RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2019-09-12_08:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.78 11.8836 0.192865
2 to 25 15.74 15.7037 0.455072
3 to 26 15.58 19.0731 0.675647
4 to 27 15.66 18.1986 0.623582
5 to 28 15.70 17.0040 0.545907
6 to 29 15.89 22.7845 0.843603
7 to 30 15.89 20.6359 0.757000
8 to 31 15.60 21.3764 0.790094
9 to 32 15.75 14.8252 0.391929
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.407023
Tough bday spacings test for dh-ranFile-2019-09-12_08:31: 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 28 76 98 96 81 63 24 17 7 4
(O-E)^2/E 1.1 2.0 0.1 0.0 0.0 0.1 2.3 1.1 0.3 0.0 0.0
Birthday Spacings: Sum(O-E)^2/E= 7.083, p= 0.282
RESULTS OF GCD FOR dh-ranFile-2019-09-12_08:31
Euclid's algorithm:
p-value, steps to gcd: 0.013206
p-value, dist. of gcd's: 0.110869
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2019-09-12_08:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.655 0.740 0.776 0.622 0.385 0.406 0.272 0.401
Bits 8 to 15---> 0.268 0.618 0.101 0.854 0.372 0.728 0.244 0.571
Bits 16 to 23---> 0.875 0.827 0.565 0.527 0.187 0.349 0.827 0.623
Bits 24 to 31---> 0.696 0.103 0.776 0.916 0.520 0.248 0.747 0.902
KS test for the above 32 p values: 0.740
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2019-09-12_08:31,
p-values for 5 runs: 0.3032, 0.4628, 0.5403, 0.9258, 0.3226
Rank test for binary matrices (31x31) for dh-ranFile-2019-09-12_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 212 211.4 0.002 0.002
r= 29 5091 5134.0 0.360 0.362
r= 30 22993 23103.0 0.524 0.886
r= 31 11704 11551.5 2.013 2.899
chi-square = 2.899 with df = 3; p-value = 0.592
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2019-09-12_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 219 211.4 0.272 0.272
r= 30 5046 5134.0 1.509 1.781
r= 31 23075 23103.0 0.034 1.815
r= 32 11660 11551.5 1.019 2.833
chi-square = 2.833 with df = 3; p-value = 0.582
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2019-09-12_08:31
b-rank test for bits 1 to 8, p=0.14062
b-rank test for bits 2 to 9, p=0.37488
b-rank test for bits 3 to 10, p=0.42526
b-rank test for bits 4 to 11, p=0.69246
b-rank test for bits 5 to 12, p=0.73906
b-rank test for bits 6 to 13, p=0.34426
b-rank test for bits 7 to 14, p=0.26077
b-rank test for bits 8 to 15, p=0.59132
b-rank test for bits 9 to 16, p=0.46776
b-rank test for bits 10 to 17, p=0.27322
b-rank test for bits 11 to 18, p=0.07093
b-rank test for bits 12 to 19, p=0.58492
b-rank test for bits 13 to 20, p=0.59272
b-rank test for bits 14 to 21, p=0.78906
b-rank test for bits 15 to 22, p=0.91618
b-rank test for bits 16 to 23, p=0.07946
b-rank test for bits 17 to 24, p=0.44776
b-rank test for bits 18 to 25, p=0.64363
b-rank test for bits 19 to 26, p=0.14860
b-rank test for bits 20 to 27, p=0.82622
b-rank test for bits 21 to 28, p=0.06538
b-rank test for bits 22 to 29, p=0.78759
b-rank test for bits 23 to 30, p=0.95898
b-rank test for bits 24 to 31, p=0.38054
b-rank test for bits 25 to 32, p=0.07500
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 = 0.857563
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2019-09-12_08:31
(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 141339 -1.33 0.091340
2 142508 1.40 0.919058
3 141336 -1.34 0.090195
4 141998 0.21 0.582063
5 141607 -0.71 0.239976
6 141748 -0.38 0.353109
7 141619 -0.68 0.248778
8 141271 -1.49 0.067925
9 142253 0.80 0.789003
10 142052 0.33 0.630562
11 141998 0.21 0.582063
12 141495 -0.97 0.166507
13 142202 0.68 0.752952
14 141890 -0.05 0.481989
15 141996 0.20 0.580237
16 142144 0.55 0.708255
17 141531 -0.88 0.188362
18 141940 0.07 0.528563
19 141729 -0.42 0.336756
20 141726 -0.43 0.334201
----------------------------------------------------------------
OPSO test for dh-ranFile-2019-09-12_08:31
Bits used No. missing words z-score p-value
23 to 32 141746 -0.5632 0.286647
22 to 31 141974 0.2230 0.588232
21 to 30 142104 0.6713 0.748978
20 to 29 142139 0.7920 0.785810
19 to 28 142042 0.4575 0.676338
18 to 27 142049 0.4816 0.684962
17 to 26 142032 0.4230 0.663852
16 to 25 141910 0.0023 0.500922
15 to 24 142049 0.4816 0.684962
14 to 23 142026 0.4023 0.656272
13 to 22 141892 -0.0598 0.476174
12 to 21 142178 0.9264 0.822894
11 to 20 141553 -1.2287 0.109588
10 to 19 141312 -2.0598 0.019711
9 to 18 142229 1.1023 0.864837
8 to 17 142148 0.8230 0.794746
7 to 16 141655 -0.8770 0.190243
6 to 15 141707 -0.6977 0.242686
5 to 14 141592 -1.0942 0.136925
4 to 13 142065 0.5368 0.704295
3 to 12 141920 0.0368 0.514675
2 to 11 141927 0.0609 0.524293
1 to 10 141447 -1.5942 0.055441
-----------------------------------------------------------------
OQSO test for dh-ranFile-2019-09-12_08:31
Bits used No. missing words z-score p-value
28 to 32 141962 0.1785 0.570852
27 to 31 142417 1.7209 0.957367
26 to 30 141890 -0.0655 0.473878
25 to 29 141409 -1.6960 0.044940
24 to 28 142068 0.5379 0.704665
23 to 27 141430 -1.6248 0.052098
22 to 26 141529 -1.2893 0.098655
21 to 25 141670 -0.8113 0.208600
20 to 24 142658 2.5379 0.994423
19 to 23 142244 1.1345 0.871702
18 to 22 141942 0.1107 0.544091
17 to 21 141747 -0.5503 0.291067
16 to 20 142154 0.8294 0.796558
15 to 19 141710 -0.6757 0.249617
14 to 18 141981 0.2429 0.595978
13 to 17 141530 -1.2859 0.099245
12 to 16 141665 -0.8282 0.203768
11 to 15 142175 0.9006 0.816093
10 to 14 142200 0.9853 0.837767
9 to 13 141728 -0.6147 0.269384
8 to 12 141650 -0.8791 0.189678
7 to 11 142069 0.5413 0.705834
6 to 10 141955 0.1548 0.561516
5 to 9 141960 0.1718 0.568188
4 to 8 141643 -0.9028 0.183312
3 to 7 141835 -0.2520 0.400534
2 to 6 141950 0.1379 0.554826
1 to 5 142504 2.0158 0.978091
-----------------------------------------------------------------
DNA test for dh-ranFile-2019-09-12_08:31
Bits used No. missing words z-score p-value
31 to 32 142103 0.5713 0.716101
30 to 31 142290 1.1229 0.869264
29 to 30 141851 -0.1721 0.431693
28 to 29 141695 -0.6322 0.263614
27 to 28 142071 0.4769 0.683284
26 to 27 141950 0.1200 0.547747
25 to 26 142118 0.6155 0.730903
24 to 25 142309 1.1790 0.880794
23 to 24 142092 0.5388 0.705005
22 to 23 141434 -1.4022 0.080435
21 to 22 141993 0.2468 0.597474
20 to 21 141777 -0.3904 0.348137
19 to 20 142129 0.6480 0.741506
18 to 19 141423 -1.4346 0.075700
17 to 18 141434 -1.4022 0.080435
16 to 17 142016 0.3147 0.623490
15 to 16 142000 0.2675 0.605444
14 to 15 141613 -0.8741 0.191024
13 to 14 141756 -0.4523 0.325526
12 to 13 141539 -1.0924 0.137325
11 to 12 141998 0.2616 0.603171
10 to 11 142391 1.4209 0.922321
9 to 10 141961 0.1524 0.560572
8 to 9 142620 2.0964 0.981975
7 to 8 140925 -2.9036 0.001844
6 to 7 141729 -0.5319 0.297381
5 to 6 141768 -0.4169 0.338375
4 to 5 142142 0.6863 0.753751
3 to 4 142016 0.3147 0.623490
2 to 3 141351 -1.6470 0.049780
1 to 2 142091 0.5359 0.703986
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2019-09-12_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2482.31 -0.250 0.401206
Test results for specific bytes for dh-ranFile-2019-09-12_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2561.17 0.865 0.806496
2 to 9 2442.28 -0.816 0.207152
3 to 10 2544.24 0.626 0.734217
4 to 11 2484.57 -0.218 0.413613
5 to 12 2482.73 -0.244 0.403514
6 to 13 2528.46 0.402 0.656325
7 to 14 2430.40 -0.984 0.162480
8 to 15 2602.38 1.448 0.926172
9 to 16 2529.71 0.420 0.662804
10 to 17 2555.63 0.787 0.784286
11 to 18 2392.16 -1.525 0.063616
12 to 19 2491.78 -0.116 0.453714
13 to 20 2467.74 -0.456 0.324108
14 to 21 2367.61 -1.872 0.030589
15 to 22 2511.17 0.158 0.562784
16 to 23 2377.36 -1.734 0.041420
17 to 24 2544.74 0.633 0.736564
18 to 25 2481.04 -0.268 0.394284
19 to 26 2511.42 0.162 0.564178
20 to 27 2601.32 1.433 0.924058
21 to 28 2511.84 0.167 0.566485
22 to 29 2399.92 -1.415 0.078475
23 to 30 2532.71 0.463 0.678175
24 to 31 2463.98 -0.509 0.305242
25 to 32 2648.55 2.101 0.982171
CDPARK for dh-ranFile-2019-09-12_08:31: 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
3506 -0.7763 0.218799
3505 -0.8219 0.205562
3546 1.0502 0.853193
3513 -0.4566 0.323972
3497 -1.1872 0.117571
3488 -1.5982 0.055002
3529 0.2740 0.607947
3491 -1.4612 0.071982
3527 0.1826 0.572463
3517 -0.2740 0.392053
Square side=100, avg. no. parked=3511.90 sample std.=17.39
p-value of the KSTEST for those 10 p-values: 0.142798
Results for the MINIMUM DISTANCE test for dh-ranFile-2019-09-12_08:31
0.7496,0.1759,0.6158,0.6966,0.8979,0.3409,0.6447,0.9685,0.3205,0.1948,
The KS test for those 10 p-values: 0.797291
The 3DSPHERES test for dh-ranFile-2019-09-12_08:31
sample no r^3 equiv. uni.
1 23.330 0.540520
2 8.883 0.256298
3 34.006 0.678104
4 25.955 0.579016
5 55.153 0.840932
6 58.696 0.858652
7 24.980 0.565118
8 3.673 0.115222
9 14.681 0.386976
10 90.684 0.951335
11 2.057 0.066256
12 14.280 0.378739
13 41.876 0.752380
14 29.849 0.630260
15 48.273 0.799934
16 35.371 0.692423
17 33.542 0.673084
18 12.429 0.339198
19 9.276 0.265972
20 10.542 0.296297
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.740265
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2019-09-12_08:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 0.5 -0.8 -0.3 -0.5 -2.4
1.6 -1.0 0.0 -0.5 0.0 0.8
1.2 -0.8 -0.7 0.5 1.4 1.1
0.1 -0.3 -1.9 -1.1 -0.5 1.9
-0.5 -0.2 0.4 -1.7 -0.7 0.3
0.5 0.3 0.2 1.2 0.1 0.1
-0.5 -0.1 -0.8 -0.1 -0.6 -1.0
0.8
Chi-square with 42 degrees of freedom:35.223640
z-score=-0.739362, p-value=0.239007
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2019-09-12_08:31
Test no p-value
1 0.511854
2 0.860177
3 0.871340
4 0.683387
5 0.666236
6 0.943125
7 0.261370
8 0.167156
9 0.272948
10 0.046711
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.954850
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2019-09-12_08:31:
(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 66522 0.31 66792 0.24
3 25000.00 24945 0.12 25105 0.44
4 6666.67 6851 5.10 6461 6.35
5 1388.89 1389 0.00 1354 0.88
6 238.10 259 1.84 242 0.06
7 34.72 31 0.40 42 1.53
8 4.96 2 1.77 3 0.77
p=0.85421 p=0.88600
Number of rngs required: 690833, p-value: 0.998
RESULTS OF CRAPS TEST for dh-ranFile-2019-09-12_08:31
No. of wins: Observed Expected
99033 98585.9
z-score= 2.000, pvalue=0.97724
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66713 66666.7 0.032 0.032
2 37532 37654.3 0.397 0.430
3 26954 26954.7 0.000 0.430
4 19421 19313.5 0.599 1.028
5 13889 13851.4 0.102 1.130
6 10112 9943.5 2.854 3.984
7 7116 7145.0 0.118 4.102
8 5139 5139.1 0.000 4.102
9 3701 3699.9 0.000 4.102
10 2582 2666.3 2.665 6.768
11 1909 1923.3 0.107 6.874
12 1457 1388.7 3.355 10.229
13 947 1003.7 3.205 13.434
14 713 726.1 0.238 13.672
15 525 525.8 0.001 13.673
16 323 381.2 8.872 22.545
17 263 276.5 0.663 23.208
18 198 200.8 0.040 23.248
19 137 146.0 0.553 23.801
20 97 106.2 0.800 24.600
21 272 287.1 0.796 25.396
Chisq= 25.40 for 20 degrees of freedom, p= 0.81330
SUMMARY of craptest
p-value for no. of wins: 0.977243
p-value for throws/game: 0.813299
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2019-09-12_08:31
No. of wins: Observed Expected
98751 98585.9
z-score= 0.739, pvalue=0.76993
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66662 66666.7 0.000 0.000
2 37594 37654.3 0.097 0.097
3 27117 26954.7 0.977 1.074
4 19243 19313.5 0.257 1.331
5 13908 13851.4 0.231 1.562
6 10093 9943.5 2.246 3.808
7 7146 7145.0 0.000 3.809
8 5148 5139.1 0.016 3.824
9 3622 3699.9 1.639 5.463
10 2572 2666.3 3.335 8.798
11 1863 1923.3 1.892 10.690
12 1334 1388.7 2.158 12.848
13 1062 1003.7 3.385 16.232
14 706 726.1 0.559 16.791
15 544 525.8 0.627 17.418
16 387 381.2 0.090 17.508
17 273 276.5 0.045 17.553
18 201 200.8 0.000 17.554
19 143 146.0 0.061 17.615
20 100 106.2 0.364 17.978
21 282 287.1 0.091 18.069
Chisq= 18.07 for 20 degrees of freedom, p= 0.41716
SUMMARY of craptest
p-value for no. of wins: 0.769928
p-value for throws/game: 0.417164
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0018,0.0132,0.0197,0.0306,0.0414,0.0449,0.0467,0.0498,0.0521,0.0550,
0.0554,0.0636,0.0654,0.0663,0.0679,0.0709,0.0720,0.0750,0.0757,0.0785,
0.0795,0.0804,0.0804,0.0902,0.0913,0.0987,0.0992,0.1012,0.1033,0.1096,
0.1109,0.1152,0.1176,0.1369,0.1373,0.1406,0.1428,0.1486,0.1625,0.1665,
0.1672,0.1759,0.1833,0.1875,0.1884,0.1897,0.1902,0.1910,0.1929,0.1948,
0.2038,0.2056,0.2072,0.2086,0.2188,0.2390,0.2400,0.2427,0.2442,0.2479,
0.2488,0.2496,0.2563,0.2608,0.2614,0.2636,0.2660,0.2681,0.2694,0.2719,
0.2729,0.2732,0.2824,0.2866,0.2911,0.2963,0.2974,0.3032,0.3052,0.3205,
0.3226,0.3240,0.3241,0.3255,0.3342,0.3368,0.3384,0.3392,0.3409,0.3443,
0.3481,0.3487,0.3531,0.3722,0.3749,0.3787,0.3805,0.3847,0.3870,0.3919,
0.3921,0.3943,0.4005,0.4012,0.4012,0.4035,0.4063,0.4070,0.4136,0.4172,
0.4253,0.4317,0.4478,0.4537,0.4551,0.4628,0.4678,0.4739,0.4762,0.4820,
0.5009,0.5119,0.5147,0.5203,0.5243,0.5269,0.5286,0.5403,0.5405,0.5441,
0.5459,0.5477,0.5548,0.5606,0.5615,0.5628,0.5642,0.5649,0.5651,0.5665,
0.5682,0.5707,0.5709,0.5725,0.5790,0.5802,0.5820,0.5821,0.5821,0.5849,
0.5882,0.5913,0.5925,0.5927,0.5960,0.5975,0.6032,0.6054,0.6079,0.6158,
0.6180,0.6225,0.6230,0.6235,0.6235,0.6236,0.6303,0.6306,0.6436,0.6447,
0.6545,0.6563,0.6563,0.6628,0.6639,0.6662,0.6731,0.6756,0.6763,0.6781,
0.6782,0.6833,0.6834,0.6850,0.6850,0.6924,0.6925,0.6957,0.6966,0.7040,
0.7043,0.7047,0.7050,0.7058,0.7083,0.7161,0.7280,0.7309,0.7342,0.7366,
0.7391,0.7395,0.7398,0.7403,0.7415,0.7470,0.7490,0.7496,0.7524,0.7530,
0.7538,0.7570,0.7699,0.7756,0.7761,0.7843,0.7858,0.7876,0.7890,0.7891,
0.7901,0.7947,0.7966,0.7973,0.7999,0.8065,0.8133,0.8161,0.8229,0.8262,
0.8270,0.8275,0.8378,0.8409,0.8436,0.8532,0.8540,0.8542,0.8576,0.8587,
0.8602,0.8648,0.8693,0.8713,0.8717,0.8748,0.8808,0.8860,0.8979,0.9024,
0.9162,0.9163,0.9191,0.9223,0.9241,0.9258,0.9262,0.9431,0.9513,0.9549,
0.9574,0.9590,0.9685,0.9772,0.9781,0.9820,0.9822,0.9944,0.9983,
Overall p-value after applying KStest on 269 p-values = 0.320168
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.