RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-24_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 16.15 23.3561 0.861988
2 to 25 15.37 19.8965 0.720444
3 to 26 15.82 12.9866 0.262918
4 to 27 15.70 19.9452 0.722960
5 to 28 15.63 22.9188 0.848086
6 to 29 15.54 19.1338 0.679094
7 to 30 15.41 26.2996 0.930827
8 to 31 15.57 24.6914 0.898167
9 to 32 15.77 15.1585 0.415930
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.046912
Tough bday spacings test for dh-ranFile-2018-06-24_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 36 78 95 99 82 47 29 17 7 4
(O-E)^2/E 1.1 0.0 0.3 0.1 0.0 0.2 0.5 0.0 0.3 0.0 0.0
Birthday Spacings: Sum(O-E)^2/E= 2.530, p= 0.010
RESULTS OF GCD FOR dh-ranFile-2018-06-24_22:31
Euclid's algorithm:
p-value, steps to gcd: 0.444295
p-value, dist. of gcd's: 0.952898
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-24_22:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.348 0.695 0.601 0.117 0.997 0.247 0.847 0.234
Bits 8 to 15---> 0.936 0.369 0.650 0.530 0.228 0.332 0.609 0.360
Bits 16 to 23---> 0.966 0.945 0.803 0.528 0.711 0.681 0.778 0.173
Bits 24 to 31---> 0.800 0.771 0.762 0.127 0.583 0.006 0.101 0.460
KS test for the above 32 p values: 0.263
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-24_22:31,
p-values for 5 runs: 0.7705, 0.2640, 0.8362, 0.2029, 0.4019
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-24_22:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 188 211.4 2.594 2.594
r= 29 5020 5134.0 2.532 5.126
r= 30 23255 23103.0 0.999 6.125
r= 31 11537 11551.5 0.018 6.143
chi-square = 6.143 with df = 3; p-value = 0.895
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-24_22:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 196 211.4 1.124 1.124
r= 30 5128 5134.0 0.007 1.131
r= 31 23041 23103.0 0.167 1.298
r= 32 11635 11551.5 0.603 1.901
chi-square = 1.901 with df = 3; p-value = 0.407
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-24_22:31
b-rank test for bits 1 to 8, p=0.92909
b-rank test for bits 2 to 9, p=0.33007
b-rank test for bits 3 to 10, p=0.74204
b-rank test for bits 4 to 11, p=0.55029
b-rank test for bits 5 to 12, p=0.02776
b-rank test for bits 6 to 13, p=0.21649
b-rank test for bits 7 to 14, p=0.09875
b-rank test for bits 8 to 15, p=0.36891
b-rank test for bits 9 to 16, p=0.65635
b-rank test for bits 10 to 17, p=0.51879
b-rank test for bits 11 to 18, p=0.29028
b-rank test for bits 12 to 19, p=0.52643
b-rank test for bits 13 to 20, p=0.48147
b-rank test for bits 14 to 21, p=0.08047
b-rank test for bits 15 to 22, p=0.77057
b-rank test for bits 16 to 23, p=0.68086
b-rank test for bits 17 to 24, p=0.82704
b-rank test for bits 18 to 25, p=0.08090
b-rank test for bits 19 to 26, p=0.93367
b-rank test for bits 20 to 27, p=0.40027
b-rank test for bits 21 to 28, p=0.49450
b-rank test for bits 22 to 29, p=0.08964
b-rank test for bits 23 to 30, p=0.14797
b-rank test for bits 24 to 31, p=0.02124
b-rank test for bits 25 to 32, p=0.43242
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 = 0.349574
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-24_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 142318 0.95 0.830170
2 141460 -1.05 0.146897
3 141492 -0.98 0.164763
4 140982 -2.17 0.015130
5 142588 1.59 0.943594
6 141663 -0.58 0.282464
7 142082 0.40 0.656686
8 141683 -0.53 0.298469
9 141240 -1.56 0.058926
10 141897 -0.03 0.488509
11 141905 -0.01 0.495964
12 141849 -0.14 0.443952
13 142427 1.21 0.886766
14 141615 -0.69 0.245825
15 142233 0.76 0.775247
16 141999 0.21 0.582975
17 141935 0.06 0.523913
18 141879 -0.07 0.471753
19 141837 -0.17 0.432900
20 141734 -0.41 0.341032
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-24_22:31
Bits used No. missing words z-score p-value
23 to 32 141959 0.1713 0.567997
22 to 31 141338 -1.9701 0.024413
21 to 30 141800 -0.3770 0.353087
20 to 29 141766 -0.4942 0.310568
19 to 28 142397 1.6816 0.953679
18 to 27 142055 0.5023 0.692275
17 to 26 141971 0.2127 0.584202
16 to 25 142378 1.6161 0.946964
15 to 24 142370 1.5885 0.943915
14 to 23 142128 0.7540 0.774586
13 to 22 142741 2.8678 0.997933
12 to 21 142614 2.4299 0.992448
11 to 20 141901 -0.0287 0.488542
10 to 19 141914 0.0161 0.506424
9 to 18 141832 -0.2667 0.394867
8 to 17 141749 -0.5529 0.290179
7 to 16 141841 -0.2356 0.406864
6 to 15 141748 -0.5563 0.288999
5 to 14 142176 0.9196 0.821097
4 to 13 141806 -0.3563 0.360804
3 to 12 142159 0.8609 0.805362
2 to 11 141749 -0.5529 0.290179
1 to 10 142100 0.6575 0.744565
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-24_22:31
Bits used No. missing words z-score p-value
28 to 32 142686 2.6328 0.995766
27 to 31 141670 -0.8113 0.208600
26 to 30 141919 0.0328 0.513075
25 to 29 142084 0.5921 0.723109
24 to 28 142054 0.4904 0.688077
23 to 27 141661 -0.8418 0.199951
22 to 26 142099 0.6429 0.739872
21 to 25 141774 -0.4587 0.323208
20 to 24 141753 -0.5299 0.298080
19 to 23 142289 1.2870 0.900956
18 to 22 142759 2.8802 0.998013
17 to 21 141903 -0.0215 0.491440
16 to 20 141827 -0.2791 0.390090
15 to 19 142148 0.8091 0.790757
14 to 18 141618 -0.9876 0.161684
13 to 17 142176 0.9040 0.816993
12 to 16 141500 -1.3876 0.082636
11 to 15 141567 -1.1604 0.122935
10 to 14 141178 -2.4791 0.006586
9 to 13 141657 -0.8554 0.196177
8 to 12 141391 -1.7571 0.039455
7 to 11 141867 -0.1435 0.442951
6 to 10 142121 0.7175 0.763475
5 to 9 141594 -1.0689 0.142554
4 to 8 141635 -0.9299 0.176203
3 to 7 141942 0.1107 0.544091
2 to 6 142151 0.8192 0.793670
1 to 5 141533 -1.2757 0.101032
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-24_22:31
Bits used No. missing words z-score p-value
31 to 32 142143 0.6893 0.754680
30 to 31 142427 1.5271 0.936626
29 to 30 142152 0.7158 0.762955
28 to 29 141761 -0.4376 0.330856
27 to 28 142164 0.7512 0.773746
26 to 27 141841 -0.2016 0.420129
25 to 26 141134 -2.2871 0.011095
24 to 25 142016 0.3147 0.623490
23 to 24 142358 1.3235 0.907167
22 to 23 142038 0.3796 0.647863
21 to 22 142156 0.7276 0.766583
20 to 21 141650 -0.7650 0.222140
19 to 20 141898 -0.0334 0.486669
18 to 19 141659 -0.7384 0.230125
17 to 18 141305 -1.7827 0.037319
16 to 17 142071 0.4769 0.683284
15 to 16 141615 -0.8682 0.192634
14 to 15 141760 -0.4405 0.329787
13 to 14 141607 -0.8918 0.186242
12 to 13 142044 0.3973 0.654411
11 to 12 142175 0.7837 0.783388
10 to 11 141918 0.0256 0.510202
9 to 10 142703 2.3412 0.990389
8 to 9 142350 1.2999 0.903184
7 to 8 141555 -1.0452 0.147960
6 to 7 142014 0.3088 0.621248
5 to 6 141410 -1.4729 0.070382
4 to 5 141759 -0.4435 0.328720
3 to 4 141786 -0.3638 0.358002
2 to 3 141509 -1.1809 0.118818
1 to 2 142176 0.7866 0.784253
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-24_22:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2386.10 -1.611 0.053619
Test results for specific bytes for dh-ranFile-2018-06-24_22:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2524.65 0.349 0.636307
2 to 9 2367.45 -1.875 0.030425
3 to 10 2391.62 -1.533 0.062678
4 to 11 2526.55 0.375 0.646340
5 to 12 2409.48 -1.280 0.100249
6 to 13 2414.79 -1.205 0.114085
7 to 14 2438.56 -0.869 0.192460
8 to 15 2661.65 2.286 0.988875
9 to 16 2525.05 0.354 0.638409
10 to 17 2516.63 0.235 0.592992
11 to 18 2584.62 1.197 0.884299
12 to 19 2412.86 -1.232 0.108904
13 to 20 2483.45 -0.234 0.407494
14 to 21 2629.02 1.825 0.965976
15 to 22 2489.88 -0.143 0.443100
16 to 23 2503.55 0.050 0.520038
17 to 24 2471.62 -0.401 0.344084
18 to 25 2554.99 0.778 0.781610
19 to 26 2471.45 -0.404 0.343221
20 to 27 2440.74 -0.838 0.200980
21 to 28 2537.53 0.531 0.702183
22 to 29 2542.34 0.599 0.725325
23 to 30 2496.41 -0.051 0.479766
24 to 31 2505.34 0.075 0.530075
25 to 32 2483.20 -0.238 0.406120
CDPARK for dh-ranFile-2018-06-24_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
3516 -0.3196 0.374623
3559 1.6438 0.949895
3546 1.0502 0.853193
3508 -0.6849 0.246694
3512 -0.5023 0.307734
3525 0.0913 0.536383
3491 -1.4612 0.071982
3500 -1.0502 0.146807
3538 0.6849 0.753306
3539 0.7306 0.767486
Square side=100, avg. no. parked=3523.40 sample std.=20.63
p-value of the KSTEST for those 10 p-values: 0.996183
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-24_22:31
0.1522,0.8813,0.3377,0.3820,0.2813,0.8559,0.2548,0.1223,0.4258,0.0474,
The KS test for those 10 p-values: 0.234749
The 3DSPHERES test for dh-ranFile-2018-06-24_22:31
sample no r^3 equiv. uni.
1 22.520 0.527953
2 60.617 0.867419
3 8.074 0.235957
4 33.694 0.674744
5 6.041 0.182376
6 11.255 0.312829
7 80.926 0.932628
8 5.663 0.172007
9 31.075 0.645069
10 165.549 0.995987
11 2.007 0.064704
12 28.391 0.611854
13 17.893 0.449224
14 133.462 0.988307
15 67.180 0.893471
16 35.366 0.692372
17 41.972 0.753171
18 112.071 0.976143
19 14.841 0.390249
20 62.597 0.875887
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.086880
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-24_22:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 0.9 0.6 0.9 0.1 -0.2
1.7 1.4 1.1 1.1 -1.1 -0.4
0.3 0.2 -0.6 0.3 0.8 0.4
0.4 -0.1 0.5 0.1 -0.3 -2.6
-1.0 -0.4 0.7 -0.5 -0.9 0.5
-0.3 0.5 -1.2 -1.3 0.1 -1.0
-0.9 0.5 0.5 0.4 0.9 -1.0
-0.1
Chi-square with 42 degrees of freedom:32.104631
z-score=-1.079673, p-value=0.134777
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-24_22:31
Test no p-value
1 0.152641
2 0.031888
3 0.926726
4 0.862000
5 0.834166
6 0.184299
7 0.286769
8 0.037950
9 0.408806
10 0.949086
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.327105
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-24_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 66590 0.09 66758 0.13
3 25000.00 24996 0.00 24926 0.22
4 6666.67 6684 0.05 6665 0.00
5 1388.89 1437 1.67 1356 0.78
6 238.10 251 0.70 265 3.04
7 34.72 38 0.31 26 2.19
8 4.96 3 0.77 3 0.77
p=0.26726 p=0.69085
Number of rngs required: 687491, p-value: 0.145
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-24_22:31
No. of wins: Observed Expected
98663 98585.9
z-score= 0.345, pvalue=0.63496
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66558 66666.7 0.177 0.177
2 37642 37654.3 0.004 0.181
3 26939 26954.7 0.009 0.190
4 19219 19313.5 0.462 0.652
5 13869 13851.4 0.022 0.675
6 9910 9943.5 0.113 0.788
7 7011 7145.0 2.514 3.302
8 5221 5139.1 1.306 4.608
9 3734 3699.9 0.315 4.923
10 2765 2666.3 3.654 8.577
11 1957 1923.3 0.589 9.166
12 1434 1388.7 1.475 10.641
13 1005 1003.7 0.002 10.643
14 726 726.1 0.000 10.643
15 577 525.8 4.978 15.621
16 379 381.2 0.012 15.633
17 280 276.5 0.043 15.677
18 199 200.8 0.017 15.693
19 132 146.0 1.340 17.033
20 126 106.2 3.685 20.718
21 317 287.1 3.111 23.829
Chisq= 23.83 for 20 degrees of freedom, p= 0.75006
SUMMARY of craptest
p-value for no. of wins: 0.634961
p-value for throws/game: 0.750063
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-24_22:31
No. of wins: Observed Expected
98601 98585.9
z-score= 0.068, pvalue=0.52700
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66638 66666.7 0.012 0.012
2 37366 37654.3 2.208 2.220
3 26984 26954.7 0.032 2.252
4 19429 19313.5 0.691 2.943
5 13852 13851.4 0.000 2.943
6 10077 9943.5 1.791 4.734
7 7175 7145.0 0.126 4.860
8 5084 5139.1 0.590 5.450
9 3649 3699.9 0.699 6.149
10 2730 2666.3 1.522 7.671
11 1947 1923.3 0.291 7.963
12 1403 1388.7 0.146 8.109
13 992 1003.7 0.137 8.246
14 682 726.1 2.683 10.929
15 534 525.8 0.127 11.056
16 417 381.2 3.372 14.428
17 284 276.5 0.201 14.629
18 205 200.8 0.087 14.716
19 146 146.0 0.000 14.716
20 119 106.2 1.539 16.254
21 287 287.1 0.000 16.254
Chisq= 16.25 for 20 degrees of freedom, p= 0.29928
SUMMARY of craptest
p-value for no. of wins: 0.526996
p-value for throws/game: 0.299279
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0062,0.0066,0.0096,0.0111,0.0151,0.0212,0.0244,0.0278,0.0304,0.0319,
0.0373,0.0380,0.0395,0.0469,0.0474,0.0536,0.0589,0.0627,0.0647,0.0704,
0.0720,0.0805,0.0809,0.0826,0.0869,0.0896,0.0987,0.1002,0.1007,0.1010,
0.1089,0.1141,0.1170,0.1188,0.1223,0.1229,0.1275,0.1348,0.1426,0.1451,
0.1468,0.1469,0.1480,0.1480,0.1522,0.1526,0.1617,0.1648,0.1720,0.1730,
0.1762,0.1824,0.1843,0.1862,0.1925,0.1926,0.1962,0.2000,0.2010,0.2029,
0.2086,0.2165,0.2221,0.2275,0.2301,0.2340,0.2347,0.2360,0.2458,0.2467,
0.2468,0.2548,0.2627,0.2629,0.2640,0.2673,0.2813,0.2825,0.2868,0.2890,
0.2902,0.2902,0.2903,0.2981,0.2985,0.2993,0.3077,0.3106,0.3128,0.3232,
0.3271,0.3287,0.3298,0.3301,0.3309,0.3321,0.3377,0.3410,0.3432,0.3441,
0.3483,0.3496,0.3531,0.3580,0.3602,0.3608,0.3689,0.3690,0.3746,0.3820,
0.3901,0.3902,0.3949,0.4003,0.4019,0.4061,0.4069,0.4069,0.4075,0.4088,
0.4159,0.4201,0.4258,0.4324,0.4329,0.4430,0.4431,0.4440,0.4443,0.4492,
0.4604,0.4718,0.4798,0.4815,0.4867,0.4885,0.4885,0.4914,0.4945,0.4960,
0.5064,0.5102,0.5131,0.5188,0.5200,0.5239,0.5264,0.5270,0.5279,0.5280,
0.5301,0.5304,0.5364,0.5441,0.5503,0.5680,0.5828,0.5830,0.5842,0.5930,
0.6013,0.6093,0.6119,0.6212,0.6235,0.6350,0.6363,0.6384,0.6451,0.6463,
0.6479,0.6496,0.6544,0.6564,0.6567,0.6747,0.6791,0.6809,0.6813,0.6833,
0.6881,0.6909,0.6923,0.6924,0.6947,0.7022,0.7113,0.7204,0.7230,0.7231,
0.7253,0.7399,0.7420,0.7446,0.7501,0.7532,0.7533,0.7547,0.7623,0.7630,
0.7635,0.7666,0.7675,0.7705,0.7706,0.7714,0.7737,0.7746,0.7752,0.7779,
0.7816,0.7834,0.7843,0.7908,0.7937,0.8003,0.8031,0.8054,0.8170,0.8211,
0.8270,0.8302,0.8342,0.8362,0.8466,0.8481,0.8532,0.8559,0.8620,0.8620,
0.8674,0.8759,0.8813,0.8843,0.8868,0.8935,0.8952,0.8982,0.9010,0.9032,
0.9072,0.9267,0.9291,0.9308,0.9326,0.9337,0.9361,0.9366,0.9436,0.9439,
0.9448,0.9470,0.9491,0.9499,0.9529,0.9537,0.9660,0.9665,0.9761,0.9883,
0.9889,0.9904,0.9924,0.9958,0.9960,0.9962,0.9967,0.9979,0.9980,
Overall p-value after applying KStest on 269 p-values = 0.645801
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.