RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-03_23:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.81 21.4476 0.793095
2 to 25 15.76 16.7053 0.525499
3 to 26 15.79 25.3416 0.912679
4 to 27 15.83 23.9074 0.878028
5 to 28 15.64 14.0908 0.339338
6 to 29 15.74 17.3248 0.567418
7 to 30 15.76 19.4941 0.699082
8 to 31 15.77 14.6009 0.375797
9 to 32 15.81 16.4332 0.506638
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.278124
Tough bday spacings test for dh-ranFile-2018-07-03_23:31: 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 28 98 108 84 71 52 25 11 5 7
(O-E)^2/E 0.4 2.0 8.4 1.1 1.9 0.7 0.0 0.8 1.0 0.4 2.1
Birthday Spacings: Sum(O-E)^2/E= 18.707, p= 0.956
RESULTS OF GCD FOR dh-ranFile-2018-07-03_23:31
Euclid's algorithm:
p-value, steps to gcd: 0.378742
p-value, dist. of gcd's: 0.233321
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-03_23:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.877 0.811 0.114 0.690 0.648 0.440 0.365 0.117
Bits 8 to 15---> 0.524 0.732 0.840 0.545 0.380 0.603 0.689 0.135
Bits 16 to 23---> 0.398 0.672 0.706 0.523 0.775 0.040 0.309 0.577
Bits 24 to 31---> 0.379 0.466 0.664 0.915 0.855 0.685 0.752 0.954
KS test for the above 32 p values: 0.847
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-03_23:31,
p-values for 5 runs: 0.1642, 0.7747, 0.9237, 0.9266, 0.2010
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-03_23:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 201 211.4 0.513 0.513
r= 29 5064 5134.0 0.955 1.468
r= 30 23136 23103.0 0.047 1.515
r= 31 11599 11551.5 0.195 1.710
chi-square = 1.710 with df = 3; p-value = 0.365
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-03_23:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 230 211.4 1.633 1.633
r= 30 5125 5134.0 0.016 1.649
r= 31 23059 23103.0 0.084 1.733
r= 32 11586 11551.5 0.103 1.836
chi-square = 1.836 with df = 3; p-value = 0.393
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-03_23:31
b-rank test for bits 1 to 8, p=0.55902
b-rank test for bits 2 to 9, p=0.36075
b-rank test for bits 3 to 10, p=0.36890
b-rank test for bits 4 to 11, p=0.79344
b-rank test for bits 5 to 12, p=0.95328
b-rank test for bits 6 to 13, p=0.64142
b-rank test for bits 7 to 14, p=0.31056
b-rank test for bits 8 to 15, p=0.25608
b-rank test for bits 9 to 16, p=0.18786
b-rank test for bits 10 to 17, p=0.51912
b-rank test for bits 11 to 18, p=0.56562
b-rank test for bits 12 to 19, p=0.42440
b-rank test for bits 13 to 20, p=0.15064
b-rank test for bits 14 to 21, p=0.81717
b-rank test for bits 15 to 22, p=0.85245
b-rank test for bits 16 to 23, p=0.98399
b-rank test for bits 17 to 24, p=0.29765
b-rank test for bits 18 to 25, p=0.86856
b-rank test for bits 19 to 26, p=0.82655
b-rank test for bits 20 to 27, p=0.98142
b-rank test for bits 21 to 28, p=0.74107
b-rank test for bits 22 to 29, p=0.83419
b-rank test for bits 23 to 30, p=0.01322
b-rank test for bits 24 to 31, p=0.06922
b-rank test for bits 25 to 32, p=0.71383
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 = 0.456165
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-03_23:31
(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 141363 -1.28 0.100894
2 142336 1.00 0.840592
3 142753 1.97 0.975649
4 142593 1.60 0.944907
5 141793 -0.27 0.392888
6 141626 -0.66 0.253990
7 141674 -0.55 0.291216
8 141946 0.09 0.534139
9 142168 0.60 0.727201
10 141915 0.01 0.505285
11 142426 1.21 0.886317
12 141872 -0.09 0.465249
13 142032 0.29 0.612795
14 141569 -0.80 0.213259
15 142060 0.35 0.637593
16 142494 1.37 0.914039
17 142245 0.78 0.783561
18 141885 -0.06 0.477334
19 141236 -1.57 0.057836
20 141676 -0.55 0.292821
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-03_23:31
Bits used No. missing words z-score p-value
23 to 32 141814 -0.3287 0.371182
22 to 31 141901 -0.0287 0.488542
21 to 30 142422 1.7678 0.961455
20 to 29 141598 -1.0736 0.141512
19 to 28 141861 -0.1667 0.433821
18 to 27 141847 -0.2149 0.414911
17 to 26 141831 -0.2701 0.393540
16 to 25 142135 0.7782 0.781766
15 to 24 142224 1.0851 0.861054
14 to 23 142317 1.4058 0.920102
13 to 22 141931 0.0747 0.529783
12 to 21 141866 -0.1494 0.440614
11 to 20 141976 0.2299 0.590914
10 to 19 141959 0.1713 0.567997
9 to 18 141894 -0.0529 0.478921
8 to 17 142060 0.5196 0.698312
7 to 16 142091 0.6264 0.734490
6 to 15 141748 -0.5563 0.288999
5 to 14 141639 -0.9322 0.175624
4 to 13 141416 -1.7011 0.044459
3 to 12 141805 -0.3598 0.359514
2 to 11 142111 0.6954 0.756602
1 to 10 141925 0.0540 0.521546
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-03_23:31
Bits used No. missing words z-score p-value
28 to 32 142232 1.0938 0.862978
27 to 31 141635 -0.9299 0.176203
26 to 30 141639 -0.9164 0.179736
25 to 29 141759 -0.5096 0.305168
24 to 28 141798 -0.3774 0.352942
23 to 27 141481 -1.4520 0.073256
22 to 26 141499 -1.3909 0.082120
21 to 25 141760 -0.5062 0.306357
20 to 24 141992 0.2802 0.610352
19 to 23 141615 -0.9977 0.159205
18 to 22 142410 1.6972 0.955169
17 to 21 142587 2.2972 0.989196
16 to 20 141963 0.1819 0.572182
15 to 19 141699 -0.7130 0.237928
14 to 18 142214 1.0328 0.849147
13 to 17 141808 -0.3435 0.365614
12 to 16 142255 1.1718 0.879354
11 to 15 141825 -0.2859 0.387491
10 to 14 141855 -0.1842 0.426940
9 to 13 142036 0.4294 0.666180
8 to 12 141645 -0.8960 0.185117
7 to 11 141851 -0.1977 0.421629
6 to 10 142112 0.6870 0.753964
5 to 9 141924 0.0497 0.519831
4 to 8 142272 1.2294 0.890537
3 to 7 142120 0.7141 0.762428
2 to 6 142196 0.9718 0.834416
1 to 5 141467 -1.4994 0.066882
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-03_23:31
Bits used No. missing words z-score p-value
31 to 32 142064 0.4563 0.675896
30 to 31 141453 -1.3461 0.089134
29 to 30 142149 0.7070 0.760214
28 to 29 141949 0.1170 0.546578
27 to 28 141795 -0.3373 0.367962
26 to 27 142276 1.0816 0.860290
25 to 26 141805 -0.3078 0.379133
24 to 25 142126 0.6391 0.738636
23 to 24 141918 0.0256 0.510202
22 to 23 142376 1.3766 0.915683
21 to 22 141394 -1.5201 0.064237
20 to 21 141825 -0.2488 0.401773
19 to 20 142240 0.9754 0.835326
18 to 19 141621 -0.8505 0.197515
17 to 18 141712 -0.5821 0.280252
16 to 17 142088 0.5271 0.700921
15 to 16 141907 -0.0069 0.497258
14 to 15 141564 -1.0187 0.154179
13 to 14 141639 -0.7974 0.212600
12 to 13 141412 -1.4671 0.071181
11 to 12 141635 -0.8092 0.209191
10 to 11 142451 1.5978 0.944961
9 to 10 142006 0.2852 0.612240
8 to 9 142453 1.6037 0.945615
7 to 8 142256 1.0226 0.846758
6 to 7 142174 0.7807 0.782522
5 to 6 142238 0.9695 0.833859
4 to 5 142203 0.8663 0.806833
3 to 4 141981 0.2114 0.583719
2 to 3 142046 0.4032 0.656583
1 to 2 141839 -0.2075 0.417824
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-03_23:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2608.30 1.532 0.937196
Test results for specific bytes for dh-ranFile-2018-07-03_23:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2612.48 1.591 0.944166
2 to 9 2517.43 0.246 0.597346
3 to 10 2502.88 0.041 0.516247
4 to 11 2447.15 -0.747 0.227391
5 to 12 2555.77 0.789 0.784840
6 to 13 2482.31 -0.250 0.401234
7 to 14 2393.00 -1.513 0.065110
8 to 15 2505.84 0.083 0.532899
9 to 16 2568.68 0.971 0.834283
10 to 17 2529.56 0.418 0.662021
11 to 18 2501.80 0.025 0.510157
12 to 19 2435.96 -0.906 0.182568
13 to 20 2535.80 0.506 0.693671
14 to 21 2613.80 1.609 0.946230
15 to 22 2404.37 -1.352 0.088131
16 to 23 2473.98 -0.368 0.356426
17 to 24 2518.82 0.266 0.604915
18 to 25 2514.51 0.205 0.581311
19 to 26 2487.74 -0.173 0.431188
20 to 27 2496.50 -0.050 0.480235
21 to 28 2442.79 -0.809 0.209253
22 to 29 2521.03 0.297 0.616903
23 to 30 2460.41 -0.560 0.287758
24 to 31 2481.42 -0.263 0.396369
25 to 32 2541.44 0.586 0.721075
CDPARK for dh-ranFile-2018-07-03_23:31: 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
3523 0.0000 0.500000
3518 -0.2283 0.409702
3531 0.3653 0.642555
3516 -0.3196 0.374623
3515 -0.3653 0.357445
3535 0.5479 0.708135
3490 -1.5068 0.065925
3547 1.0959 0.863437
3522 -0.0457 0.481790
3518 -0.2283 0.409702
Square side=100, avg. no. parked=3521.50 sample std.=14.19
p-value of the KSTEST for those 10 p-values: 0.523771
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-03_23:31
0.8609,0.8487,0.9168,0.9477,0.6866,0.8539,0.2200,0.5614,0.2468,0.0969,
The KS test for those 10 p-values: 0.188227
The 3DSPHERES test for dh-ranFile-2018-07-03_23:31
sample no r^3 equiv. uni.
1 62.172 0.874115
2 1.053 0.034491
3 41.178 0.746551
4 30.557 0.638890
5 24.222 0.553990
6 46.979 0.791112
7 20.780 0.499768
8 14.221 0.377517
9 102.975 0.967694
10 28.815 0.617295
11 13.864 0.370070
12 82.355 0.935762
13 1.828 0.059129
14 23.204 0.538594
15 108.062 0.972733
16 23.288 0.539873
17 14.787 0.389139
18 63.820 0.880844
19 18.859 0.466683
20 50.471 0.814069
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.159257
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-03_23:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 1.3 -0.4 -0.5 1.3 -0.6
-1.4 -1.6 0.0 -0.6 0.1 -0.2
0.4 0.1 0.5 1.1 -0.4 -0.0
0.1 -0.6 1.2 1.3 -2.0 0.1
-0.5 -0.5 -1.6 1.0 0.7 2.1
-0.6 -1.3 1.3 -1.3 0.9 1.0
-2.3 -0.4 -1.2 -1.3 0.1 1.0
1.8
Chi-square with 42 degrees of freedom:47.491855
z-score=0.599211, p-value=0.741179
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-03_23:31
Test no p-value
1 0.001731
2 0.204473
3 0.001691
4 0.065048
5 0.627080
6 0.575145
7 0.060314
8 0.963114
9 0.715257
10 0.965406
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.027559
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-03_23:31:
(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 66651 0.00 66570 0.14
3 25000.00 25074 0.22 25063 0.16
4 6666.67 6668 0.00 6677 0.02
5 1388.89 1362 0.52 1403 0.14
6 238.10 206 4.33 235 0.04
7 34.72 28 1.30 47 4.34
8 4.96 10 5.12 4 0.19
p=0.92569 p=0.45972
Number of rngs required: 687663, p-value: 0.196
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-03_23:31
No. of wins: Observed Expected
98457 98585.9
z-score=-0.576, pvalue=0.28220
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66513 66666.7 0.354 0.354
2 37580 37654.3 0.147 0.501
3 26816 26954.7 0.714 1.215
4 19400 19313.5 0.388 1.603
5 14023 13851.4 2.125 3.728
6 9940 9943.5 0.001 3.729
7 7250 7145.0 1.542 5.272
8 5247 5139.1 2.267 7.538
9 3640 3699.9 0.969 8.507
10 2636 2666.3 0.344 8.851
11 1916 1923.3 0.028 8.879
12 1399 1388.7 0.076 8.955
13 995 1003.7 0.076 9.031
14 713 726.1 0.238 9.268
15 513 525.8 0.313 9.582
16 402 381.2 1.140 10.722
17 260 276.5 0.989 11.711
18 212 200.8 0.621 12.333
19 145 146.0 0.007 12.339
20 101 106.2 0.256 12.595
21 299 287.1 0.492 13.087
Chisq= 13.09 for 20 degrees of freedom, p= 0.12640
SUMMARY of craptest
p-value for no. of wins: 0.282196
p-value for throws/game: 0.126398
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-03_23:31
No. of wins: Observed Expected
98480 98585.9
z-score=-0.473, pvalue=0.31794
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66562 66666.7 0.164 0.164
2 37707 37654.3 0.074 0.238
3 27059 26954.7 0.403 0.641
4 19339 19313.5 0.034 0.675
5 13838 13851.4 0.013 0.688
6 9858 9943.5 0.736 1.424
7 7062 7145.0 0.965 2.389
8 5150 5139.1 0.023 2.412
9 3727 3699.9 0.199 2.611
10 2669 2666.3 0.003 2.614
11 1969 1923.3 1.084 3.698
12 1382 1388.7 0.033 3.731
13 1010 1003.7 0.039 3.770
14 698 726.1 1.091 4.861
15 531 525.8 0.051 4.912
16 371 381.2 0.270 5.182
17 291 276.5 0.756 5.938
18 233 200.8 5.153 11.091
19 150 146.0 0.110 11.202
20 108 106.2 0.030 11.232
21 286 287.1 0.004 11.236
Chisq= 11.24 for 20 degrees of freedom, p= 0.06013
SUMMARY of craptest
p-value for no. of wins: 0.317942
p-value for throws/game: 0.060131
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0017,0.0017,0.0132,0.0276,0.0345,0.0400,0.0445,0.0578,0.0591,0.0601,
0.0603,0.0642,0.0650,0.0651,0.0659,0.0669,0.0692,0.0712,0.0733,0.0821,
0.0881,0.0891,0.0969,0.1009,0.1142,0.1167,0.1264,0.1350,0.1415,0.1506,
0.1542,0.1592,0.1593,0.1642,0.1756,0.1762,0.1797,0.1826,0.1851,0.1879,
0.1882,0.1961,0.1975,0.2010,0.2045,0.2092,0.2093,0.2126,0.2133,0.2200,
0.2274,0.2333,0.2379,0.2468,0.2540,0.2561,0.2781,0.2803,0.2822,0.2878,
0.2890,0.2912,0.2928,0.2977,0.3052,0.3064,0.3085,0.3106,0.3179,0.3393,
0.3529,0.3564,0.3574,0.3595,0.3608,0.3651,0.3653,0.3656,0.3680,0.3689,
0.3701,0.3712,0.3746,0.3758,0.3775,0.3787,0.3791,0.3793,0.3799,0.3875,
0.3891,0.3928,0.3929,0.3935,0.3964,0.3984,0.4012,0.4018,0.4097,0.4097,
0.4149,0.4178,0.4216,0.4244,0.4269,0.4312,0.4338,0.4399,0.4406,0.4562,
0.4597,0.4652,0.4661,0.4667,0.4773,0.4789,0.4802,0.4818,0.4885,0.4973,
0.4998,0.5000,0.5053,0.5066,0.5102,0.5102,0.5162,0.5191,0.5198,0.5215,
0.5228,0.5235,0.5238,0.5255,0.5298,0.5329,0.5341,0.5386,0.5399,0.5453,
0.5466,0.5540,0.5590,0.5614,0.5656,0.5674,0.5680,0.5722,0.5751,0.5767,
0.5813,0.5837,0.5909,0.5973,0.6030,0.6049,0.6104,0.6122,0.6128,0.6169,
0.6173,0.6271,0.6376,0.6389,0.6414,0.6426,0.6481,0.6566,0.6620,0.6639,
0.6662,0.6724,0.6759,0.6853,0.6866,0.6894,0.6901,0.6937,0.6983,0.6991,
0.7009,0.7057,0.7081,0.7138,0.7153,0.7211,0.7272,0.7323,0.7345,0.7386,
0.7411,0.7412,0.7466,0.7517,0.7540,0.7566,0.7602,0.7624,0.7747,0.7747,
0.7818,0.7825,0.7836,0.7848,0.7911,0.7931,0.7934,0.8068,0.8109,0.8141,
0.8172,0.8265,0.8339,0.8342,0.8343,0.8344,0.8353,0.8401,0.8406,0.8465,
0.8468,0.8487,0.8491,0.8525,0.8539,0.8549,0.8603,0.8609,0.8611,0.8630,
0.8634,0.8686,0.8741,0.8767,0.8780,0.8794,0.8808,0.8863,0.8905,0.9127,
0.9140,0.9152,0.9157,0.9168,0.9201,0.9237,0.9257,0.9266,0.9358,0.9372,
0.9442,0.9449,0.9450,0.9456,0.9462,0.9477,0.9533,0.9540,0.9552,0.9559,
0.9615,0.9631,0.9654,0.9677,0.9727,0.9756,0.9814,0.9840,0.9892,
Overall p-value after applying KStest on 269 p-values = 0.074155
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.