RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-05_11:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 16.11 16.2099 0.490995
2 to 25 15.80 16.9843 0.544570
3 to 26 15.43 22.2965 0.826415
4 to 27 15.67 20.5193 0.751465
5 to 28 15.43 29.1746 0.967050
6 to 29 15.46 19.3704 0.692312
7 to 30 15.76 15.5401 0.443360
8 to 31 15.69 35.4711 0.994608
9 to 32 16.04 15.8982 0.468935
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.061731
Tough bday spacings test for dh-ranFile-2018-07-05_11:31: 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 12 44 85 86 94 85 50 29 10 3 2
(O-E)^2/E 0.9 1.5 1.9 1.4 0.1 0.6 0.1 0.0 1.6 2.0 1.0
Birthday Spacings: Sum(O-E)^2/E= 11.116, p= 0.651
RESULTS OF GCD FOR dh-ranFile-2018-07-05_11:31
Euclid's algorithm:
p-value, steps to gcd: 0.655051
p-value, dist. of gcd's: 0.361892
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-05_11:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.991 0.007 0.467 0.415 0.980 0.805 0.792 0.223
Bits 8 to 15---> 0.529 0.624 0.677 0.197 0.464 0.292 0.895 0.811
Bits 16 to 23---> 0.436 0.964 0.166 0.044 0.533 0.156 0.979 0.293
Bits 24 to 31---> 0.749 0.942 0.576 0.749 0.797 0.304 0.012 0.707
KS test for the above 32 p values: 0.609
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-05_11:31,
p-values for 5 runs: 0.3723, 0.8715, 0.3705, 0.5381, 0.8652
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-05_11:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 204 211.4 0.260 0.260
r= 29 5143 5134.0 0.016 0.276
r= 30 22992 23103.0 0.534 0.810
r= 31 11661 11551.5 1.038 1.847
chi-square = 1.847 with df = 3; p-value = 0.395
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-05_11:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 215 211.4 0.061 0.061
r= 30 5149 5134.0 0.044 0.104
r= 31 23130 23103.0 0.031 0.136
r= 32 11506 11551.5 0.179 0.315
chi-square = 0.315 with df = 3; p-value = 0.043
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-05_11:31
b-rank test for bits 1 to 8, p=0.86375
b-rank test for bits 2 to 9, p=0.47446
b-rank test for bits 3 to 10, p=0.35406
b-rank test for bits 4 to 11, p=0.30598
b-rank test for bits 5 to 12, p=0.35955
b-rank test for bits 6 to 13, p=0.20230
b-rank test for bits 7 to 14, p=0.45424
b-rank test for bits 8 to 15, p=0.95556
b-rank test for bits 9 to 16, p=0.45903
b-rank test for bits 10 to 17, p=0.30292
b-rank test for bits 11 to 18, p=0.19842
b-rank test for bits 12 to 19, p=0.00443
b-rank test for bits 13 to 20, p=0.37628
b-rank test for bits 14 to 21, p=0.37210
b-rank test for bits 15 to 22, p=0.34381
b-rank test for bits 16 to 23, p=0.50747
b-rank test for bits 17 to 24, p=0.85416
b-rank test for bits 18 to 25, p=0.71515
b-rank test for bits 19 to 26, p=0.14877
b-rank test for bits 20 to 27, p=0.44344
b-rank test for bits 21 to 28, p=0.75009
b-rank test for bits 22 to 29, p=0.82165
b-rank test for bits 23 to 30, p=0.06475
b-rank test for bits 24 to 31, p=0.67446
b-rank test for bits 25 to 32, p=0.76044
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 = 0.620493
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-05_11:31
(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 141300 -1.42 0.077271
2 142146 0.55 0.709857
3 141109 -1.87 0.030747
4 141173 -1.72 0.042680
5 141610 -0.70 0.242161
6 141792 -0.27 0.391990
7 142268 0.84 0.798989
8 142391 1.13 0.869790
9 142780 2.03 0.979038
10 142257 0.81 0.791694
11 142088 0.42 0.661827
12 141624 -0.67 0.252495
13 142116 0.48 0.685407
14 141891 -0.04 0.482920
15 142054 0.34 0.632324
16 142158 0.58 0.719381
17 142268 0.84 0.798989
18 141614 -0.69 0.245090
19 141313 -1.39 0.081765
20 141473 -1.02 0.153992
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-05_11:31
Bits used No. missing words z-score p-value
23 to 32 142020 0.3816 0.648629
22 to 31 142342 1.4920 0.932146
21 to 30 142117 0.7161 0.763036
20 to 29 141980 0.2437 0.596264
19 to 28 141763 -0.5046 0.306925
18 to 27 142292 1.3196 0.906508
17 to 26 142222 1.0782 0.859522
16 to 25 141809 -0.3460 0.364684
15 to 24 141967 0.1989 0.578815
14 to 23 142177 0.9230 0.821996
13 to 22 142134 0.7747 0.780749
12 to 21 142061 0.5230 0.699513
11 to 20 141639 -0.9322 0.175624
10 to 19 141940 0.1058 0.542113
9 to 18 141623 -0.9873 0.161737
8 to 17 141962 0.1816 0.572060
7 to 16 141921 0.0402 0.516050
6 to 15 141743 -0.5736 0.283136
5 to 14 141281 -2.1667 0.015131
4 to 13 141843 -0.2287 0.409542
3 to 12 141813 -0.3322 0.369880
2 to 11 141356 -1.9080 0.028193
1 to 10 141497 -1.4218 0.077538
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-05_11:31
Bits used No. missing words z-score p-value
28 to 32 142072 0.5514 0.709328
27 to 31 142117 0.7040 0.759273
26 to 30 142314 1.3718 0.914931
25 to 29 141750 -0.5401 0.294564
24 to 28 141961 0.1752 0.569520
23 to 27 142255 1.1718 0.879354
22 to 26 142231 1.0904 0.862233
21 to 25 141586 -1.0960 0.136532
20 to 24 141363 -1.8520 0.032015
19 to 23 142142 0.7887 0.784860
18 to 22 141521 -1.3164 0.094024
17 to 21 142427 1.7548 0.960354
16 to 20 142479 1.9311 0.973264
15 to 19 141761 -0.5028 0.307548
14 to 18 141693 -0.7333 0.231681
13 to 17 141782 -0.4316 0.333006
12 to 16 142243 1.1311 0.870990
11 to 15 141934 0.0836 0.533324
10 to 14 141850 -0.2011 0.420303
9 to 13 141491 -1.4181 0.078086
8 to 12 141797 -0.3808 0.351683
7 to 11 142015 0.3582 0.639905
6 to 10 142219 1.0497 0.853079
5 to 9 141413 -1.6825 0.046238
4 to 8 142072 0.5514 0.709328
3 to 7 142450 1.8328 0.966582
2 to 6 142198 0.9785 0.836097
1 to 5 142014 0.3548 0.638635
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-05_11:31
Bits used No. missing words z-score p-value
31 to 32 141920 0.0315 0.512555
30 to 31 141834 -0.2222 0.412074
29 to 30 142294 1.1347 0.871754
28 to 29 141811 -0.2901 0.385886
27 to 28 142188 0.8220 0.794472
26 to 27 142149 0.7070 0.760214
25 to 26 141576 -0.9833 0.162736
24 to 25 141659 -0.7384 0.230125
23 to 24 141789 -0.3550 0.361311
22 to 23 142219 0.9135 0.819505
21 to 22 142426 1.5241 0.936258
20 to 21 142206 0.8751 0.809249
19 to 20 142007 0.2881 0.613370
18 to 19 141951 0.1229 0.548915
17 to 18 141464 -1.3137 0.094481
16 to 17 142736 2.4386 0.992627
15 to 16 142029 0.3530 0.637959
14 to 15 141527 -1.1278 0.129699
13 to 14 142191 0.8309 0.796981
12 to 13 141795 -0.3373 0.367962
11 to 12 142363 1.3383 0.909594
10 to 11 142108 0.5860 0.721078
9 to 10 141324 -1.7266 0.042116
8 to 9 142115 0.6067 0.727974
7 to 8 142143 0.6893 0.754680
6 to 7 141938 0.0846 0.533699
5 to 6 141686 -0.6588 0.255015
4 to 5 142056 0.4327 0.667367
3 to 4 142070 0.4740 0.682233
2 to 3 141576 -0.9833 0.162736
1 to 2 142696 2.3206 0.989845
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-05_11:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2558.71 0.830 0.796795
Test results for specific bytes for dh-ranFile-2018-07-05_11:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2544.36 0.627 0.734803
2 to 9 2480.95 -0.269 0.393808
3 to 10 2482.70 -0.245 0.403335
4 to 11 2495.31 -0.066 0.473582
5 to 12 2460.80 -0.554 0.289648
6 to 13 2496.48 -0.050 0.480168
7 to 14 2484.59 -0.218 0.413722
8 to 15 2426.27 -1.043 0.148546
9 to 16 2552.22 0.738 0.769892
10 to 17 2463.29 -0.519 0.301812
11 to 18 2468.35 -0.448 0.327220
12 to 19 2563.39 0.896 0.815007
13 to 20 2578.86 1.115 0.867620
14 to 21 2425.45 -1.054 0.145875
15 to 22 2524.27 0.343 0.634297
16 to 23 2385.48 -1.620 0.052661
17 to 24 2326.31 -2.456 0.007018
18 to 25 2460.65 -0.556 0.288952
19 to 26 2438.04 -0.876 0.190460
20 to 27 2441.05 -0.834 0.202212
21 to 28 2431.05 -0.975 0.164743
22 to 29 2599.69 1.410 0.920701
23 to 30 2458.01 -0.594 0.276295
24 to 31 2460.42 -0.560 0.287823
25 to 32 2453.56 -0.657 0.255671
CDPARK for dh-ranFile-2018-07-05_11:31: 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
3541 0.8219 0.794438
3501 -1.0046 0.157553
3510 -0.5936 0.276387
3576 2.4201 0.992242
3490 -1.5068 0.065925
3509 -0.6393 0.261324
3541 0.8219 0.794438
3525 0.0913 0.536383
3561 1.7352 0.958644
3541 0.8219 0.794438
Square side=100, avg. no. parked=3529.50 sample std.=25.97
p-value of the KSTEST for those 10 p-values: 0.447958
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-05_11:31
0.5286,0.3673,0.1809,0.3891,0.5557,0.2995,0.5327,0.4580,0.5756,0.4588,
The KS test for those 10 p-values: 0.111088
The 3DSPHERES test for dh-ranFile-2018-07-05_11:31
sample no r^3 equiv. uni.
1 0.609 0.020107
2 220.538 0.999358
3 18.587 0.461831
4 14.782 0.389043
5 3.738 0.117160
6 19.897 0.484824
7 75.844 0.920191
8 15.326 0.400030
9 0.220 0.007296
10 24.298 0.555112
11 10.469 0.294584
12 26.611 0.588119
13 5.002 0.153569
14 25.149 0.567556
15 43.024 0.761677
16 9.331 0.267321
17 0.160 0.005316
18 25.000 0.565403
19 48.588 0.802022
20 10.801 0.302336
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.246352
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-05_11:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 1.3 -0.1 0.5 0.7 0.1
0.1 1.2 -1.4 0.1 1.6 0.1
-0.4 -0.5 0.9 -0.9 0.6 0.1
-0.5 0.5 1.5 -1.2 -0.9 -0.5
0.7 -0.4 -0.9 -0.5 1.7 -0.3
-0.6 -0.5 -0.3 -1.2 0.1 -1.7
0.0 1.1 -0.4 -0.1 0.9 0.0
-1.1
Chi-square with 42 degrees of freedom:30.731822
z-score=-1.229459, p-value=0.099209
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-05_11:31
Test no p-value
1 0.083862
2 0.003856
3 0.778106
4 0.305760
5 0.384073
6 0.025151
7 0.088404
8 0.220547
9 0.040486
10 0.652672
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.004768
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-05_11:31:
(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 66418 0.93 66909 0.88
3 25000.00 25337 4.54 24910 0.32
4 6666.67 6550 2.04 6541 2.37
5 1388.89 1401 0.11 1354 0.88
6 238.10 255 1.20 248 0.41
7 34.72 36 0.05 32 0.21
8 4.96 2 1.77 5 0.00
p=0.89955 p=0.46586
Number of rngs required: 687122, p-value: 0.067
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-05_11:31
No. of wins: Observed Expected
98345 98585.9
z-score=-1.077, pvalue=0.14068
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66705 66666.7 0.022 0.022
2 37574 37654.3 0.171 0.193
3 27009 26954.7 0.109 0.303
4 19325 19313.5 0.007 0.310
5 13876 13851.4 0.044 0.353
6 9965 9943.5 0.046 0.399
7 7085 7145.0 0.504 0.904
8 5144 5139.1 0.005 0.908
9 3614 3699.9 1.993 2.901
10 2719 2666.3 1.042 3.943
11 1897 1923.3 0.360 4.303
12 1411 1388.7 0.357 4.660
13 999 1003.7 0.022 4.682
14 734 726.1 0.085 4.767
15 523 525.8 0.015 4.783
16 393 381.2 0.368 5.151
17 299 276.5 1.824 6.975
18 184 200.8 1.410 8.386
19 148 146.0 0.028 8.413
20 104 106.2 0.046 8.460
21 292 287.1 0.083 8.543
Chisq= 8.54 for 20 degrees of freedom, p= 0.01238
SUMMARY of craptest
p-value for no. of wins: 0.140682
p-value for throws/game: 0.012377
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-05_11:31
No. of wins: Observed Expected
98638 98585.9
z-score= 0.233, pvalue=0.59220
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66406 66666.7 1.019 1.019
2 37547 37654.3 0.306 1.325
3 27228 26954.7 2.770 4.095
4 19418 19313.5 0.566 4.661
5 13808 13851.4 0.136 4.797
6 9987 9943.5 0.190 4.987
7 6974 7145.0 4.094 9.081
8 5200 5139.1 0.722 9.803
9 3768 3699.9 1.255 11.058
10 2696 2666.3 0.331 11.389
11 1913 1923.3 0.055 11.445
12 1407 1388.7 0.240 11.685
13 949 1003.7 2.983 14.667
14 753 726.1 0.994 15.661
15 584 525.8 6.434 22.094
16 356 381.2 1.660 23.754
17 266 276.5 0.402 24.156
18 188 200.8 0.820 24.975
19 146 146.0 0.000 24.975
20 112 106.2 0.315 25.290
21 294 287.1 0.165 25.456
Chisq= 25.46 for 20 degrees of freedom, p= 0.81545
SUMMARY of craptest
p-value for no. of wins: 0.592200
p-value for throws/game: 0.815446
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0039,0.0044,0.0048,0.0053,0.0070,0.0073,0.0073,0.0124,0.0124,0.0151,
0.0201,0.0252,0.0282,0.0307,0.0320,0.0405,0.0421,0.0427,0.0429,0.0438,
0.0462,0.0527,0.0617,0.0648,0.0659,0.0673,0.0773,0.0775,0.0781,0.0818,
0.0839,0.0884,0.0940,0.0945,0.0992,0.1111,0.1172,0.1297,0.1365,0.1407,
0.1459,0.1485,0.1488,0.1536,0.1540,0.1559,0.1576,0.1617,0.1627,0.1627,
0.1647,0.1655,0.1756,0.1809,0.1905,0.1968,0.1984,0.2022,0.2023,0.2205,
0.2228,0.2301,0.2317,0.2422,0.2451,0.2464,0.2525,0.2550,0.2557,0.2613,
0.2673,0.2763,0.2764,0.2831,0.2878,0.2890,0.2896,0.2921,0.2931,0.2946,
0.2946,0.2995,0.3018,0.3023,0.3029,0.3043,0.3058,0.3060,0.3069,0.3075,
0.3272,0.3330,0.3438,0.3517,0.3541,0.3596,0.3613,0.3619,0.3647,0.3673,
0.3680,0.3699,0.3705,0.3721,0.3723,0.3763,0.3841,0.3859,0.3890,0.3891,
0.3920,0.3938,0.3953,0.4000,0.4033,0.4095,0.4121,0.4137,0.4149,0.4203,
0.4356,0.4434,0.4434,0.4480,0.4542,0.4580,0.4588,0.4590,0.4618,0.4639,
0.4659,0.4671,0.4689,0.4736,0.4745,0.4802,0.4829,0.4848,0.4910,0.5075,
0.5126,0.5160,0.5286,0.5294,0.5327,0.5327,0.5333,0.5337,0.5364,0.5381,
0.5421,0.5446,0.5489,0.5551,0.5557,0.5654,0.5676,0.5695,0.5721,0.5756,
0.5763,0.5788,0.5881,0.5922,0.5963,0.6087,0.6134,0.6205,0.6242,0.6323,
0.6343,0.6380,0.6386,0.6399,0.6486,0.6514,0.6527,0.6551,0.6618,0.6674,
0.6745,0.6774,0.6822,0.6854,0.6923,0.6995,0.7074,0.7093,0.7093,0.7099,
0.7151,0.7194,0.7211,0.7280,0.7348,0.7490,0.7493,0.7501,0.7515,0.7547,
0.7593,0.7602,0.7604,0.7617,0.7630,0.7699,0.7781,0.7807,0.7849,0.7917,
0.7923,0.7944,0.7944,0.7944,0.7945,0.7965,0.7968,0.7970,0.7990,0.7990,
0.8020,0.8050,0.8092,0.8106,0.8150,0.8154,0.8195,0.8216,0.8220,0.8264,
0.8361,0.8531,0.8542,0.8595,0.8622,0.8637,0.8652,0.8676,0.8698,0.8710,
0.8715,0.8718,0.8794,0.8955,0.8995,0.9065,0.9096,0.9149,0.9202,0.9207,
0.9321,0.9363,0.9418,0.9556,0.9586,0.9604,0.9641,0.9666,0.9671,0.9733,
0.9790,0.9790,0.9798,0.9898,0.9913,0.9922,0.9926,0.9946,0.9994,
Overall p-value after applying KStest on 269 p-values = 0.599305
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.