RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-16_22:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.68 19.1317 0.678976
2 to 25 15.91 18.0876 0.616666
3 to 26 15.62 10.0260 0.097485
4 to 27 15.94 17.9395 0.607333
5 to 28 16.12 17.6741 0.590324
6 to 29 16.18 19.6700 0.708544
7 to 30 16.01 14.2273 0.349049
8 to 31 15.38 15.5343 0.442946
9 to 32 15.68 20.1719 0.734469
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.360875
Tough bday spacings test for dh-ranFile-2018-06-16_22:31: 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 13 34 59 107 93 78 60 31 15 2 8
(O-E)^2/E 1.6 0.2 2.8 0.9 0.2 0.0 1.2 0.1 0.0 3.2 3.8
Birthday Spacings: Sum(O-E)^2/E= 13.967, p= 0.826
RESULTS OF GCD FOR dh-ranFile-2018-06-16_22:31
Euclid's algorithm:
p-value, steps to gcd: 0.468665
p-value, dist. of gcd's: 0.062200
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-16_22:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.307 0.390 0.512 0.439 0.095 0.691 0.817 0.145
Bits 8 to 15---> 0.381 0.143 0.650 0.017 0.655 0.055 0.305 0.675
Bits 16 to 23---> 0.908 0.580 0.231 0.700 0.826 0.871 0.810 0.575
Bits 24 to 31---> 0.968 0.145 0.947 0.374 0.789 0.302 0.717 0.061
KS test for the above 32 p values: 0.004
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-16_22:31,
p-values for 5 runs: 0.6623, 0.4873, 0.6889, 0.7976, 0.6731
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-16_22:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 214 211.4 0.032 0.032
r= 29 5131 5134.0 0.002 0.033
r= 30 23265 23103.0 1.135 1.169
r= 31 11390 11551.5 2.259 3.427
chi-square = 3.427 with df = 3; p-value = 0.670
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-16_22:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 228 211.4 1.301 1.301
r= 30 5077 5134.0 0.633 1.934
r= 31 23236 23103.0 0.765 2.699
r= 32 11459 11551.5 0.741 3.440
chi-square = 3.440 with df = 3; p-value = 0.671
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-16_22:31
b-rank test for bits 1 to 8, p=0.18553
b-rank test for bits 2 to 9, p=0.51352
b-rank test for bits 3 to 10, p=0.32222
b-rank test for bits 4 to 11, p=0.54976
b-rank test for bits 5 to 12, p=0.40555
b-rank test for bits 6 to 13, p=0.09372
b-rank test for bits 7 to 14, p=0.39469
b-rank test for bits 8 to 15, p=0.77440
b-rank test for bits 9 to 16, p=0.55973
b-rank test for bits 10 to 17, p=0.00320
b-rank test for bits 11 to 18, p=0.18108
b-rank test for bits 12 to 19, p=0.82003
b-rank test for bits 13 to 20, p=0.58459
b-rank test for bits 14 to 21, p=0.06259
b-rank test for bits 15 to 22, p=0.61033
b-rank test for bits 16 to 23, p=0.07370
b-rank test for bits 17 to 24, p=0.04587
b-rank test for bits 18 to 25, p=0.47997
b-rank test for bits 19 to 26, p=0.98865
b-rank test for bits 20 to 27, p=0.81666
b-rank test for bits 21 to 28, p=0.60351
b-rank test for bits 22 to 29, p=0.31890
b-rank test for bits 23 to 30, p=0.27423
b-rank test for bits 24 to 31, p=0.72737
b-rank test for bits 25 to 32, p=0.84739
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 = 0.607954
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-16_22:31
(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 141926 0.04 0.515534
2 140381 -3.57 0.000178
3 141968 0.14 0.554516
4 141686 -0.52 0.300905
5 141351 -1.30 0.096030
6 142221 0.73 0.766755
7 141664 -0.57 0.283254
8 141974 0.15 0.560051
9 142134 0.52 0.700184
10 141429 -1.12 0.130875
11 141651 -0.60 0.273063
12 142223 0.73 0.768182
13 141430 -1.12 0.131372
14 142557 1.51 0.934892
15 143137 2.87 0.997937
16 141960 0.12 0.547120
17 142602 1.62 0.947210
18 141491 -0.98 0.164184
19 142205 0.69 0.755160
20 141698 -0.49 0.310737
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-16_22:31
Bits used No. missing words z-score p-value
23 to 32 141697 -0.7322 0.232032
22 to 31 141450 -1.5839 0.056609
21 to 30 141817 -0.3184 0.375099
20 to 29 142076 0.5747 0.717261
19 to 28 141664 -0.8460 0.198786
18 to 27 142136 0.7816 0.782781
17 to 26 141526 -1.3218 0.093113
16 to 25 141943 0.1161 0.546215
15 to 24 141425 -1.6701 0.047449
14 to 23 142059 0.5161 0.697109
13 to 22 142033 0.4264 0.665109
12 to 21 142404 1.7058 0.955973
11 to 20 141847 -0.2149 0.414911
10 to 19 142084 0.6023 0.726516
9 to 18 142028 0.4092 0.658806
8 to 17 142148 0.8230 0.794746
7 to 16 141799 -0.3804 0.351806
6 to 15 142138 0.7885 0.784803
5 to 14 141799 -0.3804 0.351806
4 to 13 142248 1.1678 0.878562
3 to 12 142190 0.9678 0.833435
2 to 11 141724 -0.6391 0.261389
1 to 10 142087 0.6127 0.729948
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-16_22:31
Bits used No. missing words z-score p-value
28 to 32 142272 1.2294 0.890537
27 to 31 141872 -0.1265 0.449651
26 to 30 141702 -0.7028 0.241086
25 to 29 141659 -0.8486 0.198059
24 to 28 142315 1.3752 0.915458
23 to 27 142026 0.3955 0.653760
22 to 26 141538 -1.2587 0.104061
21 to 25 141875 -0.1164 0.453679
20 to 24 141640 -0.9130 0.180626
19 to 23 141939 0.1006 0.540057
18 to 22 142553 2.1819 0.985443
17 to 21 141548 -1.2248 0.110316
16 to 20 141894 -0.0520 0.479278
15 to 19 141802 -0.3638 0.357992
14 to 18 141888 -0.0723 0.471180
13 to 17 141507 -1.3638 0.086310
12 to 16 142080 0.5785 0.718551
11 to 15 141666 -0.8248 0.204729
10 to 14 142133 0.7582 0.775835
9 to 13 141904 -0.0181 0.492792
8 to 12 142018 0.3684 0.643702
7 to 11 141911 0.0057 0.502258
6 to 10 141686 -0.7571 0.224510
5 to 9 142078 0.5718 0.716259
4 to 8 142237 1.1107 0.866661
3 to 7 141917 0.0260 0.510371
2 to 6 141668 -0.8181 0.206659
1 to 5 141634 -0.9333 0.175327
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-16_22:31
Bits used No. missing words z-score p-value
31 to 32 142035 0.3707 0.644573
30 to 31 142323 1.2203 0.888818
29 to 30 142291 1.1259 0.869890
28 to 29 141859 -0.1485 0.440988
27 to 28 141971 0.1819 0.572176
26 to 27 141826 -0.2458 0.402914
25 to 26 141658 -0.7414 0.229230
24 to 25 141864 -0.1337 0.446813
23 to 24 141881 -0.0836 0.466699
22 to 23 142653 2.1937 0.985872
21 to 22 141890 -0.0570 0.477264
20 to 21 142085 0.5182 0.697841
19 to 20 141854 -0.1632 0.435174
18 to 19 141788 -0.3579 0.360207
17 to 18 141472 -1.2901 0.098515
16 to 17 141854 -0.1632 0.435174
15 to 16 141580 -0.9715 0.165656
14 to 15 142261 1.0374 0.850219
13 to 14 142256 1.0226 0.846758
12 to 13 141748 -0.4759 0.317073
11 to 12 142130 0.6509 0.742459
10 to 11 141973 0.1878 0.574490
9 to 10 141160 -2.2104 0.013538
8 to 9 142189 0.8250 0.795310
7 to 8 141917 0.0226 0.509025
6 to 7 142030 0.3560 0.639064
5 to 6 141719 -0.5614 0.287247
4 to 5 141532 -1.1131 0.132840
3 to 4 141525 -1.1337 0.128457
2 to 3 141360 -1.6204 0.052569
1 to 2 142154 0.7217 0.764773
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-16_22:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2433.44 -0.941 0.173280
Test results for specific bytes for dh-ranFile-2018-06-16_22:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2446.77 -0.753 0.225809
2 to 9 2531.29 0.442 0.670914
3 to 10 2581.16 1.148 0.874478
4 to 11 2362.46 -1.945 0.025884
5 to 12 2526.93 0.381 0.648334
6 to 13 2633.19 1.884 0.970191
7 to 14 2636.31 1.928 0.973058
8 to 15 2511.48 0.162 0.564478
9 to 16 2504.69 0.066 0.526459
10 to 17 2488.85 -0.158 0.437330
11 to 18 2612.66 1.593 0.944451
12 to 19 2555.35 0.783 0.783138
13 to 20 2606.34 1.504 0.933701
14 to 21 2544.85 0.634 0.737029
15 to 22 2424.48 -1.068 0.142751
16 to 23 2483.69 -0.231 0.408771
17 to 24 2506.78 0.096 0.538180
18 to 25 2460.54 -0.558 0.288418
19 to 26 2627.25 1.800 0.964037
20 to 27 2529.23 0.413 0.660327
21 to 28 2455.25 -0.633 0.263392
22 to 29 2499.50 -0.007 0.497184
23 to 30 2601.12 1.430 0.923646
24 to 31 2431.73 -0.966 0.167134
25 to 32 2569.09 0.977 0.835732
CDPARK for dh-ranFile-2018-06-16_22:31: 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
3505 -0.8219 0.205562
3535 0.5479 0.708135
3487 -1.6438 0.050105
3517 -0.2740 0.392053
3545 1.0046 0.842447
3532 0.4110 0.659449
3509 -0.6393 0.261324
3523 0.0000 0.500000
3544 0.9589 0.831196
3535 0.5479 0.708135
Square side=100, avg. no. parked=3523.20 sample std.=17.74
p-value of the KSTEST for those 10 p-values: 0.932797
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-16_22:31
0.9813,0.8288,0.2077,0.7803,0.6678,0.1838,0.4405,0.8077,0.2821,0.4256,
The KS test for those 10 p-values: 0.752734
The 3DSPHERES test for dh-ranFile-2018-06-16_22:31
sample no r^3 equiv. uni.
1 33.047 0.667646
2 21.298 0.508316
3 60.478 0.866802
4 143.748 0.991701
5 4.204 0.130771
6 10.371 0.292286
7 91.774 0.953072
8 9.244 0.265185
9 8.467 0.245905
10 36.810 0.706830
11 34.785 0.686354
12 81.353 0.933581
13 17.667 0.445061
14 2.755 0.087740
15 17.975 0.450729
16 23.800 0.547660
17 26.164 0.581938
18 0.120 0.004005
19 92.185 0.953710
20 36.965 0.708337
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.582142
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-16_22:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 0.1 0.6 0.3 -1.4 0.3
0.5 0.3 -0.5 1.8 0.8 -1.6
-0.2 0.9 0.5 0.6 -1.8 -0.8
-0.1 -1.4 -0.6 -0.8 1.0 -0.1
2.0 1.2 0.2 1.2 0.5 0.0
-0.0 1.7 -0.6 -1.3 0.8 0.2
0.3 0.2 -0.8 1.0 -1.3 1.0
-1.1
Chi-square with 42 degrees of freedom:37.412047
z-score=-0.500587, p-value=0.327593
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-16_22:31
Test no p-value
1 0.071698
2 0.549820
3 0.069701
4 0.015824
5 0.445155
6 0.087054
7 0.222474
8 0.477557
9 0.211092
10 0.524317
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.013731
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-16_22:31:
(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 66847 0.49 66746 0.09
3 25000.00 24922 0.24 24919 0.26
4 6666.67 6571 1.37 6722 0.46
5 1388.89 1373 0.18 1351 1.03
6 238.10 250 0.60 226 0.61
7 34.72 30 0.64 30 0.64
8 4.96 6 0.22 5 0.00
p=0.28830 p=0.20459
Number of rngs required: 687071, p-value: 0.060
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-16_22:31
No. of wins: Observed Expected
98696 98585.9
z-score= 0.493, pvalue=0.68886
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66614 66666.7 0.042 0.042
2 38103 37654.3 5.346 5.388
3 26812 26954.7 0.756 6.144
4 19301 19313.5 0.008 6.152
5 13837 13851.4 0.015 6.167
6 9820 9943.5 1.535 7.702
7 7106 7145.0 0.213 7.915
8 5084 5139.1 0.590 8.505
9 3813 3699.9 3.459 11.965
10 2651 2666.3 0.088 12.052
11 1929 1923.3 0.017 12.069
12 1385 1388.7 0.010 12.079
13 970 1003.7 1.132 13.212
14 741 726.1 0.304 13.516
15 513 525.8 0.313 13.829
16 358 381.2 1.406 15.235
17 257 276.5 1.381 16.616
18 173 200.8 3.857 20.472
19 127 146.0 2.469 22.941
20 113 106.2 0.433 23.374
21 293 287.1 0.121 23.495
Chisq= 23.50 for 20 degrees of freedom, p= 0.73486
SUMMARY of craptest
p-value for no. of wins: 0.688858
p-value for throws/game: 0.734859
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-16_22:31
No. of wins: Observed Expected
98239 98585.9
z-score=-1.551, pvalue=0.06041
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66495 66666.7 0.442 0.442
2 37490 37654.3 0.717 1.159
3 26926 26954.7 0.031 1.190
4 19406 19313.5 0.443 1.633
5 13646 13851.4 3.046 4.680
6 10070 9943.5 1.608 6.288
7 7302 7145.0 3.449 9.736
8 5238 5139.1 1.904 11.641
9 3627 3699.9 1.435 13.076
10 2701 2666.3 0.452 13.528
11 1960 1923.3 0.699 14.227
12 1388 1388.7 0.000 14.227
13 1069 1003.7 4.246 18.473
14 755 726.1 1.147 19.620
15 510 525.8 0.477 20.097
16 384 381.2 0.021 20.119
17 282 276.5 0.108 20.226
18 206 200.8 0.133 20.360
19 129 146.0 1.976 22.336
20 115 106.2 0.727 23.062
21 301 287.1 0.672 23.734
Chisq= 23.73 for 20 degrees of freedom, p= 0.74578
SUMMARY of craptest
p-value for no. of wins: 0.060408
p-value for throws/game: 0.745782
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0002,0.0032,0.0040,0.0045,0.0135,0.0137,0.0158,0.0169,0.0259,0.0459,
0.0474,0.0501,0.0526,0.0550,0.0566,0.0596,0.0604,0.0607,0.0622,0.0626,
0.0697,0.0717,0.0737,0.0863,0.0871,0.0877,0.0931,0.0937,0.0948,0.0960,
0.0975,0.0985,0.1041,0.1103,0.1285,0.1308,0.1309,0.1314,0.1328,0.1427,
0.1428,0.1445,0.1451,0.1642,0.1657,0.1671,0.1733,0.1753,0.1806,0.1811,
0.1838,0.1855,0.1981,0.1988,0.2046,0.2047,0.2056,0.2067,0.2077,0.2111,
0.2225,0.2245,0.2258,0.2292,0.2312,0.2320,0.2411,0.2459,0.2613,0.2614,
0.2634,0.2652,0.2731,0.2742,0.2821,0.2833,0.2872,0.2883,0.2884,0.2923,
0.3009,0.3021,0.3050,0.3066,0.3107,0.3171,0.3189,0.3222,0.3276,0.3490,
0.3518,0.3518,0.3580,0.3602,0.3609,0.3744,0.3751,0.3815,0.3903,0.3921,
0.3947,0.4029,0.4056,0.4088,0.4149,0.4256,0.4352,0.4352,0.4373,0.4388,
0.4405,0.4410,0.4429,0.4451,0.4452,0.4468,0.4497,0.4507,0.4537,0.4667,
0.4687,0.4712,0.4773,0.4776,0.4793,0.4800,0.4873,0.4928,0.4972,0.5000,
0.5023,0.5083,0.5090,0.5104,0.5122,0.5135,0.5155,0.5243,0.5265,0.5382,
0.5401,0.5462,0.5471,0.5477,0.5498,0.5498,0.5545,0.5597,0.5601,0.5645,
0.5722,0.5745,0.5752,0.5802,0.5819,0.5821,0.5846,0.5903,0.6035,0.6073,
0.6080,0.6103,0.6167,0.6391,0.6437,0.6446,0.6483,0.6499,0.6538,0.6547,
0.6588,0.6594,0.6603,0.6623,0.6651,0.6676,0.6678,0.6697,0.6709,0.6713,
0.6731,0.6753,0.6790,0.6864,0.6889,0.6889,0.6914,0.6971,0.6978,0.6998,
0.7002,0.7068,0.7081,0.7081,0.7083,0.7085,0.7163,0.7173,0.7174,0.7186,
0.7265,0.7274,0.7299,0.7345,0.7349,0.7370,0.7425,0.7458,0.7527,0.7552,
0.7648,0.7668,0.7682,0.7744,0.7758,0.7803,0.7828,0.7831,0.7848,0.7893,
0.7947,0.7953,0.7976,0.8077,0.8101,0.8167,0.8170,0.8200,0.8255,0.8258,
0.8288,0.8312,0.8334,0.8357,0.8424,0.8468,0.8474,0.8502,0.8667,0.8668,
0.8699,0.8710,0.8745,0.8786,0.8888,0.8905,0.9080,0.9155,0.9236,0.9328,
0.9336,0.9337,0.9349,0.9445,0.9467,0.9472,0.9531,0.9537,0.9560,0.9640,
0.9682,0.9702,0.9731,0.9813,0.9854,0.9859,0.9887,0.9917,0.9979,
Overall p-value after applying KStest on 269 p-values = 0.801419
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.