RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-18_10:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.99 20.5896 0.754813
2 to 25 15.72 8.3466 0.041436
3 to 26 15.91 22.3298 0.827635
4 to 27 15.46 17.8675 0.602751
5 to 28 15.68 26.7645 0.938387
6 to 29 15.93 13.5264 0.299702
7 to 30 15.85 20.0207 0.726830
8 to 31 15.77 17.9111 0.605532
9 to 32 15.52 15.0621 0.408991
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.689432
Tough bday spacings test for dh-ranFile-2018-06-18_10:31: 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 37 65 116 93 78 52 27 10 6 5
(O-E)^2/E 0.4 0.0 0.9 3.4 0.2 0.0 0.0 0.3 1.6 0.1 0.2
Birthday Spacings: Sum(O-E)^2/E= 7.098, p= 0.284
RESULTS OF GCD FOR dh-ranFile-2018-06-18_10:31
Euclid's algorithm:
p-value, steps to gcd: 0.968931
p-value, dist. of gcd's: 0.891983
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-18_10:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.658 0.013 0.614 0.659 0.855 0.651 0.808 0.122
Bits 8 to 15---> 0.923 0.570 0.965 0.798 0.905 0.200 0.644 0.313
Bits 16 to 23---> 0.984 0.552 0.441 0.824 0.637 0.935 0.261 0.294
Bits 24 to 31---> 0.649 0.750 0.125 0.873 0.272 0.751 0.185 0.101
KS test for the above 32 p values: 0.771
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-18_10:31,
p-values for 5 runs: 0.6136, 0.6038, 0.3477, 0.0884, 0.7252
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-18_10:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 190 211.4 2.170 2.170
r= 29 5102 5134.0 0.200 2.369
r= 30 23215 23103.0 0.542 2.912
r= 31 11493 11551.5 0.297 3.208
chi-square = 3.208 with df = 3; p-value = 0.639
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-18_10:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 218 211.4 0.205 0.205
r= 30 5025 5134.0 2.315 2.520
r= 31 23072 23103.0 0.042 2.561
r= 32 11685 11551.5 1.542 4.104
chi-square = 4.104 with df = 3; p-value = 0.750
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-18_10:31
b-rank test for bits 1 to 8, p=0.24949
b-rank test for bits 2 to 9, p=0.91652
b-rank test for bits 3 to 10, p=0.74085
b-rank test for bits 4 to 11, p=0.44307
b-rank test for bits 5 to 12, p=0.89158
b-rank test for bits 6 to 13, p=0.11776
b-rank test for bits 7 to 14, p=0.03123
b-rank test for bits 8 to 15, p=0.83915
b-rank test for bits 9 to 16, p=0.30136
b-rank test for bits 10 to 17, p=0.02616
b-rank test for bits 11 to 18, p=0.03864
b-rank test for bits 12 to 19, p=0.45267
b-rank test for bits 13 to 20, p=0.63815
b-rank test for bits 14 to 21, p=0.75602
b-rank test for bits 15 to 22, p=0.69699
b-rank test for bits 16 to 23, p=0.41417
b-rank test for bits 17 to 24, p=0.79731
b-rank test for bits 18 to 25, p=0.81725
b-rank test for bits 19 to 26, p=0.79620
b-rank test for bits 20 to 27, p=0.04687
b-rank test for bits 21 to 28, p=0.33953
b-rank test for bits 22 to 29, p=0.17765
b-rank test for bits 23 to 30, p=0.58795
b-rank test for bits 24 to 31, p=0.85902
b-rank test for bits 25 to 32, p=0.02692
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 = 0.368582
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-18_10:31
(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 142173 0.62 0.731070
2 141866 -0.10 0.459681
3 141580 -0.77 0.220809
4 141712 -0.46 0.322381
5 141772 -0.32 0.374157
6 142271 0.85 0.800951
7 142462 1.29 0.901698
8 142708 1.87 0.968983
9 142395 1.13 0.871759
10 142118 0.49 0.687065
11 141292 -1.44 0.074600
12 143064 2.70 0.996510
13 141756 -0.36 0.360079
14 141882 -0.06 0.474543
15 142431 1.22 0.888550
16 142355 1.04 0.851128
17 142043 0.31 0.622599
18 141712 -0.46 0.322381
19 142543 1.48 0.930635
20 142449 1.26 0.896330
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-18_10:31
Bits used No. missing words z-score p-value
23 to 32 142236 1.1264 0.870012
22 to 31 142167 0.8885 0.812869
21 to 30 141733 -0.6080 0.271582
20 to 29 141912 0.0092 0.503673
19 to 28 141835 -0.2563 0.398856
18 to 27 141811 -0.3391 0.367279
17 to 26 141788 -0.4184 0.337835
16 to 25 141938 0.0989 0.539376
15 to 24 142121 0.7299 0.767273
14 to 23 141782 -0.4391 0.330306
13 to 22 142143 0.8058 0.789809
12 to 21 141480 -1.4804 0.069377
11 to 20 141861 -0.1667 0.433821
10 to 19 142137 0.7851 0.783793
9 to 18 141741 -0.5804 0.280806
8 to 17 141924 0.0506 0.520172
7 to 16 141827 -0.2839 0.388245
6 to 15 141896 -0.0460 0.481669
5 to 14 141824 -0.2942 0.384287
4 to 13 141403 -1.7460 0.040408
3 to 12 142048 0.4782 0.683736
2 to 11 141597 -1.0770 0.140740
1 to 10 142208 1.0299 0.848471
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-18_10:31
Bits used No. missing words z-score p-value
28 to 32 142734 2.7955 0.997409
27 to 31 141887 -0.0757 0.469831
26 to 30 141731 -0.6045 0.272753
25 to 29 142323 1.4023 0.919583
24 to 28 141688 -0.7503 0.226546
23 to 27 142143 0.7921 0.785849
22 to 26 142070 0.5446 0.707001
21 to 25 141753 -0.5299 0.298080
20 to 24 141999 0.3040 0.619423
19 to 23 142450 1.8328 0.966582
18 to 22 142139 0.7785 0.781875
17 to 21 142007 0.3311 0.629710
16 to 20 141892 -0.0587 0.476577
15 to 19 141771 -0.4689 0.319565
14 to 18 142029 0.4057 0.657504
13 to 17 142319 1.3887 0.917540
12 to 16 142340 1.4599 0.927841
11 to 15 141623 -0.9706 0.165871
10 to 14 141545 -1.2350 0.108412
9 to 13 142099 0.6429 0.739872
8 to 12 142295 1.3074 0.904454
7 to 11 141820 -0.3028 0.381016
6 to 10 141570 -1.1503 0.125016
5 to 9 141845 -0.2181 0.413688
4 to 8 141993 0.2836 0.611652
3 to 7 141842 -0.2282 0.409731
2 to 6 141558 -1.1909 0.116837
1 to 5 142145 0.7989 0.787820
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-18_10:31
Bits used No. missing words z-score p-value
31 to 32 142137 0.6716 0.749079
30 to 31 141475 -1.2812 0.100060
29 to 30 142365 1.3442 0.910552
28 to 29 142158 0.7335 0.768385
27 to 28 141933 0.0698 0.527833
26 to 27 142269 1.0610 0.855649
25 to 26 142755 2.4946 0.993695
24 to 25 141459 -1.3284 0.092022
23 to 24 141457 -1.3343 0.091052
22 to 23 141798 -0.3284 0.371302
21 to 22 141569 -1.0039 0.157708
20 to 21 142014 0.3088 0.621248
19 to 20 141581 -0.9685 0.166391
18 to 19 141854 -0.1632 0.435174
17 to 18 141783 -0.3727 0.354703
16 to 17 141509 -1.1809 0.118818
15 to 16 141894 -0.0452 0.481966
14 to 15 141716 -0.5703 0.284239
13 to 14 141913 0.0108 0.504319
12 to 13 141605 -0.8977 0.184665
11 to 12 141858 -0.1514 0.439824
10 to 11 142261 1.0374 0.850219
9 to 10 142300 1.1524 0.875426
8 to 9 141941 0.0934 0.537216
7 to 8 141477 -1.2753 0.101100
6 to 7 141310 -1.7679 0.038536
5 to 6 142175 0.7837 0.783388
4 to 5 141617 -0.8623 0.194253
3 to 4 141912 0.0079 0.503142
2 to 3 141871 -0.1131 0.454988
1 to 2 141866 -0.1278 0.449147
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-18_10:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2601.48 1.435 0.924370
Test results for specific bytes for dh-ranFile-2018-06-18_10:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2516.82 0.238 0.593996
2 to 9 2531.76 0.449 0.673315
3 to 10 2571.37 1.009 0.843600
4 to 11 2434.83 -0.922 0.178349
5 to 12 2532.56 0.461 0.677435
6 to 13 2598.52 1.393 0.918227
7 to 14 2445.85 -0.766 0.221883
8 to 15 2410.03 -1.272 0.101618
9 to 16 2517.03 0.241 0.595153
10 to 17 2503.98 0.056 0.522438
11 to 18 2439.00 -0.863 0.194169
12 to 19 2375.44 -1.762 0.039074
13 to 20 2566.00 0.933 0.824684
14 to 21 2619.81 1.694 0.954904
15 to 22 2449.69 -0.712 0.238370
16 to 23 2495.66 -0.061 0.475554
17 to 24 2557.61 0.815 0.792400
18 to 25 2553.45 0.756 0.775157
19 to 26 2488.56 -0.162 0.435715
20 to 27 2559.22 0.837 0.798826
21 to 28 2465.37 -0.490 0.312172
22 to 29 2583.43 1.180 0.880964
23 to 30 2576.96 1.088 0.861797
24 to 31 2438.75 -0.866 0.193178
25 to 32 2542.61 0.603 0.726609
CDPARK for dh-ranFile-2018-06-18_10:31: 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
3531 0.3653 0.642555
3533 0.4566 0.676028
3527 0.1826 0.572463
3533 0.4566 0.676028
3480 -1.9635 0.024796
3531 0.3653 0.642555
3528 0.2283 0.590298
3531 0.3653 0.642555
3557 1.5525 0.939730
3500 -1.0502 0.146807
Square side=100, avg. no. parked=3525.10 sample std.=19.81
p-value of the KSTEST for those 10 p-values: 0.292998
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-18_10:31
0.4980,0.9449,0.1955,0.9946,0.8944,0.6004,0.4292,0.6177,0.7382,0.2801,
The KS test for those 10 p-values: 0.287266
The 3DSPHERES test for dh-ranFile-2018-06-18_10:31
sample no r^3 equiv. uni.
1 86.584 0.944208
2 95.094 0.957988
3 3.960 0.123660
4 30.423 0.637268
5 52.098 0.823883
6 42.004 0.753439
7 2.786 0.088683
8 4.834 0.148811
9 22.836 0.532892
10 3.099 0.098144
11 1.284 0.041912
12 6.542 0.195935
13 14.723 0.387843
14 31.195 0.646482
15 4.548 0.140667
16 12.521 0.341221
17 24.719 0.561310
18 55.747 0.844054
19 106.180 0.970968
20 25.476 0.572239
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.766596
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-18_10:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 0.1 -0.6 0.3 1.0 2.2
0.2 -0.7 0.2 -0.8 0.7 -0.8
-0.3 0.2 1.1 -1.2 0.2 0.9
-0.6 -1.4 -0.0 -0.6 -0.7 0.1
2.5 -0.3 2.5 -1.7 -0.1 -0.7
-0.3 0.1 0.5 2.0 0.9 0.8
-0.5 0.2 1.3 0.4 0.9 -1.0
-0.1
Chi-square with 42 degrees of freedom:41.911647
z-score=-0.009640, p-value=0.525191
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-18_10:31
Test no p-value
1 0.258874
2 0.314134
3 0.987098
4 0.581385
5 0.035546
6 0.471432
7 0.907207
8 0.958460
9 0.041011
10 0.162991
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.393372
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-18_10:31:
(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 66378 1.25 66547 0.21
3 25000.00 25158 1.00 24995 0.00
4 6666.67 6848 4.93 6788 2.21
5 1388.89 1328 2.67 1411 0.35
6 238.10 246 0.26 215 2.24
7 34.72 35 0.00 38 0.31
8 4.96 6 0.22 5 0.00
p=0.88868 p=0.49731
Number of rngs required: 688161, p-value: 0.390
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-18_10:31
No. of wins: Observed Expected
98618 98585.9
z-score= 0.144, pvalue=0.55715
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66619 66666.7 0.034 0.034
2 37582 37654.3 0.139 0.173
3 26927 26954.7 0.029 0.202
4 19299 19313.5 0.011 0.212
5 13745 13851.4 0.818 1.030
6 10008 9943.5 0.418 1.448
7 7204 7145.0 0.487 1.935
8 5193 5139.1 0.566 2.500
9 3720 3699.9 0.110 2.610
10 2713 2666.3 0.818 3.428
11 1888 1923.3 0.649 4.077
12 1428 1388.7 1.110 5.187
13 1040 1003.7 1.312 6.499
14 766 726.1 2.188 8.687
15 526 525.8 0.000 8.687
16 387 381.2 0.090 8.776
17 267 276.5 0.329 9.105
18 181 200.8 1.958 11.063
19 119 146.0 4.988 16.051
20 92 106.2 1.902 17.954
21 296 287.1 0.275 18.229
Chisq= 18.23 for 20 degrees of freedom, p= 0.42767
SUMMARY of craptest
p-value for no. of wins: 0.557153
p-value for throws/game: 0.427667
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-18_10:31
No. of wins: Observed Expected
98658 98585.9
z-score= 0.323, pvalue=0.62652
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66786 66666.7 0.214 0.214
2 37666 37654.3 0.004 0.217
3 27074 26954.7 0.528 0.745
4 19128 19313.5 1.781 2.526
5 13857 13851.4 0.002 2.528
6 9795 9943.5 2.219 4.747
7 7255 7145.0 1.693 6.440
8 5035 5139.1 2.108 8.547
9 3745 3699.9 0.551 9.098
10 2800 2666.3 6.705 15.803
11 1893 1923.3 0.478 16.281
12 1391 1388.7 0.004 16.285
13 994 1003.7 0.094 16.379
14 745 726.1 0.490 16.868
15 488 525.8 2.722 19.591
16 355 381.2 1.794 21.385
17 287 276.5 0.396 21.781
18 213 200.8 0.737 22.518
19 130 146.0 1.750 24.268
20 83 106.2 5.074 29.343
21 280 287.1 0.176 29.519
Chisq= 29.52 for 20 degrees of freedom, p= 0.92196
SUMMARY of craptest
p-value for no. of wins: 0.626523
p-value for throws/game: 0.921965
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0127,0.0248,0.0262,0.0269,0.0312,0.0355,0.0385,0.0386,0.0391,0.0404,
0.0410,0.0414,0.0419,0.0469,0.0694,0.0746,0.0884,0.0887,0.0911,0.0920,
0.0981,0.1001,0.1011,0.1011,0.1016,0.1084,0.1168,0.1178,0.1188,0.1219,
0.1237,0.1248,0.1250,0.1407,0.1407,0.1468,0.1488,0.1577,0.1630,0.1659,
0.1664,0.1777,0.1783,0.1847,0.1853,0.1932,0.1942,0.1943,0.1955,0.1959,
0.1998,0.2208,0.2219,0.2265,0.2384,0.2495,0.2589,0.2615,0.2716,0.2724,
0.2728,0.2801,0.2808,0.2839,0.2842,0.2873,0.2930,0.2941,0.2981,0.2997,
0.3014,0.3122,0.3131,0.3141,0.3196,0.3224,0.3224,0.3303,0.3378,0.3395,
0.3412,0.3477,0.3547,0.3601,0.3673,0.3686,0.3713,0.3742,0.3810,0.3843,
0.3878,0.3882,0.3903,0.3934,0.3989,0.4090,0.4097,0.4137,0.4142,0.4277,
0.4292,0.4338,0.4352,0.4357,0.4398,0.4408,0.4431,0.4491,0.4527,0.4550,
0.4597,0.4698,0.4714,0.4745,0.4756,0.4766,0.4817,0.4820,0.4973,0.4980,
0.5031,0.5037,0.5043,0.5202,0.5224,0.5252,0.5278,0.5329,0.5372,0.5394,
0.5520,0.5572,0.5613,0.5696,0.5722,0.5725,0.5814,0.5880,0.5903,0.5940,
0.5952,0.6004,0.6028,0.6038,0.6055,0.6117,0.6135,0.6136,0.6177,0.6194,
0.6212,0.6226,0.6265,0.6297,0.6366,0.6373,0.6382,0.6394,0.6426,0.6426,
0.6426,0.6436,0.6465,0.6491,0.6513,0.6575,0.6577,0.6591,0.6733,0.6760,
0.6760,0.6774,0.6837,0.6871,0.6894,0.6970,0.7070,0.7252,0.7266,0.7268,
0.7311,0.7382,0.7399,0.7408,0.7491,0.7495,0.7503,0.7509,0.7534,0.7548,
0.7560,0.7666,0.7673,0.7684,0.7707,0.7752,0.7819,0.7834,0.7838,0.7858,
0.7878,0.7898,0.7924,0.7962,0.7973,0.7979,0.7988,0.8010,0.8081,0.8129,
0.8173,0.8237,0.8239,0.8247,0.8276,0.8392,0.8436,0.8441,0.8485,0.8502,
0.8511,0.8549,0.8556,0.8590,0.8618,0.8700,0.8718,0.8734,0.8754,0.8810,
0.8886,0.8887,0.8916,0.8920,0.8944,0.8963,0.9017,0.9045,0.9045,0.9072,
0.9106,0.9165,0.9175,0.9182,0.9196,0.9220,0.9228,0.9244,0.9278,0.9306,
0.9353,0.9384,0.9397,0.9442,0.9449,0.9549,0.9580,0.9585,0.9648,0.9666,
0.9689,0.9690,0.9710,0.9838,0.9871,0.9937,0.9946,0.9965,0.9974,
Overall p-value after applying KStest on 269 p-values = 0.055576
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.