RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-17_11:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.67 11.5202 0.171718
2 to 25 15.62 18.6067 0.648435
3 to 26 15.77 25.5194 0.916327
4 to 27 15.55 20.2040 0.736074
5 to 28 15.81 13.6958 0.311495
6 to 29 15.78 8.2458 0.038995
7 to 30 15.62 18.8184 0.660946
8 to 31 15.86 19.6780 0.708969
9 to 32 15.61 17.0505 0.549051
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.880140
Tough bday spacings test for dh-ranFile-2018-06-17_11:31: 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 32 95 92 106 70 37 30 19 5 3
(O-E)^2/E 0.4 0.6 6.4 0.3 0.7 0.8 4.4 0.0 1.1 0.4 0.3
Birthday Spacings: Sum(O-E)^2/E= 15.482, p= 0.885
RESULTS OF GCD FOR dh-ranFile-2018-06-17_11:31
Euclid's algorithm:
p-value, steps to gcd: 0.898358
p-value, dist. of gcd's: 0.250639
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-17_11:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.407 0.912 0.601 0.471 0.868 0.125 0.045 0.526
Bits 8 to 15---> 0.616 0.906 0.119 0.920 0.790 0.525 0.200 0.837
Bits 16 to 23---> 0.571 0.164 0.740 0.150 0.744 0.355 0.872 0.940
Bits 24 to 31---> 0.710 0.274 0.018 0.043 0.535 0.894 0.478 0.409
KS test for the above 32 p values: 0.194
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-17_11:31,
p-values for 5 runs: 0.2048, 0.5848, 0.1883, 0.4472, 0.8036
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-17_11:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 236 211.4 2.858 2.858
r= 29 5252 5134.0 2.712 5.570
r= 30 22954 23103.0 0.962 6.531
r= 31 11558 11551.5 0.004 6.535
chi-square = 6.535 with df = 3; p-value = 0.912
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-17_11:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 219 211.4 0.272 0.272
r= 30 5096 5134.0 0.281 0.553
r= 31 23025 23103.0 0.264 0.817
r= 32 11660 11551.5 1.019 1.836
chi-square = 1.836 with df = 3; p-value = 0.393
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-17_11:31
b-rank test for bits 1 to 8, p=0.49837
b-rank test for bits 2 to 9, p=0.04329
b-rank test for bits 3 to 10, p=0.95780
b-rank test for bits 4 to 11, p=0.05522
b-rank test for bits 5 to 12, p=0.40705
b-rank test for bits 6 to 13, p=0.29328
b-rank test for bits 7 to 14, p=0.96890
b-rank test for bits 8 to 15, p=0.58887
b-rank test for bits 9 to 16, p=0.56606
b-rank test for bits 10 to 17, p=0.85058
b-rank test for bits 11 to 18, p=0.57974
b-rank test for bits 12 to 19, p=0.22739
b-rank test for bits 13 to 20, p=0.49137
b-rank test for bits 14 to 21, p=0.58897
b-rank test for bits 15 to 22, p=0.92281
b-rank test for bits 16 to 23, p=0.22391
b-rank test for bits 17 to 24, p=0.18607
b-rank test for bits 18 to 25, p=0.22624
b-rank test for bits 19 to 26, p=0.99172
b-rank test for bits 20 to 27, p=0.76885
b-rank test for bits 21 to 28, p=0.95585
b-rank test for bits 22 to 29, p=0.72781
b-rank test for bits 23 to 30, p=0.46025
b-rank test for bits 24 to 31, p=0.88228
b-rank test for bits 25 to 32, p=0.48943
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 = 0.387417
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-17_11:31
(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 142361 1.06 0.854357
2 141931 0.05 0.520190
3 140952 -2.24 0.012651
4 141188 -1.69 0.045960
5 141692 -0.51 0.305804
6 142407 1.16 0.877541
7 141485 -0.99 0.160739
8 141704 -0.48 0.315705
9 141820 -0.21 0.417335
10 142785 2.05 0.979620
11 142328 0.98 0.836013
12 141837 -0.17 0.432900
13 141156 -1.76 0.039194
14 142300 0.91 0.819321
15 142565 1.53 0.937231
16 142305 0.92 0.822377
17 141731 -0.42 0.338464
18 141502 -0.95 0.170623
19 142385 1.11 0.866797
20 142176 0.62 0.733378
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-17_11:31
Bits used No. missing words z-score p-value
23 to 32 141773 -0.4701 0.319141
22 to 31 141763 -0.5046 0.306925
21 to 30 141621 -0.9942 0.160053
20 to 29 141289 -2.1391 0.016215
19 to 28 141686 -0.7701 0.220619
18 to 27 141415 -1.7046 0.044136
17 to 26 141730 -0.6184 0.268163
16 to 25 141847 -0.2149 0.414911
15 to 24 141736 -0.5977 0.275024
14 to 23 142144 0.8092 0.790802
13 to 22 141902 -0.0253 0.489918
12 to 21 142082 0.5954 0.724217
11 to 20 141574 -1.1563 0.123777
10 to 19 141782 -0.4391 0.330306
9 to 18 142256 1.1954 0.884037
8 to 17 142168 0.8920 0.813794
7 to 16 141617 -1.0080 0.156719
6 to 15 142066 0.5402 0.705485
5 to 14 141669 -0.8287 0.203630
4 to 13 141834 -0.2598 0.397525
3 to 12 141550 -1.2391 0.107660
2 to 11 141929 0.0678 0.527039
1 to 10 141308 -2.0736 0.019060
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-17_11:31
Bits used No. missing words z-score p-value
28 to 32 142009 0.3379 0.632267
27 to 31 142216 1.0396 0.850728
26 to 30 141581 -1.1130 0.132858
25 to 29 142005 0.3243 0.627147
24 to 28 141685 -0.7604 0.223496
23 to 27 141719 -0.6452 0.259403
22 to 26 142008 0.3345 0.630989
21 to 25 141961 0.1752 0.569520
20 to 24 142091 0.6158 0.730997
19 to 23 142284 1.2701 0.897970
18 to 22 142150 0.8158 0.792702
17 to 21 141844 -0.2215 0.412368
16 to 20 141922 0.0429 0.517129
15 to 19 142370 1.5616 0.940808
14 to 18 141818 -0.3096 0.378435
13 to 17 141910 0.0023 0.500906
12 to 16 141845 -0.2181 0.413688
11 to 15 141072 -2.8384 0.002267
10 to 14 141938 0.0972 0.538711
9 to 13 142150 0.8158 0.792702
8 to 12 141585 -1.0994 0.135792
7 to 11 141586 -1.0960 0.136532
6 to 10 142380 1.5955 0.944699
5 to 9 142034 0.4226 0.663710
4 to 8 142149 0.8124 0.791731
3 to 7 141445 -1.5740 0.057744
2 to 6 141803 -0.3604 0.359259
1 to 5 142034 0.4226 0.663710
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-17_11:31
Bits used No. missing words z-score p-value
31 to 32 141875 -0.1013 0.459669
30 to 31 141777 -0.3904 0.348137
29 to 30 141901 -0.0246 0.490198
28 to 29 141899 -0.0305 0.487845
27 to 28 141640 -0.7945 0.213457
26 to 27 141811 -0.2901 0.385886
25 to 26 142104 0.5742 0.717100
24 to 25 142116 0.6096 0.728952
23 to 24 142303 1.1613 0.877234
22 to 23 142270 1.0639 0.856318
21 to 22 142274 1.0757 0.858974
20 to 21 141625 -0.8387 0.200810
19 to 20 141594 -0.9302 0.176140
18 to 19 141550 -1.0600 0.144579
17 to 18 141230 -2.0039 0.022539
16 to 17 142045 0.4002 0.655498
15 to 16 141756 -0.4523 0.325526
14 to 15 141777 -0.3904 0.348137
13 to 14 141690 -0.6470 0.258819
12 to 13 142255 1.0197 0.846059
11 to 12 142324 1.2232 0.889376
10 to 11 141564 -1.0187 0.154179
9 to 10 141898 -0.0334 0.486669
8 to 9 142076 0.4917 0.688517
7 to 8 142062 0.4504 0.673772
6 to 7 142116 0.6096 0.728952
5 to 6 141803 -0.3137 0.376891
4 to 5 141695 -0.6322 0.263614
3 to 4 141900 -0.0275 0.489022
2 to 3 141357 -1.6293 0.051626
1 to 2 142258 1.0285 0.848149
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-17_11:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2567.97 0.961 0.831768
Test results for specific bytes for dh-ranFile-2018-06-17_11:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2488.14 -0.168 0.433394
2 to 9 2471.51 -0.403 0.343516
3 to 10 2597.18 1.374 0.915333
4 to 11 2526.67 0.377 0.646983
5 to 12 2418.98 -1.146 0.125946
6 to 13 2384.98 -1.627 0.051907
7 to 14 2401.32 -1.396 0.081424
8 to 15 2569.42 0.982 0.836878
9 to 16 2580.53 1.139 0.872615
10 to 17 2559.38 0.840 0.799472
11 to 18 2449.14 -0.719 0.235966
12 to 19 2555.54 0.785 0.783888
13 to 20 2448.29 -0.731 0.232300
14 to 21 2513.45 0.190 0.575442
15 to 22 2423.35 -1.084 0.139169
16 to 23 2484.89 -0.214 0.415392
17 to 24 2477.83 -0.314 0.376921
18 to 25 2507.03 0.099 0.539600
19 to 26 2421.79 -1.106 0.134337
20 to 27 2453.42 -0.659 0.255019
21 to 28 2496.37 -0.051 0.479544
22 to 29 2535.53 0.502 0.692333
23 to 30 2449.71 -0.711 0.238497
24 to 31 2584.94 1.201 0.885174
25 to 32 2654.66 2.187 0.985635
CDPARK for dh-ranFile-2018-06-17_11:31: 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
3479 -2.0091 0.022262
3560 1.6895 0.954438
3516 -0.3196 0.374623
3551 1.2785 0.899470
3506 -0.7763 0.218799
3543 0.9132 0.819442
3513 -0.4566 0.323972
3473 -2.2831 0.011212
3536 0.5936 0.723613
3541 0.8219 0.794438
Square side=100, avg. no. parked=3521.80 sample std.=28.12
p-value of the KSTEST for those 10 p-values: 0.467127
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-17_11:31
0.6085,0.9359,0.7162,0.0310,0.7314,0.4420,0.5679,0.1278,0.3583,0.2224,
The KS test for those 10 p-values: 0.991834
The 3DSPHERES test for dh-ranFile-2018-06-17_11:31
sample no r^3 equiv. uni.
1 20.355 0.492623
2 49.368 0.807103
3 18.372 0.457949
4 45.373 0.779625
5 22.600 0.529206
6 37.098 0.709632
7 13.584 0.364157
8 44.265 0.771336
9 8.272 0.240988
10 18.759 0.464907
11 52.964 0.828893
12 3.701 0.116073
13 94.562 0.957236
14 2.621 0.083669
15 21.506 0.511712
16 94.414 0.957025
17 12.509 0.340953
18 31.523 0.650333
19 47.172 0.792455
20 16.810 0.428980
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.453787
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-17_11:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -1.2 0.1 0.5 -0.2 -2.8
0.0 -0.1 0.0 0.3 0.6 -1.4
-0.9 0.4 1.2 -0.6 -0.8 -0.4
0.6 -0.6 -1.5 1.1 1.8 1.0
0.1 -0.5 -0.2 2.5 -0.2 -0.4
1.4 0.4 -0.2 -0.2 -1.5 -1.4
0.5 -0.1 0.1 1.5 -0.6 1.0
-0.1
Chi-square with 42 degrees of freedom:40.833792
z-score=-0.127244, p-value=0.477889
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-17_11:31
Test no p-value
1 0.237941
2 0.671282
3 0.896798
4 0.932226
5 0.343636
6 0.706926
7 0.055137
8 0.271341
9 0.119646
10 0.979632
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.716766
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-17_11:31:
(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 66690 0.01 66977 1.44
3 25000.00 25040 0.06 24766 2.19
4 6666.67 6614 0.42 6594 0.79
5 1388.89 1373 0.18 1386 0.01
6 238.10 231 0.21 229 0.35
7 34.72 44 2.48 44 2.48
8 4.96 7 0.84 3 0.77
p=0.35049 p=0.76447
Number of rngs required: 687967, p-value: 0.308
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-17_11:31
No. of wins: Observed Expected
98510 98585.9
z-score=-0.339, pvalue=0.36720
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66538 66666.7 0.248 0.248
2 37581 37654.3 0.143 0.391
3 27259 26954.7 3.435 3.826
4 19293 19313.5 0.022 3.847
5 13695 13851.4 1.766 5.614
6 9920 9943.5 0.056 5.670
7 7162 7145.0 0.040 5.710
8 5200 5139.1 0.722 6.432
9 3619 3699.9 1.767 8.200
10 2759 2666.3 3.223 11.423
11 1930 1923.3 0.023 11.446
12 1356 1388.7 0.772 12.218
13 994 1003.7 0.094 12.312
14 725 726.1 0.002 12.314
15 505 525.8 0.826 13.139
16 432 381.2 6.784 19.923
17 271 276.5 0.111 20.034
18 201 200.8 0.000 20.034
19 145 146.0 0.007 20.041
20 101 106.2 0.256 20.297
21 314 287.1 2.518 22.814
Chisq= 22.81 for 20 degrees of freedom, p= 0.70200
SUMMARY of craptest
p-value for no. of wins: 0.367198
p-value for throws/game: 0.702003
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-17_11:31
No. of wins: Observed Expected
98691 98585.9
z-score= 0.470, pvalue=0.68091
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66708 66666.7 0.026 0.026
2 37535 37654.3 0.378 0.404
3 26988 26954.7 0.041 0.445
4 19227 19313.5 0.387 0.832
5 13728 13851.4 1.100 1.932
6 10200 9943.5 6.614 8.546
7 7202 7145.0 0.454 9.000
8 5118 5139.1 0.086 9.087
9 3643 3699.9 0.874 9.961
10 2621 2666.3 0.770 10.730
11 1945 1923.3 0.244 10.974
12 1397 1388.7 0.049 11.023
13 978 1003.7 0.659 11.682
14 754 726.1 1.069 12.751
15 533 525.8 0.098 12.849
16 398 381.2 0.745 13.594
17 260 276.5 0.989 14.583
18 213 200.8 0.737 15.320
19 142 146.0 0.109 15.429
20 121 106.2 2.058 17.487
21 289 287.1 0.012 17.499
Chisq= 17.50 for 20 degrees of freedom, p= 0.37966
SUMMARY of craptest
p-value for no. of wins: 0.680913
p-value for throws/game: 0.379656
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0023,0.0112,0.0127,0.0162,0.0176,0.0191,0.0223,0.0225,0.0310,0.0390,
0.0392,0.0425,0.0433,0.0441,0.0450,0.0460,0.0516,0.0519,0.0551,0.0552,
0.0577,0.0814,0.0837,0.1077,0.1161,0.1192,0.1196,0.1238,0.1246,0.1259,
0.1278,0.1329,0.1343,0.1358,0.1365,0.1392,0.1446,0.1503,0.1542,0.1567,
0.1601,0.1607,0.1642,0.1706,0.1717,0.1761,0.1861,0.1883,0.1944,0.1998,
0.2008,0.2036,0.2048,0.2135,0.2188,0.2206,0.2224,0.2235,0.2239,0.2262,
0.2274,0.2323,0.2360,0.2379,0.2385,0.2410,0.2506,0.2550,0.2588,0.2594,
0.2636,0.2682,0.2713,0.2739,0.2750,0.2933,0.3058,0.3069,0.3077,0.3115,
0.3157,0.3191,0.3240,0.3255,0.3303,0.3385,0.3410,0.3435,0.3436,0.3481,
0.3481,0.3505,0.3552,0.3583,0.3593,0.3642,0.3672,0.3746,0.3769,0.3769,
0.3784,0.3797,0.3859,0.3874,0.3928,0.3975,0.4070,0.4071,0.4090,0.4124,
0.4137,0.4149,0.4154,0.4173,0.4290,0.4329,0.4334,0.4420,0.4472,0.4538,
0.4579,0.4597,0.4602,0.4649,0.4671,0.4714,0.4776,0.4779,0.4795,0.4867,
0.4878,0.4890,0.4894,0.4899,0.4902,0.4914,0.4926,0.4984,0.5009,0.5117,
0.5171,0.5202,0.5251,0.5261,0.5270,0.5292,0.5352,0.5387,0.5396,0.5491,
0.5661,0.5679,0.5695,0.5711,0.5754,0.5797,0.5848,0.5889,0.5890,0.6013,
0.6085,0.6161,0.6271,0.6310,0.6323,0.6470,0.6484,0.6503,0.6555,0.6609,
0.6637,0.6637,0.6713,0.6738,0.6809,0.6885,0.6923,0.7020,0.7055,0.7069,
0.7090,0.7095,0.7096,0.7162,0.7168,0.7171,0.7236,0.7242,0.7278,0.7290,
0.7290,0.7310,0.7314,0.7334,0.7361,0.7396,0.7444,0.7645,0.7688,0.7713,
0.7796,0.7839,0.7904,0.7908,0.7917,0.7925,0.7927,0.7927,0.7944,0.7995,
0.8036,0.8071,0.8138,0.8193,0.8194,0.8224,0.8289,0.8318,0.8360,0.8367,
0.8369,0.8461,0.8481,0.8506,0.8507,0.8544,0.8563,0.8590,0.8668,0.8677,
0.8718,0.8726,0.8772,0.8775,0.8801,0.8823,0.8840,0.8846,0.8852,0.8894,
0.8942,0.8968,0.8980,0.8984,0.8995,0.9059,0.9117,0.9120,0.9153,0.9163,
0.9203,0.9228,0.9322,0.9359,0.9372,0.9402,0.9408,0.9447,0.9544,0.9558,
0.9570,0.9572,0.9578,0.9689,0.9796,0.9796,0.9856,0.9917,0.9918,
Overall p-value after applying KStest on 269 p-values = 0.786296
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.