RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-17_02:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.49 23.6871 0.871811
2 to 25 15.70 13.8044 0.319107
3 to 26 15.75 12.2031 0.212317
4 to 27 15.62 18.4695 0.640185
5 to 28 15.99 23.2014 0.857192
6 to 29 15.95 14.5934 0.375259
7 to 30 15.92 20.5232 0.751652
8 to 31 15.73 22.5754 0.836409
9 to 32 15.78 16.8961 0.538570
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.444802
Tough bday spacings test for dh-ranFile-2018-06-17_02:31: 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 8 37 78 115 102 65 43 22 19 5 6
(O-E)^2/E 0.1 0.0 0.3 3.1 0.2 2.2 1.6 2.0 1.1 0.4 0.9
Birthday Spacings: Sum(O-E)^2/E= 11.997, p= 0.715
RESULTS OF GCD FOR dh-ranFile-2018-06-17_02:31
Euclid's algorithm:
p-value, steps to gcd: 0.569092
p-value, dist. of gcd's: 0.047596
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-17_02:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.407 0.512 0.966 0.177 0.713 0.374 0.037 0.145
Bits 8 to 15---> 0.038 0.149 0.369 0.160 0.834 0.706 0.024 0.886
Bits 16 to 23---> 0.055 0.174 0.256 0.833 0.260 0.888 0.882 0.321
Bits 24 to 31---> 0.439 0.955 0.448 0.577 0.805 0.754 0.187 0.114
KS test for the above 32 p values: 0.627
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-17_02:31,
p-values for 5 runs: 0.2841, 0.4798, 0.2112, 0.3221, 0.5242
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-17_02:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 221 211.4 0.434 0.434
r= 29 5089 5134.0 0.395 0.829
r= 30 23113 23103.0 0.004 0.833
r= 31 11577 11551.5 0.056 0.889
chi-square = 0.889 with df = 3; p-value = 0.172
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-17_02:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 223 211.4 0.634 0.634
r= 30 5087 5134.0 0.430 1.065
r= 31 23122 23103.0 0.016 1.080
r= 32 11568 11551.5 0.024 1.104
chi-square = 1.104 with df = 3; p-value = 0.224
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-17_02:31
b-rank test for bits 1 to 8, p=0.74785
b-rank test for bits 2 to 9, p=0.76880
b-rank test for bits 3 to 10, p=0.24411
b-rank test for bits 4 to 11, p=0.37134
b-rank test for bits 5 to 12, p=0.12291
b-rank test for bits 6 to 13, p=0.23716
b-rank test for bits 7 to 14, p=0.57607
b-rank test for bits 8 to 15, p=0.12324
b-rank test for bits 9 to 16, p=0.08663
b-rank test for bits 10 to 17, p=0.34456
b-rank test for bits 11 to 18, p=0.46796
b-rank test for bits 12 to 19, p=0.79083
b-rank test for bits 13 to 20, p=0.29852
b-rank test for bits 14 to 21, p=0.31671
b-rank test for bits 15 to 22, p=0.09058
b-rank test for bits 16 to 23, p=0.18760
b-rank test for bits 17 to 24, p=0.14092
b-rank test for bits 18 to 25, p=0.41587
b-rank test for bits 19 to 26, p=0.17524
b-rank test for bits 20 to 27, p=0.59507
b-rank test for bits 21 to 28, p=0.36913
b-rank test for bits 22 to 29, p=0.91070
b-rank test for bits 23 to 30, p=0.53560
b-rank test for bits 24 to 31, p=0.63923
b-rank test for bits 25 to 32, p=0.23897
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 = 0.069696
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-17_02:31
(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 142268 0.84 0.798989
2 142442 1.24 0.893353
3 141872 -0.09 0.465249
4 141881 -0.07 0.473613
5 142303 0.92 0.821159
6 142226 0.74 0.770315
7 141940 0.07 0.528563
8 141918 0.02 0.508081
9 142014 0.24 0.596600
10 142298 0.91 0.818089
11 141193 -1.67 0.047098
12 141827 -0.19 0.423730
13 141593 -0.74 0.229927
14 142184 0.64 0.739483
15 142053 0.34 0.631443
16 142349 1.03 0.847852
17 142158 0.58 0.719381
18 141807 -0.24 0.405518
19 142308 0.93 0.824195
20 142462 1.29 0.901698
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-17_02:31
Bits used No. missing words z-score p-value
23 to 32 141818 -0.3149 0.376407
22 to 31 141875 -0.1184 0.452884
21 to 30 142019 0.3782 0.647349
20 to 29 141819 -0.3115 0.377717
19 to 28 142135 0.7782 0.781766
18 to 27 141686 -0.7701 0.220619
17 to 26 141500 -1.4115 0.079051
16 to 25 142388 1.6506 0.950588
15 to 24 141731 -0.6149 0.269300
14 to 23 141695 -0.7391 0.229933
13 to 22 141438 -1.6253 0.052052
12 to 21 142238 1.1333 0.871465
11 to 20 142228 1.0989 0.864086
10 to 19 141685 -0.7736 0.219598
9 to 18 142196 0.9885 0.838550
8 to 17 142257 1.1989 0.884709
7 to 16 142139 0.7920 0.785810
6 to 15 142249 1.1713 0.879256
5 to 14 141838 -0.2460 0.402855
4 to 13 141520 -1.3425 0.089714
3 to 12 142040 0.4506 0.673856
2 to 11 141956 0.1609 0.563926
1 to 10 141931 0.0747 0.529783
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-17_02:31
Bits used No. missing words z-score p-value
28 to 32 141759 -0.5096 0.305168
27 to 31 141749 -0.5435 0.293396
26 to 30 142100 0.6463 0.740970
25 to 29 141835 -0.2520 0.400534
24 to 28 141999 0.3040 0.619423
23 to 27 141386 -1.7740 0.038032
22 to 26 142396 1.6497 0.950501
21 to 25 142088 0.6057 0.727630
20 to 24 141784 -0.4248 0.335474
19 to 23 141940 0.1040 0.541402
18 to 22 141534 -1.2723 0.101632
17 to 21 141770 -0.4723 0.318355
16 to 20 141738 -0.5808 0.280695
15 to 19 142364 1.5413 0.938373
14 to 18 141942 0.1107 0.544091
13 to 17 142294 1.3040 0.903877
12 to 16 141917 0.0260 0.510371
11 to 15 142126 0.7345 0.768670
10 to 14 142144 0.7955 0.786836
9 to 13 142155 0.8328 0.797516
8 to 12 141626 -0.9604 0.168417
7 to 11 141889 -0.0689 0.472529
6 to 10 142008 0.3345 0.630989
5 to 9 142069 0.5413 0.705834
4 to 8 141949 0.1345 0.553486
3 to 7 141747 -0.5503 0.291067
2 to 6 141493 -1.4113 0.079080
1 to 5 141819 -0.3062 0.379725
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-17_02:31
Bits used No. missing words z-score p-value
31 to 32 142005 0.2822 0.611110
30 to 31 142182 0.8043 0.789399
29 to 30 141773 -0.4022 0.343786
28 to 29 142035 0.3707 0.644573
27 to 28 142405 1.4622 0.928150
26 to 27 142228 0.9400 0.826399
25 to 26 142271 1.0669 0.856985
24 to 25 141799 -0.3255 0.372418
23 to 24 142444 1.5772 0.942625
22 to 23 141854 -0.1632 0.435174
21 to 22 141874 -0.1042 0.458498
20 to 21 142178 0.7925 0.785976
19 to 20 141454 -1.3432 0.089611
18 to 19 142172 0.7748 0.780782
17 to 18 141743 -0.4906 0.311837
16 to 17 142065 0.4592 0.676956
15 to 16 142742 2.4563 0.992980
14 to 15 142112 0.5978 0.725029
13 to 14 142113 0.6008 0.726012
12 to 13 142159 0.7365 0.769284
11 to 12 141641 -0.7915 0.214316
10 to 11 141768 -0.4169 0.338375
9 to 10 141943 0.0993 0.539559
8 to 9 141623 -0.8446 0.199158
7 to 8 142589 2.0049 0.977515
6 to 7 142410 1.4769 0.930149
5 to 6 141335 -1.6942 0.045115
4 to 5 141856 -0.1573 0.437498
3 to 4 141486 -1.2488 0.105876
2 to 3 141692 -0.6411 0.260732
1 to 2 142373 1.3678 0.914306
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-17_02:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2414.45 -1.210 0.113158
Test results for specific bytes for dh-ranFile-2018-06-17_02:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2587.96 1.244 0.893232
2 to 9 2366.93 -1.882 0.029930
3 to 10 2428.54 -1.011 0.156092
4 to 11 2596.54 1.365 0.913910
5 to 12 2490.95 -0.128 0.449107
6 to 13 2399.38 -1.423 0.077373
7 to 14 2531.41 0.444 0.671570
8 to 15 2402.15 -1.384 0.083206
9 to 16 2467.58 -0.458 0.323304
10 to 17 2468.32 -0.448 0.327077
11 to 18 2599.09 1.401 0.919452
12 to 19 2477.26 -0.322 0.373906
13 to 20 2595.52 1.351 0.911618
14 to 21 2476.94 -0.326 0.372154
15 to 22 2515.30 0.216 0.585657
16 to 23 2610.94 1.569 0.941670
17 to 24 2478.69 -0.301 0.381593
18 to 25 2447.73 -0.739 0.229901
19 to 26 2482.28 -0.251 0.401036
20 to 27 2616.44 1.647 0.950191
21 to 28 2453.24 -0.661 0.254209
22 to 29 2436.58 -0.897 0.184883
23 to 30 2589.29 1.263 0.896667
24 to 31 2560.10 0.850 0.802330
25 to 32 2555.72 0.788 0.784667
CDPARK for dh-ranFile-2018-06-17_02:31: 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
3526 0.1370 0.554479
3521 -0.0913 0.463617
3501 -1.0046 0.157553
3507 -0.7306 0.232514
3567 2.0091 0.977738
3542 0.8676 0.807188
3518 -0.2283 0.409702
3527 0.1826 0.572463
3500 -1.0502 0.146807
3543 0.9132 0.819442
Square side=100, avg. no. parked=3525.20 sample std.=19.93
p-value of the KSTEST for those 10 p-values: 0.959731
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-17_02:31
0.3103,0.5600,0.9373,0.4744,0.9765,0.9122,0.1953,0.7017,0.4645,0.3213,
The KS test for those 10 p-values: 0.456752
The 3DSPHERES test for dh-ranFile-2018-06-17_02:31
sample no r^3 equiv. uni.
1 5.606 0.170447
2 2.049 0.066008
3 14.130 0.375622
4 62.621 0.875988
5 55.928 0.844989
6 15.142 0.396335
7 23.944 0.549832
8 5.709 0.173288
9 14.464 0.382538
10 2.740 0.087277
11 4.645 0.143434
12 0.939 0.030800
13 290.157 0.999937
14 0.537 0.017727
15 5.413 0.165098
16 4.864 0.149675
17 100.206 0.964570
18 31.379 0.648653
19 12.430 0.339212
20 70.057 0.903212
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.083410
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-17_02:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 -1.2 0.1 1.2 -0.5 1.4
0.5 0.7 -0.5 -1.7 0.4 -0.7
0.8 -1.0 -0.3 -0.9 1.1 -0.3
-0.7 2.3 -1.9 0.7 1.1 -1.3
0.7 0.4 0.3 -0.0 0.3 0.0
0.7 -0.2 0.6 -1.5 1.6 -1.4
1.4 0.2 0.5 -0.7 -1.3 0.0
0.8
Chi-square with 42 degrees of freedom:39.916637
z-score=-0.227314, p-value=0.437205
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-17_02:31
Test no p-value
1 0.007257
2 0.489110
3 0.209548
4 0.311206
5 0.266145
6 0.077124
7 0.107412
8 0.846430
9 0.291778
10 0.025147
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.010127
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-17_02:31:
(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 66666 0.00 66648 0.01
3 25000.00 25034 0.05 24969 0.04
4 6666.67 6642 0.09 6697 0.14
5 1388.89 1384 0.02 1391 0.00
6 238.10 234 0.07 247 0.33
7 34.72 35 0.00 43 1.97
8 4.96 4 0.19 4 0.19
p=0.00126 p=0.15200
Number of rngs required: 690014, p-value: 0.971
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-17_02:31
No. of wins: Observed Expected
98720 98585.9
z-score= 0.600, pvalue=0.72573
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66944 66666.7 1.154 1.154
2 37282 37654.3 3.681 4.835
3 26967 26954.7 0.006 4.841
4 19306 19313.5 0.003 4.844
5 13829 13851.4 0.036 4.880
6 9935 9943.5 0.007 4.887
7 7219 7145.0 0.766 5.653
8 5185 5139.1 0.410 6.064
9 3796 3699.9 2.498 8.562
10 2665 2666.3 0.001 8.562
11 1879 1923.3 1.022 9.584
12 1398 1388.7 0.062 9.646
13 965 1003.7 1.493 11.139
14 719 726.1 0.070 11.209
15 524 525.8 0.006 11.216
16 371 381.2 0.270 11.486
17 281 276.5 0.072 11.558
18 203 200.8 0.023 11.581
19 142 146.0 0.109 11.690
20 98 106.2 0.635 12.325
21 292 287.1 0.083 12.409
Chisq= 12.41 for 20 degrees of freedom, p= 0.09870
SUMMARY of craptest
p-value for no. of wins: 0.725733
p-value for throws/game: 0.098703
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-17_02:31
No. of wins: Observed Expected
98636 98585.9
z-score= 0.224, pvalue=0.58872
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66626 66666.7 0.025 0.025
2 37626 37654.3 0.021 0.046
3 26944 26954.7 0.004 0.050
4 19309 19313.5 0.001 0.051
5 14026 13851.4 2.200 2.252
6 9902 9943.5 0.174 2.425
7 7113 7145.0 0.144 2.569
8 5102 5139.1 0.267 2.836
9 3756 3699.9 0.852 3.688
10 2611 2666.3 1.147 4.835
11 1860 1923.3 2.085 6.920
12 1460 1388.7 3.657 10.577
13 1017 1003.7 0.176 10.752
14 696 726.1 1.251 12.003
15 510 525.8 0.477 12.480
16 382 381.2 0.002 12.482
17 291 276.5 0.756 13.238
18 235 200.8 5.814 19.052
19 130 146.0 1.750 20.802
20 102 106.2 0.167 20.970
21 302 287.1 0.772 21.742
Chisq= 21.74 for 20 degrees of freedom, p= 0.64530
SUMMARY of craptest
p-value for no. of wins: 0.588723
p-value for throws/game: 0.645303
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0013,0.0073,0.0101,0.0177,0.0241,0.0251,0.0299,0.0308,0.0368,0.0380,
0.0383,0.0451,0.0471,0.0476,0.0521,0.0549,0.0660,0.0697,0.0771,0.0774,
0.0791,0.0791,0.0832,0.0834,0.0866,0.0873,0.0896,0.0897,0.0906,0.0987,
0.1016,0.1059,0.1074,0.1132,0.1138,0.1229,0.1232,0.1409,0.1434,0.1449,
0.1468,0.1494,0.1497,0.1520,0.1561,0.1576,0.1603,0.1651,0.1684,0.1704,
0.1720,0.1733,0.1741,0.1752,0.1767,0.1849,0.1870,0.1876,0.1953,0.1992,
0.2095,0.2112,0.2123,0.2143,0.2196,0.2206,0.2239,0.2299,0.2299,0.2299,
0.2325,0.2372,0.2390,0.2441,0.2542,0.2559,0.2600,0.2607,0.2661,0.2693,
0.2807,0.2841,0.2911,0.2918,0.2934,0.2985,0.3052,0.3103,0.3112,0.3118,
0.3167,0.3184,0.3191,0.3206,0.3213,0.3221,0.3233,0.3271,0.3355,0.3384,
0.3392,0.3438,0.3446,0.3685,0.3691,0.3713,0.3722,0.3724,0.3739,0.3744,
0.3753,0.3756,0.3764,0.3777,0.3797,0.3816,0.3825,0.3963,0.4005,0.4010,
0.4029,0.4055,0.4067,0.4097,0.4159,0.4237,0.4352,0.4372,0.4375,0.4389,
0.4448,0.4480,0.4491,0.4529,0.4568,0.4585,0.4636,0.4645,0.4652,0.4680,
0.4725,0.4736,0.4744,0.4798,0.4891,0.5081,0.5104,0.5117,0.5242,0.5286,
0.5298,0.5356,0.5386,0.5396,0.5414,0.5441,0.5498,0.5535,0.5545,0.5600,
0.5639,0.5691,0.5725,0.5761,0.5773,0.5857,0.5887,0.5951,0.5966,0.6111,
0.6194,0.6274,0.6310,0.6314,0.6392,0.6402,0.6446,0.6453,0.6473,0.6487,
0.6716,0.6739,0.6770,0.7017,0.7058,0.7058,0.7126,0.7148,0.7194,0.7250,
0.7257,0.7260,0.7276,0.7395,0.7410,0.7479,0.7517,0.7541,0.7687,0.7688,
0.7693,0.7703,0.7808,0.7818,0.7847,0.7858,0.7860,0.7868,0.7894,0.7908,
0.7975,0.7990,0.8023,0.8053,0.8072,0.8181,0.8194,0.8212,0.8242,0.8264,
0.8330,0.8339,0.8364,0.8386,0.8450,0.8464,0.8479,0.8570,0.8572,0.8641,
0.8715,0.8718,0.8760,0.8793,0.8825,0.8847,0.8862,0.8876,0.8932,0.8934,
0.8967,0.9017,0.9032,0.9039,0.9107,0.9116,0.9122,0.9139,0.9143,0.9195,
0.9282,0.9301,0.9373,0.9384,0.9417,0.9426,0.9502,0.9505,0.9506,0.9554,
0.9597,0.9646,0.9658,0.9711,0.9765,0.9775,0.9777,0.9930,0.9999,
Overall p-value after applying KStest on 269 p-values = 0.513063
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.