RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-11_08:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.79 17.7185 0.593198
2 to 25 15.83 21.1453 0.780141
3 to 26 16.03 13.6586 0.308896
4 to 27 15.93 10.1786 0.104046
5 to 28 15.80 32.4942 0.986945
6 to 29 15.83 12.0341 0.201934
7 to 30 15.99 11.5128 0.171299
8 to 31 15.54 16.3670 0.502015
9 to 32 15.56 28.5764 0.961363
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.724950
Tough bday spacings test for dh-ranFile-2018-07-11_08:31: 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 11 38 69 103 103 76 57 26 6 6 5
(O-E)^2/E 0.4 0.1 0.2 0.3 0.3 0.1 0.5 0.5 5.3 0.1 0.2
Birthday Spacings: Sum(O-E)^2/E= 7.822, p= 0.354
RESULTS OF GCD FOR dh-ranFile-2018-07-11_08:31
Euclid's algorithm:
p-value, steps to gcd: 0.366988
p-value, dist. of gcd's: 0.157004
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-11_08:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.836 0.650 0.554 0.194 0.970 0.997 0.106 0.449
Bits 8 to 15---> 0.855 0.160 0.017 0.210 0.403 0.940 0.837 0.063
Bits 16 to 23---> 0.748 0.246 0.465 0.796 0.621 0.423 0.656 0.356
Bits 24 to 31---> 0.474 0.428 0.110 0.753 0.179 0.274 0.238 0.345
KS test for the above 32 p values: 0.047
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-11_08:31,
p-values for 5 runs: 0.6574, 0.9110, 0.2669, 0.1966, 0.1644
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-11_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 193 211.4 1.605 1.605
r= 29 5120 5134.0 0.038 1.643
r= 30 23040 23103.0 0.172 1.815
r= 31 11647 11551.5 0.789 2.604
chi-square = 2.604 with df = 3; p-value = 0.543
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-11_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 216 211.4 0.099 0.099
r= 30 5177 5134.0 0.360 0.459
r= 31 23082 23103.0 0.019 0.478
r= 32 11525 11551.5 0.061 0.539
chi-square = 0.539 with df = 3; p-value = 0.090
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-11_08:31
b-rank test for bits 1 to 8, p=0.79687
b-rank test for bits 2 to 9, p=0.14860
b-rank test for bits 3 to 10, p=0.46768
b-rank test for bits 4 to 11, p=0.85209
b-rank test for bits 5 to 12, p=0.77953
b-rank test for bits 6 to 13, p=0.88472
b-rank test for bits 7 to 14, p=0.75381
b-rank test for bits 8 to 15, p=0.39583
b-rank test for bits 9 to 16, p=0.11320
b-rank test for bits 10 to 17, p=0.37556
b-rank test for bits 11 to 18, p=0.37460
b-rank test for bits 12 to 19, p=0.89217
b-rank test for bits 13 to 20, p=0.96562
b-rank test for bits 14 to 21, p=0.85785
b-rank test for bits 15 to 22, p=0.18587
b-rank test for bits 16 to 23, p=0.06698
b-rank test for bits 17 to 24, p=0.27908
b-rank test for bits 18 to 25, p=0.83242
b-rank test for bits 19 to 26, p=0.49030
b-rank test for bits 20 to 27, p=0.22220
b-rank test for bits 21 to 28, p=0.79599
b-rank test for bits 22 to 29, p=0.89006
b-rank test for bits 23 to 30, p=0.69260
b-rank test for bits 24 to 31, p=0.25792
b-rank test for bits 25 to 32, p=0.53212
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 = 0.417259
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-11_08:31
(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 141543 -0.86 0.196023
2 141947 0.09 0.535067
3 142004 0.22 0.587528
4 142208 0.70 0.757357
5 142490 1.36 0.912563
6 143055 2.68 0.996284
7 142426 1.21 0.886317
8 141843 -0.15 0.438420
9 141691 -0.51 0.304985
10 141988 0.18 0.572918
11 140998 -2.13 0.016616
12 141026 -2.06 0.019516
13 141895 -0.03 0.486645
14 142410 1.17 0.878957
15 142739 1.94 0.973718
16 142463 1.29 0.902102
17 142569 1.54 0.938376
18 142518 1.42 0.922505
19 143072 2.72 0.996701
20 141919 0.02 0.509013
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-11_08:31
Bits used No. missing words z-score p-value
23 to 32 142387 1.6471 0.950235
22 to 31 141592 -1.0942 0.136925
21 to 30 141620 -0.9977 0.159215
20 to 29 141415 -1.7046 0.044136
19 to 28 141978 0.2368 0.593591
18 to 27 141628 -0.9701 0.165998
17 to 26 141919 0.0333 0.513300
16 to 25 141826 -0.2873 0.386924
15 to 24 142269 1.2402 0.892557
14 to 23 141825 -0.2908 0.385605
13 to 22 141510 -1.3770 0.084256
12 to 21 141692 -0.7494 0.226804
11 to 20 141996 0.2989 0.617477
10 to 19 142088 0.6161 0.731087
9 to 18 141827 -0.2839 0.388245
8 to 17 141921 0.0402 0.516050
7 to 16 142148 0.8230 0.794746
6 to 15 141725 -0.6356 0.262512
5 to 14 141128 -2.6942 0.003527
4 to 13 140798 -3.8322 0.000064
3 to 12 141502 -1.4046 0.080072
2 to 11 141404 -1.7425 0.040709
1 to 10 141717 -0.6632 0.253599
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-11_08:31
Bits used No. missing words z-score p-value
28 to 32 142215 1.0362 0.849938
27 to 31 141634 -0.9333 0.175327
26 to 30 141265 -2.1842 0.014475
25 to 29 141786 -0.4181 0.337949
24 to 28 141978 0.2328 0.592034
23 to 27 141698 -0.7164 0.236881
22 to 26 141476 -1.4689 0.070928
21 to 25 141786 -0.4181 0.337949
20 to 24 142110 0.6802 0.751823
19 to 23 141488 -1.4282 0.076612
18 to 22 142196 0.9718 0.834416
17 to 21 142083 0.5887 0.721973
16 to 20 141361 -1.8587 0.031532
15 to 19 141843 -0.2248 0.411049
14 to 18 142230 1.0870 0.861485
13 to 17 142018 0.3684 0.643702
12 to 16 142390 1.6294 0.948385
11 to 15 141742 -0.5672 0.285282
10 to 14 141893 -0.0554 0.477928
9 to 13 142663 2.5548 0.994688
8 to 12 142438 1.7921 0.963442
7 to 11 141668 -0.8181 0.206659
6 to 10 142056 0.4972 0.690471
5 to 9 142075 0.5616 0.712803
4 to 8 141973 0.2158 0.585440
3 to 7 141812 -0.3299 0.370726
2 to 6 142433 1.7752 0.962064
1 to 5 142183 0.9277 0.823217
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-11_08:31
Bits used No. missing words z-score p-value
31 to 32 141929 0.0580 0.523135
30 to 31 141803 -0.3137 0.376891
29 to 30 141706 -0.5998 0.274322
28 to 29 141395 -1.5172 0.064608
27 to 28 142344 1.2822 0.900116
26 to 27 142067 0.4651 0.679071
25 to 26 141761 -0.4376 0.330856
24 to 25 141972 0.1849 0.573333
23 to 24 141873 -0.1072 0.457328
22 to 23 142085 0.5182 0.697841
21 to 22 142100 0.5624 0.713095
20 to 21 142142 0.6863 0.753751
19 to 20 141870 -0.1160 0.453819
18 to 19 141013 -2.6440 0.004096
17 to 18 142000 0.2675 0.605444
16 to 17 142038 0.3796 0.647863
15 to 16 142250 1.0049 0.842534
14 to 15 141746 -0.4818 0.314974
13 to 14 142455 1.6096 0.946262
12 to 13 141867 -0.1249 0.450314
11 to 12 142761 2.5123 0.994003
10 to 11 142147 0.7011 0.758377
9 to 10 141330 -1.7089 0.043731
8 to 9 141850 -0.1750 0.430534
7 to 8 142132 0.6568 0.744359
6 to 7 141909 -0.0010 0.499612
5 to 6 141468 -1.3019 0.096482
4 to 5 141533 -1.1101 0.133474
3 to 4 142029 0.3530 0.637959
2 to 3 141395 -1.5172 0.064608
1 to 2 141708 -0.5939 0.276292
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-11_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2484.35 -0.221 0.412433
Test results for specific bytes for dh-ranFile-2018-07-11_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2417.66 -1.164 0.122124
2 to 9 2650.89 2.134 0.983575
3 to 10 2570.21 0.993 0.839627
4 to 11 2438.95 -0.863 0.193980
5 to 12 2542.63 0.603 0.726722
6 to 13 2421.65 -1.108 0.133935
7 to 14 2479.13 -0.295 0.383951
8 to 15 2503.45 0.049 0.519436
9 to 16 2522.48 0.318 0.624710
10 to 17 2556.54 0.800 0.788012
11 to 18 2551.30 0.725 0.765906
12 to 19 2560.54 0.856 0.804028
13 to 20 2616.76 1.651 0.950662
14 to 21 2625.71 1.778 0.962282
15 to 22 2611.35 1.575 0.942337
16 to 23 2584.93 1.201 0.885148
17 to 24 2547.97 0.678 0.751223
18 to 25 2556.28 0.796 0.786956
19 to 26 2334.85 -2.336 0.009757
20 to 27 2499.63 -0.005 0.497923
21 to 28 2476.15 -0.337 0.367937
22 to 29 2476.50 -0.332 0.369807
23 to 30 2501.23 0.017 0.506947
24 to 31 2505.81 0.082 0.532728
25 to 32 2524.41 0.345 0.635034
CDPARK for dh-ranFile-2018-07-11_08:31: 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
3505 -0.8219 0.205562
3515 -0.3653 0.357445
3529 0.2740 0.607947
3504 -0.8676 0.192812
3495 -1.2785 0.100530
3508 -0.6849 0.246694
3464 -2.6941 0.003529
3503 -0.9132 0.180558
3538 0.6849 0.753306
Square side=100, avg. no. parked=3509.80 sample std.=20.87
p-value of the KSTEST for those 10 p-values: 0.096997
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-11_08:31
0.4020,0.6729,0.1120,0.6461,0.7721,0.2393,0.3383,0.8101,0.3710,0.1870,
The KS test for those 10 p-values: 0.761578
The 3DSPHERES test for dh-ranFile-2018-07-11_08:31
sample no r^3 equiv. uni.
1 98.363 0.962325
2 22.074 0.520873
3 34.251 0.680723
4 2.235 0.071805
5 9.824 0.279261
6 47.326 0.793517
7 46.803 0.789884
8 33.556 0.673236
9 26.461 0.586060
10 14.366 0.380517
11 15.384 0.401181
12 33.608 0.673802
13 74.755 0.917241
14 10.060 0.284912
15 25.477 0.572260
16 14.480 0.382857
17 21.276 0.507967
18 10.068 0.285095
19 53.963 0.834499
20 0.255 0.008453
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.801970
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-11_08:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 -0.7 -0.1 -1.7 -0.4 -0.4
-1.3 1.5 0.4 1.4 0.5 -0.7
-0.1 0.4 -0.0 0.3 0.6 1.9
0.2 0.2 -1.9 -0.3 -1.9 0.1
1.0 0.2 -1.9 0.3 -2.0 0.8
-2.0 0.1 -0.4 1.2 1.6 0.2
-0.7 -1.7 -0.4 -0.7 0.9 -1.0
0.8
Chi-square with 42 degrees of freedom:47.935949
z-score=0.647665, p-value=0.755358
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-11_08:31
Test no p-value
1 0.605080
2 0.396327
3 0.013870
4 0.452395
5 0.053321
6 0.013926
7 0.170580
8 0.835484
9 0.231963
10 0.022190
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.007241
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-11_08:31:
(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 66719 0.04 66761 0.13
3 25000.00 24912 0.31 24966 0.05
4 6666.67 6697 0.14 6612 0.45
5 1388.89 1411 0.35 1379 0.07
6 238.10 226 0.61 247 0.33
7 34.72 32 0.21 29 0.94
8 4.96 2 1.77 5 0.00
p=0.24737 p=0.07794
Number of rngs required: 687552, p-value: 0.162
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-11_08:31
No. of wins: Observed Expected
98441 98585.9
z-score=-0.648, pvalue=0.25853
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66911 66666.7 0.895 0.895
2 37503 37654.3 0.608 1.504
3 26827 26954.7 0.605 2.109
4 19399 19313.5 0.379 2.488
5 13846 13851.4 0.002 2.490
6 9889 9943.5 0.299 2.789
7 7228 7145.0 0.964 3.753
8 5082 5139.1 0.634 4.386
9 3790 3699.9 2.196 6.582
10 2584 2666.3 2.540 9.122
11 1883 1923.3 0.846 9.968
12 1420 1388.7 0.704 10.672
13 1008 1003.7 0.018 10.690
14 714 726.1 0.203 10.893
15 530 525.8 0.033 10.926
16 383 381.2 0.009 10.935
17 260 276.5 0.989 11.924
18 195 200.8 0.169 12.093
19 152 146.0 0.248 12.341
20 122 106.2 2.346 14.687
21 274 287.1 0.599 15.286
Chisq= 15.29 for 20 degrees of freedom, p= 0.24019
SUMMARY of craptest
p-value for no. of wins: 0.258527
p-value for throws/game: 0.240187
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-11_08:31
No. of wins: Observed Expected
98304 98585.9
z-score=-1.261, pvalue=0.10372
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66433 66666.7 0.819 0.819
2 37739 37654.3 0.190 1.009
3 26880 26954.7 0.207 1.217
4 19349 19313.5 0.065 1.282
5 13987 13851.4 1.327 2.609
6 9958 9943.5 0.021 2.630
7 7213 7145.0 0.647 3.277
8 5075 5139.1 0.799 4.076
9 3763 3699.9 1.077 5.153
10 2663 2666.3 0.004 5.157
11 1925 1923.3 0.001 5.159
12 1375 1388.7 0.136 5.294
13 993 1003.7 0.114 5.409
14 722 726.1 0.024 5.432
15 529 525.8 0.019 5.451
16 406 381.2 1.620 7.072
17 273 276.5 0.045 7.117
18 199 200.8 0.017 7.134
19 123 146.0 3.619 10.752
20 95 106.2 1.184 11.937
21 300 287.1 0.578 12.515
Chisq= 12.51 for 20 degrees of freedom, p= 0.10278
SUMMARY of craptest
p-value for no. of wins: 0.103720
p-value for throws/game: 0.102783
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0001,0.0035,0.0035,0.0041,0.0072,0.0085,0.0098,0.0139,0.0139,0.0145,
0.0166,0.0173,0.0195,0.0222,0.0315,0.0407,0.0437,0.0441,0.0468,0.0533,
0.0633,0.0646,0.0646,0.0670,0.0709,0.0718,0.0766,0.0779,0.0801,0.0843,
0.0898,0.0965,0.0970,0.1005,0.1028,0.1037,0.1040,0.1064,0.1103,0.1120,
0.1132,0.1221,0.1335,0.1339,0.1369,0.1486,0.1570,0.1592,0.1598,0.1621,
0.1644,0.1660,0.1706,0.1713,0.1753,0.1794,0.1806,0.1859,0.1870,0.1928,
0.1940,0.1941,0.1960,0.1966,0.2019,0.2056,0.2067,0.2103,0.2222,0.2268,
0.2320,0.2369,0.2375,0.2393,0.2402,0.2460,0.2467,0.2474,0.2536,0.2579,
0.2585,0.2625,0.2669,0.2741,0.2743,0.2763,0.2791,0.2793,0.2849,0.2851,
0.2853,0.3050,0.3089,0.3150,0.3309,0.3379,0.3379,0.3383,0.3452,0.3537,
0.3556,0.3574,0.3670,0.3679,0.3698,0.3707,0.3710,0.3746,0.3756,0.3769,
0.3805,0.3829,0.3840,0.3856,0.3869,0.3882,0.3958,0.3963,0.4012,0.4020,
0.4031,0.4110,0.4124,0.4173,0.4228,0.4280,0.4305,0.4384,0.4494,0.4503,
0.4524,0.4538,0.4573,0.4651,0.4677,0.4743,0.4779,0.4866,0.4903,0.4979,
0.4996,0.5020,0.5069,0.5080,0.5090,0.5133,0.5160,0.5194,0.5209,0.5231,
0.5321,0.5327,0.5351,0.5432,0.5537,0.5723,0.5729,0.5733,0.5854,0.5861,
0.5875,0.5920,0.5932,0.5936,0.6051,0.6054,0.6079,0.6175,0.6214,0.6247,
0.6350,0.6380,0.6437,0.6461,0.6479,0.6497,0.6564,0.6574,0.6729,0.6732,
0.6738,0.6791,0.6807,0.6905,0.6926,0.6978,0.7128,0.7131,0.7220,0.7249,
0.7267,0.7311,0.7387,0.7444,0.7479,0.7512,0.7518,0.7528,0.7533,0.7538,
0.7538,0.7554,0.7574,0.7584,0.7616,0.7659,0.7721,0.7795,0.7801,0.7870,
0.7880,0.7899,0.7935,0.7947,0.7960,0.7962,0.7969,0.8020,0.8040,0.8101,
0.8232,0.8324,0.8344,0.8345,0.8355,0.8358,0.8365,0.8396,0.8425,0.8499,
0.8521,0.8548,0.8578,0.8615,0.8790,0.8847,0.8851,0.8863,0.8901,0.8922,
0.8926,0.9001,0.9021,0.9110,0.9126,0.9172,0.9225,0.9384,0.9402,0.9423,
0.9463,0.9484,0.9502,0.9507,0.9614,0.9621,0.9623,0.9623,0.9634,0.9656,
0.9701,0.9737,0.9836,0.9869,0.9940,0.9947,0.9963,0.9967,0.9969,
Overall p-value after applying KStest on 269 p-values = 0.297014
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.