RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-05_04:31
(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 26.7310 0.937867
2 to 25 15.62 25.0541 0.906495
3 to 26 15.95 20.8874 0.768633
4 to 27 15.75 13.0611 0.267915
5 to 28 15.83 36.3546 0.995888
6 to 29 15.70 25.3472 0.912795
7 to 30 15.83 17.3902 0.571755
8 to 31 15.73 19.7737 0.714034
9 to 32 15.86 21.1640 0.780961
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.007036
Tough bday spacings test for dh-ranFile-2018-07-05_04:31: 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 42 79 88 94 76 55 37 13 4 4
(O-E)^2/E 0.1 0.8 0.4 1.0 0.1 0.1 0.2 1.8 0.2 1.0 0.0
Birthday Spacings: Sum(O-E)^2/E= 5.732, p= 0.163
RESULTS OF GCD FOR dh-ranFile-2018-07-05_04:31
Euclid's algorithm:
p-value, steps to gcd: 0.165536
p-value, dist. of gcd's: 0.712366
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-05_04:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.323 0.383 0.547 0.617 0.339 0.861 0.542 0.072
Bits 8 to 15---> 0.662 0.608 0.661 0.812 0.198 0.058 0.263 0.563
Bits 16 to 23---> 0.557 0.309 0.143 0.770 0.218 0.394 0.006 0.515
Bits 24 to 31---> 0.673 0.456 0.626 0.112 0.732 0.593 0.217 0.798
KS test for the above 32 p values: 0.708
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-05_04:31,
p-values for 5 runs: 0.5521, 0.9093, 0.4478, 0.0190, 0.3412
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-05_04:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 209 211.4 0.028 0.028
r= 29 5108 5134.0 0.132 0.159
r= 30 22919 23103.0 1.466 1.626
r= 31 11764 11551.5 3.908 5.534
chi-square = 5.534 with df = 3; p-value = 0.863
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-05_04:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 222 211.4 0.530 0.530
r= 30 5179 5134.0 0.394 0.924
r= 31 23170 23103.0 0.194 1.118
r= 32 11429 11551.5 1.300 2.418
chi-square = 2.418 with df = 3; p-value = 0.510
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-05_04:31
b-rank test for bits 1 to 8, p=0.59953
b-rank test for bits 2 to 9, p=0.55802
b-rank test for bits 3 to 10, p=0.01565
b-rank test for bits 4 to 11, p=0.83274
b-rank test for bits 5 to 12, p=0.83220
b-rank test for bits 6 to 13, p=0.65478
b-rank test for bits 7 to 14, p=0.25002
b-rank test for bits 8 to 15, p=0.34946
b-rank test for bits 9 to 16, p=0.64446
b-rank test for bits 10 to 17, p=0.91874
b-rank test for bits 11 to 18, p=0.98565
b-rank test for bits 12 to 19, p=0.49971
b-rank test for bits 13 to 20, p=0.80082
b-rank test for bits 14 to 21, p=0.09075
b-rank test for bits 15 to 22, p=0.84851
b-rank test for bits 16 to 23, p=0.13425
b-rank test for bits 17 to 24, p=0.48716
b-rank test for bits 18 to 25, p=0.14788
b-rank test for bits 19 to 26, p=0.27271
b-rank test for bits 20 to 27, p=0.27534
b-rank test for bits 21 to 28, p=0.44180
b-rank test for bits 22 to 29, p=0.85052
b-rank test for bits 23 to 30, p=0.22181
b-rank test for bits 24 to 31, p=0.15875
b-rank test for bits 25 to 32, p=0.95690
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 = 0.968530
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-05_04:31
(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 141994 0.20 0.578410
2 142304 0.92 0.821769
3 142323 0.97 0.833108
4 141961 0.12 0.548045
5 141958 0.11 0.545268
6 141446 -1.08 0.139505
7 141620 -0.68 0.249519
8 141194 -1.67 0.047328
9 142519 1.42 0.922844
10 142651 1.73 0.958441
11 141735 -0.41 0.341889
12 142067 0.37 0.643708
13 141905 -0.01 0.495964
14 141230 -1.59 0.056231
15 142525 1.44 0.924851
16 142162 0.59 0.722522
17 143136 2.87 0.997922
18 141762 -0.34 0.365337
19 141803 -0.25 0.401899
20 141879 -0.07 0.471753
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-05_04:31
Bits used No. missing words z-score p-value
23 to 32 141800 -0.3770 0.353087
22 to 31 142241 1.1437 0.873624
21 to 30 142012 0.3540 0.638344
20 to 29 142446 1.8506 0.967885
19 to 28 142182 0.9402 0.826453
18 to 27 141877 -0.1115 0.455617
17 to 26 141588 -1.1080 0.133923
16 to 25 141900 -0.0322 0.487167
15 to 24 141945 0.1230 0.548947
14 to 23 142086 0.6092 0.728806
13 to 22 141917 0.0264 0.510550
12 to 21 141966 0.1954 0.577466
11 to 20 141698 -0.7287 0.233085
10 to 19 141863 -0.1598 0.436536
9 to 18 141870 -0.1356 0.446061
8 to 17 141627 -0.9736 0.165140
7 to 16 141713 -0.6770 0.249203
6 to 15 141797 -0.3873 0.349251
5 to 14 141819 -0.3115 0.377717
4 to 13 141968 0.2023 0.580163
3 to 12 141658 -0.8667 0.193066
2 to 11 141952 0.1471 0.558488
1 to 10 142128 0.7540 0.774586
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-05_04:31
Bits used No. missing words z-score p-value
28 to 32 141966 0.1921 0.576169
27 to 31 142333 1.4362 0.924523
26 to 30 142010 0.3413 0.633544
25 to 29 141755 -0.5232 0.300434
24 to 28 141938 0.0972 0.538711
23 to 27 141908 -0.0045 0.498201
22 to 26 141866 -0.1469 0.441613
21 to 25 141652 -0.8723 0.191521
20 to 24 141642 -0.9062 0.182414
19 to 23 142564 2.2192 0.986764
18 to 22 142176 0.9040 0.816993
17 to 21 141535 -1.2689 0.102236
16 to 20 141493 -1.4113 0.079080
15 to 19 142027 0.3989 0.655010
14 to 18 142095 0.6294 0.735453
13 to 17 141763 -0.4960 0.309935
12 to 16 141990 0.2735 0.607749
11 to 15 141913 0.0124 0.504963
10 to 14 142233 1.0972 0.863720
9 to 13 141842 -0.2282 0.409731
8 to 12 142251 1.1582 0.876610
7 to 11 141716 -0.6554 0.256119
6 to 10 142319 1.3887 0.917540
5 to 9 142233 1.0972 0.863720
4 to 8 142451 1.8362 0.966834
3 to 7 141595 -1.0655 0.143319
2 to 6 141677 -0.7876 0.215477
1 to 5 141993 0.2836 0.611652
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-05_04:31
Bits used No. missing words z-score p-value
31 to 32 141989 0.2350 0.592901
30 to 31 142362 1.3353 0.909113
29 to 30 141930 0.0610 0.524310
28 to 29 141942 0.0964 0.538387
27 to 28 141894 -0.0452 0.481966
26 to 27 142041 0.3884 0.651143
25 to 26 142067 0.4651 0.679071
24 to 25 141600 -0.9125 0.180759
23 to 24 142052 0.4209 0.663070
22 to 23 141969 0.1760 0.569860
21 to 22 141745 -0.4847 0.313927
20 to 21 142254 1.0167 0.845358
19 to 20 141428 -1.4199 0.077825
18 to 19 142138 0.6745 0.750017
17 to 18 141681 -0.6735 0.250302
16 to 17 142383 1.3973 0.918832
15 to 16 142202 0.8633 0.806023
14 to 15 142405 1.4622 0.928150
13 to 14 141659 -0.7384 0.230125
12 to 13 141804 -0.3107 0.378011
11 to 12 141751 -0.4671 0.320232
10 to 11 141699 -0.6204 0.267483
9 to 10 142641 2.1583 0.984548
8 to 9 142692 2.3088 0.989522
7 to 8 141481 -1.2635 0.103203
6 to 7 142022 0.3324 0.630191
5 to 6 142683 2.2822 0.988762
4 to 5 141886 -0.0688 0.472566
3 to 4 142051 0.4179 0.661992
2 to 3 141356 -1.6322 0.051314
1 to 2 141821 -0.2606 0.397216
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-05_04:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2519.76 0.279 0.610029
Test results for specific bytes for dh-ranFile-2018-07-05_04:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2555.95 0.791 0.785612
2 to 9 2486.30 -0.194 0.423189
3 to 10 2352.02 -2.093 0.018183
4 to 11 2522.71 0.321 0.625945
5 to 12 2465.47 -0.488 0.312659
6 to 13 2397.10 -1.455 0.072803
7 to 14 2516.87 0.239 0.594259
8 to 15 2518.32 0.259 0.602223
9 to 16 2532.02 0.453 0.674643
10 to 17 2349.43 -2.129 0.016610
11 to 18 2414.82 -1.205 0.114169
12 to 19 2354.12 -2.063 0.019555
13 to 20 2669.97 2.404 0.991887
14 to 21 2612.05 1.585 0.943481
15 to 22 2476.90 -0.327 0.371958
16 to 23 2482.88 -0.242 0.404373
17 to 24 2540.26 0.569 0.715451
18 to 25 2464.18 -0.507 0.306215
19 to 26 2574.30 1.051 0.853311
20 to 27 2445.39 -0.772 0.219974
21 to 28 2415.24 -1.199 0.115322
22 to 29 2639.53 1.973 0.975767
23 to 30 2492.49 -0.106 0.457706
24 to 31 2547.64 0.674 0.749744
25 to 32 2524.79 0.351 0.637051
CDPARK for dh-ranFile-2018-07-05_04:31: 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
3527 0.1826 0.572463
3582 2.6941 0.996471
3557 1.5525 0.939730
3509 -0.6393 0.261324
3532 0.4110 0.659449
3524 0.0457 0.518210
3512 -0.5023 0.307734
3554 1.4155 0.921543
3499 -1.0959 0.136563
3479 -2.0091 0.022262
Square side=100, avg. no. parked=3527.50 sample std.=28.85
p-value of the KSTEST for those 10 p-values: 0.573961
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-05_04:31
0.5818,0.0241,0.5503,0.8132,0.4981,0.1246,0.5595,0.4587,0.1236,0.2403,
The KS test for those 10 p-values: 0.362360
The 3DSPHERES test for dh-ranFile-2018-07-05_04:31
sample no r^3 equiv. uni.
1 13.066 0.353076
2 10.626 0.298261
3 48.883 0.803959
4 15.405 0.401610
5 32.086 0.656831
6 42.645 0.758647
7 4.604 0.142270
8 29.632 0.627575
9 103.491 0.968245
10 58.013 0.855398
11 25.018 0.565664
12 43.463 0.765140
13 12.560 0.342077
14 28.080 0.607813
15 14.455 0.382346
16 29.625 0.627499
17 12.883 0.349115
18 14.097 0.374933
19 36.159 0.700398
20 13.098 0.353776
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.263615
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-05_04:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 1.3 0.6 0.3 0.5 1.4
-0.3 0.3 -0.4 -1.2 0.9 0.5
-2.7 -0.7 -1.8 0.3 -0.4 0.0
1.1 0.6 1.7 1.7 -1.2 -0.6
2.4 -2.0 -1.7 1.7 0.3 1.6
-0.7 1.1 0.9 -0.8 -0.6 1.9
-0.5 -1.7 0.5 1.0 0.1 -1.0
-1.1
Chi-square with 42 degrees of freedom:59.327009
z-score=1.890532, p-value=0.959942
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-05_04:31
Test no p-value
1 0.756524
2 0.965910
3 0.300439
4 0.565696
5 0.378687
6 0.023386
7 0.053484
8 0.550784
9 0.694974
10 0.016364
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.356142
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-05_04:31:
(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 66817 0.34 66644 0.01
3 25000.00 24949 0.10 25016 0.01
4 6666.67 6611 0.46 6670 0.00
5 1388.89 1335 2.09 1391 0.00
6 238.10 252 0.81 236 0.02
7 34.72 30 0.64 38 0.31
8 4.96 5 0.00 4 0.19
p=0.38437 p=0.00264
Number of rngs required: 689034, p-value: 0.767
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-05_04:31
No. of wins: Observed Expected
98441 98585.9
z-score=-0.648, pvalue=0.25853
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66470 66666.7 0.580 0.580
2 37769 37654.3 0.349 0.929
3 26976 26954.7 0.017 0.946
4 19499 19313.5 1.782 2.729
5 13942 13851.4 0.592 3.321
6 9858 9943.5 0.736 4.057
7 7039 7145.0 1.573 5.630
8 5041 5139.1 1.872 7.502
9 3676 3699.9 0.154 7.656
10 2719 2666.3 1.042 8.697
11 1946 1923.3 0.267 8.965
12 1359 1388.7 0.637 9.602
13 1024 1003.7 0.410 10.012
14 702 726.1 0.803 10.814
15 558 525.8 1.967 12.781
16 426 381.2 5.277 18.059
17 259 276.5 1.112 19.171
18 199 200.8 0.017 19.188
19 142 146.0 0.109 19.297
20 115 106.2 0.727 20.023
21 281 287.1 0.130 20.153
Chisq= 20.15 for 20 degrees of freedom, p= 0.55163
SUMMARY of craptest
p-value for no. of wins: 0.258527
p-value for throws/game: 0.551632
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-05_04:31
No. of wins: Observed Expected
98406 98585.9
z-score=-0.804, pvalue=0.21057
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66824 66666.7 0.371 0.371
2 37231 37654.3 4.759 5.130
3 26819 26954.7 0.683 5.814
4 19443 19313.5 0.869 6.683
5 13874 13851.4 0.037 6.720
6 10127 9943.5 3.385 10.104
7 7089 7145.0 0.439 10.544
8 5089 5139.1 0.488 11.031
9 3760 3699.9 0.977 12.009
10 2764 2666.3 3.580 15.589
11 1868 1923.3 1.592 17.181
12 1429 1388.7 1.167 18.348
13 1018 1003.7 0.203 18.551
14 716 726.1 0.142 18.693
15 506 525.8 0.748 19.441
16 402 381.2 1.140 20.582
17 251 276.5 2.359 22.940
18 209 200.8 0.332 23.273
19 174 146.0 5.376 28.649
20 106 106.2 0.000 28.649
21 301 287.1 0.672 29.321
Chisq= 29.32 for 20 degrees of freedom, p= 0.91837
SUMMARY of craptest
p-value for no. of wins: 0.210574
p-value for throws/game: 0.918371
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0026,0.0056,0.0070,0.0156,0.0164,0.0166,0.0182,0.0190,0.0196,0.0223,
0.0234,0.0241,0.0473,0.0513,0.0535,0.0562,0.0583,0.0719,0.0728,0.0778,
0.0791,0.0907,0.1022,0.1032,0.1119,0.1142,0.1153,0.1236,0.1246,0.1339,
0.1343,0.1366,0.1395,0.1423,0.1431,0.1433,0.1479,0.1587,0.1627,0.1651,
0.1655,0.1808,0.1824,0.1915,0.1931,0.1976,0.2106,0.2155,0.2173,0.2178,
0.2200,0.2218,0.2301,0.2331,0.2403,0.2492,0.2495,0.2500,0.2503,0.2561,
0.2585,0.2613,0.2627,0.2636,0.2675,0.2679,0.2727,0.2753,0.2983,0.3004,
0.3004,0.3062,0.3077,0.3093,0.3099,0.3127,0.3139,0.3202,0.3229,0.3387,
0.3412,0.3419,0.3421,0.3491,0.3493,0.3495,0.3531,0.3531,0.3538,0.3561,
0.3624,0.3653,0.3720,0.3749,0.3777,0.3780,0.3787,0.3823,0.3833,0.3844,
0.3938,0.3972,0.4016,0.4019,0.4044,0.4097,0.4232,0.4365,0.4416,0.4418,
0.4461,0.4478,0.4556,0.4563,0.4577,0.4587,0.4718,0.4726,0.4820,0.4872,
0.4872,0.4960,0.4981,0.4982,0.4997,0.5050,0.5096,0.5106,0.5149,0.5182,
0.5243,0.5384,0.5387,0.5422,0.5453,0.5466,0.5480,0.5489,0.5503,0.5508,
0.5516,0.5521,0.5566,0.5580,0.5585,0.5595,0.5631,0.5657,0.5657,0.5699,
0.5718,0.5725,0.5740,0.5762,0.5775,0.5784,0.5802,0.5818,0.5925,0.5929,
0.5943,0.5995,0.6022,0.6077,0.6078,0.6079,0.6100,0.6117,0.6175,0.6259,
0.6261,0.6275,0.6276,0.6302,0.6335,0.6371,0.6383,0.6437,0.6445,0.6511,
0.6548,0.6550,0.6568,0.6594,0.6606,0.6620,0.6623,0.6631,0.6726,0.6746,
0.6791,0.6950,0.7004,0.7084,0.7124,0.7140,0.7155,0.7225,0.7288,0.7317,
0.7355,0.7497,0.7500,0.7565,0.7586,0.7651,0.7669,0.7686,0.7703,0.7746,
0.7810,0.7856,0.7979,0.8008,0.8040,0.8060,0.8119,0.8132,0.8170,0.8218,
0.8265,0.8322,0.8327,0.8331,0.8454,0.8485,0.8505,0.8533,0.8554,0.8609,
0.8634,0.8637,0.8637,0.8736,0.8766,0.9065,0.9091,0.9093,0.9128,0.9175,
0.9184,0.9187,0.9188,0.9215,0.9228,0.9245,0.9249,0.9282,0.9379,0.9397,
0.9435,0.9569,0.9584,0.9599,0.9659,0.9668,0.9679,0.9682,0.9685,0.9758,
0.9845,0.9856,0.9868,0.9888,0.9895,0.9919,0.9959,0.9965,0.9979,
Overall p-value after applying KStest on 269 p-values = 0.408624
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.