RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-09_23:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.76 13.2252 0.279013
2 to 25 15.64 29.5556 0.970266
3 to 26 15.97 15.2836 0.424940
4 to 27 15.67 22.9282 0.848396
5 to 28 15.44 27.8648 0.953457
6 to 29 15.77 15.3284 0.428160
7 to 30 15.64 24.1069 0.883441
8 to 31 15.86 10.3483 0.111627
9 to 32 15.46 29.9875 0.973564
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.057401
Tough bday spacings test for dh-ranFile-2018-07-09_23:31: 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 8 30 76 105 95 75 53 35 15 7 1
(O-E)^2/E 0.1 1.2 0.1 0.5 0.1 0.1 0.0 0.9 0.0 0.0 2.3
Birthday Spacings: Sum(O-E)^2/E= 5.467, p= 0.142
RESULTS OF GCD FOR dh-ranFile-2018-07-09_23:31
Euclid's algorithm:
p-value, steps to gcd: 0.931191
p-value, dist. of gcd's: 0.926617
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-09_23:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.612 0.531 0.641 0.470 0.335 0.644 0.844 0.561
Bits 8 to 15---> 0.673 0.153 0.941 0.343 0.319 0.662 0.676 0.389
Bits 16 to 23---> 0.312 0.581 0.208 0.113 0.343 0.913 0.577 0.975
Bits 24 to 31---> 0.676 0.053 0.416 0.796 0.130 0.017 0.762 0.052
KS test for the above 32 p values: 0.095
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-09_23:31,
p-values for 5 runs: 0.1514, 0.4859, 0.9603, 0.7011, 0.7580
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-09_23:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 218 211.4 0.205 0.205
r= 29 5213 5134.0 1.215 1.420
r= 30 22853 23103.0 2.706 4.127
r= 31 11716 11551.5 2.342 6.468
chi-square = 6.468 with df = 3; p-value = 0.909
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-09_23:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 207 211.4 0.092 0.092
r= 30 5153 5134.0 0.070 0.163
r= 31 23185 23103.0 0.291 0.453
r= 32 11455 11551.5 0.807 1.260
chi-square = 1.260 with df = 3; p-value = 0.261
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-09_23:31
b-rank test for bits 1 to 8, p=0.20515
b-rank test for bits 2 to 9, p=0.38037
b-rank test for bits 3 to 10, p=0.00368
b-rank test for bits 4 to 11, p=0.05575
b-rank test for bits 5 to 12, p=0.36308
b-rank test for bits 6 to 13, p=0.63181
b-rank test for bits 7 to 14, p=0.10613
b-rank test for bits 8 to 15, p=0.16531
b-rank test for bits 9 to 16, p=0.99226
b-rank test for bits 10 to 17, p=0.47850
b-rank test for bits 11 to 18, p=0.27202
b-rank test for bits 12 to 19, p=0.35036
b-rank test for bits 13 to 20, p=0.68626
b-rank test for bits 14 to 21, p=0.64551
b-rank test for bits 15 to 22, p=0.33030
b-rank test for bits 16 to 23, p=0.11693
b-rank test for bits 17 to 24, p=0.27803
b-rank test for bits 18 to 25, p=0.28288
b-rank test for bits 19 to 26, p=0.30237
b-rank test for bits 20 to 27, p=0.00899
b-rank test for bits 21 to 28, p=0.52286
b-rank test for bits 22 to 29, p=0.51357
b-rank test for bits 23 to 30, p=0.10226
b-rank test for bits 24 to 31, p=0.77066
b-rank test for bits 25 to 32, p=0.51275
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 = 0.023874
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-09_23:31
(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 141193 -1.67 0.047098
2 141265 -1.51 0.066105
3 142279 0.86 0.806128
4 141713 -0.46 0.323219
5 142052 0.33 0.630562
6 141938 0.07 0.526704
7 141939 0.07 0.527634
8 141277 -1.48 0.069783
9 141530 -0.89 0.187732
10 142137 0.53 0.702616
11 142036 0.30 0.616369
12 141916 0.02 0.506217
13 143295 3.24 0.999397
14 141728 -0.42 0.335904
15 141772 -0.32 0.374157
16 141793 -0.27 0.392888
17 142284 0.88 0.809321
18 141762 -0.34 0.365337
19 141898 -0.03 0.489440
20 142269 0.84 0.799644
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-09_23:31
Bits used No. missing words z-score p-value
23 to 32 142022 0.3885 0.651183
22 to 31 141346 -1.9425 0.026037
21 to 30 141898 -0.0391 0.484418
20 to 29 141588 -1.1080 0.133923
19 to 28 142005 0.3299 0.629261
18 to 27 141753 -0.5391 0.294920
17 to 26 141462 -1.5425 0.061474
16 to 25 142008 0.3402 0.633163
15 to 24 142363 1.5644 0.941136
14 to 23 141609 -1.0356 0.150190
13 to 22 141933 0.0816 0.532526
12 to 21 141566 -1.1839 0.118227
11 to 20 141859 -0.1736 0.431109
10 to 19 141904 -0.0184 0.492668
9 to 18 142386 1.6437 0.949880
8 to 17 142369 1.5851 0.943525
7 to 16 141371 -1.8563 0.031705
6 to 15 141632 -0.9563 0.169458
5 to 14 141898 -0.0391 0.484418
4 to 13 142333 1.4609 0.927983
3 to 12 142454 1.8782 0.969821
2 to 11 141245 -2.2908 0.010988
1 to 10 141924 0.0506 0.520172
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-09_23:31
Bits used No. missing words z-score p-value
28 to 32 141875 -0.1164 0.453679
27 to 31 142110 0.6802 0.751823
26 to 30 142298 1.3175 0.906169
25 to 29 141696 -0.7232 0.234793
24 to 28 142192 0.9582 0.831020
23 to 27 141858 -0.1740 0.430933
22 to 26 142202 0.9921 0.839426
21 to 25 141682 -0.7706 0.220469
20 to 24 141961 0.1752 0.569520
19 to 23 142154 0.8294 0.796558
18 to 22 141551 -1.2147 0.112244
17 to 21 142020 0.3752 0.646227
16 to 20 141932 0.0768 0.530628
15 to 19 141852 -0.1943 0.422955
14 to 18 142298 1.3175 0.906169
13 to 17 141853 -0.1909 0.424283
12 to 16 141945 0.1209 0.548121
11 to 15 141544 -1.2384 0.107783
10 to 14 141934 0.0836 0.533324
9 to 13 142009 0.3379 0.632267
8 to 12 142394 1.6429 0.949803
7 to 11 142016 0.3616 0.641172
6 to 10 141778 -0.4452 0.328093
5 to 9 141466 -1.5028 0.066444
4 to 8 141991 0.2768 0.609051
3 to 7 141881 -0.0960 0.461747
2 to 6 142233 1.0972 0.863720
1 to 5 142259 1.1853 0.882055
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-09_23:31
Bits used No. missing words z-score p-value
31 to 32 141503 -1.1986 0.115339
30 to 31 142319 1.2085 0.886566
29 to 30 141910 0.0020 0.500789
28 to 29 142371 1.3619 0.913379
27 to 28 142587 1.9990 0.977197
26 to 27 141422 -1.4376 0.075281
25 to 26 141682 -0.6706 0.251241
24 to 25 141810 -0.2930 0.384758
23 to 24 141623 -0.8446 0.199158
22 to 23 141508 -1.1839 0.118233
21 to 22 142153 0.7188 0.763865
20 to 21 141404 -1.4906 0.068027
19 to 20 141808 -0.2989 0.382505
18 to 19 141795 -0.3373 0.367962
17 to 18 141919 0.0285 0.511378
16 to 17 141877 -0.0954 0.462011
15 to 16 141484 -1.2547 0.104801
14 to 15 140846 -3.1367 0.000854
13 to 14 141555 -1.0452 0.147960
12 to 13 142131 0.6539 0.743410
11 to 12 141885 -0.0718 0.471393
10 to 11 141780 -0.3815 0.351415
9 to 10 141641 -0.7915 0.214316
8 to 9 141735 -0.5142 0.303539
7 to 8 142221 0.9194 0.821052
6 to 7 141829 -0.2370 0.406343
5 to 6 141798 -0.3284 0.371302
4 to 5 141838 -0.2104 0.416673
3 to 4 141937 0.0816 0.532527
2 to 3 141653 -0.7561 0.224784
1 to 2 141741 -0.4965 0.309754
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-09_23:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2499.08 -0.013 0.494829
Test results for specific bytes for dh-ranFile-2018-07-09_23:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2524.55 0.347 0.635764
2 to 9 2474.77 -0.357 0.360644
3 to 10 2523.55 0.333 0.630430
4 to 11 2507.06 0.100 0.539789
5 to 12 2530.92 0.437 0.669053
6 to 13 2433.14 -0.945 0.172204
7 to 14 2437.27 -0.887 0.187508
8 to 15 2490.61 -0.133 0.447177
9 to 16 2526.14 0.370 0.644206
10 to 17 2437.93 -0.878 0.190035
11 to 18 2439.13 -0.861 0.194665
12 to 19 2432.98 -0.948 0.171601
13 to 20 2497.82 -0.031 0.487677
14 to 21 2498.82 -0.017 0.493369
15 to 22 2518.73 0.265 0.604467
16 to 23 2518.40 0.260 0.602657
17 to 24 2505.99 0.085 0.533752
18 to 25 2466.15 -0.479 0.316082
19 to 26 2524.51 0.347 0.635564
20 to 27 2479.28 -0.293 0.384762
21 to 28 2462.33 -0.533 0.297112
22 to 29 2544.19 0.625 0.733991
23 to 30 2441.60 -0.826 0.204434
24 to 31 2484.06 -0.225 0.410811
25 to 32 2522.91 0.324 0.627034
CDPARK for dh-ranFile-2018-07-09_23:31: 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
3537 0.6393 0.738676
3514 -0.4110 0.340551
3541 0.8219 0.794438
3522 -0.0457 0.481790
3498 -1.1416 0.126820
3499 -1.0959 0.136563
3500 -1.0502 0.146807
3506 -0.7763 0.218799
3554 1.4155 0.921543
3470 -2.4201 0.007758
Square side=100, avg. no. parked=3514.10 sample std.=23.66
p-value of the KSTEST for those 10 p-values: 0.297692
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-09_23:31
0.6512,0.9709,0.8106,0.4640,0.1817,0.9412,0.3110,0.0554,0.7446,0.4094,
The KS test for those 10 p-values: 0.897948
The 3DSPHERES test for dh-ranFile-2018-07-09_23:31
sample no r^3 equiv. uni.
1 20.587 0.496524
2 2.383 0.076364
3 8.383 0.243800
4 34.778 0.686279
5 33.242 0.669808
6 23.429 0.542043
7 1.722 0.055796
8 14.381 0.380820
9 3.596 0.112972
10 0.675 0.022235
11 5.681 0.172530
12 50.617 0.814970
13 7.606 0.223933
14 8.500 0.246723
15 5.982 0.180767
16 82.690 0.936475
17 1.111 0.036355
18 41.892 0.752511
19 14.555 0.384399
20 2.460 0.078728
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.033028
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-09_23:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -0.3 -0.8 -1.3 0.9 -0.6
0.3 1.7 0.3 -0.3 -0.7 -0.9
-0.4 -0.4 -0.1 -0.9 0.3 -0.0
2.1 -0.1 -1.3 1.8 0.2 0.8
-0.4 -0.9 -0.1 0.6 -1.4 -0.1
1.1 -0.3 -1.8 0.5 0.2 -0.3
0.7 1.5 0.5 -0.7 -1.3 -1.0
-1.1
Chi-square with 42 degrees of freedom:35.318530
z-score=-0.729008, p-value=0.242628
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-09_23:31
Test no p-value
1 0.202904
2 0.017046
3 0.337789
4 0.052680
5 0.003862
6 0.159864
7 0.602861
8 0.850412
9 0.679038
10 0.008805
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.005529
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-09_23:31:
(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 66559 0.17 66652 0.00
3 25000.00 25042 0.07 25059 0.14
4 6666.67 6820 3.53 6633 0.17
5 1388.89 1341 1.65 1387 0.00
6 238.10 197 7.09 217 1.87
7 34.72 36 0.05 48 5.08
8 4.96 4 0.19 3 0.77
p=0.95279 p=0.76467
Number of rngs required: 687959, p-value: 0.304
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-09_23:31
No. of wins: Observed Expected
98676 98585.9
z-score= 0.403, pvalue=0.65659
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66446 66666.7 0.730 0.730
2 38013 37654.3 3.417 4.147
3 26839 26954.7 0.497 4.644
4 19109 19313.5 2.165 6.808
5 13810 13851.4 0.124 6.932
6 10011 9943.5 0.458 7.390
7 7284 7145.0 2.703 10.093
8 5123 5139.1 0.050 10.143
9 3677 3699.9 0.141 10.285
10 2767 2666.3 3.803 14.088
11 1886 1923.3 0.725 14.813
12 1392 1388.7 0.008 14.820
13 1034 1003.7 0.914 15.734
14 711 726.1 0.316 16.050
15 512 525.8 0.364 16.414
16 354 381.2 1.934 18.348
17 275 276.5 0.009 18.356
18 243 200.8 8.855 27.211
19 133 146.0 1.155 28.366
20 85 106.2 4.237 32.604
21 296 287.1 0.275 32.879
Chisq= 32.88 for 20 degrees of freedom, p= 0.96521
SUMMARY of craptest
p-value for no. of wins: 0.656587
p-value for throws/game: 0.965210
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-09_23:31
No. of wins: Observed Expected
98727 98585.9
z-score= 0.631, pvalue=0.73607
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66645 66666.7 0.007 0.007
2 37687 37654.3 0.028 0.035
3 26779 26954.7 1.146 1.181
4 19425 19313.5 0.644 1.825
5 13874 13851.4 0.037 1.862
6 10057 9943.5 1.295 3.157
7 7138 7145.0 0.007 3.164
8 5191 5139.1 0.525 3.688
9 3658 3699.9 0.474 4.162
10 2688 2666.3 0.177 4.339
11 1953 1923.3 0.458 4.796
12 1323 1388.7 3.112 7.908
13 989 1003.7 0.216 8.124
14 716 726.1 0.142 8.266
15 546 525.8 0.773 9.039
16 366 381.2 0.602 9.641
17 227 276.5 8.875 18.516
18 207 200.8 0.190 18.705
19 152 146.0 0.248 18.953
20 114 106.2 0.571 19.524
21 265 287.1 1.703 21.227
Chisq= 21.23 for 20 degrees of freedom, p= 0.61612
SUMMARY of craptest
p-value for no. of wins: 0.736067
p-value for throws/game: 0.616116
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0009,0.0037,0.0039,0.0055,0.0078,0.0088,0.0090,0.0110,0.0170,0.0171,
0.0222,0.0239,0.0260,0.0317,0.0330,0.0364,0.0471,0.0520,0.0527,0.0532,
0.0554,0.0557,0.0558,0.0574,0.0615,0.0661,0.0664,0.0680,0.0698,0.0753,
0.0764,0.0787,0.0948,0.1023,0.1048,0.1061,0.1078,0.1116,0.1122,0.1130,
0.1130,0.1153,0.1169,0.1182,0.1182,0.1268,0.1297,0.1339,0.1366,0.1421,
0.1468,0.1480,0.1502,0.1514,0.1532,0.1599,0.1653,0.1695,0.1716,0.1722,
0.1725,0.1808,0.1817,0.1875,0.1877,0.1900,0.1947,0.1992,0.2029,0.2044,
0.2052,0.2084,0.2143,0.2188,0.2205,0.2239,0.2248,0.2348,0.2426,0.2438,
0.2467,0.2512,0.2613,0.2720,0.2780,0.2790,0.2829,0.2949,0.2971,0.2977,
0.3024,0.3035,0.3044,0.3098,0.3110,0.3122,0.3161,0.3189,0.3232,0.3281,
0.3303,0.3348,0.3359,0.3378,0.3406,0.3426,0.3430,0.3504,0.3514,0.3606,
0.3631,0.3653,0.3680,0.3713,0.3742,0.3804,0.3808,0.3825,0.3844,0.3848,
0.3848,0.3892,0.3929,0.4063,0.4094,0.4108,0.4157,0.4167,0.4230,0.4243,
0.4249,0.4282,0.4309,0.4311,0.4472,0.4537,0.4617,0.4620,0.4640,0.4704,
0.4714,0.4785,0.4818,0.4844,0.4844,0.4859,0.4877,0.4894,0.4927,0.4934,
0.4948,0.4965,0.5008,0.5062,0.5114,0.5127,0.5136,0.5202,0.5229,0.5267,
0.5276,0.5306,0.5310,0.5325,0.5325,0.5333,0.5338,0.5398,0.5420,0.5481,
0.5608,0.5695,0.5772,0.5812,0.6027,0.6029,0.6045,0.6091,0.6117,0.6161,
0.6164,0.6270,0.6293,0.6304,0.6306,0.6318,0.6323,0.6332,0.6356,0.6358,
0.6407,0.6412,0.6441,0.6442,0.6455,0.6462,0.6512,0.6512,0.6566,0.6625,
0.6691,0.6698,0.6731,0.6757,0.6760,0.6790,0.6863,0.6863,0.7011,0.7026,
0.7340,0.7361,0.7387,0.7434,0.7446,0.7518,0.7525,0.7580,0.7616,0.7639,
0.7647,0.7707,0.7944,0.7956,0.7966,0.7996,0.8061,0.8093,0.8106,0.8150,
0.8211,0.8310,0.8394,0.8441,0.8484,0.8504,0.8637,0.8821,0.8834,0.8866,
0.8979,0.9062,0.9062,0.9091,0.9130,0.9134,0.9215,0.9266,0.9280,0.9312,
0.9365,0.9411,0.9412,0.9412,0.9435,0.9498,0.9499,0.9528,0.9535,0.9603,
0.9652,0.9698,0.9703,0.9709,0.9736,0.9747,0.9772,0.9923,0.9994,
Overall p-value after applying KStest on 269 p-values = 0.017212
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.