RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-17_18:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.74 26.1383 0.928022
2 to 25 15.64 8.9306 0.057586
3 to 26 15.76 19.9783 0.724661
4 to 27 16.13 18.6224 0.649367
5 to 28 15.93 15.0001 0.404528
6 to 29 16.04 13.6261 0.306628
7 to 30 15.96 12.4865 0.230173
8 to 31 16.00 15.2389 0.421723
9 to 32 15.56 23.5015 0.866375
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.998002
Tough bday spacings test for dh-ranFile-2018-06-17_18:31: 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 23 76 98 109 72 51 41 5 11 3
(O-E)^2/E 0.4 5.1 0.1 0.0 1.3 0.5 0.0 4.2 6.6 2.9 0.3
Birthday Spacings: Sum(O-E)^2/E= 21.350, p= 0.981
RESULTS OF GCD FOR dh-ranFile-2018-06-17_18:31
Euclid's algorithm:
p-value, steps to gcd: 0.733878
p-value, dist. of gcd's: 0.670768
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-17_18:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.597 0.766 0.974 0.974 0.507 0.325 0.915 0.422
Bits 8 to 15---> 0.833 0.484 0.583 0.983 0.137 0.961 0.392 0.022
Bits 16 to 23---> 0.675 0.373 0.691 0.051 0.151 0.823 0.695 0.482
Bits 24 to 31---> 0.199 0.079 0.344 0.374 0.790 0.542 0.620 0.491
KS test for the above 32 p values: 0.340
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-17_18:31,
p-values for 5 runs: 0.9157, 0.1520, 0.1320, 0.6156, 0.0398
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-17_18:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 195 211.4 1.275 1.275
r= 29 5229 5134.0 1.757 3.032
r= 30 22962 23103.0 0.861 3.894
r= 31 11614 11551.5 0.338 4.231
chi-square = 4.231 with df = 3; p-value = 0.762
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-17_18:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 201 211.4 0.513 0.513
r= 30 5218 5134.0 1.374 1.887
r= 31 22992 23103.0 0.534 2.421
r= 32 11589 11551.5 0.122 2.543
chi-square = 2.543 with df = 3; p-value = 0.532
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-17_18:31
b-rank test for bits 1 to 8, p=0.77820
b-rank test for bits 2 to 9, p=0.86722
b-rank test for bits 3 to 10, p=0.06671
b-rank test for bits 4 to 11, p=0.66399
b-rank test for bits 5 to 12, p=0.02949
b-rank test for bits 6 to 13, p=0.13062
b-rank test for bits 7 to 14, p=0.38916
b-rank test for bits 8 to 15, p=0.88132
b-rank test for bits 9 to 16, p=0.04459
b-rank test for bits 10 to 17, p=0.53767
b-rank test for bits 11 to 18, p=0.74843
b-rank test for bits 12 to 19, p=0.55576
b-rank test for bits 13 to 20, p=0.40047
b-rank test for bits 14 to 21, p=0.19276
b-rank test for bits 15 to 22, p=0.23346
b-rank test for bits 16 to 23, p=0.54123
b-rank test for bits 17 to 24, p=0.14111
b-rank test for bits 18 to 25, p=0.20504
b-rank test for bits 19 to 26, p=0.02253
b-rank test for bits 20 to 27, p=0.16933
b-rank test for bits 21 to 28, p=0.75322
b-rank test for bits 22 to 29, p=0.20772
b-rank test for bits 23 to 30, p=0.60579
b-rank test for bits 24 to 31, p=0.81036
b-rank test for bits 25 to 32, p=0.55647
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 = 0.228741
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-17_18:31
(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 141446 -1.08 0.139505
2 142891 2.29 0.989094
3 141263 -1.51 0.065507
4 142168 0.60 0.727201
5 141814 -0.22 0.411871
6 142456 1.28 0.899246
7 141326 -1.36 0.086454
8 141264 -1.51 0.065805
9 142564 1.53 0.936942
10 141722 -0.44 0.330807
11 141305 -1.41 0.078977
12 142007 0.23 0.590255
13 142382 1.10 0.865284
14 141703 -0.48 0.314875
15 141998 0.21 0.582063
16 141730 -0.42 0.337610
17 141774 -0.32 0.375929
18 141892 -0.04 0.483851
19 142383 1.11 0.865789
20 142377 1.09 0.862734
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-17_18:31
Bits used No. missing words z-score p-value
23 to 32 141876 -0.1149 0.454250
22 to 31 141914 0.0161 0.506424
21 to 30 141921 0.0402 0.516050
20 to 29 142003 0.3230 0.626652
19 to 28 141957 0.1644 0.565284
18 to 27 141864 -0.1563 0.437894
17 to 26 141456 -1.5632 0.059002
16 to 25 142659 2.5851 0.995132
15 to 24 141968 0.2023 0.580163
14 to 23 142406 1.7127 0.956612
13 to 22 141782 -0.4391 0.330306
12 to 21 142392 1.6644 0.951982
11 to 20 142703 2.7368 0.996898
10 to 19 141995 0.2954 0.616161
9 to 18 141544 -1.2598 0.103878
8 to 17 142157 0.8540 0.803457
7 to 16 142409 1.7230 0.957556
6 to 15 141884 -0.0873 0.465199
5 to 14 141790 -0.4115 0.340359
4 to 13 141932 0.0782 0.531155
3 to 12 141967 0.1989 0.578815
2 to 11 141950 0.1402 0.555765
1 to 10 142479 1.9644 0.975257
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-17_18:31
Bits used No. missing words z-score p-value
28 to 32 141821 -0.2994 0.382308
27 to 31 141101 -2.7401 0.003071
26 to 30 142138 0.7752 0.780875
25 to 29 142141 0.7853 0.783868
24 to 28 141865 -0.1503 0.440275
23 to 27 142240 1.1209 0.868838
22 to 26 141193 -2.4282 0.007586
21 to 25 142127 0.7379 0.769702
20 to 24 141783 -0.4282 0.334239
19 to 23 142132 0.7548 0.774820
18 to 22 141928 0.0633 0.525232
17 to 21 142047 0.4667 0.679635
16 to 20 142221 1.0565 0.854632
15 to 19 141965 0.1887 0.574841
14 to 18 141749 -0.5435 0.293396
13 to 17 142044 0.4565 0.675988
12 to 16 142076 0.5650 0.713957
11 to 15 141641 -0.9096 0.181519
10 to 14 141821 -0.2994 0.382308
9 to 13 142070 0.5446 0.707001
8 to 12 141410 -1.6926 0.045262
7 to 11 141978 0.2328 0.592034
6 to 10 141863 -0.1571 0.437602
5 to 9 142113 0.6904 0.755031
4 to 8 141597 -1.0587 0.144858
3 to 7 141546 -1.2316 0.109044
2 to 6 141947 0.1277 0.550805
1 to 5 141827 -0.2791 0.390090
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-17_18:31
Bits used No. missing words z-score p-value
31 to 32 142187 0.8191 0.793631
30 to 31 141567 -1.0098 0.156290
29 to 30 141681 -0.6735 0.250302
28 to 29 141794 -0.3402 0.366851
27 to 28 141807 -0.3019 0.381380
26 to 27 142178 0.7925 0.785976
25 to 26 141571 -0.9980 0.159134
24 to 25 142399 1.4445 0.925694
23 to 24 142212 0.8928 0.814026
22 to 23 141490 -1.2370 0.108051
21 to 22 142025 0.3412 0.633527
20 to 21 142152 0.7158 0.762955
19 to 20 141542 -1.0836 0.139278
18 to 19 142015 0.3117 0.622370
17 to 18 141999 0.2645 0.604308
16 to 17 141759 -0.4435 0.328720
15 to 16 141554 -1.0482 0.147280
14 to 15 142160 0.7394 0.770180
13 to 14 141864 -0.1337 0.446813
12 to 13 142485 1.6981 0.955259
11 to 12 141952 0.1259 0.550083
10 to 11 141488 -1.2429 0.106959
9 to 10 142066 0.4622 0.678014
8 to 9 142307 1.1731 0.879616
7 to 8 141270 -1.8859 0.029652
6 to 7 141376 -1.5732 0.057831
5 to 6 141999 0.2645 0.604308
4 to 5 141486 -1.2488 0.105876
3 to 4 142200 0.8574 0.804397
2 to 3 142255 1.0197 0.846059
1 to 2 141893 -0.0482 0.480790
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-17_18:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2421.01 -1.117 0.131983
Test results for specific bytes for dh-ranFile-2018-06-17_18:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2538.56 0.545 0.707236
2 to 9 2349.23 -2.132 0.016498
3 to 10 2366.59 -1.887 0.029600
4 to 11 2516.78 0.237 0.593813
5 to 12 2528.49 0.403 0.656505
6 to 13 2401.03 -1.400 0.080818
7 to 14 2464.19 -0.506 0.306281
8 to 15 2402.25 -1.382 0.083433
9 to 16 2518.59 0.263 0.603695
10 to 17 2402.45 -1.380 0.083859
11 to 18 2589.71 1.269 0.897723
12 to 19 2494.27 -0.081 0.467716
13 to 20 2559.54 0.842 0.800097
14 to 21 2594.16 1.332 0.908503
15 to 22 2430.14 -0.988 0.161579
16 to 23 2422.71 -1.093 0.137174
17 to 24 2451.51 -0.686 0.246447
18 to 25 2587.12 1.232 0.891028
19 to 26 2544.24 0.626 0.734209
20 to 27 2391.44 -1.535 0.062350
21 to 28 2469.69 -0.429 0.334074
22 to 29 2550.04 0.708 0.760429
23 to 30 2435.37 -0.914 0.180352
24 to 31 2534.60 0.489 0.687702
25 to 32 2518.81 0.266 0.604891
CDPARK for dh-ranFile-2018-06-17_18:31: 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
3505 -0.8219 0.205562
3534 0.5023 0.692266
3544 0.9589 0.831196
3505 -0.8219 0.205562
3546 1.0502 0.853193
3526 0.1370 0.554479
3548 1.1416 0.873180
3525 0.0913 0.536383
3562 1.7808 0.962529
3520 -0.1370 0.445521
Square side=100, avg. no. parked=3531.50 sample std.=17.85
p-value of the KSTEST for those 10 p-values: 0.354613
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-17_18:31
0.1506,0.4119,0.5953,0.3585,0.9526,0.8357,0.5392,0.9308,0.6704,0.4039,
The KS test for those 10 p-values: 0.571953
The 3DSPHERES test for dh-ranFile-2018-06-17_18:31
sample no r^3 equiv. uni.
1 28.711 0.615968
2 9.430 0.269728
3 11.462 0.317552
4 25.301 0.569741
5 166.134 0.996065
6 10.599 0.297629
7 20.242 0.490702
8 3.472 0.109282
9 3.696 0.115903
10 62.495 0.875463
11 51.964 0.823092
12 49.481 0.807828
13 120.295 0.981863
14 3.308 0.104395
15 0.003 0.000098
16 25.870 0.577830
17 3.453 0.108722
18 56.321 0.847010
19 7.865 0.230622
20 10.315 0.290949
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.416310
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-17_18:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 0.9 -1.1 -0.1 1.7 1.4
0.1 0.2 0.7 0.4 0.3 -0.3
-1.2 -0.9 -0.3 -0.5 0.4 -0.9
0.1 1.2 0.2 0.5 -0.2 -0.7
0.1 0.1 0.3 -0.2 1.1 0.7
-0.4 0.3 1.3 0.8 -0.1 -1.2
0.7 -0.7 0.5 0.4 -0.6 1.0
-0.1
Chi-square with 42 degrees of freedom:23.949397
z-score=-1.969482, p-value=0.011355
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-17_18:31
Test no p-value
1 0.557280
2 0.113721
3 0.168789
4 0.147405
5 0.116874
6 0.811093
7 0.300429
8 0.009916
9 0.435720
10 0.645204
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.094029
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-17_18:31:
(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 66585 0.10 66621 0.03
3 25000.00 25036 0.05 25064 0.16
4 6666.67 6689 0.07 6664 0.00
5 1388.89 1384 0.02 1380 0.06
6 238.10 252 0.81 227 0.52
7 34.72 48 5.08 36 0.05
8 4.96 5 0.00 7 0.84
p=0.59184 p=0.05156
Number of rngs required: 688521, p-value: 0.554
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-17_18:31
No. of wins: Observed Expected
99108 98585.9
z-score= 2.335, pvalue=0.99024
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66975 66666.7 1.426 1.426
2 37614 37654.3 0.043 1.469
3 27169 26954.7 1.703 3.172
4 19410 19313.5 0.483 3.655
5 13686 13851.4 1.976 5.631
6 9893 9943.5 0.257 5.887
7 6934 7145.0 6.233 12.120
8 5105 5139.1 0.226 12.346
9 3595 3699.9 2.972 15.318
10 2693 2666.3 0.267 15.586
11 1910 1923.3 0.092 15.678
12 1411 1388.7 0.357 16.035
13 992 1003.7 0.137 16.171
14 731 726.1 0.033 16.204
15 532 525.8 0.072 16.276
16 352 381.2 2.229 18.506
17 258 276.5 1.243 19.749
18 198 200.8 0.040 19.788
19 146 146.0 0.000 19.788
20 111 106.2 0.216 20.004
21 285 287.1 0.016 20.020
Chisq= 20.02 for 20 degrees of freedom, p= 0.54329
SUMMARY of craptest
p-value for no. of wins: 0.990237
p-value for throws/game: 0.543291
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-17_18:31
No. of wins: Observed Expected
98573 98585.9
z-score=-0.058, pvalue=0.47707
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66885 66666.7 0.715 0.715
2 37531 37654.3 0.404 1.119
3 26801 26954.7 0.877 1.996
4 19181 19313.5 0.908 2.904
5 13899 13851.4 0.163 3.068
6 9940 9943.5 0.001 3.069
7 7213 7145.0 0.647 3.716
8 5145 5139.1 0.007 3.722
9 3703 3699.9 0.003 3.725
10 2720 2666.3 1.082 4.807
11 1880 1923.3 0.976 5.783
12 1409 1388.7 0.296 6.078
13 1033 1003.7 0.854 6.933
14 707 726.1 0.505 7.437
15 534 525.8 0.127 7.564
16 413 381.2 2.661 10.226
17 270 276.5 0.155 10.380
18 194 200.8 0.232 10.612
19 161 146.0 1.544 12.157
20 99 106.2 0.490 12.647
21 282 287.1 0.091 12.738
Chisq= 12.74 for 20 degrees of freedom, p= 0.11166
SUMMARY of craptest
p-value for no. of wins: 0.477069
p-value for throws/game: 0.111665
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0001,0.0031,0.0076,0.0099,0.0114,0.0165,0.0215,0.0225,0.0295,0.0296,
0.0297,0.0398,0.0446,0.0453,0.0510,0.0516,0.0576,0.0578,0.0590,0.0624,
0.0655,0.0658,0.0667,0.0790,0.0794,0.0808,0.0834,0.0839,0.0865,0.0940,
0.1039,0.1044,0.1059,0.1070,0.1081,0.1087,0.1090,0.1093,0.1117,0.1137,
0.1159,0.1169,0.1306,0.1320,0.1320,0.1372,0.1373,0.1393,0.1395,0.1411,
0.1449,0.1473,0.1474,0.1506,0.1509,0.1520,0.1563,0.1591,0.1616,0.1688,
0.1693,0.1804,0.1815,0.1928,0.1990,0.2050,0.2056,0.2056,0.2077,0.2287,
0.2302,0.2306,0.2335,0.2464,0.2503,0.2697,0.2909,0.2934,0.2976,0.3004,
0.3063,0.3066,0.3149,0.3176,0.3246,0.3287,0.3303,0.3308,0.3341,0.3342,
0.3376,0.3399,0.3404,0.3443,0.3546,0.3585,0.3669,0.3731,0.3738,0.3759,
0.3814,0.3823,0.3823,0.3892,0.3901,0.3917,0.4005,0.4039,0.4045,0.4119,
0.4119,0.4163,0.4216,0.4217,0.4357,0.4376,0.4379,0.4403,0.4455,0.4468,
0.4542,0.4652,0.4677,0.4771,0.4808,0.4816,0.4837,0.4839,0.4907,0.4915,
0.5064,0.5068,0.5160,0.5252,0.5312,0.5324,0.5364,0.5377,0.5392,0.5412,
0.5421,0.5433,0.5501,0.5508,0.5540,0.5545,0.5558,0.5558,0.5565,0.5573,
0.5653,0.5697,0.5720,0.5748,0.5778,0.5788,0.5802,0.5821,0.5835,0.5903,
0.5918,0.5920,0.5938,0.5953,0.5969,0.6037,0.6043,0.6043,0.6049,0.6058,
0.6156,0.6160,0.6162,0.6203,0.6224,0.6267,0.6335,0.6452,0.6494,0.6565,
0.6640,0.6704,0.6708,0.6746,0.6760,0.6780,0.6796,0.6877,0.6915,0.6923,
0.6953,0.7070,0.7072,0.7140,0.7247,0.7272,0.7339,0.7342,0.7484,0.7532,
0.7550,0.7604,0.7625,0.7630,0.7664,0.7697,0.7702,0.7748,0.7782,0.7809,
0.7839,0.7860,0.7899,0.7936,0.8001,0.8035,0.8044,0.8078,0.8104,0.8111,
0.8140,0.8226,0.8231,0.8312,0.8334,0.8357,0.8461,0.8470,0.8532,0.8546,
0.8627,0.8653,0.8658,0.8664,0.8672,0.8688,0.8732,0.8755,0.8796,0.8813,
0.8910,0.8977,0.8992,0.9085,0.9151,0.9157,0.9257,0.9280,0.9308,0.9369,
0.9520,0.9526,0.9553,0.9566,0.9576,0.9613,0.9625,0.9743,0.9744,0.9753,
0.9812,0.9819,0.9828,0.9891,0.9902,0.9951,0.9961,0.9969,0.9980,
Overall p-value after applying KStest on 269 p-values = 0.530331
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.