RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-03_09:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.71 25.0662 0.906763
2 to 25 15.98 12.7471 0.247054
3 to 26 15.64 15.6432 0.450742
4 to 27 15.78 13.6333 0.307134
5 to 28 15.83 28.6778 0.962384
6 to 29 15.81 17.8382 0.600883
7 to 30 15.38 19.6233 0.706053
8 to 31 15.49 16.0366 0.478756
9 to 32 15.77 5.3502 0.003405
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.835076
Tough bday spacings test for dh-ranFile-2018-07-03_09:31: 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 6 42 96 106 93 65 38 25 15 9 5
(O-E)^2/E 1.1 0.8 7.1 0.7 0.2 2.2 3.8 0.8 0.0 0.9 0.2
Birthday Spacings: Sum(O-E)^2/E= 17.731, p= 0.940
RESULTS OF GCD FOR dh-ranFile-2018-07-03_09:31
Euclid's algorithm:
p-value, steps to gcd: 0.789422
p-value, dist. of gcd's: 0.948414
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-03_09:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.294 0.444 0.191 0.075 0.640 0.802 0.665 0.287
Bits 8 to 15---> 0.821 0.401 0.812 0.026 0.586 0.117 0.326 0.079
Bits 16 to 23---> 0.494 0.440 0.675 0.316 0.619 0.243 0.649 0.752
Bits 24 to 31---> 0.166 0.874 0.779 0.689 0.496 0.972 0.263 0.088
KS test for the above 32 p values: 0.181
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-03_09:31,
p-values for 5 runs: 0.2568, 0.7606, 0.8672, 0.6323, 0.7866
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-03_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 213 211.4 0.012 0.012
r= 29 5138 5134.0 0.003 0.015
r= 30 23177 23103.0 0.237 0.252
r= 31 11472 11551.5 0.547 0.799
chi-square = 0.799 with df = 3; p-value = 0.150
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-03_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 220 211.4 0.348 0.348
r= 30 5105 5134.0 0.164 0.512
r= 31 23141 23103.0 0.062 0.575
r= 32 11534 11551.5 0.027 0.601
chi-square = 0.601 with df = 3; p-value = 0.104
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-03_09:31
b-rank test for bits 1 to 8, p=0.65713
b-rank test for bits 2 to 9, p=0.46301
b-rank test for bits 3 to 10, p=0.96966
b-rank test for bits 4 to 11, p=0.00031
b-rank test for bits 5 to 12, p=0.21540
b-rank test for bits 6 to 13, p=0.25760
b-rank test for bits 7 to 14, p=0.26760
b-rank test for bits 8 to 15, p=0.44348
b-rank test for bits 9 to 16, p=0.33768
b-rank test for bits 10 to 17, p=0.46674
b-rank test for bits 11 to 18, p=0.39267
b-rank test for bits 12 to 19, p=0.45267
b-rank test for bits 13 to 20, p=0.05318
b-rank test for bits 14 to 21, p=0.60113
b-rank test for bits 15 to 22, p=0.49349
b-rank test for bits 16 to 23, p=0.20906
b-rank test for bits 17 to 24, p=0.33897
b-rank test for bits 18 to 25, p=0.27194
b-rank test for bits 19 to 26, p=0.59443
b-rank test for bits 20 to 27, p=0.11930
b-rank test for bits 21 to 28, p=0.23403
b-rank test for bits 22 to 29, p=0.28094
b-rank test for bits 23 to 30, p=0.42054
b-rank test for bits 24 to 31, p=0.48998
b-rank test for bits 25 to 32, p=0.32167
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 = 0.013730
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-03_09:31
(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 141446 -1.08 0.139505
2 142007 0.23 0.590255
3 142235 0.76 0.776645
4 142051 0.33 0.629680
5 141206 -1.64 0.050161
6 142058 0.35 0.635840
7 141423 -1.14 0.127919
8 141507 -0.94 0.173603
9 141909 -0.00 0.499692
10 141881 -0.07 0.473613
11 141422 -1.14 0.127431
12 142638 1.70 0.955669
13 142176 0.62 0.733378
14 142017 0.25 0.599312
15 141866 -0.10 0.459681
16 141500 -0.96 0.169441
17 141507 -0.94 0.173603
18 141452 -1.07 0.142641
19 142216 0.72 0.763164
20 141755 -0.36 0.359205
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-03_09:31
Bits used No. missing words z-score p-value
23 to 32 141662 -0.8529 0.196868
22 to 31 142027 0.4058 0.657540
21 to 30 141549 -1.2425 0.107023
20 to 29 141728 -0.6253 0.265895
19 to 28 142306 1.3678 0.914317
18 to 27 142482 1.9747 0.975850
17 to 26 141984 0.2575 0.601597
16 to 25 142099 0.6540 0.743455
15 to 24 142219 1.0678 0.857201
14 to 23 141563 -1.1942 0.116192
13 to 22 141879 -0.1046 0.458352
12 to 21 141553 -1.2287 0.109588
11 to 20 141935 0.0885 0.535267
10 to 19 142088 0.6161 0.731087
9 to 18 141721 -0.6494 0.258036
8 to 17 141699 -0.7253 0.234141
7 to 16 141769 -0.4839 0.314230
6 to 15 141548 -1.2460 0.106389
5 to 14 142386 1.6437 0.949880
4 to 13 142207 1.0264 0.847660
3 to 12 141995 0.2954 0.616161
2 to 11 142080 0.5885 0.721907
1 to 10 142180 0.9333 0.824679
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-03_09:31
Bits used No. missing words z-score p-value
28 to 32 142025 0.3921 0.652509
27 to 31 141283 -2.1232 0.016871
26 to 30 141944 0.1175 0.546778
25 to 29 141734 -0.5943 0.276143
24 to 28 142261 1.1921 0.883389
23 to 27 142056 0.4972 0.690471
22 to 26 142182 0.9243 0.822336
21 to 25 141783 -0.4282 0.334239
20 to 24 141724 -0.6282 0.264924
19 to 23 141915 0.0192 0.507667
18 to 22 141869 -0.1367 0.445629
17 to 21 142302 1.3311 0.908419
16 to 20 141964 0.1853 0.573512
15 to 19 142029 0.4057 0.657504
14 to 18 141999 0.3040 0.619423
13 to 17 141729 -0.6113 0.270504
12 to 16 141979 0.2362 0.593349
11 to 15 141339 -1.9333 0.026598
10 to 14 142322 1.3989 0.919076
9 to 13 142117 0.7040 0.759273
8 to 12 141895 -0.0486 0.480629
7 to 11 142382 1.6023 0.945452
6 to 10 141826 -0.2825 0.388790
5 to 9 142424 1.7446 0.959477
4 to 8 142090 0.6124 0.729877
3 to 7 141576 -1.1299 0.129252
2 to 6 141680 -0.7774 0.218464
1 to 5 141729 -0.6113 0.270504
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-03_09:31
Bits used No. missing words z-score p-value
31 to 32 141776 -0.3933 0.347048
30 to 31 141951 0.1229 0.548915
29 to 30 141631 -0.8210 0.205814
28 to 29 141588 -0.9479 0.171596
27 to 28 141799 -0.3255 0.372418
26 to 27 142481 1.6863 0.954135
25 to 26 142500 1.7424 0.959280
24 to 25 142356 1.3176 0.906183
23 to 24 142162 0.7453 0.771967
22 to 23 141465 -1.3107 0.094978
21 to 22 141848 -0.1809 0.428217
20 to 21 141751 -0.4671 0.320232
19 to 20 142770 2.5388 0.994439
18 to 19 142051 0.4179 0.661992
17 to 18 142198 0.8515 0.802764
16 to 17 141073 -2.4671 0.006812
15 to 16 141593 -0.9331 0.175377
14 to 15 141978 0.2026 0.580263
13 to 14 141816 -0.2753 0.391539
12 to 13 141077 -2.4553 0.007039
11 to 12 142207 0.8781 0.810051
10 to 11 142183 0.8073 0.790249
9 to 10 142133 0.6598 0.745307
8 to 9 141722 -0.5526 0.290270
7 to 8 142341 1.2734 0.898555
6 to 7 142144 0.6922 0.755607
5 to 6 141479 -1.2694 0.102147
4 to 5 142273 1.0728 0.858314
3 to 4 141611 -0.8800 0.189422
2 to 3 141724 -0.5467 0.292294
1 to 2 141822 -0.2576 0.398354
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-03_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2494.53 -0.077 0.469155
Test results for specific bytes for dh-ranFile-2018-07-03_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2568.64 0.971 0.834163
2 to 9 2501.30 0.018 0.507336
3 to 10 2421.81 -1.106 0.134422
4 to 11 2532.04 0.453 0.674769
5 to 12 2456.51 -0.615 0.269247
6 to 13 2452.77 -0.668 0.252107
7 to 14 2625.23 1.771 0.961722
8 to 15 2437.85 -0.879 0.189725
9 to 16 2476.80 -0.328 0.371408
10 to 17 2632.34 1.872 0.969370
11 to 18 2366.32 -1.891 0.029340
12 to 19 2492.49 -0.106 0.457716
13 to 20 2419.08 -1.144 0.126246
14 to 21 2557.46 0.813 0.791794
15 to 22 2421.32 -1.113 0.132921
16 to 23 2538.02 0.538 0.704581
17 to 24 2509.91 0.140 0.555702
18 to 25 2618.37 1.674 0.952938
19 to 26 2401.27 -1.396 0.081321
20 to 27 2603.00 1.457 0.927396
21 to 28 2642.23 2.011 0.977862
22 to 29 2546.48 0.657 0.744531
23 to 30 2423.58 -1.081 0.139896
24 to 31 2510.44 0.148 0.558670
25 to 32 2446.05 -0.763 0.222749
CDPARK for dh-ranFile-2018-07-03_09:31: 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
3531 0.3653 0.642555
3517 -0.2740 0.392053
3505 -0.8219 0.205562
3510 -0.5936 0.276387
3502 -0.9589 0.168804
3508 -0.6849 0.246694
3497 -1.1872 0.117571
3517 -0.2740 0.392053
3545 1.0046 0.842447
3535 0.5479 0.708135
Square side=100, avg. no. parked=3516.70 sample std.=14.84
p-value of the KSTEST for those 10 p-values: 0.365066
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-03_09:31
0.5350,0.4118,0.1037,0.2087,0.5194,0.0203,0.9816,0.7594,0.4086,0.3164,
The KS test for those 10 p-values: 0.665339
The 3DSPHERES test for dh-ranFile-2018-07-03_09:31
sample no r^3 equiv. uni.
1 101.307 0.965847
2 20.121 0.488643
3 1.504 0.048910
4 39.216 0.729425
5 66.061 0.889421
6 20.683 0.498137
7 29.354 0.624112
8 20.067 0.487722
9 8.680 0.251241
10 102.474 0.967150
11 34.752 0.686013
12 82.405 0.935869
13 126.576 0.985289
14 28.183 0.609146
15 69.743 0.902194
16 13.439 0.361065
17 36.369 0.702489
18 3.924 0.122601
19 9.399 0.268963
20 62.037 0.873550
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.081588
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-03_09:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 0.1 0.1 1.4 0.1 0.9
-0.8 -1.7 -0.2 2.6 -0.6 0.5
0.4 -1.1 -0.8 -0.0 0.1 -1.1
-0.8 0.0 -0.7 0.1 2.6 -0.6
-0.3 -0.7 1.1 2.4 1.0 1.5
-0.2 -0.1 -2.3 0.5 1.3 0.2
-0.2 1.1 0.5 1.0 -0.6 0.0
-1.1
Chi-square with 42 degrees of freedom:47.602167
z-score=0.611246, p-value=0.744748
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-03_09:31
Test no p-value
1 0.348724
2 0.717236
3 0.205462
4 0.275914
5 0.337454
6 0.058238
7 0.663295
8 0.008303
9 0.476855
10 0.444885
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.161675
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-03_09:31:
(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 66709 0.03 66576 0.12
3 25000.00 24952 0.09 25097 0.38
4 6666.67 6639 0.11 6626 0.25
5 1388.89 1398 0.06 1419 0.65
6 238.10 264 2.82 251 0.70
7 34.72 27 1.72 26 2.19
8 4.96 10 5.12 4 0.19
p=0.87322 p=0.38744
Number of rngs required: 689357, p-value: 0.866
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-03_09:31
No. of wins: Observed Expected
98537 98585.9
z-score=-0.219, pvalue=0.41351
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66783 66666.7 0.203 0.203
2 37349 37654.3 2.476 2.679
3 26802 26954.7 0.865 3.544
4 19329 19313.5 0.013 3.557
5 13940 13851.4 0.566 4.123
6 9804 9943.5 1.958 6.081
7 7072 7145.0 0.746 6.828
8 5229 5139.1 1.574 8.401
9 3782 3699.9 1.823 10.225
10 2800 2666.3 6.705 16.929
11 1923 1923.3 0.000 16.929
12 1424 1388.7 0.895 17.825
13 1029 1003.7 0.637 18.462
14 739 726.1 0.228 18.689
15 553 525.8 1.403 20.093
16 381 381.2 0.000 20.093
17 312 276.5 4.547 24.640
18 202 200.8 0.007 24.647
19 154 146.0 0.440 25.087
20 100 106.2 0.364 25.450
21 293 287.1 0.121 25.571
Chisq= 25.57 for 20 degrees of freedom, p= 0.81955
SUMMARY of craptest
p-value for no. of wins: 0.413510
p-value for throws/game: 0.819547
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-03_09:31
No. of wins: Observed Expected
98381 98585.9
z-score=-0.916, pvalue=0.17977
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66454 66666.7 0.678 0.678
2 37759 37654.3 0.291 0.969
3 26835 26954.7 0.532 1.501
4 19359 19313.5 0.107 1.609
5 13880 13851.4 0.059 1.668
6 9992 9943.5 0.236 1.904
7 7175 7145.0 0.126 2.029
8 5149 5139.1 0.019 2.049
9 3698 3699.9 0.001 2.050
10 2714 2666.3 0.853 2.903
11 1906 1923.3 0.156 3.059
12 1439 1388.7 1.819 4.878
13 969 1003.7 1.201 6.079
14 735 726.1 0.108 6.187
15 539 525.8 0.330 6.516
16 392 381.2 0.309 6.825
17 279 276.5 0.022 6.847
18 196 200.8 0.116 6.963
19 144 146.0 0.027 6.990
20 106 106.2 0.000 6.991
21 280 287.1 0.176 7.167
Chisq= 7.17 for 20 degrees of freedom, p= 0.00390
SUMMARY of craptest
p-value for no. of wins: 0.179769
p-value for throws/game: 0.003900
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0003,0.0034,0.0039,0.0068,0.0070,0.0083,0.0137,0.0169,0.0203,0.0257,
0.0266,0.0293,0.0489,0.0502,0.0532,0.0582,0.0752,0.0790,0.0813,0.0816,
0.0877,0.0950,0.1021,0.1037,0.1038,0.1064,0.1070,0.1096,0.1162,0.1170,
0.1176,0.1193,0.1226,0.1262,0.1274,0.1279,0.1293,0.1329,0.1344,0.1395,
0.1399,0.1426,0.1503,0.1617,0.1662,0.1688,0.1694,0.1716,0.1736,0.1736,
0.1754,0.1798,0.1813,0.1894,0.1897,0.1913,0.1969,0.2055,0.2056,0.2058,
0.2087,0.2091,0.2154,0.2185,0.2227,0.2340,0.2341,0.2426,0.2467,0.2471,
0.2512,0.2521,0.2568,0.2576,0.2580,0.2634,0.2649,0.2659,0.2676,0.2690,
0.2692,0.2705,0.2705,0.2719,0.2759,0.2761,0.2764,0.2809,0.2870,0.2903,
0.2923,0.2938,0.3071,0.3142,0.3159,0.3164,0.3202,0.3217,0.3258,0.3342,
0.3375,0.3377,0.3390,0.3470,0.3487,0.3592,0.3611,0.3651,0.3714,0.3724,
0.3874,0.3888,0.3915,0.3921,0.3921,0.3927,0.3984,0.4007,0.4086,0.4118,
0.4135,0.4205,0.4282,0.4397,0.4435,0.4440,0.4449,0.4456,0.4507,0.4527,
0.4577,0.4584,0.4597,0.4630,0.4667,0.4692,0.4736,0.4769,0.4788,0.4806,
0.4877,0.4886,0.4900,0.4935,0.4938,0.4956,0.4981,0.4997,0.5073,0.5077,
0.5194,0.5350,0.5353,0.5468,0.5489,0.5557,0.5587,0.5735,0.5803,0.5858,
0.5903,0.5933,0.5944,0.5993,0.6009,0.6011,0.6016,0.6091,0.6162,0.6190,
0.6194,0.6241,0.6297,0.6323,0.6358,0.6402,0.6426,0.6489,0.6525,0.6571,
0.6575,0.6575,0.6620,0.6633,0.6653,0.6654,0.6748,0.6750,0.6860,0.6889,
0.6905,0.7025,0.7046,0.7061,0.7081,0.7172,0.7219,0.7294,0.7299,0.7311,
0.7334,0.7435,0.7445,0.7447,0.7453,0.7520,0.7556,0.7593,0.7594,0.7606,
0.7632,0.7720,0.7766,0.7789,0.7866,0.7894,0.7902,0.7918,0.8021,0.8028,
0.8101,0.8117,0.8195,0.8208,0.8223,0.8247,0.8342,0.8351,0.8424,0.8477,
0.8572,0.8583,0.8659,0.8672,0.8732,0.8735,0.8740,0.8834,0.8894,0.8986,
0.9022,0.9062,0.9068,0.9084,0.9143,0.9191,0.9274,0.9359,0.9403,0.9455,
0.9484,0.9499,0.9529,0.9541,0.9557,0.9593,0.9595,0.9617,0.9624,0.9658,
0.9672,0.9694,0.9697,0.9718,0.9759,0.9779,0.9816,0.9853,0.9944,
Overall p-value after applying KStest on 269 p-values = 0.563308
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.