RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-25_03:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 16.09 12.4749 0.229435
2 to 25 15.67 18.3902 0.635369
3 to 26 15.96 6.4163 0.010077
4 to 27 15.80 20.7904 0.764196
5 to 28 15.71 21.6500 0.801443
6 to 29 15.72 12.3772 0.223223
7 to 30 15.76 17.6320 0.587597
8 to 31 15.71 19.0750 0.675755
9 to 32 15.90 16.4750 0.509553
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.730375
Tough bday spacings test for dh-ranFile-2018-06-25_03:31: 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 31 65 125 92 81 49 32 9 6 4
(O-E)^2/E 1.1 0.9 0.9 7.6 0.3 0.1 0.2 0.2 2.3 0.1 0.0
Birthday Spacings: Sum(O-E)^2/E= 13.697, p= 0.813
RESULTS OF GCD FOR dh-ranFile-2018-06-25_03:31
Euclid's algorithm:
p-value, steps to gcd: 0.675020
p-value, dist. of gcd's: 0.872291
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-25_03:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.924 0.794 0.755 0.451 0.513 0.392 0.499 0.704
Bits 8 to 15---> 0.542 0.848 0.812 0.784 0.447 0.682 0.179 0.942
Bits 16 to 23---> 0.467 0.863 0.528 0.832 0.290 0.713 0.168 0.526
Bits 24 to 31---> 0.371 0.724 0.240 0.271 0.916 0.985 0.600 0.208
KS test for the above 32 p values: 0.912
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-25_03:31,
p-values for 5 runs: 0.3435, 0.8701, 0.8956, 0.5882, 0.8284
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-25_03:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 224 211.4 0.749 0.749
r= 29 5078 5134.0 0.611 1.360
r= 30 23134 23103.0 0.041 1.401
r= 31 11564 11551.5 0.013 1.415
chi-square = 1.415 with df = 3; p-value = 0.298
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-25_03:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 184 211.4 3.556 3.556
r= 30 5183 5134.0 0.467 4.023
r= 31 23141 23103.0 0.062 4.086
r= 32 11492 11551.5 0.307 4.392
chi-square = 4.392 with df = 3; p-value = 0.778
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-25_03:31
b-rank test for bits 1 to 8, p=0.70236
b-rank test for bits 2 to 9, p=0.31107
b-rank test for bits 3 to 10, p=0.29826
b-rank test for bits 4 to 11, p=0.39786
b-rank test for bits 5 to 12, p=0.41701
b-rank test for bits 6 to 13, p=0.27664
b-rank test for bits 7 to 14, p=0.73877
b-rank test for bits 8 to 15, p=0.16218
b-rank test for bits 9 to 16, p=0.75733
b-rank test for bits 10 to 17, p=0.42796
b-rank test for bits 11 to 18, p=0.38604
b-rank test for bits 12 to 19, p=0.48898
b-rank test for bits 13 to 20, p=0.02952
b-rank test for bits 14 to 21, p=0.60523
b-rank test for bits 15 to 22, p=0.52047
b-rank test for bits 16 to 23, p=0.02359
b-rank test for bits 17 to 24, p=0.25506
b-rank test for bits 18 to 25, p=0.87594
b-rank test for bits 19 to 26, p=0.11598
b-rank test for bits 20 to 27, p=0.79161
b-rank test for bits 21 to 28, p=0.30222
b-rank test for bits 22 to 29, p=0.86503
b-rank test for bits 23 to 30, p=0.08642
b-rank test for bits 24 to 31, p=0.74345
b-rank test for bits 25 to 32, p=0.79789
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 = 0.613527
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-25_03:31
(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 141784 -0.29 0.384827
2 142310 0.94 0.825401
3 142057 0.35 0.634962
4 142272 0.85 0.801603
5 142448 1.26 0.895908
6 142024 0.27 0.605620
7 141534 -0.88 0.190260
8 141518 -0.91 0.180274
9 141058 -1.99 0.023346
10 141808 -0.24 0.406425
11 142537 1.47 0.928746
12 141635 -0.64 0.260775
13 140817 -2.55 0.005353
14 141564 -0.81 0.209878
15 142234 0.76 0.775947
16 142190 0.66 0.744014
17 142659 1.75 0.960076
18 141949 0.09 0.536924
19 142301 0.92 0.819935
20 141819 -0.21 0.416424
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-25_03:31
Bits used No. missing words z-score p-value
23 to 32 141928 0.0644 0.525666
22 to 31 142344 1.4989 0.933045
21 to 30 141772 -0.4736 0.317910
20 to 29 141833 -0.2632 0.396196
19 to 28 141971 0.2127 0.584202
18 to 27 142438 1.8230 0.965848
17 to 26 142157 0.8540 0.803457
16 to 25 141615 -1.0149 0.155069
15 to 24 141752 -0.5425 0.293731
14 to 23 141922 0.0437 0.517424
13 to 22 142069 0.5506 0.709041
12 to 21 142309 1.3782 0.915925
11 to 20 142161 0.8678 0.807256
10 to 19 141932 0.0782 0.531155
9 to 18 141664 -0.8460 0.198786
8 to 17 141802 -0.3701 0.355653
7 to 16 141950 0.1402 0.555765
6 to 15 142339 1.4816 0.930779
5 to 14 141754 -0.5356 0.296110
4 to 13 142463 1.9092 0.971882
3 to 12 141715 -0.6701 0.251396
2 to 11 141834 -0.2598 0.397525
1 to 10 142392 1.6644 0.951982
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-25_03:31
Bits used No. missing words z-score p-value
28 to 32 142244 1.1345 0.871702
27 to 31 142071 0.5480 0.708166
26 to 30 142284 1.2701 0.897970
25 to 29 141773 -0.4621 0.321992
24 to 28 141924 0.0497 0.519831
23 to 27 141864 -0.1537 0.438939
22 to 26 141892 -0.0587 0.476577
21 to 25 141511 -1.3503 0.088465
20 to 24 141850 -0.2011 0.420303
19 to 23 141913 0.0124 0.504963
18 to 22 141853 -0.1909 0.424283
17 to 21 141357 -1.8723 0.030582
16 to 20 142344 1.4735 0.929686
15 to 19 142381 1.5989 0.945077
14 to 18 142468 1.8938 0.970874
13 to 17 142119 0.7107 0.761379
12 to 16 141433 -1.6147 0.053190
11 to 15 141768 -0.4791 0.315939
10 to 14 142129 0.7446 0.771757
9 to 13 141739 -0.5774 0.281838
8 to 12 141943 0.1141 0.545435
7 to 11 142588 2.3006 0.989292
6 to 10 141691 -0.7401 0.229619
5 to 9 142027 0.3989 0.655010
4 to 8 141958 0.1650 0.565521
3 to 7 141450 -1.5571 0.059729
2 to 6 141777 -0.4486 0.326869
1 to 5 142015 0.3582 0.639905
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-25_03:31
Bits used No. missing words z-score p-value
31 to 32 141978 0.2026 0.580263
30 to 31 141801 -0.3196 0.374652
29 to 30 142319 1.2085 0.886566
28 to 29 141688 -0.6529 0.256913
27 to 28 142387 1.4091 0.920591
26 to 27 141811 -0.2901 0.385886
25 to 26 142030 0.3560 0.639064
24 to 25 142011 0.2999 0.617878
23 to 24 141706 -0.5998 0.274322
22 to 23 142333 1.2498 0.894307
21 to 22 141734 -0.5172 0.302509
20 to 21 141753 -0.4612 0.322345
19 to 20 141277 -1.8653 0.031071
18 to 19 142418 1.5005 0.933258
17 to 18 141454 -1.3432 0.089611
16 to 17 141432 -1.4081 0.079558
15 to 16 141792 -0.3461 0.364632
14 to 15 141872 -0.1101 0.456158
13 to 14 141862 -0.1396 0.444482
12 to 13 141608 -0.8889 0.187034
11 to 12 142354 1.3117 0.905191
10 to 11 141713 -0.5791 0.281246
9 to 10 142029 0.3530 0.637959
8 to 9 142359 1.3265 0.907656
7 to 8 141595 -0.9272 0.176904
6 to 7 142003 0.2763 0.608846
5 to 6 141925 0.0462 0.518434
4 to 5 141694 -0.6352 0.262652
3 to 4 142327 1.2321 0.891038
2 to 3 141533 -1.1101 0.133474
1 to 2 141648 -0.7709 0.220388
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-25_03:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2564.65 0.914 0.819708
Test results for specific bytes for dh-ranFile-2018-06-25_03:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2628.92 1.823 0.965858
2 to 9 2487.51 -0.177 0.429924
3 to 10 2481.18 -0.266 0.395037
4 to 11 2631.44 1.859 0.968475
5 to 12 2444.67 -0.782 0.216962
6 to 13 2561.21 0.866 0.806657
7 to 14 2417.20 -1.171 0.120795
8 to 15 2638.63 1.961 0.975035
9 to 16 2586.82 1.228 0.890243
10 to 17 2527.98 0.396 0.653861
11 to 18 2554.02 0.764 0.777548
12 to 19 2500.90 0.013 0.505055
13 to 20 2481.67 -0.259 0.397736
14 to 21 2470.01 -0.424 0.335741
15 to 22 2511.74 0.166 0.565954
16 to 23 2477.76 -0.315 0.376562
17 to 24 2436.55 -0.897 0.184756
18 to 25 2439.29 -0.859 0.195287
19 to 26 2524.02 0.340 0.632964
20 to 27 2537.45 0.530 0.701806
21 to 28 2478.87 -0.299 0.382536
22 to 29 2406.92 -1.316 0.094033
23 to 30 2573.97 1.046 0.852239
24 to 31 2518.04 0.255 0.600689
25 to 32 2492.24 -0.110 0.456295
CDPARK for dh-ranFile-2018-06-25_03:31: 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
3505 -0.8219 0.205562
3522 -0.0457 0.481790
3505 -0.8219 0.205562
3515 -0.3653 0.357445
3540 0.7763 0.781201
3517 -0.2740 0.392053
3525 0.0913 0.536383
3526 0.1370 0.554479
3519 -0.1826 0.427537
3500 -1.0502 0.146807
Square side=100, avg. no. parked=3517.40 sample std.=11.32
p-value of the KSTEST for those 10 p-values: 0.262963
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-25_03:31
0.2560,0.5486,0.7134,0.0889,0.5715,0.7767,0.1018,0.0743,0.3174,0.4203,
The KS test for those 10 p-values: 0.352446
The 3DSPHERES test for dh-ranFile-2018-06-25_03:31
sample no r^3 equiv. uni.
1 2.861 0.090966
2 73.229 0.912923
3 10.543 0.296329
4 12.225 0.334684
5 4.670 0.144143
6 4.125 0.128472
7 31.282 0.647505
8 0.372 0.012335
9 27.383 0.598584
10 13.077 0.353315
11 25.998 0.579620
12 11.010 0.307188
13 38.268 0.720733
14 6.705 0.200282
15 52.021 0.823427
16 27.676 0.602485
17 9.341 0.267565
18 4.005 0.124960
19 47.992 0.798049
20 73.597 0.913985
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.624087
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-25_03:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 0.5 0.1 -1.4 -2.2 -0.1
0.7 -0.0 1.1 -0.8 0.5 -0.8
-0.6 1.8 0.4 -0.5 -0.4 -0.7
-1.0 1.1 -1.5 1.7 1.4 -0.7
0.6 0.5 -0.7 0.4 0.0 -0.9
-0.1 -1.6 -0.7 -1.6 0.3 1.1
1.9 1.1 -1.2 -0.7 0.9 -1.0
-1.1
Chi-square with 42 degrees of freedom:43.821092
z-score=0.198697, p-value=0.605827
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-25_03:31
Test no p-value
1 0.477802
2 0.201984
3 0.029985
4 0.168632
5 0.012577
6 0.737114
7 0.585995
8 0.066113
9 0.670473
10 0.604577
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.110431
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-25_03:31:
(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 66695 0.01 66591 0.09
3 25000.00 24914 0.30 25317 4.02
4 6666.67 6689 0.07 6427 8.62
5 1388.89 1431 1.28 1392 0.01
6 238.10 236 0.02 232 0.16
7 34.72 34 0.01 37 0.15
8 4.96 0 4.96 3 0.77
p=0.64585 p=0.96816
Number of rngs required: 687187, p-value: 0.078
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-25_03:31
No. of wins: Observed Expected
98651 98585.9
z-score= 0.291, pvalue=0.61461
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66921 66666.7 0.970 0.970
2 37390 37654.3 1.855 2.826
3 26981 26954.7 0.026 2.851
4 19290 19313.5 0.029 2.880
5 13880 13851.4 0.059 2.939
6 10017 9943.5 0.543 3.481
7 7226 7145.0 0.918 4.399
8 5120 5139.1 0.071 4.470
9 3651 3699.9 0.645 5.115
10 2621 2666.3 0.770 5.885
11 1860 1923.3 2.085 7.970
12 1378 1388.7 0.083 8.053
13 1018 1003.7 0.203 8.256
14 696 726.1 1.251 9.508
15 532 525.8 0.072 9.580
16 398 381.2 0.745 10.325
17 268 276.5 0.264 10.588
18 203 200.8 0.023 10.612
19 152 146.0 0.248 10.860
20 92 106.2 1.902 12.762
21 306 287.1 1.242 14.004
Chisq= 14.00 for 20 degrees of freedom, p= 0.16973
SUMMARY of craptest
p-value for no. of wins: 0.614608
p-value for throws/game: 0.169729
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-25_03:31
No. of wins: Observed Expected
98570 98585.9
z-score=-0.071, pvalue=0.47173
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66583 66666.7 0.105 0.105
2 37802 37654.3 0.579 0.684
3 27012 26954.7 0.122 0.806
4 19346 19313.5 0.055 0.861
5 13856 13851.4 0.002 0.862
6 9952 9943.5 0.007 0.869
7 7151 7145.0 0.005 0.874
8 5043 5139.1 1.796 2.670
9 3594 3699.9 3.029 5.700
10 2703 2666.3 0.505 6.205
11 1990 1923.3 2.311 8.516
12 1390 1388.7 0.001 8.517
13 995 1003.7 0.076 8.593
14 773 726.1 3.024 11.617
15 465 525.8 7.038 18.655
16 362 381.2 0.962 19.617
17 248 276.5 2.945 22.562
18 215 200.8 1.000 23.562
19 131 146.0 1.538 25.100
20 94 106.2 1.405 26.505
21 295 287.1 0.217 26.722
Chisq= 26.72 for 20 degrees of freedom, p= 0.85672
SUMMARY of craptest
p-value for no. of wins: 0.471727
p-value for throws/game: 0.856724
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0054,0.0101,0.0123,0.0126,0.0233,0.0236,0.0295,0.0300,0.0306,0.0311,
0.0532,0.0597,0.0661,0.0743,0.0780,0.0796,0.0864,0.0885,0.0889,0.0896,
0.0910,0.0940,0.1018,0.1104,0.1160,0.1208,0.1250,0.1285,0.1335,0.1441,
0.1468,0.1551,0.1622,0.1680,0.1686,0.1697,0.1769,0.1795,0.1803,0.1848,
0.1870,0.1903,0.1953,0.1988,0.2003,0.2020,0.2056,0.2056,0.2084,0.2099,
0.2170,0.2204,0.2232,0.2294,0.2296,0.2397,0.2514,0.2551,0.2560,0.2569,
0.2608,0.2627,0.2630,0.2676,0.2715,0.2743,0.2766,0.2812,0.2818,0.2898,
0.2937,0.2961,0.2963,0.2979,0.2983,0.3022,0.3025,0.3072,0.3111,0.3159,
0.3174,0.3179,0.3220,0.3223,0.3269,0.3347,0.3357,0.3435,0.3524,0.3533,
0.3557,0.3574,0.3646,0.3713,0.3747,0.3766,0.3825,0.3848,0.3859,0.3860,
0.3916,0.3921,0.3950,0.3962,0.3975,0.3977,0.3979,0.4064,0.4164,0.4170,
0.4203,0.4203,0.4243,0.4275,0.4280,0.4299,0.4389,0.4445,0.4470,0.4507,
0.4562,0.4563,0.4667,0.4717,0.4766,0.4778,0.4818,0.4890,0.4994,0.5050,
0.5051,0.5096,0.5134,0.5174,0.5184,0.5198,0.5205,0.5257,0.5257,0.5276,
0.5312,0.5364,0.5369,0.5416,0.5454,0.5486,0.5545,0.5558,0.5655,0.5660,
0.5715,0.5796,0.5803,0.5842,0.5860,0.5876,0.5882,0.5986,0.6002,0.6007,
0.6025,0.6046,0.6052,0.6056,0.6058,0.6088,0.6135,0.6146,0.6179,0.6241,
0.6330,0.6350,0.6354,0.6380,0.6391,0.6399,0.6458,0.6475,0.6539,0.6550,
0.6705,0.6750,0.6758,0.6815,0.7018,0.7024,0.7038,0.7082,0.7090,0.7129,
0.7134,0.7207,0.7242,0.7304,0.7371,0.7388,0.7435,0.7440,0.7553,0.7573,
0.7614,0.7642,0.7718,0.7759,0.7767,0.7775,0.7779,0.7812,0.7836,0.7916,
0.7944,0.7979,0.7980,0.8014,0.8016,0.8035,0.8067,0.8073,0.8124,0.8127,
0.8197,0.8199,0.8234,0.8254,0.8284,0.8320,0.8478,0.8522,0.8567,0.8634,
0.8650,0.8701,0.8717,0.8723,0.8759,0.8866,0.8902,0.8910,0.8943,0.8956,
0.8959,0.8980,0.9052,0.9077,0.9122,0.9129,0.9140,0.9159,0.9163,0.9206,
0.9239,0.9287,0.9297,0.9308,0.9330,0.9333,0.9424,0.9451,0.9520,0.9601,
0.9658,0.9659,0.9682,0.9685,0.9709,0.9719,0.9750,0.9851,0.9893,
Overall p-value after applying KStest on 269 p-values = 0.590116
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.