RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-19_10:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.70 17.8582 0.602162
2 to 25 15.72 14.1820 0.345821
3 to 26 15.66 16.5782 0.516719
4 to 27 15.53 32.7588 0.987909
5 to 28 15.97 16.0239 0.477861
6 to 29 15.69 26.4314 0.933048
7 to 30 15.84 6.3479 0.009474
8 to 31 15.82 21.2273 0.783714
9 to 32 15.75 12.1488 0.208957
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.770424
Tough bday spacings test for dh-ranFile-2018-06-19_10:31: 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 40 66 109 89 64 68 27 13 10 5
(O-E)^2/E 0.0 0.3 0.7 1.3 0.8 2.6 4.9 0.3 0.2 1.7 0.2
Birthday Spacings: Sum(O-E)^2/E= 12.973, p= 0.775
RESULTS OF GCD FOR dh-ranFile-2018-06-19_10:31
Euclid's algorithm:
p-value, steps to gcd: 0.981297
p-value, dist. of gcd's: 0.985023
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-19_10:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.672 0.225 0.662 0.491 0.003 0.142 0.495 0.963
Bits 8 to 15---> 0.788 0.911 0.195 0.427 0.705 0.428 0.424 0.342
Bits 16 to 23---> 0.158 0.027 0.796 0.881 0.476 0.794 0.139 0.109
Bits 24 to 31---> 0.974 0.604 0.215 0.662 0.088 0.466 0.257 0.978
KS test for the above 32 p values: 0.068
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-19_10:31,
p-values for 5 runs: 0.4040, 0.4541, 0.5483, 0.4327, 0.3768
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-19_10:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 231 211.4 1.814 1.814
r= 29 5072 5134.0 0.749 2.563
r= 30 23043 23103.0 0.156 2.719
r= 31 11654 11551.5 0.909 3.628
chi-square = 3.628 with df = 3; p-value = 0.695
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-19_10:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 218 211.4 0.205 0.205
r= 30 5102 5134.0 0.200 0.405
r= 31 23025 23103.0 0.264 0.668
r= 32 11655 11551.5 0.927 1.595
chi-square = 1.595 with df = 3; p-value = 0.339
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-19_10:31
b-rank test for bits 1 to 8, p=0.06265
b-rank test for bits 2 to 9, p=0.69091
b-rank test for bits 3 to 10, p=0.94405
b-rank test for bits 4 to 11, p=0.62518
b-rank test for bits 5 to 12, p=0.69045
b-rank test for bits 6 to 13, p=0.04613
b-rank test for bits 7 to 14, p=0.11465
b-rank test for bits 8 to 15, p=0.28173
b-rank test for bits 9 to 16, p=0.76791
b-rank test for bits 10 to 17, p=0.78765
b-rank test for bits 11 to 18, p=0.36063
b-rank test for bits 12 to 19, p=0.51521
b-rank test for bits 13 to 20, p=0.47971
b-rank test for bits 14 to 21, p=0.79427
b-rank test for bits 15 to 22, p=0.51361
b-rank test for bits 16 to 23, p=0.09541
b-rank test for bits 17 to 24, p=0.95334
b-rank test for bits 18 to 25, p=0.73329
b-rank test for bits 19 to 26, p=0.93049
b-rank test for bits 20 to 27, p=0.62851
b-rank test for bits 21 to 28, p=0.70401
b-rank test for bits 22 to 29, p=0.61883
b-rank test for bits 23 to 30, p=0.01493
b-rank test for bits 24 to 31, p=0.73094
b-rank test for bits 25 to 32, p=0.44761
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 = 0.462185
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-19_10:31
(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 141991 0.19 0.575666
2 141489 -0.98 0.163030
3 142119 0.49 0.687892
4 142153 0.57 0.715431
5 141856 -0.12 0.450419
6 141200 -1.66 0.048728
7 142062 0.36 0.639344
8 141651 -0.60 0.273063
9 140966 -2.20 0.013761
10 142732 1.92 0.972705
11 140936 -2.27 0.011479
12 142344 1.02 0.845086
13 141597 -0.73 0.232774
14 142373 1.08 0.860672
15 142776 2.02 0.978563
16 141747 -0.38 0.352242
17 141488 -0.98 0.162456
18 142175 0.62 0.732610
19 142016 0.25 0.598408
20 141872 -0.09 0.465249
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-19_10:31
Bits used No. missing words z-score p-value
23 to 32 141863 -0.1598 0.436536
22 to 31 141616 -1.0115 0.155893
21 to 30 142086 0.6092 0.728806
20 to 29 141805 -0.3598 0.359514
19 to 28 141284 -2.1563 0.015530
18 to 27 141931 0.0747 0.529783
17 to 26 141906 -0.0115 0.495419
16 to 25 141478 -1.4873 0.068462
15 to 24 140989 -3.1736 0.000753
14 to 23 141155 -2.6011 0.004646
13 to 22 141776 -0.4598 0.322845
12 to 21 142331 1.4540 0.927032
11 to 20 141423 -1.6770 0.046771
10 to 19 141732 -0.6115 0.270440
9 to 18 141782 -0.4391 0.330306
8 to 17 142163 0.8747 0.809138
7 to 16 141512 -1.3701 0.085327
6 to 15 141689 -0.7598 0.223699
5 to 14 141850 -0.2046 0.418948
4 to 13 142442 1.8368 0.966880
3 to 12 142469 1.9299 0.973190
2 to 11 142066 0.5402 0.705485
1 to 10 142275 1.2609 0.896333
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-19_10:31
Bits used No. missing words z-score p-value
28 to 32 141919 0.0328 0.513075
27 to 31 141875 -0.1164 0.453679
26 to 30 142708 2.7074 0.996609
25 to 29 142179 0.9141 0.819677
24 to 28 141708 -0.6825 0.247470
23 to 27 142132 0.7548 0.774820
22 to 26 142087 0.6023 0.726503
21 to 25 142178 0.9107 0.818785
20 to 24 142227 1.0768 0.859226
19 to 23 142583 2.2836 0.988803
18 to 22 142233 1.0972 0.863720
17 to 21 141904 -0.0181 0.492792
16 to 20 142029 0.4057 0.657504
15 to 19 142106 0.6667 0.747511
14 to 18 141689 -0.7469 0.227568
13 to 17 141568 -1.1571 0.123626
12 to 16 141742 -0.5672 0.285282
11 to 15 141701 -0.7062 0.240031
10 to 14 142154 0.8294 0.796558
9 to 13 141579 -1.1198 0.131407
8 to 12 142213 1.0294 0.848352
7 to 11 141938 0.0972 0.538711
6 to 10 141885 -0.0825 0.467135
5 to 9 141742 -0.5672 0.285282
4 to 8 141870 -0.1333 0.446969
3 to 7 142123 0.7243 0.765561
2 to 6 141786 -0.4181 0.337949
1 to 5 141710 -0.6757 0.249617
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-19_10:31
Bits used No. missing words z-score p-value
31 to 32 141603 -0.9036 0.183096
30 to 31 142287 1.1141 0.867376
29 to 30 141382 -1.5555 0.059908
28 to 29 141761 -0.4376 0.330856
27 to 28 141938 0.0846 0.533699
26 to 27 141625 -0.8387 0.200810
25 to 26 141559 -1.0334 0.150703
24 to 25 141929 0.0580 0.523135
23 to 24 142005 0.2822 0.611110
22 to 23 142343 1.2793 0.899598
21 to 22 141431 -1.4110 0.079122
20 to 21 141706 -0.5998 0.274322
19 to 20 141897 -0.0364 0.485493
18 to 19 141620 -0.8535 0.196696
17 to 18 141536 -1.1013 0.135390
16 to 17 142243 0.9843 0.837510
15 to 16 142103 0.5713 0.716101
14 to 15 141962 0.1554 0.561735
13 to 14 142302 1.1583 0.876633
12 to 13 141453 -1.3461 0.089134
11 to 12 141970 0.1790 0.571018
10 to 11 141616 -0.8653 0.193443
9 to 10 142319 1.2085 0.886566
8 to 9 142207 0.8781 0.810051
7 to 8 141472 -1.2901 0.098515
6 to 7 142180 0.7984 0.787691
5 to 6 142278 1.0875 0.861597
4 to 5 141908 -0.0039 0.498435
3 to 4 141317 -1.7473 0.040294
2 to 3 142155 0.7247 0.765679
1 to 2 141518 -1.1544 0.124175
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-19_10:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2569.18 0.978 0.836057
Test results for specific bytes for dh-ranFile-2018-06-19_10:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2535.72 0.505 0.693273
2 to 9 2427.19 -1.030 0.151565
3 to 10 2501.89 0.027 0.510647
4 to 11 2445.07 -0.777 0.218648
5 to 12 2418.43 -1.154 0.124346
6 to 13 2405.44 -1.337 0.090561
7 to 14 2573.81 1.044 0.851710
8 to 15 2504.51 0.064 0.525430
9 to 16 2491.19 -0.125 0.450406
10 to 17 2665.43 2.340 0.990347
11 to 18 2501.57 0.022 0.508881
12 to 19 2474.44 -0.361 0.358874
13 to 20 2459.21 -0.577 0.282041
14 to 21 2525.60 0.362 0.641356
15 to 22 2555.34 0.783 0.783064
16 to 23 2566.87 0.946 0.827855
17 to 24 2483.12 -0.239 0.405671
18 to 25 2591.92 1.300 0.903192
19 to 26 2519.91 0.282 0.610880
20 to 27 2460.93 -0.553 0.290271
21 to 28 2536.44 0.515 0.696861
22 to 29 2663.24 2.309 0.989516
23 to 30 2510.93 0.155 0.561423
24 to 31 2491.81 -0.116 0.453915
25 to 32 2428.39 -1.013 0.155584
CDPARK for dh-ranFile-2018-06-19_10:31: 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
3535 0.5479 0.708135
3552 1.3242 0.907282
3525 0.0913 0.536383
3538 0.6849 0.753306
3513 -0.4566 0.323972
3531 0.3653 0.642555
3544 0.9589 0.831196
3502 -0.9589 0.168804
3536 0.5936 0.723613
Square side=100, avg. no. parked=3532.40 sample std.=14.73
p-value of the KSTEST for those 10 p-values: 0.152033
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-19_10:31
0.3116,0.4894,0.7318,0.6929,0.7953,0.6514,0.9131,0.6018,0.0154,0.3416,
The KS test for those 10 p-values: 0.675597
The 3DSPHERES test for dh-ranFile-2018-06-19_10:31
sample no r^3 equiv. uni.
1 6.830 0.203602
2 11.528 0.319042
3 3.582 0.112551
4 16.145 0.416188
5 5.615 0.170701
6 7.350 0.217295
7 25.539 0.573144
8 105.110 0.969913
9 0.211 0.007002
10 55.784 0.844244
11 31.422 0.649151
12 17.505 0.442052
13 55.348 0.841963
14 107.765 0.972462
15 3.464 0.109061
16 5.358 0.163554
17 18.474 0.459794
18 77.213 0.923752
19 0.046 0.001518
20 28.996 0.619606
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.353772
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-19_10:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 0.5 0.1 -1.6 0.5 0.7
-0.1 0.9 -1.2 1.2 -0.5 1.6
0.4 0.2 -0.5 -0.6 -0.3 1.6
-1.4 -1.1 0.1 1.7 -0.3 -0.7
0.2 -0.7 0.0 -0.1 0.5 -0.7
-0.1 -0.1 -1.2 0.3 -0.8 1.0
0.0 -0.4 0.1 -0.1 -0.6 0.0
-0.1
Chi-square with 42 degrees of freedom:27.679100
z-score=-1.562538, p-value=0.043476
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-19_10:31
Test no p-value
1 0.061272
2 0.661134
3 0.493699
4 0.955032
5 0.078455
6 0.769235
7 0.452789
8 0.608309
9 0.019183
10 0.018626
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.165985
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-19_10:31:
(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 66672 0.00 66767 0.15
3 25000.00 24979 0.02 24936 0.16
4 6666.67 6662 0.00 6676 0.01
5 1388.89 1400 0.09 1365 0.41
6 238.10 249 0.50 212 2.86
7 34.72 32 0.21 36 0.05
8 4.96 5 0.00 7 0.84
p=0.00856 p=0.38867
Number of rngs required: 689053, p-value: 0.774
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-19_10:31
No. of wins: Observed Expected
98388 98585.9
z-score=-0.885, pvalue=0.18809
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66592 66666.7 0.084 0.084
2 37844 37654.3 0.955 1.039
3 27047 26954.7 0.316 1.355
4 19221 19313.5 0.443 1.798
5 13860 13851.4 0.005 1.803
6 9951 9943.5 0.006 1.809
7 7170 7145.0 0.087 1.896
8 5111 5139.1 0.153 2.049
9 3642 3699.9 0.905 2.954
10 2635 2666.3 0.367 3.322
11 1869 1923.3 1.535 4.856
12 1407 1388.7 0.240 5.096
13 1014 1003.7 0.105 5.202
14 709 726.1 0.405 5.606
15 532 525.8 0.072 5.679
16 377 381.2 0.045 5.724
17 287 276.5 0.396 6.119
18 187 200.8 0.952 7.072
19 141 146.0 0.170 7.242
20 93 106.2 1.644 8.886
21 311 287.1 1.987 10.873
Chisq= 10.87 for 20 degrees of freedom, p= 0.05056
SUMMARY of craptest
p-value for no. of wins: 0.188095
p-value for throws/game: 0.050559
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-19_10:31
No. of wins: Observed Expected
98507 98585.9
z-score=-0.353, pvalue=0.36216
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66577 66666.7 0.121 0.121
2 37785 37654.3 0.454 0.574
3 27158 26954.7 1.533 2.107
4 19320 19313.5 0.002 2.109
5 13807 13851.4 0.142 2.252
6 9788 9943.5 2.433 4.685
7 7044 7145.0 1.428 6.113
8 5127 5139.1 0.028 6.142
9 3568 3699.9 4.700 10.841
10 2764 2666.3 3.580 14.421
11 2018 1923.3 4.660 19.081
12 1357 1388.7 0.725 19.807
13 1011 1003.7 0.053 19.860
14 727 726.1 0.001 19.861
15 553 525.8 1.403 21.264
16 351 381.2 2.385 23.649
17 295 276.5 1.232 24.881
18 193 200.8 0.305 25.187
19 161 146.0 1.544 26.731
20 125 106.2 3.322 30.053
21 271 287.1 0.904 30.958
Chisq= 30.96 for 20 degrees of freedom, p= 0.94425
SUMMARY of craptest
p-value for no. of wins: 0.362156
p-value for throws/game: 0.944248
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0008,0.0015,0.0030,0.0046,0.0070,0.0086,0.0095,0.0115,0.0138,0.0149,
0.0154,0.0155,0.0186,0.0192,0.0274,0.0403,0.0435,0.0461,0.0468,0.0487,
0.0506,0.0599,0.0613,0.0626,0.0682,0.0685,0.0785,0.0791,0.0853,0.0882,
0.0891,0.0906,0.0954,0.0985,0.1086,0.1091,0.1126,0.1146,0.1236,0.1242,
0.1243,0.1314,0.1354,0.1392,0.1425,0.1507,0.1516,0.1520,0.1556,0.1559,
0.1577,0.1625,0.1630,0.1636,0.1660,0.1688,0.1707,0.1831,0.1881,0.1934,
0.1951,0.1967,0.2008,0.2036,0.2090,0.2153,0.2173,0.2186,0.2237,0.2251,
0.2276,0.2328,0.2400,0.2475,0.2496,0.2568,0.2704,0.2731,0.2743,0.2817,
0.2820,0.2853,0.2853,0.2903,0.3116,0.3190,0.3228,0.3240,0.3303,0.3309,
0.3379,0.3395,0.3416,0.3418,0.3458,0.3522,0.3538,0.3589,0.3595,0.3606,
0.3622,0.3768,0.3887,0.4040,0.4057,0.4162,0.4189,0.4244,0.4272,0.4278,
0.4327,0.4365,0.4421,0.4470,0.4476,0.4504,0.4504,0.4528,0.4537,0.4539,
0.4541,0.4598,0.4622,0.4652,0.4664,0.4671,0.4755,0.4779,0.4797,0.4855,
0.4894,0.4905,0.4928,0.4937,0.4950,0.4954,0.4984,0.5089,0.5106,0.5131,
0.5136,0.5152,0.5167,0.5231,0.5254,0.5298,0.5337,0.5364,0.5387,0.5483,
0.5614,0.5617,0.5710,0.5731,0.5757,0.5984,0.6018,0.6022,0.6044,0.6083,
0.6109,0.6111,0.6188,0.6196,0.6252,0.6285,0.6393,0.6414,0.6426,0.6492,
0.6514,0.6575,0.6611,0.6617,0.6617,0.6715,0.6756,0.6879,0.6904,0.6909,
0.6929,0.6933,0.6954,0.6969,0.7040,0.7046,0.7055,0.7081,0.7154,0.7161,
0.7236,0.7265,0.7288,0.7309,0.7318,0.7326,0.7333,0.7475,0.7533,0.7656,
0.7657,0.7679,0.7692,0.7704,0.7736,0.7748,0.7748,0.7831,0.7837,0.7876,
0.7877,0.7879,0.7943,0.7943,0.7953,0.7956,0.7966,0.8091,0.8101,0.8188,
0.8197,0.8279,0.8312,0.8361,0.8375,0.8420,0.8442,0.8451,0.8484,0.8517,
0.8592,0.8607,0.8616,0.8637,0.8674,0.8732,0.8766,0.8810,0.8866,0.8963,
0.8996,0.9032,0.9073,0.9111,0.9131,0.9238,0.9270,0.9305,0.9330,0.9440,
0.9442,0.9533,0.9550,0.9631,0.9669,0.9699,0.9725,0.9727,0.9732,0.9745,
0.9782,0.9786,0.9813,0.9850,0.9879,0.9888,0.9895,0.9903,0.9966,
Overall p-value after applying KStest on 269 p-values = 0.435359
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.