RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-29_22:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.79 25.1253 0.908060
2 to 25 15.94 8.2888 0.040026
3 to 26 15.78 14.1686 0.344865
4 to 27 15.70 16.4261 0.506147
5 to 28 15.92 18.1009 0.617498
6 to 29 15.82 11.9349 0.195935
7 to 30 15.69 9.0525 0.061400
8 to 31 15.77 25.2513 0.910775
9 to 32 15.45 20.3526 0.743410
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.901496
Tough bday spacings test for dh-ranFile-2018-06-29_22:31: 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 5 35 84 97 107 61 49 31 15 12 4
(O-E)^2/E 1.9 0.1 1.6 0.0 0.9 3.8 0.2 0.1 0.0 4.4 0.0
Birthday Spacings: Sum(O-E)^2/E= 12.809, p= 0.765
RESULTS OF GCD FOR dh-ranFile-2018-06-29_22:31
Euclid's algorithm:
p-value, steps to gcd: 0.113441
p-value, dist. of gcd's: 0.406504
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-29_22:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.550 0.563 0.106 0.421 0.919 0.638 0.345 0.954
Bits 8 to 15---> 0.790 0.106 0.622 0.459 0.226 0.714 0.912 0.816
Bits 16 to 23---> 0.442 0.502 0.770 0.297 0.829 0.089 0.998 0.123
Bits 24 to 31---> 0.483 0.084 0.396 0.237 0.236 0.957 0.471 0.642
KS test for the above 32 p values: 0.116
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-29_22:31,
p-values for 5 runs: 0.6104, 0.1602, 0.0733, 0.5916, 0.5153
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-29_22:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 231 211.4 1.814 1.814
r= 29 5192 5134.0 0.655 2.469
r= 30 22945 23103.0 1.081 3.550
r= 31 11632 11551.5 0.561 4.111
chi-square = 4.111 with df = 3; p-value = 0.750
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-29_22:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 215 211.4 0.061 0.061
r= 30 5057 5134.0 1.155 1.216
r= 31 23187 23103.0 0.305 1.521
r= 32 11541 11551.5 0.010 1.531
chi-square = 1.531 with df = 3; p-value = 0.325
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-29_22:31
b-rank test for bits 1 to 8, p=0.17441
b-rank test for bits 2 to 9, p=0.88248
b-rank test for bits 3 to 10, p=0.26656
b-rank test for bits 4 to 11, p=0.05800
b-rank test for bits 5 to 12, p=0.90152
b-rank test for bits 6 to 13, p=0.12023
b-rank test for bits 7 to 14, p=0.25417
b-rank test for bits 8 to 15, p=0.01266
b-rank test for bits 9 to 16, p=0.54759
b-rank test for bits 10 to 17, p=0.81399
b-rank test for bits 11 to 18, p=0.00390
b-rank test for bits 12 to 19, p=0.85050
b-rank test for bits 13 to 20, p=0.42573
b-rank test for bits 14 to 21, p=0.58437
b-rank test for bits 15 to 22, p=0.48686
b-rank test for bits 16 to 23, p=0.39444
b-rank test for bits 17 to 24, p=0.18597
b-rank test for bits 18 to 25, p=0.25076
b-rank test for bits 19 to 26, p=0.70942
b-rank test for bits 20 to 27, p=0.55432
b-rank test for bits 21 to 28, p=0.96064
b-rank test for bits 22 to 29, p=0.32180
b-rank test for bits 23 to 30, p=0.46959
b-rank test for bits 24 to 31, p=0.72492
b-rank test for bits 25 to 32, p=0.57067
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 = 0.802612
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-29_22:31
(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 141853 -0.13 0.447646
2 142409 1.17 0.878486
3 141500 -0.96 0.169441
4 142331 0.99 0.837740
5 141916 0.02 0.506217
6 141872 -0.09 0.465249
7 141558 -0.82 0.205862
8 141556 -0.83 0.204533
9 141774 -0.32 0.375929
10 142442 1.24 0.893353
11 141941 0.07 0.529493
12 141828 -0.19 0.424645
13 142244 0.78 0.782875
14 141548 -0.84 0.199271
15 141685 -0.52 0.300092
16 142433 1.22 0.889435
17 142405 1.16 0.876590
18 142214 0.71 0.761720
19 141773 -0.32 0.375042
20 141675 -0.55 0.292018
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-29_22:31
Bits used No. missing words z-score p-value
23 to 32 141772 -0.4736 0.317910
22 to 31 141655 -0.8770 0.190243
21 to 30 141712 -0.6804 0.248110
20 to 29 142159 0.8609 0.805362
19 to 28 142282 1.2851 0.900616
18 to 27 142108 0.6851 0.753350
17 to 26 141873 -0.1253 0.450153
16 to 25 141457 -1.5598 0.059408
15 to 24 141390 -1.7908 0.036663
14 to 23 142088 0.6161 0.731087
13 to 22 141633 -0.9529 0.170330
12 to 21 141273 -2.1942 0.014109
11 to 20 141841 -0.2356 0.406864
10 to 19 141962 0.1816 0.572060
9 to 18 142433 1.8058 0.964522
8 to 17 142088 0.6161 0.731087
7 to 16 141571 -1.1667 0.121675
6 to 15 141601 -1.0632 0.143844
5 to 14 141801 -0.3736 0.354369
4 to 13 141907 -0.0080 0.496795
3 to 12 141859 -0.1736 0.431109
2 to 11 141761 -0.5115 0.304507
1 to 10 141580 -1.1356 0.128058
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-29_22:31
Bits used No. missing words z-score p-value
28 to 32 142140 0.7819 0.782873
27 to 31 142112 0.6870 0.753964
26 to 30 142185 0.9345 0.824970
25 to 29 142011 0.3446 0.634819
24 to 28 142670 2.5785 0.995039
23 to 27 141833 -0.2587 0.397916
22 to 26 141917 0.0260 0.510371
21 to 25 141641 -0.9096 0.181519
20 to 24 142010 0.3413 0.633544
19 to 23 142576 2.2599 0.988086
18 to 22 141908 -0.0045 0.498201
17 to 21 141986 0.2599 0.602529
16 to 20 141994 0.2870 0.612950
15 to 19 142378 1.5887 0.943937
14 to 18 142145 0.7989 0.787820
13 to 17 141716 -0.6554 0.256119
12 to 16 141729 -0.6113 0.270504
11 to 15 142455 1.8497 0.967824
10 to 14 141505 -1.3706 0.085248
9 to 13 142147 0.8057 0.789781
8 to 12 142063 0.5209 0.698787
7 to 11 141880 -0.0994 0.460401
6 to 10 142317 1.3819 0.916504
5 to 9 141700 -0.7096 0.238978
4 to 8 142095 0.6294 0.735453
3 to 7 141901 -0.0282 0.488737
2 to 6 141587 -1.0926 0.137275
1 to 5 142108 0.6735 0.749672
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-29_22:31
Bits used No. missing words z-score p-value
31 to 32 141979 0.2055 0.581416
30 to 31 141790 -0.3520 0.362417
29 to 30 142041 0.3884 0.651143
28 to 29 141802 -0.3166 0.375771
27 to 28 141342 -1.6735 0.047111
26 to 27 141662 -0.7296 0.232821
25 to 26 141903 -0.0187 0.492551
24 to 25 141782 -0.3756 0.353605
23 to 24 142051 0.4179 0.661992
22 to 23 142665 2.2291 0.987097
21 to 22 142070 0.4740 0.682233
20 to 21 142299 1.1495 0.874819
19 to 20 142186 0.8161 0.792789
18 to 19 141644 -0.7827 0.216906
17 to 18 141981 0.2114 0.583719
16 to 17 142056 0.4327 0.667367
15 to 16 141872 -0.1101 0.456158
14 to 15 142036 0.3737 0.645671
13 to 14 142161 0.7424 0.771074
12 to 13 141643 -0.7856 0.216041
11 to 12 141493 -1.2281 0.109702
10 to 11 141788 -0.3579 0.360207
9 to 10 141653 -0.7561 0.224784
8 to 9 141965 0.1642 0.565220
7 to 8 142109 0.5890 0.722068
6 to 7 142402 1.4533 0.926930
5 to 6 141565 -1.0157 0.154881
4 to 5 141995 0.2527 0.599755
3 to 4 142291 1.1259 0.869890
2 to 3 142357 1.3206 0.906676
1 to 2 141066 -2.4877 0.006429
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-29_22:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2457.19 -0.605 0.272471
Test results for specific bytes for dh-ranFile-2018-06-29_22:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2573.17 1.035 0.849618
2 to 9 2483.16 -0.238 0.405890
3 to 10 2540.52 0.573 0.716670
4 to 11 2483.54 -0.233 0.407959
5 to 12 2536.58 0.517 0.697544
6 to 13 2560.86 0.861 0.805311
7 to 14 2453.01 -0.665 0.253164
8 to 15 2492.01 -0.113 0.454998
9 to 16 2502.07 0.029 0.511700
10 to 17 2457.16 -0.606 0.272311
11 to 18 2478.46 -0.305 0.380328
12 to 19 2532.28 0.456 0.675966
13 to 20 2413.32 -1.226 0.110138
14 to 21 2496.36 -0.051 0.479487
15 to 22 2413.28 -1.226 0.110035
16 to 23 2508.46 0.120 0.547636
17 to 24 2421.76 -1.106 0.134262
18 to 25 2469.33 -0.434 0.332256
19 to 26 2490.38 -0.136 0.445907
20 to 27 2453.06 -0.664 0.253413
21 to 28 2408.53 -1.294 0.097909
22 to 29 2526.35 0.373 0.645270
23 to 30 2520.37 0.288 0.613372
24 to 31 2585.57 1.210 0.886877
25 to 32 2536.70 0.519 0.698137
CDPARK for dh-ranFile-2018-06-29_22:31: 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
3504 -0.8676 0.192812
3532 0.4110 0.659449
3539 0.7306 0.767486
3520 -0.1370 0.445521
3539 0.7306 0.767486
3523 0.0000 0.500000
3538 0.6849 0.753306
3505 -0.8219 0.205562
3544 0.9589 0.831196
3511 -0.5479 0.291865
Square side=100, avg. no. parked=3525.50 sample std.=14.26
p-value of the KSTEST for those 10 p-values: 0.640203
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-29_22:31
0.0382,0.5355,0.7796,0.5689,0.6647,0.0194,0.0697,0.4478,0.8663,0.2541,
The KS test for those 10 p-values: 0.451044
The 3DSPHERES test for dh-ranFile-2018-06-29_22:31
sample no r^3 equiv. uni.
1 55.307 0.841747
2 9.290 0.266298
3 2.129 0.068520
4 2.734 0.087089
5 23.381 0.541305
6 4.089 0.127414
7 1.339 0.043654
8 64.566 0.883771
9 7.248 0.214640
10 106.560 0.971333
11 1.410 0.045903
12 6.778 0.202228
13 53.464 0.831723
14 6.480 0.194266
15 12.719 0.345559
16 53.392 0.831319
17 46.728 0.789359
18 155.385 0.994369
19 6.750 0.201478
20 48.975 0.804561
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.171934
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-29_22:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -0.3 -0.8 0.0 0.0 1.1
0.3 0.7 -1.6 -0.1 0.5 -0.6
1.2 -0.6 0.3 1.1 -0.5 0.3
-0.1 -0.5 -0.5 0.6 -0.3 -0.9
-1.4 -0.7 -0.3 1.8 1.0 0.2
0.1 0.9 0.8 0.2 -0.8 0.6
0.7 0.5 1.7 1.0 -0.6 -1.0
-0.1
Chi-square with 42 degrees of freedom:26.497821
z-score=-1.691426, p-value=0.029709
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-29_22:31
Test no p-value
1 0.873514
2 0.869732
3 0.010970
4 0.948469
5 0.007280
6 0.011603
7 0.479943
8 0.320418
9 0.416054
10 0.009790
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.007759
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-29_22:31:
(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 66694 0.01 66448 0.72
3 25000.00 24841 1.01 25280 3.14
4 6666.67 6757 1.22 6598 0.71
5 1388.89 1406 0.21 1380 0.06
6 238.10 266 3.27 254 1.06
7 34.72 31 0.40 33 0.09
8 4.96 4 0.19 6 0.22
p=0.61084 p=0.57493
Number of rngs required: 690752, p-value: 0.998
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-29_22:31
No. of wins: Observed Expected
98463 98585.9
z-score=-0.549, pvalue=0.29133
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66883 66666.7 0.702 0.702
2 37574 37654.3 0.171 0.873
3 26778 26954.7 1.159 2.032
4 19321 19313.5 0.003 2.035
5 13813 13851.4 0.107 2.142
6 10006 9943.5 0.392 2.534
7 7158 7145.0 0.024 2.557
8 5092 5139.1 0.431 2.989
9 3772 3699.9 1.406 4.395
10 2636 2666.3 0.344 4.739
11 1865 1923.3 1.769 6.508
12 1426 1388.7 1.000 7.508
13 996 1003.7 0.059 7.567
14 748 726.1 0.658 8.225
15 510 525.8 0.477 8.702
16 350 381.2 2.546 11.248
17 282 276.5 0.108 11.356
18 229 200.8 3.951 15.307
19 153 146.0 0.337 15.644
20 115 106.2 0.727 16.371
21 293 287.1 0.121 16.492
Chisq= 16.49 for 20 degrees of freedom, p= 0.31431
SUMMARY of craptest
p-value for no. of wins: 0.291333
p-value for throws/game: 0.314306
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-29_22:31
No. of wins: Observed Expected
98604 98585.9
z-score= 0.081, pvalue=0.53233
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66582 66666.7 0.108 0.108
2 37427 37654.3 1.372 1.480
3 27148 26954.7 1.386 2.866
4 19470 19313.5 1.269 4.134
5 13997 13851.4 1.530 5.664
6 9812 9943.5 1.740 7.405
7 7119 7145.0 0.095 7.499
8 5191 5139.1 0.525 8.024
9 3692 3699.9 0.017 8.041
10 2665 2666.3 0.001 8.041
11 1952 1923.3 0.427 8.469
12 1344 1388.7 1.441 9.910
13 963 1003.7 1.652 11.562
14 741 726.1 0.304 11.866
15 490 525.8 2.442 14.308
16 384 381.2 0.021 14.329
17 271 276.5 0.111 14.440
18 192 200.8 0.388 14.829
19 152 146.0 0.248 15.077
20 104 106.2 0.046 15.123
21 304 287.1 0.993 16.116
Chisq= 16.12 for 20 degrees of freedom, p= 0.29059
SUMMARY of craptest
p-value for no. of wins: 0.532334
p-value for throws/game: 0.290586
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0039,0.0064,0.0073,0.0078,0.0098,0.0110,0.0116,0.0127,0.0141,0.0194,
0.0297,0.0367,0.0382,0.0400,0.0437,0.0459,0.0471,0.0580,0.0594,0.0614,
0.0685,0.0697,0.0733,0.0837,0.0852,0.0871,0.0890,0.0979,0.1059,0.1064,
0.1097,0.1100,0.1101,0.1134,0.1163,0.1202,0.1217,0.1230,0.1274,0.1281,
0.1343,0.1373,0.1438,0.1549,0.1602,0.1694,0.1703,0.1719,0.1744,0.1815,
0.1860,0.1902,0.1928,0.1943,0.1959,0.1993,0.2015,0.2022,0.2045,0.2056,
0.2059,0.2146,0.2160,0.2169,0.2248,0.2259,0.2328,0.2364,0.2368,0.2390,
0.2481,0.2508,0.2532,0.2534,0.2541,0.2542,0.2561,0.2663,0.2666,0.2705,
0.2723,0.2725,0.2906,0.2913,0.2919,0.2920,0.2974,0.3001,0.3045,0.3143,
0.3179,0.3204,0.3218,0.3248,0.3323,0.3449,0.3454,0.3456,0.3536,0.3544,
0.3602,0.3624,0.3750,0.3758,0.3759,0.3803,0.3944,0.3957,0.3979,0.4059,
0.4065,0.4069,0.4080,0.4161,0.4209,0.4246,0.4257,0.4311,0.4417,0.4455,
0.4459,0.4476,0.4478,0.4502,0.4510,0.4550,0.4562,0.4592,0.4604,0.4652,
0.4696,0.4714,0.4795,0.4799,0.4826,0.4869,0.4887,0.4926,0.4968,0.4982,
0.5000,0.5017,0.5061,0.5062,0.5104,0.5117,0.5153,0.5295,0.5323,0.5355,
0.5413,0.5476,0.5476,0.5498,0.5543,0.5631,0.5652,0.5689,0.5707,0.5721,
0.5749,0.5814,0.5837,0.5844,0.5916,0.5998,0.6025,0.6104,0.6108,0.6130,
0.6134,0.6175,0.6223,0.6335,0.6348,0.6383,0.6402,0.6420,0.6453,0.6457,
0.6511,0.6594,0.6620,0.6647,0.6674,0.6760,0.6822,0.6975,0.6981,0.6988,
0.7094,0.7135,0.7167,0.7221,0.7249,0.7311,0.7311,0.7355,0.7434,0.7497,
0.7502,0.7533,0.7533,0.7540,0.7617,0.7655,0.7675,0.7675,0.7704,0.7711,
0.7796,0.7829,0.7829,0.7878,0.7894,0.7898,0.7904,0.7928,0.8026,0.8046,
0.8053,0.8054,0.8140,0.8156,0.8250,0.8288,0.8312,0.8313,0.8317,0.8377,
0.8417,0.8496,0.8505,0.8663,0.8697,0.8699,0.8735,0.8748,0.8766,0.8785,
0.8825,0.8838,0.8869,0.8894,0.8934,0.9006,0.9015,0.9015,0.9067,0.9081,
0.9108,0.9123,0.9165,0.9191,0.9269,0.9439,0.9485,0.9541,0.9568,0.9606,
0.9645,0.9678,0.9713,0.9871,0.9881,0.9944,0.9950,0.9976,0.9977,
Overall p-value after applying KStest on 269 p-values = 0.830278
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.