RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-19_09:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.43 18.1433 0.620143
2 to 25 15.60 26.3188 0.931156
3 to 26 15.76 23.4772 0.865648
4 to 27 15.58 41.0131 0.999071
5 to 28 15.62 22.0590 0.817540
6 to 29 15.67 20.6652 0.758373
7 to 30 15.72 16.3814 0.503023
8 to 31 15.96 28.0984 0.956198
9 to 32 15.77 18.5855 0.647162
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.002900
Tough bday spacings test for dh-ranFile-2018-06-19_09:31: 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 71 88 95 82 54 31 19 7 4
(O-E)^2/E 0.0 0.3 0.1 1.0 0.1 0.2 0.1 0.1 1.1 0.0 0.0
Birthday Spacings: Sum(O-E)^2/E= 2.887, p= 0.016
RESULTS OF GCD FOR dh-ranFile-2018-06-19_09:31
Euclid's algorithm:
p-value, steps to gcd: 0.218642
p-value, dist. of gcd's: 0.073080
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-19_09:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.734 0.660 0.205 0.504 0.505 0.963 0.246 0.344
Bits 8 to 15---> 0.697 0.770 0.971 0.176 0.763 0.940 0.467 0.292
Bits 16 to 23---> 0.791 0.363 0.391 0.154 0.157 0.966 0.938 0.770
Bits 24 to 31---> 0.191 0.625 0.311 0.615 0.398 0.456 0.958 0.288
KS test for the above 32 p values: 0.699
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-19_09:31,
p-values for 5 runs: 0.3736, 0.5037, 0.9249, 0.9554, 0.2748
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-19_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 212 211.4 0.002 0.002
r= 29 5193 5134.0 0.678 0.679
r= 30 23132 23103.0 0.036 0.716
r= 31 11463 11551.5 0.678 1.394
chi-square = 1.394 with df = 3; p-value = 0.293
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-19_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 212 211.4 0.002 0.002
r= 30 5023 5134.0 2.400 2.402
r= 31 23253 23103.0 0.973 3.375
r= 32 11512 11551.5 0.135 3.510
chi-square = 3.510 with df = 3; p-value = 0.681
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-19_09:31
b-rank test for bits 1 to 8, p=0.28650
b-rank test for bits 2 to 9, p=0.32893
b-rank test for bits 3 to 10, p=0.78130
b-rank test for bits 4 to 11, p=0.91884
b-rank test for bits 5 to 12, p=0.05030
b-rank test for bits 6 to 13, p=0.68752
b-rank test for bits 7 to 14, p=0.37675
b-rank test for bits 8 to 15, p=0.09472
b-rank test for bits 9 to 16, p=0.75700
b-rank test for bits 10 to 17, p=0.33251
b-rank test for bits 11 to 18, p=0.31263
b-rank test for bits 12 to 19, p=0.91200
b-rank test for bits 13 to 20, p=0.05362
b-rank test for bits 14 to 21, p=0.04861
b-rank test for bits 15 to 22, p=0.33980
b-rank test for bits 16 to 23, p=0.51795
b-rank test for bits 17 to 24, p=0.07689
b-rank test for bits 18 to 25, p=0.23247
b-rank test for bits 19 to 26, p=0.35107
b-rank test for bits 20 to 27, p=0.14457
b-rank test for bits 21 to 28, p=0.12280
b-rank test for bits 22 to 29, p=0.87615
b-rank test for bits 23 to 30, p=0.51921
b-rank test for bits 24 to 31, p=0.02281
b-rank test for bits 25 to 32, p=0.12576
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 = 0.026912
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-19_09:31
(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 141880 -0.07 0.472683
2 141239 -1.57 0.058652
3 141325 -1.37 0.086086
4 142184 0.64 0.739483
5 141803 -0.25 0.401899
6 141205 -1.65 0.049920
7 142101 0.45 0.672861
8 142104 0.45 0.675387
9 141134 -1.81 0.035030
10 141884 -0.06 0.476404
11 141828 -0.19 0.424645
12 141979 0.16 0.564654
13 141629 -0.65 0.256241
14 141618 -0.68 0.248038
15 142299 0.91 0.818706
16 141899 -0.02 0.490372
17 141940 0.07 0.528563
18 141076 -1.95 0.025765
19 142087 0.42 0.660972
20 142108 0.46 0.678741
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-19_09:31
Bits used No. missing words z-score p-value
23 to 32 141920 0.0368 0.514675
22 to 31 141651 -0.8908 0.186520
21 to 30 142029 0.4127 0.660070
20 to 29 141953 0.1506 0.559849
19 to 28 141348 -1.9356 0.026457
18 to 27 141507 -1.3873 0.082668
17 to 26 141686 -0.7701 0.220619
16 to 25 141748 -0.5563 0.288999
15 to 24 142092 0.6299 0.735619
14 to 23 142364 1.5678 0.941539
13 to 22 141493 -1.4356 0.075555
12 to 21 141811 -0.3391 0.367279
11 to 20 141689 -0.7598 0.223699
10 to 19 141850 -0.2046 0.418948
9 to 18 142496 2.0230 0.978463
8 to 17 142296 1.3333 0.908791
7 to 16 142235 1.1230 0.869281
6 to 15 142426 1.7816 0.962594
5 to 14 141612 -1.0253 0.152617
4 to 13 141663 -0.8494 0.197826
3 to 12 141792 -0.4046 0.342891
2 to 11 141404 -1.7425 0.040709
1 to 10 142159 0.8609 0.805362
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-19_09:31
Bits used No. missing words z-score p-value
28 to 32 141583 -1.1062 0.134319
27 to 31 142069 0.5413 0.705834
26 to 30 141964 0.1853 0.573512
25 to 29 142094 0.6260 0.734343
24 to 28 141305 -2.0486 0.020252
23 to 27 141448 -1.5638 0.058929
22 to 26 141738 -0.5808 0.280695
21 to 25 141429 -1.6282 0.051737
20 to 24 142159 0.8463 0.801318
19 to 23 141642 -0.9062 0.182414
18 to 22 142226 1.0735 0.858467
17 to 21 141837 -0.2452 0.403156
16 to 20 141689 -0.7469 0.227568
15 to 19 142045 0.4599 0.677205
14 to 18 142218 1.0463 0.852298
13 to 17 141835 -0.2520 0.400534
12 to 16 141800 -0.3706 0.355464
11 to 15 141602 -1.0418 0.148753
10 to 14 141963 0.1819 0.572182
9 to 13 141262 -2.1943 0.014106
8 to 12 141590 -1.0825 0.139521
7 to 11 142018 0.3684 0.643702
6 to 10 141925 0.0531 0.521181
5 to 9 142268 1.2158 0.887975
4 to 8 141649 -0.8825 0.188760
3 to 7 141962 0.1785 0.570852
2 to 6 141605 -1.0316 0.151123
1 to 5 141407 -1.7028 0.044301
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-19_09:31
Bits used No. missing words z-score p-value
31 to 32 141997 0.2586 0.602033
30 to 31 142202 0.8633 0.806023
29 to 30 141863 -0.1367 0.445647
28 to 29 141627 -0.8328 0.202470
27 to 28 141859 -0.1485 0.440988
26 to 27 141564 -1.0187 0.154179
25 to 26 142153 0.7188 0.763865
24 to 25 142561 1.9223 0.972718
23 to 24 141220 -2.0334 0.021005
22 to 23 141842 -0.1986 0.421283
21 to 22 141628 -0.8299 0.203303
20 to 21 141724 -0.5467 0.292294
19 to 20 142001 0.2704 0.606579
18 to 19 141722 -0.5526 0.290270
17 to 18 141959 0.1465 0.558244
16 to 17 142059 0.4415 0.670576
15 to 16 141721 -0.5555 0.289261
14 to 15 141818 -0.2694 0.393807
13 to 14 142141 0.6834 0.752821
12 to 13 141565 -1.0157 0.154881
11 to 12 142020 0.3265 0.627962
10 to 11 142281 1.0964 0.863542
9 to 10 141755 -0.4553 0.324464
8 to 9 142100 0.5624 0.713095
7 to 8 142221 0.9194 0.821052
6 to 7 141874 -0.1042 0.458498
5 to 6 141740 -0.4995 0.308714
4 to 5 141557 -1.0393 0.149328
3 to 4 141831 -0.2311 0.408633
2 to 3 141846 -0.1868 0.425903
1 to 2 141902 -0.0216 0.491375
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-19_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2564.33 0.910 0.818521
Test results for specific bytes for dh-ranFile-2018-06-19_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2439.45 -0.856 0.195930
2 to 9 2516.88 0.239 0.594330
3 to 10 2428.69 -1.008 0.156616
4 to 11 2525.27 0.357 0.639585
5 to 12 2532.38 0.458 0.676514
6 to 13 2536.57 0.517 0.697490
7 to 14 2553.97 0.763 0.777338
8 to 15 2550.20 0.710 0.761113
9 to 16 2354.44 -2.058 0.019772
10 to 17 2583.74 1.184 0.881845
11 to 18 2406.68 -1.320 0.093470
12 to 19 2610.31 1.560 0.940630
13 to 20 2585.38 1.207 0.886365
14 to 21 2464.52 -0.502 0.307902
15 to 22 2433.18 -0.945 0.172350
16 to 23 2552.58 0.744 0.771441
17 to 24 2494.23 -0.082 0.467470
18 to 25 2419.23 -1.142 0.126665
19 to 26 2494.04 -0.084 0.466410
20 to 27 2379.24 -1.708 0.043839
21 to 28 2403.48 -1.365 0.086127
22 to 29 2618.31 1.673 0.952856
23 to 30 2601.84 1.440 0.925105
24 to 31 2505.89 0.083 0.533174
25 to 32 2447.44 -0.743 0.228627
CDPARK for dh-ranFile-2018-06-19_09:31: 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
3526 0.1370 0.554479
3553 1.3699 0.914635
3509 -0.6393 0.261324
3512 -0.5023 0.307734
3510 -0.5936 0.276387
3528 0.2283 0.590298
3563 1.8265 0.966111
3510 -0.5936 0.276387
3512 -0.5023 0.307734
3554 1.4155 0.921543
Square side=100, avg. no. parked=3527.70 sample std.=20.12
p-value of the KSTEST for those 10 p-values: 0.414823
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-19_09:31
0.0870,0.1448,0.4389,0.6864,0.5520,0.9802,0.9601,0.4614,0.1978,0.4150,
The KS test for those 10 p-values: 0.802688
The 3DSPHERES test for dh-ranFile-2018-06-19_09:31
sample no r^3 equiv. uni.
1 7.166 0.212471
2 50.496 0.814220
3 14.048 0.373915
4 60.090 0.865072
5 31.453 0.649515
6 1.050 0.034392
7 18.148 0.453892
8 31.430 0.649240
9 22.449 0.526829
10 89.525 0.949418
11 29.355 0.624124
12 6.631 0.198321
13 2.665 0.085006
14 49.334 0.806886
15 5.119 0.156863
16 31.438 0.649338
17 15.673 0.406933
18 0.624 0.020575
19 0.256 0.008484
20 137.013 0.989612
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.649845
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-19_09:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
2.0 -0.3 -1.6 2.1 0.3 0.1
0.8 -0.6 1.0 -0.8 -0.8 -0.5
-2.1 -0.1 0.4 0.9 0.7 -1.2
0.1 0.7 0.1 1.1 0.4 -1.1
0.2 -0.4 -1.0 0.7 1.4 0.5
0.0 1.6 -0.5 -0.1 -0.2 0.1
1.0 -1.3 -1.2 0.4 0.1 0.0
-1.1
Chi-square with 42 degrees of freedom:37.262892
z-score=-0.516861, p-value=0.321268
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-19_09:31
Test no p-value
1 0.038574
2 0.199651
3 0.878201
4 0.168186
5 0.012724
6 0.016074
7 0.436216
8 0.027390
9 0.008958
10 0.048601
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000017
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-19_09:31:
(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 66622 0.03 66645 0.01
3 25000.00 25156 0.97 24941 0.14
4 6666.67 6630 0.20 6714 0.34
5 1388.89 1345 1.39 1408 0.26
6 238.10 200 6.10 259 1.84
7 34.72 39 0.53 29 0.94
8 4.96 7 0.84 3 0.77
p=0.87760 p=0.36352
Number of rngs required: 690417, p-value: 0.992
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-19_09:31
No. of wins: Observed Expected
98826 98585.9
z-score= 1.074, pvalue=0.85860
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66621 66666.7 0.031 0.031
2 37597 37654.3 0.087 0.119
3 26892 26954.7 0.146 0.265
4 19469 19313.5 1.253 1.517
5 13927 13851.4 0.412 1.930
6 9781 9943.5 2.657 4.587
7 7091 7145.0 0.409 4.995
8 5126 5139.1 0.033 5.028
9 3669 3699.9 0.257 5.286
10 2638 2666.3 0.300 5.586
11 1944 1923.3 0.222 5.808
12 1451 1388.7 2.791 8.599
13 1011 1003.7 0.053 8.652
14 764 726.1 1.974 10.626
15 547 525.8 0.852 11.478
16 400 381.2 0.932 12.410
17 303 276.5 2.532 14.942
18 212 200.8 0.621 15.563
19 149 146.0 0.062 15.626
20 116 106.2 0.901 16.527
21 292 287.1 0.083 16.610
Chisq= 16.61 for 20 degrees of freedom, p= 0.32188
SUMMARY of craptest
p-value for no. of wins: 0.858600
p-value for throws/game: 0.321882
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-19_09:31
No. of wins: Observed Expected
98519 98585.9
z-score=-0.299, pvalue=0.38246
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67122 66666.7 3.110 3.110
2 37769 37654.3 0.349 3.459
3 27003 26954.7 0.086 3.546
4 19083 19313.5 2.750 6.296
5 13625 13851.4 3.701 9.997
6 9961 9943.5 0.031 10.027
7 7068 7145.0 0.830 10.858
8 4959 5139.1 6.310 17.168
9 3671 3699.9 0.225 17.393
10 2684 2666.3 0.118 17.510
11 1863 1923.3 1.892 19.403
12 1417 1388.7 0.575 19.978
13 1008 1003.7 0.018 19.996
14 760 726.1 1.579 21.575
15 521 525.8 0.044 21.619
16 415 381.2 3.006 24.625
17 292 276.5 0.864 25.490
18 211 200.8 0.515 26.005
19 137 146.0 0.553 26.558
20 118 106.2 1.308 27.865
21 313 287.1 2.334 30.199
Chisq= 30.20 for 20 degrees of freedom, p= 0.93331
SUMMARY of craptest
p-value for no. of wins: 0.382458
p-value for throws/game: 0.933308
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0000,0.0029,0.0085,0.0090,0.0127,0.0141,0.0160,0.0161,0.0198,0.0203,
0.0206,0.0210,0.0228,0.0258,0.0265,0.0269,0.0274,0.0344,0.0350,0.0386,
0.0407,0.0438,0.0443,0.0486,0.0486,0.0499,0.0503,0.0517,0.0536,0.0587,
0.0589,0.0731,0.0756,0.0769,0.0827,0.0850,0.0861,0.0861,0.0870,0.0935,
0.0947,0.1228,0.1258,0.1267,0.1343,0.1395,0.1446,0.1448,0.1488,0.1493,
0.1511,0.1526,0.1542,0.1543,0.1549,0.1566,0.1567,0.1569,0.1682,0.1723,
0.1756,0.1824,0.1865,0.1888,0.1910,0.1959,0.1978,0.1978,0.1983,0.1997,
0.2025,0.2033,0.2047,0.2125,0.2186,0.2206,0.2237,0.2276,0.2286,0.2325,
0.2456,0.2480,0.2562,0.2613,0.2748,0.2764,0.2764,0.2807,0.2865,0.2878,
0.2890,0.2893,0.2903,0.2921,0.2923,0.2931,0.3077,0.3077,0.3079,0.3087,
0.3110,0.3126,0.3213,0.3219,0.3245,0.3289,0.3325,0.3398,0.3429,0.3438,
0.3511,0.3555,0.3634,0.3635,0.3673,0.3736,0.3739,0.3767,0.3825,0.3907,
0.3938,0.3984,0.4005,0.4019,0.4032,0.4069,0.4086,0.4148,0.4150,0.4189,
0.4213,0.4246,0.4259,0.4362,0.4389,0.4410,0.4456,0.4539,0.4563,0.4585,
0.4614,0.4664,0.4665,0.4675,0.4727,0.4764,0.4904,0.4914,0.5030,0.5037,
0.5043,0.5053,0.5147,0.5179,0.5192,0.5212,0.5268,0.5286,0.5332,0.5520,
0.5545,0.5582,0.5598,0.5647,0.5709,0.5722,0.5735,0.5903,0.5943,0.6020,
0.6066,0.6151,0.6201,0.6241,0.6247,0.6280,0.6396,0.6437,0.6472,0.6492,
0.6493,0.6495,0.6498,0.6601,0.6601,0.6610,0.6706,0.6729,0.6754,0.6765,
0.6772,0.6787,0.6806,0.6864,0.6875,0.6966,0.6975,0.6994,0.7058,0.7131,
0.7336,0.7343,0.7356,0.7395,0.7528,0.7570,0.7584,0.7611,0.7626,0.7639,
0.7696,0.7701,0.7714,0.7773,0.7813,0.7911,0.8013,0.8027,0.8054,0.8060,
0.8069,0.8142,0.8175,0.8185,0.8187,0.8211,0.8523,0.8585,0.8586,0.8635,
0.8651,0.8656,0.8693,0.8762,0.8776,0.8782,0.8818,0.8864,0.8880,0.9088,
0.9120,0.9146,0.9188,0.9215,0.9249,0.9251,0.9312,0.9333,0.9376,0.9401,
0.9406,0.9415,0.9494,0.9529,0.9554,0.9562,0.9576,0.9601,0.9626,0.9628,
0.9656,0.9661,0.9712,0.9727,0.9785,0.9802,0.9896,0.9917,0.9991,
Overall p-value after applying KStest on 269 p-values = 0.031161
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.