test for those 10 p-values: 0.134546
The 3DSPHERES test for dh-ranFile-2018-06-15_22:31
sample no r^3 equiv. uni.
1 88.658 0.947935
2 20.876 0.501353
3 15.601 0.405506
4 47.212 0.792733
5 29.722 0.628701
6 22.050 0.520497
7 90.476 0.950997
8 5.876 0.177876
9 63.447 0.879355
10 76.733 0.922522
11 18.992 0.469033
12 11.955 0.328670
13 57.807 0.854402
14 4.797 0.147767
15 36.159 0.700394
16 78.718 0.927484
17 10.828 0.302984
18 70.237 0.903791
19 48.658 0.802483
20 4.979 0.152916
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.090024
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-15_22:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -0.7 -2.3 -0.1 -0.2 0.0
0.3 0.8 0.9 0.5 -2.1 1.2
-0.7 0.3 -0.6 -0.3 1.5 -0.2
-0.6 0.8 0.2 -0.2 -1.0 -0.7
1.0 0.9 -0.6 -1.0 0.7 0.2
0.7 -1.9 0.4 -0.5 -0.8 0.4
1.9 -0.7 0.1 1.0 0.1 0.0
0.8
Chi-square with 42 degrees of freedom:34.320113
z-score=-0.837944, p-value=0.205743
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-15_22:31
Test no p-value
1 0.066410
2 0.051052
3 0.149458
4 0.288053
5 0.767827
6 0.001400
7 0.764023
8 0.859081
9 0.613299
10 0.019944
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.035284
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-15_22:31:
(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 66844 0.47 66488 0.48
3 25000.00 24812 1.41 25031 0.04
4 6666.67 6714 0.34 6798 2.59
5 1388.89 1361 0.56 1396 0.04
6 238.10 228 0.43 251 0.70
7 34.72 36 0.05 32 0.21
8 4.96 4 0.19 3 0.77
p=0.24840 p=0.43393
Number of rngs required: 688141, p-value: 0.381
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-15_22:31
No. of wins: Observed Expected
98648 98585.9
z-score= 0.278, pvalue=0.60947
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66392 66666.7 1.132 1.132
2 37718 37654.3 0.108 1.239
3 26976 26954.7 0.017 1.256
4 19480 19313.5 1.436 2.692
5 13918 13851.4 0.320 3.012
6 9864 9943.5 0.636 3.648
7 7167 7145.0 0.068 3.716
8 5195 5139.1 0.609 4.325
9 3675 3699.9 0.167 4.492
10 2661 2666.3 0.011 4.502
11 1898 1923.3 0.334 4.836
12 1390 1388.7 0.001 4.837
13 1000 1003.7 0.014 4.851
14 743 726.1 0.391 5.242
15 540 525.8 0.382 5.624
16 361 381.2 1.065 6.689
17 256 276.5 1.526 8.215
18 201 200.8 0.000 8.215
19 137 146.0 0.553 8.768
20 121 106.2 2.058 10.826
21 307 287.1 1.377 12.203
Chisq= 12.20 for 20 degrees of freedom, p= 0.09109
SUMMARY of craptest
p-value for no. of wins: 0.609468
p-value for throws/game: 0.091089
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-15_22:31
No. of wins: Observed Expected
98564 98585.9
z-score=-0.098, pvalue=0.46106
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66779 66666.7 0.189 0.189
2 37661 37654.3 0.001 0.190
3 26902 26954.7 0.103 0.294
4 19136 19313.5 1.631 1.924
5 13805 13851.4 0.156 2.080
6 9924 9943.5 0.038 2.118
7 7160 7145.0 0.031 2.150
8 5179 5139.1 0.310 2.460
9 3756 3699.9 0.852 3.312
10 2666 2666.3 0.000 3.312
11 1930 1923.3 0.023 3.335
12 1382 1388.7 0.033 3.367
13 1018 1003.7 0.203 3.571
14 702 726.1 0.803 4.373
15 518 525.8 0.117 4.490
16 377 381.2 0.045 4.535
17 298 276.5 1.665 6.201
18 221 200.8 2.026 8.226
19 156 146.0 0.687 8.914
20 127 106.2 4.067 12.981
21 303 287.1 0.879 13.860
Chisq= 13.86 for 20 degrees of freedom, p= 0.16247
SUMMARY of craptest
p-value for no. of wins: 0.461060
p-value for throws/game: 0.162467
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0014,0.0056,0.0118,0.0126,0.0199,0.0236,0.0286,0.0317,0.0353,0.0356,
0.0378,0.0429,0.0431,0.0435,0.0511,0.0517,0.0536,0.0539,0.0583,0.0640,
0.0664,0.0673,0.0759,0.0765,0.0800,0.0801,0.0857,0.0892,0.0893,0.0900,
0.0900,0.0911,0.1012,0.1044,0.1110,0.1176,0.1186,0.1221,0.1241,0.1300,
0.1345,0.1478,0.1492,0.1495,0.1518,0.1529,0.1625,0.1759,0.1779,0.1815,
0.1846,0.1877,0.1987,0.2057,0.2057,0.2072,0.2188,0.2211,0.2255,0.2264,
0.2276,0.2340,0.2406,0.2434,0.2484,0.2518,0.2537,0.2594,0.2726,0.2732,
0.2807,0.2828,0.2832,0.2840,0.2874,0.2881,0.2923,0.2985,0.3030,0.3064,
0.3145,0.3167,0.3183,0.3204,0.3207,0.3241,0.3287,0.3287,0.3291,0.3316,
0.3335,0.3377,0.3391,0.3420,0.3440,0.3454,0.3558,0.3574,0.3579,0.3641,
0.3667,0.3708,0.3709,0.3715,0.3719,0.3795,0.3815,0.3843,0.3848,0.3850,
0.3922,0.3992,0.4005,0.4041,0.4045,0.4055,0.4084,0.4109,0.4190,0.4283,
0.4323,0.4339,0.4352,0.4380,0.4445,0.4486,0.4532,0.4556,0.4611,0.4617,
0.4636,0.4690,0.4759,0.4867,0.4874,0.4929,0.4973,0.5014,0.5028,0.5052,
0.5083,0.5105,0.5205,0.5224,0.5262,0.5266,0.5272,0.5364,0.5393,0.5499,
0.5512,0.5545,0.5562,0.5607,0.5623,0.5708,0.5722,0.5725,0.5730,0.5801,
0.5826,0.5923,0.5933,0.5973,0.5975,0.5985,0.6040,0.6066,0.6095,0.6111,
0.6133,0.6168,0.6227,0.6242,0.6287,0.6297,0.6334,0.6357,0.6382,0.6402,
0.6479,0.6499,0.6507,0.6508,0.6524,0.6525,0.6583,0.6610,0.6712,0.6804,
0.6849,0.6853,0.6872,0.6903,0.6934,0.6935,0.6995,0.7002,0.7004,0.7095,
0.7140,0.7146,0.7196,0.7387,0.7453,0.7475,0.7475,0.7481,0.7497,0.7640,
0.7662,0.7678,0.7687,0.7715,0.7843,0.7868,0.7902,0.7927,0.8025,0.8068,
0.8172,0.8194,0.8203,0.8279,0.8302,0.8353,0.8360,0.8372,0.8387,0.8423,
0.8459,0.8532,0.8544,0.8544,0.8576,0.8591,0.8603,0.8617,0.8730,0.8765,
0.8794,0.8826,0.8871,0.8912,0.8937,0.8957,0.8976,0.8988,0.8998,0.9038,
0.9042,0.9052,0.9057,0.9113,0.9225,0.9275,0.9362,0.9396,0.9466,0.9479,
0.9484,0.9509,0.9510,0.9529,0.9554,0.9671,0.9774,0.9911,0.9966,
Overall p-value after applying KStest on 269 p-values = 0.661928
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.