RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-28_07:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.60 14.8483 0.393592
2 to 25 15.56 22.1380 0.820528
3 to 26 15.69 12.1781 0.210768
4 to 27 15.93 12.2657 0.216214
5 to 28 15.69 16.0723 0.481284
6 to 29 15.92 6.2149 0.008378
7 to 30 15.72 19.2943 0.688099
8 to 31 15.84 13.4677 0.295641
9 to 32 15.85 16.6608 0.522431
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.480318
Tough bday spacings test for dh-ranFile-2018-06-28_07:31: 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 27 61 110 86 89 64 21 18 6 7
(O-E)^2/E 0.4 2.5 2.1 1.6 1.4 1.5 2.7 2.6 0.7 0.1 2.1
Birthday Spacings: Sum(O-E)^2/E= 17.542, p= 0.937
RESULTS OF GCD FOR dh-ranFile-2018-06-28_07:31
Euclid's algorithm:
p-value, steps to gcd: 0.573127
p-value, dist. of gcd's: 0.668742
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-28_07:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.306 0.985 0.589 0.097 0.743 0.129 0.323 0.940
Bits 8 to 15---> 0.763 0.153 0.977 0.464 0.046 0.960 0.536 0.807
Bits 16 to 23---> 0.499 0.102 0.861 0.150 0.090 0.538 0.175 0.842
Bits 24 to 31---> 0.795 0.656 0.977 0.853 0.269 0.041 0.541 0.748
KS test for the above 32 p values: 0.612
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-28_07:31,
p-values for 5 runs: 0.3314, 0.3311, 0.4442, 0.5039, 0.9024
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-28_07:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 201 211.4 0.513 0.513
r= 29 5189 5134.0 0.589 1.102
r= 30 22879 23103.0 2.173 3.275
r= 31 11731 11551.5 2.789 6.064
chi-square = 6.064 with df = 3; p-value = 0.891
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-28_07:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 219 211.4 0.272 0.272
r= 30 5148 5134.0 0.038 0.310
r= 31 23176 23103.0 0.230 0.540
r= 32 11457 11551.5 0.773 1.314
chi-square = 1.314 with df = 3; p-value = 0.274
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-28_07:31
b-rank test for bits 1 to 8, p=0.68125
b-rank test for bits 2 to 9, p=0.94013
b-rank test for bits 3 to 10, p=0.91631
b-rank test for bits 4 to 11, p=0.02969
b-rank test for bits 5 to 12, p=0.39161
b-rank test for bits 6 to 13, p=0.80966
b-rank test for bits 7 to 14, p=0.57307
b-rank test for bits 8 to 15, p=0.91434
b-rank test for bits 9 to 16, p=0.20099
b-rank test for bits 10 to 17, p=0.36286
b-rank test for bits 11 to 18, p=0.31700
b-rank test for bits 12 to 19, p=0.93644
b-rank test for bits 13 to 20, p=0.54020
b-rank test for bits 14 to 21, p=0.20448
b-rank test for bits 15 to 22, p=0.78370
b-rank test for bits 16 to 23, p=0.96018
b-rank test for bits 17 to 24, p=0.31300
b-rank test for bits 18 to 25, p=0.60890
b-rank test for bits 19 to 26, p=0.58378
b-rank test for bits 20 to 27, p=0.65223
b-rank test for bits 21 to 28, p=0.86842
b-rank test for bits 22 to 29, p=0.34184
b-rank test for bits 23 to 30, p=0.52599
b-rank test for bits 24 to 31, p=0.40780
b-rank test for bits 25 to 32, p=0.67707
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 = 0.240302
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-28_07:31
(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 142043 0.31 0.622599
2 142263 0.83 0.795692
3 142354 1.04 0.850586
4 141798 -0.26 0.397387
5 141692 -0.51 0.305804
6 142677 1.79 0.963563
7 142130 0.52 0.696928
8 142010 0.24 0.592977
9 141690 -0.51 0.304167
10 141040 -2.03 0.021120
11 142121 0.49 0.689543
12 141455 -1.06 0.144227
13 141734 -0.41 0.341032
14 141260 -1.52 0.064617
15 141903 -0.01 0.494100
16 141903 -0.01 0.494100
17 141145 -1.79 0.037064
18 142174 0.62 0.731840
19 141396 -1.20 0.115192
20 141808 -0.24 0.406425
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-28_07:31
Bits used No. missing words z-score p-value
23 to 32 141685 -0.7736 0.219598
22 to 31 141762 -0.5080 0.305715
21 to 30 142340 1.4851 0.931237
20 to 29 141937 0.0954 0.538007
19 to 28 141451 -1.5804 0.057002
18 to 27 141637 -0.9391 0.173848
17 to 26 142024 0.3954 0.653731
16 to 25 141946 0.1264 0.550312
15 to 24 141916 0.0230 0.509175
14 to 23 141991 0.2816 0.610883
13 to 22 142761 2.9368 0.998342
12 to 21 141799 -0.3804 0.351806
11 to 20 142364 1.5678 0.941539
10 to 19 141765 -0.4977 0.309351
9 to 18 141889 -0.0701 0.472056
8 to 17 141715 -0.6701 0.251396
7 to 16 142825 3.1575 0.999204
6 to 15 141937 0.0954 0.538007
5 to 14 141956 0.1609 0.563926
4 to 13 142270 1.2437 0.893193
3 to 12 141688 -0.7632 0.222670
2 to 11 142175 0.9161 0.820194
1 to 10 141672 -0.8184 0.206570
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-28_07:31
Bits used No. missing words z-score p-value
28 to 32 142448 1.8260 0.966075
27 to 31 142302 1.3311 0.908419
26 to 30 142311 1.3616 0.913337
25 to 29 142658 2.5379 0.994423
24 to 28 141784 -0.4248 0.335474
23 to 27 142196 0.9718 0.834416
22 to 26 141746 -0.5537 0.289905
21 to 25 141784 -0.4248 0.335474
20 to 24 142201 0.9887 0.838598
19 to 23 141871 -0.1299 0.448310
18 to 22 141481 -1.4520 0.073256
17 to 21 141690 -0.7435 0.228592
16 to 20 141886 -0.0791 0.468483
15 to 19 141768 -0.4791 0.315939
14 to 18 142022 0.3819 0.648744
13 to 17 141932 0.0768 0.530628
12 to 16 141824 -0.2893 0.386193
11 to 15 141795 -0.3876 0.349171
10 to 14 141748 -0.5469 0.292230
9 to 13 141841 -0.2316 0.408414
8 to 12 141441 -1.5876 0.056193
7 to 11 141596 -1.0621 0.144087
6 to 10 141959 0.1684 0.566855
5 to 9 142163 0.8599 0.805077
4 to 8 142076 0.5650 0.713957
3 to 7 142665 2.5616 0.994790
2 to 6 142083 0.5887 0.721973
1 to 5 141447 -1.5672 0.058532
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-28_07:31
Bits used No. missing words z-score p-value
31 to 32 141552 -1.0541 0.145925
30 to 31 142036 0.3737 0.645671
29 to 30 142136 0.6686 0.748138
28 to 29 141844 -0.1927 0.423592
27 to 28 141800 -0.3225 0.373534
26 to 27 142313 1.1908 0.883127
25 to 26 141933 0.0698 0.527833
24 to 25 142168 0.7630 0.777280
23 to 24 141594 -0.9302 0.176140
22 to 23 141822 -0.2576 0.398354
21 to 22 142273 1.0728 0.858314
20 to 21 142449 1.5919 0.944302
19 to 20 142002 0.2734 0.607713
18 to 19 141926 0.0492 0.519610
17 to 18 141723 -0.5496 0.291281
16 to 17 141622 -0.8476 0.198336
15 to 16 141313 -1.7591 0.039282
14 to 15 141873 -0.1072 0.457328
13 to 14 141725 -0.5437 0.293308
12 to 13 142081 0.5064 0.693713
11 to 12 141777 -0.3904 0.348137
10 to 11 142411 1.4799 0.930544
9 to 10 141468 -1.3019 0.096482
8 to 9 141934 0.0728 0.529007
7 to 8 142169 0.7660 0.778158
6 to 7 141286 -1.8387 0.032977
5 to 6 141950 0.1200 0.547747
4 to 5 141931 0.0639 0.525484
3 to 4 141762 -0.4346 0.331926
2 to 3 141625 -0.8387 0.200810
1 to 2 142259 1.0315 0.848841
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-28_07:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2627.26 1.800 0.964049
Test results for specific bytes for dh-ranFile-2018-06-28_07:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2477.56 -0.317 0.375473
2 to 9 2544.68 0.632 0.736242
3 to 10 2575.78 1.072 0.858067
4 to 11 2477.67 -0.316 0.376064
5 to 12 2460.32 -0.561 0.287356
6 to 13 2425.64 -1.052 0.146493
7 to 14 2492.90 -0.100 0.459985
8 to 15 2501.09 0.015 0.506176
9 to 16 2402.81 -1.374 0.084645
10 to 17 2497.00 -0.042 0.483053
11 to 18 2489.89 -0.143 0.443137
12 to 19 2473.91 -0.369 0.356063
13 to 20 2506.97 0.099 0.539285
14 to 21 2566.78 0.944 0.827520
15 to 22 2557.13 0.808 0.790446
16 to 23 2452.98 -0.665 0.253032
17 to 24 2633.15 1.883 0.970150
18 to 25 2490.64 -0.132 0.447327
19 to 26 2555.57 0.786 0.784050
20 to 27 2461.73 -0.541 0.294178
21 to 28 2601.12 1.430 0.923648
22 to 29 2557.02 0.806 0.789982
23 to 30 2583.10 1.175 0.880034
24 to 31 2439.05 -0.862 0.194351
25 to 32 2473.05 -0.381 0.351540
CDPARK for dh-ranFile-2018-06-28_07:31: 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
3527 0.1826 0.572463
3558 1.5982 0.944998
3513 -0.4566 0.323972
3534 0.5023 0.692266
3546 1.0502 0.853193
3497 -1.1872 0.117571
3544 0.9589 0.831196
3520 -0.1370 0.445521
3584 2.7854 0.997327
3524 0.0457 0.518210
Square side=100, avg. no. parked=3534.70 sample std.=23.39
p-value of the KSTEST for those 10 p-values: 0.231394
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-28_07:31
0.0694,0.0727,0.5458,0.2625,0.8073,0.0501,0.5210,0.8577,0.0254,0.5507,
The KS test for those 10 p-values: 0.139881
The 3DSPHERES test for dh-ranFile-2018-06-28_07:31
sample no r^3 equiv. uni.
1 48.825 0.803579
2 65.830 0.888568
3 62.066 0.873671
4 0.717 0.023622
5 14.650 0.386342
6 16.171 0.416681
7 43.591 0.766138
8 20.546 0.495843
9 87.141 0.945234
10 62.179 0.874144
11 65.686 0.888032
12 21.202 0.506741
13 35.004 0.688635
14 1.869 0.060398
15 14.539 0.384086
16 126.080 0.985044
17 18.940 0.468111
18 28.926 0.618717
19 23.318 0.540334
20 4.884 0.150225
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.260190
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-28_07:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 0.5 0.1 0.6 1.9 0.0
0.0 0.9 -0.9 0.4 0.6 -0.2
0.8 0.9 0.6 -1.0 0.9 0.5
-0.6 -0.4 0.4 0.7 -1.3 -0.7
-3.3 -1.0 0.4 1.2 -0.2 -0.7
0.3 0.1 -0.5 0.4 0.5 -0.3
0.5 0.2 0.5 2.1 0.1 -1.0
-0.1
Chi-square with 42 degrees of freedom:35.843250
z-score=-0.671756, p-value=0.263053
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-28_07:31
Test no p-value
1 0.534675
2 0.103945
3 0.018991
4 0.593779
5 0.013006
6 0.831027
7 0.929110
8 0.010382
9 0.622868
10 0.163915
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.049567
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-28_07:31:
(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 66614 0.04 66804 0.28
3 25000.00 25064 0.16 25049 0.10
4 6666.67 6641 0.10 6539 2.44
5 1388.89 1378 0.09 1345 1.39
6 238.10 254 1.06 224 0.83
7 34.72 43 1.97 35 0.00
8 4.96 5 0.00 3 0.77
p=0.24635 p=0.55658
Number of rngs required: 688146, p-value: 0.384
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-28_07:31
No. of wins: Observed Expected
98553 98585.9
z-score=-0.147, pvalue=0.44158
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66383 66666.7 1.207 1.207
2 37865 37654.3 1.179 2.386
3 27023 26954.7 0.173 2.559
4 19333 19313.5 0.020 2.578
5 13912 13851.4 0.265 2.843
6 9910 9943.5 0.113 2.957
7 7101 7145.0 0.271 3.228
8 5129 5139.1 0.020 3.248
9 3661 3699.9 0.408 3.656
10 2651 2666.3 0.088 3.744
11 2028 1923.3 5.696 9.440
12 1337 1388.7 1.928 11.368
13 1001 1003.7 0.007 11.375
14 733 726.1 0.065 11.440
15 530 525.8 0.033 11.473
16 396 381.2 0.579 12.051
17 271 276.5 0.111 12.162
18 202 200.8 0.007 12.169
19 151 146.0 0.172 12.341
20 111 106.2 0.216 12.557
21 272 287.1 0.796 13.353
Chisq= 13.35 for 20 degrees of freedom, p= 0.13825
SUMMARY of craptest
p-value for no. of wins: 0.441581
p-value for throws/game: 0.138249
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-28_07:31
No. of wins: Observed Expected
99002 98585.9
z-score= 1.861, pvalue=0.96864
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67108 66666.7 2.922 2.922
2 37807 37654.3 0.619 3.541
3 26782 26954.7 1.107 4.648
4 19253 19313.5 0.189 4.837
5 13755 13851.4 0.671 5.508
6 9824 9943.5 1.437 6.945
7 7116 7145.0 0.118 7.063
8 5180 5139.1 0.326 7.389
9 3661 3699.9 0.408 7.797
10 2646 2666.3 0.155 7.952
11 1899 1923.3 0.308 8.260
12 1412 1388.7 0.390 8.649
13 965 1003.7 1.493 10.143
14 716 726.1 0.142 10.284
15 568 525.8 3.381 13.665
16 351 381.2 2.385 16.050
17 267 276.5 0.329 16.379
18 182 200.8 1.765 18.145
19 142 146.0 0.109 18.253
20 102 106.2 0.167 18.421
21 264 287.1 1.861 20.281
Chisq= 20.28 for 20 degrees of freedom, p= 0.55955
SUMMARY of craptest
p-value for no. of wins: 0.968644
p-value for throws/game: 0.559550
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0084,0.0104,0.0130,0.0190,0.0211,0.0236,0.0254,0.0297,0.0330,0.0371,
0.0393,0.0413,0.0464,0.0496,0.0501,0.0562,0.0570,0.0585,0.0604,0.0646,
0.0694,0.0727,0.0733,0.0846,0.0897,0.0965,0.0970,0.1016,0.1039,0.1152,
0.1176,0.1293,0.1382,0.1399,0.1441,0.1442,0.1459,0.1465,0.1502,0.1502,
0.1529,0.1639,0.1738,0.1746,0.1761,0.1944,0.1983,0.2008,0.2010,0.2045,
0.2066,0.2108,0.2162,0.2196,0.2227,0.2286,0.2314,0.2403,0.2464,0.2514,
0.2530,0.2602,0.2625,0.2631,0.2691,0.2742,0.2874,0.2899,0.2913,0.2922,
0.2933,0.2942,0.2956,0.3042,0.3057,0.3058,0.3064,0.3094,0.3130,0.3159,
0.3170,0.3230,0.3240,0.3311,0.3314,0.3319,0.3355,0.3355,0.3410,0.3418,
0.3481,0.3492,0.3515,0.3518,0.3561,0.3629,0.3735,0.3755,0.3761,0.3837,
0.3841,0.3862,0.3863,0.3916,0.3936,0.3974,0.3984,0.4064,0.4078,0.4084,
0.4167,0.4236,0.4416,0.4431,0.4442,0.4455,0.4473,0.4483,0.4573,0.4600,
0.4638,0.4681,0.4685,0.4721,0.4803,0.4813,0.4831,0.4941,0.4941,0.4958,
0.4986,0.5039,0.5062,0.5067,0.5092,0.5182,0.5196,0.5210,0.5224,0.5255,
0.5260,0.5278,0.5290,0.5306,0.5347,0.5360,0.5378,0.5380,0.5380,0.5393,
0.5402,0.5403,0.5412,0.5458,0.5477,0.5503,0.5507,0.5566,0.5595,0.5639,
0.5669,0.5725,0.5731,0.5731,0.5838,0.5892,0.5930,0.5938,0.6077,0.6089,
0.6109,0.6122,0.6187,0.6226,0.6229,0.6457,0.6487,0.6522,0.6537,0.6559,
0.6687,0.6771,0.6812,0.6881,0.6886,0.6895,0.6923,0.6937,0.6969,0.7140,
0.7220,0.7318,0.7362,0.7429,0.7477,0.7481,0.7626,0.7661,0.7773,0.7782,
0.7837,0.7841,0.7900,0.7904,0.7948,0.7957,0.8036,0.8051,0.8067,0.8073,
0.8097,0.8202,0.8205,0.8275,0.8310,0.8312,0.8344,0.8386,0.8418,0.8488,
0.8506,0.8526,0.8532,0.8577,0.8581,0.8583,0.8608,0.8684,0.8737,0.8741,
0.8800,0.8831,0.8880,0.8886,0.8914,0.8932,0.9024,0.9084,0.9133,0.9143,
0.9163,0.9236,0.9291,0.9305,0.9312,0.9364,0.9368,0.9400,0.9401,0.9415,
0.9443,0.9450,0.9452,0.9602,0.9602,0.9636,0.9640,0.9661,0.9686,0.9701,
0.9772,0.9772,0.9846,0.9850,0.9944,0.9948,0.9973,0.9983,0.9992,
Overall p-value after applying KStest on 269 p-values = 0.534650
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.