RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-18_17:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.66 26.6349 0.936356
2 to 25 15.69 19.5893 0.704228
3 to 26 15.77 14.3746 0.359567
4 to 27 15.68 17.7639 0.596122
5 to 28 15.75 24.7764 0.900171
6 to 29 15.51 23.6737 0.871425
7 to 30 15.71 18.9426 0.668165
8 to 31 15.80 13.2609 0.281449
9 to 32 15.90 23.9607 0.879492
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.073784
Tough bday spacings test for dh-ranFile-2018-06-18_17:31: 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 32 83 99 101 76 45 36 11 5 4
(O-E)^2/E 0.1 0.6 1.3 0.0 0.1 0.1 1.0 1.3 1.0 0.4 0.0
Birthday Spacings: Sum(O-E)^2/E= 5.896, p= 0.176
RESULTS OF GCD FOR dh-ranFile-2018-06-18_17:31
Euclid's algorithm:
p-value, steps to gcd: 0.672778
p-value, dist. of gcd's: 0.957682
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-18_17:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.677 0.354 0.653 0.760 0.884 0.872 0.706 0.809
Bits 8 to 15---> 0.724 0.995 0.888 0.454 0.635 0.055 0.539 0.934
Bits 16 to 23---> 0.870 0.566 0.102 0.240 0.748 0.716 0.145 0.130
Bits 24 to 31---> 0.174 0.990 0.352 0.782 0.036 0.350 0.600 0.209
KS test for the above 32 p values: 0.664
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-18_17:31,
p-values for 5 runs: 0.1228, 0.1123, 0.0981, 0.4027, 0.1865
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-18_17:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 206 211.4 0.139 0.139
r= 29 5098 5134.0 0.253 0.391
r= 30 23140 23103.0 0.059 0.451
r= 31 11556 11551.5 0.002 0.452
chi-square = 0.452 with df = 3; p-value = 0.071
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-18_17:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 212 211.4 0.002 0.002
r= 30 5126 5134.0 0.012 0.014
r= 31 23065 23103.0 0.063 0.077
r= 32 11597 11551.5 0.179 0.256
chi-square = 0.256 with df = 3; p-value = 0.032
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-18_17:31
b-rank test for bits 1 to 8, p=0.55122
b-rank test for bits 2 to 9, p=0.66044
b-rank test for bits 3 to 10, p=0.82477
b-rank test for bits 4 to 11, p=0.75687
b-rank test for bits 5 to 12, p=0.44153
b-rank test for bits 6 to 13, p=0.94464
b-rank test for bits 7 to 14, p=0.46749
b-rank test for bits 8 to 15, p=0.38734
b-rank test for bits 9 to 16, p=0.89076
b-rank test for bits 10 to 17, p=0.32727
b-rank test for bits 11 to 18, p=0.47116
b-rank test for bits 12 to 19, p=0.56123
b-rank test for bits 13 to 20, p=0.10782
b-rank test for bits 14 to 21, p=0.19701
b-rank test for bits 15 to 22, p=0.80018
b-rank test for bits 16 to 23, p=0.29953
b-rank test for bits 17 to 24, p=0.08132
b-rank test for bits 18 to 25, p=0.22246
b-rank test for bits 19 to 26, p=0.12129
b-rank test for bits 20 to 27, p=0.02237
b-rank test for bits 21 to 28, p=0.21607
b-rank test for bits 22 to 29, p=0.13271
b-rank test for bits 23 to 30, p=0.25680
b-rank test for bits 24 to 31, p=0.26336
b-rank test for bits 25 to 32, p=0.16943
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 = 0.174778
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-18_17:31
(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 142464 1.30 0.902505
2 141688 -0.52 0.302534
3 142268 0.84 0.798989
4 141706 -0.48 0.317369
5 142744 1.95 0.974422
6 142381 1.10 0.864776
7 141983 0.17 0.568331
8 142049 0.33 0.627913
9 141542 -0.86 0.195378
10 141855 -0.13 0.449494
11 141401 -1.19 0.117478
12 142437 1.23 0.891189
13 141828 -0.19 0.424645
14 141640 -0.63 0.264584
15 142501 1.38 0.916577
16 141944 0.08 0.532281
17 141692 -0.51 0.305804
18 141753 -0.37 0.357460
19 142617 1.65 0.950879
20 141483 -1.00 0.159601
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-18_17:31
Bits used No. missing words z-score p-value
23 to 32 142140 0.7954 0.786814
22 to 31 142283 1.2885 0.901217
21 to 30 142113 0.7023 0.758757
20 to 29 141372 -1.8529 0.031951
19 to 28 141496 -1.4253 0.077039
18 to 27 141627 -0.9736 0.165140
17 to 26 141696 -0.7356 0.230981
16 to 25 142251 1.1782 0.880636
15 to 24 141482 -1.4736 0.070301
14 to 23 141975 0.2264 0.589574
13 to 22 142163 0.8747 0.809138
12 to 21 141816 -0.3218 0.373792
11 to 20 142186 0.9540 0.829967
10 to 19 142023 0.3920 0.652458
9 to 18 141978 0.2368 0.593591
8 to 17 141854 -0.1908 0.424344
7 to 16 141996 0.2989 0.617477
6 to 15 141946 0.1264 0.550312
5 to 14 141783 -0.4356 0.331556
4 to 13 142248 1.1678 0.878562
3 to 12 142080 0.5885 0.721907
2 to 11 141786 -0.4253 0.335318
1 to 10 141523 -1.3322 0.091402
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-18_17:31
Bits used No. missing words z-score p-value
28 to 32 141713 -0.6655 0.252857
27 to 31 141095 -2.7604 0.002886
26 to 30 141785 -0.4215 0.336711
25 to 29 141857 -0.1774 0.429601
24 to 28 142242 1.1277 0.870276
23 to 27 142271 1.2260 0.889901
22 to 26 142083 0.5887 0.721973
21 to 25 141975 0.2226 0.588081
20 to 24 141772 -0.4655 0.320778
19 to 23 141573 -1.1401 0.127122
18 to 22 141277 -2.1435 0.016037
17 to 21 142019 0.3718 0.644965
16 to 20 142061 0.5141 0.696421
15 to 19 141768 -0.4791 0.315939
14 to 18 142455 1.8497 0.967824
13 to 17 141890 -0.0655 0.473878
12 to 16 141895 -0.0486 0.480629
11 to 15 142100 0.6463 0.740970
10 to 14 141877 -0.1096 0.456366
9 to 13 141768 -0.4791 0.315939
8 to 12 141631 -0.9435 0.172715
7 to 11 141746 -0.5537 0.289905
6 to 10 142178 0.9107 0.818785
5 to 9 141404 -1.7130 0.043358
4 to 8 142152 0.8226 0.794635
3 to 7 142572 2.2463 0.987659
2 to 6 141761 -0.5028 0.307548
1 to 5 141694 -0.7299 0.232716
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-18_17:31
Bits used No. missing words z-score p-value
31 to 32 142232 0.9518 0.829408
30 to 31 142040 0.3855 0.650051
29 to 30 142017 0.3176 0.624610
28 to 29 142058 0.4386 0.669508
27 to 28 141599 -0.9154 0.179984
26 to 27 142140 0.6804 0.751888
25 to 26 141906 -0.0098 0.496081
24 to 25 141905 -0.0128 0.494905
23 to 24 142659 2.2114 0.986496
22 to 23 142265 1.0492 0.852951
21 to 22 142002 0.2734 0.607713
20 to 21 141729 -0.5319 0.297381
19 to 20 142284 1.1052 0.865468
18 to 19 142212 0.8928 0.814026
17 to 18 142107 0.5831 0.720086
16 to 17 140998 -2.6883 0.003591
15 to 16 141842 -0.1986 0.421283
14 to 15 142194 0.8397 0.799471
13 to 14 142318 1.2055 0.885998
12 to 13 142280 1.0934 0.862896
11 to 12 141517 -1.1573 0.123572
10 to 11 141828 -0.2399 0.405199
9 to 10 141632 -0.8181 0.206655
8 to 9 142461 1.6273 0.948168
7 to 8 141207 -2.0718 0.019143
6 to 7 141926 0.0492 0.519610
5 to 6 142072 0.4799 0.684334
4 to 5 140965 -2.7856 0.002671
3 to 4 141881 -0.0836 0.466699
2 to 3 141865 -0.1308 0.447980
1 to 2 142271 1.0669 0.856985
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-18_17:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2597.52 1.379 0.916082
Test results for specific bytes for dh-ranFile-2018-06-18_17:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2519.56 0.277 0.608949
2 to 9 2461.80 -0.540 0.294526
3 to 10 2439.27 -0.859 0.195212
4 to 11 2493.97 -0.085 0.466042
5 to 12 2450.30 -0.703 0.241054
6 to 13 2499.69 -0.004 0.498267
7 to 14 2697.22 2.789 0.997358
8 to 15 2592.92 1.314 0.905588
9 to 16 2500.48 0.007 0.502728
10 to 17 2496.36 -0.052 0.479447
11 to 18 2372.74 -1.800 0.035953
12 to 19 2491.69 -0.117 0.453250
13 to 20 2553.60 0.758 0.775779
14 to 21 2569.46 0.982 0.837019
15 to 22 2530.03 0.425 0.664462
16 to 23 2459.49 -0.573 0.283379
17 to 24 2506.03 0.085 0.534004
18 to 25 2438.77 -0.866 0.193282
19 to 26 2415.82 -1.191 0.116924
20 to 27 2476.10 -0.338 0.367658
21 to 28 2534.85 0.493 0.688933
22 to 29 2523.95 0.339 0.632609
23 to 30 2629.62 1.833 0.966611
24 to 31 2478.26 -0.307 0.379254
25 to 32 2441.60 -0.826 0.204424
CDPARK for dh-ranFile-2018-06-18_17:31: 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
3512 -0.5023 0.307734
3487 -1.6438 0.050105
3512 -0.5023 0.307734
3545 1.0046 0.842447
3518 -0.2283 0.409702
3544 0.9589 0.831196
3521 -0.0913 0.463617
3562 1.7808 0.962529
3483 -1.8265 0.033889
3509 -0.6393 0.261324
Square side=100, avg. no. parked=3519.30 sample std.=23.82
p-value of the KSTEST for those 10 p-values: 0.659267
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-18_17:31
0.3014,0.6694,0.3876,0.8356,0.3664,0.2469,0.3959,0.9318,0.5593,0.8780,
The KS test for those 10 p-values: 0.625236
The 3DSPHERES test for dh-ranFile-2018-06-18_17:31
sample no r^3 equiv. uni.
1 4.795 0.147715
2 12.843 0.348244
3 77.170 0.923643
4 2.981 0.094579
5 2.483 0.079423
6 10.218 0.288652
7 58.353 0.857028
8 7.928 0.232238
9 65.509 0.887367
10 8.400 0.244228
11 46.195 0.785586
12 51.356 0.819473
13 25.500 0.572584
14 4.398 0.136357
15 13.576 0.363987
16 10.338 0.291492
17 25.367 0.570685
18 7.320 0.216503
19 0.448 0.014826
20 10.431 0.293688
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.192599
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-18_17:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 0.9 -0.8 0.9 1.6 -0.2
-0.1 -0.7 0.0 -0.9 0.3 0.5
-1.4 1.5 -0.3 0.3 -1.3 -1.2
0.6 0.0 1.6 -0.4 -1.0 1.7
1.2 0.6 0.1 -2.5 -0.7 -0.7
0.6 1.4 0.3 0.0 -0.1 0.8
1.0 -0.1 -0.8 -0.1 -1.3 -1.0
-1.1
Chi-square with 42 degrees of freedom:38.650508
z-score=-0.365460, p-value=0.381197
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-18_17:31
Test no p-value
1 0.399987
2 0.540476
3 0.635355
4 0.770213
5 0.591802
6 0.001166
7 0.052176
8 0.231945
9 0.020178
10 0.698478
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.139326
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-18_17:31:
(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 66573 0.13 66686 0.01
3 25000.00 25164 1.08 24894 0.45
4 6666.67 6601 0.65 6676 0.01
5 1388.89 1399 0.07 1479 5.85
6 238.10 227 0.52 229 0.35
7 34.72 34 0.01 25 2.72
8 4.96 1 3.16 10 5.12
p=0.53311 p=0.97552
Number of rngs required: 689390, p-value: 0.874
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-18_17:31
No. of wins: Observed Expected
98774 98585.9
z-score= 0.841, pvalue=0.79996
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66617 66666.7 0.037 0.037
2 37633 37654.3 0.012 0.049
3 27090 26954.7 0.679 0.728
4 19206 19313.5 0.598 1.326
5 13882 13851.4 0.068 1.393
6 10004 9943.5 0.368 1.761
7 7117 7145.0 0.110 1.871
8 5083 5139.1 0.612 2.483
9 3682 3699.9 0.086 2.569
10 2666 2666.3 0.000 2.569
11 1954 1923.3 0.489 3.058
12 1378 1388.7 0.083 3.141
13 1028 1003.7 0.588 3.729
14 710 726.1 0.359 4.087
15 560 525.8 2.220 6.307
16 370 381.2 0.326 6.633
17 277 276.5 0.001 6.634
18 190 200.8 0.584 7.218
19 159 146.0 1.160 8.379
20 109 106.2 0.073 8.452
21 285 287.1 0.016 8.467
Chisq= 8.47 for 20 degrees of freedom, p= 0.01170
SUMMARY of craptest
p-value for no. of wins: 0.799960
p-value for throws/game: 0.011702
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-18_17:31
No. of wins: Observed Expected
98564 98585.9
z-score=-0.098, pvalue=0.46106
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66517 66666.7 0.336 0.336
2 37873 37654.3 1.270 1.606
3 26920 26954.7 0.045 1.651
4 19209 19313.5 0.565 2.216
5 13775 13851.4 0.422 2.637
6 9992 9943.5 0.236 2.874
7 7195 7145.0 0.350 3.223
8 5108 5139.1 0.188 3.411
9 3759 3699.9 0.945 4.356
10 2629 2666.3 0.522 4.878
11 1919 1923.3 0.010 4.888
12 1420 1388.7 0.704 5.591
13 1032 1003.7 0.797 6.388
14 744 726.1 0.439 6.828
15 512 525.8 0.364 7.192
16 381 381.2 0.000 7.192
17 285 276.5 0.259 7.450
18 218 200.8 1.468 8.918
19 123 146.0 3.619 12.537
20 103 106.2 0.097 12.635
21 286 287.1 0.004 12.639
Chisq= 12.64 for 20 degrees of freedom, p= 0.10766
SUMMARY of craptest
p-value for no. of wins: 0.461060
p-value for throws/game: 0.107664
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0012,0.0027,0.0029,0.0036,0.0117,0.0148,0.0160,0.0191,0.0202,0.0224,
0.0319,0.0320,0.0339,0.0358,0.0360,0.0434,0.0501,0.0522,0.0551,0.0703,
0.0708,0.0738,0.0770,0.0794,0.0813,0.0914,0.0946,0.0981,0.1020,0.1077,
0.1078,0.1123,0.1169,0.1175,0.1213,0.1228,0.1236,0.1271,0.1303,0.1327,
0.1364,0.1393,0.1454,0.1477,0.1596,0.1651,0.1694,0.1727,0.1735,0.1748,
0.1761,0.1800,0.1865,0.1926,0.1933,0.1952,0.1954,0.1970,0.2044,0.2067,
0.2092,0.2161,0.2165,0.2225,0.2310,0.2319,0.2322,0.2327,0.2400,0.2411,
0.2442,0.2469,0.2529,0.2568,0.2613,0.2634,0.2646,0.2814,0.2834,0.2887,
0.2899,0.2915,0.2937,0.2945,0.2974,0.2995,0.3014,0.3025,0.3058,0.3075,
0.3077,0.3077,0.3159,0.3159,0.3174,0.3208,0.3273,0.3316,0.3353,0.3367,
0.3482,0.3503,0.3519,0.3539,0.3575,0.3596,0.3640,0.3664,0.3677,0.3738,
0.3793,0.3812,0.3873,0.3876,0.3959,0.4000,0.4027,0.4052,0.4097,0.4213,
0.4243,0.4246,0.4296,0.4415,0.4480,0.4495,0.4532,0.4535,0.4564,0.4611,
0.4636,0.4660,0.4667,0.4675,0.4712,0.4739,0.4794,0.4806,0.4949,0.4961,
0.4983,0.5027,0.5196,0.5323,0.5331,0.5340,0.5392,0.5405,0.5503,0.5512,
0.5593,0.5612,0.5665,0.5683,0.5707,0.5726,0.5881,0.5896,0.5918,0.5936,
0.5961,0.5997,0.6077,0.6089,0.6175,0.6246,0.6252,0.6279,0.6326,0.6348,
0.6354,0.6450,0.6501,0.6525,0.6529,0.6593,0.6604,0.6637,0.6645,0.6682,
0.6694,0.6695,0.6728,0.6767,0.6843,0.6889,0.6964,0.6985,0.7042,0.7056,
0.7157,0.7201,0.7219,0.7220,0.7241,0.7410,0.7479,0.7519,0.7569,0.7588,
0.7603,0.7702,0.7758,0.7823,0.7856,0.7868,0.7946,0.7990,0.7995,0.8000,
0.8002,0.8090,0.8091,0.8140,0.8188,0.8195,0.8248,0.8294,0.8300,0.8312,
0.8356,0.8370,0.8424,0.8530,0.8570,0.8570,0.8629,0.8648,0.8655,0.8697,
0.8703,0.8714,0.8721,0.8741,0.8780,0.8786,0.8795,0.8806,0.8844,0.8860,
0.8874,0.8881,0.8899,0.8908,0.8912,0.9002,0.9012,0.9025,0.9056,0.9161,
0.9166,0.9236,0.9318,0.9344,0.9364,0.9446,0.9482,0.9509,0.9577,0.9625,
0.9666,0.9678,0.9744,0.9755,0.9865,0.9877,0.9897,0.9954,0.9974,
Overall p-value after applying KStest on 269 p-values = 0.775488
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.