RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-26_06:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 16.00 15.9470 0.472408
2 to 25 15.99 14.7550 0.386875
3 to 26 15.44 20.3799 0.744741
4 to 27 15.75 19.6219 0.705976
5 to 28 15.80 19.8804 0.719610
6 to 29 15.91 11.4465 0.167563
7 to 30 15.67 22.3657 0.828937
8 to 31 15.75 22.2005 0.822870
9 to 32 15.87 9.2301 0.067237
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.714633
Tough bday spacings test for dh-ranFile-2018-06-26_06:31: 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 30 54 115 108 87 54 24 11 5 1
(O-E)^2/E 0.4 1.2 5.1 3.1 1.1 1.0 0.1 1.1 1.0 0.4 2.3
Birthday Spacings: Sum(O-E)^2/E= 16.706, p= 0.919
RESULTS OF GCD FOR dh-ranFile-2018-06-26_06:31
Euclid's algorithm:
p-value, steps to gcd: 0.801683
p-value, dist. of gcd's: 0.025503
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-26_06:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.279 0.250 0.929 0.912 0.425 0.524 0.257 0.708
Bits 8 to 15---> 0.403 0.173 0.452 0.707 0.228 0.583 0.275 0.641
Bits 16 to 23---> 0.836 0.805 0.272 0.112 0.727 0.287 0.913 0.199
Bits 24 to 31---> 0.436 0.409 0.901 0.472 0.144 0.220 0.875 0.501
KS test for the above 32 p values: 0.481
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-26_06:31,
p-values for 5 runs: 0.1044, 0.8152, 0.6406, 0.5325, 0.0374
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-26_06:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 226 211.4 1.006 1.006
r= 29 5139 5134.0 0.005 1.011
r= 30 23046 23103.0 0.141 1.151
r= 31 11589 11551.5 0.122 1.273
chi-square = 1.273 with df = 3; p-value = 0.264
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-26_06:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 213 211.4 0.012 0.012
r= 30 5155 5134.0 0.086 0.098
r= 31 23220 23103.0 0.592 0.690
r= 32 11412 11551.5 1.685 2.375
chi-square = 2.375 with df = 3; p-value = 0.502
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-26_06:31
b-rank test for bits 1 to 8, p=0.56259
b-rank test for bits 2 to 9, p=0.53467
b-rank test for bits 3 to 10, p=0.96229
b-rank test for bits 4 to 11, p=0.76685
b-rank test for bits 5 to 12, p=0.62743
b-rank test for bits 6 to 13, p=0.30822
b-rank test for bits 7 to 14, p=0.63629
b-rank test for bits 8 to 15, p=0.07431
b-rank test for bits 9 to 16, p=0.50311
b-rank test for bits 10 to 17, p=0.41224
b-rank test for bits 11 to 18, p=0.06055
b-rank test for bits 12 to 19, p=0.41811
b-rank test for bits 13 to 20, p=0.17410
b-rank test for bits 14 to 21, p=0.38505
b-rank test for bits 15 to 22, p=0.18065
b-rank test for bits 16 to 23, p=0.84687
b-rank test for bits 17 to 24, p=0.55803
b-rank test for bits 18 to 25, p=0.12954
b-rank test for bits 19 to 26, p=0.17084
b-rank test for bits 20 to 27, p=0.72590
b-rank test for bits 21 to 28, p=0.55679
b-rank test for bits 22 to 29, p=0.59096
b-rank test for bits 23 to 30, p=0.33248
b-rank test for bits 24 to 31, p=0.12785
b-rank test for bits 25 to 32, p=0.11025
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 = 0.291174
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-26_06:31
(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 142052 0.33 0.630562
2 141860 -0.12 0.454121
3 142096 0.44 0.668634
4 141852 -0.13 0.446722
5 142490 1.36 0.912563
6 141846 -0.15 0.441184
7 142865 2.23 0.987221
8 141205 -1.65 0.049920
9 142644 1.72 0.956966
10 141781 -0.30 0.382151
11 141184 -1.69 0.045067
12 142259 0.82 0.793032
13 141845 -0.15 0.440263
14 142242 0.78 0.781499
15 142201 0.68 0.752214
16 142489 1.35 0.912191
17 142370 1.08 0.859111
18 141736 -0.40 0.342747
19 141653 -0.60 0.274619
20 142159 0.58 0.720168
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-26_06:31
Bits used No. missing words z-score p-value
23 to 32 141662 -0.8529 0.196868
22 to 31 141599 -1.0701 0.142286
21 to 30 141869 -0.1391 0.444698
20 to 29 141965 0.1920 0.576115
19 to 28 141858 -0.1770 0.429754
18 to 27 141657 -0.8701 0.192122
17 to 26 141901 -0.0287 0.488542
16 to 25 141926 0.0575 0.522920
15 to 24 141587 -1.1115 0.133180
14 to 23 141882 -0.0942 0.462459
13 to 22 141491 -1.4425 0.074578
12 to 21 142196 0.9885 0.838550
11 to 20 141696 -0.7356 0.230981
10 to 19 141660 -0.8598 0.194961
9 to 18 142228 1.0989 0.864086
8 to 17 141964 0.1885 0.574764
7 to 16 141737 -0.5942 0.276175
6 to 15 142124 0.7402 0.770423
5 to 14 141822 -0.3011 0.381655
4 to 13 141607 -1.0425 0.148586
3 to 12 141698 -0.7287 0.233085
2 to 11 141797 -0.3873 0.349251
1 to 10 141413 -1.7115 0.043496
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-26_06:31
Bits used No. missing words z-score p-value
28 to 32 141487 -1.4316 0.076125
27 to 31 141639 -0.9164 0.179736
26 to 30 141784 -0.4248 0.335474
25 to 29 141539 -1.2554 0.104675
24 to 28 141344 -1.9164 0.027659
23 to 27 142201 0.9887 0.838598
22 to 26 141630 -0.9469 0.171850
21 to 25 141462 -1.5164 0.064713
20 to 24 141893 -0.0554 0.477928
19 to 23 141918 0.0294 0.511723
18 to 22 141574 -1.1367 0.127829
17 to 21 141801 -0.3672 0.356727
16 to 20 141971 0.2091 0.582796
15 to 19 141788 -0.4113 0.340431
14 to 18 141790 -0.4045 0.342919
13 to 17 141877 -0.1096 0.456366
12 to 16 141912 0.0091 0.503611
11 to 15 141919 0.0328 0.513075
10 to 14 141668 -0.8181 0.206659
9 to 13 141463 -1.5130 0.065142
8 to 12 141697 -0.7198 0.235836
7 to 11 141757 -0.5164 0.302797
6 to 10 141979 0.2362 0.593349
5 to 9 142393 1.6396 0.949452
4 to 8 141720 -0.6418 0.260503
3 to 7 142002 0.3141 0.623291
2 to 6 141734 -0.5943 0.276143
1 to 5 141988 0.2667 0.605141
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-26_06:31
Bits used No. missing words z-score p-value
31 to 32 142443 1.5742 0.942285
30 to 31 141882 -0.0806 0.467872
29 to 30 141924 0.0433 0.517259
28 to 29 141752 -0.4641 0.321288
27 to 28 141385 -1.5467 0.060968
26 to 27 142299 1.1495 0.874819
25 to 26 142376 1.3766 0.915683
24 to 25 141851 -0.1721 0.431693
23 to 24 141593 -0.9331 0.175377
22 to 23 141966 0.1672 0.566381
21 to 22 142501 1.7453 0.959537
20 to 21 141585 -0.9567 0.169353
19 to 20 142047 0.4061 0.657668
18 to 19 142102 0.5683 0.715101
17 to 18 142203 0.8663 0.806833
16 to 17 142430 1.5359 0.937719
15 to 16 142253 1.0138 0.844655
14 to 15 142290 1.1229 0.869264
13 to 14 142270 1.0639 0.856318
12 to 13 141654 -0.7532 0.225669
11 to 12 141432 -1.4081 0.079558
10 to 11 141732 -0.5231 0.300453
9 to 10 142155 0.7247 0.765679
8 to 9 141648 -0.7709 0.220388
7 to 8 141836 -0.2163 0.414372
6 to 7 141342 -1.6735 0.047111
5 to 6 141771 -0.4081 0.341617
4 to 5 142084 0.5153 0.696811
3 to 4 141377 -1.5703 0.058173
2 to 3 142042 0.3914 0.652233
1 to 2 142165 0.7542 0.774632
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-26_06:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2467.68 -0.457 0.323786
Test results for specific bytes for dh-ranFile-2018-06-26_06:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2496.31 -0.052 0.479171
2 to 9 2411.87 -1.246 0.106307
3 to 10 2579.04 1.118 0.868164
4 to 11 2485.67 -0.203 0.419705
5 to 12 2492.98 -0.099 0.460462
6 to 13 2556.64 0.801 0.788444
7 to 14 2372.78 -1.799 0.035997
8 to 15 2430.20 -0.987 0.161788
9 to 16 2392.19 -1.525 0.063680
10 to 17 2437.27 -0.887 0.187501
11 to 18 2492.10 -0.112 0.455538
12 to 19 2466.83 -0.469 0.319489
13 to 20 2593.38 1.321 0.906689
14 to 21 2450.78 -0.696 0.243176
15 to 22 2441.99 -0.820 0.206004
16 to 23 2471.32 -0.406 0.342519
17 to 24 2486.24 -0.195 0.422879
18 to 25 2589.69 1.268 0.897685
19 to 26 2455.77 -0.626 0.265815
20 to 27 2482.77 -0.244 0.403740
21 to 28 2444.91 -0.779 0.217956
22 to 29 2631.92 1.866 0.968952
23 to 30 2565.96 0.933 0.824559
24 to 31 2650.74 2.132 0.983489
25 to 32 2570.04 0.991 0.839055
CDPARK for dh-ranFile-2018-06-26_06:31: 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
3500 -1.0502 0.146807
3505 -0.8219 0.205562
3537 0.6393 0.738676
3542 0.8676 0.807188
3526 0.1370 0.554479
3541 0.8219 0.794438
3499 -1.0959 0.136563
3513 -0.4566 0.323972
3506 -0.7763 0.218799
3490 -1.5068 0.065925
Square side=100, avg. no. parked=3515.90 sample std.=18.15
p-value of the KSTEST for those 10 p-values: 0.368289
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-26_06:31
0.4546,0.6232,0.9212,0.5862,0.8077,0.4901,0.1875,0.1578,0.1536,0.1635,
The KS test for those 10 p-values: 0.737426
The 3DSPHERES test for dh-ranFile-2018-06-26_06:31
sample no r^3 equiv. uni.
1 47.482 0.794590
2 88.262 0.947243
3 0.430 0.014246
4 36.811 0.706835
5 25.851 0.577557
6 34.091 0.679019
7 30.977 0.643904
8 20.216 0.490268
9 71.836 0.908786
10 13.387 0.359955
11 64.276 0.882643
12 30.416 0.637189
13 64.455 0.883341
14 0.041 0.001360
15 11.548 0.319501
16 0.398 0.013193
17 11.018 0.307379
18 37.190 0.710515
19 11.958 0.328746
20 22.668 0.530275
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.327884
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-26_06:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 0.5 -0.6 1.9 -0.7 0.1
0.3 0.3 0.2 0.0 0.0 0.4
0.2 -0.6 -1.2 1.3 -0.9 0.3
-0.5 -0.8 -0.4 -0.2 1.8 0.0
0.7 -0.6 0.2 0.4 0.6 0.5
-1.3 0.6 -1.3 1.6 -1.0 -1.6
1.2 -0.4 0.5 -0.1 0.1 -1.0
0.8
Chi-square with 42 degrees of freedom:31.705126
z-score=-1.123263, p-value=0.123740
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-26_06:31
Test no p-value
1 0.902334
2 0.614995
3 0.000462
4 0.031757
5 0.515605
6 0.010844
7 0.079348
8 0.806156
9 0.932270
10 0.500542
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.064359
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-26_06:31:
(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 66644 0.01 66595 0.08
3 25000.00 25045 0.08 25112 0.50
4 6666.67 6679 0.02 6602 0.63
5 1388.89 1373 0.18 1389 0.00
6 238.10 220 1.38 260 2.02
7 34.72 34 0.01 33 0.09
8 4.96 4 0.19 8 1.86
p=0.06868 p=0.47778
Number of rngs required: 688014, p-value: 0.327
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-26_06:31
No. of wins: Observed Expected
98283 98585.9
z-score=-1.355, pvalue=0.08778
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66652 66666.7 0.003 0.003
2 37429 37654.3 1.348 1.352
3 27114 26954.7 0.941 2.293
4 19224 19313.5 0.414 2.707
5 14061 13851.4 3.171 5.878
6 9838 9943.5 1.120 6.998
7 7158 7145.0 0.024 7.022
8 5121 5139.1 0.064 7.085
9 3807 3699.9 3.102 10.188
10 2639 2666.3 0.279 10.467
11 1908 1923.3 0.122 10.589
12 1395 1388.7 0.028 10.618
13 988 1003.7 0.246 10.864
14 740 726.1 0.265 11.128
15 494 525.8 1.927 13.056
16 394 381.2 0.433 13.489
17 287 276.5 0.396 13.884
18 199 200.8 0.017 13.901
19 163 146.0 1.983 15.884
20 108 106.2 0.030 15.914
21 281 287.1 0.130 16.045
Chisq= 16.04 for 20 degrees of freedom, p= 0.28615
SUMMARY of craptest
p-value for no. of wins: 0.087779
p-value for throws/game: 0.286146
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-26_06:31
No. of wins: Observed Expected
98731 98585.9
z-score= 0.649, pvalue=0.74188
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66606 66666.7 0.055 0.055
2 37973 37654.3 2.697 2.752
3 26610 26954.7 4.409 7.161
4 19314 19313.5 0.000 7.161
5 13751 13851.4 0.728 7.889
6 9978 9943.5 0.119 8.009
7 7218 7145.0 0.745 8.754
8 5166 5139.1 0.141 8.895
9 3679 3699.9 0.118 9.013
10 2630 2666.3 0.494 9.507
11 2000 1923.3 3.056 12.563
12 1433 1388.7 1.411 13.974
13 1019 1003.7 0.233 14.207
14 700 726.1 0.941 15.148
15 536 525.8 0.196 15.344
16 392 381.2 0.309 15.653
17 274 276.5 0.023 15.676
18 196 200.8 0.116 15.792
19 132 146.0 1.340 17.132
20 102 106.2 0.167 17.299
21 291 287.1 0.053 17.352
Chisq= 17.35 for 20 degrees of freedom, p= 0.36998
SUMMARY of craptest
p-value for no. of wins: 0.741882
p-value for throws/game: 0.369977
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0005,0.0014,0.0108,0.0132,0.0142,0.0255,0.0277,0.0318,0.0360,0.0374,
0.0435,0.0451,0.0471,0.0499,0.0582,0.0606,0.0610,0.0637,0.0644,0.0647,
0.0651,0.0659,0.0672,0.0687,0.0743,0.0746,0.0761,0.0793,0.0796,0.0878,
0.1044,0.1047,0.1063,0.1103,0.1119,0.1237,0.1278,0.1278,0.1295,0.1332,
0.1366,0.1423,0.1439,0.1468,0.1486,0.1536,0.1578,0.1618,0.1635,0.1676,
0.1694,0.1708,0.1718,0.1732,0.1741,0.1754,0.1797,0.1807,0.1875,0.1875,
0.1921,0.1950,0.1969,0.1988,0.2056,0.2060,0.2067,0.2180,0.2188,0.2200,
0.2204,0.2257,0.2278,0.2310,0.2331,0.2358,0.2432,0.2498,0.2569,0.2605,
0.2645,0.2658,0.2722,0.2746,0.2755,0.2761,0.2762,0.2792,0.2861,0.2865,
0.2912,0.3005,0.3028,0.3074,0.3082,0.3195,0.3195,0.3213,0.3238,0.3240,
0.3270,0.3279,0.3287,0.3325,0.3355,0.3404,0.3416,0.3425,0.3427,0.3429,
0.3493,0.3567,0.3600,0.3683,0.3700,0.3817,0.3822,0.3851,0.3869,0.4031,
0.4037,0.4094,0.4122,0.4144,0.4181,0.4197,0.4229,0.4250,0.4298,0.4317,
0.4360,0.4403,0.4412,0.4447,0.4467,0.4520,0.4541,0.4546,0.4555,0.4564,
0.4605,0.4625,0.4679,0.4721,0.4724,0.4778,0.4779,0.4792,0.4815,0.4885,
0.4901,0.4903,0.5005,0.5011,0.5017,0.5031,0.5036,0.5117,0.5131,0.5156,
0.5173,0.5229,0.5239,0.5303,0.5325,0.5347,0.5545,0.5568,0.5580,0.5626,
0.5664,0.5748,0.5761,0.5776,0.5828,0.5828,0.5862,0.5910,0.5933,0.6051,
0.6150,0.6232,0.6233,0.6274,0.6306,0.6363,0.6372,0.6406,0.6410,0.6439,
0.6522,0.6577,0.6686,0.6790,0.6968,0.7060,0.7068,0.7069,0.7085,0.7105,
0.7146,0.7151,0.7196,0.7202,0.7259,0.7269,0.7374,0.7387,0.7419,0.7447,
0.7522,0.7657,0.7669,0.7704,0.7746,0.7815,0.7884,0.7930,0.7944,0.7946,
0.8017,0.8054,0.8062,0.8068,0.8072,0.8077,0.8152,0.8229,0.8246,0.8289,
0.8358,0.8386,0.8386,0.8391,0.8447,0.8469,0.8563,0.8591,0.8641,0.8682,
0.8693,0.8747,0.8748,0.8826,0.8833,0.8977,0.9008,0.9023,0.9067,0.9088,
0.9121,0.9122,0.9126,0.9134,0.9157,0.9189,0.9212,0.9294,0.9323,0.9377,
0.9423,0.9472,0.9495,0.9570,0.9595,0.9623,0.9690,0.9835,0.9872,
Overall p-value after applying KStest on 269 p-values = 0.054211
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.