RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-26_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 15.60 30.1866 0.974969
2 to 25 15.89 10.6731 0.126955
3 to 26 16.05 23.4219 0.863989
4 to 27 15.95 26.7399 0.938006
5 to 28 15.86 16.2109 0.491062
6 to 29 15.61 21.6144 0.799995
7 to 30 15.60 13.0230 0.265357
8 to 31 15.60 20.5289 0.751925
9 to 32 15.83 17.2114 0.559866
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.238450
Tough bday spacings test for dh-ranFile-2018-06-26_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 6 33 69 103 97 90 44 33 17 6 2
(O-E)^2/E 1.1 0.4 0.2 0.3 0.0 1.8 1.3 0.4 0.3 0.1 1.0
Birthday Spacings: Sum(O-E)^2/E= 6.806, p= 0.256
RESULTS OF GCD FOR dh-ranFile-2018-06-26_22:31
Euclid's algorithm:
p-value, steps to gcd: 0.570921
p-value, dist. of gcd's: 0.934918
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-26_22:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.516 0.950 0.299 0.165 0.560 0.320 0.290 0.862
Bits 8 to 15---> 0.441 0.701 0.894 0.393 0.750 0.388 0.898 0.607
Bits 16 to 23---> 0.155 0.872 0.522 0.166 0.338 0.013 0.347 0.687
Bits 24 to 31---> 0.897 0.311 0.682 0.331 0.221 0.971 0.609 0.161
KS test for the above 32 p values: 0.205
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-26_22:31,
p-values for 5 runs: 0.4904, 0.3740, 0.5278, 0.5070, 0.1255
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-26_22:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 236 211.4 2.858 2.858
r= 29 5264 5134.0 3.291 6.149
r= 30 22829 23103.0 3.251 9.400
r= 31 11671 11551.5 1.236 10.636
chi-square = 10.636 with df = 3; p-value = 0.986
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-26_22:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 189 211.4 2.377 2.377
r= 30 5144 5134.0 0.019 2.397
r= 31 23028 23103.0 0.244 2.640
r= 32 11639 11551.5 0.662 3.303
chi-square = 3.303 with df = 3; p-value = 0.653
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-26_22:31
b-rank test for bits 1 to 8, p=0.89094
b-rank test for bits 2 to 9, p=0.94573
b-rank test for bits 3 to 10, p=0.90942
b-rank test for bits 4 to 11, p=0.77869
b-rank test for bits 5 to 12, p=0.56354
b-rank test for bits 6 to 13, p=0.72328
b-rank test for bits 7 to 14, p=0.00297
b-rank test for bits 8 to 15, p=0.83101
b-rank test for bits 9 to 16, p=0.48794
b-rank test for bits 10 to 17, p=0.48639
b-rank test for bits 11 to 18, p=0.22103
b-rank test for bits 12 to 19, p=0.46260
b-rank test for bits 13 to 20, p=0.15387
b-rank test for bits 14 to 21, p=0.58324
b-rank test for bits 15 to 22, p=0.37148
b-rank test for bits 16 to 23, p=0.75363
b-rank test for bits 17 to 24, p=0.93791
b-rank test for bits 18 to 25, p=0.86110
b-rank test for bits 19 to 26, p=0.07963
b-rank test for bits 20 to 27, p=0.52365
b-rank test for bits 21 to 28, p=0.65716
b-rank test for bits 22 to 29, p=0.28363
b-rank test for bits 23 to 30, p=0.44465
b-rank test for bits 24 to 31, p=0.06780
b-rank test for bits 25 to 32, p=0.75796
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 = 0.606830
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-26_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 142205 0.69 0.755160
2 141198 -1.66 0.048258
3 141926 0.04 0.515534
4 142502 1.38 0.916934
5 141544 -0.85 0.196670
6 142345 1.02 0.845642
7 142426 1.21 0.886317
8 142519 1.42 0.922844
9 141983 0.17 0.568331
10 141517 -0.92 0.179661
11 141790 -0.28 0.390196
12 141382 -1.23 0.108960
13 141538 -0.87 0.192808
14 141598 -0.73 0.233489
15 142478 1.33 0.908021
16 141964 0.13 0.550820
17 142024 0.27 0.605620
18 141853 -0.13 0.447646
19 141328 -1.36 0.087193
20 141713 -0.46 0.323219
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-26_22:31
Bits used No. missing words z-score p-value
23 to 32 142302 1.3540 0.912137
22 to 31 142407 1.7161 0.956928
21 to 30 141990 0.2782 0.609560
20 to 29 141948 0.1333 0.553040
19 to 28 142023 0.3920 0.652458
18 to 27 142119 0.7230 0.765160
17 to 26 141767 -0.4908 0.311786
16 to 25 141279 -2.1736 0.014869
15 to 24 141767 -0.4908 0.311786
14 to 23 141538 -1.2804 0.100194
13 to 22 141513 -1.3667 0.085867
12 to 21 141328 -2.0046 0.022504
11 to 20 142058 0.5127 0.695904
10 to 19 141627 -0.9736 0.165140
9 to 18 141798 -0.3839 0.350528
8 to 17 141729 -0.6218 0.267028
7 to 16 142043 0.4609 0.677576
6 to 15 142065 0.5368 0.704295
5 to 14 142445 1.8471 0.967636
4 to 13 141666 -0.8391 0.200715
3 to 12 141930 0.0713 0.528411
2 to 11 141563 -1.1942 0.116192
1 to 10 141880 -0.1011 0.459721
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-26_22:31
Bits used No. missing words z-score p-value
28 to 32 141942 0.1107 0.544091
27 to 31 141692 -0.7367 0.230649
26 to 30 141407 -1.7028 0.044301
25 to 29 141834 -0.2554 0.399224
24 to 28 141691 -0.7401 0.229619
23 to 27 141543 -1.2418 0.107156
22 to 26 142063 0.5209 0.698787
21 to 25 141880 -0.0994 0.460401
20 to 24 142132 0.7548 0.774820
19 to 23 141716 -0.6554 0.256119
18 to 22 141879 -0.1028 0.459056
17 to 21 142112 0.6870 0.753964
16 to 20 141872 -0.1265 0.449651
15 to 19 142005 0.3243 0.627147
14 to 18 142071 0.5480 0.708166
13 to 17 142206 1.0057 0.842711
12 to 16 142220 1.0531 0.853857
11 to 15 141905 -0.0147 0.494145
10 to 14 141919 0.0328 0.513075
9 to 13 142380 1.5955 0.944699
8 to 12 141689 -0.7469 0.227568
7 to 11 142256 1.1752 0.880033
6 to 10 141744 -0.5604 0.287589
5 to 9 142223 1.0633 0.856174
4 to 8 141928 0.0633 0.525232
3 to 7 142116 0.7006 0.758216
2 to 6 141894 -0.0520 0.479278
1 to 5 141548 -1.2248 0.110316
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-26_22:31
Bits used No. missing words z-score p-value
31 to 32 142495 1.7276 0.957974
30 to 31 141987 0.2291 0.590610
29 to 30 141934 0.0728 0.529007
28 to 29 141782 -0.3756 0.353605
27 to 28 141612 -0.8771 0.190222
26 to 27 142168 0.7630 0.777280
25 to 26 141319 -1.7414 0.040808
24 to 25 142105 0.5772 0.718097
23 to 24 142179 0.7955 0.786835
22 to 23 141431 -1.4110 0.079122
21 to 22 141707 -0.5968 0.275306
20 to 21 141627 -0.8328 0.202470
19 to 20 141857 -0.1544 0.438661
18 to 19 141545 -1.0747 0.141250
17 to 18 142644 2.1672 0.984889
16 to 17 142404 1.4592 0.927745
15 to 16 142727 2.4120 0.992067
14 to 15 141752 -0.4641 0.321288
13 to 14 142285 1.1082 0.866106
12 to 13 141405 -1.4877 0.068415
11 to 12 142043 0.3943 0.653323
10 to 11 141532 -1.1131 0.132840
9 to 10 141768 -0.4169 0.338375
8 to 9 141823 -0.2547 0.399493
7 to 8 141301 -1.7945 0.036368
6 to 7 141982 0.2144 0.584869
5 to 6 141854 -0.1632 0.435174
4 to 5 141791 -0.3491 0.363524
3 to 4 142416 1.4946 0.932491
2 to 3 141543 -1.0806 0.139933
1 to 2 141951 0.1229 0.548915
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-26_22:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2532.46 0.459 0.676923
Test results for specific bytes for dh-ranFile-2018-06-26_22:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2555.99 0.792 0.785764
2 to 9 2650.74 2.132 0.983488
3 to 10 2458.15 -0.592 0.276984
4 to 11 2482.40 -0.249 0.401693
5 to 12 2519.04 0.269 0.606158
6 to 13 2457.10 -0.607 0.272026
7 to 14 2543.33 0.613 0.730004
8 to 15 2457.73 -0.598 0.275011
9 to 16 2720.90 3.124 0.999108
10 to 17 2577.72 1.099 0.864135
11 to 18 2632.03 1.867 0.969065
12 to 19 2432.38 -0.956 0.169461
13 to 20 2584.14 1.190 0.882971
14 to 21 2401.71 -1.390 0.082261
15 to 22 2485.68 -0.202 0.419775
16 to 23 2509.12 0.129 0.551299
17 to 24 2605.13 1.487 0.931465
18 to 25 2535.36 0.500 0.691486
19 to 26 2509.68 0.137 0.554429
20 to 27 2511.89 0.168 0.566769
21 to 28 2422.63 -1.094 0.136935
22 to 29 2420.97 -1.118 0.131846
23 to 30 2473.07 -0.381 0.351650
24 to 31 2507.96 0.113 0.544831
25 to 32 2452.15 -0.677 0.249283
CDPARK for dh-ranFile-2018-06-26_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
3489 -1.5525 0.060270
3539 0.7306 0.767486
3511 -0.5479 0.291865
3510 -0.5936 0.276387
3525 0.0913 0.536383
3532 0.4110 0.659449
3533 0.4566 0.676028
3528 0.2283 0.590298
3519 -0.1826 0.427537
3512 -0.5023 0.307734
Square side=100, avg. no. parked=3519.80 sample std.=14.03
p-value of the KSTEST for those 10 p-values: 0.600174
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-26_22:31
0.4423,0.8863,0.4577,0.0606,0.2383,0.0107,0.0813,0.6511,0.8123,0.9107,
The KS test for those 10 p-values: 0.585484
The 3DSPHERES test for dh-ranFile-2018-06-26_22:31
sample no r^3 equiv. uni.
1 5.031 0.154385
2 14.263 0.378393
3 12.622 0.343424
4 48.258 0.799830
5 4.879 0.150105
6 52.356 0.825392
7 39.067 0.728077
8 40.396 0.739858
9 44.770 0.775154
10 6.829 0.203589
11 33.722 0.675039
12 4.380 0.135855
13 21.485 0.511381
14 11.459 0.317477
15 0.386 0.012784
16 82.281 0.935603
17 4.440 0.137567
18 8.047 0.235283
19 38.534 0.723202
20 69.742 0.902192
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.798167
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-26_22:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 0.5 0.1 -0.7 1.1 -0.8
-0.4 0.5 -0.2 0.9 1.4 -0.4
-0.8 0.5 -1.2 -0.4 0.4 0.3
0.6 1.8 -0.2 -0.9 -1.1 -0.4
-0.1 0.7 0.1 -0.7 0.1 -0.6
0.2 0.1 0.4 -0.9 1.0 -0.8
-0.9 1.1 -1.2 -1.3 -0.6 -1.0
-0.1
Chi-square with 42 degrees of freedom:25.662490
z-score=-1.782568, p-value=0.022165
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-26_22:31
Test no p-value
1 0.306648
2 0.392657
3 0.041166
4 0.082877
5 0.757196
6 0.509596
7 0.783537
8 0.377969
9 0.494593
10 0.054477
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.269387
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-26_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 66748 0.10 66522 0.31
3 25000.00 24902 0.38 24998 0.00
4 6666.67 6674 0.01 6778 1.86
5 1388.89 1397 0.05 1429 1.16
6 238.10 244 0.15 234 0.07
7 34.72 29 0.94 36 0.05
8 4.96 5 0.00 2 1.77
p=0.04945 p=0.48354
Number of rngs required: 688189, p-value: 0.403
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-26_22:31
No. of wins: Observed Expected
98722 98585.9
z-score= 0.609, pvalue=0.72871
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66422 66666.7 0.898 0.898
2 37659 37654.3 0.001 0.899
3 27405 26954.7 7.522 8.420
4 19298 19313.5 0.012 8.432
5 13814 13851.4 0.101 8.534
6 9811 9943.5 1.767 10.300
7 7122 7145.0 0.074 10.374
8 5149 5139.1 0.019 10.394
9 3645 3699.9 0.814 11.207
10 2624 2666.3 0.671 11.878
11 1968 1923.3 1.038 12.916
12 1376 1388.7 0.117 13.033
13 1015 1003.7 0.127 13.159
14 729 726.1 0.011 13.171
15 511 525.8 0.419 13.589
16 391 381.2 0.255 13.844
17 300 276.5 1.990 15.834
18 224 200.8 2.673 18.507
19 164 146.0 2.223 20.731
20 101 106.2 0.256 20.987
21 272 287.1 0.796 21.782
Chisq= 21.78 for 20 degrees of freedom, p= 0.64756
SUMMARY of craptest
p-value for no. of wins: 0.728706
p-value for throws/game: 0.647559
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-26_22:31
No. of wins: Observed Expected
98412 98585.9
z-score=-0.778, pvalue=0.21840
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66617 66666.7 0.037 0.037
2 37539 37654.3 0.353 0.390
3 26949 26954.7 0.001 0.391
4 19144 19313.5 1.487 1.878
5 13964 13851.4 0.915 2.793
6 10027 9943.5 0.700 3.494
7 7277 7145.0 2.438 5.931
8 5146 5139.1 0.009 5.941
9 3760 3699.9 0.977 6.918
10 2601 2666.3 1.599 8.517
11 1963 1923.3 0.818 9.336
12 1426 1388.7 1.000 10.335
13 974 1003.7 0.880 11.215
14 719 726.1 0.070 11.285
15 507 525.8 0.675 11.960
16 400 381.2 0.932 12.892
17 258 276.5 1.243 14.135
18 188 200.8 0.820 14.955
19 131 146.0 1.538 16.493
20 122 106.2 2.346 18.838
21 288 287.1 0.003 18.841
Chisq= 18.84 for 20 degrees of freedom, p= 0.46783
SUMMARY of craptest
p-value for no. of wins: 0.218403
p-value for throws/game: 0.467831
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0030,0.0107,0.0128,0.0133,0.0149,0.0222,0.0225,0.0364,0.0408,0.0412,
0.0443,0.0483,0.0494,0.0545,0.0603,0.0606,0.0678,0.0684,0.0791,0.0796,
0.0813,0.0823,0.0829,0.0859,0.0872,0.1002,0.1072,0.1090,0.1103,0.1162,
0.1255,0.1270,0.1318,0.1328,0.1359,0.1369,0.1376,0.1399,0.1413,0.1501,
0.1539,0.1544,0.1549,0.1607,0.1650,0.1651,0.1663,0.1695,0.1797,0.1902,
0.1928,0.1967,0.2007,0.2025,0.2036,0.2052,0.2184,0.2205,0.2210,0.2276,
0.2296,0.2306,0.2335,0.2353,0.2383,0.2384,0.2493,0.2561,0.2563,0.2654,
0.2670,0.2694,0.2720,0.2750,0.2753,0.2764,0.2770,0.2836,0.2876,0.2896,
0.2919,0.2992,0.3066,0.3077,0.3107,0.3118,0.3118,0.3175,0.3200,0.3213,
0.3232,0.3307,0.3375,0.3384,0.3434,0.3474,0.3505,0.3516,0.3536,0.3635,
0.3715,0.3740,0.3780,0.3784,0.3881,0.3902,0.3927,0.3930,0.3992,0.3995,
0.4017,0.4027,0.4198,0.4275,0.4352,0.4387,0.4408,0.4423,0.4447,0.4476,
0.4497,0.4577,0.4591,0.4597,0.4604,0.4626,0.4678,0.4793,0.4835,0.4864,
0.4879,0.4904,0.4911,0.4941,0.4946,0.5070,0.5096,0.5114,0.5131,0.5155,
0.5164,0.5218,0.5236,0.5252,0.5278,0.5284,0.5290,0.5364,0.5441,0.5448,
0.5489,0.5508,0.5513,0.5530,0.5544,0.5599,0.5600,0.5635,0.5668,0.5683,
0.5709,0.5832,0.5849,0.5855,0.5903,0.5906,0.6002,0.6056,0.6062,0.6068,
0.6069,0.6087,0.6096,0.6271,0.6476,0.6511,0.6525,0.6527,0.6533,0.6572,
0.6594,0.6750,0.6760,0.6769,0.6776,0.6824,0.6874,0.6915,0.6959,0.6988,
0.7005,0.7043,0.7082,0.7181,0.7232,0.7233,0.7281,0.7287,0.7300,0.7399,
0.7503,0.7519,0.7536,0.7540,0.7552,0.7572,0.7580,0.7582,0.7652,0.7675,
0.7748,0.7752,0.7773,0.7787,0.7835,0.7858,0.7868,0.7982,0.7998,0.8000,
0.8123,0.8254,0.8310,0.8427,0.8456,0.8539,0.8562,0.8611,0.8615,0.8640,
0.8641,0.8661,0.8717,0.8800,0.8830,0.8863,0.8863,0.8909,0.8943,0.8969,
0.8980,0.9022,0.9080,0.9094,0.9107,0.9121,0.9169,0.9228,0.9277,0.9315,
0.9325,0.9349,0.9356,0.9379,0.9380,0.9447,0.9457,0.9501,0.9569,0.9580,
0.9676,0.9691,0.9715,0.9750,0.9835,0.9849,0.9861,0.9921,0.9991,
Overall p-value after applying KStest on 269 p-values = 0.999042
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.