RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-30_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 15.86 26.6792 0.937057
2 to 25 15.69 14.3537 0.358074
3 to 26 16.11 25.2947 0.911694
4 to 27 15.64 25.6989 0.919876
5 to 28 15.79 13.7219 0.313320
6 to 29 15.84 17.3942 0.572020
7 to 30 15.87 12.3231 0.219808
8 to 31 15.78 15.8533 0.465745
9 to 32 15.80 15.1119 0.412582
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.462222
Tough bday spacings test for dh-ranFile-2018-06-30_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 9 44 80 91 96 73 46 36 11 9 5
(O-E)^2/E 0.0 1.5 0.6 0.5 0.0 0.3 0.7 1.3 1.0 0.9 0.2
Birthday Spacings: Sum(O-E)^2/E= 7.035, p= 0.278
RESULTS OF GCD FOR dh-ranFile-2018-06-30_18:31
Euclid's algorithm:
p-value, steps to gcd: 0.121729
p-value, dist. of gcd's: 0.395189
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-30_18:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.872 0.748 0.380 0.580 0.186 0.814 0.639 0.868
Bits 8 to 15---> 0.640 0.933 0.321 0.320 0.478 0.998 0.946 0.177
Bits 16 to 23---> 0.437 0.968 0.100 0.849 0.574 0.991 0.818 0.086
Bits 24 to 31---> 0.728 0.760 0.947 0.463 0.449 0.960 0.150 0.924
KS test for the above 32 p values: 0.989
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-30_18:31,
p-values for 5 runs: 0.6557, 0.5243, 0.9497, 0.9015, 0.0278
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-30_18:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 226 211.4 1.006 1.006
r= 29 5064 5134.0 0.955 1.960
r= 30 23177 23103.0 0.237 2.197
r= 31 11533 11551.5 0.030 2.227
chi-square = 2.227 with df = 3; p-value = 0.473
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-30_18:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 190 211.4 2.170 2.170
r= 30 5112 5134.0 0.094 2.264
r= 31 23181 23103.0 0.263 2.527
r= 32 11517 11551.5 0.103 2.630
chi-square = 2.630 with df = 3; p-value = 0.548
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-30_18:31
b-rank test for bits 1 to 8, p=0.61584
b-rank test for bits 2 to 9, p=0.51764
b-rank test for bits 3 to 10, p=0.67303
b-rank test for bits 4 to 11, p=0.14321
b-rank test for bits 5 to 12, p=0.49393
b-rank test for bits 6 to 13, p=0.05375
b-rank test for bits 7 to 14, p=0.19172
b-rank test for bits 8 to 15, p=0.58071
b-rank test for bits 9 to 16, p=0.27206
b-rank test for bits 10 to 17, p=0.49149
b-rank test for bits 11 to 18, p=0.07599
b-rank test for bits 12 to 19, p=0.08304
b-rank test for bits 13 to 20, p=0.00687
b-rank test for bits 14 to 21, p=0.16586
b-rank test for bits 15 to 22, p=0.69186
b-rank test for bits 16 to 23, p=0.27279
b-rank test for bits 17 to 24, p=0.03142
b-rank test for bits 18 to 25, p=0.82979
b-rank test for bits 19 to 26, p=0.67424
b-rank test for bits 20 to 27, p=0.89668
b-rank test for bits 21 to 28, p=0.07441
b-rank test for bits 22 to 29, p=0.77249
b-rank test for bits 23 to 30, p=0.21836
b-rank test for bits 24 to 31, p=0.12768
b-rank test for bits 25 to 32, p=0.02823
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 = 0.012870
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-30_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 141517 -0.92 0.179661
2 141681 -0.53 0.296850
3 142095 0.43 0.667786
4 141961 0.12 0.548045
5 141283 -1.46 0.071681
6 141972 0.15 0.558207
7 141684 -0.53 0.299280
8 141359 -1.29 0.099253
9 141643 -0.62 0.266883
10 142337 1.00 0.841158
11 142182 0.64 0.737963
12 142126 0.51 0.693655
13 142165 0.60 0.724866
14 142017 0.25 0.599312
15 141843 -0.15 0.438420
16 142127 0.51 0.694475
17 141367 -1.27 0.102555
18 140904 -2.35 0.009414
19 142205 0.69 0.755160
20 141384 -1.23 0.109835
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-30_18:31
Bits used No. missing words z-score p-value
23 to 32 141942 0.1127 0.544848
22 to 31 142291 1.3161 0.905930
21 to 30 141814 -0.3287 0.371182
20 to 29 142029 0.4127 0.660070
19 to 28 141725 -0.6356 0.262512
18 to 27 142014 0.3609 0.640925
17 to 26 141734 -0.6046 0.272727
16 to 25 141818 -0.3149 0.376407
15 to 24 141870 -0.1356 0.446061
14 to 23 141524 -1.3287 0.091970
13 to 22 141787 -0.4218 0.336575
12 to 21 141890 -0.0667 0.473428
11 to 20 141727 -0.6287 0.264765
10 to 19 141887 -0.0770 0.469312
9 to 18 141260 -2.2391 0.012576
8 to 17 142225 1.0885 0.861817
7 to 16 141873 -0.1253 0.450153
6 to 15 141432 -1.6460 0.049885
5 to 14 141612 -1.0253 0.152617
4 to 13 142044 0.4644 0.678812
3 to 12 141664 -0.8460 0.198786
2 to 11 141279 -2.1736 0.014869
1 to 10 141485 -1.4632 0.071705
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-30_18:31
Bits used No. missing words z-score p-value
28 to 32 141973 0.2158 0.585440
27 to 31 141900 -0.0316 0.487385
26 to 30 141954 0.1514 0.560179
25 to 29 141840 -0.2350 0.407098
24 to 28 142074 0.5582 0.711647
23 to 27 141694 -0.7299 0.232716
22 to 26 142025 0.3921 0.652509
21 to 25 141701 -0.7062 0.240031
20 to 24 141364 -1.8486 0.032260
19 to 23 141535 -1.2689 0.102236
18 to 22 142075 0.5616 0.712803
17 to 21 142128 0.7413 0.770730
16 to 20 141720 -0.6418 0.260503
15 to 19 141726 -0.6215 0.267149
14 to 18 141966 0.1921 0.576169
13 to 17 141735 -0.5909 0.277277
12 to 16 141519 -1.3232 0.092892
11 to 15 142622 2.4158 0.992150
10 to 14 141871 -0.1299 0.448310
9 to 13 141955 0.1548 0.561516
8 to 12 142568 2.2328 0.987218
7 to 11 142447 1.8226 0.965819
6 to 10 142192 0.9582 0.831020
5 to 9 142008 0.3345 0.630989
4 to 8 142192 0.9582 0.831020
3 to 7 141855 -0.1842 0.426940
2 to 6 142215 1.0362 0.849938
1 to 5 141887 -0.0757 0.469831
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-30_18:31
Bits used No. missing words z-score p-value
31 to 32 142650 2.1849 0.985551
30 to 31 141650 -0.7650 0.222140
29 to 30 141921 0.0344 0.513731
28 to 29 141604 -0.9007 0.183880
27 to 28 141672 -0.7001 0.241936
26 to 27 142087 0.5241 0.699896
25 to 26 142093 0.5418 0.706022
24 to 25 142112 0.5978 0.725029
23 to 24 141345 -1.6647 0.047987
22 to 23 141747 -0.4788 0.316023
21 to 22 141861 -0.1426 0.443316
20 to 21 142026 0.3442 0.634637
19 to 20 141962 0.1554 0.561735
18 to 19 141923 0.0403 0.516083
17 to 18 141968 0.1731 0.568701
16 to 17 141625 -0.8387 0.200810
15 to 16 142267 1.0551 0.854304
14 to 15 141963 0.1583 0.562897
13 to 14 141592 -0.9361 0.174617
12 to 13 142272 1.0698 0.857651
11 to 12 141280 -1.8564 0.031696
10 to 11 141595 -0.9272 0.176904
9 to 10 142115 0.6067 0.727974
8 to 9 142001 0.2704 0.606579
7 to 8 141415 -1.4582 0.072393
6 to 7 141712 -0.5821 0.280252
5 to 6 141539 -1.0924 0.137325
4 to 5 142274 1.0757 0.858974
3 to 4 141818 -0.2694 0.393807
2 to 3 141732 -0.5231 0.300453
1 to 2 141505 -1.1927 0.116491
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-30_18:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2226.24 -3.872 0.000054
Test results for specific bytes for dh-ranFile-2018-06-30_18:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2418.21 -1.157 0.123709
2 to 9 2402.25 -1.382 0.083428
3 to 10 2545.02 0.637 0.737814
4 to 11 2440.58 -0.840 0.200376
5 to 12 2493.22 -0.096 0.461792
6 to 13 2521.14 0.299 0.617535
7 to 14 2528.13 0.398 0.654609
8 to 15 2489.85 -0.144 0.442909
9 to 16 2393.19 -1.511 0.065447
10 to 17 2370.88 -1.826 0.033923
11 to 18 2295.25 -2.896 0.001893
12 to 19 2512.31 0.174 0.569103
13 to 20 2410.32 -1.268 0.102339
14 to 21 2498.65 -0.019 0.492411
15 to 22 2434.15 -0.931 0.175876
16 to 23 2416.76 -1.177 0.119546
17 to 24 2559.12 0.836 0.798435
18 to 25 2444.31 -0.788 0.215461
19 to 26 2475.06 -0.353 0.362149
20 to 27 2433.46 -0.941 0.173351
21 to 28 2519.53 0.276 0.608811
22 to 29 2509.02 0.128 0.550767
23 to 30 2473.93 -0.369 0.356196
24 to 31 2419.32 -1.141 0.126925
25 to 32 2430.22 -0.987 0.161871
CDPARK for dh-ranFile-2018-06-30_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
3554 1.4155 0.921543
3510 -0.5936 0.276387
3540 0.7763 0.781201
3540 0.7763 0.781201
3543 0.9132 0.819442
3473 -2.2831 0.011212
3522 -0.0457 0.481790
3530 0.3196 0.625377
3520 -0.1370 0.445521
3534 0.5023 0.692266
Square side=100, avg. no. parked=3526.60 sample std.=21.58
p-value of the KSTEST for those 10 p-values: 0.477182
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-30_18:31
0.4873,0.9221,0.4668,0.9911,0.4107,0.6101,0.2344,0.2091,0.3174,0.8552,
The KS test for those 10 p-values: 0.635323
The 3DSPHERES test for dh-ranFile-2018-06-30_18:31
sample no r^3 equiv. uni.
1 58.549 0.857959
2 32.839 0.665338
3 16.394 0.421016
4 1.305 0.042582
5 23.113 0.537180
6 13.010 0.351878
7 0.268 0.008887
8 24.276 0.554781
9 42.246 0.755415
10 4.779 0.147253
11 48.417 0.800889
12 99.319 0.963507
13 29.168 0.621781
14 1.150 0.037599
15 110.580 0.974928
16 205.760 0.998950
17 3.800 0.118976
18 10.063 0.284963
19 2.276 0.073067
20 14.208 0.377243
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.423926
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-30_18:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -0.7 1.3 -1.1 -1.7 0.5
-1.8 0.0 0.7 0.7 -0.7 -0.1
0.0 0.3 -0.2 1.0 0.0 -1.3
-0.1 -1.5 1.9 0.6 -0.1 0.1
0.3 -1.2 -0.4 0.7 0.3 0.8
0.7 0.8 1.1 -1.5 0.3 -1.9
0.3 -0.7 -1.2 0.4 0.1 0.0
1.8
Chi-square with 42 degrees of freedom:37.455547
z-score=-0.495840, p-value=0.329444
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-30_18:31
Test no p-value
1 0.018548
2 0.431352
3 0.525828
4 0.345641
5 0.229847
6 0.463564
7 0.026036
8 0.000071
9 0.005520
10 0.280649
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000595
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-30_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 66867 0.60 66894 0.78
3 25000.00 24908 0.34 24898 0.42
4 6666.67 6596 0.75 6601 0.65
5 1388.89 1345 1.39 1339 1.79
6 238.10 239 0.00 242 0.06
7 34.72 40 0.80 21 5.42
8 4.96 4 0.19 4 0.19
p=0.33264 p=0.84270
Number of rngs required: 689242, p-value: 0.834
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-30_18:31
No. of wins: Observed Expected
98373 98585.9
z-score=-0.952, pvalue=0.17054
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66272 66666.7 2.336 2.336
2 37926 37654.3 1.960 4.297
3 26963 26954.7 0.003 4.299
4 19556 19313.5 3.046 7.345
5 13944 13851.4 0.619 7.964
6 9858 9943.5 0.736 8.700
7 6899 7145.0 8.471 17.171
8 5235 5139.1 1.791 18.962
9 3713 3699.9 0.047 19.008
10 2704 2666.3 0.533 19.541
11 1902 1923.3 0.237 19.778
12 1389 1388.7 0.000 19.778
13 1026 1003.7 0.495 20.273
14 725 726.1 0.002 20.275
15 528 525.8 0.009 20.284
16 392 381.2 0.309 20.592
17 252 276.5 2.178 22.770
18 199 200.8 0.017 22.787
19 134 146.0 0.984 23.770
20 100 106.2 0.364 24.134
21 283 287.1 0.059 24.193
Chisq= 24.19 for 20 degrees of freedom, p= 0.76594
SUMMARY of craptest
p-value for no. of wins: 0.170541
p-value for throws/game: 0.765940
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-30_18:31
No. of wins: Observed Expected
98456 98585.9
z-score=-0.581, pvalue=0.28069
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66567 66666.7 0.149 0.149
2 37856 37654.3 1.080 1.229
3 26806 26954.7 0.821 2.050
4 19442 19313.5 0.855 2.905
5 14048 13851.4 2.790 5.695
6 9822 9943.5 1.486 7.181
7 7126 7145.0 0.051 7.232
8 5035 5139.1 2.108 9.339
9 3670 3699.9 0.241 9.580
10 2685 2666.3 0.131 9.711
11 1883 1923.3 0.846 10.557
12 1353 1388.7 0.920 11.477
13 1007 1003.7 0.011 11.488
14 733 726.1 0.065 11.552
15 574 525.8 4.412 15.964
16 423 381.2 4.595 20.559
17 266 276.5 0.402 20.961
18 194 200.8 0.232 21.193
19 142 146.0 0.109 21.302
20 105 106.2 0.014 21.316
21 263 287.1 2.025 23.341
Chisq= 23.34 for 20 degrees of freedom, p= 0.72763
SUMMARY of craptest
p-value for no. of wins: 0.280687
p-value for throws/game: 0.727629
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0001,0.0001,0.0006,0.0019,0.0055,0.0069,0.0089,0.0094,0.0112,0.0126,
0.0129,0.0149,0.0185,0.0260,0.0278,0.0282,0.0314,0.0317,0.0323,0.0339,
0.0376,0.0426,0.0480,0.0499,0.0538,0.0654,0.0717,0.0717,0.0724,0.0731,
0.0744,0.0760,0.0830,0.0834,0.0857,0.0920,0.0929,0.0993,0.0995,0.1022,
0.1023,0.1026,0.1098,0.1165,0.1190,0.1195,0.1217,0.1237,0.1269,0.1277,
0.1373,0.1432,0.1473,0.1500,0.1526,0.1619,0.1659,0.1705,0.1734,0.1746,
0.1759,0.1769,0.1773,0.1797,0.1839,0.1859,0.1917,0.1988,0.2004,0.2008,
0.2091,0.2155,0.2184,0.2198,0.2221,0.2298,0.2327,0.2344,0.2400,0.2419,
0.2605,0.2625,0.2648,0.2669,0.2671,0.2721,0.2727,0.2728,0.2764,0.2773,
0.2779,0.2803,0.2806,0.2807,0.2850,0.2969,0.2993,0.3005,0.3133,0.3160,
0.3174,0.3200,0.3212,0.3294,0.3326,0.3366,0.3456,0.3519,0.3562,0.3581,
0.3621,0.3712,0.3764,0.3772,0.3804,0.3938,0.3952,0.4071,0.4107,0.4126,
0.4210,0.4239,0.4269,0.4314,0.4371,0.4384,0.4429,0.4433,0.4455,0.4461,
0.4483,0.4493,0.4502,0.4618,0.4622,0.4631,0.4636,0.4657,0.4668,0.4693,
0.4698,0.4733,0.4734,0.4772,0.4776,0.4818,0.4873,0.4874,0.4915,0.4924,
0.4939,0.5137,0.5161,0.5176,0.5243,0.5258,0.5372,0.5448,0.5478,0.5480,
0.5508,0.5548,0.5582,0.5602,0.5615,0.5617,0.5629,0.5687,0.5691,0.5720,
0.5745,0.5762,0.5805,0.5807,0.5854,0.5993,0.6066,0.6088,0.6101,0.6158,
0.6175,0.6218,0.6254,0.6310,0.6346,0.6353,0.6387,0.6397,0.6409,0.6525,
0.6546,0.6557,0.6601,0.6653,0.6678,0.6730,0.6742,0.6788,0.6919,0.6923,
0.6937,0.6945,0.6999,0.7060,0.7116,0.7128,0.7249,0.7250,0.7276,0.7280,
0.7284,0.7378,0.7380,0.7480,0.7552,0.7554,0.7596,0.7659,0.7707,0.7725,
0.7812,0.7812,0.7984,0.8009,0.8135,0.8177,0.8194,0.8298,0.8310,0.8310,
0.8344,0.8412,0.8427,0.8488,0.8499,0.8543,0.8552,0.8577,0.8580,0.8590,
0.8618,0.8682,0.8718,0.8967,0.9015,0.9059,0.9117,0.9199,0.9215,0.9221,
0.9243,0.9329,0.9371,0.9463,0.9473,0.9497,0.9600,0.9635,0.9658,0.9683,
0.9749,0.9856,0.9872,0.9891,0.9909,0.9911,0.9922,0.9975,0.9989,
Overall p-value after applying KStest on 269 p-values = 0.018321
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.