RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-20_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 16.15 20.2681 0.739251
2 to 25 15.59 12.9928 0.263335
3 to 26 15.62 20.2605 0.738880
4 to 27 15.68 22.1958 0.822694
5 to 28 15.50 18.9004 0.665719
6 to 29 15.82 19.5626 0.702790
7 to 30 15.99 10.0172 0.097114
8 to 31 16.05 13.8750 0.324073
9 to 32 15.90 16.9874 0.544778
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.643038
Tough bday spacings test for dh-ranFile-2018-06-20_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 11 43 81 93 96 75 48 31 14 5 3
(O-E)^2/E 0.4 1.1 0.8 0.2 0.0 0.1 0.3 0.1 0.1 0.4 0.3
Birthday Spacings: Sum(O-E)^2/E= 3.775, p= 0.043
RESULTS OF GCD FOR dh-ranFile-2018-06-20_04:31
Euclid's algorithm:
p-value, steps to gcd: 0.913389
p-value, dist. of gcd's: 0.227378
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-20_04:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.024 0.543 0.788 0.412 0.640 0.171 0.560 0.996
Bits 8 to 15---> 0.522 0.533 0.092 0.265 0.493 0.024 0.924 0.315
Bits 16 to 23---> 0.819 0.733 0.593 0.970 0.903 0.420 0.852 0.536
Bits 24 to 31---> 0.646 0.024 0.103 0.851 0.057 0.263 0.759 0.635
KS test for the above 32 p values: 0.229
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-20_04:31,
p-values for 5 runs: 0.0175, 0.8960, 0.5521, 0.3747, 0.9018
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-20_04:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 195 211.4 1.275 1.275
r= 29 5042 5134.0 1.649 2.924
r= 30 23104 23103.0 0.000 2.924
r= 31 11659 11551.5 1.000 3.924
chi-square = 3.924 with df = 3; p-value = 0.730
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-20_04:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 228 211.4 1.301 1.301
r= 30 5151 5134.0 0.056 1.357
r= 31 23022 23103.0 0.284 1.641
r= 32 11599 11551.5 0.195 1.836
chi-square = 1.836 with df = 3; p-value = 0.393
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-20_04:31
b-rank test for bits 1 to 8, p=0.42928
b-rank test for bits 2 to 9, p=0.96336
b-rank test for bits 3 to 10, p=0.38767
b-rank test for bits 4 to 11, p=0.76281
b-rank test for bits 5 to 12, p=0.45595
b-rank test for bits 6 to 13, p=0.12446
b-rank test for bits 7 to 14, p=0.21919
b-rank test for bits 8 to 15, p=0.72903
b-rank test for bits 9 to 16, p=0.96477
b-rank test for bits 10 to 17, p=0.83235
b-rank test for bits 11 to 18, p=0.12404
b-rank test for bits 12 to 19, p=0.47834
b-rank test for bits 13 to 20, p=0.44246
b-rank test for bits 14 to 21, p=0.81227
b-rank test for bits 15 to 22, p=0.19027
b-rank test for bits 16 to 23, p=0.51411
b-rank test for bits 17 to 24, p=0.66825
b-rank test for bits 18 to 25, p=0.61153
b-rank test for bits 19 to 26, p=0.33809
b-rank test for bits 20 to 27, p=0.72825
b-rank test for bits 21 to 28, p=0.46586
b-rank test for bits 22 to 29, p=0.74715
b-rank test for bits 23 to 30, p=0.57932
b-rank test for bits 24 to 31, p=0.39264
b-rank test for bits 25 to 32, p=0.10355
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 = 0.681687
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-20_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 142238 0.77 0.778733
2 142092 0.43 0.665237
3 142208 0.70 0.757357
4 141916 0.02 0.506217
5 141575 -0.78 0.217359
6 142185 0.64 0.740241
7 142534 1.46 0.927788
8 141640 -0.63 0.264584
9 141427 -1.13 0.129884
10 141704 -0.48 0.315705
11 141205 -1.65 0.049920
12 141846 -0.15 0.441184
13 141398 -1.19 0.116103
14 142089 0.42 0.662681
15 141466 -1.04 0.150144
16 141517 -0.92 0.179661
17 140656 -2.93 0.001704
18 142863 2.23 0.987066
19 141650 -0.61 0.272287
20 142098 0.44 0.670328
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-20_04:31
Bits used No. missing words z-score p-value
23 to 32 141865 -0.1529 0.439254
22 to 31 141625 -0.9804 0.163432
21 to 30 141497 -1.4218 0.077538
20 to 29 141510 -1.3770 0.084256
19 to 28 141746 -0.5632 0.286647
18 to 27 141627 -0.9736 0.165140
17 to 26 142099 0.6540 0.743455
16 to 25 142225 1.0885 0.861817
15 to 24 142063 0.5299 0.701908
14 to 23 141677 -0.8011 0.211526
13 to 22 142064 0.5333 0.703103
12 to 21 141799 -0.3804 0.351806
11 to 20 141299 -2.1046 0.017664
10 to 19 141787 -0.4218 0.336575
9 to 18 141685 -0.7736 0.219598
8 to 17 141184 -2.5011 0.006190
7 to 16 141368 -1.8667 0.030975
6 to 15 141986 0.2644 0.604256
5 to 14 141477 -1.4908 0.068008
4 to 13 142269 1.2402 0.892557
3 to 12 141793 -0.4011 0.344159
2 to 11 141803 -0.3667 0.356938
1 to 10 141817 -0.3184 0.375099
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-20_04:31
Bits used No. missing words z-score p-value
28 to 32 142161 0.8531 0.803203
27 to 31 141949 0.1345 0.553486
26 to 30 141663 -0.8350 0.201854
25 to 29 141938 0.0972 0.538711
24 to 28 142555 2.1887 0.985691
23 to 27 141980 0.2396 0.594664
22 to 26 141675 -0.7943 0.213499
21 to 25 142164 0.8633 0.806011
20 to 24 142015 0.3582 0.639905
19 to 23 141996 0.2938 0.615543
18 to 22 142573 2.2497 0.987767
17 to 21 141483 -1.4452 0.074203
16 to 20 142379 1.5921 0.944319
15 to 19 142070 0.5446 0.707001
14 to 18 141760 -0.5062 0.306357
13 to 17 142676 2.5989 0.995324
12 to 16 141790 -0.4045 0.342919
11 to 15 141541 -1.2486 0.105910
10 to 14 141824 -0.2893 0.386193
9 to 13 142038 0.4362 0.668643
8 to 12 141703 -0.6994 0.242144
7 to 11 142266 1.2091 0.886678
6 to 10 141726 -0.6215 0.267149
5 to 9 141727 -0.6181 0.268265
4 to 8 142225 1.0701 0.857706
3 to 7 141683 -0.7672 0.221475
2 to 6 141870 -0.1333 0.446969
1 to 5 141905 -0.0147 0.494145
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-20_04:31
Bits used No. missing words z-score p-value
31 to 32 141815 -0.2783 0.390407
30 to 31 142267 1.0551 0.854304
29 to 30 141664 -0.7237 0.234629
28 to 29 141812 -0.2871 0.387014
27 to 28 141504 -1.1957 0.115914
26 to 27 141969 0.1760 0.569860
25 to 26 141851 -0.1721 0.431693
24 to 25 141626 -0.8358 0.201639
23 to 24 142054 0.4268 0.665221
22 to 23 142621 2.0993 0.982106
21 to 22 141990 0.2380 0.594046
20 to 21 141302 -1.7915 0.036604
19 to 20 141787 -0.3609 0.359104
18 to 19 141868 -0.1219 0.451482
17 to 18 141521 -1.1455 0.125998
16 to 17 142029 0.3530 0.637959
15 to 16 142383 1.3973 0.918832
14 to 15 142206 0.8751 0.809249
13 to 14 141569 -1.0039 0.157708
12 to 13 141665 -0.7207 0.235536
11 to 12 142198 0.8515 0.802764
10 to 11 142579 1.9754 0.975890
9 to 10 142236 0.9636 0.832384
8 to 9 142252 1.0108 0.843950
7 to 8 141533 -1.1101 0.133474
6 to 7 141606 -0.8948 0.185453
5 to 6 142038 0.3796 0.647863
4 to 5 141817 -0.2724 0.392673
3 to 4 141203 -2.0836 0.018600
2 to 3 142564 1.9312 0.973270
1 to 2 141943 0.0993 0.539559
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-20_04:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2592.14 1.303 0.903723
Test results for specific bytes for dh-ranFile-2018-06-20_04:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2532.12 0.454 0.675168
2 to 9 2567.22 0.951 0.829104
3 to 10 2424.68 -1.065 0.143387
4 to 11 2418.95 -1.146 0.125841
5 to 12 2479.73 -0.287 0.387202
6 to 13 2516.60 0.235 0.592778
7 to 14 2560.87 0.861 0.805316
8 to 15 2423.06 -1.088 0.138282
9 to 16 2650.12 2.123 0.983121
10 to 17 2524.32 0.344 0.634550
11 to 18 2428.07 -1.017 0.154512
12 to 19 2433.74 -0.937 0.174348
13 to 20 2404.48 -1.351 0.088378
14 to 21 2474.88 -0.355 0.361216
15 to 22 2474.15 -0.366 0.357341
16 to 23 2609.89 1.554 0.939918
17 to 24 2493.82 -0.087 0.465172
18 to 25 2390.55 -1.548 0.060826
19 to 26 2474.87 -0.355 0.361126
20 to 27 2513.41 0.190 0.575182
21 to 28 2555.85 0.790 0.785177
22 to 29 2397.51 -1.449 0.073606
23 to 30 2614.19 1.615 0.946833
24 to 31 2506.17 0.087 0.534748
25 to 32 2441.37 -0.829 0.203499
CDPARK for dh-ranFile-2018-06-20_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
3525 0.0913 0.536383
3550 1.2329 0.891189
3523 0.0000 0.500000
3514 -0.4110 0.340551
3518 -0.2283 0.409702
3555 1.4612 0.928018
3541 0.8219 0.794438
3514 -0.4110 0.340551
3527 0.1826 0.572463
3545 1.0046 0.842447
Square side=100, avg. no. parked=3531.20 sample std.=14.48
p-value of the KSTEST for those 10 p-values: 0.270718
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-20_04:31
0.3032,0.7651,0.5200,0.3170,0.1230,0.1065,0.3601,0.6715,0.2658,0.9417,
The KS test for those 10 p-values: 0.741430
The 3DSPHERES test for dh-ranFile-2018-06-20_04:31
sample no r^3 equiv. uni.
1 9.859 0.280105
2 47.604 0.795420
3 40.459 0.740406
4 22.233 0.523415
5 14.665 0.386668
6 5.666 0.172112
7 8.420 0.244713
8 8.226 0.239820
9 1.009 0.033078
10 15.634 0.406157
11 5.069 0.155475
12 20.258 0.490982
13 10.002 0.283508
14 32.304 0.659314
15 57.152 0.851187
16 12.959 0.350775
17 12.929 0.350113
18 18.636 0.462693
19 3.013 0.095567
20 22.404 0.526123
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.148797
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-20_04:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 0.1 -0.1 -0.1 -0.1 -0.6
-0.9 0.4 0.0 0.7 -1.3 0.7
0.1 0.3 0.2 0.4 -1.0 2.3
-2.2 0.3 1.4 -0.6 -0.4 -0.1
1.2 0.9 -3.5 -0.8 0.8 -0.6
-0.3 -0.5 0.4 1.2 0.1 -0.3
-0.9 0.8 -0.8 -0.1 -0.6 0.0
0.8
Chi-square with 42 degrees of freedom:40.446135
z-score=-0.169541, p-value=0.460716
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-20_04:31
Test no p-value
1 0.812308
2 0.116745
3 0.020493
4 0.038484
5 0.560988
6 0.049973
7 0.275939
8 0.645194
9 0.479780
10 0.151859
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.043650
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-20_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 66717 0.04 66431 0.83
3 25000.00 25044 0.08 25062 0.15
4 6666.67 6539 2.44 6806 2.91
5 1388.89 1402 0.12 1388 0.00
6 238.10 252 0.81 258 1.66
7 34.72 40 0.80 46 3.66
8 4.96 5 0.00 8 1.86
p=0.36378 p=0.91441
Number of rngs required: 689814, p-value: 0.951
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-20_04:31
No. of wins: Observed Expected
98415 98585.9
z-score=-0.764, pvalue=0.22238
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67007 66666.7 1.737 1.737
2 37549 37654.3 0.295 2.032
3 26848 26954.7 0.423 2.455
4 19298 19313.5 0.012 2.467
5 13888 13851.4 0.097 2.564
6 9822 9943.5 1.486 4.049
7 7237 7145.0 1.184 5.233
8 5086 5139.1 0.548 5.781
9 3694 3699.9 0.009 5.791
10 2638 2666.3 0.300 6.091
11 1920 1923.3 0.006 6.097
12 1400 1388.7 0.091 6.188
13 1000 1003.7 0.014 6.202
14 706 726.1 0.559 6.760
15 485 525.8 3.171 9.932
16 382 381.2 0.002 9.934
17 276 276.5 0.001 9.935
18 242 200.8 8.440 18.374
19 156 146.0 0.687 19.062
20 93 106.2 1.644 20.706
21 273 287.1 0.694 21.400
Chisq= 21.40 for 20 degrees of freedom, p= 0.62604
SUMMARY of craptest
p-value for no. of wins: 0.222380
p-value for throws/game: 0.626044
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-20_04:31
No. of wins: Observed Expected
98619 98585.9
z-score= 0.148, pvalue=0.55892
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66231 66666.7 2.847 2.847
2 37748 37654.3 0.233 3.080
3 27085 26954.7 0.630 3.710
4 19362 19313.5 0.122 3.832
5 13827 13851.4 0.043 3.875
6 10134 9943.5 3.648 7.523
7 7133 7145.0 0.020 7.543
8 5118 5139.1 0.086 7.629
9 3693 3699.9 0.013 7.642
10 2687 2666.3 0.161 7.803
11 1930 1923.3 0.023 7.826
12 1410 1388.7 0.325 8.151
13 980 1003.7 0.560 8.712
14 737 726.1 0.162 8.874
15 482 525.8 3.654 12.529
16 383 381.2 0.009 12.537
17 294 276.5 1.102 13.640
18 221 200.8 2.026 15.666
19 159 146.0 1.160 16.826
20 104 106.2 0.046 16.872
21 282 287.1 0.091 16.963
Chisq= 16.96 for 20 degrees of freedom, p= 0.34465
SUMMARY of craptest
p-value for no. of wins: 0.558918
p-value for throws/game: 0.344652
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0017,0.0062,0.0175,0.0177,0.0186,0.0205,0.0236,0.0239,0.0240,0.0310,
0.0331,0.0366,0.0385,0.0431,0.0436,0.0499,0.0500,0.0568,0.0608,0.0680,
0.0736,0.0742,0.0775,0.0843,0.0884,0.0922,0.0956,0.0971,0.1026,0.1035,
0.1059,0.1065,0.1159,0.1161,0.1167,0.1230,0.1240,0.1245,0.1258,0.1260,
0.1299,0.1335,0.1383,0.1434,0.1488,0.1501,0.1519,0.1545,0.1555,0.1577,
0.1634,0.1651,0.1713,0.1721,0.1743,0.1797,0.1855,0.1903,0.2016,0.2019,
0.2035,0.2115,0.2135,0.2174,0.2192,0.2196,0.2215,0.2224,0.2274,0.2289,
0.2346,0.2355,0.2398,0.2421,0.2447,0.2631,0.2633,0.2646,0.2652,0.2658,
0.2671,0.2683,0.2707,0.2723,0.2759,0.2801,0.2835,0.2866,0.3032,0.3064,
0.3151,0.3157,0.3170,0.3241,0.3366,0.3381,0.3406,0.3406,0.3429,0.3442,
0.3447,0.3501,0.3508,0.3518,0.3569,0.3573,0.3591,0.3601,0.3611,0.3612,
0.3638,0.3747,0.3751,0.3862,0.3867,0.3870,0.3872,0.3877,0.3904,0.3926,
0.3927,0.3929,0.4062,0.4097,0.4118,0.4197,0.4293,0.4317,0.4393,0.4412,
0.4425,0.4470,0.4515,0.4560,0.4607,0.4627,0.4652,0.4659,0.4783,0.4798,
0.4910,0.4926,0.4941,0.5000,0.5062,0.5141,0.5200,0.5215,0.5234,0.5261,
0.5335,0.5347,0.5360,0.5364,0.5387,0.5396,0.5434,0.5448,0.5521,0.5535,
0.5589,0.5601,0.5610,0.5699,0.5725,0.5752,0.5793,0.5928,0.5932,0.5940,
0.5947,0.6043,0.6115,0.6155,0.6260,0.6345,0.6352,0.6380,0.6399,0.6401,
0.6430,0.6452,0.6463,0.6479,0.6593,0.6627,0.6652,0.6652,0.6657,0.6682,
0.6686,0.6703,0.6715,0.6752,0.6817,0.7019,0.7028,0.7031,0.7070,0.7282,
0.7290,0.7302,0.7334,0.7389,0.7393,0.7402,0.7404,0.7414,0.7435,0.7471,
0.7574,0.7591,0.7628,0.7651,0.7787,0.7852,0.7884,0.7944,0.7954,0.8028,
0.8032,0.8053,0.8060,0.8092,0.8123,0.8123,0.8189,0.8227,0.8291,0.8323,
0.8324,0.8424,0.8440,0.8512,0.8515,0.8522,0.8543,0.8577,0.8618,0.8867,
0.8912,0.8926,0.8960,0.9018,0.9026,0.9037,0.9134,0.9144,0.9188,0.9237,
0.9278,0.9280,0.9399,0.9417,0.9443,0.9468,0.9509,0.9634,0.9648,0.9697,
0.9733,0.9759,0.9821,0.9831,0.9857,0.9871,0.9878,0.9953,0.9961,
Overall p-value after applying KStest on 269 p-values = 0.364246
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.