RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-03_08:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 16.01 12.4609 0.228542
2 to 25 15.89 10.3679 0.112524
3 to 26 15.82 9.2588 0.068210
4 to 27 15.84 11.2560 0.157049
5 to 28 15.52 16.8497 0.535409
6 to 29 15.70 16.3523 0.500991
7 to 30 15.87 19.2720 0.686854
8 to 31 15.93 18.1066 0.617853
9 to 32 15.84 10.3436 0.111415
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.117553
Tough bday spacings test for dh-ranFile-2018-07-03_08:31: 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 11 45 77 93 80 69 64 30 17 8 6
(O-E)^2/E 0.4 1.9 0.2 0.2 3.2 1.1 2.7 0.0 0.3 0.3 0.9
Birthday Spacings: Sum(O-E)^2/E= 11.200, p= 0.658
RESULTS OF GCD FOR dh-ranFile-2018-07-03_08:31
Euclid's algorithm:
p-value, steps to gcd: 0.195499
p-value, dist. of gcd's: 0.581151
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-03_08:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.378 0.230 0.960 0.865 0.523 0.436 0.394 0.753
Bits 8 to 15---> 0.147 0.635 0.060 0.545 0.338 0.090 0.960 0.459
Bits 16 to 23---> 0.100 0.594 0.061 0.867 0.022 0.449 0.103 0.580
Bits 24 to 31---> 0.730 0.621 0.094 0.577 0.476 0.850 0.103 0.888
KS test for the above 32 p values: 0.411
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-03_08:31,
p-values for 5 runs: 0.5704, 0.7640, 0.1075, 0.6373, 0.0113
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-03_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 224 211.4 0.749 0.749
r= 29 5237 5134.0 2.066 2.815
r= 30 22915 23103.0 1.531 4.345
r= 31 11624 11551.5 0.455 4.800
chi-square = 4.800 with df = 3; p-value = 0.813
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-03_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 200 211.4 0.617 0.617
r= 30 5107 5134.0 0.142 0.759
r= 31 23133 23103.0 0.039 0.798
r= 32 11560 11551.5 0.006 0.804
chi-square = 0.804 with df = 3; p-value = 0.151
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-03_08:31
b-rank test for bits 1 to 8, p=0.77513
b-rank test for bits 2 to 9, p=0.33589
b-rank test for bits 3 to 10, p=0.53126
b-rank test for bits 4 to 11, p=0.38288
b-rank test for bits 5 to 12, p=0.07960
b-rank test for bits 6 to 13, p=0.52704
b-rank test for bits 7 to 14, p=0.33591
b-rank test for bits 8 to 15, p=0.31562
b-rank test for bits 9 to 16, p=0.63421
b-rank test for bits 10 to 17, p=0.36001
b-rank test for bits 11 to 18, p=0.86767
b-rank test for bits 12 to 19, p=0.92284
b-rank test for bits 13 to 20, p=0.92466
b-rank test for bits 14 to 21, p=0.79568
b-rank test for bits 15 to 22, p=0.49900
b-rank test for bits 16 to 23, p=0.17521
b-rank test for bits 17 to 24, p=0.50893
b-rank test for bits 18 to 25, p=0.08186
b-rank test for bits 19 to 26, p=0.23367
b-rank test for bits 20 to 27, p=0.01663
b-rank test for bits 21 to 28, p=0.06693
b-rank test for bits 22 to 29, p=0.13836
b-rank test for bits 23 to 30, p=0.87176
b-rank test for bits 24 to 31, p=0.06082
b-rank test for bits 25 to 32, p=0.59768
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 = 0.516167
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-03_08:31
(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 141570 -0.79 0.213939
2 142197 0.67 0.749248
3 141601 -0.72 0.235640
4 142088 0.42 0.661827
5 142571 1.55 0.938943
6 141482 -1.00 0.159034
7 142115 0.48 0.684577
8 142071 0.38 0.647186
9 142492 1.36 0.913303
10 142382 1.10 0.865284
11 141861 -0.11 0.455047
12 141980 0.17 0.565574
13 142065 0.36 0.641965
14 141692 -0.51 0.305804
15 141788 -0.28 0.388404
16 142037 0.30 0.617261
17 141863 -0.11 0.456900
18 141961 0.12 0.548045
19 141266 -1.50 0.066406
20 142367 1.07 0.857538
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-03_08:31
Bits used No. missing words z-score p-value
23 to 32 141873 -0.1253 0.450153
22 to 31 141939 0.1023 0.540745
21 to 30 141726 -0.6322 0.263637
20 to 29 141946 0.1264 0.550312
19 to 28 142005 0.3299 0.629261
18 to 27 142464 1.9127 0.972104
17 to 26 141817 -0.3184 0.375099
16 to 25 141882 -0.0942 0.462459
15 to 24 141863 -0.1598 0.436536
14 to 23 142215 1.0540 0.854066
13 to 22 141674 -0.8115 0.208544
12 to 21 141807 -0.3529 0.362096
11 to 20 142022 0.3885 0.651183
10 to 19 141479 -1.4839 0.068918
9 to 18 142194 0.9816 0.836857
8 to 17 141950 0.1402 0.555765
7 to 16 141994 0.2920 0.614844
6 to 15 142049 0.4816 0.684962
5 to 14 141989 0.2747 0.608236
4 to 13 142168 0.8920 0.813794
3 to 12 142526 2.1264 0.983267
2 to 11 142272 1.2506 0.894457
1 to 10 142197 0.9920 0.839393
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-03_08:31
Bits used No. missing words z-score p-value
28 to 32 141907 -0.0079 0.496849
27 to 31 141852 -0.1943 0.422955
26 to 30 141698 -0.7164 0.236881
25 to 29 142164 0.8633 0.806011
24 to 28 141928 0.0633 0.525232
23 to 27 142013 0.3514 0.637365
22 to 26 141570 -1.1503 0.125016
21 to 25 141927 0.0599 0.523882
20 to 24 141652 -0.8723 0.191521
19 to 23 141616 -0.9943 0.160029
18 to 22 141914 0.0158 0.506315
17 to 21 141986 0.2599 0.602529
16 to 20 141944 0.1175 0.546778
15 to 19 141729 -0.6113 0.270504
14 to 18 142263 1.1989 0.884713
13 to 17 141634 -0.9333 0.175327
12 to 16 141844 -0.2215 0.412368
11 to 15 142246 1.1413 0.873118
10 to 14 142134 0.7616 0.776849
9 to 13 142014 0.3548 0.638635
8 to 12 141689 -0.7469 0.227568
7 to 11 141407 -1.7028 0.044301
6 to 10 141598 -1.0554 0.145631
5 to 9 142197 0.9752 0.835258
4 to 8 141431 -1.6215 0.052460
3 to 7 141600 -1.0486 0.147187
2 to 6 142071 0.5480 0.708166
1 to 5 141654 -0.8655 0.193375
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-03_08:31
Bits used No. missing words z-score p-value
31 to 32 141927 0.0521 0.520785
30 to 31 141905 -0.0128 0.494905
29 to 30 141890 -0.0570 0.477264
28 to 29 142039 0.3825 0.648958
27 to 28 142714 2.3737 0.991194
26 to 27 142167 0.7601 0.776399
25 to 26 141629 -0.8269 0.204138
24 to 25 141785 -0.3668 0.356901
23 to 24 142196 0.8456 0.801122
22 to 23 142139 0.6775 0.750953
21 to 22 142008 0.2911 0.614498
20 to 21 142338 1.2645 0.896977
19 to 20 141906 -0.0098 0.496081
18 to 19 141791 -0.3491 0.363524
17 to 18 142088 0.5271 0.700921
16 to 17 141236 -1.9862 0.023504
15 to 16 141640 -0.7945 0.213457
14 to 15 141730 -0.5290 0.298404
13 to 14 141884 -0.0747 0.470219
12 to 13 142259 1.0315 0.848841
11 to 12 141857 -0.1544 0.438661
10 to 11 142163 0.7483 0.772857
9 to 10 141516 -1.1603 0.122970
8 to 9 142092 0.5388 0.705005
7 to 8 141788 -0.3579 0.360207
6 to 7 142572 1.9548 0.974695
5 to 6 141950 0.1200 0.547747
4 to 5 142342 1.2763 0.899078
3 to 4 141619 -0.8564 0.195880
2 to 3 141549 -1.0629 0.143909
1 to 2 142314 1.1937 0.883706
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-03_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2483.02 -0.240 0.405120
Test results for specific bytes for dh-ranFile-2018-07-03_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2475.97 -0.340 0.367009
2 to 9 2551.73 0.732 0.767772
3 to 10 2443.56 -0.798 0.212371
4 to 11 2538.07 0.538 0.704837
5 to 12 2378.14 -1.723 0.042418
6 to 13 2403.09 -1.370 0.085266
7 to 14 2608.36 1.532 0.937300
8 to 15 2575.33 1.065 0.856636
9 to 16 2595.92 1.356 0.912521
10 to 17 2594.26 1.333 0.908737
11 to 18 2389.75 -1.559 0.059478
12 to 19 2426.72 -1.036 0.150028
13 to 20 2589.35 1.264 0.896817
14 to 21 2532.67 0.462 0.677992
15 to 22 2487.56 -0.176 0.430167
16 to 23 2523.78 0.336 0.631662
17 to 24 2459.68 -0.570 0.284270
18 to 25 2476.78 -0.328 0.371293
19 to 26 2572.06 1.019 0.845934
20 to 27 2461.69 -0.542 0.293961
21 to 28 2476.49 -0.332 0.369782
22 to 29 2485.41 -0.206 0.418290
23 to 30 2423.48 -1.082 0.139587
24 to 31 2549.55 0.701 0.758289
25 to 32 2535.51 0.502 0.692224
CDPARK for dh-ranFile-2018-07-03_08:31: 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
3503 -0.9132 0.180558
3522 -0.0457 0.481790
3525 0.0913 0.536383
3564 1.8721 0.969407
3521 -0.0913 0.463617
3540 0.7763 0.781201
3487 -1.6438 0.050105
3525 0.0913 0.536383
3547 1.0959 0.863437
3542 0.8676 0.807188
Square side=100, avg. no. parked=3527.60 sample std.=20.99
p-value of the KSTEST for those 10 p-values: 0.746343
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-03_08:31
0.9388,0.9281,0.8842,0.7312,0.5462,0.9932,0.8277,0.3229,0.9782,0.9103,
The KS test for those 10 p-values: 0.000406
The 3DSPHERES test for dh-ranFile-2018-07-03_08:31
sample no r^3 equiv. uni.
1 107.627 0.972335
2 75.911 0.920371
3 1.181 0.038614
4 74.801 0.917368
5 24.204 0.553716
6 10.738 0.300873
7 22.039 0.520312
8 22.488 0.527446
9 8.060 0.235605
10 42.450 0.757075
11 78.944 0.928027
12 12.143 0.332878
13 5.836 0.176770
14 6.434 0.193033
15 33.985 0.677877
16 39.225 0.729508
17 2.285 0.073350
18 62.502 0.875494
19 30.277 0.635506
20 29.498 0.625907
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.738653
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-03_08:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -1.2 -0.6 -0.4 1.1 -0.4
1.1 -1.1 0.0 0.3 0.1 0.5
-1.3 1.8 1.6 -0.5 0.0 -1.7
1.2 -0.6 0.4 -0.6 0.2 -0.6
-0.3 -0.1 -0.9 -0.5 -0.2 0.2
1.4 -0.5 0.3 1.6 0.2 1.0
0.3 -1.3 -0.4 -0.7 0.9 0.0
-0.1
Chi-square with 42 degrees of freedom:30.781544
z-score=-1.224034, p-value=0.100381
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-03_08:31
Test no p-value
1 0.899240
2 0.688242
3 0.340400
4 0.009294
5 0.114957
6 0.019971
7 0.695121
8 0.325648
9 0.250238
10 0.076415
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.074637
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-03_08:31:
(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 66837 0.44 66792 0.24
3 25000.00 24796 1.66 24862 0.76
4 6666.67 6710 0.28 6673 0.01
5 1388.89 1368 0.31 1384 0.02
6 238.10 244 0.15 246 0.26
7 34.72 39 0.53 34 0.01
8 4.96 5 0.00 8 1.86
p=0.23882 p=0.21164
Number of rngs required: 687251, p-value: 0.090
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-03_08:31
No. of wins: Observed Expected
98541 98585.9
z-score=-0.201, pvalue=0.42049
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66325 66666.7 1.751 1.751
2 37866 37654.3 1.190 2.941
3 26947 26954.7 0.002 2.943
4 19104 19313.5 2.272 5.215
5 13925 13851.4 0.391 5.606
6 10154 9943.5 4.454 10.060
7 7117 7145.0 0.110 10.170
8 5126 5139.1 0.033 10.203
9 3755 3699.9 0.822 11.025
10 2622 2666.3 0.736 11.761
11 1997 1923.3 2.822 14.583
12 1390 1388.7 0.001 14.584
13 1002 1003.7 0.003 14.587
14 720 726.1 0.052 14.639
15 544 525.8 0.627 15.266
16 396 381.2 0.579 15.845
17 297 276.5 1.514 17.359
18 192 200.8 0.388 17.747
19 133 146.0 1.155 18.902
20 121 106.2 2.058 20.960
21 267 287.1 1.409 22.369
Chisq= 22.37 for 20 degrees of freedom, p= 0.67916
SUMMARY of craptest
p-value for no. of wins: 0.420492
p-value for throws/game: 0.679161
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-03_08:31
No. of wins: Observed Expected
98438 98585.9
z-score=-0.661, pvalue=0.25421
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66527 66666.7 0.293 0.293
2 37632 37654.3 0.013 0.306
3 27081 26954.7 0.591 0.897
4 19262 19313.5 0.137 1.034
5 13964 13851.4 0.915 1.949
6 9863 9943.5 0.652 2.602
7 7155 7145.0 0.014 2.616
8 5188 5139.1 0.466 3.082
9 3650 3699.9 0.672 3.754
10 2629 2666.3 0.522 4.275
11 1934 1923.3 0.059 4.335
12 1402 1388.7 0.127 4.461
13 1032 1003.7 0.797 5.258
14 763 726.1 1.871 7.129
15 536 525.8 0.196 7.326
16 378 381.2 0.026 7.352
17 275 276.5 0.009 7.360
18 190 200.8 0.584 7.944
19 150 146.0 0.110 8.055
20 96 106.2 0.982 9.037
21 293 287.1 0.121 9.158
Chisq= 9.16 for 20 degrees of freedom, p= 0.01900
SUMMARY of craptest
p-value for no. of wins: 0.254207
p-value for throws/game: 0.018996
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0004,0.0093,0.0113,0.0166,0.0190,0.0200,0.0217,0.0235,0.0386,0.0424,
0.0443,0.0501,0.0525,0.0595,0.0598,0.0606,0.0608,0.0664,0.0669,0.0682,
0.0689,0.0734,0.0746,0.0764,0.0796,0.0819,0.0853,0.0898,0.0904,0.0939,
0.0997,0.1004,0.1026,0.1031,0.1075,0.1114,0.1125,0.1150,0.1176,0.1230,
0.1250,0.1384,0.1396,0.1439,0.1456,0.1467,0.1472,0.1500,0.1514,0.1570,
0.1590,0.1600,0.1752,0.1753,0.1768,0.1806,0.1915,0.1930,0.1934,0.1955,
0.1959,0.2041,0.2085,0.2116,0.2124,0.2135,0.2139,0.2276,0.2285,0.2301,
0.2337,0.2356,0.2356,0.2369,0.2388,0.2502,0.2542,0.2636,0.2705,0.2843,
0.2940,0.2984,0.3009,0.3058,0.3156,0.3229,0.3256,0.3329,0.3359,0.3359,
0.3383,0.3404,0.3569,0.3600,0.3602,0.3621,0.3635,0.3670,0.3698,0.3713,
0.3751,0.3776,0.3829,0.3884,0.3945,0.4051,0.4110,0.4124,0.4183,0.4205,
0.4230,0.4302,0.4365,0.4365,0.4387,0.4489,0.4502,0.4550,0.4569,0.4595,
0.4625,0.4636,0.4702,0.4758,0.4773,0.4818,0.4949,0.4961,0.4968,0.4990,
0.5010,0.5063,0.5089,0.5162,0.5203,0.5208,0.5233,0.5239,0.5252,0.5270,
0.5274,0.5313,0.5354,0.5364,0.5364,0.5407,0.5448,0.5462,0.5468,0.5477,
0.5480,0.5503,0.5537,0.5558,0.5656,0.5704,0.5765,0.5805,0.5812,0.5943,
0.5977,0.6025,0.6082,0.6145,0.6148,0.6173,0.6179,0.6211,0.6259,0.6293,
0.6317,0.6342,0.6352,0.6355,0.6373,0.6374,0.6386,0.6420,0.6472,0.6490,
0.6512,0.6579,0.6618,0.6779,0.6780,0.6792,0.6846,0.6850,0.6869,0.6882,
0.6922,0.6951,0.7009,0.7048,0.7050,0.7082,0.7295,0.7296,0.7312,0.7387,
0.7463,0.7492,0.7510,0.7531,0.7571,0.7583,0.7640,0.7678,0.7729,0.7751,
0.7764,0.7768,0.7812,0.7957,0.8011,0.8060,0.8072,0.8130,0.8138,0.8277,
0.8353,0.8369,0.8394,0.8459,0.8488,0.8504,0.8541,0.8566,0.8575,0.8634,
0.8649,0.8653,0.8673,0.8677,0.8718,0.8731,0.8755,0.8837,0.8842,0.8847,
0.8878,0.8945,0.8968,0.8970,0.8991,0.8992,0.9087,0.9103,0.9125,0.9133,
0.9174,0.9204,0.9228,0.9247,0.9280,0.9281,0.9373,0.9388,0.9389,0.9601,
0.9602,0.9694,0.9721,0.9723,0.9747,0.9782,0.9833,0.9912,0.9932,
Overall p-value after applying KStest on 269 p-values = 0.827916
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.