RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-28_02:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.56 17.6081 0.586039
2 to 25 15.59 18.9358 0.667769
3 to 26 15.54 23.4895 0.866017
4 to 27 16.17 12.4695 0.229085
5 to 28 15.96 35.7310 0.995019
6 to 29 15.86 13.0756 0.268889
7 to 30 15.83 12.2049 0.212427
8 to 31 15.66 24.2034 0.885988
9 to 32 15.99 19.9272 0.722032
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.372293
Tough bday spacings test for dh-ranFile-2018-06-28_02:31: 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 34 60 112 89 71 60 35 19 5 3
(O-E)^2/E 0.9 0.2 2.4 2.1 0.8 0.7 1.2 0.9 1.1 0.4 0.3
Birthday Spacings: Sum(O-E)^2/E= 10.925, p= 0.637
RESULTS OF GCD FOR dh-ranFile-2018-06-28_02:31
Euclid's algorithm:
p-value, steps to gcd: 0.412592
p-value, dist. of gcd's: 0.076581
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-28_02:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.827 0.973 0.018 0.880 0.693 0.748 0.455 0.771
Bits 8 to 15---> 0.077 0.202 0.136 0.867 0.845 0.923 0.168 0.533
Bits 16 to 23---> 0.420 0.994 0.534 0.781 0.749 0.359 0.824 0.826
Bits 24 to 31---> 0.002 0.577 0.988 0.681 0.601 0.493 0.372 0.433
KS test for the above 32 p values: 0.885
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-28_02:31,
p-values for 5 runs: 0.7093, 0.3848, 0.7629, 0.3093, 0.6126
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-28_02:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 226 211.4 1.006 1.006
r= 29 5131 5134.0 0.002 1.008
r= 30 23119 23103.0 0.011 1.019
r= 31 11524 11551.5 0.066 1.084
chi-square = 1.084 with df = 3; p-value = 0.219
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-28_02:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 219 211.4 0.272 0.272
r= 30 5211 5134.0 1.155 1.426
r= 31 23056 23103.0 0.096 1.522
r= 32 11514 11551.5 0.122 1.644
chi-square = 1.644 with df = 3; p-value = 0.351
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-28_02:31
b-rank test for bits 1 to 8, p=0.08219
b-rank test for bits 2 to 9, p=0.76020
b-rank test for bits 3 to 10, p=0.43232
b-rank test for bits 4 to 11, p=0.65229
b-rank test for bits 5 to 12, p=0.21776
b-rank test for bits 6 to 13, p=0.78093
b-rank test for bits 7 to 14, p=0.38125
b-rank test for bits 8 to 15, p=0.04946
b-rank test for bits 9 to 16, p=0.20502
b-rank test for bits 10 to 17, p=0.30584
b-rank test for bits 11 to 18, p=0.85316
b-rank test for bits 12 to 19, p=0.68779
b-rank test for bits 13 to 20, p=0.84771
b-rank test for bits 14 to 21, p=0.21290
b-rank test for bits 15 to 22, p=0.22809
b-rank test for bits 16 to 23, p=0.85180
b-rank test for bits 17 to 24, p=0.15532
b-rank test for bits 18 to 25, p=0.92259
b-rank test for bits 19 to 26, p=0.87297
b-rank test for bits 20 to 27, p=0.32713
b-rank test for bits 21 to 28, p=0.14262
b-rank test for bits 22 to 29, p=0.84043
b-rank test for bits 23 to 30, p=0.60088
b-rank test for bits 24 to 31, p=0.85125
b-rank test for bits 25 to 32, p=0.38768
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 = 0.672587
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-28_02:31
(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 141478 -1.01 0.156780
2 141975 0.15 0.560972
3 141107 -1.87 0.030424
4 141707 -0.47 0.318202
5 141871 -0.09 0.464320
6 141594 -0.74 0.230637
7 141480 -1.00 0.157905
8 142067 0.37 0.643708
9 142343 1.01 0.844529
10 142812 2.11 0.982530
11 142387 1.12 0.867800
12 142332 0.99 0.838313
13 140961 -2.22 0.013355
14 141458 -1.05 0.145825
15 142185 0.64 0.740241
16 141968 0.14 0.554516
17 141947 0.09 0.535067
18 142193 0.66 0.746264
19 141271 -1.49 0.067925
20 142091 0.42 0.664386
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-28_02:31
Bits used No. missing words z-score p-value
23 to 32 141848 -0.2115 0.416255
22 to 31 142097 0.6471 0.741229
21 to 30 142122 0.7333 0.768326
20 to 29 141930 0.0713 0.528411
19 to 28 142151 0.8333 0.797675
18 to 27 142306 1.3678 0.914317
17 to 26 141973 0.2196 0.586890
16 to 25 141896 -0.0460 0.481669
15 to 24 142466 1.9196 0.972543
14 to 23 142208 1.0299 0.848471
13 to 22 141408 -1.7287 0.041929
12 to 21 141830 -0.2736 0.392215
11 to 20 141761 -0.5115 0.304507
10 to 19 142151 0.8333 0.797675
9 to 18 142151 0.8333 0.797675
8 to 17 141995 0.2954 0.616161
7 to 16 142220 1.0713 0.857977
6 to 15 142049 0.4816 0.684962
5 to 14 142170 0.8989 0.815637
4 to 13 141927 0.0609 0.524293
3 to 12 141055 -2.9460 0.001610
2 to 11 142080 0.5885 0.721907
1 to 10 141501 -1.4080 0.079560
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-28_02:31
Bits used No. missing words z-score p-value
28 to 32 141782 -0.4316 0.333006
27 to 31 142025 0.3921 0.652509
26 to 30 141646 -0.8926 0.186024
25 to 29 141827 -0.2791 0.390090
24 to 28 142023 0.3853 0.650001
23 to 27 141666 -0.8248 0.204729
22 to 26 142351 1.4972 0.932828
21 to 25 141242 -2.2621 0.011845
20 to 24 142575 2.2565 0.987981
19 to 23 141861 -0.1638 0.434932
18 to 22 142314 1.3718 0.914931
17 to 21 141487 -1.4316 0.076125
16 to 20 141259 -2.2045 0.013744
15 to 19 141924 0.0497 0.519831
14 to 18 142016 0.3616 0.641172
13 to 17 141912 0.0091 0.503611
12 to 16 141828 -0.2757 0.391391
11 to 15 141608 -1.0215 0.153519
10 to 14 141559 -1.1876 0.117504
9 to 13 142061 0.5141 0.696421
8 to 12 142029 0.4057 0.657504
7 to 11 142011 0.3446 0.634819
6 to 10 142033 0.4192 0.662473
5 to 9 142273 1.2328 0.891171
4 to 8 141979 0.2362 0.593349
3 to 7 141224 -2.3232 0.010085
2 to 6 141910 0.0023 0.500906
1 to 5 142654 2.5243 0.994204
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-28_02:31
Bits used No. missing words z-score p-value
31 to 32 142014 0.3088 0.621248
30 to 31 141609 -0.8859 0.187828
29 to 30 142296 1.1406 0.872986
28 to 29 142151 0.7129 0.762043
27 to 28 141919 0.0285 0.511378
26 to 27 142057 0.4356 0.668438
25 to 26 141174 -2.1691 0.015037
24 to 25 141811 -0.2901 0.385886
23 to 24 142216 0.9046 0.817170
22 to 23 142262 1.0403 0.850905
21 to 22 142335 1.2557 0.895381
20 to 21 141424 -1.4317 0.076122
19 to 20 141633 -0.8151 0.207498
18 to 19 141620 -0.8535 0.196696
17 to 18 141411 -1.4700 0.070781
16 to 17 142587 1.9990 0.977197
15 to 16 141964 0.1613 0.564059
14 to 15 141825 -0.2488 0.401773
13 to 14 141269 -1.8889 0.029454
12 to 13 141792 -0.3461 0.364632
11 to 12 142009 0.2940 0.615626
10 to 11 141713 -0.5791 0.281246
9 to 10 141774 -0.3992 0.344872
8 to 9 142361 1.3324 0.908629
7 to 8 141926 0.0492 0.519610
6 to 7 142089 0.5300 0.701944
5 to 6 142196 0.8456 0.801122
4 to 5 142384 1.4002 0.919274
3 to 4 142139 0.6775 0.750953
2 to 3 142192 0.8338 0.797813
1 to 2 142476 1.6716 0.952698
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-28_02:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2408.36 -1.296 0.097496
Test results for specific bytes for dh-ranFile-2018-06-28_02:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2477.58 -0.317 0.375620
2 to 9 2488.14 -0.168 0.433422
3 to 10 2517.07 0.241 0.595401
4 to 11 2344.06 -2.205 0.013715
5 to 12 2372.97 -1.796 0.036209
6 to 13 2432.73 -0.951 0.170713
7 to 14 2657.82 2.232 0.987188
8 to 15 2505.24 0.074 0.529522
9 to 16 2536.14 0.511 0.695379
10 to 17 2396.14 -1.469 0.070936
11 to 18 2420.60 -1.123 0.130740
12 to 19 2520.12 0.285 0.612008
13 to 20 2350.41 -2.115 0.017195
14 to 21 2519.63 0.278 0.609337
15 to 22 2469.24 -0.435 0.331754
16 to 23 2490.41 -0.136 0.446082
17 to 24 2384.90 -1.628 0.051783
18 to 25 2340.81 -2.251 0.012183
19 to 26 2444.90 -0.779 0.217912
20 to 27 2479.75 -0.286 0.387311
21 to 28 2403.29 -1.368 0.085702
22 to 29 2524.49 0.346 0.635443
23 to 30 2427.63 -1.024 0.153032
24 to 31 2496.30 -0.052 0.479128
25 to 32 2473.29 -0.378 0.352817
CDPARK for dh-ranFile-2018-06-28_02:31: 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
3522 -0.0457 0.481790
3534 0.5023 0.692266
3514 -0.4110 0.340551
3472 -2.3288 0.009936
3518 -0.2283 0.409702
3534 0.5023 0.692266
3535 0.5479 0.708135
3562 1.7808 0.962529
3509 -0.6393 0.261324
3541 0.8219 0.794438
Square side=100, avg. no. parked=3524.10 sample std.=22.63
p-value of the KSTEST for those 10 p-values: 0.829141
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-28_02:31
0.0898,0.9558,0.3789,0.5730,0.8730,0.8245,0.5122,0.0283,0.0196,0.1708,
The KS test for those 10 p-values: 0.425436
The 3DSPHERES test for dh-ranFile-2018-06-28_02:31
sample no r^3 equiv. uni.
1 114.972 0.978342
2 35.210 0.690769
3 21.093 0.504953
4 38.480 0.722706
5 14.617 0.385672
6 56.771 0.849284
7 98.314 0.962264
8 30.004 0.632168
9 4.807 0.148041
10 23.765 0.547145
11 31.318 0.647932
12 11.655 0.321933
13 26.857 0.591492
14 32.525 0.661816
15 5.724 0.173707
16 4.893 0.150507
17 39.164 0.728958
18 18.287 0.456408
19 94.457 0.957086
20 5.004 0.153636
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.435164
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-28_02:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 1.3 1.3 -1.1 0.6 -0.1
-0.1 0.2 1.7 0.1 0.4 0.1
0.8 0.7 0.0 -2.0 -0.7 -0.3
0.1 0.2 -0.3 1.4 -0.6 -0.3
-0.0 -0.7 -0.1 0.1 0.5 0.1
0.8 0.1 -0.4 0.8 1.9 -1.2
0.5 -0.4 -0.4 1.5 0.9 1.0
-1.1
Chi-square with 42 degrees of freedom:29.283817
z-score=-1.387449, p-value=0.068884
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-28_02:31
Test no p-value
1 0.162609
2 0.005534
3 0.571043
4 0.264594
5 0.171597
6 0.487881
7 0.054383
8 0.016531
9 0.349936
10 0.059333
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.001448
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-28_02:31:
(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 66587 0.10 66789 0.22
3 25000.00 25152 0.92 24849 0.91
4 6666.67 6589 0.90 6675 0.01
5 1388.89 1386 0.01 1404 0.16
6 238.10 243 0.10 245 0.20
7 34.72 37 0.15 33 0.09
8 4.96 5 0.00 4 0.19
p=0.09771 p=0.06143
Number of rngs required: 688821, p-value: 0.685
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-28_02:31
No. of wins: Observed Expected
98343 98585.9
z-score=-1.086, pvalue=0.13869
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66535 66666.7 0.260 0.260
2 38011 37654.3 3.379 3.639
3 26896 26954.7 0.128 3.767
4 19156 19313.5 1.284 5.050
5 13885 13851.4 0.081 5.132
6 10013 9943.5 0.485 5.617
7 7208 7145.0 0.555 6.172
8 5163 5139.1 0.111 6.283
9 3597 3699.9 2.860 9.143
10 2627 2666.3 0.579 9.723
11 1855 1923.3 2.427 12.150
12 1330 1388.7 2.485 14.635
13 1032 1003.7 0.797 15.432
14 726 726.1 0.000 15.432
15 528 525.8 0.009 15.441
16 372 381.2 0.220 15.660
17 293 276.5 0.980 16.640
18 219 200.8 1.644 18.284
19 145 146.0 0.007 18.291
20 100 106.2 0.364 18.654
21 309 287.1 1.668 20.323
Chisq= 20.32 for 20 degrees of freedom, p= 0.56208
SUMMARY of craptest
p-value for no. of wins: 0.138694
p-value for throws/game: 0.562084
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-28_02:31
No. of wins: Observed Expected
98419 98585.9
z-score=-0.746, pvalue=0.22775
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66584 66666.7 0.103 0.103
2 37897 37654.3 1.564 1.667
3 26853 26954.7 0.384 2.051
4 19204 19313.5 0.620 2.671
5 13827 13851.4 0.043 2.714
6 10037 9943.5 0.878 3.592
7 7178 7145.0 0.152 3.745
8 5146 5139.1 0.009 3.754
9 3655 3699.9 0.544 4.298
10 2659 2666.3 0.020 4.318
11 1916 1923.3 0.028 4.346
12 1394 1388.7 0.020 4.366
13 1025 1003.7 0.451 4.817
14 706 726.1 0.559 5.376
15 536 525.8 0.196 5.572
16 362 381.2 0.962 6.534
17 279 276.5 0.022 6.556
18 204 200.8 0.050 6.606
19 136 146.0 0.683 7.289
20 117 106.2 1.095 8.384
21 285 287.1 0.016 8.400
Chisq= 8.40 for 20 degrees of freedom, p= 0.01113
SUMMARY of craptest
p-value for no. of wins: 0.227746
p-value for throws/game: 0.011125
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0014,0.0016,0.0022,0.0055,0.0099,0.0101,0.0111,0.0118,0.0122,0.0134,
0.0137,0.0137,0.0150,0.0165,0.0172,0.0182,0.0196,0.0283,0.0295,0.0304,
0.0362,0.0419,0.0495,0.0518,0.0544,0.0593,0.0614,0.0679,0.0689,0.0708,
0.0709,0.0761,0.0761,0.0766,0.0772,0.0796,0.0822,0.0857,0.0898,0.0975,
0.0977,0.1175,0.1307,0.1363,0.1387,0.1426,0.1458,0.1480,0.1505,0.1530,
0.1535,0.1536,0.1553,0.1568,0.1579,0.1626,0.1677,0.1707,0.1708,0.1716,
0.1737,0.1860,0.1878,0.1967,0.2016,0.2047,0.2050,0.2075,0.2124,0.2129,
0.2178,0.2179,0.2191,0.2277,0.2281,0.2291,0.2306,0.2613,0.2646,0.2689,
0.2812,0.3045,0.3058,0.3093,0.3182,0.3219,0.3271,0.3318,0.3330,0.3406,
0.3449,0.3499,0.3506,0.3528,0.3586,0.3646,0.3716,0.3723,0.3756,0.3789,
0.3812,0.3848,0.3857,0.3859,0.3873,0.3877,0.3901,0.3914,0.3922,0.4018,
0.4097,0.4126,0.4163,0.4196,0.4254,0.4323,0.4334,0.4334,0.4349,0.4352,
0.4461,0.4546,0.4564,0.4643,0.4791,0.4817,0.4818,0.4879,0.4930,0.5009,
0.5036,0.5050,0.5114,0.5122,0.5196,0.5198,0.5243,0.5284,0.5295,0.5331,
0.5336,0.5351,0.5471,0.5545,0.5610,0.5621,0.5641,0.5710,0.5730,0.5769,
0.5860,0.5869,0.5915,0.5933,0.5954,0.6009,0.6013,0.6093,0.6120,0.6126,
0.6156,0.6162,0.6212,0.6322,0.6348,0.6354,0.6366,0.6412,0.6437,0.6479,
0.6500,0.6523,0.6525,0.6575,0.6618,0.6625,0.6644,0.6678,0.6684,0.6726,
0.6808,0.6850,0.6850,0.6878,0.6908,0.6923,0.6923,0.6934,0.6954,0.6964,
0.7019,0.7081,0.7093,0.7219,0.7220,0.7227,0.7290,0.7402,0.7412,0.7463,
0.7477,0.7487,0.7510,0.7602,0.7620,0.7629,0.7683,0.7705,0.7809,0.7815,
0.7944,0.7977,0.7977,0.7977,0.7978,0.8011,0.8156,0.8172,0.8239,0.8245,
0.8260,0.8269,0.8291,0.8383,0.8404,0.8445,0.8448,0.8477,0.8485,0.8493,
0.8509,0.8513,0.8518,0.8532,0.8580,0.8660,0.8669,0.8678,0.8730,0.8730,
0.8730,0.8797,0.8849,0.8860,0.8912,0.8954,0.9086,0.9143,0.9149,0.9193,
0.9226,0.9232,0.9328,0.9527,0.9558,0.9571,0.9623,0.9625,0.9725,0.9732,
0.9772,0.9783,0.9825,0.9872,0.9880,0.9884,0.9942,0.9942,0.9950,
Overall p-value after applying KStest on 269 p-values = 0.143123
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.