RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-03-23_18:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.98 24.2680 0.887666
2 to 25 15.40 35.5086 0.994669
3 to 26 15.73 21.2596 0.785107
4 to 27 15.66 17.7129 0.592837
5 to 28 15.54 20.2360 0.737663
6 to 29 15.42 21.8532 0.809571
7 to 30 15.75 12.0884 0.205244
8 to 31 15.79 15.4592 0.437556
9 to 32 15.95 13.6891 0.311023
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.233914
Tough bday spacings test for dh-ranFile-2017-03-23_18:31: 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 37 57 94 106 84 53 36 11 7 6
(O-E)^2/E 0.0 0.0 3.6 0.1 0.7 0.4 0.0 1.3 1.0 0.0 0.9
Birthday Spacings: Sum(O-E)^2/E= 8.177, p= 0.388
RESULTS OF GCD FOR dh-ranFile-2017-03-23_18:31
Euclid's algorithm:
p-value, steps to gcd: 0.680478
p-value, dist. of gcd's: 0.644050
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-03-23_18:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.317 0.732 0.153 0.319 0.588 0.996 0.489 0.124
Bits 8 to 15---> 0.033 0.131 0.899 0.844 0.878 0.514 0.310 0.331
Bits 16 to 23---> 0.652 0.436 0.260 0.758 0.129 0.845 0.228 0.836
Bits 24 to 31---> 0.143 0.950 0.027 0.976 0.129 0.174 0.965 0.363
KS test for the above 32 p values: 0.552
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-03-23_18:31,
p-values for 5 runs: 0.9727, 0.3045, 0.1406, 0.5751, 0.4795
Rank test for binary matrices (31x31) for dh-ranFile-2017-03-23_18:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 211 211.4 0.001 0.001
r= 29 5049 5134.0 1.408 1.408
r= 30 23227 23103.0 0.665 2.073
r= 31 11513 11551.5 0.128 2.202
chi-square = 2.202 with df = 3; p-value = 0.468
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2017-03-23_18:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 238 211.4 3.342 3.342
r= 30 5081 5134.0 0.547 3.890
r= 31 23127 23103.0 0.025 3.914
r= 32 11554 11551.5 0.001 3.915
chi-square = 3.915 with df = 3; p-value = 0.729
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2017-03-23_18:31
b-rank test for bits 1 to 8, p=0.97914
b-rank test for bits 2 to 9, p=0.21228
b-rank test for bits 3 to 10, p=0.46872
b-rank test for bits 4 to 11, p=0.15325
b-rank test for bits 5 to 12, p=0.35916
b-rank test for bits 6 to 13, p=0.38298
b-rank test for bits 7 to 14, p=0.26296
b-rank test for bits 8 to 15, p=0.43712
b-rank test for bits 9 to 16, p=0.19912
b-rank test for bits 10 to 17, p=0.05335
b-rank test for bits 11 to 18, p=0.11830
b-rank test for bits 12 to 19, p=0.75163
b-rank test for bits 13 to 20, p=0.61341
b-rank test for bits 14 to 21, p=0.68563
b-rank test for bits 15 to 22, p=0.98447
b-rank test for bits 16 to 23, p=0.64354
b-rank test for bits 17 to 24, p=0.96412
b-rank test for bits 18 to 25, p=0.92932
b-rank test for bits 19 to 26, p=0.37896
b-rank test for bits 20 to 27, p=0.58803
b-rank test for bits 21 to 28, p=0.02607
b-rank test for bits 22 to 29, p=0.16067
b-rank test for bits 23 to 30, p=0.88656
b-rank test for bits 24 to 31, p=0.99698
b-rank test for bits 25 to 32, p=0.34562
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 = 0.460563
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-03-23_18:31
(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 141628 -0.66 0.255490
2 142037 0.30 0.617261
3 141435 -1.11 0.133877
4 141671 -0.56 0.288816
5 141677 -0.54 0.293624
6 141618 -0.68 0.248038
7 141581 -0.77 0.221503
8 141841 -0.16 0.436579
9 141779 -0.30 0.380370
10 141862 -0.11 0.455973
11 141674 -0.55 0.291216
12 141422 -1.14 0.127431
13 142099 0.44 0.671173
14 141874 -0.08 0.467106
15 141847 -0.15 0.442106
16 141200 -1.66 0.048728
17 141975 0.15 0.560972
18 142239 0.77 0.779426
19 142041 0.31 0.620822
20 142369 1.07 0.858588
----------------------------------------------------------------
OPSO test for dh-ranFile-2017-03-23_18:31
Bits used No. missing words z-score p-value
23 to 32 141621 -0.9942 0.160053
22 to 31 141654 -0.8804 0.189308
21 to 30 142140 0.7954 0.786814
20 to 29 141884 -0.0873 0.465199
19 to 28 142053 0.4954 0.689846
18 to 27 142247 1.1644 0.877865
17 to 26 141929 0.0678 0.527039
16 to 25 141830 -0.2736 0.392215
15 to 24 141843 -0.2287 0.409542
14 to 23 142026 0.4023 0.656272
13 to 22 141784 -0.4322 0.332808
12 to 21 141561 -1.2011 0.114849
11 to 20 141753 -0.5391 0.294920
10 to 19 141715 -0.6701 0.251396
9 to 18 141763 -0.5046 0.306925
8 to 17 141966 0.1954 0.577466
7 to 16 141486 -1.4598 0.072178
6 to 15 142252 1.1816 0.881322
5 to 14 141903 -0.0218 0.491293
4 to 13 141858 -0.1770 0.429754
3 to 12 141705 -0.7046 0.240534
2 to 11 141549 -1.2425 0.107023
1 to 10 141285 -2.1529 0.015665
-----------------------------------------------------------------
OQSO test for dh-ranFile-2017-03-23_18:31
Bits used No. missing words z-score p-value
28 to 32 141985 0.2565 0.601221
27 to 31 141864 -0.1537 0.438939
26 to 30 142654 2.5243 0.994204
25 to 29 142231 1.0904 0.862233
24 to 28 141887 -0.0757 0.469831
23 to 27 141774 -0.4587 0.323208
22 to 26 141963 0.1819 0.572182
21 to 25 141996 0.2938 0.615543
20 to 24 142018 0.3684 0.643702
19 to 23 142166 0.8701 0.807868
18 to 22 141550 -1.2181 0.111599
17 to 21 141872 -0.1265 0.449651
16 to 20 142459 1.8633 0.968789
15 to 19 142110 0.6802 0.751823
14 to 18 141522 -1.3130 0.094594
13 to 17 142050 0.4768 0.683265
12 to 16 142283 1.2667 0.897365
11 to 15 142418 1.7243 0.957674
10 to 14 142226 1.0735 0.858467
9 to 13 142206 1.0057 0.842711
8 to 12 142360 1.5277 0.936706
7 to 11 141953 0.1480 0.558842
6 to 10 142035 0.4260 0.664946
5 to 9 141771 -0.4689 0.319565
4 to 8 142504 2.0158 0.978091
3 to 7 142254 1.1684 0.878672
2 to 6 141767 -0.4825 0.314734
1 to 5 142214 1.0328 0.849147
-----------------------------------------------------------------
DNA test for dh-ranFile-2017-03-23_18:31
Bits used No. missing words z-score p-value
31 to 32 142145 0.6952 0.756532
30 to 31 141446 -1.3668 0.085851
29 to 30 142037 0.3766 0.646767
28 to 29 141776 -0.3933 0.347048
27 to 28 141655 -0.7502 0.226556
26 to 27 142208 0.8810 0.810850
25 to 26 141628 -0.8299 0.203303
24 to 25 141960 0.1495 0.559408
23 to 24 141329 -1.7119 0.043459
22 to 23 141788 -0.3579 0.360207
21 to 22 141759 -0.4435 0.328720
20 to 21 141454 -1.3432 0.089611
19 to 20 142408 1.4710 0.929355
18 to 19 141756 -0.4523 0.325526
17 to 18 141757 -0.4494 0.326589
16 to 17 141803 -0.3137 0.376891
15 to 16 142051 0.4179 0.661992
14 to 15 142325 1.2262 0.889932
13 to 14 142327 1.2321 0.891038
12 to 13 141467 -1.3048 0.095979
11 to 12 141374 -1.5791 0.057151
10 to 11 142131 0.6539 0.743410
9 to 10 141784 -0.3697 0.355801
8 to 9 142013 0.3058 0.620126
7 to 8 142013 0.3058 0.620126
6 to 7 141970 0.1790 0.571018
5 to 6 141726 -0.5408 0.294324
4 to 5 142047 0.4061 0.657668
3 to 4 141686 -0.6588 0.255015
2 to 3 141816 -0.2753 0.391539
1 to 2 141875 -0.1013 0.459669
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2017-03-23_18:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2544.05 0.623 0.733353
Test results for specific bytes for dh-ranFile-2017-03-23_18:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2532.99 0.466 0.679568
2 to 9 2406.26 -1.326 0.092479
3 to 10 2402.61 -1.377 0.084203
4 to 11 2532.87 0.465 0.679004
5 to 12 2474.74 -0.357 0.360439
6 to 13 2472.09 -0.395 0.346521
7 to 14 2498.24 -0.025 0.490085
8 to 15 2544.33 0.627 0.734630
9 to 16 2503.12 0.044 0.517573
10 to 17 2328.80 -2.421 0.007735
11 to 18 2530.51 0.432 0.666952
12 to 19 2519.41 0.274 0.608127
13 to 20 2435.11 -0.918 0.179385
14 to 21 2592.83 1.313 0.905389
15 to 22 2515.73 0.222 0.587999
16 to 23 2529.43 0.416 0.661362
17 to 24 2540.73 0.576 0.717686
18 to 25 2416.22 -1.185 0.118035
19 to 26 2551.84 0.733 0.768242
20 to 27 2477.13 -0.323 0.373190
21 to 28 2408.52 -1.294 0.097876
22 to 29 2433.81 -0.936 0.174624
23 to 30 2450.14 -0.705 0.240356
24 to 31 2472.58 -0.388 0.349089
25 to 32 2508.01 0.113 0.545098
CDPARK for dh-ranFile-2017-03-23_18:31: 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
3556 1.5068 0.934075
3524 0.0457 0.518210
3567 2.0091 0.977738
3470 -2.4201 0.007758
3552 1.3242 0.907282
3517 -0.2740 0.392053
3554 1.4155 0.921543
3487 -1.6438 0.050105
3548 1.1416 0.873180
3515 -0.3653 0.357445
Square side=100, avg. no. parked=3529.00 sample std.=30.49
p-value of the KSTEST for those 10 p-values: 0.102686
Results for the MINIMUM DISTANCE test for dh-ranFile-2017-03-23_18:31
0.2855,0.5112,0.7713,0.1009,0.5471,0.4217,0.9214,0.4052,0.7171,0.3548,
The KS test for those 10 p-values: 0.861836
The 3DSPHERES test for dh-ranFile-2017-03-23_18:31
sample no r^3 equiv. uni.
1 13.664 0.365854
2 14.157 0.376185
3 0.495 0.016365
4 54.468 0.837261
5 37.768 0.716043
6 135.248 0.988982
7 2.657 0.084748
8 5.715 0.173456
9 14.060 0.374170
10 20.178 0.489624
11 2.461 0.078764
12 14.980 0.393066
13 15.783 0.409103
14 33.841 0.676328
15 6.046 0.182518
16 3.939 0.123033
17 10.279 0.290113
18 21.865 0.517524
19 1.336 0.043541
20 8.175 0.238534
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.065374
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-03-23_18:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 1.3 -0.4 -0.3 -0.4 -1.8
0.4 -0.4 0.6 -0.1 1.8 -0.2
0.2 0.9 -0.7 0.1 -0.6 -0.2
1.6 -0.1 -0.5 0.6 -1.0 -0.8
-0.7 0.2 -0.6 -0.1 -0.5 0.6
-0.4 0.7 -0.0 0.0 0.9 -0.5
-0.7 -1.3 -0.8 -1.3 -0.6 0.0
-0.1
Chi-square with 42 degrees of freedom:25.676434
z-score=-1.781047, p-value=0.022278
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2017-03-23_18:31
Test no p-value
1 0.789103
2 0.974733
3 0.278298
4 0.523651
5 0.071400
6 0.015071
7 0.008196
8 0.001482
9 0.998237
10 0.560702
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.019133
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-03-23_18:31:
(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 66707 0.02 66627 0.02
3 25000.00 25011 0.00 25030 0.04
4 6666.67 6646 0.06 6625 0.26
5 1388.89 1349 1.15 1438 1.74
6 238.10 243 0.10 247 0.33
7 34.72 39 0.53 24 3.31
8 4.96 4 0.19 8 1.86
p=0.08528 p=0.72808
Number of rngs required: 687838, p-value: 0.257
RESULTS OF CRAPS TEST for dh-ranFile-2017-03-23_18:31
No. of wins: Observed Expected
98435 98585.9
z-score=-0.675, pvalue=0.24992
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66628 66666.7 0.022 0.022
2 37723 37654.3 0.125 0.148
3 27057 26954.7 0.388 0.536
4 19231 19313.5 0.352 0.888
5 13705 13851.4 1.548 2.436
6 10048 9943.5 1.097 3.533
7 7093 7145.0 0.379 3.912
8 5177 5139.1 0.280 4.192
9 3656 3699.9 0.520 4.712
10 2677 2666.3 0.043 4.755
11 1937 1923.3 0.097 4.852
12 1434 1388.7 1.475 6.327
13 977 1003.7 0.711 7.038
14 764 726.1 1.974 9.012
15 509 525.8 0.539 9.551
16 378 381.2 0.026 9.577
17 272 276.5 0.075 9.651
18 194 200.8 0.232 9.884
19 149 146.0 0.062 9.946
20 110 106.2 0.135 10.081
21 281 287.1 0.130 10.211
Chisq= 10.21 for 20 degrees of freedom, p= 0.03582
SUMMARY of craptest
p-value for no. of wins: 0.249924
p-value for throws/game: 0.035818
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2017-03-23_18:31
No. of wins: Observed Expected
98630 98585.9
z-score= 0.197, pvalue=0.57825
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66951 66666.7 1.213 1.213
2 37584 37654.3 0.131 1.344
3 26822 26954.7 0.654 1.998
4 19227 19313.5 0.387 2.385
5 13829 13851.4 0.036 2.421
6 9949 9943.5 0.003 2.424
7 7115 7145.0 0.126 2.550
8 5142 5139.1 0.002 2.552
9 3648 3699.9 0.727 3.279
10 2758 2666.3 3.154 6.433
11 1920 1923.3 0.006 6.439
12 1399 1388.7 0.076 6.514
13 1051 1003.7 2.228 8.742
14 746 726.1 0.543 9.285
15 502 525.8 1.080 10.366
16 359 381.2 1.287 11.653
17 269 276.5 0.206 11.858
18 214 200.8 0.864 12.722
19 156 146.0 0.687 13.409
20 86 106.2 3.847 17.257
21 273 287.1 0.694 17.950
Chisq= 17.95 for 20 degrees of freedom, p= 0.40933
SUMMARY of craptest
p-value for no. of wins: 0.578253
p-value for throws/game: 0.409329
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0015,0.0077,0.0078,0.0082,0.0151,0.0157,0.0164,0.0191,0.0223,0.0261,
0.0268,0.0333,0.0358,0.0435,0.0435,0.0487,0.0501,0.0534,0.0572,0.0654,
0.0714,0.0722,0.0788,0.0842,0.0847,0.0853,0.0859,0.0896,0.0925,0.0946,
0.0960,0.0979,0.1009,0.1027,0.1070,0.1116,0.1148,0.1180,0.1183,0.1230,
0.1239,0.1274,0.1290,0.1293,0.1315,0.1339,0.1406,0.1431,0.1532,0.1534,
0.1601,0.1607,0.1735,0.1738,0.1746,0.1794,0.1825,0.1893,0.1991,0.2033,
0.2052,0.2123,0.2215,0.2266,0.2281,0.2339,0.2385,0.2404,0.2405,0.2480,
0.2499,0.2514,0.2550,0.2555,0.2572,0.2599,0.2630,0.2783,0.2855,0.2888,
0.2901,0.2912,0.2936,0.2943,0.2949,0.3045,0.3069,0.3104,0.3110,0.3147,
0.3172,0.3187,0.3196,0.3232,0.3255,0.3266,0.3287,0.3307,0.3328,0.3456,
0.3465,0.3470,0.3491,0.3548,0.3558,0.3574,0.3592,0.3602,0.3604,0.3627,
0.3659,0.3732,0.3742,0.3762,0.3769,0.3790,0.3804,0.3830,0.3885,0.3915,
0.3921,0.3922,0.3931,0.4052,0.4091,0.4093,0.4095,0.4217,0.4298,0.4357,
0.4366,0.4371,0.4376,0.4389,0.4421,0.4497,0.4560,0.4597,0.4606,0.4652,
0.4671,0.4684,0.4687,0.4698,0.4795,0.4890,0.4896,0.4901,0.4913,0.5112,
0.5144,0.5175,0.5176,0.5182,0.5237,0.5270,0.5451,0.5471,0.5517,0.5588,
0.5594,0.5607,0.5610,0.5710,0.5722,0.5751,0.5775,0.5783,0.5879,0.5880,
0.5880,0.5928,0.6012,0.6081,0.6134,0.6155,0.6173,0.6201,0.6201,0.6208,
0.6435,0.6437,0.6441,0.6468,0.6521,0.6563,0.6577,0.6614,0.6620,0.6649,
0.6670,0.6712,0.6763,0.6790,0.6796,0.6805,0.6833,0.6856,0.6898,0.7160,
0.7171,0.7177,0.7281,0.7292,0.7322,0.7334,0.7346,0.7377,0.7434,0.7516,
0.7518,0.7565,0.7576,0.7682,0.7713,0.7794,0.7851,0.7868,0.7891,0.8079,
0.8096,0.8108,0.8361,0.8373,0.8427,0.8444,0.8448,0.8491,0.8585,0.8586,
0.8618,0.8622,0.8732,0.8779,0.8781,0.8787,0.8813,0.8866,0.8877,0.8899,
0.8910,0.8974,0.8987,0.9054,0.9073,0.9214,0.9215,0.9293,0.9294,0.9341,
0.9367,0.9501,0.9577,0.9641,0.9648,0.9688,0.9727,0.9747,0.9759,0.9777,
0.9781,0.9791,0.9845,0.9890,0.9942,0.9947,0.9959,0.9970,0.9982,
Overall p-value after applying KStest on 269 p-values = 0.206659
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.