RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-18_00:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.41 29.4693 0.969564
2 to 25 15.88 8.1941 0.037781
3 to 26 15.75 20.8303 0.766025
4 to 27 15.74 22.9412 0.848825
5 to 28 15.81 17.1401 0.555086
6 to 29 15.83 28.7288 0.962890
7 to 30 15.67 23.5898 0.868984
8 to 31 15.70 16.8251 0.533722
9 to 32 15.59 16.5222 0.512838
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.082559
Tough bday spacings test for dh-ranFile-2018-06-18_00:31: 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 10 39 68 97 100 84 56 23 16 6 1
(O-E)^2/E 0.1 0.2 0.4 0.0 0.1 0.4 0.3 1.5 0.1 0.1 2.3
Birthday Spacings: Sum(O-E)^2/E= 5.392, p= 0.136
RESULTS OF GCD FOR dh-ranFile-2018-06-18_00:31
Euclid's algorithm:
p-value, steps to gcd: 0.973758
p-value, dist. of gcd's: 0.595110
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-18_00:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.719 0.158 0.870 0.561 0.362 0.899 0.422 0.226
Bits 8 to 15---> 0.707 0.378 0.694 0.932 0.105 0.492 0.317 0.773
Bits 16 to 23---> 0.032 0.090 0.430 0.656 0.756 0.852 0.012 0.695
Bits 24 to 31---> 0.232 0.052 0.371 0.729 0.414 0.284 0.517 0.513
KS test for the above 32 p values: 0.142
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-18_00:31,
p-values for 5 runs: 0.8102, 0.7486, 0.6975, 0.9677, 0.7650
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-18_00:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 236 211.4 2.858 2.858
r= 29 5230 5134.0 1.795 4.653
r= 30 23053 23103.0 0.108 4.761
r= 31 11481 11551.5 0.431 5.192
chi-square = 5.192 with df = 3; p-value = 0.842
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-18_00:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 228 211.4 1.301 1.301
r= 30 5121 5134.0 0.033 1.334
r= 31 23258 23103.0 1.039 2.373
r= 32 11393 11551.5 2.175 4.548
chi-square = 4.548 with df = 3; p-value = 0.792
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-18_00:31
b-rank test for bits 1 to 8, p=0.88795
b-rank test for bits 2 to 9, p=0.95196
b-rank test for bits 3 to 10, p=0.29069
b-rank test for bits 4 to 11, p=0.05806
b-rank test for bits 5 to 12, p=0.84524
b-rank test for bits 6 to 13, p=0.50983
b-rank test for bits 7 to 14, p=0.36639
b-rank test for bits 8 to 15, p=0.41039
b-rank test for bits 9 to 16, p=0.29540
b-rank test for bits 10 to 17, p=0.93313
b-rank test for bits 11 to 18, p=0.73994
b-rank test for bits 12 to 19, p=0.94096
b-rank test for bits 13 to 20, p=0.66610
b-rank test for bits 14 to 21, p=0.84169
b-rank test for bits 15 to 22, p=0.59401
b-rank test for bits 16 to 23, p=0.58459
b-rank test for bits 17 to 24, p=0.51090
b-rank test for bits 18 to 25, p=0.15296
b-rank test for bits 19 to 26, p=0.29279
b-rank test for bits 20 to 27, p=0.42601
b-rank test for bits 21 to 28, p=0.11299
b-rank test for bits 22 to 29, p=0.90434
b-rank test for bits 23 to 30, p=0.88625
b-rank test for bits 24 to 31, p=0.99259
b-rank test for bits 25 to 32, p=0.71136
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 = 0.140817
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-18_00:31
(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 141924 0.03 0.513671
2 141677 -0.54 0.293624
3 141707 -0.47 0.318202
4 141642 -0.62 0.266116
5 141669 -0.56 0.287222
6 141590 -0.75 0.227804
7 141981 0.17 0.566493
8 141740 -0.40 0.346189
9 141475 -1.01 0.155103
10 142024 0.27 0.605620
11 141733 -0.41 0.340175
12 141928 0.04 0.517397
13 142036 0.30 0.616369
14 142149 0.56 0.712252
15 141659 -0.58 0.279313
16 142533 1.46 0.927466
17 140877 -2.41 0.007933
18 142851 2.20 0.986102
19 142103 0.45 0.674546
20 142170 0.61 0.728752
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-18_00:31
Bits used No. missing words z-score p-value
23 to 32 141609 -1.0356 0.150190
22 to 31 141453 -1.5736 0.057796
21 to 30 142145 0.8127 0.791792
20 to 29 142058 0.5127 0.695904
19 to 28 141918 0.0299 0.511925
18 to 27 141694 -0.7425 0.228887
17 to 26 141014 -3.0873 0.001010
16 to 25 141874 -0.1218 0.451518
15 to 24 141710 -0.6873 0.245933
14 to 23 142043 0.4609 0.677576
13 to 22 141829 -0.2770 0.390890
12 to 21 141507 -1.3873 0.082668
11 to 20 142218 1.0644 0.856422
10 to 19 142136 0.7816 0.782781
9 to 18 142537 2.1644 0.984782
8 to 17 141767 -0.4908 0.311786
7 to 16 142143 0.8058 0.789809
6 to 15 142202 1.0092 0.843562
5 to 14 141939 0.1023 0.540745
4 to 13 142203 1.0127 0.844388
3 to 12 141937 0.0954 0.538007
2 to 11 141654 -0.8804 0.189308
1 to 10 142479 1.9644 0.975257
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-18_00:31
Bits used No. missing words z-score p-value
28 to 32 141929 0.0667 0.526581
27 to 31 141775 -0.4554 0.324427
26 to 30 141690 -0.7435 0.228592
25 to 29 141813 -0.3265 0.372007
24 to 28 141881 -0.0960 0.461747
23 to 27 141683 -0.7672 0.221475
22 to 26 141770 -0.4723 0.318355
21 to 25 141649 -0.8825 0.188760
20 to 24 142154 0.8294 0.796558
19 to 23 141965 0.1887 0.574841
18 to 22 142207 1.0091 0.843525
17 to 21 141705 -0.6926 0.244267
16 to 20 141997 0.2972 0.616838
15 to 19 142387 1.6192 0.947300
14 to 18 141918 0.0294 0.511723
13 to 17 142106 0.6667 0.747511
12 to 16 142485 1.9514 0.974497
11 to 15 142080 0.5785 0.718551
10 to 14 142199 0.9819 0.836933
9 to 13 142068 0.5379 0.704665
8 to 12 141647 -0.8893 0.186933
7 to 11 141375 -1.8113 0.035048
6 to 10 141660 -0.8452 0.199003
5 to 9 141575 -1.1333 0.128540
4 to 8 141757 -0.5164 0.302797
3 to 7 142507 2.0260 0.978618
2 to 6 141830 -0.2689 0.393998
1 to 5 142253 1.1650 0.877987
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-18_00:31
Bits used No. missing words z-score p-value
31 to 32 142116 0.6096 0.728952
30 to 31 142528 1.8250 0.965998
29 to 30 141879 -0.0895 0.464355
28 to 29 141781 -0.3786 0.352509
27 to 28 141902 -0.0216 0.491375
26 to 27 142213 0.8958 0.814815
25 to 26 142025 0.3412 0.633527
24 to 25 141643 -0.7856 0.216041
23 to 24 142118 0.6155 0.730903
22 to 23 141881 -0.0836 0.466699
21 to 22 142449 1.5919 0.944302
20 to 21 141825 -0.2488 0.401773
19 to 20 141914 0.0138 0.505496
18 to 19 141972 0.1849 0.573333
17 to 18 142346 1.2881 0.901147
16 to 17 141797 -0.3314 0.370187
15 to 16 142028 0.3501 0.636853
14 to 15 141678 -0.6824 0.247496
13 to 14 141440 -1.3845 0.083110
12 to 13 141450 -1.3550 0.087716
11 to 12 141791 -0.3491 0.363524
10 to 11 141746 -0.4818 0.314974
9 to 10 142033 0.3648 0.642373
8 to 9 141006 -2.6647 0.003853
7 to 8 142848 2.7689 0.997188
6 to 7 141608 -0.8889 0.187034
5 to 6 141600 -0.9125 0.180759
4 to 5 142348 1.2940 0.902169
3 to 4 141575 -0.9862 0.162012
2 to 3 141649 -0.7679 0.221263
1 to 2 141959 0.1465 0.558244
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-18_00:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2585.69 1.212 0.887207
Test results for specific bytes for dh-ranFile-2018-06-18_00:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2505.94 0.084 0.533478
2 to 9 2484.22 -0.223 0.411691
3 to 10 2434.05 -0.933 0.175484
4 to 11 2424.17 -1.072 0.141762
5 to 12 2428.44 -1.012 0.155782
6 to 13 2622.99 1.739 0.959009
7 to 14 2408.35 -1.296 0.097458
8 to 15 2435.47 -0.913 0.180720
9 to 16 2540.22 0.569 0.715241
10 to 17 2550.11 0.709 0.760749
11 to 18 2539.97 0.565 0.714048
12 to 19 2456.93 -0.609 0.271227
13 to 20 2571.29 1.008 0.843321
14 to 21 2463.68 -0.514 0.303741
15 to 22 2461.48 -0.545 0.292977
16 to 23 2545.22 0.640 0.738772
17 to 24 2555.63 0.787 0.784279
18 to 25 2577.65 1.098 0.863919
19 to 26 2498.07 -0.027 0.489099
20 to 27 2558.04 0.821 0.794124
21 to 28 2662.92 2.304 0.989391
22 to 29 2481.64 -0.260 0.397544
23 to 30 2541.33 0.584 0.720546
24 to 31 2412.87 -1.232 0.108931
25 to 32 2583.36 1.179 0.880767
CDPARK for dh-ranFile-2018-06-18_00:31: 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
3482 -1.8721 0.030593
3497 -1.1872 0.117571
3503 -0.9132 0.180558
3526 0.1370 0.554479
3504 -0.8676 0.192812
3522 -0.0457 0.481790
3537 0.6393 0.738676
3513 -0.4566 0.323972
3514 -0.4110 0.340551
Square side=100, avg. no. parked=3511.90 sample std.=15.09
p-value of the KSTEST for those 10 p-values: 0.141083
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-18_00:31
0.3883,0.9976,0.9107,0.3551,0.2501,0.0033,0.6586,0.7531,0.0203,0.2639,
The KS test for those 10 p-values: 0.333386
The 3DSPHERES test for dh-ranFile-2018-06-18_00:31
sample no r^3 equiv. uni.
1 33.589 0.673602
2 16.961 0.431839
3 14.749 0.388382
4 52.454 0.825960
5 48.472 0.801254
6 3.781 0.118428
7 6.889 0.205183
8 19.792 0.483006
9 8.539 0.247719
10 22.233 0.523403
11 70.646 0.905093
12 7.123 0.211356
13 18.328 0.457163
14 17.166 0.435723
15 20.093 0.488172
16 39.392 0.731008
17 41.686 0.750809
18 0.319 0.010577
19 6.470 0.194001
20 2.175 0.069939
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.647267
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-18_00:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 0.5 0.3 2.7 1.0 -0.9
1.0 -0.6 -1.7 -0.2 -0.1 0.7
0.6 -0.6 -0.5 -0.3 -0.2 0.9
0.3 0.6 0.5 -0.8 -1.2 0.2
1.1 -0.1 -2.0 2.1 0.1 0.9
-0.8 -1.3 0.1 -0.6 0.2 0.8
-0.5 -0.4 -1.2 -1.3 -0.6 -1.0
-1.1
Chi-square with 42 degrees of freedom:39.104019
z-score=-0.315977, p-value=0.401177
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-18_00:31
Test no p-value
1 0.085593
2 0.388824
3 0.231874
4 0.723818
5 0.090132
6 0.674189
7 0.293511
8 0.075600
9 0.634544
10 0.397628
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.185072
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-18_00:31:
(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 66863 0.58 66715 0.04
3 25000.00 24782 1.90 24850 0.90
4 6666.67 6682 0.04 6740 0.81
5 1388.89 1380 0.06 1410 0.32
6 238.10 266 3.27 255 1.20
7 34.72 22 4.66 28 1.30
8 4.96 4 0.19 1 3.16
p=0.90148 p=0.74105
Number of rngs required: 689802, p-value: 0.949
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-18_00:31
No. of wins: Observed Expected
98357 98585.9
z-score=-1.024, pvalue=0.15301
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66387 66666.7 1.173 1.173
2 37728 37654.3 0.144 1.317
3 26893 26954.7 0.141 1.459
4 19099 19313.5 2.381 3.840
5 13952 13851.4 0.730 4.571
6 10073 9943.5 1.685 6.256
7 7142 7145.0 0.001 6.257
8 5092 5139.1 0.431 6.688
9 3821 3699.9 3.966 10.654
10 2700 2666.3 0.426 11.080
11 1940 1923.3 0.144 11.225
12 1398 1388.7 0.062 11.287
13 1006 1003.7 0.005 11.292
14 786 726.1 4.935 16.226
15 562 525.8 2.487 18.714
16 364 381.2 0.772 19.485
17 295 276.5 1.232 20.718
18 196 200.8 0.116 20.834
19 142 146.0 0.109 20.943
20 106 106.2 0.000 20.943
21 318 287.1 3.323 24.265
Chisq= 24.27 for 20 degrees of freedom, p= 0.76901
SUMMARY of craptest
p-value for no. of wins: 0.153015
p-value for throws/game: 0.769013
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-18_00:31
No. of wins: Observed Expected
98615 98585.9
z-score= 0.130, pvalue=0.55185
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66398 66666.7 1.083 1.083
2 37921 37654.3 1.889 2.971
3 26802 26954.7 0.865 3.837
4 19310 19313.5 0.001 3.837
5 13886 13851.4 0.086 3.924
6 10100 9943.5 2.462 6.386
7 7146 7145.0 0.000 6.386
8 5072 5139.1 0.875 7.261
9 3673 3699.9 0.195 7.456
10 2647 2666.3 0.140 7.596
11 1908 1923.3 0.122 7.718
12 1455 1388.7 3.161 10.879
13 1003 1003.7 0.001 10.880
14 709 726.1 0.405 11.285
15 511 525.8 0.419 11.703
16 405 381.2 1.492 13.195
17 298 276.5 1.665 14.861
18 214 200.8 0.864 15.724
19 153 146.0 0.337 16.062
20 125 106.2 3.322 19.384
21 264 287.1 1.861 21.245
Chisq= 21.24 for 20 degrees of freedom, p= 0.61714
SUMMARY of craptest
p-value for no. of wins: 0.551850
p-value for throws/game: 0.617137
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0010,0.0033,0.0039,0.0079,0.0106,0.0123,0.0203,0.0306,0.0321,0.0350,
0.0378,0.0521,0.0578,0.0581,0.0699,0.0756,0.0826,0.0827,0.0831,0.0856,
0.0877,0.0899,0.0901,0.0975,0.1054,0.1089,0.1130,0.1176,0.1184,0.1285,
0.1365,0.1408,0.1411,0.1418,0.1418,0.1502,0.1530,0.1530,0.1551,0.1558,
0.1580,0.1620,0.1755,0.1806,0.1807,0.1808,0.1851,0.1869,0.1870,0.1888,
0.1893,0.1928,0.1940,0.1990,0.2052,0.2114,0.2160,0.2213,0.2215,0.2260,
0.2278,0.2286,0.2289,0.2318,0.2319,0.2443,0.2459,0.2475,0.2477,0.2501,
0.2639,0.2661,0.2712,0.2793,0.2843,0.2872,0.2907,0.2928,0.2930,0.2935,
0.2936,0.2954,0.3028,0.3037,0.3118,0.3150,0.3174,0.3182,0.3184,0.3240,
0.3244,0.3334,0.3402,0.3406,0.3462,0.3525,0.3551,0.3624,0.3635,0.3664,
0.3702,0.3709,0.3720,0.3777,0.3883,0.3884,0.3888,0.3909,0.3940,0.3975,
0.3976,0.4012,0.4018,0.4104,0.4117,0.4145,0.4221,0.4260,0.4301,0.4318,
0.4357,0.4515,0.4572,0.4617,0.4636,0.4644,0.4667,0.4818,0.4830,0.4882,
0.4891,0.4914,0.4918,0.5055,0.5098,0.5109,0.5117,0.5119,0.5128,0.5131,
0.5137,0.5169,0.5174,0.5234,0.5266,0.5335,0.5337,0.5380,0.5407,0.5519,
0.5545,0.5551,0.5582,0.5610,0.5665,0.5733,0.5748,0.5846,0.5940,0.5951,
0.6056,0.6164,0.6168,0.6171,0.6335,0.6345,0.6369,0.6424,0.6473,0.6557,
0.6586,0.6661,0.6736,0.6742,0.6745,0.6776,0.6939,0.6952,0.6959,0.6975,
0.7047,0.7075,0.7114,0.7123,0.7140,0.7152,0.7186,0.7195,0.7205,0.7238,
0.7288,0.7290,0.7295,0.7309,0.7310,0.7387,0.7388,0.7399,0.7410,0.7475,
0.7486,0.7508,0.7531,0.7557,0.7607,0.7650,0.7660,0.7690,0.7730,0.7828,
0.7843,0.7898,0.7918,0.7920,0.7941,0.7966,0.8013,0.8102,0.8148,0.8260,
0.8369,0.8417,0.8417,0.8433,0.8435,0.8436,0.8444,0.8452,0.8488,0.8517,
0.8564,0.8639,0.8690,0.8698,0.8780,0.8808,0.8863,0.8872,0.8879,0.8992,
0.9011,0.9015,0.9022,0.9043,0.9051,0.9107,0.9275,0.9321,0.9331,0.9410,
0.9443,0.9473,0.9494,0.9520,0.9590,0.9629,0.9660,0.9677,0.9696,0.9738,
0.9745,0.9753,0.9786,0.9848,0.9861,0.9894,0.9926,0.9972,0.9976,
Overall p-value after applying KStest on 269 p-values = 0.944506
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.