RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-18_07:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 16.09 11.8001 0.187909
2 to 25 15.74 24.1143 0.883637
3 to 26 15.81 11.6736 0.180515
4 to 27 15.80 10.2650 0.107869
5 to 28 15.76 14.2204 0.348555
6 to 29 15.88 12.7598 0.247887
7 to 30 15.84 36.6910 0.996295
8 to 31 15.84 10.8201 0.134240
9 to 32 15.64 16.7160 0.526237
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.213144
Tough bday spacings test for dh-ranFile-2018-06-18_07:31: 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 69 110 101 67 45 33 16 7 4
(O-E)^2/E 0.4 0.0 0.2 1.6 0.1 1.6 1.0 0.4 0.1 0.0 0.0
Birthday Spacings: Sum(O-E)^2/E= 5.302, p= 0.130
RESULTS OF GCD FOR dh-ranFile-2018-06-18_07:31
Euclid's algorithm:
p-value, steps to gcd: 0.461374
p-value, dist. of gcd's: 0.199841
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-18_07:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.796 0.584 0.595 0.610 0.713 0.828 0.851 0.232
Bits 8 to 15---> 0.156 0.462 0.882 0.301 0.514 0.324 0.707 0.131
Bits 16 to 23---> 0.068 0.663 0.896 0.753 0.430 0.537 0.494 0.168
Bits 24 to 31---> 0.328 0.822 0.953 0.487 0.517 0.403 0.930 0.256
KS test for the above 32 p values: 0.476
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-18_07:31,
p-values for 5 runs: 0.8856, 0.0763, 0.7387, 0.1415, 0.1703
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-18_07:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 204 211.4 0.260 0.260
r= 29 5257 5134.0 2.946 3.207
r= 30 23172 23103.0 0.206 3.412
r= 31 11367 11551.5 2.948 6.360
chi-square = 6.360 with df = 3; p-value = 0.905
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-18_07:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 213 211.4 0.012 0.012
r= 30 5089 5134.0 0.395 0.406
r= 31 23059 23103.0 0.084 0.490
r= 32 11639 11551.5 0.662 1.153
chi-square = 1.153 with df = 3; p-value = 0.236
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-18_07:31
b-rank test for bits 1 to 8, p=0.83738
b-rank test for bits 2 to 9, p=0.33784
b-rank test for bits 3 to 10, p=0.38507
b-rank test for bits 4 to 11, p=0.47306
b-rank test for bits 5 to 12, p=0.26029
b-rank test for bits 6 to 13, p=0.57005
b-rank test for bits 7 to 14, p=0.33863
b-rank test for bits 8 to 15, p=0.12516
b-rank test for bits 9 to 16, p=0.14016
b-rank test for bits 10 to 17, p=0.68732
b-rank test for bits 11 to 18, p=0.61262
b-rank test for bits 12 to 19, p=0.65662
b-rank test for bits 13 to 20, p=0.96725
b-rank test for bits 14 to 21, p=0.74997
b-rank test for bits 15 to 22, p=0.52867
b-rank test for bits 16 to 23, p=0.15942
b-rank test for bits 17 to 24, p=0.09871
b-rank test for bits 18 to 25, p=0.89022
b-rank test for bits 19 to 26, p=0.95096
b-rank test for bits 20 to 27, p=0.63038
b-rank test for bits 21 to 28, p=0.83514
b-rank test for bits 22 to 29, p=0.57308
b-rank test for bits 23 to 30, p=0.85273
b-rank test for bits 24 to 31, p=0.14022
b-rank test for bits 25 to 32, p=0.14831
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 = 0.913377
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-18_07:31
(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 142823 2.13 0.983609
2 142139 0.54 0.704232
3 142141 0.54 0.705844
4 141986 0.18 0.571084
5 142163 0.59 0.723305
6 142228 0.74 0.771730
7 142963 2.46 0.993089
8 142368 1.07 0.858063
9 141796 -0.26 0.395586
10 142244 0.78 0.782875
11 142120 0.49 0.688718
12 142180 0.63 0.736439
13 142426 1.21 0.886317
14 142534 1.46 0.927788
15 141783 -0.30 0.383935
16 141837 -0.17 0.432900
17 141720 -0.44 0.329114
18 141377 -1.24 0.106794
19 141241 -1.56 0.059201
20 141858 -0.12 0.452269
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-18_07:31
Bits used No. missing words z-score p-value
23 to 32 141509 -1.3804 0.083724
22 to 31 141828 -0.2804 0.389567
21 to 30 142176 0.9196 0.821097
20 to 29 141789 -0.4149 0.339096
19 to 28 141915 0.0196 0.507800
18 to 27 142281 1.2816 0.900012
17 to 26 141993 0.2885 0.613525
16 to 25 142231 1.1092 0.866330
15 to 24 141856 -0.1839 0.427047
14 to 23 141565 -1.1873 0.117546
13 to 22 142561 2.2471 0.987684
12 to 21 142023 0.3920 0.652458
11 to 20 142549 2.2058 0.986300
10 to 19 141758 -0.5218 0.300895
9 to 18 141401 -1.7529 0.039813
8 to 17 141436 -1.6322 0.051322
7 to 16 141437 -1.6287 0.051686
6 to 15 141940 0.1058 0.542113
5 to 14 141875 -0.1184 0.452884
4 to 13 141934 0.0851 0.533897
3 to 12 141586 -1.1149 0.132440
2 to 11 142150 0.8299 0.796701
1 to 10 141805 -0.3598 0.359514
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-18_07:31
Bits used No. missing words z-score p-value
28 to 32 142023 0.3853 0.650001
27 to 31 141842 -0.2282 0.409731
26 to 30 142315 1.3752 0.915458
25 to 29 141878 -0.1062 0.457711
24 to 28 141663 -0.8350 0.201854
23 to 27 141459 -1.5265 0.063437
22 to 26 141963 0.1819 0.572182
21 to 25 142000 0.3074 0.620714
20 to 24 141895 -0.0486 0.480629
19 to 23 142213 1.0294 0.848352
18 to 22 142018 0.3684 0.643702
17 to 21 141725 -0.6248 0.266036
16 to 20 142267 1.2124 0.887328
15 to 19 141717 -0.6520 0.257212
14 to 18 141682 -0.7706 0.220469
13 to 17 142537 2.1277 0.983319
12 to 16 141822 -0.2960 0.383602
11 to 15 141910 0.0023 0.500906
10 to 14 142317 1.3819 0.916504
9 to 13 142169 0.8802 0.810635
8 to 12 141565 -1.1672 0.121561
7 to 11 142161 0.8531 0.803203
6 to 10 141523 -1.3096 0.095167
5 to 9 141440 -1.5909 0.055811
4 to 8 141749 -0.5435 0.293396
3 to 7 142415 1.7141 0.956748
2 to 6 142001 0.3107 0.622003
1 to 5 141753 -0.5299 0.298080
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-18_07:31
Bits used No. missing words z-score p-value
31 to 32 142380 1.3884 0.917493
30 to 31 142244 0.9872 0.838234
29 to 30 142482 1.6893 0.954418
28 to 29 141980 0.2085 0.582568
27 to 28 141921 0.0344 0.513731
26 to 27 142096 0.5506 0.709063
25 to 26 140958 -2.8063 0.002506
24 to 25 142131 0.6539 0.743410
23 to 24 142024 0.3383 0.632416
22 to 23 142264 1.0462 0.852271
21 to 22 142468 1.6480 0.950323
20 to 21 141516 -1.1603 0.122970
19 to 20 141280 -1.8564 0.031696
18 to 19 141878 -0.0924 0.463183
17 to 18 142320 1.2114 0.887132
16 to 17 142386 1.4061 0.920154
15 to 16 142116 0.6096 0.728952
14 to 15 141662 -0.7296 0.232821
13 to 14 142250 1.0049 0.842534
12 to 13 141622 -0.8476 0.198336
11 to 12 141521 -1.1455 0.125998
10 to 11 141932 0.0669 0.526659
9 to 10 141463 -1.3166 0.093985
8 to 9 142154 0.7217 0.764773
7 to 8 141728 -0.5349 0.296361
6 to 7 142134 0.6627 0.746253
5 to 6 141583 -0.9626 0.167868
4 to 5 142032 0.3619 0.641271
3 to 4 142042 0.3914 0.652233
2 to 3 142416 1.4946 0.932491
1 to 2 141656 -0.7473 0.227445
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-18_07:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2485.86 -0.200 0.420749
Test results for specific bytes for dh-ranFile-2018-06-18_07:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2466.18 -0.478 0.316214
2 to 9 2583.73 1.184 0.881826
3 to 10 2398.89 -1.430 0.076366
4 to 11 2438.92 -0.864 0.193859
5 to 12 2662.00 2.291 0.989021
6 to 13 2596.65 1.367 0.914169
7 to 14 2565.86 0.931 0.824169
8 to 15 2467.93 -0.453 0.325105
9 to 16 2591.89 1.300 0.903125
10 to 17 2433.19 -0.945 0.172371
11 to 18 2463.61 -0.515 0.303424
12 to 19 2418.74 -1.149 0.125248
13 to 20 2448.26 -0.732 0.232166
14 to 21 2661.90 2.290 0.988977
15 to 22 2474.48 -0.361 0.359064
16 to 23 2514.24 0.201 0.579803
17 to 24 2580.92 1.144 0.873763
18 to 25 2324.64 -2.480 0.006569
19 to 26 2377.69 -1.730 0.041842
20 to 27 2640.26 1.984 0.976345
21 to 28 2525.19 0.356 0.639183
22 to 29 2523.27 0.329 0.628959
23 to 30 2383.68 -1.645 0.049979
24 to 31 2517.08 0.241 0.595412
25 to 32 2490.63 -0.132 0.447299
CDPARK for dh-ranFile-2018-06-18_07:31: 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
3528 0.2283 0.590298
3518 -0.2283 0.409702
3516 -0.3196 0.374623
3551 1.2785 0.899470
3514 -0.4110 0.340551
3532 0.4110 0.659449
3504 -0.8676 0.192812
3519 -0.1826 0.427537
3522 -0.0457 0.481790
3536 0.5936 0.723613
Square side=100, avg. no. parked=3524.00 sample std.=12.58
p-value of the KSTEST for those 10 p-values: 0.541896
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-18_07:31
0.6518,0.5617,0.2071,0.3654,0.4381,0.4657,0.1686,0.9487,0.3163,0.9445,
The KS test for those 10 p-values: 0.770022
The 3DSPHERES test for dh-ranFile-2018-06-18_07:31
sample no r^3 equiv. uni.
1 3.830 0.119842
2 1.923 0.062103
3 8.441 0.245254
4 70.365 0.904200
5 17.382 0.439767
6 55.822 0.844442
7 60.559 0.867163
8 4.043 0.126086
9 26.260 0.583278
10 55.631 0.843450
11 1.372 0.044710
12 46.308 0.786390
13 185.850 0.997960
14 24.016 0.550913
15 3.792 0.118727
16 52.987 0.829021
17 12.617 0.343321
18 3.172 0.100340
19 20.437 0.494004
20 10.280 0.290128
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.557227
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-18_07:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 1.8 -1.1 0.6 -0.3 -1.9
0.8 0.0 1.3 -2.1 -0.9 -1.4
-1.0 1.2 0.9 -0.7 -1.0 0.8
-0.1 0.1 1.9 -0.9 0.9 0.2
0.5 -0.9 0.2 1.4 1.4 -0.1
-0.7 -0.2 -0.7 -1.6 -1.2 0.2
-0.9 -0.7 0.5 -0.7 0.9 -1.0
-1.1
Chi-square with 42 degrees of freedom:44.215275
z-score=0.241706, p-value=0.621754
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-18_07:31
Test no p-value
1 0.001921
2 0.012964
3 0.324539
4 0.367647
5 0.259282
6 0.006872
7 0.523783
8 0.097471
9 0.031245
10 0.053924
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000034
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-18_07:31:
(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 66435 0.81 66810 0.31
3 25000.00 24977 0.02 24869 0.69
4 6666.67 6878 6.70 6598 0.71
5 1388.89 1439 1.81 1419 0.65
6 238.10 232 0.16 259 1.84
7 34.72 36 0.05 40 0.80
8 4.96 2 1.77 4 0.19
p=0.92055 p=0.47892
Number of rngs required: 688733, p-value: 0.648
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-18_07:31
No. of wins: Observed Expected
98341 98585.9
z-score=-1.095, pvalue=0.13673
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66803 66666.7 0.279 0.279
2 37786 37654.3 0.460 0.739
3 27003 26954.7 0.086 0.826
4 19193 19313.5 0.751 1.577
5 13827 13851.4 0.043 1.620
6 9902 9943.5 0.174 1.794
7 7104 7145.0 0.236 2.029
8 5221 5139.1 1.306 3.335
9 3660 3699.9 0.430 3.765
10 2703 2666.3 0.505 4.270
11 1844 1923.3 3.272 7.542
12 1357 1388.7 0.725 8.268
13 968 1003.7 1.271 9.538
14 734 726.1 0.085 9.623
15 491 525.8 2.308 11.931
16 366 381.2 0.602 12.534
17 279 276.5 0.022 12.555
18 209 200.8 0.332 12.888
19 141 146.0 0.170 13.058
20 106 106.2 0.000 13.058
21 303 287.1 0.879 13.937
Chisq= 13.94 for 20 degrees of freedom, p= 0.16634
SUMMARY of craptest
p-value for no. of wins: 0.136725
p-value for throws/game: 0.166342
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-18_07:31
No. of wins: Observed Expected
98638 98585.9
z-score= 0.233, pvalue=0.59220
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66664 66666.7 0.000 0.000
2 37835 37654.3 0.867 0.867
3 26658 26954.7 3.267 4.134
4 19286 19313.5 0.039 4.173
5 13620 13851.4 3.866 8.039
6 10054 9943.5 1.227 9.266
7 7187 7145.0 0.247 9.513
8 5346 5139.1 8.332 17.845
9 3751 3699.9 0.707 18.552
10 2700 2666.3 0.426 18.978
11 1879 1923.3 1.022 19.999
12 1419 1388.7 0.659 20.659
13 1002 1003.7 0.003 20.661
14 746 726.1 0.543 21.205
15 498 525.8 1.474 22.678
16 357 381.2 1.530 24.208
17 262 276.5 0.764 24.973
18 196 200.8 0.116 25.089
19 146 146.0 0.000 25.089
20 104 106.2 0.046 25.135
21 290 287.1 0.029 25.164
Chisq= 25.16 for 20 degrees of freedom, p= 0.80478
SUMMARY of craptest
p-value for no. of wins: 0.592200
p-value for throws/game: 0.804779
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0000,0.0019,0.0025,0.0066,0.0069,0.0130,0.0312,0.0317,0.0398,0.0418,
0.0447,0.0500,0.0513,0.0517,0.0539,0.0558,0.0592,0.0621,0.0634,0.0677,
0.0763,0.0764,0.0837,0.0940,0.0952,0.0975,0.0987,0.1003,0.1068,0.1079,
0.1175,0.1187,0.1198,0.1216,0.1230,0.1252,0.1252,0.1260,0.1261,0.1299,
0.1313,0.1324,0.1342,0.1367,0.1402,0.1402,0.1415,0.1483,0.1565,0.1594,
0.1663,0.1679,0.1683,0.1686,0.1703,0.1724,0.1805,0.1879,0.1928,0.1939,
0.1983,0.1998,0.2019,0.2071,0.2131,0.2205,0.2274,0.2322,0.2322,0.2328,
0.2357,0.2453,0.2479,0.2562,0.2572,0.2593,0.2603,0.2660,0.2901,0.2934,
0.2964,0.2981,0.3009,0.3012,0.3034,0.3162,0.3163,0.3244,0.3245,0.3251,
0.3280,0.3291,0.3378,0.3386,0.3391,0.3406,0.3433,0.3486,0.3591,0.3595,
0.3654,0.3676,0.3746,0.3836,0.3839,0.3851,0.3896,0.3956,0.4028,0.4097,
0.4097,0.4207,0.4270,0.4275,0.4296,0.4329,0.4381,0.4398,0.4473,0.4523,
0.4529,0.4577,0.4614,0.4624,0.4632,0.4657,0.4731,0.4758,0.4789,0.4806,
0.4818,0.4865,0.4938,0.4940,0.5009,0.5078,0.5136,0.5137,0.5166,0.5238,
0.5262,0.5267,0.5287,0.5339,0.5367,0.5419,0.5421,0.5509,0.5572,0.5617,
0.5701,0.5711,0.5722,0.5731,0.5798,0.5826,0.5833,0.5844,0.5903,0.5922,
0.5949,0.5954,0.6105,0.6126,0.6135,0.6207,0.6218,0.6220,0.6290,0.6304,
0.6324,0.6392,0.6413,0.6437,0.6480,0.6500,0.6518,0.6522,0.6525,0.6566,
0.6594,0.6627,0.6873,0.6887,0.7042,0.7058,0.7066,0.7091,0.7130,0.7233,
0.7236,0.7290,0.7364,0.7387,0.7434,0.7463,0.7500,0.7525,0.7648,0.7700,
0.7717,0.7829,0.7864,0.7959,0.7967,0.8032,0.8048,0.8106,0.8211,0.8221,
0.8242,0.8280,0.8290,0.8351,0.8374,0.8382,0.8425,0.8434,0.8444,0.8484,
0.8512,0.8523,0.8527,0.8581,0.8663,0.8672,0.8738,0.8818,0.8825,0.8836,
0.8856,0.8863,0.8871,0.8873,0.8902,0.8963,0.8995,0.9000,0.9031,0.9042,
0.9046,0.9134,0.9142,0.9155,0.9165,0.9175,0.9202,0.9205,0.9278,0.9302,
0.9325,0.9445,0.9487,0.9503,0.9510,0.9534,0.9544,0.9567,0.9672,0.9763,
0.9833,0.9836,0.9863,0.9877,0.9890,0.9890,0.9931,0.9963,0.9980,
Overall p-value after applying KStest on 269 p-values = 0.615717
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.