RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-27_09:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.47 28.7291 0.962893
2 to 25 15.78 20.8926 0.768869
3 to 26 15.89 17.5793 0.584164
4 to 27 16.02 19.8275 0.716852
5 to 28 15.87 16.2001 0.490306
6 to 29 15.43 16.7854 0.531002
7 to 30 15.67 21.5920 0.799077
8 to 31 15.84 18.1001 0.617445
9 to 32 15.39 23.3726 0.862491
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.046274
Tough bday spacings test for dh-ranFile-2018-06-27_09:31: 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 9 32 78 93 104 71 55 29 17 8 4
(O-E)^2/E 0.0 0.6 0.3 0.2 0.4 0.7 0.2 0.0 0.3 0.3 0.0
Birthday Spacings: Sum(O-E)^2/E= 2.954, p= 0.018
RESULTS OF GCD FOR dh-ranFile-2018-06-27_09:31
Euclid's algorithm:
p-value, steps to gcd: 0.367617
p-value, dist. of gcd's: 0.119144
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-27_09:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.717 0.990 0.975 0.281 0.680 0.339 0.621 0.273
Bits 8 to 15---> 0.355 0.008 0.763 0.094 0.742 0.801 0.804 0.188
Bits 16 to 23---> 0.213 0.095 0.924 0.867 0.166 0.472 0.714 0.918
Bits 24 to 31---> 0.795 0.210 0.202 0.106 0.893 0.749 0.393 0.360
KS test for the above 32 p values: 0.340
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-27_09:31,
p-values for 5 runs: 0.3927, 0.6323, 0.5840, 0.3564, 0.0591
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-27_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 215 211.4 0.061 0.061
r= 29 5155 5134.0 0.086 0.146
r= 30 23030 23103.0 0.231 0.377
r= 31 11600 11551.5 0.203 0.581
chi-square = 0.581 with df = 3; p-value = 0.099
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-27_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 194 211.4 1.435 1.435
r= 30 5151 5134.0 0.056 1.491
r= 31 23054 23103.0 0.104 1.595
r= 32 11601 11551.5 0.212 1.807
chi-square = 1.807 with df = 3; p-value = 0.387
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-27_09:31
b-rank test for bits 1 to 8, p=0.63959
b-rank test for bits 2 to 9, p=0.53473
b-rank test for bits 3 to 10, p=0.74616
b-rank test for bits 4 to 11, p=0.62223
b-rank test for bits 5 to 12, p=0.36803
b-rank test for bits 6 to 13, p=0.12529
b-rank test for bits 7 to 14, p=0.09505
b-rank test for bits 8 to 15, p=0.35791
b-rank test for bits 9 to 16, p=0.42248
b-rank test for bits 10 to 17, p=0.06189
b-rank test for bits 11 to 18, p=0.96535
b-rank test for bits 12 to 19, p=0.87753
b-rank test for bits 13 to 20, p=0.81248
b-rank test for bits 14 to 21, p=0.98036
b-rank test for bits 15 to 22, p=0.67007
b-rank test for bits 16 to 23, p=0.84944
b-rank test for bits 17 to 24, p=0.87417
b-rank test for bits 18 to 25, p=0.57504
b-rank test for bits 19 to 26, p=0.97885
b-rank test for bits 20 to 27, p=0.91703
b-rank test for bits 21 to 28, p=0.81656
b-rank test for bits 22 to 29, p=0.88296
b-rank test for bits 23 to 30, p=0.38967
b-rank test for bits 24 to 31, p=0.53610
b-rank test for bits 25 to 32, p=0.56906
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 = 0.040830
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-27_09:31
(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 141294 -1.44 0.075261
2 141570 -0.79 0.213939
3 141760 -0.35 0.363582
4 141848 -0.14 0.443029
5 142749 1.96 0.975110
6 141662 -0.58 0.281675
7 141655 -0.59 0.276180
8 142443 1.25 0.893782
9 142642 1.71 0.956537
10 142059 0.35 0.636717
11 142068 0.37 0.644579
12 141778 -0.31 0.379480
13 141694 -0.50 0.307444
14 142437 1.23 0.891189
15 142802 2.09 0.981496
16 141953 0.10 0.540635
17 141284 -1.46 0.072001
18 141159 -1.75 0.039792
19 141842 -0.16 0.437499
20 142802 2.09 0.981496
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-27_09:31
Bits used No. missing words z-score p-value
23 to 32 141449 -1.5873 0.056217
22 to 31 141862 -0.1632 0.435178
21 to 30 141999 0.3092 0.621418
20 to 29 141504 -1.3977 0.081103
19 to 28 141843 -0.2287 0.409542
18 to 27 142019 0.3782 0.647349
17 to 26 141773 -0.4701 0.319141
16 to 25 141889 -0.0701 0.472056
15 to 24 141328 -2.0046 0.022504
14 to 23 141667 -0.8356 0.201684
13 to 22 141907 -0.0080 0.496795
12 to 21 141505 -1.3942 0.081622
11 to 20 141938 0.0989 0.539376
10 to 19 141822 -0.3011 0.381655
9 to 18 141581 -1.1322 0.128781
8 to 17 142041 0.4540 0.675098
7 to 16 141692 -0.7494 0.226804
6 to 15 142148 0.8230 0.794746
5 to 14 141944 0.1196 0.547581
4 to 13 142179 0.9299 0.823788
3 to 12 142315 1.3989 0.919073
2 to 11 142069 0.5506 0.709041
1 to 10 142277 1.2678 0.897570
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-27_09:31
Bits used No. missing words z-score p-value
28 to 32 142011 0.3446 0.634819
27 to 31 142260 1.1887 0.882723
26 to 30 141762 -0.4994 0.308741
25 to 29 142091 0.6158 0.730997
24 to 28 142097 0.6362 0.737667
23 to 27 142067 0.5345 0.703493
22 to 26 142433 1.7752 0.962064
21 to 25 142141 0.7853 0.783868
20 to 24 141980 0.2396 0.594664
19 to 23 141713 -0.6655 0.252857
18 to 22 142364 1.5413 0.938373
17 to 21 142130 0.7480 0.772780
16 to 20 141983 0.2497 0.598602
15 to 19 142321 1.3955 0.918566
14 to 18 141984 0.2531 0.599912
13 to 17 141797 -0.3808 0.351683
12 to 16 142122 0.7209 0.764519
11 to 15 142388 1.6226 0.947664
10 to 14 141869 -0.1367 0.445629
9 to 13 142207 1.0091 0.843525
8 to 12 141657 -0.8554 0.196177
7 to 11 141607 -1.0248 0.152718
6 to 10 142459 1.8633 0.968789
5 to 9 141667 -0.8215 0.205693
4 to 8 141502 -1.3808 0.083673
3 to 7 141503 -1.3774 0.084196
2 to 6 141555 -1.2011 0.114853
1 to 5 142080 0.5785 0.718551
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-27_09:31
Bits used No. missing words z-score p-value
31 to 32 141592 -0.9361 0.174617
30 to 31 141878 -0.0924 0.463183
29 to 30 141542 -1.0836 0.139278
28 to 29 142201 0.8604 0.805211
27 to 28 142103 0.5713 0.716101
26 to 27 141986 0.2262 0.589464
25 to 26 142048 0.4091 0.658751
24 to 25 141880 -0.0865 0.465527
23 to 24 141274 -1.8741 0.030456
22 to 23 142197 0.8486 0.801944
21 to 22 142049 0.4120 0.659832
20 to 21 142212 0.8928 0.814026
19 to 20 142035 0.3707 0.644573
18 to 19 142156 0.7276 0.766583
17 to 18 141545 -1.0747 0.141250
16 to 17 142219 0.9135 0.819505
15 to 16 141594 -0.9302 0.176140
14 to 15 141335 -1.6942 0.045115
13 to 14 142018 0.3206 0.625728
12 to 13 141722 -0.5526 0.290270
11 to 12 141959 0.1465 0.558244
10 to 11 142016 0.3147 0.623490
9 to 10 141655 -0.7502 0.226556
8 to 9 141526 -1.1308 0.129077
7 to 8 142438 1.5595 0.940561
6 to 7 141559 -1.0334 0.150703
5 to 6 141944 0.1023 0.540729
4 to 5 141813 -0.2842 0.388144
3 to 4 141694 -0.6352 0.262652
2 to 3 141878 -0.0924 0.463183
1 to 2 142224 0.9282 0.823356
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-27_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2523.01 0.325 0.627545
Test results for specific bytes for dh-ranFile-2018-06-27_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2466.17 -0.478 0.316185
2 to 9 2580.54 1.139 0.872650
3 to 10 2455.58 -0.628 0.264940
4 to 11 2597.16 1.374 0.915296
5 to 12 2601.74 1.439 0.924907
6 to 13 2621.62 1.720 0.957282
7 to 14 2383.58 -1.646 0.049839
8 to 15 2580.36 1.137 0.872132
9 to 16 2416.68 -1.178 0.119344
10 to 17 2503.97 0.056 0.522379
11 to 18 2517.15 0.243 0.595825
12 to 19 2584.55 1.196 0.884083
13 to 20 2487.09 -0.183 0.427574
14 to 21 2436.53 -0.898 0.184692
15 to 22 2454.20 -0.648 0.258583
16 to 23 2615.71 1.636 0.949120
17 to 24 2523.65 0.334 0.630984
18 to 25 2433.23 -0.944 0.172506
19 to 26 2484.67 -0.217 0.414162
20 to 27 2499.18 -0.012 0.495388
21 to 28 2423.71 -1.079 0.140302
22 to 29 2478.85 -0.299 0.382437
23 to 30 2354.72 -2.055 0.019958
24 to 31 2597.59 1.380 0.916220
25 to 32 2550.30 0.711 0.761584
CDPARK for dh-ranFile-2018-06-27_09:31: 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
3550 1.2329 0.891189
3554 1.4155 0.921543
3520 -0.1370 0.445521
3542 0.8676 0.807188
3507 -0.7306 0.232514
3502 -0.9589 0.168804
3514 -0.4110 0.340551
3471 -2.3744 0.008788
3504 -0.8676 0.192812
3522 -0.0457 0.481790
Square side=100, avg. no. parked=3518.60 sample std.=23.90
p-value of the KSTEST for those 10 p-values: 0.726297
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-27_09:31
0.8947,0.1508,0.3734,0.3274,0.2009,0.9243,0.4075,0.8121,0.9345,0.5382,
The KS test for those 10 p-values: 0.632728
The 3DSPHERES test for dh-ranFile-2018-06-27_09:31
sample no r^3 equiv. uni.
1 55.914 0.844920
2 8.615 0.249621
3 15.328 0.400063
4 0.786 0.025875
5 28.706 0.615911
6 56.697 0.848912
7 2.901 0.092162
8 91.300 0.952324
9 12.448 0.339612
10 9.187 0.263796
11 11.694 0.322819
12 1.578 0.051249
13 10.099 0.285827
14 41.622 0.750280
15 79.342 0.928975
16 1.660 0.053836
17 9.766 0.277869
18 28.013 0.606934
19 1.136 0.037148
20 107.529 0.972244
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.295526
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-27_09:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 -0.7 0.6 -0.3 -1.6 0.5
0.3 -1.2 -0.8 -1.4 -1.1 0.2
0.5 2.0 -0.1 1.9 -2.3 -0.9
0.2 1.1 1.1 -1.6 1.0 0.6
-0.1 0.6 -2.1 0.2 -1.0 0.9
1.0 0.8 -1.1 0.9 0.2 -1.4
-0.5 -1.3 -1.6 -0.7 -0.6 0.0
0.8
Chi-square with 42 degrees of freedom:47.772793
z-score=0.629863, p-value=0.750208
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-27_09:31
Test no p-value
1 0.195260
2 0.640587
3 0.120499
4 0.020125
5 0.036209
6 0.331303
7 0.583449
8 0.307828
9 0.476432
10 0.052098
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.019096
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-27_09:31:
(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 66704 0.02 66802 0.27
3 25000.00 25072 0.21 25013 0.01
4 6666.67 6546 2.18 6553 1.94
5 1388.89 1407 0.24 1343 1.52
6 238.10 232 0.16 232 0.16
7 34.72 33 0.09 45 3.04
8 4.96 5 0.00 11 7.36
p=0.17750 p=0.97345
Number of rngs required: 688114, p-value: 0.370
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-27_09:31
No. of wins: Observed Expected
98611 98585.9
z-score= 0.112, pvalue=0.54477
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66827 66666.7 0.386 0.386
2 37375 37654.3 2.072 2.458
3 26924 26954.7 0.035 2.493
4 19383 19313.5 0.250 2.743
5 13864 13851.4 0.011 2.754
6 10016 9943.5 0.528 3.282
7 7115 7145.0 0.126 3.409
8 5093 5139.1 0.413 3.822
9 3802 3699.9 2.819 6.641
10 2596 2666.3 1.853 8.494
11 1960 1923.3 0.699 9.194
12 1386 1388.7 0.005 9.199
13 1050 1003.7 2.134 11.333
14 693 726.1 1.513 12.846
15 540 525.8 0.382 13.227
16 387 381.2 0.090 13.317
17 286 276.5 0.324 13.641
18 205 200.8 0.087 13.728
19 132 146.0 1.340 15.067
20 98 106.2 0.635 15.703
21 268 287.1 1.272 16.975
Chisq= 16.98 for 20 degrees of freedom, p= 0.34540
SUMMARY of craptest
p-value for no. of wins: 0.544766
p-value for throws/game: 0.345404
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-27_09:31
No. of wins: Observed Expected
98444 98585.9
z-score=-0.634, pvalue=0.26289
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66454 66666.7 0.678 0.678
2 37746 37654.3 0.223 0.902
3 27017 26954.7 0.144 1.045
4 19477 19313.5 1.385 2.430
5 14017 13851.4 1.979 4.410
6 10003 9943.5 0.356 4.765
7 7051 7145.0 1.237 6.002
8 5035 5139.1 2.108 8.110
9 3714 3699.9 0.054 8.164
10 2562 2666.3 4.080 12.244
11 1960 1923.3 0.699 12.943
12 1363 1388.7 0.477 13.420
13 973 1003.7 0.940 14.360
14 715 726.1 0.171 14.531
15 523 525.8 0.015 14.546
16 386 381.2 0.062 14.608
17 290 276.5 0.655 15.263
18 206 200.8 0.133 15.396
19 135 146.0 0.827 16.223
20 89 106.2 2.790 19.013
21 284 287.1 0.034 19.047
Chisq= 19.05 for 20 degrees of freedom, p= 0.48121
SUMMARY of craptest
p-value for no. of wins: 0.262886
p-value for throws/game: 0.481209
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0079,0.0088,0.0175,0.0191,0.0200,0.0201,0.0225,0.0259,0.0305,0.0362,
0.0371,0.0398,0.0408,0.0451,0.0463,0.0498,0.0512,0.0521,0.0538,0.0562,
0.0591,0.0619,0.0720,0.0753,0.0811,0.0816,0.0837,0.0842,0.0922,0.0939,
0.0951,0.0954,0.0992,0.1064,0.1149,0.1191,0.1193,0.1205,0.1253,0.1288,
0.1291,0.1393,0.1403,0.1413,0.1507,0.1508,0.1527,0.1659,0.1688,0.1725,
0.1746,0.1761,0.1775,0.1847,0.1877,0.1928,0.1953,0.1962,0.2009,0.2017,
0.2021,0.2057,0.2104,0.2133,0.2139,0.2266,0.2268,0.2325,0.2496,0.2529,
0.2586,0.2627,0.2629,0.2638,0.2649,0.2726,0.2762,0.2779,0.2813,0.2817,
0.2858,0.2903,0.2955,0.3074,0.3078,0.3087,0.3162,0.3191,0.3228,0.3274,
0.3313,0.3386,0.3396,0.3402,0.3406,0.3454,0.3517,0.3553,0.3564,0.3579,
0.3595,0.3636,0.3676,0.3680,0.3697,0.3734,0.3795,0.3817,0.3824,0.3866,
0.3881,0.3897,0.3927,0.3934,0.4001,0.4075,0.4095,0.4142,0.4225,0.4276,
0.4352,0.4375,0.4430,0.4455,0.4456,0.4632,0.4632,0.4655,0.4715,0.4721,
0.4764,0.4812,0.4818,0.4903,0.4954,0.4968,0.5224,0.5310,0.5347,0.5361,
0.5382,0.5394,0.5406,0.5407,0.5448,0.5476,0.5582,0.5691,0.5750,0.5834,
0.5840,0.5842,0.5895,0.5947,0.5958,0.5986,0.5999,0.6069,0.6159,0.6174,
0.6209,0.6214,0.6222,0.6235,0.6257,0.6275,0.6310,0.6323,0.6327,0.6348,
0.6367,0.6396,0.6406,0.6446,0.6446,0.6473,0.6588,0.6598,0.6701,0.6751,
0.6801,0.7035,0.7090,0.7135,0.7161,0.7169,0.7169,0.7186,0.7263,0.7310,
0.7377,0.7424,0.7462,0.7491,0.7502,0.7503,0.7616,0.7628,0.7645,0.7666,
0.7689,0.7728,0.7839,0.7947,0.7952,0.7991,0.8007,0.8019,0.8042,0.8052,
0.8072,0.8121,0.8125,0.8140,0.8166,0.8195,0.8234,0.8238,0.8435,0.8449,
0.8489,0.8494,0.8625,0.8665,0.8721,0.8726,0.8742,0.8775,0.8827,0.8830,
0.8841,0.8912,0.8912,0.8929,0.8938,0.8947,0.8976,0.9153,0.9162,0.9170,
0.9177,0.9186,0.9191,0.9215,0.9235,0.9243,0.9249,0.9290,0.9345,0.9384,
0.9406,0.9477,0.9491,0.9523,0.9565,0.9573,0.9621,0.9629,0.9653,0.9688,
0.9722,0.9734,0.9750,0.9751,0.9788,0.9804,0.9815,0.9815,0.9897,
Overall p-value after applying KStest on 269 p-values = 0.586811
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.