RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-07_06:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.83 19.2949 0.688130
2 to 25 15.84 18.0794 0.616149
3 to 26 15.76 41.3381 0.999165
4 to 27 15.50 35.0709 0.993911
5 to 28 15.69 17.8168 0.599516
6 to 29 15.90 5.9134 0.006251
7 to 30 15.55 24.5096 0.893763
8 to 31 15.44 26.7329 0.937898
9 to 32 15.81 18.0779 0.616056
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.008464
Tough bday spacings test for dh-ranFile-2018-07-07_06:31: 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 7 38 82 109 85 81 47 33 13 3 2
(O-E)^2/E 0.5 0.1 1.0 1.3 1.6 0.1 0.5 0.4 0.2 2.0 1.0
Birthday Spacings: Sum(O-E)^2/E= 8.778, p= 0.447
RESULTS OF GCD FOR dh-ranFile-2018-07-07_06:31
Euclid's algorithm:
p-value, steps to gcd: 0.775108
p-value, dist. of gcd's: 0.893431
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-07_06:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.824 0.877 0.684 0.952 0.017 0.606 0.764 0.556
Bits 8 to 15---> 0.756 0.735 0.830 0.746 0.076 0.394 0.245 0.936
Bits 16 to 23---> 0.805 0.203 0.697 0.403 0.768 0.068 0.540 0.928
Bits 24 to 31---> 0.106 0.059 0.927 0.308 0.761 0.961 0.162 0.562
KS test for the above 32 p values: 0.841
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-07_06:31,
p-values for 5 runs: 0.6345, 0.3258, 0.3616, 0.0708, 0.3129
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-07_06:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 207 211.4 0.092 0.092
r= 29 5118 5134.0 0.050 0.142
r= 30 23161 23103.0 0.145 0.288
r= 31 11514 11551.5 0.122 0.410
chi-square = 0.410 with df = 3; p-value = 0.062
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-07_06:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 218 211.4 0.205 0.205
r= 30 5077 5134.0 0.633 0.838
r= 31 23069 23103.0 0.050 0.888
r= 32 11636 11551.5 0.618 1.506
chi-square = 1.506 with df = 3; p-value = 0.319
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-07_06:31
b-rank test for bits 1 to 8, p=0.07617
b-rank test for bits 2 to 9, p=0.02952
b-rank test for bits 3 to 10, p=0.30563
b-rank test for bits 4 to 11, p=0.40120
b-rank test for bits 5 to 12, p=0.96126
b-rank test for bits 6 to 13, p=0.43415
b-rank test for bits 7 to 14, p=0.04319
b-rank test for bits 8 to 15, p=0.46179
b-rank test for bits 9 to 16, p=0.88696
b-rank test for bits 10 to 17, p=0.41215
b-rank test for bits 11 to 18, p=0.60310
b-rank test for bits 12 to 19, p=0.12254
b-rank test for bits 13 to 20, p=0.46242
b-rank test for bits 14 to 21, p=0.27838
b-rank test for bits 15 to 22, p=0.27423
b-rank test for bits 16 to 23, p=0.50018
b-rank test for bits 17 to 24, p=0.39074
b-rank test for bits 18 to 25, p=0.54578
b-rank test for bits 19 to 26, p=0.41704
b-rank test for bits 20 to 27, p=0.78126
b-rank test for bits 21 to 28, p=0.40228
b-rank test for bits 22 to 29, p=0.55907
b-rank test for bits 23 to 30, p=0.60848
b-rank test for bits 24 to 31, p=0.86412
b-rank test for bits 25 to 32, p=0.45445
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 = 0.271581
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-07_06:31
(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 142510 1.40 0.919756
2 141698 -0.49 0.310737
3 142267 0.84 0.798332
4 142268 0.84 0.798989
5 141206 -1.64 0.050161
6 141904 -0.01 0.495032
7 141771 -0.32 0.373272
8 142087 0.42 0.660972
9 141514 -0.92 0.177830
10 141530 -0.89 0.187732
11 141994 0.20 0.578410
12 142071 0.38 0.647186
13 142305 0.92 0.822377
14 141846 -0.15 0.441184
15 141711 -0.46 0.321543
16 141466 -1.04 0.150144
17 141857 -0.12 0.451344
18 142104 0.45 0.675387
19 142335 0.99 0.840024
20 141830 -0.19 0.426477
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-07_06:31
Bits used No. missing words z-score p-value
23 to 32 141949 0.1368 0.554403
22 to 31 141601 -1.0632 0.143844
21 to 30 142135 0.7782 0.781766
20 to 29 141627 -0.9736 0.165140
19 to 28 142316 1.4023 0.919589
18 to 27 142100 0.6575 0.744565
17 to 26 141510 -1.3770 0.084256
16 to 25 141315 -2.0494 0.020211
15 to 24 142011 0.3506 0.637051
14 to 23 141575 -1.1529 0.124484
13 to 22 141726 -0.6322 0.263637
12 to 21 141437 -1.6287 0.051686
11 to 20 141935 0.0885 0.535267
10 to 19 142446 1.8506 0.967885
9 to 18 141244 -2.2942 0.010888
8 to 17 141518 -1.3494 0.088602
7 to 16 141920 0.0368 0.514675
6 to 15 142156 0.8506 0.802500
5 to 14 142310 1.3816 0.916456
4 to 13 142411 1.7299 0.958176
3 to 12 142118 0.7196 0.764100
2 to 11 142341 1.4885 0.931693
1 to 10 142237 1.1299 0.870740
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-07_06:31
Bits used No. missing words z-score p-value
28 to 32 141783 -0.4282 0.334239
27 to 31 141914 0.0158 0.506315
26 to 30 141673 -0.8011 0.211532
25 to 29 142593 2.3175 0.989762
24 to 28 142101 0.6497 0.742066
23 to 27 141704 -0.6960 0.243204
22 to 26 141741 -0.5706 0.284132
21 to 25 141531 -1.2825 0.099838
20 to 24 141867 -0.1435 0.442951
19 to 23 142023 0.3853 0.650001
18 to 22 142066 0.5311 0.702320
17 to 21 142011 0.3446 0.634819
16 to 20 142346 1.4802 0.930595
15 to 19 141824 -0.2893 0.386193
14 to 18 142026 0.3955 0.653760
13 to 17 141803 -0.3604 0.359259
12 to 16 141948 0.1311 0.552146
11 to 15 141427 -1.6350 0.051023
10 to 14 141700 -0.7096 0.238978
9 to 13 141828 -0.2757 0.391391
8 to 12 141438 -1.5977 0.055052
7 to 11 142066 0.5311 0.702320
6 to 10 142323 1.4023 0.919583
5 to 9 141982 0.2463 0.597290
4 to 8 141809 -0.3401 0.366890
3 to 7 142118 0.7074 0.760327
2 to 6 141944 0.1175 0.546778
1 to 5 142039 0.4396 0.669872
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-07_06:31
Bits used No. missing words z-score p-value
31 to 32 141625 -0.8387 0.200810
30 to 31 141526 -1.1308 0.129077
29 to 30 141882 -0.0806 0.467872
28 to 29 142051 0.4179 0.661992
27 to 28 141805 -0.3078 0.379133
26 to 27 142256 1.0226 0.846758
25 to 26 142220 0.9164 0.820280
24 to 25 142082 0.5094 0.694747
23 to 24 141940 0.0905 0.536044
22 to 23 142000 0.2675 0.605444
21 to 22 142128 0.6450 0.740551
20 to 21 142053 0.4238 0.664146
19 to 20 141631 -0.8210 0.205814
18 to 19 142107 0.5831 0.720086
17 to 18 141801 -0.3196 0.374652
16 to 17 141794 -0.3402 0.366851
15 to 16 141461 -1.3225 0.093000
14 to 15 141943 0.0993 0.539559
13 to 14 142068 0.4681 0.680127
12 to 13 142117 0.6126 0.729928
11 to 12 141638 -0.8004 0.211744
10 to 11 142235 0.9607 0.831643
9 to 10 142388 1.4120 0.921026
8 to 9 141621 -0.8505 0.197515
7 to 8 141335 -1.6942 0.045115
6 to 7 142330 1.2409 0.892681
5 to 6 141468 -1.3019 0.096482
4 to 5 141922 0.0374 0.514907
3 to 4 141840 -0.2045 0.418976
2 to 3 141545 -1.0747 0.141250
1 to 2 142282 1.0993 0.864186
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-07_06:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2434.05 -0.933 0.175512
Test results for specific bytes for dh-ranFile-2018-07-07_06:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2477.47 -0.319 0.374996
2 to 9 2746.75 3.490 0.999758
3 to 10 2662.07 2.292 0.989048
4 to 11 2645.04 2.051 0.979876
5 to 12 2519.38 0.274 0.607980
6 to 13 2402.99 -1.372 0.085046
7 to 14 2394.40 -1.493 0.067660
8 to 15 2552.98 0.749 0.773158
9 to 16 2501.10 0.016 0.506230
10 to 17 2388.93 -1.571 0.058125
11 to 18 2379.10 -1.710 0.043654
12 to 19 2445.79 -0.767 0.221661
13 to 20 2418.96 -1.146 0.125893
14 to 21 2469.46 -0.432 0.332908
15 to 22 2367.22 -1.878 0.030209
16 to 23 2535.96 0.508 0.694447
17 to 24 2584.44 1.194 0.883802
18 to 25 2500.56 0.008 0.503144
19 to 26 2509.97 0.141 0.556061
20 to 27 2463.74 -0.513 0.304032
21 to 28 2509.78 0.138 0.555009
22 to 29 2569.41 0.982 0.836846
23 to 30 2432.12 -0.960 0.168527
24 to 31 2428.33 -1.014 0.155393
25 to 32 2503.18 0.045 0.517951
CDPARK for dh-ranFile-2018-07-07_06:31: 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
3511 -0.5479 0.291865
3494 -1.3242 0.092718
3544 0.9589 0.831196
3497 -1.1872 0.117571
3531 0.3653 0.642555
3488 -1.5982 0.055002
3501 -1.0046 0.157553
3540 0.7763 0.781201
3527 0.1826 0.572463
3514 -0.4110 0.340551
Square side=100, avg. no. parked=3514.70 sample std.=18.90
p-value of the KSTEST for those 10 p-values: 0.356641
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-07_06:31
0.4052,0.6961,0.0318,0.2722,0.9203,0.6118,0.5823,0.4070,0.1356,0.5230,
The KS test for those 10 p-values: 0.887692
The 3DSPHERES test for dh-ranFile-2018-07-07_06:31
sample no r^3 equiv. uni.
1 17.257 0.437421
2 14.722 0.387816
3 33.593 0.673648
4 10.810 0.302563
5 53.662 0.832829
6 5.381 0.164205
7 3.967 0.123861
8 30.983 0.643975
9 39.817 0.734792
10 38.648 0.724254
11 10.740 0.300922
12 25.844 0.577454
13 16.707 0.427017
14 13.385 0.359914
15 58.998 0.860068
16 2.585 0.082558
17 14.075 0.374487
18 42.761 0.759578
19 19.195 0.472612
20 26.588 0.587811
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.548456
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-07_06:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 1.8 0.6 -1.1 1.3 1.1
0.0 1.5 1.1 -0.5 -0.2 0.2
0.4 1.5 0.7 -0.8 -0.8 -0.9
1.1 1.4 1.0 -2.0 -0.3 -1.2
-0.7 -0.7 -0.3 0.1 -1.2 -1.1
0.0 1.4 -1.2 -0.2 1.6 -0.1
-0.7 0.2 -1.2 2.1 -0.6 1.0
-1.1
Chi-square with 42 degrees of freedom:44.562055
z-score=0.279543, p-value=0.635521
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-07_06:31
Test no p-value
1 0.623685
2 0.477824
3 0.865570
4 0.637939
5 0.006006
6 0.777674
7 0.967455
8 0.209994
9 0.690772
10 0.975072
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.196058
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-07_06:31:
(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 66758 0.13 66671 0.00
3 25000.00 24891 0.48 24978 0.02
4 6666.67 6639 0.11 6675 0.01
5 1388.89 1440 1.88 1409 0.29
6 238.10 231 0.21 218 1.70
7 34.72 37 0.15 39 0.53
8 4.96 3 0.77 9 3.29
p=0.28707 p=0.55813
Number of rngs required: 687466, p-value: 0.139
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-07_06:31
No. of wins: Observed Expected
98090 98585.9
z-score=-2.218, pvalue=0.01329
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66459 66666.7 0.647 0.647
2 37653 37654.3 0.000 0.647
3 27070 26954.7 0.493 1.140
4 19242 19313.5 0.264 1.404
5 13916 13851.4 0.301 1.705
6 9981 9943.5 0.141 1.846
7 7131 7145.0 0.028 1.874
8 5176 5139.1 0.265 2.139
9 3749 3699.9 0.653 2.792
10 2686 2666.3 0.146 2.937
11 1915 1923.3 0.036 2.974
12 1397 1388.7 0.049 3.023
13 982 1003.7 0.470 3.492
14 751 726.1 0.851 4.344
15 548 525.8 0.934 5.278
16 353 381.2 2.079 7.357
17 254 276.5 1.837 9.194
18 211 200.8 0.515 9.709
19 170 146.0 3.951 13.660
20 99 106.2 0.490 14.150
21 257 287.1 3.159 17.308
Chisq= 17.31 for 20 degrees of freedom, p= 0.36713
SUMMARY of craptest
p-value for no. of wins: 0.013285
p-value for throws/game: 0.367132
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-07_06:31
No. of wins: Observed Expected
98504 98585.9
z-score=-0.366, pvalue=0.35714
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66866 66666.7 0.596 0.596
2 37216 37654.3 5.102 5.698
3 27050 26954.7 0.337 6.035
4 19290 19313.5 0.029 6.064
5 14056 13851.4 3.022 9.085
6 9958 9943.5 0.021 9.106
7 7185 7145.0 0.224 9.330
8 5032 5139.1 2.231 11.561
9 3731 3699.9 0.262 11.823
10 2680 2666.3 0.070 11.893
11 1868 1923.3 1.592 13.485
12 1445 1388.7 2.279 15.764
13 946 1003.7 3.319 19.083
14 772 726.1 2.896 21.979
15 542 525.8 0.497 22.476
16 357 381.2 1.530 24.006
17 255 276.5 1.678 25.684
18 185 200.8 1.248 26.931
19 156 146.0 0.687 27.619
20 106 106.2 0.000 27.619
21 304 287.1 0.993 28.612
Chisq= 28.61 for 20 degrees of freedom, p= 0.90432
SUMMARY of craptest
p-value for no. of wins: 0.357138
p-value for throws/game: 0.904317
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0060,0.0063,0.0085,0.0109,0.0133,0.0175,0.0202,0.0295,0.0302,0.0318,
0.0432,0.0437,0.0451,0.0502,0.0510,0.0517,0.0550,0.0551,0.0581,0.0586,
0.0617,0.0677,0.0681,0.0708,0.0759,0.0762,0.0826,0.0843,0.0850,0.0886,
0.0927,0.0930,0.0965,0.0998,0.1055,0.1176,0.1225,0.1239,0.1245,0.1259,
0.1291,0.1356,0.1385,0.1413,0.1438,0.1501,0.1554,0.1576,0.1623,0.1642,
0.1651,0.1685,0.1755,0.1778,0.1877,0.1961,0.1975,0.2008,0.2027,0.2058,
0.2100,0.2115,0.2117,0.2217,0.2390,0.2432,0.2447,0.2636,0.2716,0.2722,
0.2742,0.2784,0.2841,0.2871,0.2919,0.3009,0.3026,0.3040,0.3056,0.3081,
0.3107,0.3129,0.3191,0.3215,0.3258,0.3329,0.3342,0.3406,0.3566,0.3571,
0.3593,0.3599,0.3616,0.3669,0.3669,0.3671,0.3733,0.3745,0.3747,0.3750,
0.3791,0.3862,0.3878,0.3907,0.3914,0.3939,0.4012,0.4023,0.4025,0.4052,
0.4070,0.4121,0.4170,0.4190,0.4265,0.4270,0.4341,0.4374,0.4412,0.4430,
0.4467,0.4513,0.4545,0.4618,0.4624,0.4679,0.4726,0.4778,0.4950,0.5002,
0.5031,0.5062,0.5063,0.5147,0.5149,0.5180,0.5230,0.5353,0.5360,0.5396,
0.5404,0.5458,0.5468,0.5485,0.5521,0.5544,0.5550,0.5556,0.5561,0.5581,
0.5591,0.5617,0.5725,0.5775,0.5784,0.5823,0.5878,0.5973,0.5995,0.6031,
0.6054,0.6064,0.6080,0.6085,0.6118,0.6161,0.6161,0.6237,0.6345,0.6348,
0.6355,0.6371,0.6379,0.6426,0.6440,0.6472,0.6500,0.6538,0.6610,0.6620,
0.6641,0.6699,0.6736,0.6754,0.6801,0.6836,0.6881,0.6908,0.6944,0.6947,
0.6961,0.6972,0.7023,0.7023,0.7201,0.7243,0.7299,0.7348,0.7355,0.7406,
0.7421,0.7446,0.7456,0.7556,0.7596,0.7603,0.7608,0.7639,0.7641,0.7681,
0.7732,0.7751,0.7777,0.7812,0.7813,0.7818,0.7983,0.7990,0.8025,0.8050,
0.8203,0.8224,0.8239,0.8301,0.8312,0.8316,0.8328,0.8368,0.8400,0.8409,
0.8468,0.8601,0.8641,0.8642,0.8656,0.8707,0.8774,0.8838,0.8870,0.8877,
0.8927,0.8934,0.8938,0.9043,0.9165,0.9196,0.9196,0.9198,0.9203,0.9210,
0.9272,0.9282,0.9306,0.9317,0.9357,0.9379,0.9524,0.9582,0.9613,0.9613,
0.9675,0.9679,0.9751,0.9799,0.9890,0.9898,0.9939,0.9992,0.9998,
Overall p-value after applying KStest on 269 p-values = 0.953782
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.