RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-05_00:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.82 22.9221 0.848195
2 to 25 15.83 27.8778 0.953614
3 to 26 15.76 19.2867 0.687677
4 to 27 15.55 19.0542 0.674570
5 to 28 15.77 12.2220 0.213486
6 to 29 15.42 25.3275 0.912385
7 to 30 15.84 11.9241 0.195289
8 to 31 15.81 10.3470 0.111568
9 to 32 16.20 25.1471 0.908536
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.224296
Tough bday spacings test for dh-ranFile-2018-07-05_00:31: 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 12 39 60 78 101 103 50 37 11 4 5
(O-E)^2/E 0.9 0.2 2.4 4.0 0.1 7.9 0.1 1.8 1.0 1.0 0.2
Birthday Spacings: Sum(O-E)^2/E= 19.522, p= 0.966
RESULTS OF GCD FOR dh-ranFile-2018-07-05_00:31
Euclid's algorithm:
p-value, steps to gcd: 0.570519
p-value, dist. of gcd's: 0.511091
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-05_00:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.750 0.231 0.101 0.057 0.877 0.724 0.925 0.919
Bits 8 to 15---> 0.664 0.881 0.249 0.318 0.397 0.864 0.579 0.512
Bits 16 to 23---> 0.838 0.378 0.558 0.236 0.501 0.253 0.263 0.769
Bits 24 to 31---> 0.878 0.172 0.750 0.557 0.556 0.009 0.494 0.128
KS test for the above 32 p values: 0.063
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-05_00:31,
p-values for 5 runs: 0.4060, 0.9400, 0.5100, 0.4472, 0.3395
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-05_00:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 216 211.4 0.099 0.099
r= 29 5114 5134.0 0.078 0.177
r= 30 23127 23103.0 0.025 0.202
r= 31 11543 11551.5 0.006 0.208
chi-square = 0.208 with df = 3; p-value = 0.024
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-05_00:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 214 211.4 0.032 0.032
r= 30 5191 5134.0 0.633 0.664
r= 31 23123 23103.0 0.017 0.681
r= 32 11472 11551.5 0.547 1.229
chi-square = 1.229 with df = 3; p-value = 0.254
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-05_00:31
b-rank test for bits 1 to 8, p=0.40004
b-rank test for bits 2 to 9, p=0.49152
b-rank test for bits 3 to 10, p=0.55849
b-rank test for bits 4 to 11, p=0.49669
b-rank test for bits 5 to 12, p=0.21540
b-rank test for bits 6 to 13, p=0.37761
b-rank test for bits 7 to 14, p=0.60557
b-rank test for bits 8 to 15, p=0.91492
b-rank test for bits 9 to 16, p=0.45442
b-rank test for bits 10 to 17, p=0.38865
b-rank test for bits 11 to 18, p=0.78317
b-rank test for bits 12 to 19, p=0.07007
b-rank test for bits 13 to 20, p=0.92005
b-rank test for bits 14 to 21, p=0.71618
b-rank test for bits 15 to 22, p=0.77426
b-rank test for bits 16 to 23, p=0.08788
b-rank test for bits 17 to 24, p=0.33516
b-rank test for bits 18 to 25, p=0.24889
b-rank test for bits 19 to 26, p=0.84927
b-rank test for bits 20 to 27, p=0.23894
b-rank test for bits 21 to 28, p=0.28806
b-rank test for bits 22 to 29, p=0.92802
b-rank test for bits 23 to 30, p=0.48816
b-rank test for bits 24 to 31, p=0.88778
b-rank test for bits 25 to 32, p=0.65123
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 = 0.772770
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-05_00:31
(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 141513 -0.93 0.177222
2 141428 -1.12 0.130379
3 141524 -0.90 0.183979
4 142002 0.22 0.585708
5 142083 0.41 0.657545
6 142201 0.68 0.752214
7 141787 -0.29 0.387509
8 141815 -0.22 0.412781
9 141896 -0.03 0.487577
10 142158 0.58 0.719381
11 142319 0.96 0.830760
12 142255 0.81 0.790351
13 141404 -1.18 0.118865
14 141797 -0.26 0.396486
15 141929 0.05 0.518328
16 142224 0.74 0.768894
17 142249 0.79 0.786292
18 141464 -1.04 0.149056
19 141422 -1.14 0.127431
20 142253 0.80 0.789003
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-05_00:31
Bits used No. missing words z-score p-value
23 to 32 141710 -0.6873 0.245933
22 to 31 141838 -0.2460 0.402855
21 to 30 142305 1.3644 0.913776
20 to 29 141770 -0.4804 0.315454
19 to 28 142008 0.3402 0.633163
18 to 27 141506 -1.3908 0.082144
17 to 26 141628 -0.9701 0.165998
16 to 25 142176 0.9196 0.821097
15 to 24 142419 1.7575 0.960582
14 to 23 141871 -0.1322 0.447424
13 to 22 142191 0.9713 0.834295
12 to 21 142306 1.3678 0.914317
11 to 20 141891 -0.0632 0.474801
10 to 19 141746 -0.5632 0.286647
9 to 18 141934 0.0851 0.533897
8 to 17 141915 0.0196 0.507800
7 to 16 142025 0.3989 0.655003
6 to 15 141774 -0.4667 0.320373
5 to 14 142056 0.5058 0.693487
4 to 13 141338 -1.9701 0.024413
3 to 12 141639 -0.9322 0.175624
2 to 11 141675 -0.8080 0.209535
1 to 10 141924 0.0506 0.520172
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-05_00:31
Bits used No. missing words z-score p-value
28 to 32 141950 0.1379 0.554826
27 to 31 142025 0.3921 0.652509
26 to 30 141659 -0.8486 0.198059
25 to 29 141808 -0.3435 0.365614
24 to 28 142112 0.6870 0.753964
23 to 27 142034 0.4226 0.663710
22 to 26 141841 -0.2316 0.408414
21 to 25 141928 0.0633 0.525232
20 to 24 142051 0.4802 0.684471
19 to 23 141793 -0.3943 0.346665
18 to 22 142281 1.2599 0.896147
17 to 21 142363 1.5379 0.937959
16 to 20 142298 1.3175 0.906169
15 to 19 141957 0.1616 0.564187
14 to 18 142523 2.0802 0.981248
13 to 17 141936 0.0904 0.536018
12 to 16 141893 -0.0554 0.477928
11 to 15 141901 -0.0282 0.488737
10 to 14 142172 0.8904 0.813376
9 to 13 141636 -0.9265 0.177082
8 to 12 141827 -0.2791 0.390090
7 to 11 142354 1.5074 0.934140
6 to 10 142389 1.6260 0.948025
5 to 9 141591 -1.0791 0.140275
4 to 8 142134 0.7616 0.776849
3 to 7 142042 0.4497 0.673547
2 to 6 142843 3.1650 0.999225
1 to 5 142113 0.6904 0.755031
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-05_00:31
Bits used No. missing words z-score p-value
31 to 32 141844 -0.1927 0.423592
30 to 31 141059 -2.5083 0.006065
29 to 30 141886 -0.0688 0.472566
28 to 29 141456 -1.3373 0.090569
27 to 28 142318 1.2055 0.885998
26 to 27 142384 1.4002 0.919274
25 to 26 142294 1.1347 0.871754
24 to 25 142011 0.2999 0.617878
23 to 24 142295 1.1377 0.872371
22 to 23 142116 0.6096 0.728952
21 to 22 141840 -0.2045 0.418976
20 to 21 141277 -1.8653 0.031071
19 to 20 141982 0.2144 0.584869
18 to 19 142511 1.7748 0.962038
17 to 18 141434 -1.4022 0.080435
16 to 17 142402 1.4533 0.926930
15 to 16 142041 0.3884 0.651143
14 to 15 141885 -0.0718 0.471393
13 to 14 142208 0.8810 0.810850
12 to 13 142276 1.0816 0.860290
11 to 12 141118 -2.3343 0.009790
10 to 11 141947 0.1111 0.544240
9 to 10 141611 -0.8800 0.189422
8 to 9 141761 -0.4376 0.330856
7 to 8 141137 -2.2783 0.011356
6 to 7 142744 2.4622 0.993095
5 to 6 141858 -0.1514 0.439824
4 to 5 142223 0.9253 0.822590
3 to 4 142135 0.6657 0.747196
2 to 3 141402 -1.4965 0.067255
1 to 2 141918 0.0256 0.510202
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-05_00:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2568.61 0.970 0.834067
Test results for specific bytes for dh-ranFile-2018-07-05_00:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2415.11 -1.201 0.114956
2 to 9 2584.21 1.191 0.883149
3 to 10 2395.66 -1.476 0.070030
4 to 11 2535.38 0.500 0.691579
5 to 12 2519.51 0.276 0.608683
6 to 13 2530.96 0.438 0.669262
7 to 14 2485.31 -0.208 0.417712
8 to 15 2487.50 -0.177 0.429818
9 to 16 2456.73 -0.612 0.270315
10 to 17 2503.07 0.043 0.517298
11 to 18 2529.59 0.418 0.662180
12 to 19 2517.45 0.247 0.597449
13 to 20 2448.37 -0.730 0.232626
14 to 21 2539.15 0.554 0.710091
15 to 22 2427.84 -1.021 0.153736
16 to 23 2468.56 -0.445 0.328270
17 to 24 2548.71 0.689 0.754537
18 to 25 2466.46 -0.474 0.317656
19 to 26 2494.21 -0.082 0.467372
20 to 27 2518.70 0.265 0.604309
21 to 28 2439.72 -0.852 0.196987
22 to 29 2463.28 -0.519 0.301793
23 to 30 2423.88 -1.077 0.140838
24 to 31 2470.18 -0.422 0.336612
25 to 32 2378.93 -1.712 0.043425
CDPARK for dh-ranFile-2018-07-05_00:31: 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
3533 0.4566 0.676028
3521 -0.0913 0.463617
3525 0.0913 0.536383
3524 0.0457 0.518210
3558 1.5982 0.944998
3534 0.5023 0.692266
3524 0.0457 0.518210
3568 2.0548 0.980051
3508 -0.6849 0.246694
3543 0.9132 0.819442
Square side=100, avg. no. parked=3533.80 sample std.=17.15
p-value of the KSTEST for those 10 p-values: 0.174884
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-05_00:31
0.6385,0.9058,0.1885,0.7555,0.6662,0.8384,0.5817,0.7872,0.5529,0.0632,
The KS test for those 10 p-values: 0.366338
The 3DSPHERES test for dh-ranFile-2018-07-05_00:31
sample no r^3 equiv. uni.
1 212.366 0.999157
2 14.855 0.390540
3 19.000 0.469177
4 4.980 0.152941
5 5.482 0.167017
6 4.571 0.141337
7 6.510 0.195063
8 15.115 0.395795
9 94.273 0.956823
10 6.517 0.195248
11 275.813 0.999898
12 104.825 0.969626
13 16.239 0.418011
14 12.716 0.345492
15 0.941 0.030872
16 92.454 0.954123
17 1.405 0.045761
18 9.043 0.260247
19 6.725 0.200812
20 16.636 0.425663
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.025855
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-05_00:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 0.1 2.5 -0.4 -1.3 -0.4
-0.7 -2.5 -0.2 1.2 1.4 2.0
-1.1 0.9 1.1 0.4 1.3 -0.6
0.1 -3.3 -0.3 -0.8 1.3 0.0
0.2 -1.1 0.7 -0.2 -0.8 0.4
0.0 0.4 -1.0 -0.9 -0.8 -1.6
-0.5 -0.1 0.5 -0.1 -0.6 0.0
-1.1
Chi-square with 42 degrees of freedom:50.686416
z-score=0.947766, p-value=0.831718
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-05_00:31
Test no p-value
1 0.131827
2 0.470259
3 0.225329
4 0.092557
5 0.631524
6 0.009267
7 0.545912
8 0.885402
9 0.818520
10 0.056031
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.253271
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-05_00:31:
(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 66737 0.07 66557 0.18
3 25000.00 24903 0.38 25124 0.62
4 6666.67 6678 0.02 6713 0.32
5 1388.89 1386 0.01 1353 0.93
6 238.10 267 3.51 217 1.87
7 34.72 24 3.31 27 1.72
8 4.96 4 0.19 8 1.86
p=0.72132 p=0.72241
Number of rngs required: 687798, p-value: 0.242
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-05_00:31
No. of wins: Observed Expected
97893 98585.9
z-score=-3.099, pvalue=0.00097
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 65904 66666.7 8.725 8.725
2 37842 37654.3 0.935 9.660
3 27155 26954.7 1.488 11.148
4 19489 19313.5 1.595 12.744
5 13885 13851.4 0.081 12.825
6 10011 9943.5 0.458 13.283
7 7087 7145.0 0.471 13.754
8 5317 5139.1 6.160 19.914
9 3688 3699.9 0.038 19.952
10 2710 2666.3 0.716 20.669
11 1921 1923.3 0.003 20.672
12 1410 1388.7 0.325 20.997
13 1001 1003.7 0.007 21.004
14 718 726.1 0.091 21.096
15 527 525.8 0.003 21.098
16 345 381.2 3.429 24.527
17 264 276.5 0.569 25.095
18 194 200.8 0.232 25.328
19 138 146.0 0.437 25.764
20 108 106.2 0.030 25.794
21 286 287.1 0.004 25.799
Chisq= 25.80 for 20 degrees of freedom, p= 0.82744
SUMMARY of craptest
p-value for no. of wins: 0.000971
p-value for throws/game: 0.827438
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-05_00:31
No. of wins: Observed Expected
98508 98585.9
z-score=-0.348, pvalue=0.36383
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66354 66666.7 1.466 1.466
2 37628 37654.3 0.018 1.485
3 26954 26954.7 0.000 1.485
4 19345 19313.5 0.051 1.536
5 13876 13851.4 0.044 1.580
6 10078 9943.5 1.818 3.398
7 7247 7145.0 1.455 4.853
8 5146 5139.1 0.009 4.863
9 3725 3699.9 0.171 5.034
10 2623 2666.3 0.703 5.737
11 1954 1923.3 0.489 6.226
12 1426 1388.7 1.000 7.225
13 1009 1003.7 0.028 7.253
14 699 726.1 1.014 8.268
15 523 525.8 0.015 8.283
16 333 381.2 6.083 14.366
17 296 276.5 1.369 15.735
18 227 200.8 3.410 19.146
19 141 146.0 0.170 19.316
20 122 106.2 2.346 21.661
21 294 287.1 0.165 21.827
Chisq= 21.83 for 20 degrees of freedom, p= 0.65001
SUMMARY of craptest
p-value for no. of wins: 0.363834
p-value for throws/game: 0.650008
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0010,0.0061,0.0087,0.0093,0.0098,0.0114,0.0238,0.0244,0.0259,0.0309,
0.0311,0.0434,0.0458,0.0560,0.0574,0.0625,0.0632,0.0673,0.0700,0.0701,
0.0804,0.0821,0.0879,0.0906,0.0926,0.1015,0.1116,0.1150,0.1189,0.1274,
0.1277,0.1304,0.1318,0.1403,0.1408,0.1413,0.1491,0.1529,0.1537,0.1660,
0.1670,0.1719,0.1749,0.1756,0.1771,0.1772,0.1840,0.1885,0.1894,0.1951,
0.1952,0.1953,0.1970,0.1981,0.2008,0.2095,0.2135,0.2154,0.2243,0.2253,
0.2313,0.2326,0.2363,0.2389,0.2425,0.2459,0.2467,0.2489,0.2492,0.2533,
0.2533,0.2539,0.2602,0.2633,0.2703,0.2866,0.2881,0.3018,0.3155,0.3177,
0.3180,0.3204,0.3283,0.3309,0.3352,0.3366,0.3395,0.3455,0.3467,0.3638,
0.3656,0.3663,0.3776,0.3784,0.3875,0.3886,0.3901,0.3905,0.3958,0.3965,
0.3967,0.4000,0.4029,0.4060,0.4084,0.4128,0.4177,0.4180,0.4190,0.4236,
0.4257,0.4298,0.4398,0.4472,0.4474,0.4544,0.4636,0.4674,0.4692,0.4703,
0.4714,0.4726,0.4748,0.4779,0.4876,0.4882,0.4887,0.4915,0.4937,0.4967,
0.5011,0.5078,0.5100,0.5102,0.5111,0.5117,0.5173,0.5182,0.5182,0.5183,
0.5202,0.5252,0.5339,0.5360,0.5364,0.5442,0.5459,0.5529,0.5548,0.5560,
0.5568,0.5577,0.5585,0.5642,0.5705,0.5792,0.5817,0.5849,0.5857,0.5974,
0.6043,0.6056,0.6087,0.6179,0.6315,0.6332,0.6385,0.6500,0.6511,0.6512,
0.6525,0.6550,0.6575,0.6622,0.6637,0.6641,0.6662,0.6693,0.6735,0.6746,
0.6760,0.6845,0.6877,0.6916,0.6923,0.6935,0.7101,0.7162,0.7194,0.7213,
0.7224,0.7242,0.7290,0.7472,0.7496,0.7498,0.7522,0.7540,0.7545,0.7550,
0.7555,0.7689,0.7695,0.7728,0.7743,0.7768,0.7832,0.7863,0.7872,0.7890,
0.7904,0.8108,0.8134,0.8185,0.8194,0.8211,0.8226,0.8274,0.8308,0.8317,
0.8341,0.8343,0.8377,0.8384,0.8482,0.8493,0.8603,0.8644,0.8718,0.8724,
0.8773,0.8775,0.8813,0.8831,0.8854,0.8860,0.8878,0.8961,0.9058,0.9062,
0.9085,0.9124,0.9138,0.9143,0.9149,0.9189,0.9193,0.9200,0.9249,0.9269,
0.9280,0.9341,0.9380,0.9400,0.9450,0.9480,0.9536,0.9541,0.9568,0.9606,
0.9620,0.9659,0.9696,0.9801,0.9812,0.9931,0.9992,0.9992,0.9999,
Overall p-value after applying KStest on 269 p-values = 0.858048
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.