RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-09_15:31
(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 19.9289 0.722116
2 to 25 15.64 17.6011 0.585586
3 to 26 15.67 19.9437 0.722882
4 to 27 15.55 25.2393 0.910521
5 to 28 15.78 22.2839 0.825956
6 to 29 15.68 29.5965 0.970593
7 to 30 15.86 15.5459 0.443780
8 to 31 15.82 15.3054 0.426509
9 to 32 15.59 16.6071 0.518722
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.095776
Tough bday spacings test for dh-ranFile-2018-07-09_15:31: 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 13 44 76 93 92 79 44 29 14 10 6
(O-E)^2/E 1.6 1.5 0.1 0.2 0.3 0.0 1.3 0.0 0.1 1.7 0.9
Birthday Spacings: Sum(O-E)^2/E= 7.743, p= 0.346
RESULTS OF GCD FOR dh-ranFile-2018-07-09_15:31
Euclid's algorithm:
p-value, steps to gcd: 0.873022
p-value, dist. of gcd's: 0.965274
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-09_15:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.357 0.616 0.145 0.725 0.613 0.733 0.508 0.763
Bits 8 to 15---> 0.483 0.193 0.294 0.105 0.721 0.498 0.465 0.504
Bits 16 to 23---> 0.810 0.107 0.322 0.236 0.983 0.804 0.905 0.886
Bits 24 to 31---> 0.532 0.226 0.348 0.142 0.932 0.196 0.329 0.558
KS test for the above 32 p values: 0.146
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-09_15:31,
p-values for 5 runs: 0.3995, 0.2932, 0.2673, 0.1828, 0.4666
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-09_15:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 223 211.4 0.634 0.634
r= 29 5234 5134.0 1.947 2.582
r= 30 23071 23103.0 0.044 2.626
r= 31 11472 11551.5 0.547 3.174
chi-square = 3.174 with df = 3; p-value = 0.634
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-09_15:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 191 211.4 1.972 1.972
r= 30 5149 5134.0 0.044 2.016
r= 31 23292 23103.0 1.545 3.561
r= 32 11368 11551.5 2.916 6.477
chi-square = 6.477 with df = 3; p-value = 0.909
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-09_15:31
b-rank test for bits 1 to 8, p=0.16995
b-rank test for bits 2 to 9, p=0.83670
b-rank test for bits 3 to 10, p=0.84035
b-rank test for bits 4 to 11, p=0.88904
b-rank test for bits 5 to 12, p=0.76120
b-rank test for bits 6 to 13, p=0.83525
b-rank test for bits 7 to 14, p=0.84275
b-rank test for bits 8 to 15, p=0.87084
b-rank test for bits 9 to 16, p=0.96754
b-rank test for bits 10 to 17, p=0.09429
b-rank test for bits 11 to 18, p=0.58975
b-rank test for bits 12 to 19, p=0.31412
b-rank test for bits 13 to 20, p=0.70913
b-rank test for bits 14 to 21, p=0.42914
b-rank test for bits 15 to 22, p=0.84126
b-rank test for bits 16 to 23, p=0.01243
b-rank test for bits 17 to 24, p=0.50027
b-rank test for bits 18 to 25, p=0.77667
b-rank test for bits 19 to 26, p=0.74005
b-rank test for bits 20 to 27, p=0.20871
b-rank test for bits 21 to 28, p=0.21293
b-rank test for bits 22 to 29, p=0.88689
b-rank test for bits 23 to 30, p=0.82460
b-rank test for bits 24 to 31, p=0.03022
b-rank test for bits 25 to 32, p=0.45679
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 = 0.090195
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-09_15:31
(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 141827 -0.19 0.423730
2 141679 -0.54 0.295235
3 142380 1.10 0.864268
4 140876 -2.41 0.007882
5 141757 -0.36 0.360954
6 141031 -2.05 0.020076
7 141698 -0.49 0.310737
8 142001 0.21 0.584798
9 142012 0.24 0.594790
10 142219 0.72 0.765322
11 141943 0.08 0.531352
12 141805 -0.24 0.403708
13 141039 -2.03 0.021002
14 142236 0.76 0.777342
15 142093 0.43 0.666088
16 141195 -1.67 0.047559
17 141764 -0.34 0.367095
18 142379 1.10 0.863758
19 142435 1.23 0.890314
20 141038 -2.04 0.020884
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-09_15:31
Bits used No. missing words z-score p-value
23 to 32 142166 0.8851 0.811940
22 to 31 142209 1.0333 0.849279
21 to 30 142207 1.0264 0.847660
20 to 29 142016 0.3678 0.643499
19 to 28 141404 -1.7425 0.040709
18 to 27 142076 0.5747 0.717261
17 to 26 141830 -0.2736 0.392215
16 to 25 142018 0.3747 0.646067
15 to 24 141830 -0.2736 0.392215
14 to 23 141362 -1.8873 0.029557
13 to 22 141926 0.0575 0.522920
12 to 21 141782 -0.4391 0.330306
11 to 20 141406 -1.7356 0.041315
10 to 19 141768 -0.4873 0.313007
9 to 18 141877 -0.1115 0.455617
8 to 17 142339 1.4816 0.930779
7 to 16 142138 0.7885 0.784803
6 to 15 141991 0.2816 0.610883
5 to 14 141359 -1.8977 0.028868
4 to 13 141503 -1.4011 0.080586
3 to 12 141395 -1.7736 0.038069
2 to 11 141479 -1.4839 0.068918
1 to 10 141456 -1.5632 0.059002
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-09_15:31
Bits used No. missing words z-score p-value
28 to 32 142328 1.4192 0.922083
27 to 31 142086 0.5989 0.725374
26 to 30 141744 -0.5604 0.287589
25 to 29 142180 0.9175 0.820566
24 to 28 141651 -0.8757 0.190598
23 to 27 141553 -1.2079 0.113543
22 to 26 141928 0.0633 0.525232
21 to 25 141654 -0.8655 0.193375
20 to 24 142137 0.7718 0.779873
19 to 23 141939 0.1006 0.540057
18 to 22 142020 0.3752 0.646227
17 to 21 142141 0.7853 0.783868
16 to 20 141306 -2.0452 0.020418
15 to 19 142236 1.1074 0.865930
14 to 18 141906 -0.0113 0.495497
13 to 17 142069 0.5413 0.705834
12 to 16 141592 -1.0757 0.141032
11 to 15 141693 -0.7333 0.231681
10 to 14 141727 -0.6181 0.268265
9 to 13 142068 0.5379 0.704665
8 to 12 142270 1.2226 0.889262
7 to 11 141560 -1.1842 0.118173
6 to 10 142215 1.0362 0.849938
5 to 9 141931 0.0735 0.529279
4 to 8 142136 0.7684 0.778867
3 to 7 142149 0.8124 0.791731
2 to 6 141901 -0.0282 0.488737
1 to 5 141800 -0.3706 0.355464
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-09_15:31
Bits used No. missing words z-score p-value
31 to 32 142189 0.8250 0.795310
30 to 31 141981 0.2114 0.583719
29 to 30 141768 -0.4169 0.338375
28 to 29 141820 -0.2635 0.396079
27 to 28 142469 1.6509 0.950625
26 to 27 142010 0.2970 0.616752
25 to 26 141733 -0.5201 0.301480
24 to 25 141903 -0.0187 0.492551
23 to 24 141498 -1.2134 0.112496
22 to 23 142637 2.1465 0.984084
21 to 22 142012 0.3029 0.619002
20 to 21 142262 1.0403 0.850905
19 to 20 142246 0.9931 0.839676
18 to 19 141840 -0.2045 0.418976
17 to 18 141551 -1.0570 0.145251
16 to 17 142069 0.4710 0.681181
15 to 16 142194 0.8397 0.799471
14 to 15 142760 2.5094 0.993952
13 to 14 142225 0.9312 0.824120
12 to 13 141995 0.2527 0.599755
11 to 12 142433 1.5447 0.938797
10 to 11 141908 -0.0039 0.498435
9 to 10 142698 2.3265 0.990003
8 to 9 141851 -0.1721 0.431693
7 to 8 142689 2.2999 0.989273
6 to 7 141678 -0.6824 0.247496
5 to 6 142192 0.8338 0.797813
4 to 5 141486 -1.2488 0.105876
3 to 4 142098 0.5565 0.711082
2 to 3 141739 -0.5024 0.307676
1 to 2 142262 1.0403 0.850905
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-09_15:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2529.74 0.421 0.662968
Test results for specific bytes for dh-ranFile-2018-07-09_15:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2490.32 -0.137 0.445566
2 to 9 2491.59 -0.119 0.452666
3 to 10 2414.70 -1.206 0.113836
4 to 11 2524.05 0.340 0.633137
5 to 12 2371.04 -1.824 0.034089
6 to 13 2642.00 2.008 0.977689
7 to 14 2445.41 -0.772 0.220039
8 to 15 2534.51 0.488 0.687229
9 to 16 2585.87 1.214 0.887688
10 to 17 2470.82 -0.413 0.339909
11 to 18 2474.78 -0.357 0.360677
12 to 19 2459.93 -0.567 0.285445
13 to 20 2540.34 0.571 0.715852
14 to 21 2459.22 -0.577 0.282080
15 to 22 2492.39 -0.108 0.457123
16 to 23 2504.32 0.061 0.524338
17 to 24 2528.51 0.403 0.656578
18 to 25 2626.29 1.786 0.962956
19 to 26 2555.61 0.787 0.784213
20 to 27 2473.56 -0.374 0.354257
21 to 28 2497.37 -0.037 0.485159
22 to 29 2484.39 -0.221 0.412642
23 to 30 2440.56 -0.841 0.200275
24 to 31 2563.50 0.898 0.815413
25 to 32 2477.43 -0.319 0.374783
CDPARK for dh-ranFile-2018-07-09_15:31: 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
3544 0.9589 0.831196
3548 1.1416 0.873180
3515 -0.3653 0.357445
3544 0.9589 0.831196
3490 -1.5068 0.065925
3463 -2.7397 0.003075
3518 -0.2283 0.409702
3553 1.3699 0.914635
3537 0.6393 0.738676
3550 1.2329 0.891189
Square side=100, avg. no. parked=3526.20 sample std.=28.30
p-value of the KSTEST for those 10 p-values: 0.163624
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-09_15:31
0.7009,0.8970,0.5334,0.9806,0.6471,0.7041,0.3188,0.9218,0.2601,0.8404,
The KS test for those 10 p-values: 0.081690
The 3DSPHERES test for dh-ranFile-2018-07-09_15:31
sample no r^3 equiv. uni.
1 48.157 0.799158
2 16.899 0.430674
3 17.486 0.441701
4 56.621 0.848528
5 2.697 0.085985
6 3.422 0.107808
7 86.560 0.944164
8 102.004 0.966631
9 105.882 0.970678
10 80.460 0.931574
11 5.723 0.173678
12 30.451 0.637607
13 2.625 0.083772
14 57.516 0.852981
15 14.877 0.390986
16 27.621 0.601756
17 1.627 0.052786
18 8.348 0.242910
19 37.162 0.710245
20 10.370 0.292244
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.563547
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-09_15:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 -1.2 -0.4 1.5 -0.7 3.1
0.7 -2.2 -0.8 0.0 0.5 -1.4
-1.6 0.7 0.4 0.4 -0.2 1.9
1.0 -0.4 0.4 -1.6 0.4 1.5
-0.6 -2.3 -1.4 0.4 -0.2 -0.7
1.8 0.4 -0.8 0.7 0.8 -0.3
-1.4 2.4 0.1 -0.7 -1.3 0.0
2.7
Chi-square with 42 degrees of freedom:66.419503
z-score=2.664386, p-value=0.990450
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-09_15:31
Test no p-value
1 0.040510
2 0.590246
3 0.079015
4 0.635479
5 0.072281
6 0.539377
7 0.618085
8 0.004754
9 0.586850
10 0.375004
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.064791
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-09_15:31:
(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 66644 0.01 66599 0.07
3 25000.00 24968 0.04 25144 0.83
4 6666.67 6687 0.06 6636 0.14
5 1388.89 1419 0.65 1356 0.78
6 238.10 245 0.20 230 0.28
7 34.72 31 0.40 31 0.40
8 4.96 5 0.00 3 0.77
p=0.03190 p=0.22526
Number of rngs required: 687734, p-value: 0.220
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-09_15:31
No. of wins: Observed Expected
98427 98585.9
z-score=-0.711, pvalue=0.23869
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66496 66666.7 0.437 0.437
2 37799 37654.3 0.556 0.993
3 26829 26954.7 0.586 1.579
4 19277 19313.5 0.069 1.648
5 13862 13851.4 0.008 1.656
6 9962 9943.5 0.034 1.690
7 7186 7145.0 0.235 1.925
8 5115 5139.1 0.113 2.038
9 3742 3699.9 0.480 2.518
10 2621 2666.3 0.770 3.288
11 1947 1923.3 0.291 3.579
12 1442 1388.7 2.043 5.621
13 996 1003.7 0.059 5.681
14 745 726.1 0.490 6.171
15 552 525.8 1.302 7.472
16 385 381.2 0.039 7.511
17 283 276.5 0.151 7.662
18 202 200.8 0.007 7.669
19 147 146.0 0.007 7.676
20 108 106.2 0.030 7.706
21 304 287.1 0.993 8.699
Chisq= 8.70 for 20 degrees of freedom, p= 0.01386
SUMMARY of craptest
p-value for no. of wins: 0.238695
p-value for throws/game: 0.013864
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-09_15:31
No. of wins: Observed Expected
98580 98585.9
z-score=-0.026, pvalue=0.48955
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66861 66666.7 0.566 0.566
2 37661 37654.3 0.001 0.568
3 26717 26954.7 2.097 2.664
4 19396 19313.5 0.353 3.017
5 13959 13851.4 0.836 3.853
6 9886 9943.5 0.333 4.186
7 7176 7145.0 0.134 4.320
8 5095 5139.1 0.378 4.698
9 3682 3699.9 0.086 4.784
10 2589 2666.3 2.241 7.025
11 1843 1923.3 3.355 10.380
12 1423 1388.7 0.845 11.225
13 994 1003.7 0.094 11.319
14 729 726.1 0.011 11.331
15 538 525.8 0.281 11.612
16 368 381.2 0.454 12.066
17 302 276.5 2.344 14.410
18 217 200.8 1.302 15.712
19 164 146.0 2.223 17.935
20 97 106.2 0.800 18.734
21 303 287.1 0.879 19.613
Chisq= 19.61 for 20 degrees of freedom, p= 0.51767
SUMMARY of craptest
p-value for no. of wins: 0.489548
p-value for throws/game: 0.517669
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0031,0.0048,0.0079,0.0124,0.0139,0.0201,0.0204,0.0209,0.0210,0.0289,
0.0296,0.0302,0.0319,0.0341,0.0381,0.0405,0.0407,0.0413,0.0476,0.0528,
0.0590,0.0648,0.0659,0.0689,0.0723,0.0790,0.0806,0.0817,0.0838,0.0860,
0.0902,0.0943,0.0958,0.1052,0.1059,0.1070,0.1078,0.1125,0.1135,0.1138,
0.1182,0.1410,0.1416,0.1450,0.1453,0.1461,0.1636,0.1699,0.1737,0.1828,
0.1906,0.1928,0.1934,0.1959,0.2003,0.2087,0.2129,0.2198,0.2200,0.2253,
0.2265,0.2317,0.2357,0.2387,0.2429,0.2475,0.2601,0.2673,0.2683,0.2821,
0.2854,0.2876,0.2922,0.2932,0.2943,0.2952,0.3015,0.3077,0.3107,0.3130,
0.3141,0.3188,0.3220,0.3291,0.3303,0.3384,0.3399,0.3461,0.3478,0.3543,
0.3555,0.3571,0.3574,0.3607,0.3610,0.3671,0.3748,0.3750,0.3910,0.3922,
0.3922,0.3961,0.3995,0.4037,0.4097,0.4126,0.4190,0.4237,0.4265,0.4291,
0.4307,0.4317,0.4417,0.4438,0.4456,0.4527,0.4556,0.4568,0.4571,0.4649,
0.4666,0.4832,0.4852,0.4887,0.4895,0.4926,0.4955,0.4979,0.4984,0.5003,
0.5035,0.5082,0.5177,0.5187,0.5229,0.5243,0.5252,0.5293,0.5314,0.5316,
0.5334,0.5394,0.5401,0.5582,0.5635,0.5837,0.5848,0.5856,0.5869,0.5897,
0.5902,0.5948,0.5998,0.6018,0.6109,0.6127,0.6158,0.6168,0.6181,0.6190,
0.6331,0.6344,0.6355,0.6376,0.6435,0.6461,0.6462,0.6471,0.6566,0.6630,
0.6661,0.6812,0.6872,0.7009,0.7041,0.7047,0.7058,0.7091,0.7102,0.7111,
0.7159,0.7173,0.7213,0.7221,0.7229,0.7249,0.7254,0.7334,0.7387,0.7400,
0.7612,0.7634,0.7653,0.7767,0.7773,0.7789,0.7799,0.7839,0.7842,0.7848,
0.7917,0.7953,0.7978,0.7992,0.7995,0.8039,0.8103,0.8119,0.8154,0.8206,
0.8241,0.8246,0.8260,0.8312,0.8312,0.8352,0.8367,0.8397,0.8404,0.8404,
0.8413,0.8427,0.8477,0.8485,0.8493,0.8499,0.8509,0.8509,0.8530,0.8638,
0.8643,0.8659,0.8708,0.8730,0.8732,0.8859,0.8869,0.8877,0.8890,0.8893,
0.8903,0.8912,0.8970,0.9054,0.9094,0.9105,0.9146,0.9218,0.9221,0.9308,
0.9316,0.9321,0.9388,0.9442,0.9506,0.9630,0.9653,0.9666,0.9675,0.9706,
0.9707,0.9777,0.9806,0.9827,0.9841,0.9893,0.9900,0.9905,0.9940,
Overall p-value after applying KStest on 269 p-values = 0.343808
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.