RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-27_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 15.66 11.1615 0.151954
2 to 25 15.81 11.4130 0.165694
3 to 26 15.94 11.4652 0.168613
4 to 27 15.71 19.3954 0.693687
5 to 28 16.08 18.0317 0.613157
6 to 29 15.97 13.2001 0.277312
7 to 30 15.60 16.8917 0.538272
8 to 31 15.65 19.3418 0.690733
9 to 32 15.81 13.9929 0.332396
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.357228
Tough bday spacings test for dh-ranFile-2018-06-27_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 10 33 79 86 106 71 58 35 9 10 3
(O-E)^2/E 0.1 0.4 0.4 1.4 0.7 0.7 0.7 0.9 2.3 1.7 0.3
Birthday Spacings: Sum(O-E)^2/E= 9.571, p= 0.521
RESULTS OF GCD FOR dh-ranFile-2018-06-27_18:31
Euclid's algorithm:
p-value, steps to gcd: 0.594829
p-value, dist. of gcd's: 0.178108
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-27_18:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.460 0.283 0.753 0.267 0.207 0.766 0.981 0.641
Bits 8 to 15---> 0.832 0.721 0.155 0.944 0.449 0.893 0.368 0.068
Bits 16 to 23---> 0.343 0.415 0.570 0.527 0.537 0.950 0.136 0.315
Bits 24 to 31---> 0.582 0.449 0.848 0.133 0.234 0.381 0.782 0.826
KS test for the above 32 p values: 0.154
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-27_18:31,
p-values for 5 runs: 0.6313, 0.1105, 0.6513, 0.2867, 0.1957
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-27_18:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 210 211.4 0.010 0.010
r= 29 5201 5134.0 0.874 0.884
r= 30 23074 23103.0 0.037 0.920
r= 31 11515 11551.5 0.115 1.036
chi-square = 1.036 with df = 3; p-value = 0.207
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-27_18:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 214 211.4 0.032 0.032
r= 30 5229 5134.0 1.757 1.789
r= 31 23027 23103.0 0.250 2.039
r= 32 11530 11551.5 0.040 2.079
chi-square = 2.079 with df = 3; p-value = 0.444
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-27_18:31
b-rank test for bits 1 to 8, p=0.79272
b-rank test for bits 2 to 9, p=0.59294
b-rank test for bits 3 to 10, p=0.26555
b-rank test for bits 4 to 11, p=0.24624
b-rank test for bits 5 to 12, p=0.75745
b-rank test for bits 6 to 13, p=0.60975
b-rank test for bits 7 to 14, p=0.36527
b-rank test for bits 8 to 15, p=0.71785
b-rank test for bits 9 to 16, p=0.88570
b-rank test for bits 10 to 17, p=0.73499
b-rank test for bits 11 to 18, p=0.42397
b-rank test for bits 12 to 19, p=0.74384
b-rank test for bits 13 to 20, p=0.33202
b-rank test for bits 14 to 21, p=0.18230
b-rank test for bits 15 to 22, p=0.20855
b-rank test for bits 16 to 23, p=0.46538
b-rank test for bits 17 to 24, p=0.95236
b-rank test for bits 18 to 25, p=0.98560
b-rank test for bits 19 to 26, p=0.38104
b-rank test for bits 20 to 27, p=0.25425
b-rank test for bits 21 to 28, p=0.77829
b-rank test for bits 22 to 29, p=0.93371
b-rank test for bits 23 to 30, p=0.24941
b-rank test for bits 24 to 31, p=0.19802
b-rank test for bits 25 to 32, p=0.17441
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 = 0.557602
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-27_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 142060 0.35 0.637593
2 141625 -0.66 0.253242
3 141380 -1.24 0.108090
4 141943 0.08 0.531352
5 141274 -1.48 0.068849
6 141681 -0.53 0.296850
7 142077 0.39 0.652379
8 142165 0.60 0.724866
9 142564 1.53 0.936942
10 141551 -0.84 0.201235
11 142295 0.90 0.816232
12 142021 0.26 0.602920
13 141556 -0.83 0.204533
14 141842 -0.16 0.437499
15 142907 2.33 0.990123
16 142494 1.37 0.914039
17 142187 0.65 0.741754
18 141580 -0.77 0.220809
19 141498 -0.96 0.168263
20 141678 -0.54 0.294429
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-27_18:31
Bits used No. missing words z-score p-value
23 to 32 141700 -0.7218 0.235200
22 to 31 142017 0.3713 0.644784
21 to 30 141892 -0.0598 0.476174
20 to 29 141667 -0.8356 0.201684
19 to 28 142200 1.0023 0.841903
18 to 27 142348 1.5127 0.934816
17 to 26 142184 0.9471 0.828216
16 to 25 142097 0.6471 0.741229
15 to 24 142160 0.8644 0.806310
14 to 23 142202 1.0092 0.843562
13 to 22 142202 1.0092 0.843562
12 to 21 141747 -0.5598 0.287822
11 to 20 141595 -1.0839 0.139205
10 to 19 141530 -1.3080 0.095431
9 to 18 142289 1.3092 0.904768
8 to 17 142251 1.1782 0.880636
7 to 16 141792 -0.4046 0.342891
6 to 15 141901 -0.0287 0.488542
5 to 14 141704 -0.7080 0.239462
4 to 13 142069 0.5506 0.709041
3 to 12 141875 -0.1184 0.452884
2 to 11 141681 -0.7873 0.215540
1 to 10 141581 -1.1322 0.128781
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-27_18:31
Bits used No. missing words z-score p-value
28 to 32 141838 -0.2418 0.404469
27 to 31 142229 1.0836 0.860735
26 to 30 142102 0.6531 0.743160
25 to 29 141544 -1.2384 0.107783
24 to 28 142126 0.7345 0.768670
23 to 27 141963 0.1819 0.572182
22 to 26 142088 0.6057 0.727630
21 to 25 141907 -0.0079 0.496849
20 to 24 142048 0.4701 0.680847
19 to 23 142391 1.6328 0.948742
18 to 22 142379 1.5921 0.944319
17 to 21 141847 -0.2113 0.416331
16 to 20 141719 -0.6452 0.259403
15 to 19 141907 -0.0079 0.496849
14 to 18 142221 1.0565 0.854632
13 to 17 141382 -1.7876 0.036924
12 to 16 141370 -1.8282 0.033757
11 to 15 141951 0.1413 0.556166
10 to 14 141826 -0.2825 0.388790
9 to 13 141627 -0.9571 0.169271
8 to 12 142252 1.1616 0.877300
7 to 11 142252 1.1616 0.877300
6 to 10 142162 0.8565 0.804142
5 to 9 141636 -0.9265 0.177082
4 to 8 142334 1.4396 0.925004
3 to 7 142116 0.7006 0.758216
2 to 6 142192 0.9582 0.831020
1 to 5 141977 0.2294 0.590717
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-27_18:31
Bits used No. missing words z-score p-value
31 to 32 141930 0.0610 0.524310
30 to 31 142190 0.8279 0.796146
29 to 30 141535 -1.1042 0.134749
28 to 29 141195 -2.1072 0.017552
27 to 28 142032 0.3619 0.641271
26 to 27 142258 1.0285 0.848149
25 to 26 141555 -1.0452 0.147960
24 to 25 142137 0.6716 0.749079
23 to 24 141831 -0.2311 0.408633
22 to 23 141880 -0.0865 0.465527
21 to 22 142106 0.5801 0.719092
20 to 21 141343 -1.6706 0.047401
19 to 20 141452 -1.3491 0.088660
18 to 19 141753 -0.4612 0.322345
17 to 18 142020 0.3265 0.627962
16 to 17 141509 -1.1809 0.118818
15 to 16 142121 0.6244 0.733816
14 to 15 142193 0.8368 0.798643
13 to 14 141779 -0.3845 0.350321
12 to 13 142452 1.6008 0.945289
11 to 12 141527 -1.1278 0.129699
10 to 11 141866 -0.1278 0.449147
9 to 10 141355 -1.6352 0.051004
8 to 9 141820 -0.2635 0.396079
7 to 8 141952 0.1259 0.550083
6 to 7 141865 -0.1308 0.447980
5 to 6 141915 0.0167 0.506672
4 to 5 142294 1.1347 0.871754
3 to 4 141597 -0.9213 0.178440
2 to 3 141793 -0.3432 0.365740
1 to 2 142061 0.4474 0.672708
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-27_18:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2487.79 -0.173 0.431452
Test results for specific bytes for dh-ranFile-2018-06-27_18:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2465.86 -0.483 0.314609
2 to 9 2674.80 2.472 0.993282
3 to 10 2509.08 0.128 0.551113
4 to 11 2602.92 1.456 0.927240
5 to 12 2536.07 0.510 0.695005
6 to 13 2486.61 -0.189 0.424892
7 to 14 2476.48 -0.333 0.369728
8 to 15 2457.14 -0.606 0.272230
9 to 16 2508.76 0.124 0.549273
10 to 17 2453.85 -0.653 0.257002
11 to 18 2421.90 -1.105 0.134686
12 to 19 2486.07 -0.197 0.421926
13 to 20 2649.92 2.120 0.983003
14 to 21 2593.71 1.325 0.907449
15 to 22 2564.38 0.910 0.818719
16 to 23 2468.74 -0.442 0.329227
17 to 24 2483.75 -0.230 0.409105
18 to 25 2698.56 2.808 0.997508
19 to 26 2473.39 -0.376 0.353357
20 to 27 2421.15 -1.115 0.132392
21 to 28 2539.73 0.562 0.712875
22 to 29 2582.38 1.165 0.877989
23 to 30 2485.34 -0.207 0.417890
24 to 31 2492.32 -0.109 0.456758
25 to 32 2371.74 -1.814 0.034845
CDPARK for dh-ranFile-2018-06-27_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
3530 0.3196 0.625377
3490 -1.5068 0.065925
3545 1.0046 0.842447
3520 -0.1370 0.445521
3546 1.0502 0.853193
3514 -0.4110 0.340551
3505 -0.8219 0.205562
3523 0.0000 0.500000
3523 0.0000 0.500000
3539 0.7306 0.767486
Square side=100, avg. no. parked=3523.50 sample std.=16.79
p-value of the KSTEST for those 10 p-values: 0.939005
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-27_18:31
0.8954,0.9491,0.6498,0.8726,0.3595,0.8138,0.8241,0.9919,0.9111,0.8039,
The KS test for those 10 p-values: 0.000637
The 3DSPHERES test for dh-ranFile-2018-06-27_18:31
sample no r^3 equiv. uni.
1 13.754 0.367746
2 2.251 0.072292
3 14.982 0.393102
4 18.764 0.464986
5 34.298 0.681226
6 42.703 0.759112
7 15.200 0.397505
8 13.448 0.361271
9 5.950 0.179912
10 108.031 0.972705
11 66.822 0.892191
12 18.786 0.465372
13 9.461 0.270474
14 21.171 0.506245
15 70.362 0.904190
16 57.447 0.852644
17 28.280 0.610418
18 23.441 0.542221
19 70.902 0.905900
20 0.656 0.021619
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.866902
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-27_18:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -0.7 -0.6 0.5 -0.7 -1.5
0.0 -0.0 -0.1 -1.6 0.1 -1.6
-1.1 -0.8 1.8 -0.8 -0.8 0.7
0.9 0.3 2.2 -0.6 0.1 0.4
-0.4 0.1 0.3 0.8 0.3 0.4
-0.7 -0.8 -1.2 -0.1 0.6 1.7
-1.6 -1.3 1.7 -0.7 -0.6 1.0
0.8
Chi-square with 42 degrees of freedom:39.919716
z-score=-0.226978, p-value=0.437341
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-27_18:31
Test no p-value
1 0.771449
2 0.032497
3 0.495014
4 0.005826
5 0.633583
6 0.859281
7 0.926174
8 0.026452
9 0.070150
10 0.331374
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.106878
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-27_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 66690 0.01 66613 0.04
3 25000.00 25060 0.14 25111 0.49
4 6666.67 6603 0.61 6574 1.29
5 1388.89 1384 0.02 1401 0.11
6 238.10 223 0.96 255 1.20
7 34.72 34 0.01 40 0.80
8 4.96 5 0.00 5 0.00
p=0.05878 p=0.31430
Number of rngs required: 687871, p-value: 0.270
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-27_18:31
No. of wins: Observed Expected
98512 98585.9
z-score=-0.330, pvalue=0.37057
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66457 66666.7 0.659 0.659
2 37720 37654.3 0.115 0.774
3 26818 26954.7 0.694 1.468
4 19565 19313.5 3.276 4.744
5 13875 13851.4 0.040 4.784
6 9983 9943.5 0.157 4.940
7 7175 7145.0 0.126 5.066
8 5074 5139.1 0.824 5.890
9 3709 3699.9 0.023 5.913
10 2675 2666.3 0.028 5.941
11 1839 1923.3 3.697 9.638
12 1355 1388.7 0.820 10.458
13 1048 1003.7 1.954 12.412
14 780 726.1 3.995 16.407
15 500 525.8 1.269 17.676
16 398 381.2 0.745 18.421
17 301 276.5 2.164 20.585
18 207 200.8 0.190 20.774
19 138 146.0 0.437 21.211
20 113 106.2 0.433 21.644
21 270 287.1 1.020 22.665
Chisq= 22.66 for 20 degrees of freedom, p= 0.69443
SUMMARY of craptest
p-value for no. of wins: 0.370572
p-value for throws/game: 0.694433
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-27_18:31
No. of wins: Observed Expected
98540 98585.9
z-score=-0.205, pvalue=0.41874
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66197 66666.7 3.309 3.309
2 37775 37654.3 0.387 3.696
3 27095 26954.7 0.730 4.425
4 19655 19313.5 6.040 10.465
5 13988 13851.4 1.347 11.812
6 9910 9943.5 0.113 11.925
7 7029 7145.0 1.884 13.809
8 5010 5139.1 3.242 17.051
9 3685 3699.9 0.060 17.111
10 2678 2666.3 0.051 17.162
11 1941 1923.3 0.162 17.324
12 1431 1388.7 1.286 18.610
13 967 1003.7 1.343 19.953
14 725 726.1 0.002 19.955
15 517 525.8 0.148 20.104
16 394 381.2 0.433 20.537
17 259 276.5 1.112 21.649
18 205 200.8 0.087 21.736
19 135 146.0 0.827 22.562
20 116 106.2 0.901 23.464
21 288 287.1 0.003 23.466
Chisq= 23.47 for 20 degrees of freedom, p= 0.73353
SUMMARY of craptest
p-value for no. of wins: 0.418745
p-value for throws/game: 0.733527
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0006,0.0058,0.0176,0.0216,0.0265,0.0325,0.0338,0.0348,0.0369,0.0474,
0.0510,0.0588,0.0659,0.0684,0.0688,0.0702,0.0723,0.0887,0.0954,0.1069,
0.1078,0.1081,0.1105,0.1188,0.1288,0.1297,0.1324,0.1328,0.1347,0.1347,
0.1362,0.1392,0.1480,0.1520,0.1541,0.1549,0.1657,0.1683,0.1686,0.1693,
0.1744,0.1771,0.1781,0.1784,0.1799,0.1823,0.1957,0.1980,0.2012,0.2017,
0.2045,0.2056,0.2074,0.2074,0.2086,0.2155,0.2208,0.2340,0.2352,0.2395,
0.2462,0.2494,0.2532,0.2542,0.2570,0.2594,0.2655,0.2674,0.2697,0.2705,
0.2722,0.2773,0.2834,0.2867,0.2878,0.2944,0.2969,0.3143,0.3146,0.3151,
0.3223,0.3292,0.3314,0.3320,0.3324,0.3406,0.3428,0.3429,0.3503,0.3534,
0.3572,0.3595,0.3613,0.3653,0.3657,0.3677,0.3680,0.3697,0.3706,0.3810,
0.3812,0.3888,0.3931,0.3961,0.3975,0.4045,0.4086,0.4091,0.4150,0.4163,
0.4179,0.4187,0.4219,0.4240,0.4249,0.4315,0.4373,0.4375,0.4439,0.4455,
0.4480,0.4488,0.4490,0.4491,0.4529,0.4568,0.4604,0.4650,0.4654,0.4654,
0.4655,0.4762,0.4885,0.4950,0.4968,0.4968,0.5000,0.5000,0.5062,0.5067,
0.5211,0.5243,0.5267,0.5314,0.5373,0.5383,0.5422,0.5493,0.5501,0.5511,
0.5562,0.5576,0.5700,0.5722,0.5820,0.5907,0.5929,0.5948,0.6029,0.6097,
0.6104,0.6132,0.6254,0.6280,0.6313,0.6336,0.6376,0.6413,0.6413,0.6448,
0.6498,0.6513,0.6524,0.6727,0.6808,0.6812,0.6907,0.6937,0.6944,0.6950,
0.7090,0.7129,0.7179,0.7191,0.7212,0.7249,0.7276,0.7335,0.7338,0.7350,
0.7412,0.7418,0.7432,0.7438,0.7491,0.7525,0.7575,0.7582,0.7591,0.7658,
0.7675,0.7687,0.7714,0.7783,0.7823,0.7927,0.7961,0.7986,0.8039,0.8041,
0.8063,0.8138,0.8162,0.8187,0.8241,0.8257,0.8282,0.8310,0.8321,0.8419,
0.8424,0.8436,0.8436,0.8478,0.8481,0.8526,0.8532,0.8546,0.8593,0.8607,
0.8669,0.8718,0.8726,0.8773,0.8773,0.8780,0.8806,0.8857,0.8922,0.8933,
0.8954,0.9042,0.9048,0.9059,0.9074,0.9111,0.9140,0.9250,0.9262,0.9272,
0.9337,0.9348,0.9369,0.9390,0.9438,0.9443,0.9453,0.9487,0.9491,0.9497,
0.9524,0.9727,0.9813,0.9830,0.9856,0.9901,0.9919,0.9933,0.9975,
Overall p-value after applying KStest on 269 p-values = 0.624627
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.