RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-07-28_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 15.70 12.1926 0.211663
2 to 25 15.55 21.0098 0.774147
3 to 26 15.22 32.0910 0.985339
4 to 27 15.92 17.5345 0.581239
5 to 28 15.87 20.5713 0.753944
6 to 29 15.98 18.3669 0.633947
7 to 30 15.55 19.7199 0.711195
8 to 31 15.70 12.6544 0.241001
9 to 32 15.73 14.2282 0.349111
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.561725
Tough bday spacings test for dh-ranFile-2017-07-28_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 12 47 86 89 86 67 53 32 20 4 4
(O-E)^2/E 0.9 2.9 2.2 0.8 1.4 1.6 0.0 0.2 1.8 1.0 0.0
Birthday Spacings: Sum(O-E)^2/E= 12.766, p= 0.763
RESULTS OF GCD FOR dh-ranFile-2017-07-28_04:31
Euclid's algorithm:
p-value, steps to gcd: 0.803486
p-value, dist. of gcd's: 0.634016
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-07-28_04:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.895 0.274 0.846 0.779 0.673 0.836 0.838 0.569
Bits 8 to 15---> 0.907 0.288 0.503 0.456 0.666 0.172 0.421 0.796
Bits 16 to 23---> 0.428 0.433 0.450 0.231 0.791 0.627 0.036 0.977
Bits 24 to 31---> 0.183 0.654 0.729 0.471 0.588 0.891 0.939 0.467
KS test for the above 32 p values: 0.881
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-07-28_04:31,
p-values for 5 runs: 0.2217, 0.5182, 0.0232, 0.2162, 0.4351
Rank test for binary matrices (31x31) for dh-ranFile-2017-07-28_04:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 227 211.4 1.148 1.148
r= 29 5186 5134.0 0.526 1.675
r= 30 23120 23103.0 0.012 1.687
r= 31 11467 11551.5 0.618 2.306
chi-square = 2.306 with df = 3; p-value = 0.489
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2017-07-28_04:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 218 211.4 0.205 0.205
r= 30 5177 5134.0 0.360 0.565
r= 31 23139 23103.0 0.056 0.621
r= 32 11466 11551.5 0.633 1.254
chi-square = 1.254 with df = 3; p-value = 0.260
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2017-07-28_04:31
b-rank test for bits 1 to 8, p=0.96583
b-rank test for bits 2 to 9, p=0.53922
b-rank test for bits 3 to 10, p=0.69759
b-rank test for bits 4 to 11, p=0.00191
b-rank test for bits 5 to 12, p=0.96336
b-rank test for bits 6 to 13, p=0.37807
b-rank test for bits 7 to 14, p=0.70282
b-rank test for bits 8 to 15, p=0.11465
b-rank test for bits 9 to 16, p=0.36319
b-rank test for bits 10 to 17, p=0.91550
b-rank test for bits 11 to 18, p=0.42264
b-rank test for bits 12 to 19, p=0.07764
b-rank test for bits 13 to 20, p=0.43542
b-rank test for bits 14 to 21, p=0.50052
b-rank test for bits 15 to 22, p=0.14618
b-rank test for bits 16 to 23, p=0.19096
b-rank test for bits 17 to 24, p=0.09575
b-rank test for bits 18 to 25, p=0.10226
b-rank test for bits 19 to 26, p=0.10944
b-rank test for bits 20 to 27, p=0.52327
b-rank test for bits 21 to 28, p=0.75110
b-rank test for bits 22 to 29, p=0.87466
b-rank test for bits 23 to 30, p=0.23100
b-rank test for bits 24 to 31, p=0.05970
b-rank test for bits 25 to 32, p=0.93844
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 = 0.279125
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-07-28_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 142532 1.45 0.927143
2 141606 -0.71 0.239251
3 141635 -0.64 0.260775
4 142249 0.79 0.786292
5 141318 -1.38 0.083545
6 142313 0.94 0.827199
7 141577 -0.78 0.218735
8 141924 0.03 0.513671
9 141134 -1.81 0.035030
10 141598 -0.73 0.233489
11 142123 0.50 0.691191
12 142565 1.53 0.937231
13 141957 0.11 0.544342
14 141684 -0.53 0.299280
15 142298 0.91 0.818089
16 141864 -0.11 0.457826
17 141971 0.14 0.557285
18 141519 -0.91 0.180888
19 142407 1.16 0.877541
20 142270 0.84 0.800298
----------------------------------------------------------------
OPSO test for dh-ranFile-2017-07-28_04:31
Bits used No. missing words z-score p-value
23 to 32 142093 0.6333 0.736746
22 to 31 142028 0.4092 0.658806
21 to 30 141958 0.1678 0.566641
20 to 29 142073 0.5644 0.713752
19 to 28 141877 -0.1115 0.455617
18 to 27 142206 1.0230 0.846846
17 to 26 142133 0.7713 0.779728
16 to 25 142031 0.4196 0.662594
15 to 24 141708 -0.6942 0.243765
14 to 23 142287 1.3023 0.903595
13 to 22 141651 -0.8908 0.186520
12 to 21 141771 -0.4770 0.316681
11 to 20 141316 -2.0460 0.020380
10 to 19 142211 1.0402 0.850886
9 to 18 142413 1.7368 0.958788
8 to 17 142408 1.7196 0.957243
7 to 16 142080 0.5885 0.721907
6 to 15 142340 1.4851 0.931237
5 to 14 141573 -1.1598 0.123074
4 to 13 141772 -0.4736 0.317910
3 to 12 141682 -0.7839 0.216550
2 to 11 142182 0.9402 0.826453
1 to 10 142320 1.4161 0.921627
-----------------------------------------------------------------
OQSO test for dh-ranFile-2017-07-28_04:31
Bits used No. missing words z-score p-value
28 to 32 141573 -1.1401 0.127122
27 to 31 142024 0.3887 0.651255
26 to 30 141873 -0.1232 0.450993
25 to 29 141929 0.0667 0.526581
24 to 28 142681 2.6158 0.995549
23 to 27 142300 1.3243 0.907299
22 to 26 141838 -0.2418 0.404469
21 to 25 142017 0.3650 0.642438
20 to 24 141594 -1.0689 0.142554
19 to 23 141778 -0.4452 0.328093
18 to 22 141947 0.1277 0.550805
17 to 21 141710 -0.6757 0.249617
16 to 20 142516 2.0565 0.980133
15 to 19 141422 -1.6520 0.049271
14 to 18 142316 1.3785 0.915982
13 to 17 142062 0.5175 0.697605
12 to 16 142222 1.0599 0.855405
11 to 15 142219 1.0497 0.853079
10 to 14 141947 0.1277 0.550805
9 to 13 141911 0.0057 0.502258
8 to 12 141822 -0.2960 0.383602
7 to 11 142657 2.5345 0.994369
6 to 10 142121 0.7175 0.763475
5 to 9 142574 2.2531 0.987874
4 to 8 141934 0.0836 0.533324
3 to 7 141594 -1.0689 0.142554
2 to 6 141737 -0.5842 0.279553
1 to 5 141275 -2.1503 0.015767
-----------------------------------------------------------------
DNA test for dh-ranFile-2017-07-28_04:31
Bits used No. missing words z-score p-value
31 to 32 141780 -0.3815 0.351415
30 to 31 141474 -1.2842 0.099543
29 to 30 141742 -0.4936 0.310795
28 to 29 142044 0.3973 0.654411
27 to 28 141860 -0.1455 0.442152
26 to 27 142061 0.4474 0.672708
25 to 26 142459 1.6214 0.947539
24 to 25 141831 -0.2311 0.408633
23 to 24 141400 -1.5024 0.066491
22 to 23 141794 -0.3402 0.366851
21 to 22 141892 -0.0511 0.479615
20 to 21 141971 0.1819 0.572176
19 to 20 141490 -1.2370 0.108051
18 to 19 141748 -0.4759 0.317073
17 to 18 142169 0.7660 0.778158
16 to 17 141493 -1.2281 0.109702
15 to 16 142181 0.8014 0.788546
14 to 15 141536 -1.1013 0.135390
13 to 14 141619 -0.8564 0.195880
12 to 13 141889 -0.0600 0.476090
11 to 12 142217 0.9076 0.817950
10 to 11 141231 -2.0010 0.022698
9 to 10 141865 -0.1308 0.447980
8 to 9 142011 0.2999 0.617878
7 to 8 142376 1.3766 0.915683
6 to 7 141709 -0.5909 0.277279
5 to 6 142010 0.2970 0.616752
4 to 5 141820 -0.2635 0.396079
3 to 4 142288 1.1170 0.868007
2 to 3 141806 -0.3048 0.380256
1 to 2 141241 -1.9715 0.024335
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2017-07-28_04:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2492.56 -0.105 0.458093
Test results for specific bytes for dh-ranFile-2017-07-28_04:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2556.24 0.795 0.786792
2 to 9 2426.19 -1.044 0.148271
3 to 10 2484.88 -0.214 0.415358
4 to 11 2587.23 1.234 0.891339
5 to 12 2591.23 1.290 0.901514
6 to 13 2551.29 0.725 0.765871
7 to 14 2531.66 0.448 0.672843
8 to 15 2480.77 -0.272 0.392811
9 to 16 2451.64 -0.684 0.247033
10 to 17 2382.96 -1.655 0.048944
11 to 18 2474.81 -0.356 0.360855
12 to 19 2470.41 -0.418 0.337828
13 to 20 2511.35 0.160 0.563738
14 to 21 2438.74 -0.866 0.193150
15 to 22 2501.99 0.028 0.511248
16 to 23 2477.03 -0.325 0.372652
17 to 24 2478.82 -0.299 0.382282
18 to 25 2441.55 -0.827 0.204230
19 to 26 2439.14 -0.861 0.194694
20 to 27 2342.59 -2.226 0.013005
21 to 28 2474.05 -0.367 0.356805
22 to 29 2608.66 1.537 0.937811
23 to 30 2515.43 0.218 0.586367
24 to 31 2602.69 1.452 0.926783
25 to 32 2411.12 -1.257 0.104374
CDPARK for dh-ranFile-2017-07-28_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
3528 0.2283 0.590298
3524 0.0457 0.518210
3552 1.3242 0.907282
3543 0.9132 0.819442
3539 0.7306 0.767486
3511 -0.5479 0.291865
3533 0.4566 0.676028
3542 0.8676 0.807188
3555 1.4612 0.928018
3548 1.1416 0.873180
Square side=100, avg. no. parked=3537.50 sample std.=12.94
p-value of the KSTEST for those 10 p-values: 0.024474
Results for the MINIMUM DISTANCE test for dh-ranFile-2017-07-28_04:31
0.5130,0.0657,0.5139,0.4702,0.2423,0.8505,0.9607,0.2153,0.7982,0.2074,
The KS test for those 10 p-values: 0.960916
The 3DSPHERES test for dh-ranFile-2017-07-28_04:31
sample no r^3 equiv. uni.
1 13.853 0.369820
2 5.329 0.162758
3 50.591 0.814806
4 6.201 0.186736
5 64.931 0.885177
6 19.070 0.470425
7 58.114 0.855881
8 0.052 0.001729
9 0.177 0.005871
10 10.044 0.284527
11 0.204 0.006792
12 19.663 0.480779
13 2.448 0.078365
14 25.896 0.578186
15 5.043 0.154740
16 11.478 0.317924
17 37.510 0.713591
18 7.156 0.212213
19 24.583 0.559312
20 39.846 0.735048
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.074562
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-07-28_04:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 -0.7 -0.1 0.6 1.2 2.8
-1.1 -3.2 1.7 -0.7 2.2 -1.2
1.3 -0.6 0.1 -0.2 -0.6 0.7
2.7 -1.1 -1.9 0.3 0.5 -0.2
-0.7 -0.3 -0.9 -0.6 0.7 0.2
1.5 -1.1 0.8 -2.2 -0.8 -0.5
-0.7 0.5 0.1 -0.7 0.1 -1.0
-0.1
Chi-square with 42 degrees of freedom:62.770360
z-score=2.266232, p-value=0.979503
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2017-07-28_04:31
Test no p-value
1 0.518510
2 0.076913
3 0.923681
4 0.070543
5 0.230734
6 0.036539
7 0.027692
8 0.817706
9 0.310654
10 0.163142
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.031802
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-07-28_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 67000 1.67 66493 0.45
3 25000.00 24650 4.90 24946 0.12
4 6666.67 6655 0.02 6853 5.21
5 1388.89 1425 0.94 1421 0.74
6 238.10 234 0.07 243 0.10
7 34.72 32 0.21 36 0.05
8 4.96 3 0.77 7 0.84
p=0.80164 p=0.72347
Number of rngs required: 687738, p-value: 0.221
RESULTS OF CRAPS TEST for dh-ranFile-2017-07-28_04:31
No. of wins: Observed Expected
98235 98585.9
z-score=-1.569, pvalue=0.05830
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66585 66666.7 0.100 0.100
2 37741 37654.3 0.200 0.300
3 27036 26954.7 0.245 0.545
4 19350 19313.5 0.069 0.614
5 13977 13851.4 1.139 1.752
6 9989 9943.5 0.208 1.960
7 7046 7145.0 1.372 3.332
8 5068 5139.1 0.983 4.315
9 3665 3699.9 0.329 4.644
10 2732 2666.3 1.619 6.263
11 1804 1923.3 7.404 13.667
12 1360 1388.7 0.595 14.261
13 973 1003.7 0.940 15.201
14 758 726.1 1.398 16.599
15 512 525.8 0.364 16.963
16 376 381.2 0.070 17.033
17 293 276.5 0.980 18.012
18 212 200.8 0.621 18.634
19 144 146.0 0.027 18.661
20 103 106.2 0.097 18.758
21 276 287.1 0.430 19.188
Chisq= 19.19 for 20 degrees of freedom, p= 0.49038
SUMMARY of craptest
p-value for no. of wins: 0.058296
p-value for throws/game: 0.490381
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2017-07-28_04:31
No. of wins: Observed Expected
98491 98585.9
z-score=-0.424, pvalue=0.33569
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66475 66666.7 0.551 0.551
2 37483 37654.3 0.779 1.331
3 27168 26954.7 1.687 3.018
4 19266 19313.5 0.117 3.135
5 14106 13851.4 4.679 7.814
6 10029 9943.5 0.734 8.548
7 7134 7145.0 0.017 8.565
8 5047 5139.1 1.650 10.215
9 3656 3699.9 0.520 10.735
10 2642 2666.3 0.221 10.956
11 1885 1923.3 0.764 11.720
12 1423 1388.7 0.845 12.565
13 994 1003.7 0.094 12.659
14 737 726.1 0.162 12.822
15 560 525.8 2.220 15.041
16 379 381.2 0.012 15.053
17 296 276.5 1.369 16.423
18 211 200.8 0.515 16.938
19 137 146.0 0.553 17.491
20 90 106.2 2.475 19.966
21 282 287.1 0.091 20.057
Chisq= 20.06 for 20 degrees of freedom, p= 0.54565
SUMMARY of craptest
p-value for no. of wins: 0.335687
p-value for throws/game: 0.545650
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0017,0.0019,0.0059,0.0068,0.0130,0.0158,0.0204,0.0227,0.0232,0.0243,
0.0245,0.0277,0.0318,0.0350,0.0361,0.0365,0.0489,0.0493,0.0583,0.0597,
0.0657,0.0665,0.0705,0.0746,0.0769,0.0776,0.0784,0.0835,0.0957,0.0995,
0.1023,0.1044,0.1081,0.1094,0.1097,0.1146,0.1231,0.1271,0.1354,0.1426,
0.1426,0.1462,0.1483,0.1547,0.1628,0.1631,0.1724,0.1809,0.1832,0.1865,
0.1867,0.1910,0.1932,0.1947,0.1959,0.2042,0.2074,0.2117,0.2122,0.2153,
0.2162,0.2166,0.2187,0.2212,0.2217,0.2307,0.2310,0.2314,0.2335,0.2393,
0.2410,0.2423,0.2438,0.2470,0.2496,0.2599,0.2608,0.2744,0.2773,0.2791,
0.2796,0.2845,0.2877,0.2919,0.2993,0.3107,0.3108,0.3167,0.3171,0.3179,
0.3179,0.3281,0.3357,0.3378,0.3491,0.3514,0.3568,0.3609,0.3632,0.3669,
0.3698,0.3727,0.3781,0.3803,0.3823,0.3836,0.3928,0.3961,0.4045,0.4086,
0.4154,0.4205,0.4226,0.4276,0.4334,0.4351,0.4354,0.4422,0.4480,0.4504,
0.4510,0.4556,0.4562,0.4578,0.4581,0.4672,0.4702,0.4704,0.4714,0.4761,
0.4796,0.4808,0.4886,0.4904,0.5005,0.5023,0.5026,0.5112,0.5130,0.5137,
0.5139,0.5182,0.5182,0.5185,0.5233,0.5266,0.5333,0.5392,0.5443,0.5456,
0.5508,0.5508,0.5573,0.5593,0.5617,0.5637,0.5666,0.5691,0.5722,0.5782,
0.5812,0.5864,0.5877,0.5903,0.6168,0.6179,0.6272,0.6339,0.6340,0.6424,
0.6513,0.6540,0.6544,0.6588,0.6626,0.6663,0.6727,0.6728,0.6732,0.6760,
0.6912,0.6976,0.6976,0.7028,0.7112,0.7136,0.7138,0.7219,0.7235,0.7289,
0.7350,0.7367,0.7511,0.7539,0.7630,0.7635,0.7659,0.7675,0.7741,0.7782,
0.7787,0.7797,0.7863,0.7868,0.7885,0.7910,0.7959,0.7982,0.8003,0.8016,
0.8035,0.8072,0.8148,0.8177,0.8180,0.8181,0.8194,0.8265,0.8272,0.8359,
0.8384,0.8456,0.8468,0.8505,0.8509,0.8531,0.8554,0.8559,0.8680,0.8732,
0.8747,0.8775,0.8806,0.8852,0.8910,0.8913,0.8946,0.9015,0.9036,0.9068,
0.9073,0.9073,0.9155,0.9157,0.9160,0.9216,0.9237,0.9268,0.9271,0.9280,
0.9312,0.9372,0.9378,0.9384,0.9389,0.9475,0.9572,0.9588,0.9607,0.9609,
0.9634,0.9658,0.9766,0.9795,0.9801,0.9853,0.9879,0.9944,0.9955,
Overall p-value after applying KStest on 269 p-values = 0.799173
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.