RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-12_04:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.98 13.3017 0.284236
2 to 25 15.44 21.9370 0.812846
3 to 26 15.72 17.4103 0.573079
4 to 27 15.61 23.9390 0.878899
5 to 28 15.98 13.7414 0.314685
6 to 29 15.90 19.0455 0.674073
7 to 30 15.74 10.6103 0.123907
8 to 31 15.62 18.2041 0.623927
9 to 32 15.82 11.8860 0.193006
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.970067
Tough bday spacings test for dh-ranFile-2018-07-12_04:31: 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 45 74 83 100 94 49 21 16 5 8
(O-E)^2/E 1.9 1.9 0.0 2.2 0.1 3.2 0.2 2.6 0.1 0.4 3.8
Birthday Spacings: Sum(O-E)^2/E= 16.337, p= 0.910
RESULTS OF GCD FOR dh-ranFile-2018-07-12_04:31
Euclid's algorithm:
p-value, steps to gcd: 0.674103
p-value, dist. of gcd's: 0.683507
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-12_04:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.900 0.743 0.910 0.218 0.632 0.533 0.225 0.716
Bits 8 to 15---> 0.351 0.861 0.512 0.778 0.480 0.841 0.040 0.290
Bits 16 to 23---> 0.296 0.987 0.972 0.938 0.430 0.308 0.029 0.536
Bits 24 to 31---> 0.699 0.741 0.018 0.450 0.328 0.625 0.100 0.757
KS test for the above 32 p values: 0.224
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-12_04:31,
p-values for 5 runs: 0.7949, 0.6101, 0.6760, 0.4000, 0.6089
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-12_04:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 198 211.4 0.852 0.852
r= 29 5051 5134.0 1.342 2.194
r= 30 23182 23103.0 0.270 2.464
r= 31 11569 11551.5 0.026 2.490
chi-square = 2.490 with df = 3; p-value = 0.523
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-12_04:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 220 211.4 0.348 0.348
r= 30 5218 5134.0 1.374 1.722
r= 31 22921 23103.0 1.435 3.157
r= 32 11641 11551.5 0.693 3.850
chi-square = 3.850 with df = 3; p-value = 0.722
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-12_04:31
b-rank test for bits 1 to 8, p=0.51676
b-rank test for bits 2 to 9, p=0.66671
b-rank test for bits 3 to 10, p=0.83819
b-rank test for bits 4 to 11, p=0.11210
b-rank test for bits 5 to 12, p=0.30125
b-rank test for bits 6 to 13, p=0.33242
b-rank test for bits 7 to 14, p=0.22885
b-rank test for bits 8 to 15, p=0.80204
b-rank test for bits 9 to 16, p=0.10278
b-rank test for bits 10 to 17, p=0.13348
b-rank test for bits 11 to 18, p=0.67948
b-rank test for bits 12 to 19, p=0.29551
b-rank test for bits 13 to 20, p=0.84921
b-rank test for bits 14 to 21, p=0.07399
b-rank test for bits 15 to 22, p=0.01904
b-rank test for bits 16 to 23, p=0.62490
b-rank test for bits 17 to 24, p=0.48693
b-rank test for bits 18 to 25, p=0.48992
b-rank test for bits 19 to 26, p=0.48812
b-rank test for bits 20 to 27, p=0.86034
b-rank test for bits 21 to 28, p=0.90228
b-rank test for bits 22 to 29, p=0.86562
b-rank test for bits 23 to 30, p=0.90272
b-rank test for bits 24 to 31, p=0.98995
b-rank test for bits 25 to 32, p=0.35203
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 = 0.929098
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-12_04:31
(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 141881 -0.07 0.473613
2 141740 -0.40 0.346189
3 141546 -0.85 0.197968
4 141638 -0.63 0.263057
5 142236 0.76 0.777342
6 141650 -0.61 0.272287
7 141703 -0.48 0.314875
8 141753 -0.37 0.357460
9 141294 -1.44 0.075261
10 141494 -0.97 0.165924
11 141830 -0.19 0.426477
12 140984 -2.16 0.015310
13 142095 0.43 0.667786
14 141489 -0.98 0.163030
15 141983 0.17 0.568331
16 142166 0.60 0.725646
17 142759 1.99 0.976439
18 141836 -0.17 0.431981
19 142505 1.39 0.918001
20 142203 0.69 0.753689
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-12_04:31
Bits used No. missing words z-score p-value
23 to 32 142106 0.6782 0.751169
22 to 31 142048 0.4782 0.683736
21 to 30 142337 1.4747 0.929857
20 to 29 141985 0.2609 0.602927
19 to 28 142101 0.6609 0.745672
18 to 27 141818 -0.3149 0.376407
17 to 26 142241 1.1437 0.873624
16 to 25 142069 0.5506 0.709041
15 to 24 142006 0.3333 0.630563
14 to 23 142206 1.0230 0.846846
13 to 22 141623 -0.9873 0.161737
12 to 21 142277 1.2678 0.897570
11 to 20 141642 -0.9218 0.178309
10 to 19 142126 0.7471 0.772510
9 to 18 141782 -0.4391 0.330306
8 to 17 141816 -0.3218 0.373792
7 to 16 142362 1.5609 0.940730
6 to 15 142594 2.3609 0.990885
5 to 14 141963 0.1851 0.573413
4 to 13 141943 0.1161 0.546215
3 to 12 141797 -0.3873 0.349251
2 to 11 142203 1.0127 0.844388
1 to 10 141963 0.1851 0.573413
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-12_04:31
Bits used No. missing words z-score p-value
28 to 32 142230 1.0870 0.861485
27 to 31 142114 0.6938 0.756095
26 to 30 142219 1.0497 0.853079
25 to 29 141737 -0.5842 0.279553
24 to 28 142157 0.8396 0.799422
23 to 27 142064 0.5243 0.699967
22 to 26 141781 -0.4350 0.331775
21 to 25 141752 -0.5333 0.296905
20 to 24 141784 -0.4248 0.335474
19 to 23 141726 -0.6215 0.267149
18 to 22 141781 -0.4350 0.331775
17 to 21 141554 -1.2045 0.114197
16 to 20 142075 0.5616 0.712803
15 to 19 142362 1.5345 0.937544
14 to 18 141706 -0.6893 0.245332
13 to 17 142020 0.3752 0.646227
12 to 16 141908 -0.0045 0.498201
11 to 15 141685 -0.7604 0.223496
10 to 14 142248 1.1480 0.874523
9 to 13 141566 -1.1638 0.122246
8 to 12 141664 -0.8316 0.202810
7 to 11 142060 0.5107 0.695236
6 to 10 142507 2.0260 0.978618
5 to 9 141383 -1.7842 0.037198
4 to 8 142269 1.2192 0.888620
3 to 7 141883 -0.0893 0.464440
2 to 6 142092 0.6192 0.732114
1 to 5 142002 0.3141 0.623291
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-12_04:31
Bits used No. missing words z-score p-value
31 to 32 141859 -0.1485 0.440988
30 to 31 142169 0.7660 0.778158
29 to 30 142421 1.5094 0.934395
28 to 29 141665 -0.7207 0.235536
27 to 28 142525 1.8161 0.965325
26 to 27 142065 0.4592 0.676956
25 to 26 141477 -1.2753 0.101100
24 to 25 141627 -0.8328 0.202470
23 to 24 141654 -0.7532 0.225669
22 to 23 141520 -1.1485 0.125388
21 to 22 141970 0.1790 0.571018
20 to 21 142068 0.4681 0.680127
19 to 20 141672 -0.7001 0.241936
18 to 19 141427 -1.4228 0.077397
17 to 18 141885 -0.0718 0.471393
16 to 17 141907 -0.0069 0.497258
15 to 16 141965 0.1642 0.565220
14 to 15 142038 0.3796 0.647863
13 to 14 141688 -0.6529 0.256913
12 to 13 141755 -0.4553 0.324464
11 to 12 141703 -0.6086 0.271381
10 to 11 141660 -0.7355 0.231022
9 to 10 142018 0.3206 0.625728
8 to 9 141831 -0.2311 0.408633
7 to 8 141727 -0.5378 0.295342
6 to 7 141926 0.0492 0.519610
5 to 6 141814 -0.2812 0.389275
4 to 5 142055 0.4297 0.666295
3 to 4 141853 -0.1662 0.434014
2 to 3 141363 -1.6116 0.053525
1 to 2 141746 -0.4818 0.314974
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-12_04:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2426.99 -1.032 0.150923
Test results for specific bytes for dh-ranFile-2018-07-12_04:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2412.09 -1.243 0.106879
2 to 9 2441.50 -0.827 0.204046
3 to 10 2563.78 0.902 0.816479
4 to 11 2438.80 -0.865 0.193391
5 to 12 2408.39 -1.296 0.097570
6 to 13 2549.21 0.696 0.756782
7 to 14 2502.63 0.037 0.514836
8 to 15 2519.84 0.281 0.610470
9 to 16 2708.81 2.953 0.998427
10 to 17 2492.09 -0.112 0.455448
11 to 18 2438.33 -0.872 0.191583
12 to 19 2404.31 -1.353 0.087995
13 to 20 2479.38 -0.292 0.385301
14 to 21 2444.93 -0.779 0.218044
15 to 22 2426.95 -1.033 0.150787
16 to 23 2601.86 1.441 0.925142
17 to 24 2467.18 -0.464 0.321282
18 to 25 2313.68 -2.635 0.004208
19 to 26 2482.45 -0.248 0.401976
20 to 27 2406.76 -1.319 0.093645
21 to 28 2426.57 -1.038 0.149525
22 to 29 2496.53 -0.049 0.480430
23 to 30 2442.76 -0.810 0.209105
24 to 31 2591.16 1.289 0.901326
25 to 32 2527.75 0.392 0.652636
CDPARK for dh-ranFile-2018-07-12_04:31: 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
3529 0.2740 0.607947
3508 -0.6849 0.246694
3491 -1.4612 0.071982
3541 0.8219 0.794438
3525 0.0913 0.536383
3553 1.3699 0.914635
3482 -1.8721 0.030593
3541 0.8219 0.794438
3491 -1.4612 0.071982
3525 0.0913 0.536383
Square side=100, avg. no. parked=3518.60 sample std.=23.14
p-value of the KSTEST for those 10 p-values: 0.645024
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-12_04:31
0.6610,0.7674,0.8543,0.1241,0.5878,0.2311,0.8663,0.3605,0.4069,0.9993,
The KS test for those 10 p-values: 0.438718
The 3DSPHERES test for dh-ranFile-2018-07-12_04:31
sample no r^3 equiv. uni.
1 2.287 0.073398
2 83.154 0.937451
3 15.809 0.409611
4 75.167 0.918370
5 33.150 0.668784
6 62.367 0.874933
7 1.283 0.041867
8 31.474 0.649755
9 47.970 0.797901
10 6.920 0.205988
11 39.194 0.729223
12 25.904 0.578308
13 67.734 0.895419
14 17.819 0.447875
15 48.033 0.798327
16 12.271 0.335712
17 22.100 0.521293
18 0.526 0.017380
19 15.986 0.413071
20 21.508 0.511758
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.759587
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-12_04:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -0.7 -1.6 0.6 0.9 0.9
0.9 -0.2 -1.3 -0.0 -0.0 -1.2
-2.5 1.2 0.5 -0.1 0.8 0.6
1.3 -0.6 0.5 0.9 0.7 -1.6
-0.4 -1.5 0.1 -0.7 0.4 0.2
-0.0 -0.7 -1.8 1.4 -0.1 -0.7
1.4 0.8 -0.8 1.0 0.1 2.0
-0.1
Chi-square with 42 degrees of freedom:41.876583
z-score=-0.013466, p-value=0.523667
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-12_04:31
Test no p-value
1 0.030116
2 0.018752
3 0.939282
4 0.383937
5 0.700064
6 0.937873
7 0.905073
8 0.136397
9 0.725444
10 0.290582
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.399000
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-12_04:31:
(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 66854 0.53 66834 0.42
3 25000.00 24825 1.23 24915 0.29
4 6666.67 6631 0.19 6583 1.05
5 1388.89 1410 0.32 1370 0.26
6 238.10 240 0.02 253 0.93
7 34.72 33 0.09 37 0.15
8 4.96 6 0.22 7 0.84
p=0.14077 p=0.31491
Number of rngs required: 687532, p-value: 0.156
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-12_04:31
No. of wins: Observed Expected
98431 98585.9
z-score=-0.693, pvalue=0.24427
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66616 66666.7 0.039 0.039
2 37629 37654.3 0.017 0.056
3 27104 26954.7 0.827 0.882
4 19412 19313.5 0.503 1.385
5 13765 13851.4 0.539 1.924
6 9887 9943.5 0.322 2.246
7 7125 7145.0 0.056 2.302
8 5253 5139.1 2.526 4.827
9 3615 3699.9 1.947 6.774
10 2671 2666.3 0.008 6.782
11 1875 1923.3 1.214 7.997
12 1419 1388.7 0.659 8.656
13 979 1003.7 0.609 9.265
14 709 726.1 0.405 9.669
15 533 525.8 0.098 9.767
16 380 381.2 0.003 9.770
17 269 276.5 0.206 9.976
18 187 200.8 0.952 10.928
19 148 146.0 0.028 10.956
20 115 106.2 0.727 11.683
21 309 287.1 1.668 13.351
Chisq= 13.35 for 20 degrees of freedom, p= 0.13817
SUMMARY of craptest
p-value for no. of wins: 0.244275
p-value for throws/game: 0.138173
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-12_04:31
No. of wins: Observed Expected
98615 98585.9
z-score= 0.130, pvalue=0.55185
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66398 66666.7 1.083 1.083
2 37691 37654.3 0.036 1.118
3 27115 26954.7 0.953 2.071
4 19166 19313.5 1.126 3.197
5 14011 13851.4 1.838 5.036
6 10145 9943.5 4.082 9.117
7 7229 7145.0 0.987 10.104
8 4985 5139.1 4.619 14.723
9 3671 3699.9 0.225 14.949
10 2672 2666.3 0.012 14.961
11 1883 1923.3 0.846 15.806
12 1338 1388.7 1.854 17.660
13 981 1003.7 0.514 18.174
14 708 726.1 0.453 18.628
15 580 525.8 5.579 24.207
16 411 381.2 2.338 26.544
17 267 276.5 0.329 26.874
18 229 200.8 3.951 30.825
19 151 146.0 0.172 30.997
20 99 106.2 0.490 31.487
21 270 287.1 1.020 32.507
Chisq= 32.51 for 20 degrees of freedom, p= 0.96182
SUMMARY of craptest
p-value for no. of wins: 0.551850
p-value for throws/game: 0.961818
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0042,0.0153,0.0174,0.0175,0.0188,0.0190,0.0287,0.0301,0.0306,0.0372,
0.0397,0.0419,0.0535,0.0720,0.0720,0.0734,0.0740,0.0753,0.0774,0.0880,
0.0936,0.0976,0.0996,0.1011,0.1028,0.1069,0.1121,0.1142,0.1222,0.1239,
0.1241,0.1254,0.1335,0.1364,0.1382,0.1408,0.1495,0.1508,0.1509,0.1564,
0.1617,0.1630,0.1659,0.1783,0.1916,0.1930,0.1934,0.1980,0.2025,0.2028,
0.2040,0.2060,0.2091,0.2180,0.2182,0.2235,0.2236,0.2252,0.2257,0.2288,
0.2310,0.2311,0.2355,0.2419,0.2443,0.2453,0.2467,0.2569,0.2631,0.2671,
0.2714,0.2723,0.2796,0.2842,0.2901,0.2906,0.2953,0.2955,0.2962,0.2969,
0.3013,0.3080,0.3147,0.3149,0.3149,0.3150,0.3213,0.3245,0.3284,0.3303,
0.3318,0.3318,0.3324,0.3355,0.3357,0.3462,0.3493,0.3508,0.3520,0.3575,
0.3605,0.3738,0.3764,0.3839,0.3853,0.3893,0.3990,0.4000,0.4020,0.4069,
0.4086,0.4096,0.4131,0.4265,0.4302,0.4320,0.4340,0.4387,0.4410,0.4479,
0.4498,0.4554,0.4644,0.4714,0.4736,0.4801,0.4804,0.4869,0.4881,0.4899,
0.4973,0.4982,0.5116,0.5118,0.5148,0.5168,0.5196,0.5213,0.5229,0.5237,
0.5332,0.5362,0.5364,0.5364,0.5462,0.5519,0.5652,0.5683,0.5710,0.5731,
0.5734,0.5734,0.5783,0.5878,0.6029,0.6079,0.6089,0.6101,0.6105,0.6233,
0.6239,0.6249,0.6250,0.6257,0.6306,0.6318,0.6450,0.6462,0.6479,0.6498,
0.6526,0.6610,0.6663,0.6667,0.6678,0.6688,0.6741,0.6741,0.6760,0.6770,
0.6795,0.6801,0.6835,0.6837,0.6952,0.6989,0.7000,0.7001,0.7090,0.7128,
0.7157,0.7219,0.7254,0.7256,0.7292,0.7321,0.7406,0.7426,0.7457,0.7512,
0.7537,0.7561,0.7568,0.7572,0.7596,0.7674,0.7725,0.7773,0.7782,0.7783,
0.7944,0.7944,0.7949,0.7979,0.7983,0.7994,0.8020,0.8128,0.8165,0.8382,
0.8410,0.8444,0.8468,0.8492,0.8531,0.8543,0.8603,0.8612,0.8615,0.8656,
0.8663,0.8736,0.8745,0.8749,0.8789,0.8886,0.8954,0.8976,0.9003,0.9013,
0.9023,0.9027,0.9051,0.9096,0.9104,0.9146,0.9180,0.9184,0.9251,0.9291,
0.9299,0.9344,0.9375,0.9375,0.9377,0.9379,0.9393,0.9407,0.9618,0.9653,
0.9701,0.9717,0.9764,0.9786,0.9873,0.9899,0.9909,0.9984,0.9993,
Overall p-value after applying KStest on 269 p-values = 0.951410
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.