RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-17_20:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.59 19.4743 0.698006
2 to 25 15.39 20.2472 0.738218
3 to 26 15.49 29.5697 0.970379
4 to 27 15.75 19.7716 0.713924
5 to 28 15.95 13.2996 0.284088
6 to 29 15.67 20.5695 0.753861
7 to 30 15.88 15.9261 0.470920
8 to 31 15.74 22.9090 0.847765
9 to 32 15.37 22.9340 0.848589
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.048453
Tough bday spacings test for dh-ranFile-2018-06-17_20:31: 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 5 38 66 105 110 77 42 28 13 11 5
(O-E)^2/E 1.9 0.1 0.7 0.5 1.6 0.0 2.0 0.1 0.2 2.9 0.2
Birthday Spacings: Sum(O-E)^2/E= 10.198, p= 0.577
RESULTS OF GCD FOR dh-ranFile-2018-06-17_20:31
Euclid's algorithm:
p-value, steps to gcd: 0.606192
p-value, dist. of gcd's: 0.972976
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-17_20:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.403 0.128 0.336 0.427 0.307 0.304 0.996 0.566
Bits 8 to 15---> 0.706 0.826 0.544 0.502 0.163 0.830 0.516 0.612
Bits 16 to 23---> 0.157 0.837 0.396 0.522 0.629 0.202 0.873 0.051
Bits 24 to 31---> 0.592 0.177 0.774 0.285 0.485 0.841 0.972 0.592
KS test for the above 32 p values: 0.267
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-17_20:31,
p-values for 5 runs: 0.3976, 0.2432, 0.0692, 0.1818, 0.6990
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-17_20:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 199 211.4 0.729 0.729
r= 29 5141 5134.0 0.010 0.739
r= 30 23163 23103.0 0.156 0.894
r= 31 11497 11551.5 0.257 1.152
chi-square = 1.152 with df = 3; p-value = 0.235
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-17_20:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 197 211.4 0.983 0.983
r= 30 5288 5134.0 4.619 5.602
r= 31 22999 23103.0 0.469 6.071
r= 32 11516 11551.5 0.109 6.180
chi-square = 6.180 with df = 3; p-value = 0.897
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-17_20:31
b-rank test for bits 1 to 8, p=0.92258
b-rank test for bits 2 to 9, p=0.63157
b-rank test for bits 3 to 10, p=0.60475
b-rank test for bits 4 to 11, p=0.36254
b-rank test for bits 5 to 12, p=0.80100
b-rank test for bits 6 to 13, p=0.24912
b-rank test for bits 7 to 14, p=0.65281
b-rank test for bits 8 to 15, p=0.17916
b-rank test for bits 9 to 16, p=0.34452
b-rank test for bits 10 to 17, p=0.76175
b-rank test for bits 11 to 18, p=0.06992
b-rank test for bits 12 to 19, p=0.33927
b-rank test for bits 13 to 20, p=0.57844
b-rank test for bits 14 to 21, p=0.39694
b-rank test for bits 15 to 22, p=0.66826
b-rank test for bits 16 to 23, p=0.32484
b-rank test for bits 17 to 24, p=0.79570
b-rank test for bits 18 to 25, p=0.35365
b-rank test for bits 19 to 26, p=0.45846
b-rank test for bits 20 to 27, p=0.95534
b-rank test for bits 21 to 28, p=0.94473
b-rank test for bits 22 to 29, p=0.58713
b-rank test for bits 23 to 30, p=0.64949
b-rank test for bits 24 to 31, p=0.58530
b-rank test for bits 25 to 32, p=0.78816
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 = 0.299330
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-17_20:31
(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 142592 1.60 0.944647
2 142268 0.84 0.798989
3 142083 0.41 0.657545
4 142696 1.84 0.966970
5 141083 -1.93 0.026761
6 141786 -0.29 0.386614
7 142338 1.00 0.841723
8 142265 0.83 0.797015
9 141287 -1.45 0.072967
10 142038 0.30 0.618152
11 141418 -1.15 0.125491
12 141763 -0.34 0.366216
13 141758 -0.35 0.361829
14 141510 -0.93 0.175406
15 142722 1.90 0.971202
16 142388 1.12 0.868299
17 141379 -1.24 0.107656
18 141267 -1.50 0.066707
19 141188 -1.69 0.045960
20 141501 -0.95 0.170031
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-17_20:31
Bits used No. missing words z-score p-value
23 to 32 142166 0.8851 0.811940
22 to 31 141531 -1.3046 0.096017
21 to 30 141171 -2.5460 0.005449
20 to 29 141768 -0.4873 0.313007
19 to 28 141807 -0.3529 0.362096
18 to 27 141539 -1.2770 0.100801
17 to 26 141487 -1.4563 0.072653
16 to 25 142053 0.4954 0.689846
15 to 24 141974 0.2230 0.588232
14 to 23 142205 1.0196 0.846029
13 to 22 141212 -2.4046 0.008095
12 to 21 141614 -1.0184 0.154249
11 to 20 141236 -2.3218 0.010121
10 to 19 142101 0.6609 0.745672
9 to 18 142083 0.5989 0.725368
8 to 17 141845 -0.2218 0.412224
7 to 16 141771 -0.4770 0.316681
6 to 15 141552 -1.2322 0.108942
5 to 14 141598 -1.0736 0.141512
4 to 13 141842 -0.2322 0.408202
3 to 12 141872 -0.1287 0.448788
2 to 11 141756 -0.5287 0.298498
1 to 10 141286 -2.1494 0.015801
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-17_20:31
Bits used No. missing words z-score p-value
28 to 32 141923 0.0463 0.518480
27 to 31 142294 1.3040 0.903877
26 to 30 142296 1.3107 0.905028
25 to 29 142087 0.6023 0.726503
24 to 28 142762 2.8904 0.998076
23 to 27 141535 -1.2689 0.102236
22 to 26 141546 -1.2316 0.109044
21 to 25 141981 0.2429 0.595978
20 to 24 141955 0.1548 0.561516
19 to 23 141833 -0.2587 0.397916
18 to 22 141991 0.2768 0.609051
17 to 21 141841 -0.2316 0.408414
16 to 20 141864 -0.1537 0.438939
15 to 19 142062 0.5175 0.697605
14 to 18 141862 -0.1604 0.436267
13 to 17 141963 0.1819 0.572182
12 to 16 141957 0.1616 0.564187
11 to 15 141813 -0.3265 0.372007
10 to 14 141426 -1.6384 0.050668
9 to 13 141945 0.1209 0.548121
8 to 12 141765 -0.4893 0.312331
7 to 11 141610 -1.0147 0.155130
6 to 10 142327 1.4158 0.921587
5 to 9 141731 -0.6045 0.272753
4 to 8 141748 -0.5469 0.292230
3 to 7 141430 -1.6248 0.052098
2 to 6 141849 -0.2045 0.418978
1 to 5 142199 0.9819 0.836933
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-17_20:31
Bits used No. missing words z-score p-value
31 to 32 141314 -1.7561 0.039533
30 to 31 141967 0.1701 0.567541
29 to 30 141793 -0.3432 0.365740
28 to 29 141690 -0.6470 0.258819
27 to 28 141951 0.1229 0.548915
26 to 27 141632 -0.8181 0.206655
25 to 26 141881 -0.0836 0.466699
24 to 25 142148 0.7040 0.759297
23 to 24 142163 0.7483 0.772857
22 to 23 141817 -0.2724 0.392673
21 to 22 142171 0.7719 0.779910
20 to 21 141689 -0.6499 0.257865
19 to 20 142197 0.8486 0.801944
18 to 19 141465 -1.3107 0.094978
17 to 18 141812 -0.2871 0.387014
16 to 17 141922 0.0374 0.514907
15 to 16 141539 -1.0924 0.137325
14 to 15 142163 0.7483 0.772857
13 to 14 141854 -0.1632 0.435174
12 to 13 142060 0.4445 0.671643
11 to 12 141756 -0.4523 0.325526
10 to 11 141918 0.0256 0.510202
9 to 10 141998 0.2616 0.603171
8 to 9 141954 0.1318 0.552417
7 to 8 141754 -0.4582 0.323404
6 to 7 141990 0.2380 0.594046
5 to 6 142584 1.9902 0.976714
4 to 5 141694 -0.6352 0.262652
3 to 4 142364 1.3412 0.910074
2 to 3 141958 0.1436 0.557080
1 to 2 142394 1.4297 0.923599
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-17_20:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2498.96 -0.015 0.494128
Test results for specific bytes for dh-ranFile-2018-06-17_20:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2564.35 0.910 0.818616
2 to 9 2408.24 -1.298 0.097200
3 to 10 2449.66 -0.712 0.238275
4 to 11 2459.63 -0.571 0.284035
5 to 12 2481.13 -0.267 0.394798
6 to 13 2483.98 -0.227 0.410405
7 to 14 2683.85 2.600 0.995339
8 to 15 2475.83 -0.342 0.366260
9 to 16 2449.68 -0.712 0.238335
10 to 17 2435.18 -0.917 0.179654
11 to 18 2471.49 -0.403 0.343387
12 to 19 2448.69 -0.726 0.234012
13 to 20 2497.94 -0.029 0.488386
14 to 21 2400.94 -1.401 0.080618
15 to 22 2559.59 0.843 0.800323
16 to 23 2480.06 -0.282 0.388992
17 to 24 2524.36 0.345 0.634781
18 to 25 2680.05 2.546 0.994557
19 to 26 2589.27 1.262 0.896605
20 to 27 2515.79 0.223 0.588371
21 to 28 2463.72 -0.513 0.303964
22 to 29 2387.37 -1.593 0.055602
23 to 30 2553.25 0.753 0.774276
24 to 31 2595.05 1.344 0.910555
25 to 32 2421.27 -1.113 0.132776
CDPARK for dh-ranFile-2018-06-17_20:31: 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
3549 1.1872 0.882429
3531 0.3653 0.642555
3490 -1.5068 0.065925
3513 -0.4566 0.323972
3510 -0.5936 0.276387
3487 -1.6438 0.050105
3493 -1.3699 0.085365
3523 0.0000 0.500000
3500 -1.0502 0.146807
3518 -0.2283 0.409702
Square side=100, avg. no. parked=3511.40 sample std.=18.71
p-value of the KSTEST for those 10 p-values: 0.122300
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-17_20:31
0.5626,0.5100,0.3873,0.3025,0.5828,0.8990,0.4736,0.4605,0.7625,0.0856,
The KS test for those 10 p-values: 0.648115
The 3DSPHERES test for dh-ranFile-2018-06-17_20:31
sample no r^3 equiv. uni.
1 15.234 0.398173
2 97.536 0.961273
3 47.810 0.796821
4 6.715 0.200555
5 20.346 0.492475
6 17.848 0.448407
7 12.375 0.338002
8 44.995 0.776833
9 0.039 0.001305
10 10.747 0.301086
11 101.423 0.965979
12 18.051 0.452114
13 14.190 0.376870
14 12.587 0.342675
15 31.685 0.652217
16 14.143 0.375889
17 33.980 0.677826
18 112.375 0.976384
19 3.738 0.117164
20 26.471 0.586202
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.622905
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-17_20:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -0.3 0.1 -0.1 0.3 -0.8
0.4 1.1 0.8 -0.1 -0.1 1.4
-0.2 0.5 -0.4 0.9 -1.4 0.9
-1.4 -0.5 -1.0 0.3 1.4 -0.3
-1.3 0.1 0.2 2.3 -0.6 -1.5
2.2 0.0 -0.3 -1.2 -1.0 0.1
0.3 2.4 -0.8 1.0 0.9 0.0
-0.1
Chi-square with 42 degrees of freedom:39.564267
z-score=-0.265760, p-value=0.421561
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-17_20:31
Test no p-value
1 0.016544
2 0.447195
3 0.303603
4 0.270999
5 0.247439
6 0.618702
7 0.064793
8 0.830019
9 0.258769
10 0.320171
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.105751
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-17_20:31:
(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 66758 0.13 66513 0.35
3 25000.00 25032 0.04 25143 0.82
4 6666.67 6575 1.26 6663 0.00
5 1388.89 1367 0.35 1379 0.07
6 238.10 223 0.96 253 0.93
7 34.72 38 0.31 42 1.53
8 4.96 6 0.22 6 0.22
p=0.22397 p=0.31279
Number of rngs required: 687763, p-value: 0.230
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-17_20:31
No. of wins: Observed Expected
98895 98585.9
z-score= 1.383, pvalue=0.91662
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66812 66666.7 0.317 0.317
2 37328 37654.3 2.828 3.145
3 26845 26954.7 0.447 3.592
4 19262 19313.5 0.137 3.729
5 14066 13851.4 3.324 7.053
6 10171 9943.5 5.203 12.256
7 7113 7145.0 0.144 12.399
8 5086 5139.1 0.548 12.947
9 3630 3699.9 1.319 14.267
10 2665 2666.3 0.001 14.267
11 1966 1923.3 0.947 15.214
12 1389 1388.7 0.000 15.214
13 1003 1003.7 0.001 15.215
14 715 726.1 0.171 15.386
15 545 525.8 0.698 16.084
16 389 381.2 0.162 16.246
17 299 276.5 1.824 18.070
18 174 200.8 3.584 21.654
19 139 146.0 0.334 21.988
20 107 106.2 0.006 21.994
21 296 287.1 0.275 22.269
Chisq= 22.27 for 20 degrees of freedom, p= 0.67392
SUMMARY of craptest
p-value for no. of wins: 0.916616
p-value for throws/game: 0.673917
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-17_20:31
No. of wins: Observed Expected
98646 98585.9
z-score= 0.269, pvalue=0.60603
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67299 66666.7 5.998 5.998
2 37571 37654.3 0.184 6.182
3 26986 26954.7 0.036 6.218
4 19330 19313.5 0.014 6.232
5 13613 13851.4 4.104 10.336
6 9772 9943.5 2.959 13.296
7 7201 7145.0 0.439 13.734
8 5079 5139.1 0.702 14.436
9 3607 3699.9 2.331 16.767
10 2625 2666.3 0.640 17.407
11 1887 1923.3 0.686 18.093
12 1419 1388.7 0.659 18.752
13 980 1003.7 0.560 19.313
14 696 726.1 1.251 20.564
15 543 525.8 0.560 21.124
16 388 381.2 0.123 21.247
17 275 276.5 0.009 21.256
18 190 200.8 0.584 21.840
19 146 146.0 0.000 21.840
20 101 106.2 0.256 22.096
21 292 287.1 0.083 22.179
Chisq= 22.18 for 20 degrees of freedom, p= 0.66913
SUMMARY of craptest
p-value for no. of wins: 0.606030
p-value for throws/game: 0.669125
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0013,0.0054,0.0081,0.0101,0.0158,0.0165,0.0268,0.0395,0.0460,0.0485,
0.0501,0.0507,0.0514,0.0521,0.0556,0.0648,0.0659,0.0667,0.0692,0.0699,
0.0727,0.0730,0.0806,0.0854,0.0856,0.0950,0.0960,0.0972,0.1008,0.1022,
0.1058,0.1077,0.1089,0.1090,0.1172,0.1223,0.1255,0.1284,0.1328,0.1373,
0.1415,0.1468,0.1542,0.1551,0.1565,0.1631,0.1700,0.1754,0.1772,0.1792,
0.1797,0.1818,0.2006,0.2021,0.2067,0.2240,0.2299,0.2340,0.2354,0.2383,
0.2383,0.2432,0.2474,0.2491,0.2579,0.2588,0.2588,0.2627,0.2672,0.2710,
0.2728,0.2764,0.2840,0.2841,0.2847,0.2922,0.2985,0.2993,0.3011,0.3025,
0.3036,0.3036,0.3040,0.3072,0.3123,0.3128,0.3130,0.3167,0.3202,0.3234,
0.3240,0.3248,0.3255,0.3357,0.3380,0.3393,0.3427,0.3434,0.3445,0.3537,
0.3618,0.3621,0.3625,0.3657,0.3662,0.3663,0.3720,0.3759,0.3769,0.3866,
0.3870,0.3873,0.3890,0.3927,0.3948,0.3956,0.3969,0.3976,0.3979,0.3982,
0.4034,0.4082,0.4084,0.4097,0.4104,0.4122,0.4190,0.4216,0.4267,0.4352,
0.4363,0.4389,0.4472,0.4484,0.4488,0.4521,0.4585,0.4605,0.4667,0.4709,
0.4736,0.4850,0.4884,0.4925,0.4941,0.5000,0.5020,0.5100,0.5102,0.5149,
0.5157,0.5185,0.5215,0.5444,0.5481,0.5489,0.5524,0.5571,0.5615,0.5626,
0.5642,0.5657,0.5675,0.5722,0.5767,0.5784,0.5828,0.5853,0.5862,0.5871,
0.5882,0.5884,0.5922,0.5923,0.5940,0.5960,0.6032,0.6047,0.6060,0.6062,
0.6091,0.6118,0.6182,0.6187,0.6229,0.6286,0.6316,0.6348,0.6426,0.6481,
0.6495,0.6522,0.6528,0.6575,0.6683,0.6691,0.6716,0.6739,0.6778,0.6898,
0.6976,0.6980,0.6990,0.7063,0.7139,0.7254,0.7265,0.7382,0.7457,0.7539,
0.7593,0.7618,0.7625,0.7729,0.7729,0.7743,0.7743,0.7768,0.7799,0.7882,
0.7957,0.7968,0.7970,0.7990,0.8003,0.8010,0.8019,0.8119,0.8186,0.8260,
0.8300,0.8305,0.8368,0.8369,0.8412,0.8417,0.8460,0.8478,0.8486,0.8683,
0.8726,0.8824,0.8966,0.8968,0.8990,0.9039,0.9050,0.9101,0.9106,0.9166,
0.9216,0.9226,0.9236,0.9446,0.9447,0.9553,0.9613,0.9660,0.9670,0.9704,
0.9712,0.9717,0.9730,0.9764,0.9767,0.9946,0.9953,0.9958,0.9981,
Overall p-value after applying KStest on 269 p-values = 0.233968
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.