RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-11_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 15.85 9.5704 0.079348
2 to 25 15.94 21.0312 0.775103
3 to 26 15.95 13.9515 0.329468
4 to 27 16.12 8.5343 0.046251
5 to 28 15.87 13.3629 0.288425
6 to 29 16.01 6.6463 0.012316
7 to 30 15.81 7.6144 0.025888
8 to 31 15.76 17.4244 0.574009
9 to 32 16.12 11.8549 0.191159
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.009171
Tough bday spacings test for dh-ranFile-2018-07-11_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 9 45 75 101 104 69 49 14 20 9 5
(O-E)^2/E 0.0 1.9 0.0 0.1 0.4 1.1 0.2 8.4 1.8 0.9 0.2
Birthday Spacings: Sum(O-E)^2/E= 14.917, p= 0.865
RESULTS OF GCD FOR dh-ranFile-2018-07-11_07:31
Euclid's algorithm:
p-value, steps to gcd: 0.546281
p-value, dist. of gcd's: 0.964054
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-11_07:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.384 0.435 0.061 0.784 0.494 0.663 0.430 0.426
Bits 8 to 15---> 0.210 0.830 0.263 0.265 0.267 0.297 0.772 0.229
Bits 16 to 23---> 0.608 0.035 0.458 0.893 0.240 0.870 0.151 0.000
Bits 24 to 31---> 0.764 0.084 0.004 0.397 0.049 0.763 0.815 0.355
KS test for the above 32 p values: 0.898
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-11_07:31,
p-values for 5 runs: 0.3160, 0.3685, 0.8997, 0.2390, 0.8046
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-11_07:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 215 211.4 0.061 0.061
r= 29 5165 5134.0 0.187 0.248
r= 30 23109 23103.0 0.002 0.249
r= 31 11511 11551.5 0.142 0.391
chi-square = 0.391 with df = 3; p-value = 0.058
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-11_07:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 252 211.4 7.790 7.790
r= 30 5034 5134.0 1.948 9.738
r= 31 23230 23103.0 0.698 10.436
r= 32 11484 11551.5 0.395 10.830
chi-square = 10.830 with df = 3; p-value = 0.987
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-11_07:31
b-rank test for bits 1 to 8, p=0.93531
b-rank test for bits 2 to 9, p=0.56210
b-rank test for bits 3 to 10, p=0.68366
b-rank test for bits 4 to 11, p=0.95060
b-rank test for bits 5 to 12, p=0.90991
b-rank test for bits 6 to 13, p=0.83488
b-rank test for bits 7 to 14, p=0.62142
b-rank test for bits 8 to 15, p=0.05619
b-rank test for bits 9 to 16, p=0.98858
b-rank test for bits 10 to 17, p=0.35584
b-rank test for bits 11 to 18, p=0.57814
b-rank test for bits 12 to 19, p=0.35289
b-rank test for bits 13 to 20, p=0.00057
b-rank test for bits 14 to 21, p=0.75426
b-rank test for bits 15 to 22, p=0.08004
b-rank test for bits 16 to 23, p=0.71411
b-rank test for bits 17 to 24, p=0.62586
b-rank test for bits 18 to 25, p=0.89910
b-rank test for bits 19 to 26, p=0.92888
b-rank test for bits 20 to 27, p=0.69969
b-rank test for bits 21 to 28, p=0.90372
b-rank test for bits 22 to 29, p=0.41791
b-rank test for bits 23 to 30, p=0.80914
b-rank test for bits 24 to 31, p=0.59428
b-rank test for bits 25 to 32, p=0.05194
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 = 0.039464
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-11_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 141688 -0.52 0.302534
2 141160 -1.75 0.039993
3 141391 -1.21 0.112938
4 142279 0.86 0.806128
5 141983 0.17 0.568331
6 141783 -0.30 0.383935
7 142126 0.51 0.693655
8 141800 -0.26 0.399190
9 141920 0.02 0.509945
10 142537 1.47 0.928746
11 142358 1.05 0.852749
12 141353 -1.30 0.096829
13 142277 0.86 0.804841
14 142277 0.86 0.804841
15 142338 1.00 0.841723
16 142162 0.59 0.722522
17 141520 -0.91 0.181504
18 142427 1.21 0.886766
19 141521 -0.91 0.182121
20 141845 -0.15 0.440263
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-11_07:31
Bits used No. missing words z-score p-value
23 to 32 142134 0.7747 0.780749
22 to 31 141966 0.1954 0.577466
21 to 30 142223 1.0816 0.860289
20 to 29 142217 1.0609 0.855639
19 to 28 142271 1.2471 0.893827
18 to 27 141895 -0.0494 0.480295
17 to 26 142097 0.6471 0.741229
16 to 25 141903 -0.0218 0.491293
15 to 24 142363 1.5644 0.941136
14 to 23 142022 0.3885 0.651183
13 to 22 142027 0.4058 0.657540
12 to 21 141697 -0.7322 0.232032
11 to 20 141908 -0.0046 0.498170
10 to 19 141743 -0.5736 0.283136
9 to 18 142113 0.7023 0.758757
8 to 17 141955 0.1575 0.562568
7 to 16 142350 1.5196 0.935688
6 to 15 142011 0.3506 0.637051
5 to 14 141882 -0.0942 0.462459
4 to 13 141903 -0.0218 0.491293
3 to 12 141980 0.2437 0.596264
2 to 11 141976 0.2299 0.590914
1 to 10 142015 0.3644 0.642213
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-11_07:31
Bits used No. missing words z-score p-value
28 to 32 141762 -0.4994 0.308741
27 to 31 142555 2.1887 0.985691
26 to 30 142260 1.1887 0.882723
25 to 29 141959 0.1684 0.566855
24 to 28 142089 0.6091 0.728755
23 to 27 142293 1.3006 0.903298
22 to 26 141972 0.2124 0.584118
21 to 25 141764 -0.4926 0.311132
20 to 24 141830 -0.2689 0.393998
19 to 23 142266 1.2091 0.886678
18 to 22 141572 -1.1435 0.126417
17 to 21 141918 0.0294 0.511723
16 to 20 142302 1.3311 0.908419
15 to 19 142269 1.2192 0.888620
14 to 18 141646 -0.8926 0.186024
13 to 17 141844 -0.2215 0.412368
12 to 16 141809 -0.3401 0.366890
11 to 15 142219 1.0497 0.853079
10 to 14 141871 -0.1299 0.448310
9 to 13 141649 -0.8825 0.188760
8 to 12 141452 -1.5503 0.060538
7 to 11 142014 0.3548 0.638635
6 to 10 142035 0.4260 0.664946
5 to 9 141601 -1.0452 0.147968
4 to 8 141860 -0.1672 0.433598
3 to 7 141771 -0.4689 0.319565
2 to 6 141668 -0.8181 0.206659
1 to 5 141451 -1.5537 0.060133
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-11_07:31
Bits used No. missing words z-score p-value
31 to 32 141964 0.1613 0.564059
30 to 31 141846 -0.1868 0.425903
29 to 30 141715 -0.5732 0.283240
28 to 29 141826 -0.2458 0.402914
27 to 28 141845 -0.1898 0.424747
26 to 27 141960 0.1495 0.559408
25 to 26 142144 0.6922 0.755607
24 to 25 142042 0.3914 0.652233
23 to 24 142035 0.3707 0.644573
22 to 23 142236 0.9636 0.832384
21 to 22 142115 0.6067 0.727974
20 to 21 141918 0.0256 0.510202
19 to 20 142393 1.4268 0.923175
18 to 19 141694 -0.6352 0.262652
17 to 18 141564 -1.0187 0.154179
16 to 17 141694 -0.6352 0.262652
15 to 16 141664 -0.7237 0.234629
14 to 15 142098 0.5565 0.711082
13 to 14 141621 -0.8505 0.197515
12 to 13 141346 -1.6617 0.048282
11 to 12 141850 -0.1750 0.430534
10 to 11 141443 -1.3756 0.084472
9 to 10 141591 -0.9390 0.173859
8 to 9 142031 0.3589 0.640168
7 to 8 141514 -1.1662 0.121774
6 to 7 141206 -2.0747 0.019006
5 to 6 141821 -0.2606 0.397216
4 to 5 141816 -0.2753 0.391539
3 to 4 142020 0.3265 0.627962
2 to 3 141934 0.0728 0.529007
1 to 2 142355 1.3147 0.905688
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-11_07:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2417.86 -1.162 0.122682
Test results for specific bytes for dh-ranFile-2018-07-11_07:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2571.66 1.013 0.844564
2 to 9 2556.13 0.794 0.786357
3 to 10 2571.99 1.018 0.845678
4 to 11 2527.50 0.389 0.651332
5 to 12 2391.61 -1.533 0.062658
6 to 13 2615.85 1.638 0.949326
7 to 14 2593.12 1.317 0.906071
8 to 15 2420.45 -1.125 0.130282
9 to 16 2516.95 0.240 0.594748
10 to 17 2464.93 -0.496 0.309945
11 to 18 2401.73 -1.390 0.082312
12 to 19 2440.34 -0.844 0.199423
13 to 20 2462.38 -0.532 0.297357
14 to 21 2356.90 -2.024 0.021500
15 to 22 2518.95 0.268 0.605665
16 to 23 2500.61 0.009 0.503463
17 to 24 2553.77 0.760 0.776498
18 to 25 2596.64 1.367 0.914138
19 to 26 2436.03 -0.905 0.182833
20 to 27 2428.02 -1.018 0.154350
21 to 28 2506.85 0.097 0.538584
22 to 29 2551.62 0.730 0.767292
23 to 30 2508.12 0.115 0.545686
24 to 31 2496.62 -0.048 0.480910
25 to 32 2519.39 0.274 0.608065
CDPARK for dh-ranFile-2018-07-11_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
3548 1.1416 0.873180
3527 0.1826 0.572463
3533 0.4566 0.676028
3548 1.1416 0.873180
3524 0.0457 0.518210
3539 0.7306 0.767486
3478 -2.0548 0.019949
3540 0.7763 0.781201
3530 0.3196 0.625377
3501 -1.0046 0.157553
Square side=100, avg. no. parked=3526.80 sample std.=20.80
p-value of the KSTEST for those 10 p-values: 0.383465
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-11_07:31
0.9263,0.0520,0.3743,0.7595,0.8549,0.5616,0.7024,0.2885,0.2056,0.3619,
The KS test for those 10 p-values: 0.998422
The 3DSPHERES test for dh-ranFile-2018-07-11_07:31
sample no r^3 equiv. uni.
1 27.143 0.595364
2 23.097 0.536935
3 23.911 0.549336
4 21.046 0.504182
5 2.117 0.068139
6 39.291 0.730097
7 7.301 0.216018
8 53.029 0.829261
9 5.507 0.167704
10 44.903 0.776146
11 11.097 0.309196
12 86.975 0.944932
13 1.720 0.055736
14 3.733 0.116999
15 48.137 0.799021
16 27.955 0.606163
17 5.582 0.169770
18 9.299 0.266520
19 1.730 0.056034
20 3.283 0.103672
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.300022
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-11_07:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -0.7 -0.8 -1.7 -0.4 1.7
-1.6 0.7 1.6 -0.7 -0.0 -0.0
0.3 0.2 0.3 -0.2 1.3 -0.1
-1.5 -0.9 1.4 0.3 -0.8 1.6
-1.5 -0.4 0.0 0.5 -0.5 0.6
-1.9 -0.5 -0.1 -1.0 1.2 -0.3
0.3 0.2 -0.4 0.4 -0.6 2.0
0.8
Chi-square with 42 degrees of freedom:39.201745
z-score=-0.305315, p-value=0.405498
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-11_07:31
Test no p-value
1 0.628873
2 0.072192
3 0.491544
4 0.330194
5 0.524817
6 0.088898
7 0.046338
8 0.975437
9 0.284181
10 0.579807
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.401864
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-11_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 66791 0.23 66721 0.04
3 25000.00 24869 0.69 24831 1.14
4 6666.67 6581 1.10 6756 1.20
5 1388.89 1473 5.09 1436 1.60
6 238.10 258 1.66 211 3.08
7 34.72 25 2.72 36 0.05
8 4.96 2 1.77 8 1.86
p=0.96098 p=0.82504
Number of rngs required: 687733, p-value: 0.219
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-11_07:31
No. of wins: Observed Expected
98379 98585.9
z-score=-0.925, pvalue=0.17743
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66589 66666.7 0.090 0.090
2 37705 37654.3 0.068 0.159
3 26833 26954.7 0.550 0.708
4 19627 19313.5 5.090 5.798
5 13857 13851.4 0.002 5.801
6 9897 9943.5 0.218 6.019
7 7239 7145.0 1.236 7.255
8 5251 5139.1 2.438 9.692
9 3623 3699.9 1.597 11.289
10 2519 2666.3 8.137 19.427
11 1835 1923.3 4.057 23.483
12 1411 1388.7 0.357 23.840
13 979 1003.7 0.609 24.448
14 706 726.1 0.559 25.007
15 542 525.8 0.497 25.504
16 393 381.2 0.368 25.872
17 279 276.5 0.022 25.894
18 175 200.8 3.322 29.216
19 145 146.0 0.007 29.223
20 113 106.2 0.433 29.656
21 282 287.1 0.091 29.747
Chisq= 29.75 for 20 degrees of freedom, p= 0.92595
SUMMARY of craptest
p-value for no. of wins: 0.177433
p-value for throws/game: 0.925950
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-11_07:31
No. of wins: Observed Expected
98556 98585.9
z-score=-0.134, pvalue=0.44688
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66917 66666.7 0.940 0.940
2 37505 37654.3 0.592 1.532
3 27182 26954.7 1.916 3.448
4 19089 19313.5 2.609 6.057
5 13827 13851.4 0.043 6.100
6 10030 9943.5 0.752 6.852
7 6995 7145.0 3.150 10.002
8 5113 5139.1 0.132 10.134
9 3668 3699.9 0.274 10.409
10 2708 2666.3 0.652 11.061
11 1957 1923.3 0.589 11.650
12 1464 1388.7 4.079 15.729
13 995 1003.7 0.076 15.805
14 709 726.1 0.405 16.209
15 494 525.8 1.927 18.137
16 351 381.2 2.385 20.522
17 275 276.5 0.009 20.530
18 205 200.8 0.087 20.617
19 134 146.0 0.984 21.601
20 113 106.2 0.433 22.034
21 269 287.1 1.143 23.177
Chisq= 23.18 for 20 degrees of freedom, p= 0.71981
SUMMARY of craptest
p-value for no. of wins: 0.446881
p-value for throws/game: 0.719807
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0002,0.0006,0.0040,0.0092,0.0123,0.0190,0.0199,0.0215,0.0259,0.0354,
0.0395,0.0400,0.0463,0.0463,0.0483,0.0495,0.0519,0.0520,0.0557,0.0560,
0.0562,0.0580,0.0601,0.0605,0.0614,0.0627,0.0681,0.0722,0.0793,0.0800,
0.0823,0.0840,0.0845,0.0889,0.0968,0.1037,0.1129,0.1170,0.1218,0.1227,
0.1264,0.1303,0.1480,0.1511,0.1542,0.1544,0.1576,0.1677,0.1698,0.1739,
0.1774,0.1815,0.1821,0.1828,0.1860,0.1888,0.1912,0.1975,0.1994,0.2056,
0.2067,0.2095,0.2160,0.2194,0.2291,0.2320,0.2346,0.2390,0.2404,0.2626,
0.2627,0.2627,0.2648,0.2665,0.2670,0.2831,0.2832,0.2842,0.2884,0.2885,
0.2972,0.2974,0.3000,0.3025,0.3087,0.3092,0.3099,0.3111,0.3160,0.3196,
0.3295,0.3302,0.3529,0.3548,0.3558,0.3619,0.3669,0.3685,0.3743,0.3835,
0.3836,0.3839,0.3915,0.3940,0.3972,0.3972,0.3992,0.4019,0.4029,0.4055,
0.4124,0.4179,0.4247,0.4259,0.4262,0.4298,0.4305,0.4336,0.4346,0.4403,
0.4469,0.4483,0.4577,0.4625,0.4803,0.4809,0.4913,0.4913,0.4915,0.4942,
0.4982,0.5035,0.5042,0.5099,0.5102,0.5117,0.5182,0.5248,0.5290,0.5369,
0.5386,0.5457,0.5463,0.5493,0.5594,0.5616,0.5621,0.5626,0.5641,0.5669,
0.5683,0.5725,0.5740,0.5775,0.5781,0.5798,0.5841,0.5909,0.5943,0.5947,
0.5954,0.5963,0.6057,0.6062,0.6079,0.6081,0.6214,0.6254,0.6259,0.6280,
0.6289,0.6371,0.6386,0.6402,0.6422,0.6446,0.6512,0.6513,0.6522,0.6575,
0.6630,0.6649,0.6760,0.6837,0.6937,0.6997,0.7024,0.7111,0.7141,0.7198,
0.7225,0.7280,0.7288,0.7301,0.7412,0.7543,0.7556,0.7588,0.7595,0.7626,
0.7641,0.7673,0.7675,0.7723,0.7751,0.7761,0.7765,0.7807,0.7812,0.7844,
0.7864,0.7990,0.8046,0.8048,0.8048,0.8061,0.8091,0.8146,0.8250,0.8293,
0.8303,0.8324,0.8349,0.8417,0.8446,0.8457,0.8527,0.8531,0.8549,0.8556,
0.8603,0.8649,0.8699,0.8732,0.8732,0.8827,0.8867,0.8868,0.8886,0.8927,
0.8938,0.8976,0.8991,0.8997,0.9033,0.9037,0.9057,0.9061,0.9084,0.9099,
0.9141,0.9232,0.9259,0.9263,0.9287,0.9289,0.9353,0.9357,0.9411,0.9449,
0.9493,0.9506,0.9610,0.9641,0.9754,0.9857,0.9873,0.9886,0.9984,
Overall p-value after applying KStest on 269 p-values = 0.749867
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.