RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-15_16:31
(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 22.1517 0.821046
2 to 25 15.70 22.0687 0.817909
3 to 26 15.77 24.6782 0.897852
4 to 27 15.82 12.2595 0.215828
5 to 28 15.49 26.5332 0.934722
6 to 29 15.77 29.7137 0.971515
7 to 30 15.87 7.2464 0.019872
8 to 31 15.80 29.6666 0.971147
9 to 32 15.96 16.2247 0.492032
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.023842
Tough bday spacings test for dh-ranFile-2018-06-15_16:31: 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 5 36 60 102 102 73 69 32 9 8 4
(O-E)^2/E 1.9 0.0 2.4 0.2 0.2 0.3 5.5 0.2 2.3 0.3 0.0
Birthday Spacings: Sum(O-E)^2/E= 13.288, p= 0.792
RESULTS OF GCD FOR dh-ranFile-2018-06-15_16:31
Euclid's algorithm:
p-value, steps to gcd: 0.033416
p-value, dist. of gcd's: 0.677678
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-15_16:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.528 0.718 0.836 0.493 0.746 0.656 0.740 0.222
Bits 8 to 15---> 0.821 0.274 0.811 0.391 0.860 0.157 0.227 0.526
Bits 16 to 23---> 0.808 0.854 0.591 0.548 0.633 0.064 0.917 0.592
Bits 24 to 31---> 0.163 0.821 0.268 0.153 0.553 0.334 0.197 0.077
KS test for the above 32 p values: 0.370
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-15_16:31,
p-values for 5 runs: 0.9751, 0.5842, 0.4810, 0.3782, 0.0973
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-15_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 227 211.4 1.148 1.148
r= 29 5156 5134.0 0.094 1.243
r= 30 23067 23103.0 0.056 1.299
r= 31 11550 11551.5 0.000 1.299
chi-square = 1.299 with df = 3; p-value = 0.271
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-15_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 250 211.4 7.041 7.041
r= 30 5201 5134.0 0.874 7.915
r= 31 23041 23103.0 0.167 8.082
r= 32 11508 11551.5 0.164 8.246
chi-square = 8.246 with df = 3; p-value = 0.959
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-15_16:31
b-rank test for bits 1 to 8, p=0.69913
b-rank test for bits 2 to 9, p=0.98586
b-rank test for bits 3 to 10, p=0.80852
b-rank test for bits 4 to 11, p=0.86802
b-rank test for bits 5 to 12, p=0.00664
b-rank test for bits 6 to 13, p=0.49276
b-rank test for bits 7 to 14, p=0.60343
b-rank test for bits 8 to 15, p=0.65515
b-rank test for bits 9 to 16, p=0.60699
b-rank test for bits 10 to 17, p=0.53222
b-rank test for bits 11 to 18, p=0.42664
b-rank test for bits 12 to 19, p=0.40683
b-rank test for bits 13 to 20, p=0.90620
b-rank test for bits 14 to 21, p=0.07345
b-rank test for bits 15 to 22, p=0.07203
b-rank test for bits 16 to 23, p=0.45213
b-rank test for bits 17 to 24, p=0.48346
b-rank test for bits 18 to 25, p=0.67221
b-rank test for bits 19 to 26, p=0.74224
b-rank test for bits 20 to 27, p=0.45882
b-rank test for bits 21 to 28, p=0.62313
b-rank test for bits 22 to 29, p=0.12291
b-rank test for bits 23 to 30, p=0.95438
b-rank test for bits 24 to 31, p=0.70085
b-rank test for bits 25 to 32, p=0.17676
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 = 0.570765
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-15_16:31
(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 141552 -0.83 0.201892
2 141518 -0.91 0.180274
3 142142 0.54 0.706649
4 142687 1.82 0.965390
5 142588 1.59 0.943594
6 141401 -1.19 0.117478
7 142582 1.57 0.941985
8 142423 1.20 0.884962
9 141353 -1.30 0.096829
10 142537 1.47 0.928746
11 142397 1.14 0.872735
12 142795 2.07 0.980742
13 142578 1.56 0.940893
14 141573 -0.79 0.215987
15 141508 -0.94 0.174203
16 141609 -0.70 0.241431
17 141547 -0.85 0.198619
18 142392 1.13 0.870284
19 142615 1.65 0.950402
20 142662 1.76 0.960675
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-15_16:31
Bits used No. missing words z-score p-value
23 to 32 142183 0.9437 0.827336
22 to 31 141619 -1.0011 0.158380
21 to 30 141509 -1.3804 0.083724
20 to 29 142582 2.3196 0.989817
19 to 28 142041 0.4540 0.675098
18 to 27 141674 -0.8115 0.208544
17 to 26 141709 -0.6908 0.244848
16 to 25 141279 -2.1736 0.014869
15 to 24 141928 0.0644 0.525666
14 to 23 141662 -0.8529 0.196868
13 to 22 141950 0.1402 0.555765
12 to 21 141703 -0.7115 0.238393
11 to 20 141846 -0.2184 0.413567
10 to 19 142706 2.7471 0.996994
9 to 18 141509 -1.3804 0.083724
8 to 17 141893 -0.0563 0.477547
7 to 16 142293 1.3230 0.907082
6 to 15 141901 -0.0287 0.488542
5 to 14 142096 0.6437 0.740112
4 to 13 142160 0.8644 0.806310
3 to 12 141982 0.2506 0.598933
2 to 11 141744 -0.5701 0.284304
1 to 10 141672 -0.8184 0.206570
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-15_16:31
Bits used No. missing words z-score p-value
28 to 32 142202 0.9921 0.839426
27 to 31 141565 -1.1672 0.121561
26 to 30 142002 0.3141 0.623291
25 to 29 141934 0.0836 0.533324
24 to 28 142059 0.5074 0.694048
23 to 27 142034 0.4226 0.663710
22 to 26 142368 1.5548 0.940005
21 to 25 142313 1.3684 0.914402
20 to 24 141737 -0.5842 0.279553
19 to 23 141580 -1.1164 0.132131
18 to 22 141658 -0.8520 0.197116
17 to 21 141834 -0.2554 0.399224
16 to 20 141757 -0.5164 0.302797
15 to 19 141151 -2.5706 0.005076
14 to 18 142131 0.7514 0.773801
13 to 17 141754 -0.5265 0.299256
12 to 16 141713 -0.6655 0.252857
11 to 15 141652 -0.8723 0.191521
10 to 14 141808 -0.3435 0.365614
9 to 13 141931 0.0735 0.529279
8 to 12 142006 0.3277 0.628429
7 to 11 141409 -1.6960 0.044940
6 to 10 141702 -0.7028 0.241086
5 to 9 142422 1.7379 0.958883
4 to 8 141628 -0.9537 0.170128
3 to 7 142065 0.5277 0.701145
2 to 6 141844 -0.2215 0.412368
1 to 5 141209 -2.3740 0.008798
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-15_16:31
Bits used No. missing words z-score p-value
31 to 32 141675 -0.6912 0.244708
30 to 31 141767 -0.4199 0.337297
29 to 30 141185 -2.1367 0.016313
28 to 29 141773 -0.4022 0.343786
27 to 28 142523 1.8102 0.964870
26 to 27 142120 0.6214 0.732847
25 to 26 141515 -1.1632 0.122371
24 to 25 141739 -0.5024 0.307676
23 to 24 142160 0.7394 0.770180
22 to 23 141852 -0.1691 0.432853
21 to 22 142783 2.5772 0.995020
20 to 21 142383 1.3973 0.918832
19 to 20 142521 1.8043 0.964411
18 to 19 141934 0.0728 0.529007
17 to 18 141324 -1.7266 0.042116
16 to 17 142103 0.5713 0.716101
15 to 16 141891 -0.0541 0.478439
14 to 15 142427 1.5271 0.936626
13 to 14 141618 -0.8594 0.195065
12 to 13 141213 -2.0541 0.019984
11 to 12 141470 -1.2960 0.097495
10 to 11 142506 1.7601 0.960804
9 to 10 141969 0.1760 0.569860
8 to 9 141391 -1.5290 0.063133
7 to 8 142088 0.5271 0.700921
6 to 7 141858 -0.1514 0.439824
5 to 6 141654 -0.7532 0.225669
4 to 5 141957 0.1406 0.555915
3 to 4 141948 0.1141 0.545409
2 to 3 142720 2.3914 0.991607
1 to 2 141816 -0.2753 0.391539
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-15_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2545.80 0.648 0.741427
Test results for specific bytes for dh-ranFile-2018-06-15_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2397.60 -1.448 0.073786
2 to 9 2502.97 0.042 0.516767
3 to 10 2502.34 0.033 0.513212
4 to 11 2548.99 0.693 0.755795
5 to 12 2439.62 -0.854 0.196585
6 to 13 2507.60 0.108 0.542807
7 to 14 2537.50 0.530 0.702082
8 to 15 2454.66 -0.641 0.260714
9 to 16 2526.28 0.372 0.644932
10 to 17 2371.36 -1.819 0.034434
11 to 18 2478.01 -0.311 0.377882
12 to 19 2609.17 1.544 0.938693
13 to 20 2503.23 0.046 0.518196
14 to 21 2607.56 1.521 0.935887
15 to 22 2432.50 -0.955 0.169897
16 to 23 2643.87 2.035 0.979055
17 to 24 2582.84 1.171 0.879299
18 to 25 2612.68 1.594 0.944481
19 to 26 2529.87 0.422 0.663643
20 to 27 2470.27 -0.420 0.337076
21 to 28 2497.75 -0.032 0.487324
22 to 29 2437.12 -0.889 0.186942
23 to 30 2538.75 0.548 0.708138
24 to 31 2460.27 -0.562 0.287114
25 to 32 2537.95 0.537 0.704267
CDPARK for dh-ranFile-2018-06-15_16:31: 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
3521 -0.0913 0.463617
3510 -0.5936 0.276387
3546 1.0502 0.853193
3545 1.0046 0.842447
3486 -1.6895 0.045562
3528 0.2283 0.590298
3512 -0.5023 0.307734
3523 0.0000 0.500000
3537 0.6393 0.738676
3527 0.1826 0.572463
Square side=100, avg. no. parked=3523.50 sample std.=17.06
p-value of the KSTEST for those 10 p-values: 0.886094
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-15_16:31
0.0541,0.3341,0.7100,0.3489,0.9292,0.0910,0.4299,0.0157,0.7044,0.5222,
The KS test for those 10 p-values: 0.509823
The 3DSPHERES test for dh-ranFile-2018-06-15_16:31
sample no r^3 equiv. uni.
1 9.216 0.264488
2 150.780 0.993435
3 117.749 0.980257
4 5.809 0.176047
5 12.454 0.339749
6 101.642 0.966226
7 19.510 0.478122
8 4.552 0.140776
9 66.835 0.892239
10 61.483 0.871194
11 0.522 0.017236
12 35.928 0.698082
13 32.543 0.662021
14 48.672 0.802575
15 10.200 0.288224
16 108.748 0.973349
17 11.840 0.326089
18 18.845 0.466436
19 0.691 0.022781
20 2.769 0.088163
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.241791
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-15_16:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 0.5 1.5 -0.7 -0.9 -0.6
-1.3 1.1 1.0 1.2 -0.4 -0.5
-0.3 -0.7 -0.5 -0.0 0.9 0.6
-0.7 0.3 0.3 -0.9 0.9 0.3
1.6 -0.5 -0.1 -1.6 0.8 -0.9
-0.3 -2.4 -0.8 -1.3 1.0 0.4
1.2 1.5 -0.4 0.4 -1.3 2.0
-0.1
Chi-square with 42 degrees of freedom:41.255701
z-score=-0.081210, p-value=0.496503
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-15_16:31
Test no p-value
1 0.498174
2 0.525571
3 0.044594
4 0.141988
5 0.367443
6 0.331366
7 0.586231
8 0.517448
9 0.499855
10 0.535720
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.161286
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-15_16:31:
(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 66818 0.34 66822 0.36
3 25000.00 24915 0.29 24912 0.31
4 6666.67 6531 2.76 6608 0.52
5 1388.89 1450 2.69 1374 0.16
6 238.10 251 0.70 244 0.15
7 34.72 29 0.94 31 0.40
8 4.96 5 0.00 8 1.86
p=0.74100 p=0.29033
Number of rngs required: 687786, p-value: 0.238
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-15_16:31
No. of wins: Observed Expected
98709 98585.9
z-score= 0.551, pvalue=0.70910
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66933 66666.7 1.064 1.064
2 37226 37654.3 4.872 5.936
3 27127 26954.7 1.101 7.037
4 19351 19313.5 0.073 7.110
5 13942 13851.4 0.592 7.702
6 10001 9943.5 0.332 8.034
7 7147 7145.0 0.001 8.035
8 5063 5139.1 1.126 9.161
9 3664 3699.9 0.348 9.509
10 2643 2666.3 0.204 9.712
11 1920 1923.3 0.006 9.718
12 1432 1388.7 1.348 11.066
13 964 1003.7 1.571 12.637
14 694 726.1 1.423 14.060
15 522 525.8 0.028 14.088
16 372 381.2 0.220 14.307
17 266 276.5 0.402 14.709
18 195 200.8 0.169 14.878
19 153 146.0 0.337 15.215
20 118 106.2 1.308 16.523
21 267 287.1 1.409 17.932
Chisq= 17.93 for 20 degrees of freedom, p= 0.40812
SUMMARY of craptest
p-value for no. of wins: 0.709101
p-value for throws/game: 0.408116
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-15_16:31
No. of wins: Observed Expected
98394 98585.9
z-score=-0.858, pvalue=0.19542
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66901 66666.7 0.824 0.824
2 37676 37654.3 0.012 0.836
3 27107 26954.7 0.860 1.696
4 19309 19313.5 0.001 1.697
5 13824 13851.4 0.054 1.752
6 9819 9943.5 1.560 3.312
7 7120 7145.0 0.088 3.399
8 5086 5139.1 0.548 3.947
9 3702 3699.9 0.001 3.949
10 2574 2666.3 3.195 7.144
11 1903 1923.3 0.215 7.358
12 1380 1388.7 0.055 7.413
13 949 1003.7 2.983 10.396
14 701 726.1 0.870 11.266
15 539 525.8 0.330 11.596
16 412 381.2 2.497 14.093
17 263 276.5 0.663 14.756
18 193 200.8 0.305 15.061
19 149 146.0 0.062 15.123
20 96 106.2 0.982 16.106
21 297 287.1 0.340 16.446
Chisq= 16.45 for 20 degrees of freedom, p= 0.31141
SUMMARY of craptest
p-value for no. of wins: 0.195418
p-value for throws/game: 0.311415
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0051,0.0066,0.0088,0.0149,0.0157,0.0163,0.0172,0.0199,0.0200,0.0228,
0.0238,0.0334,0.0344,0.0421,0.0446,0.0449,0.0456,0.0541,0.0631,0.0635,
0.0720,0.0735,0.0738,0.0769,0.0837,0.0837,0.0882,0.0910,0.0968,0.0973,
0.0975,0.1175,0.1216,0.1224,0.1229,0.1321,0.1408,0.1420,0.1533,0.1571,
0.1584,0.1613,0.1634,0.1699,0.1701,0.1742,0.1760,0.1768,0.1803,0.1869,
0.1915,0.1951,0.1954,0.1966,0.1969,0.1971,0.1974,0.1986,0.2019,0.2066,
0.2085,0.2158,0.2160,0.2215,0.2257,0.2272,0.2381,0.2384,0.2411,0.2414,
0.2418,0.2447,0.2448,0.2529,0.2607,0.2645,0.2683,0.2706,0.2739,0.2764,
0.2796,0.2843,0.2871,0.2882,0.2903,0.2993,0.3028,0.3077,0.3077,0.3114,
0.3261,0.3314,0.3341,0.3342,0.3371,0.3373,0.3397,0.3438,0.3489,0.3656,
0.3674,0.3704,0.3779,0.3782,0.3905,0.3915,0.3992,0.4068,0.4081,0.4124,
0.4136,0.4266,0.4299,0.4329,0.4398,0.4521,0.4588,0.4636,0.4664,0.4775,
0.4781,0.4784,0.4810,0.4835,0.4873,0.4885,0.4920,0.4926,0.4928,0.4965,
0.4982,0.4999,0.5000,0.5098,0.5132,0.5168,0.5174,0.5182,0.5222,0.5256,
0.5257,0.5261,0.5279,0.5290,0.5293,0.5322,0.5333,0.5357,0.5428,0.5454,
0.5477,0.5527,0.5558,0.5559,0.5699,0.5708,0.5725,0.5842,0.5862,0.5903,
0.5912,0.5923,0.5989,0.6034,0.6070,0.6231,0.6233,0.6284,0.6332,0.6449,
0.6552,0.6564,0.6620,0.6636,0.6637,0.6722,0.6751,0.6777,0.6940,0.6981,
0.6991,0.7009,0.7009,0.7011,0.7021,0.7043,0.7044,0.7066,0.7081,0.7091,
0.7100,0.7161,0.7184,0.7328,0.7387,0.7401,0.7404,0.7410,0.7414,0.7422,
0.7459,0.7558,0.7702,0.7738,0.7920,0.8026,0.8063,0.8084,0.8085,0.8105,
0.8179,0.8206,0.8210,0.8214,0.8273,0.8357,0.8394,0.8424,0.8532,0.8541,
0.8603,0.8680,0.8703,0.8712,0.8727,0.8793,0.8850,0.8861,0.8922,0.8979,
0.9062,0.9071,0.9144,0.9170,0.9188,0.9287,0.9292,0.9347,0.9359,0.9366,
0.9387,0.9400,0.9409,0.9420,0.9436,0.9445,0.9504,0.9544,0.9588,0.9589,
0.9607,0.9608,0.9644,0.9649,0.9654,0.9662,0.9711,0.9715,0.9733,0.9751,
0.9791,0.9803,0.9807,0.9859,0.9898,0.9916,0.9934,0.9950,0.9970,
Overall p-value after applying KStest on 269 p-values = 0.284430
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.