RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-15_01:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.94 9.2705 0.068608
2 to 25 15.93 16.8578 0.535961
3 to 26 15.59 24.4788 0.893002
4 to 27 15.67 12.4160 0.225679
5 to 28 15.93 12.4174 0.225773
6 to 29 15.82 15.5077 0.441036
7 to 30 16.08 18.2131 0.624481
8 to 31 15.98 12.7084 0.244526
9 to 32 15.71 10.0844 0.099967
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.315776
Tough bday spacings test for dh-ranFile-2018-06-15_01:31: 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 12 40 68 91 116 74 44 35 11 7 2
(O-E)^2/E 0.9 0.3 0.4 0.5 3.4 0.2 1.3 0.9 1.0 0.0 1.0
Birthday Spacings: Sum(O-E)^2/E= 9.945, p= 0.555
RESULTS OF GCD FOR dh-ranFile-2018-06-15_01:31
Euclid's algorithm:
p-value, steps to gcd: 0.806935
p-value, dist. of gcd's: 0.111840
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-15_01:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.770 0.520 0.468 0.377 0.506 0.713 0.085 0.979
Bits 8 to 15---> 0.676 0.231 0.224 0.353 0.459 0.460 0.901 0.681
Bits 16 to 23---> 0.636 0.680 0.015 0.449 0.311 0.398 0.542 0.658
Bits 24 to 31---> 0.824 0.237 0.497 0.995 0.771 0.514 0.172 0.937
KS test for the above 32 p values: 0.502
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-15_01:31,
p-values for 5 runs: 0.1999, 0.5666, 0.8584, 0.5577, 0.0235
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-15_01:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 209 211.4 0.028 0.028
r= 29 5166 5134.0 0.199 0.227
r= 30 23148 23103.0 0.087 0.314
r= 31 11477 11551.5 0.481 0.795
chi-square = 0.795 with df = 3; p-value = 0.149
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-15_01:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 208 211.4 0.055 0.055
r= 30 5125 5134.0 0.016 0.071
r= 31 23120 23103.0 0.012 0.084
r= 32 11547 11551.5 0.002 0.085
chi-square = 0.085 with df = 3; p-value = 0.006
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-15_01:31
b-rank test for bits 1 to 8, p=0.96647
b-rank test for bits 2 to 9, p=0.70767
b-rank test for bits 3 to 10, p=0.25817
b-rank test for bits 4 to 11, p=0.68235
b-rank test for bits 5 to 12, p=0.06520
b-rank test for bits 6 to 13, p=0.19773
b-rank test for bits 7 to 14, p=0.96470
b-rank test for bits 8 to 15, p=0.77119
b-rank test for bits 9 to 16, p=0.55257
b-rank test for bits 10 to 17, p=0.75413
b-rank test for bits 11 to 18, p=0.48685
b-rank test for bits 12 to 19, p=0.57446
b-rank test for bits 13 to 20, p=0.91362
b-rank test for bits 14 to 21, p=0.70898
b-rank test for bits 15 to 22, p=0.98749
b-rank test for bits 16 to 23, p=0.95058
b-rank test for bits 17 to 24, p=0.51469
b-rank test for bits 18 to 25, p=0.77303
b-rank test for bits 19 to 26, p=0.75024
b-rank test for bits 20 to 27, p=0.62427
b-rank test for bits 21 to 28, p=0.20839
b-rank test for bits 22 to 29, p=0.54850
b-rank test for bits 23 to 30, p=0.98520
b-rank test for bits 24 to 31, p=0.98779
b-rank test for bits 25 to 32, p=0.74074
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 = 0.003030
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-15_01:31
(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 142165 0.60 0.724866
2 141286 -1.46 0.072644
3 141560 -0.82 0.207195
4 142160 0.59 0.720954
5 141949 0.09 0.536924
6 141903 -0.01 0.494100
7 140931 -2.29 0.011132
8 141341 -1.33 0.092110
9 141742 -0.39 0.347914
10 142155 0.57 0.717015
11 141932 0.05 0.521121
12 141526 -0.90 0.185225
13 142077 0.39 0.652379
14 142081 0.40 0.655826
15 141973 0.15 0.559129
16 141665 -0.57 0.284046
17 141990 0.19 0.574750
18 141546 -0.85 0.197968
19 142317 0.95 0.829578
20 141940 0.07 0.528563
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-15_01:31
Bits used No. missing words z-score p-value
23 to 32 141881 -0.0977 0.461089
22 to 31 141617 -1.0080 0.156719
21 to 30 141730 -0.6184 0.268163
20 to 29 142038 0.4437 0.671367
19 to 28 141681 -0.7873 0.215540
18 to 27 142007 0.3368 0.631864
17 to 26 141508 -1.3839 0.083195
16 to 25 141680 -0.7908 0.214532
15 to 24 141863 -0.1598 0.436536
14 to 23 142314 1.3954 0.918554
13 to 22 142034 0.4299 0.666365
12 to 21 141988 0.2713 0.606911
11 to 20 142543 2.1851 0.985558
10 to 19 141819 -0.3115 0.377717
9 to 18 141611 -1.0287 0.151805
8 to 17 141838 -0.2460 0.402855
7 to 16 141711 -0.6839 0.247020
6 to 15 141822 -0.3011 0.381655
5 to 14 141670 -0.8253 0.204608
4 to 13 141847 -0.2149 0.414911
3 to 12 141274 -2.1908 0.014233
2 to 11 141500 -1.4115 0.079051
1 to 10 141713 -0.6770 0.249203
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-15_01:31
Bits used No. missing words z-score p-value
28 to 32 141889 -0.0689 0.472529
27 to 31 141951 0.1413 0.556166
26 to 30 141455 -1.5401 0.061768
25 to 29 141829 -0.2723 0.392694
24 to 28 142194 0.9650 0.832723
23 to 27 141769 -0.4757 0.317146
22 to 26 141922 0.0429 0.517129
21 to 25 141539 -1.2554 0.104675
20 to 24 141585 -1.0994 0.135792
19 to 23 141885 -0.0825 0.467135
18 to 22 142424 1.7446 0.959477
17 to 21 141889 -0.0689 0.472529
16 to 20 141907 -0.0079 0.496849
15 to 19 141373 -1.8181 0.034527
14 to 18 141847 -0.2113 0.416331
13 to 17 141879 -0.1028 0.459056
12 to 16 142250 1.1548 0.875917
11 to 15 141943 0.1141 0.545435
10 to 14 141665 -0.8282 0.203768
9 to 13 142267 1.2124 0.887328
8 to 12 141863 -0.1571 0.437602
7 to 11 141521 -1.3164 0.094024
6 to 10 141502 -1.3808 0.083673
5 to 9 141999 0.3040 0.619423
4 to 8 142042 0.4497 0.673547
3 to 7 141679 -0.7808 0.217466
2 to 6 141975 0.2226 0.588081
1 to 5 141899 -0.0350 0.486033
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-15_01:31
Bits used No. missing words z-score p-value
31 to 32 142059 0.4415 0.670576
30 to 31 142367 1.3501 0.911501
29 to 30 141392 -1.5260 0.063499
28 to 29 141884 -0.0747 0.470219
27 to 28 142261 1.0374 0.850219
26 to 27 142092 0.5388 0.705005
25 to 26 141626 -0.8358 0.201639
24 to 25 141504 -1.1957 0.115914
23 to 24 141900 -0.0275 0.489022
22 to 23 142147 0.7011 0.758377
21 to 22 142692 2.3088 0.989522
20 to 21 142518 1.7955 0.963712
19 to 20 141834 -0.2222 0.412074
18 to 19 141396 -1.5142 0.064982
17 to 18 141975 0.1937 0.576801
16 to 17 142024 0.3383 0.632416
15 to 16 141810 -0.2930 0.384758
14 to 15 142333 1.2498 0.894307
13 to 14 142050 0.4150 0.660913
12 to 13 142185 0.8132 0.791944
11 to 12 141688 -0.6529 0.256913
10 to 11 141747 -0.4788 0.316023
9 to 10 142256 1.0226 0.846758
8 to 9 142032 0.3619 0.641271
7 to 8 141622 -0.8476 0.198336
6 to 7 141643 -0.7856 0.216041
5 to 6 141932 0.0669 0.526659
4 to 5 141998 0.2616 0.603171
3 to 4 141840 -0.2045 0.418976
2 to 3 142757 2.5005 0.993799
1 to 2 141596 -0.9243 0.177671
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-15_01:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2628.00 1.810 0.964864
Test results for specific bytes for dh-ranFile-2018-06-15_01:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2605.72 1.495 0.932563
2 to 9 2476.11 -0.338 0.367746
3 to 10 2549.21 0.696 0.756754
4 to 11 2605.32 1.489 0.931811
5 to 12 2463.07 -0.522 0.300765
6 to 13 2385.68 -1.617 0.052974
7 to 14 2548.96 0.692 0.755658
8 to 15 2511.16 0.158 0.562696
9 to 16 2578.90 1.116 0.867755
10 to 17 2645.73 2.061 0.980345
11 to 18 2513.82 0.195 0.577469
12 to 19 2613.68 1.608 0.946050
13 to 20 2499.24 -0.011 0.495699
14 to 21 2594.10 1.331 0.908367
15 to 22 2503.29 0.047 0.518568
16 to 23 2369.69 -1.843 0.032671
17 to 24 2515.09 0.213 0.584467
18 to 25 2488.62 -0.161 0.436094
19 to 26 2576.43 1.081 0.860132
20 to 27 2585.62 1.211 0.887034
21 to 28 2516.86 0.238 0.594208
22 to 29 2486.10 -0.197 0.422076
23 to 30 2640.42 1.986 0.976477
24 to 31 2397.10 -1.455 0.072808
25 to 32 2477.30 -0.321 0.374107
CDPARK for dh-ranFile-2018-06-15_01:31: 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
3501 -1.0046 0.157553
3524 0.0457 0.518210
3516 -0.3196 0.374623
3486 -1.6895 0.045562
3496 -1.2329 0.108811
3530 0.3196 0.625377
3506 -0.7763 0.218799
3560 1.6895 0.954438
3489 -1.5525 0.060270
3509 -0.6393 0.261324
Square side=100, avg. no. parked=3511.70 sample std.=21.01
p-value of the KSTEST for those 10 p-values: 0.094119
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-15_01:31
0.5980,0.9390,0.6844,0.1047,0.1054,0.4865,0.3684,0.5138,0.5868,0.9468,
The KS test for those 10 p-values: 0.819626
The 3DSPHERES test for dh-ranFile-2018-06-15_01:31
sample no r^3 equiv. uni.
1 114.586 0.978062
2 22.694 0.530681
3 10.898 0.304599
4 25.497 0.572545
5 68.228 0.897128
6 38.789 0.725541
7 14.757 0.388545
8 3.718 0.116547
9 15.672 0.406911
10 50.884 0.816612
11 26.994 0.593344
12 9.794 0.278529
13 3.761 0.117826
14 39.444 0.731472
15 70.955 0.906066
16 6.228 0.187461
17 1.936 0.062509
18 5.747 0.174323
19 21.233 0.507255
20 33.802 0.675908
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.999367
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-15_01:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
2.0 0.9 0.1 -1.3 0.7 2.5
-0.4 -0.3 -0.9 0.7 0.8 0.1
-1.9 -1.1 -0.5 0.9 0.0 0.4
0.1 1.2 -1.2 1.6 0.2 -0.9
1.2 0.8 -1.2 0.4 -1.9 -1.1
-0.5 0.7 -0.1 -0.5 0.8 -0.1
-0.5 -1.3 0.1 -0.1 0.9 -1.0
-1.1
Chi-square with 42 degrees of freedom:43.126509
z-score=0.122912, p-value=0.577104
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-15_01:31
Test no p-value
1 0.791535
2 0.529533
3 0.154752
4 0.168732
5 0.907970
6 0.149445
7 0.633931
8 0.076787
9 0.164401
10 0.046483
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.118817
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-15_01:31:
(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 66587 0.10 66579 0.12
3 25000.00 24933 0.18 25160 1.02
4 6666.67 6793 2.39 6616 0.39
5 1388.89 1401 0.11 1347 1.26
6 238.10 243 0.10 252 0.81
7 34.72 36 0.05 36 0.05
8 4.96 6 0.22 9 3.29
p=0.20899 p=0.67335
Number of rngs required: 688819, p-value: 0.684
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-15_01:31
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 66766 66666.7 0.148 0.148
2 37634 37654.3 0.011 0.159
3 26829 26954.7 0.586 0.745
4 19245 19313.5 0.243 0.988
5 13779 13851.4 0.379 1.367
6 10092 9943.5 2.216 3.583
7 7221 7145.0 0.808 4.391
8 5111 5139.1 0.153 4.544
9 3646 3699.9 0.784 5.329
10 2679 2666.3 0.061 5.389
11 1941 1923.3 0.162 5.552
12 1427 1388.7 1.054 6.606
13 1020 1003.7 0.264 6.870
14 736 726.1 0.134 7.004
15 534 525.8 0.127 7.130
16 365 381.2 0.684 7.815
17 254 276.5 1.837 9.652
18 186 200.8 1.095 10.747
19 149 146.0 0.062 10.809
20 101 106.2 0.256 11.065
21 285 287.1 0.016 11.081
Chisq= 11.08 for 20 degrees of freedom, p= 0.05590
SUMMARY of craptest
p-value for no. of wins: 0.258527
p-value for throws/game: 0.055901
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-15_01:31
No. of wins: Observed Expected
98485 98585.9
z-score=-0.451, pvalue=0.32596
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66413 66666.7 0.965 0.965
2 37921 37654.3 1.889 2.854
3 26879 26954.7 0.213 3.067
4 19292 19313.5 0.024 3.091
5 13671 13851.4 2.350 5.441
6 9975 9943.5 0.100 5.540
7 7109 7145.0 0.182 5.722
8 5085 5139.1 0.569 6.291
9 3777 3699.9 1.608 7.899
10 2747 2666.3 2.443 10.341
11 1996 1923.3 2.746 13.087
12 1419 1388.7 0.659 13.747
13 1009 1003.7 0.028 13.774
14 731 726.1 0.033 13.807
15 550 525.8 1.110 14.917
16 381 381.2 0.000 14.917
17 296 276.5 1.369 16.287
18 215 200.8 1.000 17.287
19 149 146.0 0.062 17.349
20 98 106.2 0.635 17.984
21 287 287.1 0.000 17.984
Chisq= 17.98 for 20 degrees of freedom, p= 0.41157
SUMMARY of craptest
p-value for no. of wins: 0.325959
p-value for throws/game: 0.411568
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0030,0.0065,0.0111,0.0142,0.0148,0.0235,0.0327,0.0345,0.0456,0.0465,
0.0530,0.0559,0.0603,0.0618,0.0625,0.0635,0.0650,0.0652,0.0686,0.0726,
0.0728,0.0768,0.0791,0.0832,0.0837,0.0855,0.0921,0.0940,0.0941,0.1000,
0.1047,0.1047,0.1054,0.1088,0.1118,0.1159,0.1165,0.1178,0.1188,0.1358,
0.1494,0.1494,0.1518,0.1548,0.1567,0.1576,0.1644,0.1687,0.1718,0.1743,
0.1777,0.1852,0.1875,0.1977,0.1980,0.1983,0.1999,0.2016,0.2038,0.2046,
0.2072,0.2084,0.2090,0.2145,0.2155,0.2160,0.2175,0.2188,0.2243,0.2257,
0.2258,0.2311,0.2367,0.2445,0.2470,0.2492,0.2569,0.2582,0.2585,0.2613,
0.2682,0.2785,0.2840,0.3008,0.3046,0.3113,0.3158,0.3160,0.3171,0.3260,
0.3479,0.3531,0.3677,0.3684,0.3741,0.3746,0.3772,0.3777,0.3817,0.3848,
0.3885,0.3927,0.3985,0.4029,0.4069,0.4116,0.4121,0.4149,0.4163,0.4190,
0.4221,0.4361,0.4365,0.4376,0.4410,0.4486,0.4591,0.4594,0.4598,0.4611,
0.4671,0.4679,0.4702,0.4725,0.4725,0.4860,0.4865,0.4869,0.4890,0.4941,
0.4957,0.4966,0.4968,0.5017,0.5061,0.5073,0.5138,0.5142,0.5147,0.5171,
0.5182,0.5186,0.5196,0.5211,0.5267,0.5286,0.5295,0.5307,0.5360,0.5369,
0.5418,0.5454,0.5485,0.5526,0.5547,0.5562,0.5577,0.5591,0.5627,0.5666,
0.5725,0.5745,0.5748,0.5768,0.5771,0.5775,0.5845,0.5868,0.5881,0.5933,
0.5942,0.5980,0.6032,0.6069,0.6194,0.6243,0.6245,0.6254,0.6319,0.6324,
0.6339,0.6361,0.6413,0.6524,0.6558,0.6580,0.6609,0.6664,0.6706,0.6714,
0.6734,0.6735,0.6757,0.6759,0.6800,0.6811,0.6824,0.6842,0.6844,0.7050,
0.7077,0.7090,0.7126,0.7170,0.7210,0.7249,0.7255,0.7315,0.7407,0.7502,
0.7541,0.7557,0.7568,0.7584,0.7701,0.7712,0.7713,0.7730,0.7915,0.7919,
0.8069,0.8166,0.8196,0.8240,0.8296,0.8327,0.8468,0.8502,0.8584,0.8601,
0.8678,0.8759,0.8870,0.8873,0.8930,0.8943,0.8971,0.9009,0.9061,0.9080,
0.9084,0.9115,0.9136,0.9186,0.9318,0.9326,0.9369,0.9390,0.9461,0.9468,
0.9506,0.9544,0.9595,0.9637,0.9647,0.9649,0.9665,0.9765,0.9781,0.9789,
0.9803,0.9852,0.9856,0.9875,0.9878,0.9895,0.9938,0.9949,0.9994,
Overall p-value after applying KStest on 269 p-values = 0.458680
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.