RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-14_13:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.88 11.6422 0.178697
2 to 25 15.92 12.5890 0.236765
3 to 26 15.91 18.8972 0.665537
4 to 27 16.02 14.1569 0.344034
5 to 28 16.03 10.0374 0.097966
6 to 29 15.38 28.3192 0.958656
7 to 30 15.69 20.7455 0.762120
8 to 31 15.81 15.5008 0.440542
9 to 32 15.83 13.4747 0.296128
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.823171
Tough bday spacings test for dh-ranFile-2018-06-14_13:31: 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 15 47 82 85 96 78 42 28 19 5 3
(O-E)^2/E 3.7 2.9 1.0 1.6 0.0 0.0 2.0 0.1 1.1 0.4 0.3
Birthday Spacings: Sum(O-E)^2/E= 13.254, p= 0.790
RESULTS OF GCD FOR dh-ranFile-2018-06-14_13:31
Euclid's algorithm:
p-value, steps to gcd: 0.431276
p-value, dist. of gcd's: 0.357740
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-14_13:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.545 0.812 0.813 0.213 0.751 0.218 0.169 0.808
Bits 8 to 15---> 0.804 0.933 0.721 0.856 0.371 0.678 0.040 0.054
Bits 16 to 23---> 0.615 0.002 0.606 0.953 0.819 0.697 0.997 0.337
Bits 24 to 31---> 0.779 0.735 0.034 0.913 0.216 0.035 0.050 0.067
KS test for the above 32 p values: 0.865
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-14_13:31,
p-values for 5 runs: 0.4694, 0.9528, 0.8817, 0.9300, 0.2957
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-14_13:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 192 211.4 1.783 1.783
r= 29 5169 5134.0 0.238 2.022
r= 30 23044 23103.0 0.151 2.173
r= 31 11595 11551.5 0.164 2.336
chi-square = 2.336 with df = 3; p-value = 0.494
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-14_13:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 202 211.4 0.420 0.420
r= 30 5102 5134.0 0.200 0.619
r= 31 23125 23103.0 0.021 0.640
r= 32 11571 11551.5 0.033 0.673
chi-square = 0.673 with df = 3; p-value = 0.120
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-14_13:31
b-rank test for bits 1 to 8, p=0.27659
b-rank test for bits 2 to 9, p=0.81005
b-rank test for bits 3 to 10, p=0.53697
b-rank test for bits 4 to 11, p=0.57016
b-rank test for bits 5 to 12, p=0.36075
b-rank test for bits 6 to 13, p=0.57169
b-rank test for bits 7 to 14, p=0.02371
b-rank test for bits 8 to 15, p=0.41542
b-rank test for bits 9 to 16, p=0.45273
b-rank test for bits 10 to 17, p=0.15764
b-rank test for bits 11 to 18, p=0.28771
b-rank test for bits 12 to 19, p=0.92145
b-rank test for bits 13 to 20, p=0.80279
b-rank test for bits 14 to 21, p=0.69514
b-rank test for bits 15 to 22, p=0.79566
b-rank test for bits 16 to 23, p=0.90858
b-rank test for bits 17 to 24, p=0.91840
b-rank test for bits 18 to 25, p=0.13648
b-rank test for bits 19 to 26, p=0.21009
b-rank test for bits 20 to 27, p=0.62908
b-rank test for bits 21 to 28, p=0.56638
b-rank test for bits 22 to 29, p=0.30335
b-rank test for bits 23 to 30, p=0.51468
b-rank test for bits 24 to 31, p=0.72877
b-rank test for bits 25 to 32, p=0.67629
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 = 0.764180
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-14_13:31
(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 142105 0.46 0.676227
2 141932 0.05 0.521121
3 141136 -1.81 0.035393
4 142851 2.20 0.986102
5 141901 -0.02 0.492236
6 141724 -0.43 0.332502
7 141885 -0.06 0.477334
8 141986 0.18 0.571084
9 141291 -1.44 0.074272
10 141502 -0.95 0.170623
11 142492 1.36 0.913303
12 141316 -1.39 0.082830
13 142685 1.81 0.965031
14 141013 -2.09 0.018120
15 141948 0.09 0.535996
16 142102 0.45 0.673704
17 141187 -1.69 0.045736
18 142283 0.87 0.808685
19 141665 -0.57 0.284046
20 141846 -0.15 0.441184
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-14_13:31
Bits used No. missing words z-score p-value
23 to 32 142121 0.7299 0.767273
22 to 31 142119 0.7230 0.765160
21 to 30 141746 -0.5632 0.286647
20 to 29 141851 -0.2011 0.420295
19 to 28 141692 -0.7494 0.226804
18 to 27 141833 -0.2632 0.396196
17 to 26 141821 -0.3046 0.380341
16 to 25 141394 -1.7770 0.037784
15 to 24 141945 0.1230 0.548947
14 to 23 142077 0.5782 0.718426
13 to 22 141608 -1.0391 0.149386
12 to 21 141678 -0.7977 0.212525
11 to 20 141968 0.2023 0.580163
10 to 19 142172 0.9058 0.817468
9 to 18 141808 -0.3494 0.363389
8 to 17 141735 -0.6011 0.273874
7 to 16 141800 -0.3770 0.353087
6 to 15 141158 -2.5908 0.004788
5 to 14 141895 -0.0494 0.480295
4 to 13 142068 0.5471 0.707858
3 to 12 141758 -0.5218 0.300895
2 to 11 142010 0.3471 0.635756
1 to 10 142276 1.2644 0.896953
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-14_13:31
Bits used No. missing words z-score p-value
28 to 32 141763 -0.4960 0.309935
27 to 31 141736 -0.5876 0.278414
26 to 30 141890 -0.0655 0.473878
25 to 29 142127 0.7379 0.769702
24 to 28 141892 -0.0587 0.476577
23 to 27 141595 -1.0655 0.143319
22 to 26 141886 -0.0791 0.468483
21 to 25 141732 -0.6011 0.273881
20 to 24 141799 -0.3740 0.354202
19 to 23 141451 -1.5537 0.060133
18 to 22 142115 0.6972 0.757157
17 to 21 141783 -0.4282 0.334239
16 to 20 141951 0.1413 0.556166
15 to 19 142090 0.6124 0.729877
14 to 18 142580 2.2735 0.988501
13 to 17 141696 -0.7232 0.234793
12 to 16 141639 -0.9164 0.179736
11 to 15 142092 0.6192 0.732114
10 to 14 141788 -0.4113 0.340431
9 to 13 141689 -0.7469 0.227568
8 to 12 141648 -0.8859 0.187845
7 to 11 141579 -1.1198 0.131407
6 to 10 141350 -1.8960 0.028978
5 to 9 141793 -0.3943 0.346665
4 to 8 141984 0.2531 0.599912
3 to 7 142302 1.3311 0.908419
2 to 6 142005 0.3243 0.627147
1 to 5 142093 0.6226 0.733230
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-14_13:31
Bits used No. missing words z-score p-value
31 to 32 141951 0.1229 0.548915
30 to 31 142388 1.4120 0.921026
29 to 30 142265 1.0492 0.852951
28 to 29 142128 0.6450 0.740551
27 to 28 141371 -1.5880 0.056144
26 to 27 141796 -0.3343 0.369074
25 to 26 142203 0.8663 0.806833
24 to 25 141996 0.2557 0.600895
23 to 24 142012 0.3029 0.619002
22 to 23 141901 -0.0246 0.490198
21 to 22 141400 -1.5024 0.066491
20 to 21 141512 -1.1721 0.120586
19 to 20 141531 -1.1160 0.132207
18 to 19 141304 -1.7856 0.037079
17 to 18 141773 -0.4022 0.343786
16 to 17 141329 -1.7119 0.043459
15 to 16 141148 -2.2458 0.012358
14 to 15 142234 0.9577 0.830900
13 to 14 141961 0.1524 0.560572
12 to 13 141683 -0.6676 0.252182
11 to 12 141290 -1.8269 0.033855
10 to 11 141864 -0.1337 0.446813
9 to 10 141965 0.1642 0.565220
8 to 9 142000 0.2675 0.605444
7 to 8 142226 0.9341 0.824882
6 to 7 141803 -0.3137 0.376891
5 to 6 142165 0.7542 0.774632
4 to 5 142114 0.6037 0.726994
3 to 4 142044 0.3973 0.654411
2 to 3 141778 -0.3874 0.349229
1 to 2 141268 -1.8918 0.029257
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-14_13:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2479.45 -0.291 0.385673
Test results for specific bytes for dh-ranFile-2018-06-14_13:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2524.28 0.343 0.634336
2 to 9 2440.76 -0.838 0.201093
3 to 10 2504.75 0.067 0.526794
4 to 11 2513.90 0.197 0.577945
5 to 12 2517.55 0.248 0.597983
6 to 13 2374.94 -1.769 0.038475
7 to 14 2503.06 0.043 0.517277
8 to 15 2441.55 -0.827 0.204220
9 to 16 2431.59 -0.967 0.166655
10 to 17 2391.69 -1.532 0.062791
11 to 18 2540.04 0.566 0.714392
12 to 19 2537.00 0.523 0.699622
13 to 20 2403.18 -1.369 0.085465
14 to 21 2407.03 -1.315 0.094298
15 to 22 2534.68 0.490 0.688075
16 to 23 2485.92 -0.199 0.421103
17 to 24 2512.99 0.184 0.572869
18 to 25 2585.80 1.213 0.887515
19 to 26 2490.89 -0.129 0.448728
20 to 27 2668.00 2.376 0.991247
21 to 28 2517.71 0.251 0.598901
22 to 29 2502.79 0.039 0.515736
23 to 30 2554.36 0.769 0.778970
24 to 31 2494.30 -0.081 0.467864
25 to 32 2543.87 0.620 0.732513
CDPARK for dh-ranFile-2018-06-14_13:31: 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
3525 0.0913 0.536383
3513 -0.4566 0.323972
3498 -1.1416 0.126820
3498 -1.1416 0.126820
3538 0.6849 0.753306
3530 0.3196 0.625377
3560 1.6895 0.954438
3521 -0.0913 0.463617
3515 -0.3653 0.357445
3519 -0.1826 0.427537
Square side=100, avg. no. parked=3521.70 sample std.=17.50
p-value of the KSTEST for those 10 p-values: 0.861996
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-14_13:31
0.3531,0.9845,0.8198,0.3584,0.8169,0.9051,0.7972,0.5843,0.2649,0.2611,
The KS test for those 10 p-values: 0.281792
The 3DSPHERES test for dh-ranFile-2018-06-14_13:31
sample no r^3 equiv. uni.
1 120.609 0.982053
2 3.693 0.115829
3 14.489 0.383042
4 4.519 0.139838
5 3.737 0.117124
6 89.513 0.949398
7 5.605 0.170417
8 25.679 0.575128
9 2.443 0.078195
10 7.590 0.223540
11 9.183 0.263692
12 31.814 0.653702
13 38.704 0.724761
14 43.696 0.766960
15 59.883 0.864137
16 47.713 0.796162
17 99.448 0.963663
18 52.384 0.825551
19 22.997 0.535392
20 26.218 0.582695
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.672585
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-14_13:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 0.9 -0.1 -0.3 0.2 -1.5
-0.2 -0.4 -0.2 -0.6 -0.3 0.9
-2.1 0.2 1.6 -0.4 0.6 0.2
0.1 -0.4 -0.4 -1.8 -0.2 -0.1
0.1 2.4 1.7 -0.2 -0.0 -0.6
-0.7 0.8 1.7 -0.3 1.9 0.4
1.2 -0.4 -0.4 1.0 0.1 -1.0
1.8
Chi-square with 42 degrees of freedom:40.463009
z-score=-0.167699, p-value=0.461464
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-14_13:31
Test no p-value
1 0.926891
2 0.739255
3 0.547362
4 0.131301
5 0.003700
6 0.035432
7 0.092083
8 0.779138
9 0.462805
10 0.231206
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.221909
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-14_13:31:
(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 66407 1.01 66752 0.11
3 25000.00 25252 2.54 25025 0.03
4 6666.67 6711 0.29 6532 2.72
5 1388.89 1348 1.20 1419 0.65
6 238.10 245 0.20 235 0.04
7 34.72 35 0.00 33 0.09
8 4.96 1 3.16 3 0.77
p=0.79071 p=0.37827
Number of rngs required: 688290, p-value: 0.448
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-14_13:31
No. of wins: Observed Expected
98773 98585.9
z-score= 0.837, pvalue=0.79871
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66663 66666.7 0.000 0.000
2 37744 37654.3 0.214 0.214
3 27132 26954.7 1.166 1.380
4 19415 19313.5 0.534 1.913
5 13885 13851.4 0.081 1.995
6 9778 9943.5 2.756 4.751
7 7086 7145.0 0.488 5.238
8 5078 5139.1 0.726 5.964
9 3673 3699.9 0.195 6.159
10 2697 2666.3 0.354 6.513
11 1886 1923.3 0.725 7.237
12 1410 1388.7 0.325 7.563
13 992 1003.7 0.137 7.700
14 719 726.1 0.070 7.770
15 495 525.8 1.808 9.578
16 354 381.2 1.934 11.512
17 262 276.5 0.764 12.276
18 209 200.8 0.332 12.609
19 143 146.0 0.061 12.670
20 95 106.2 1.184 13.854
21 284 287.1 0.034 13.888
Chisq= 13.89 for 20 degrees of freedom, p= 0.16386
SUMMARY of craptest
p-value for no. of wins: 0.798705
p-value for throws/game: 0.163863
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-14_13:31
No. of wins: Observed Expected
98780 98585.9
z-score= 0.868, pvalue=0.80739
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66737 66666.7 0.074 0.074
2 37873 37654.3 1.270 1.344
3 26739 26954.7 1.727 3.071
4 19281 19313.5 0.055 3.125
5 13911 13851.4 0.256 3.382
6 9916 9943.5 0.076 3.458
7 7139 7145.0 0.005 3.463
8 5076 5139.1 0.774 4.237
9 3742 3699.9 0.480 4.717
10 2655 2666.3 0.048 4.765
11 1851 1923.3 2.720 7.485
12 1431 1388.7 1.286 8.771
13 998 1003.7 0.033 8.803
14 760 726.1 1.579 10.382
15 505 525.8 0.826 11.208
16 351 381.2 2.385 13.593
17 279 276.5 0.022 13.615
18 208 200.8 0.256 13.871
19 142 146.0 0.109 13.979
20 123 106.2 2.652 16.632
21 283 287.1 0.059 16.691
Chisq= 16.69 for 20 degrees of freedom, p= 0.32705
SUMMARY of craptest
p-value for no. of wins: 0.807389
p-value for throws/game: 0.327053
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0020,0.0037,0.0048,0.0124,0.0181,0.0237,0.0290,0.0293,0.0338,0.0339,
0.0347,0.0354,0.0354,0.0371,0.0378,0.0385,0.0404,0.0435,0.0457,0.0503,
0.0542,0.0561,0.0601,0.0628,0.0665,0.0673,0.0743,0.0782,0.0828,0.0855,
0.0921,0.0943,0.0980,0.1158,0.1171,0.1204,0.1206,0.1268,0.1268,0.1313,
0.1314,0.1322,0.1365,0.1398,0.1433,0.1494,0.1576,0.1639,0.1667,0.1691,
0.1704,0.1706,0.1787,0.1797,0.1878,0.2011,0.2042,0.2101,0.2125,0.2135,
0.2162,0.2176,0.2219,0.2235,0.2268,0.2276,0.2312,0.2348,0.2368,0.2522,
0.2611,0.2637,0.2649,0.2739,0.2739,0.2766,0.2784,0.2818,0.2840,0.2866,
0.2877,0.2957,0.2961,0.3009,0.3033,0.3099,0.3240,0.3271,0.3325,0.3342,
0.3366,0.3404,0.3438,0.3440,0.3467,0.3492,0.3531,0.3531,0.3542,0.3574,
0.3577,0.3584,0.3608,0.3634,0.3691,0.3712,0.3769,0.3783,0.3803,0.3830,
0.3857,0.3962,0.4154,0.4203,0.4211,0.4275,0.4313,0.4405,0.4412,0.4468,
0.4483,0.4487,0.4527,0.4615,0.4628,0.4636,0.4679,0.4685,0.4694,0.4739,
0.4766,0.4773,0.4803,0.4902,0.4922,0.4944,0.5147,0.5157,0.5173,0.5211,
0.5268,0.5354,0.5360,0.5364,0.5370,0.5448,0.5474,0.5489,0.5489,0.5562,
0.5606,0.5652,0.5664,0.5702,0.5711,0.5717,0.5729,0.5751,0.5779,0.5802,
0.5827,0.5843,0.5980,0.5989,0.5999,0.6009,0.6054,0.6064,0.6150,0.6190,
0.6254,0.6271,0.6291,0.6343,0.6358,0.6537,0.6544,0.6655,0.6726,0.6737,
0.6762,0.6763,0.6783,0.6881,0.6951,0.6969,0.6996,0.7079,0.7144,0.7184,
0.7206,0.7248,0.7270,0.7288,0.7299,0.7321,0.7325,0.7332,0.7347,0.7393,
0.7406,0.7506,0.7533,0.7572,0.7621,0.7642,0.7652,0.7670,0.7673,0.7697,
0.7746,0.7790,0.7791,0.7794,0.7902,0.7907,0.7957,0.7962,0.7972,0.7987,
0.8028,0.8041,0.8068,0.8074,0.8080,0.8087,0.8101,0.8122,0.8128,0.8169,
0.8175,0.8191,0.8198,0.8232,0.8249,0.8256,0.8309,0.8530,0.8560,0.8620,
0.8641,0.8650,0.8817,0.8875,0.8970,0.9051,0.9084,0.9086,0.9130,0.9133,
0.9184,0.9210,0.9215,0.9269,0.9300,0.9327,0.9494,0.9526,0.9528,0.9544,
0.9587,0.9637,0.9650,0.9821,0.9845,0.9861,0.9885,0.9912,0.9966,
Overall p-value after applying KStest on 269 p-values = 0.693279
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.