RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-03_10:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 16.30 18.4463 0.638780
2 to 25 16.00 19.9912 0.725319
3 to 26 15.64 16.0946 0.482862
4 to 27 15.75 15.2504 0.422546
5 to 28 15.82 22.3134 0.827035
6 to 29 15.60 11.3382 0.161547
7 to 30 15.98 15.7350 0.457310
8 to 31 15.76 12.2915 0.217828
9 to 32 15.75 10.5257 0.119867
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.798069
Tough bday spacings test for dh-ranFile-2018-07-03_10:31: 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 42 88 110 98 59 48 27 11 5 4
(O-E)^2/E 0.1 0.8 3.0 1.6 0.0 4.7 0.3 0.3 1.0 0.4 0.0
Birthday Spacings: Sum(O-E)^2/E= 12.133, p= 0.724
RESULTS OF GCD FOR dh-ranFile-2018-07-03_10:31
Euclid's algorithm:
p-value, steps to gcd: 0.273390
p-value, dist. of gcd's: 0.170500
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-03_10:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.057 0.337 0.635 0.948 0.327 0.047 0.735 0.543
Bits 8 to 15---> 0.498 0.157 0.577 0.758 0.037 0.366 0.805 0.941
Bits 16 to 23---> 0.457 0.374 0.921 0.585 0.280 0.323 0.086 0.585
Bits 24 to 31---> 0.534 0.459 0.254 0.421 0.475 0.650 0.112 0.614
KS test for the above 32 p values: 0.460
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-03_10:31,
p-values for 5 runs: 0.3345, 0.0584, 0.2716, 0.4341, 0.9773
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-03_10:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 200 211.4 0.617 0.617
r= 29 5141 5134.0 0.010 0.626
r= 30 22999 23103.0 0.469 1.095
r= 31 11660 11551.5 1.019 2.113
chi-square = 2.113 with df = 3; p-value = 0.451
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-03_10:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 205 211.4 0.195 0.195
r= 30 5140 5134.0 0.007 0.202
r= 31 23259 23103.0 1.053 1.255
r= 32 11396 11551.5 2.094 3.348
chi-square = 3.348 with df = 3; p-value = 0.659
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-03_10:31
b-rank test for bits 1 to 8, p=0.77172
b-rank test for bits 2 to 9, p=0.74358
b-rank test for bits 3 to 10, p=0.23255
b-rank test for bits 4 to 11, p=0.41009
b-rank test for bits 5 to 12, p=0.07804
b-rank test for bits 6 to 13, p=0.12096
b-rank test for bits 7 to 14, p=0.30502
b-rank test for bits 8 to 15, p=0.30980
b-rank test for bits 9 to 16, p=0.33048
b-rank test for bits 10 to 17, p=0.70541
b-rank test for bits 11 to 18, p=0.09933
b-rank test for bits 12 to 19, p=0.49785
b-rank test for bits 13 to 20, p=0.67623
b-rank test for bits 14 to 21, p=0.62556
b-rank test for bits 15 to 22, p=0.65654
b-rank test for bits 16 to 23, p=0.86235
b-rank test for bits 17 to 24, p=0.89302
b-rank test for bits 18 to 25, p=0.89693
b-rank test for bits 19 to 26, p=0.98734
b-rank test for bits 20 to 27, p=0.53318
b-rank test for bits 21 to 28, p=0.04441
b-rank test for bits 22 to 29, p=0.04970
b-rank test for bits 23 to 30, p=0.55570
b-rank test for bits 24 to 31, p=0.15779
b-rank test for bits 25 to 32, p=0.79573
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 = 0.986380
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-03_10:31
(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 142530 1.45 0.926494
2 142115 0.48 0.684577
3 141692 -0.51 0.305804
4 142318 0.95 0.830170
5 141960 0.12 0.547120
6 141742 -0.39 0.347914
7 141048 -2.01 0.022086
8 142145 0.55 0.709057
9 141865 -0.10 0.458753
10 141484 -0.99 0.160169
11 141762 -0.34 0.365337
12 142170 0.61 0.728752
13 142068 0.37 0.644579
14 142498 1.38 0.915496
15 141921 0.03 0.510876
16 141941 0.07 0.529493
17 141779 -0.30 0.380370
18 142158 0.58 0.719381
19 141908 -0.00 0.498760
20 141443 -1.09 0.137954
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-03_10:31
Bits used No. missing words z-score p-value
23 to 32 141961 0.1782 0.570706
22 to 31 141498 -1.4184 0.078040
21 to 30 141384 -1.8115 0.035033
20 to 29 142166 0.8851 0.811940
19 to 28 142173 0.9092 0.818380
18 to 27 141790 -0.4115 0.340359
17 to 26 142177 0.9230 0.821996
16 to 25 142144 0.8092 0.790802
15 to 24 141919 0.0333 0.513300
14 to 23 141307 -2.0770 0.018901
13 to 22 141868 -0.1425 0.443336
12 to 21 141817 -0.3184 0.375099
11 to 20 141799 -0.3804 0.351806
10 to 19 142279 1.2747 0.898797
9 to 18 141773 -0.4701 0.319141
8 to 17 141707 -0.6977 0.242686
7 to 16 142291 1.3161 0.905930
6 to 15 142021 0.3851 0.649907
5 to 14 141919 0.0333 0.513300
4 to 13 141811 -0.3391 0.367279
3 to 12 141694 -0.7425 0.228887
2 to 11 142193 0.9782 0.836006
1 to 10 141574 -1.1563 0.123777
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-03_10:31
Bits used No. missing words z-score p-value
28 to 32 142388 1.6226 0.947664
27 to 31 141738 -0.5808 0.280695
26 to 30 141959 0.1684 0.566855
25 to 29 142094 0.6260 0.734343
24 to 28 142044 0.4565 0.675988
23 to 27 141976 0.2260 0.589399
22 to 26 141811 -0.3333 0.369446
21 to 25 142128 0.7413 0.770730
20 to 24 141786 -0.4181 0.337949
19 to 23 141504 -1.3740 0.084721
18 to 22 141548 -1.2248 0.110316
17 to 21 141789 -0.4079 0.341674
16 to 20 141548 -1.2248 0.110316
15 to 19 141616 -0.9943 0.160029
14 to 18 141941 0.1074 0.542747
13 to 17 141909 -0.0011 0.499554
12 to 16 141894 -0.0520 0.479278
11 to 15 141881 -0.0960 0.461747
10 to 14 141566 -1.1638 0.122246
9 to 13 141910 0.0023 0.500906
8 to 12 141696 -0.7232 0.234793
7 to 11 141649 -0.8825 0.188760
6 to 10 141884 -0.0859 0.465787
5 to 9 142387 1.6192 0.947300
4 to 8 141452 -1.5503 0.060538
3 to 7 141833 -0.2587 0.397916
2 to 6 142068 0.5379 0.704665
1 to 5 142057 0.5006 0.691665
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-03_10:31
Bits used No. missing words z-score p-value
31 to 32 141982 0.2144 0.584869
30 to 31 141936 0.0787 0.531354
29 to 30 141717 -0.5673 0.285240
28 to 29 142035 0.3707 0.644573
27 to 28 142314 1.1937 0.883706
26 to 27 142695 2.3176 0.989765
25 to 26 141611 -0.8800 0.189422
24 to 25 141890 -0.0570 0.477264
23 to 24 141821 -0.2606 0.397216
22 to 23 141537 -1.0983 0.136033
21 to 22 141747 -0.4788 0.316023
20 to 21 142059 0.4415 0.670576
19 to 20 141938 0.0846 0.533699
18 to 19 141680 -0.6765 0.249365
17 to 18 141823 -0.2547 0.399493
16 to 17 142272 1.0698 0.857651
15 to 16 141944 0.1023 0.540729
14 to 15 141033 -2.5850 0.004868
13 to 14 141744 -0.4877 0.312882
12 to 13 141334 -1.6971 0.044835
11 to 12 142328 1.2350 0.891588
10 to 11 142159 0.7365 0.769284
9 to 10 142049 0.4120 0.659832
8 to 9 142167 0.7601 0.776399
7 to 8 141468 -1.3019 0.096482
6 to 7 141727 -0.5378 0.295342
5 to 6 141681 -0.6735 0.250302
4 to 5 141272 -1.8800 0.030052
3 to 4 142707 2.3530 0.990689
2 to 3 141498 -1.2134 0.112496
1 to 2 141815 -0.2783 0.390407
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-03_10:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2528.33 0.401 0.655656
Test results for specific bytes for dh-ranFile-2018-07-03_10:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2529.27 0.414 0.660522
2 to 9 2546.13 0.652 0.742914
3 to 10 2452.12 -0.677 0.249162
4 to 11 2385.82 -1.615 0.053178
5 to 12 2596.75 1.368 0.914388
6 to 13 2468.74 -0.442 0.329234
7 to 14 2471.65 -0.401 0.344257
8 to 15 2509.83 0.139 0.555285
9 to 16 2511.56 0.164 0.564950
10 to 17 2554.61 0.772 0.780025
11 to 18 2672.53 2.440 0.992655
12 to 19 2458.09 -0.593 0.276677
13 to 20 2412.06 -1.244 0.106800
14 to 21 2560.40 0.854 0.803510
15 to 22 2549.36 0.698 0.757450
16 to 23 2455.91 -0.624 0.266459
17 to 24 2456.38 -0.617 0.268644
18 to 25 2473.29 -0.378 0.352830
19 to 26 2420.05 -1.131 0.129108
20 to 27 2440.77 -0.838 0.201124
21 to 28 2502.40 0.034 0.513544
22 to 29 2420.52 -1.124 0.130496
23 to 30 2406.27 -1.326 0.092497
24 to 31 2574.60 1.055 0.854290
25 to 32 2454.69 -0.641 0.260812
CDPARK for dh-ranFile-2018-07-03_10:31: 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
3512 -0.5023 0.307734
3533 0.4566 0.676028
3486 -1.6895 0.045562
3488 -1.5982 0.055002
3554 1.4155 0.921543
3502 -0.9589 0.168804
3544 0.9589 0.831196
3508 -0.6849 0.246694
3532 0.4110 0.659449
3579 2.5571 0.994722
Square side=100, avg. no. parked=3523.80 sample std.=28.45
p-value of the KSTEST for those 10 p-values: 0.581720
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-03_10:31
0.8631,0.4029,0.4033,0.2597,0.6055,0.9777,0.0570,0.0015,0.5292,0.2058,
The KS test for those 10 p-values: 0.499876
The 3DSPHERES test for dh-ranFile-2018-07-03_10:31
sample no r^3 equiv. uni.
1 28.751 0.616484
2 10.893 0.304483
3 1.804 0.058370
4 17.992 0.451050
5 0.772 0.025393
6 32.152 0.657581
7 0.614 0.020266
8 10.318 0.291021
9 68.143 0.896837
10 43.988 0.769218
11 74.411 0.916287
12 33.940 0.677398
13 74.306 0.915994
14 24.505 0.558166
15 8.627 0.249924
16 40.227 0.738393
17 21.434 0.510540
18 23.331 0.540542
19 22.014 0.519924
20 13.700 0.366617
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.841442
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-03_10:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 -1.2 -0.4 -2.0 1.4 1.7
0.0 -0.7 -0.7 -2.7 -0.2 1.9
0.2 0.2 0.4 0.8 0.8 -0.6
0.2 0.2 -0.4 -1.0 0.2 -0.4
-0.9 0.4 -0.5 -0.9 0.3 -0.1
1.1 0.6 -0.6 2.4 -1.5 -0.1
-0.2 0.5 0.5 -0.1 0.9 0.0
-1.1
Chi-square with 42 degrees of freedom:43.068214
z-score=0.116552, p-value=0.574658
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-03_10:31
Test no p-value
1 0.029969
2 0.015967
3 0.152345
4 0.030573
5 0.005391
6 0.590236
7 0.341806
8 0.032414
9 0.379548
10 0.551036
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000282
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-03_10:31:
(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 66631 0.02 66774 0.17
3 25000.00 24937 0.16 24993 0.00
4 6666.67 6674 0.01 6615 0.40
5 1388.89 1462 3.85 1330 2.50
6 238.10 259 1.84 249 0.50
7 34.72 29 0.94 35 0.00
8 4.96 7 0.84 3 0.77
p=0.73521 p=0.37036
Number of rngs required: 689436, p-value: 0.885
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-03_10:31
No. of wins: Observed Expected
98664 98585.9
z-score= 0.349, pvalue=0.63664
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66683 66666.7 0.004 0.004
2 37580 37654.3 0.147 0.151
3 26689 26954.7 2.620 2.770
4 19358 19313.5 0.103 2.873
5 13910 13851.4 0.248 3.121
6 9888 9943.5 0.310 3.431
7 7201 7145.0 0.439 3.870
8 5171 5139.1 0.198 4.068
9 3768 3699.9 1.255 5.323
10 2713 2666.3 0.818 6.141
11 1898 1923.3 0.334 6.474
12 1384 1388.7 0.016 6.491
13 1038 1003.7 1.171 7.662
14 737 726.1 0.162 7.824
15 533 525.8 0.098 7.922
16 387 381.2 0.090 8.011
17 274 276.5 0.023 8.035
18 239 200.8 7.255 15.289
19 145 146.0 0.007 15.296
20 103 106.2 0.097 15.393
21 301 287.1 0.672 16.065
Chisq= 16.06 for 20 degrees of freedom, p= 0.28741
SUMMARY of craptest
p-value for no. of wins: 0.636641
p-value for throws/game: 0.287413
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-03_10:31
No. of wins: Observed Expected
98623 98585.9
z-score= 0.166, pvalue=0.56597
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66532 66666.7 0.272 0.272
2 37625 37654.3 0.023 0.295
3 27037 26954.7 0.251 0.546
4 19363 19313.5 0.127 0.673
5 14063 13851.4 3.232 3.905
6 10016 9943.5 0.528 4.433
7 7087 7145.0 0.471 4.904
8 5053 5139.1 1.442 6.346
9 3632 3699.9 1.245 7.591
10 2652 2666.3 0.077 7.667
11 1899 1923.3 0.308 7.975
12 1357 1388.7 0.725 8.700
13 998 1003.7 0.033 8.733
14 753 726.1 0.994 9.726
15 538 525.8 0.281 10.008
16 386 381.2 0.062 10.069
17 255 276.5 1.678 11.747
18 204 200.8 0.050 11.797
19 137 146.0 0.553 12.350
20 105 106.2 0.014 12.364
21 308 287.1 1.519 13.883
Chisq= 13.88 for 20 degrees of freedom, p= 0.16364
SUMMARY of craptest
p-value for no. of wins: 0.565968
p-value for throws/game: 0.163642
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0003,0.0015,0.0049,0.0054,0.0160,0.0189,0.0203,0.0221,0.0254,0.0300,
0.0301,0.0306,0.0324,0.0350,0.0368,0.0444,0.0448,0.0456,0.0471,0.0497,
0.0532,0.0550,0.0565,0.0570,0.0584,0.0584,0.0605,0.0780,0.0780,0.0847,
0.0856,0.0925,0.0965,0.0993,0.1068,0.1103,0.1103,0.1119,0.1125,0.1199,
0.1210,0.1222,0.1238,0.1291,0.1305,0.1360,0.1380,0.1523,0.1567,0.1578,
0.1600,0.1602,0.1615,0.1636,0.1688,0.1705,0.1888,0.1894,0.2011,0.2058,
0.2178,0.2289,0.2325,0.2348,0.2427,0.2467,0.2492,0.2494,0.2499,0.2503,
0.2541,0.2597,0.2608,0.2665,0.2686,0.2716,0.2734,0.2767,0.2805,0.2807,
0.2852,0.2874,0.2910,0.2953,0.3045,0.3050,0.3058,0.3077,0.3098,0.3129,
0.3160,0.3191,0.3231,0.3271,0.3292,0.3305,0.3345,0.3375,0.3379,0.3404,
0.3417,0.3418,0.3443,0.3479,0.3518,0.3528,0.3653,0.3659,0.3666,0.3673,
0.3694,0.3704,0.3743,0.3751,0.3795,0.3804,0.3904,0.3972,0.3979,0.3995,
0.4029,0.4033,0.4101,0.4207,0.4225,0.4341,0.4433,0.4508,0.4510,0.4566,
0.4573,0.4586,0.4588,0.4596,0.4617,0.4658,0.4750,0.4773,0.4793,0.4829,
0.4979,0.4981,0.4988,0.4996,0.4999,0.5009,0.5105,0.5109,0.5133,0.5133,
0.5135,0.5199,0.5292,0.5295,0.5314,0.5332,0.5337,0.5337,0.5405,0.5407,
0.5427,0.5431,0.5471,0.5510,0.5553,0.5557,0.5582,0.5649,0.5660,0.5669,
0.5707,0.5747,0.5766,0.5817,0.5849,0.5849,0.5852,0.5894,0.5902,0.6055,
0.6141,0.6165,0.6256,0.6351,0.6366,0.6388,0.6446,0.6446,0.6497,0.6499,
0.6557,0.6565,0.6576,0.6590,0.6594,0.6598,0.6605,0.6706,0.6760,0.6760,
0.6762,0.6774,0.6846,0.6917,0.7047,0.7054,0.7091,0.7194,0.7237,0.7253,
0.7288,0.7343,0.7352,0.7354,0.7384,0.7429,0.7436,0.7575,0.7580,0.7692,
0.7693,0.7707,0.7717,0.7764,0.7800,0.7908,0.7957,0.7981,0.8035,0.8048,
0.8119,0.8184,0.8220,0.8270,0.8302,0.8312,0.8360,0.8414,0.8543,0.8577,
0.8623,0.8631,0.8837,0.8850,0.8916,0.8930,0.8968,0.8969,0.8988,0.9059,
0.9144,0.9155,0.9160,0.9163,0.9215,0.9215,0.9265,0.9415,0.9473,0.9477,
0.9485,0.9773,0.9777,0.9864,0.9873,0.9898,0.9907,0.9927,0.9947,
Overall p-value after applying KStest on 269 p-values = 0.066840
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.