RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-03_12:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.91 9.5835 0.079837
2 to 25 15.70 29.5826 0.970483
3 to 26 15.81 18.4998 0.642012
4 to 27 15.83 23.0840 0.853464
5 to 28 15.86 11.2202 0.155107
6 to 29 15.66 25.6495 0.918913
7 to 30 15.81 16.5824 0.517016
8 to 31 15.74 30.9990 0.980022
9 to 32 16.04 16.5957 0.517937
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.168413
Tough bday spacings test for dh-ranFile-2018-07-03_12:31: 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 9 40 81 85 91 70 56 39 20 7 2
(O-E)^2/E 0.0 0.3 0.8 1.6 0.5 0.8 0.3 2.9 1.8 0.0 1.0
Birthday Spacings: Sum(O-E)^2/E= 10.067, p= 0.565
RESULTS OF GCD FOR dh-ranFile-2018-07-03_12:31
Euclid's algorithm:
p-value, steps to gcd: 0.404449
p-value, dist. of gcd's: 0.498356
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-03_12:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.507 0.982 0.799 0.958 0.153 0.444 0.846 0.052
Bits 8 to 15---> 0.808 0.729 0.725 0.735 0.690 0.186 0.968 0.287
Bits 16 to 23---> 0.654 0.155 0.688 0.350 0.113 0.338 0.110 0.866
Bits 24 to 31---> 0.533 0.956 0.240 0.491 0.982 0.952 0.108 0.032
KS test for the above 32 p values: 0.722
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-03_12:31,
p-values for 5 runs: 0.2651, 0.4545, 0.7941, 0.6454, 0.5769
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-03_12:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 211 211.4 0.001 0.001
r= 29 5254 5134.0 2.804 2.805
r= 30 22995 23103.0 0.505 3.310
r= 31 11540 11551.5 0.011 3.322
chi-square = 3.322 with df = 3; p-value = 0.655
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-03_12:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 197 211.4 0.983 0.983
r= 30 4963 5134.0 5.696 6.680
r= 31 23336 23103.0 2.349 9.028
r= 32 11504 11551.5 0.196 9.224
chi-square = 9.224 with df = 3; p-value = 0.974
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-03_12:31
b-rank test for bits 1 to 8, p=0.49673
b-rank test for bits 2 to 9, p=0.09908
b-rank test for bits 3 to 10, p=0.07939
b-rank test for bits 4 to 11, p=0.57266
b-rank test for bits 5 to 12, p=0.10938
b-rank test for bits 6 to 13, p=0.67690
b-rank test for bits 7 to 14, p=0.43637
b-rank test for bits 8 to 15, p=0.33735
b-rank test for bits 9 to 16, p=0.47348
b-rank test for bits 10 to 17, p=0.96044
b-rank test for bits 11 to 18, p=0.16230
b-rank test for bits 12 to 19, p=0.08370
b-rank test for bits 13 to 20, p=0.29412
b-rank test for bits 14 to 21, p=0.85643
b-rank test for bits 15 to 22, p=0.82003
b-rank test for bits 16 to 23, p=0.70632
b-rank test for bits 17 to 24, p=0.93519
b-rank test for bits 18 to 25, p=0.72098
b-rank test for bits 19 to 26, p=0.67640
b-rank test for bits 20 to 27, p=0.48530
b-rank test for bits 21 to 28, p=0.30780
b-rank test for bits 22 to 29, p=0.60012
b-rank test for bits 23 to 30, p=0.78024
b-rank test for bits 24 to 31, p=0.74448
b-rank test for bits 25 to 32, p=0.02094
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 = 0.973843
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-03_12:31
(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 141355 -1.30 0.097632
2 141605 -0.71 0.238526
3 141626 -0.66 0.253990
4 141811 -0.23 0.409146
5 141983 0.17 0.568331
6 141665 -0.57 0.284046
7 142498 1.38 0.915496
8 141977 0.16 0.562814
9 141709 -0.47 0.319871
10 141717 -0.45 0.326583
11 142069 0.37 0.645448
12 142179 0.63 0.735676
13 142049 0.33 0.627913
14 141411 -1.16 0.122147
15 141008 -2.11 0.017606
16 142212 0.71 0.760271
17 141789 -0.28 0.389300
18 141892 -0.04 0.483851
19 141537 -0.87 0.192169
20 141851 -0.14 0.445798
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-03_12:31
Bits used No. missing words z-score p-value
23 to 32 142057 0.5092 0.694696
22 to 31 142555 2.2264 0.987008
21 to 30 142210 1.0368 0.850084
20 to 29 141999 0.3092 0.621418
19 to 28 142049 0.4816 0.684962
18 to 27 142208 1.0299 0.848471
17 to 26 142187 0.9575 0.830838
16 to 25 142277 1.2678 0.897570
15 to 24 142441 1.8333 0.966624
14 to 23 141287 -2.1460 0.015938
13 to 22 141913 0.0127 0.505049
12 to 21 141660 -0.8598 0.194961
11 to 20 141871 -0.1322 0.447424
10 to 19 141670 -0.8253 0.204608
9 to 18 141647 -0.9046 0.182842
8 to 17 141648 -0.9011 0.183758
7 to 16 142366 1.5747 0.942340
6 to 15 141672 -0.8184 0.206570
5 to 14 142030 0.4161 0.661333
4 to 13 141494 -1.4322 0.076047
3 to 12 141754 -0.5356 0.296110
2 to 11 142142 0.8023 0.788813
1 to 10 142306 1.3678 0.914317
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-03_12:31
Bits used No. missing words z-score p-value
28 to 32 141152 -2.5672 0.005126
27 to 31 142198 0.9785 0.836097
26 to 30 141512 -1.3469 0.089009
25 to 29 142167 0.8735 0.808793
24 to 28 141909 -0.0011 0.499554
23 to 27 142073 0.5548 0.710489
22 to 26 141393 -1.7503 0.040036
21 to 25 141731 -0.6045 0.272753
20 to 24 141826 -0.2825 0.388790
19 to 23 142218 1.0463 0.852298
18 to 22 142184 0.9311 0.824095
17 to 21 141396 -1.7401 0.040921
16 to 20 142139 0.7785 0.781875
15 to 19 141518 -1.3265 0.092330
14 to 18 142355 1.5107 0.934573
13 to 17 142277 1.2463 0.893680
12 to 16 142030 0.4091 0.658749
11 to 15 142353 1.5040 0.933705
10 to 14 141178 -2.4791 0.006586
9 to 13 141976 0.2260 0.589399
8 to 12 142121 0.7175 0.763475
7 to 11 141568 -1.1571 0.123626
6 to 10 141767 -0.4825 0.314734
5 to 9 141507 -1.3638 0.086310
4 to 8 141926 0.0565 0.522532
3 to 7 141796 -0.3842 0.350426
2 to 6 142234 1.1006 0.864459
1 to 5 141820 -0.3028 0.381016
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-03_12:31
Bits used No. missing words z-score p-value
31 to 32 142340 1.2704 0.898031
30 to 31 141388 -1.5378 0.062043
29 to 30 141546 -1.0718 0.141912
28 to 29 141882 -0.0806 0.467872
27 to 28 142208 0.8810 0.810850
26 to 27 141824 -0.2517 0.400632
25 to 26 142035 0.3707 0.644573
24 to 25 141910 0.0020 0.500789
23 to 24 141959 0.1465 0.558244
22 to 23 142043 0.3943 0.653323
21 to 22 142218 0.9105 0.818729
20 to 21 142505 1.7571 0.960553
19 to 20 141979 0.2055 0.581416
18 to 19 142017 0.3176 0.624610
17 to 18 142115 0.6067 0.727974
16 to 17 141865 -0.1308 0.447980
15 to 16 141841 -0.2016 0.420129
14 to 15 141450 -1.3550 0.087716
13 to 14 141570 -1.0010 0.158420
12 to 13 142283 1.1023 0.864828
11 to 12 142102 0.5683 0.715101
10 to 11 142235 0.9607 0.831643
9 to 10 141538 -1.0954 0.136678
8 to 9 142161 0.7424 0.771074
7 to 8 141561 -1.0275 0.152087
6 to 7 141768 -0.4169 0.338375
5 to 6 141851 -0.1721 0.431693
4 to 5 141817 -0.2724 0.392673
3 to 4 142069 0.4710 0.681181
2 to 3 142505 1.7571 0.960553
1 to 2 141910 0.0020 0.500789
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-03_12:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2600.98 1.428 0.923364
Test results for specific bytes for dh-ranFile-2018-07-03_12:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2491.21 -0.124 0.450557
2 to 9 2588.99 1.259 0.895907
3 to 10 2615.25 1.630 0.948442
4 to 11 2632.32 1.871 0.969350
5 to 12 2581.20 1.148 0.874583
6 to 13 2432.92 -0.949 0.171383
7 to 14 2582.29 1.164 0.877729
8 to 15 2484.07 -0.225 0.410885
9 to 16 2531.68 0.448 0.672908
10 to 17 2660.48 2.270 0.988382
11 to 18 2658.77 2.245 0.987627
12 to 19 2556.04 0.793 0.785976
13 to 20 2376.66 -1.744 0.040557
14 to 21 2329.22 -2.415 0.007863
15 to 22 2391.95 -1.528 0.063246
16 to 23 2515.28 0.216 0.585532
17 to 24 2480.59 -0.275 0.391845
18 to 25 2466.97 -0.467 0.320209
19 to 26 2518.92 0.268 0.605509
20 to 27 2652.32 2.154 0.984384
21 to 28 2471.01 -0.410 0.340927
22 to 29 2354.15 -2.063 0.019576
23 to 30 2593.73 1.326 0.907513
24 to 31 2435.99 -0.905 0.182681
25 to 32 2605.43 1.491 0.932028
CDPARK for dh-ranFile-2018-07-03_12:31: 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
3533 0.4566 0.676028
3483 -1.8265 0.033889
3526 0.1370 0.554479
3522 -0.0457 0.481790
3533 0.4566 0.676028
3484 -1.7808 0.037471
3545 1.0046 0.842447
3538 0.6849 0.753306
3525 0.0913 0.536383
3519 -0.1826 0.427537
Square side=100, avg. no. parked=3520.80 sample std.=20.03
p-value of the KSTEST for those 10 p-values: 0.538386
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-03_12:31
0.7954,0.7365,0.1232,0.4929,0.2258,0.5530,0.5518,0.4891,0.5544,0.1637,
The KS test for those 10 p-values: 0.555375
The 3DSPHERES test for dh-ranFile-2018-07-03_12:31
sample no r^3 equiv. uni.
1 11.594 0.320554
2 44.001 0.769312
3 12.437 0.339384
4 16.504 0.423131
5 1.684 0.054572
6 4.852 0.149343
7 41.995 0.753362
8 19.334 0.475056
9 2.275 0.073029
10 22.531 0.528129
11 23.835 0.548198
12 6.662 0.199150
13 17.757 0.446728
14 0.921 0.030228
15 76.803 0.922704
16 13.534 0.363102
17 94.783 0.957551
18 2.363 0.075739
19 1.212 0.039597
20 33.721 0.675033
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.219209
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-03_12:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
2.0 0.9 1.1 -1.1 0.3 0.3
1.6 -1.0 -1.6 -0.9 0.8 -1.4
1.1 -0.6 -0.2 1.2 0.2 -0.3
-1.1 0.3 0.2 -0.0 -0.3 1.7
-0.1 -0.3 -0.3 0.3 -0.4 -0.9
3.3 -0.2 -0.2 -0.8 0.1 1.7
0.0 -0.4 0.5 0.4 0.1 -1.0
-1.1
Chi-square with 42 degrees of freedom:42.540608
z-score=0.058985, p-value=0.552301
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-03_12:31
Test no p-value
1 0.995525
2 0.409456
3 0.001228
4 0.336263
5 0.072580
6 0.433047
7 0.830880
8 0.261057
9 0.061250
10 0.437907
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.139867
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-03_12:31:
(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 66587 0.10 66814 0.33
3 25000.00 25038 0.06 24936 0.16
4 6666.67 6697 0.14 6650 0.04
5 1388.89 1415 0.49 1317 3.72
6 238.10 227 0.52 250 0.60
7 34.72 32 0.21 24 3.31
8 4.96 3 0.77 8 1.86
p=0.10844 p=0.87621
Number of rngs required: 687188, p-value: 0.078
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-03_12:31
No. of wins: Observed Expected
98925 98585.9
z-score= 1.517, pvalue=0.93535
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66314 66666.7 1.866 1.866
2 37728 37654.3 0.144 2.010
3 27103 26954.7 0.816 2.825
4 19414 19313.5 0.523 3.349
5 13892 13851.4 0.119 3.468
6 9879 9943.5 0.419 3.887
7 7170 7145.0 0.087 3.974
8 5084 5139.1 0.590 4.564
9 3668 3699.9 0.274 4.838
10 2739 2666.3 1.982 6.821
11 1963 1923.3 0.818 7.639
12 1360 1388.7 0.595 8.234
13 981 1003.7 0.514 8.748
14 723 726.1 0.014 8.762
15 561 525.8 2.352 11.113
16 355 381.2 1.794 12.907
17 302 276.5 2.344 15.251
18 196 200.8 0.116 15.368
19 155 146.0 0.557 15.924
20 112 106.2 0.315 16.239
21 301 287.1 0.672 16.911
Chisq= 16.91 for 20 degrees of freedom, p= 0.34125
SUMMARY of craptest
p-value for no. of wins: 0.935346
p-value for throws/game: 0.341250
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-03_12:31
No. of wins: Observed Expected
98302 98585.9
z-score=-1.270, pvalue=0.10212
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66156 66666.7 3.912 3.912
2 37841 37654.3 0.925 4.837
3 27089 26954.7 0.669 5.506
4 19273 19313.5 0.085 5.591
5 14047 13851.4 2.762 8.352
6 9753 9943.5 3.651 12.004
7 7121 7145.0 0.081 12.084
8 5245 5139.1 2.183 14.268
9 3650 3699.9 0.672 14.940
10 2801 2666.3 6.805 21.745
11 1946 1923.3 0.267 22.012
12 1427 1388.7 1.054 23.066
13 988 1003.7 0.246 23.312
14 674 726.1 3.744 27.056
15 512 525.8 0.364 27.420
16 408 381.2 1.891 29.312
17 286 276.5 0.324 29.635
18 210 200.8 0.419 30.054
19 151 146.0 0.172 30.227
20 114 106.2 0.571 30.797
21 308 287.1 1.519 32.316
Chisq= 32.32 for 20 degrees of freedom, p= 0.95996
SUMMARY of craptest
p-value for no. of wins: 0.102117
p-value for throws/game: 0.959959
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0012,0.0051,0.0066,0.0079,0.0159,0.0176,0.0196,0.0209,0.0302,0.0323,
0.0339,0.0375,0.0396,0.0400,0.0406,0.0409,0.0523,0.0546,0.0613,0.0620,
0.0632,0.0726,0.0730,0.0757,0.0760,0.0782,0.0794,0.0798,0.0837,0.0863,
0.0877,0.0890,0.0923,0.0976,0.0991,0.1021,0.1076,0.1084,0.1094,0.1096,
0.1127,0.1221,0.1232,0.1236,0.1367,0.1399,0.1419,0.1493,0.1521,0.1530,
0.1551,0.1552,0.1584,0.1623,0.1637,0.1684,0.1714,0.1827,0.1828,0.1838,
0.1860,0.1922,0.1950,0.1992,0.2046,0.2066,0.2192,0.2258,0.2385,0.2403,
0.2540,0.2611,0.2651,0.2728,0.2840,0.2867,0.2941,0.2961,0.3078,0.3147,
0.3199,0.3202,0.3206,0.3266,0.3363,0.3374,0.3377,0.3384,0.3394,0.3409,
0.3412,0.3500,0.3504,0.3631,0.3810,0.3888,0.3893,0.3918,0.3927,0.4006,
0.4044,0.4091,0.4095,0.4109,0.4201,0.4231,0.4275,0.4317,0.4330,0.4364,
0.4379,0.4437,0.4458,0.4467,0.4474,0.4480,0.4506,0.4545,0.4679,0.4735,
0.4751,0.4818,0.4839,0.4853,0.4891,0.4913,0.4929,0.4967,0.4984,0.4996,
0.5008,0.5008,0.5050,0.5067,0.5170,0.5179,0.5225,0.5281,0.5326,0.5364,
0.5384,0.5482,0.5518,0.5523,0.5530,0.5544,0.5545,0.5554,0.5582,0.5628,
0.5653,0.5683,0.5727,0.5769,0.5814,0.5855,0.5894,0.6001,0.6055,0.6214,
0.6246,0.6279,0.6420,0.6446,0.6454,0.6454,0.6533,0.6539,0.6554,0.6587,
0.6613,0.6729,0.6750,0.6760,0.6760,0.6764,0.6769,0.6812,0.6850,0.6880,
0.6897,0.6947,0.7063,0.7105,0.7151,0.7210,0.7222,0.7254,0.7280,0.7286,
0.7353,0.7357,0.7365,0.7445,0.7533,0.7534,0.7603,0.7635,0.7693,0.7711,
0.7802,0.7819,0.7860,0.7888,0.7941,0.7954,0.7995,0.8077,0.8088,0.8108,
0.8187,0.8200,0.8241,0.8308,0.8309,0.8316,0.8361,0.8424,0.8456,0.8485,
0.8501,0.8523,0.8535,0.8564,0.8645,0.8648,0.8662,0.8746,0.8762,0.8777,
0.8937,0.8959,0.8976,0.8980,0.9075,0.9143,0.9155,0.9189,0.9227,0.9234,
0.9320,0.9337,0.9346,0.9352,0.9353,0.9423,0.9484,0.9517,0.9562,0.9576,
0.9579,0.9600,0.9604,0.9606,0.9606,0.9666,0.9677,0.9693,0.9705,0.9735,
0.9738,0.9800,0.9818,0.9818,0.9844,0.9870,0.9876,0.9884,0.9955,
Overall p-value after applying KStest on 269 p-values = 0.233307
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.