RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-25_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 15.76 32.7598 0.987912
2 to 25 15.74 22.6533 0.839118
3 to 26 15.78 28.2929 0.958370
4 to 27 15.55 26.3624 0.931894
5 to 28 15.86 16.1944 0.489903
6 to 29 15.69 25.1714 0.909061
7 to 30 15.75 13.3454 0.287226
8 to 31 15.98 21.9555 0.813563
9 to 32 15.59 18.9469 0.668412
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.005627
Tough bday spacings test for dh-ranFile-2018-06-25_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 16 36 71 93 91 78 68 25 9 6 7
(O-E)^2/E 5.1 0.0 0.1 0.2 0.5 0.0 4.9 0.8 2.3 0.1 2.1
Birthday Spacings: Sum(O-E)^2/E= 15.994, p= 0.900
RESULTS OF GCD FOR dh-ranFile-2018-06-25_08:31
Euclid's algorithm:
p-value, steps to gcd: 0.225203
p-value, dist. of gcd's: 0.298625
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-25_08:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.548 0.391 0.230 0.762 0.436 0.463 0.407 0.835
Bits 8 to 15---> 0.265 0.410 0.484 0.670 0.647 0.643 0.880 0.760
Bits 16 to 23---> 0.563 0.436 0.941 0.386 0.574 0.186 0.174 0.449
Bits 24 to 31---> 0.405 0.356 0.647 0.507 0.497 0.228 0.794 0.305
KS test for the above 32 p values: 0.900
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-25_08:31,
p-values for 5 runs: 0.9689, 0.8388, 0.1838, 0.4658, 0.0285
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-25_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 184 211.4 3.556 3.556
r= 29 5138 5134.0 0.003 3.559
r= 30 23153 23103.0 0.108 3.667
r= 31 11525 11551.5 0.061 3.728
chi-square = 3.728 with df = 3; p-value = 0.708
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-25_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 215 211.4 0.061 0.061
r= 30 5227 5134.0 1.684 1.745
r= 31 22968 23103.0 0.789 2.534
r= 32 11590 11551.5 0.128 2.663
chi-square = 2.663 with df = 3; p-value = 0.553
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-25_08:31
b-rank test for bits 1 to 8, p=0.38856
b-rank test for bits 2 to 9, p=0.75553
b-rank test for bits 3 to 10, p=0.71230
b-rank test for bits 4 to 11, p=0.80066
b-rank test for bits 5 to 12, p=0.72390
b-rank test for bits 6 to 13, p=0.58592
b-rank test for bits 7 to 14, p=0.47383
b-rank test for bits 8 to 15, p=0.13078
b-rank test for bits 9 to 16, p=0.58976
b-rank test for bits 10 to 17, p=0.18659
b-rank test for bits 11 to 18, p=0.01202
b-rank test for bits 12 to 19, p=0.02162
b-rank test for bits 13 to 20, p=0.71890
b-rank test for bits 14 to 21, p=0.16615
b-rank test for bits 15 to 22, p=0.89643
b-rank test for bits 16 to 23, p=0.32269
b-rank test for bits 17 to 24, p=0.66852
b-rank test for bits 18 to 25, p=0.29692
b-rank test for bits 19 to 26, p=0.18751
b-rank test for bits 20 to 27, p=0.05075
b-rank test for bits 21 to 28, p=0.28975
b-rank test for bits 22 to 29, p=0.59586
b-rank test for bits 23 to 30, p=0.76055
b-rank test for bits 24 to 31, p=0.87102
b-rank test for bits 25 to 32, p=0.37391
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 = 0.671971
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-25_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 142298 0.91 0.818089
2 141492 -0.98 0.164763
3 141502 -0.95 0.170623
4 141878 -0.07 0.470823
5 141163 -1.74 0.040600
6 141805 -0.24 0.403708
7 141942 0.08 0.530422
8 143295 3.24 0.999397
9 141811 -0.23 0.409146
10 141905 -0.01 0.495964
11 142717 1.89 0.970425
12 141762 -0.34 0.365337
13 141678 -0.54 0.294429
14 142336 1.00 0.840592
15 141199 -1.66 0.048492
16 142612 1.64 0.949679
17 141773 -0.32 0.375042
18 141114 -1.86 0.031567
19 141944 0.08 0.532281
20 141203 -1.65 0.049440
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-25_08:31
Bits used No. missing words z-score p-value
23 to 32 141880 -0.1011 0.459721
22 to 31 141840 -0.2391 0.405526
21 to 30 141779 -0.4494 0.326567
20 to 29 141876 -0.1149 0.454250
19 to 28 141937 0.0954 0.538007
18 to 27 141918 0.0299 0.511925
17 to 26 141546 -1.2529 0.105128
16 to 25 142070 0.5540 0.710222
15 to 24 141599 -1.0701 0.142286
14 to 23 142105 0.6747 0.750075
13 to 22 141591 -1.0977 0.136170
12 to 21 141904 -0.0184 0.492668
11 to 20 141757 -0.5253 0.299696
10 to 19 141559 -1.2080 0.113517
9 to 18 141911 0.0058 0.502297
8 to 17 141596 -1.0804 0.139971
7 to 16 141685 -0.7736 0.219598
6 to 15 142191 0.9713 0.834295
5 to 14 141764 -0.5011 0.308137
4 to 13 141621 -0.9942 0.160053
3 to 12 141928 0.0644 0.525666
2 to 11 141463 -1.5391 0.061894
1 to 10 141682 -0.7839 0.216550
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-25_08:31
Bits used No. missing words z-score p-value
28 to 32 142075 0.5616 0.712803
27 to 31 141643 -0.9028 0.183312
26 to 30 142418 1.7243 0.957674
25 to 29 141932 0.0768 0.530628
24 to 28 141963 0.1819 0.572182
23 to 27 142053 0.4870 0.686877
22 to 26 141861 -0.1638 0.434932
21 to 25 141844 -0.2215 0.412368
20 to 24 141918 0.0294 0.511723
19 to 23 141699 -0.7130 0.237928
18 to 22 141687 -0.7537 0.225526
17 to 21 142252 1.1616 0.877300
16 to 20 141748 -0.5469 0.292230
15 to 19 141256 -2.2147 0.013391
14 to 18 142360 1.5277 0.936706
13 to 17 141976 0.2260 0.589399
12 to 16 141724 -0.6282 0.264924
11 to 15 141878 -0.1062 0.457711
10 to 14 142293 1.3006 0.903298
9 to 13 141485 -1.4384 0.075159
8 to 12 141748 -0.5469 0.292230
7 to 11 142269 1.2192 0.888620
6 to 10 142379 1.5921 0.944319
5 to 9 141908 -0.0045 0.498201
4 to 8 141712 -0.6689 0.251775
3 to 7 141970 0.2057 0.581472
2 to 6 141696 -0.7232 0.234793
1 to 5 142109 0.6768 0.750749
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-25_08:31
Bits used No. missing words z-score p-value
31 to 32 142356 1.3176 0.906183
30 to 31 142219 0.9135 0.819505
29 to 30 141357 -1.6293 0.051626
28 to 29 142285 1.1082 0.866106
27 to 28 142117 0.6126 0.729928
26 to 27 141976 0.1967 0.577956
25 to 26 141436 -1.3963 0.081319
24 to 25 141601 -0.9095 0.181536
23 to 24 142104 0.5742 0.717100
22 to 23 141181 -2.1485 0.015838
21 to 22 141903 -0.0187 0.492551
20 to 21 141972 0.1849 0.573333
19 to 20 141655 -0.7502 0.226556
18 to 19 141604 -0.9007 0.183880
17 to 18 141511 -1.1750 0.119994
16 to 17 142447 1.5860 0.943636
15 to 16 142232 0.9518 0.829408
14 to 15 141342 -1.6735 0.047111
13 to 14 141749 -0.4729 0.318125
12 to 13 142104 0.5742 0.717100
11 to 12 141713 -0.5791 0.281246
10 to 11 141647 -0.7738 0.219514
9 to 10 142161 0.7424 0.771074
8 to 9 141930 0.0610 0.524310
7 to 8 141943 0.0993 0.539559
6 to 7 141596 -0.9243 0.177671
5 to 6 141536 -1.1013 0.135390
4 to 5 141883 -0.0777 0.469045
3 to 4 141581 -0.9685 0.166391
2 to 3 141375 -1.5762 0.057490
1 to 2 141715 -0.5732 0.283240
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-25_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2465.33 -0.490 0.311965
Test results for specific bytes for dh-ranFile-2018-06-25_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2450.33 -0.702 0.241218
2 to 9 2510.54 0.149 0.559246
3 to 10 2444.54 -0.784 0.216406
4 to 11 2438.41 -0.871 0.191854
5 to 12 2511.83 0.167 0.566448
6 to 13 2453.26 -0.661 0.254291
7 to 14 2423.46 -1.082 0.139524
8 to 15 2509.38 0.133 0.552783
9 to 16 2459.69 -0.570 0.284313
10 to 17 2652.31 2.154 0.984381
11 to 18 2551.22 0.724 0.765574
12 to 19 2421.24 -1.114 0.132668
13 to 20 2555.29 0.782 0.782865
14 to 21 2459.26 -0.576 0.282246
15 to 22 2504.19 0.059 0.523628
16 to 23 2557.83 0.818 0.793264
17 to 24 2497.09 -0.041 0.483584
18 to 25 2452.51 -0.672 0.250903
19 to 26 2516.78 0.237 0.593766
20 to 27 2421.76 -1.106 0.134256
21 to 28 2504.12 0.058 0.523216
22 to 29 2464.13 -0.507 0.305981
23 to 30 2484.25 -0.223 0.411878
24 to 31 2527.86 0.394 0.653225
25 to 32 2373.09 -1.795 0.036345
CDPARK for dh-ranFile-2018-06-25_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
3505 -0.8219 0.205562
3542 0.8676 0.807188
3518 -0.2283 0.409702
3557 1.5525 0.939730
3532 0.4110 0.659449
3495 -1.2785 0.100530
3571 2.1918 0.985802
3518 -0.2283 0.409702
3558 1.5982 0.944998
3548 1.1416 0.873180
Square side=100, avg. no. parked=3534.40 sample std.=23.69
p-value of the KSTEST for those 10 p-values: 0.142585
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-25_08:31
0.8318,0.4777,0.6707,0.7862,0.6967,0.6074,0.3289,0.3757,0.6370,0.9301,
The KS test for those 10 p-values: 0.171671
The 3DSPHERES test for dh-ranFile-2018-06-25_08:31
sample no r^3 equiv. uni.
1 27.707 0.602898
2 41.272 0.747344
3 8.601 0.249252
4 14.199 0.377063
5 1.708 0.055340
6 34.174 0.679909
7 12.311 0.336599
8 23.125 0.537374
9 13.607 0.364640
10 35.659 0.695363
11 6.030 0.182083
12 51.162 0.818301
13 81.941 0.934870
14 100.247 0.964618
15 17.757 0.446721
16 52.292 0.825018
17 20.094 0.488188
18 62.617 0.875970
19 82.622 0.936332
20 27.268 0.597051
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.350225
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-25_08:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
2.7 -1.2 0.3 0.5 -0.2 0.2
-0.1 0.1 -0.1 -0.9 -0.1 -0.2
0.7 -1.2 1.9 0.1 0.6 1.3
-1.5 0.3 0.8 0.1 0.1 -1.3
1.8 -1.9 0.0 -0.7 -2.9 -1.5
-0.4 -0.3 -0.5 0.2 0.5 -1.2
0.3 1.5 0.9 -1.3 0.9 1.0
0.8
Chi-square with 42 degrees of freedom:49.567785
z-score=0.825713, p-value=0.803045
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-25_08:31
Test no p-value
1 0.457662
2 0.010286
3 0.464051
4 0.461869
5 0.558663
6 0.149500
7 0.001364
8 0.341328
9 0.063705
10 0.016133
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.002324
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-25_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 66811 0.31 66488 0.48
3 25000.00 24809 1.46 25230 2.12
4 6666.67 6713 0.32 6635 0.15
5 1388.89 1389 0.00 1385 0.01
6 238.10 238 0.00 221 1.23
7 34.72 36 0.05 34 0.01
8 4.96 3 0.77 6 0.22
p=0.18062 p=0.35261
Number of rngs required: 688555, p-value: 0.569
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-25_08:31
No. of wins: Observed Expected
98568 98585.9
z-score=-0.080, pvalue=0.46817
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66828 66666.7 0.390 0.390
2 37463 37654.3 0.972 1.363
3 27184 26954.7 1.950 3.313
4 19139 19313.5 1.576 4.889
5 13863 13851.4 0.010 4.898
6 9844 9943.5 0.997 5.895
7 7204 7145.0 0.487 6.382
8 5064 5139.1 1.097 7.478
9 3802 3699.9 2.819 10.298
10 2634 2666.3 0.391 10.689
11 2008 1923.3 3.727 14.416
12 1296 1388.7 6.193 20.610
13 987 1003.7 0.278 20.888
14 707 726.1 0.505 21.392
15 555 525.8 1.618 23.010
16 394 381.2 0.433 23.443
17 284 276.5 0.201 23.644
18 204 200.8 0.050 23.694
19 130 146.0 1.750 25.445
20 118 106.2 1.308 26.752
21 292 287.1 0.083 26.835
Chisq= 26.84 for 20 degrees of freedom, p= 0.86004
SUMMARY of craptest
p-value for no. of wins: 0.468169
p-value for throws/game: 0.860039
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-25_08:31
No. of wins: Observed Expected
98328 98585.9
z-score=-1.153, pvalue=0.12439
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66596 66666.7 0.075 0.075
2 37491 37654.3 0.708 0.783
3 27103 26954.7 0.816 1.599
4 19153 19313.5 1.333 2.932
5 13972 13851.4 1.050 3.982
6 10031 9943.5 0.769 4.751
7 7220 7145.0 0.787 5.538
8 5229 5139.1 1.574 7.111
9 3713 3699.9 0.047 7.158
10 2602 2666.3 1.551 8.708
11 1897 1923.3 0.360 9.069
12 1331 1388.7 2.401 11.470
13 1016 1003.7 0.150 11.620
14 717 726.1 0.115 11.735
15 510 525.8 0.477 12.212
16 383 381.2 0.009 12.221
17 257 276.5 1.381 13.601
18 220 200.8 1.830 15.431
19 141 146.0 0.170 15.602
20 111 106.2 0.216 15.817
21 307 287.1 1.377 17.194
Chisq= 17.19 for 20 degrees of freedom, p= 0.35968
SUMMARY of craptest
p-value for no. of wins: 0.124395
p-value for throws/game: 0.359683
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0014,0.0023,0.0056,0.0103,0.0120,0.0134,0.0158,0.0161,0.0216,0.0285,
0.0316,0.0363,0.0406,0.0471,0.0485,0.0494,0.0507,0.0516,0.0553,0.0575,
0.0619,0.0637,0.0752,0.0813,0.1005,0.1051,0.1135,0.1200,0.1244,0.1308,
0.1327,0.1343,0.1354,0.1362,0.1395,0.1400,0.1423,0.1426,0.1495,0.1601,
0.1648,0.1662,0.1664,0.1706,0.1717,0.1737,0.1777,0.1806,0.1815,0.1821,
0.1833,0.1838,0.1839,0.1856,0.1866,0.1875,0.1919,0.2056,0.2164,0.2166,
0.2195,0.2196,0.2252,0.2255,0.2266,0.2283,0.2296,0.2348,0.2379,0.2412,
0.2493,0.2509,0.2518,0.2543,0.2649,0.2649,0.2812,0.2822,0.2832,0.2843,
0.2872,0.2897,0.2922,0.2922,0.2944,0.2969,0.2986,0.2997,0.3052,0.3060,
0.3081,0.3120,0.3181,0.3227,0.3266,0.3289,0.3366,0.3413,0.3502,0.3526,
0.3559,0.3597,0.3646,0.3653,0.3739,0.3750,0.3757,0.3771,0.3862,0.3886,
0.3907,0.4037,0.4053,0.4055,0.4071,0.4091,0.4097,0.4097,0.4103,0.4119,
0.4124,0.4349,0.4365,0.4365,0.4467,0.4486,0.4542,0.4577,0.4577,0.4597,
0.4619,0.4629,0.4641,0.4658,0.4682,0.4690,0.4708,0.4738,0.4777,0.4835,
0.4836,0.4882,0.4899,0.4926,0.4927,0.4960,0.4966,0.4982,0.5023,0.5072,
0.5117,0.5119,0.5232,0.5236,0.5243,0.5257,0.5304,0.5306,0.5323,0.5374,
0.5380,0.5396,0.5481,0.5528,0.5534,0.5587,0.5592,0.5629,0.5664,0.5694,
0.5722,0.5733,0.5737,0.5780,0.5815,0.5859,0.5894,0.5898,0.5938,0.5959,
0.5971,0.6029,0.6074,0.6370,0.6425,0.6468,0.6474,0.6532,0.6594,0.6684,
0.6685,0.6705,0.6707,0.6720,0.6799,0.6869,0.6954,0.6967,0.7076,0.7102,
0.7123,0.7128,0.7171,0.7171,0.7189,0.7239,0.7299,0.7473,0.7501,0.7507,
0.7555,0.7603,0.7605,0.7625,0.7656,0.7711,0.7829,0.7862,0.7933,0.7940,
0.8007,0.8030,0.8072,0.8136,0.8181,0.8183,0.8195,0.8250,0.8294,0.8318,
0.8343,0.8352,0.8388,0.8391,0.8406,0.8600,0.8661,0.8710,0.8732,0.8760,
0.8773,0.8800,0.8886,0.8964,0.8998,0.9002,0.9033,0.9062,0.9091,0.9301,
0.9319,0.9349,0.9363,0.9367,0.9397,0.9405,0.9436,0.9443,0.9450,0.9497,
0.9577,0.9584,0.9646,0.9689,0.9704,0.9844,0.9858,0.9879,0.9994,
Overall p-value after applying KStest on 269 p-values = 0.263978
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.