RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-15_15:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.79 10.8913 0.137843
2 to 25 16.05 16.6723 0.523227
3 to 26 16.17 14.0924 0.339450
4 to 27 15.71 7.5926 0.025500
5 to 28 16.10 18.6015 0.648120
6 to 29 15.57 18.9399 0.668009
7 to 30 15.45 25.8323 0.922430
8 to 31 15.69 20.8244 0.765756
9 to 32 15.74 15.1051 0.412089
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.992063
Tough bday spacings test for dh-ranFile-2018-06-15_15:31: 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 35 83 107 80 79 50 35 9 7 4
(O-E)^2/E 0.4 0.1 1.3 0.9 3.2 0.0 0.1 0.9 2.3 0.0 0.0
Birthday Spacings: Sum(O-E)^2/E= 9.190, p= 0.486
RESULTS OF GCD FOR dh-ranFile-2018-06-15_15:31
Euclid's algorithm:
p-value, steps to gcd: 0.036831
p-value, dist. of gcd's: 0.323028
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-15_15:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.253 0.446 0.256 0.161 0.897 0.287 0.710 0.962
Bits 8 to 15---> 0.456 0.281 0.643 0.376 0.359 0.694 0.389 0.760
Bits 16 to 23---> 0.801 0.659 0.895 0.434 0.215 0.092 0.596 0.243
Bits 24 to 31---> 0.631 0.228 0.052 0.613 0.403 0.765 0.352 0.355
KS test for the above 32 p values: 0.553
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-15_15:31,
p-values for 5 runs: 0.5491, 0.1216, 0.5791, 0.1610, 0.8908
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-15_15:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 221 211.4 0.434 0.434
r= 29 5154 5134.0 0.078 0.512
r= 30 23036 23103.0 0.195 0.707
r= 31 11589 11551.5 0.122 0.828
chi-square = 0.828 with df = 3; p-value = 0.157
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-15_15:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 207 211.4 0.092 0.092
r= 30 5228 5134.0 1.721 1.813
r= 31 23034 23103.0 0.206 2.019
r= 32 11531 11551.5 0.036 2.056
chi-square = 2.056 with df = 3; p-value = 0.439
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-15_15:31
b-rank test for bits 1 to 8, p=0.56218
b-rank test for bits 2 to 9, p=0.50247
b-rank test for bits 3 to 10, p=0.45192
b-rank test for bits 4 to 11, p=0.11423
b-rank test for bits 5 to 12, p=0.81899
b-rank test for bits 6 to 13, p=0.32921
b-rank test for bits 7 to 14, p=0.66528
b-rank test for bits 8 to 15, p=0.97743
b-rank test for bits 9 to 16, p=0.06106
b-rank test for bits 10 to 17, p=0.48739
b-rank test for bits 11 to 18, p=0.45189
b-rank test for bits 12 to 19, p=0.16995
b-rank test for bits 13 to 20, p=0.67208
b-rank test for bits 14 to 21, p=0.04517
b-rank test for bits 15 to 22, p=0.30111
b-rank test for bits 16 to 23, p=0.44021
b-rank test for bits 17 to 24, p=0.73549
b-rank test for bits 18 to 25, p=0.53490
b-rank test for bits 19 to 26, p=0.95146
b-rank test for bits 20 to 27, p=0.98062
b-rank test for bits 21 to 28, p=0.61028
b-rank test for bits 22 to 29, p=0.65735
b-rank test for bits 23 to 30, p=0.44911
b-rank test for bits 24 to 31, p=0.37864
b-rank test for bits 25 to 32, p=0.12676
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 = 0.768891
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-15_15:31
(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 141980 0.17 0.565574
2 142358 1.05 0.852749
3 142681 1.80 0.964303
4 141838 -0.17 0.433819
5 141616 -0.69 0.246561
6 141866 -0.10 0.459681
7 142649 1.73 0.958024
8 141904 -0.01 0.495032
9 141623 -0.67 0.251749
10 141588 -0.75 0.226395
11 142041 0.31 0.620822
12 142493 1.36 0.913671
13 142209 0.70 0.758087
14 142286 0.88 0.810589
15 141816 -0.22 0.413691
16 141455 -1.06 0.144227
17 142547 1.49 0.931873
18 142031 0.28 0.611900
19 142583 1.57 0.942256
20 141693 -0.51 0.306624
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-15_15:31
Bits used No. missing words z-score p-value
23 to 32 142069 0.5506 0.709041
22 to 31 142027 0.4058 0.657540
21 to 30 141756 -0.5287 0.298498
20 to 29 141483 -1.4701 0.070767
19 to 28 141508 -1.3839 0.083195
18 to 27 141765 -0.4977 0.309351
17 to 26 141974 0.2230 0.588232
16 to 25 142624 2.4644 0.993137
15 to 24 141477 -1.4908 0.068008
14 to 23 141833 -0.2632 0.396196
13 to 22 141895 -0.0494 0.480295
12 to 21 142042 0.4575 0.676338
11 to 20 141435 -1.6356 0.050960
10 to 19 141960 0.1747 0.569352
9 to 18 141639 -0.9322 0.175624
8 to 17 142153 0.8402 0.799614
7 to 16 142568 2.2713 0.988435
6 to 15 142092 0.6299 0.735619
5 to 14 141855 -0.1873 0.425695
4 to 13 141695 -0.7391 0.229933
3 to 12 141890 -0.0667 0.473428
2 to 11 142931 3.5230 0.999787
1 to 10 142649 2.5506 0.994623
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-15_15:31
Bits used No. missing words z-score p-value
28 to 32 141915 0.0192 0.507667
27 to 31 141764 -0.4926 0.311132
26 to 30 141736 -0.5876 0.278414
25 to 29 141469 -1.4926 0.067765
24 to 28 142213 1.0294 0.848352
23 to 27 141615 -0.9977 0.159205
22 to 26 142275 1.2396 0.892431
21 to 25 142130 0.7480 0.772780
20 to 24 141735 -0.5909 0.277277
19 to 23 141709 -0.6791 0.248542
18 to 22 141687 -0.7537 0.225526
17 to 21 141654 -0.8655 0.193375
16 to 20 142138 0.7752 0.780875
15 to 19 141728 -0.6147 0.269384
14 to 18 141691 -0.7401 0.229619
13 to 17 141830 -0.2689 0.393998
12 to 16 142205 1.0023 0.841894
11 to 15 141962 0.1785 0.570852
10 to 14 142105 0.6633 0.746427
9 to 13 142409 1.6938 0.954848
8 to 12 141613 -1.0045 0.157567
7 to 11 141623 -0.9706 0.165871
6 to 10 141875 -0.1164 0.453679
5 to 9 141742 -0.5672 0.285282
4 to 8 141411 -1.6893 0.045585
3 to 7 141693 -0.7333 0.231681
2 to 6 141736 -0.5876 0.278414
1 to 5 141959 0.1684 0.566855
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-15_15:31
Bits used No. missing words z-score p-value
31 to 32 141973 0.1878 0.574490
30 to 31 142213 0.8958 0.814815
29 to 30 141653 -0.7561 0.224784
28 to 29 141528 -1.1249 0.130323
27 to 28 141783 -0.3727 0.354703
26 to 27 141759 -0.4435 0.328720
25 to 26 141936 0.0787 0.531354
24 to 25 141536 -1.1013 0.135390
23 to 24 141392 -1.5260 0.063499
22 to 23 142020 0.3265 0.627962
21 to 22 142586 1.9961 0.977037
20 to 21 141389 -1.5349 0.062405
19 to 20 141339 -1.6824 0.046247
18 to 19 141945 0.1052 0.541900
17 to 18 141979 0.2055 0.581416
16 to 17 142077 0.4946 0.689559
15 to 16 141865 -0.1308 0.447980
14 to 15 141466 -1.3078 0.095478
13 to 14 141883 -0.0777 0.469045
12 to 13 141975 0.1937 0.576801
11 to 12 141621 -0.8505 0.197515
10 to 11 142244 0.9872 0.838234
9 to 10 142185 0.8132 0.791944
8 to 9 141976 0.1967 0.577956
7 to 8 141338 -1.6853 0.045962
6 to 7 141947 0.1111 0.544240
5 to 6 141689 -0.6499 0.257865
4 to 5 142076 0.4917 0.688517
3 to 4 141517 -1.1573 0.123572
2 to 3 142550 1.8899 0.970613
1 to 2 141885 -0.0718 0.471393
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-15_15:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2548.19 0.681 0.752219
Test results for specific bytes for dh-ranFile-2018-06-15_15:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2360.76 -1.969 0.024468
2 to 9 2494.97 -0.071 0.471630
3 to 10 2463.13 -0.521 0.301027
4 to 11 2583.06 1.175 0.879923
5 to 12 2540.30 0.570 0.715627
6 to 13 2474.92 -0.355 0.361418
7 to 14 2440.53 -0.841 0.200163
8 to 15 2362.25 -1.948 0.025699
9 to 16 2495.93 -0.058 0.477027
10 to 17 2633.51 1.888 0.970491
11 to 18 2556.65 0.801 0.788462
12 to 19 2534.17 0.483 0.685525
13 to 20 2406.82 -1.318 0.093800
14 to 21 2532.58 0.461 0.677534
15 to 22 2525.40 0.359 0.640297
16 to 23 2533.98 0.481 0.684594
17 to 24 2476.41 -0.334 0.369319
18 to 25 2520.59 0.291 0.614560
19 to 26 2550.85 0.719 0.763969
20 to 27 2526.77 0.379 0.647518
21 to 28 2587.15 1.233 0.891127
22 to 29 2422.99 -1.089 0.138045
23 to 30 2404.46 -1.351 0.088315
24 to 31 2433.84 -0.936 0.174727
25 to 32 2433.28 -0.943 0.172714
CDPARK for dh-ranFile-2018-06-15_15:31: 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
3507 -0.7306 0.232514
3504 -0.8676 0.192812
3526 0.1370 0.554479
3520 -0.1370 0.445521
3533 0.4566 0.676028
3508 -0.6849 0.246694
3488 -1.5982 0.055002
3565 1.9178 0.972432
3560 1.6895 0.954438
3514 -0.4110 0.340551
Square side=100, avg. no. parked=3522.50 sample std.=23.23
p-value of the KSTEST for those 10 p-values: 0.768345
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-15_15:31
0.8981,0.6238,0.0016,0.9355,0.5871,0.3299,0.0234,0.5261,0.8418,0.6538,
The KS test for those 10 p-values: 0.366868
The 3DSPHERES test for dh-ranFile-2018-06-15_15:31
sample no r^3 equiv. uni.
1 4.248 0.132045
2 9.968 0.282708
3 5.874 0.177820
4 10.245 0.289302
5 13.088 0.353546
6 6.825 0.203475
7 8.463 0.245809
8 51.905 0.822743
9 104.908 0.969710
10 48.610 0.802167
11 16.634 0.425623
12 26.245 0.583071
13 35.363 0.692342
14 9.229 0.264808
15 15.214 0.397781
16 4.812 0.148197
17 5.252 0.160610
18 5.169 0.158274
19 36.198 0.700788
20 5.509 0.167770
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.090550
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-15_15:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 0.9 -0.8 -0.5 -0.5 -0.1
-1.2 -2.1 -1.1 -0.9 -0.0 -1.0
-0.3 1.0 0.1 -1.1 0.3 0.1
0.6 1.4 -0.1 -0.2 1.9 0.6
-0.4 0.2 0.5 0.5 -0.9 -1.5
-1.7 -0.2 0.2 -2.2 -1.7 1.0
1.4 -1.0 0.1 1.0 -0.6 -1.0
-0.1
Chi-square with 42 degrees of freedom:40.282033
z-score=-0.187446, p-value=0.453433
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-15_15:31
Test no p-value
1 0.565365
2 0.105140
3 0.947640
4 0.870770
5 0.010154
6 0.729473
7 0.658157
8 0.404021
9 0.820347
10 0.100256
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.715386
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-15_15:31:
(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 66737 0.07 66816 0.33
3 25000.00 24899 0.41 24860 0.78
4 6666.67 6737 0.74 6667 0.00
5 1388.89 1399 0.07 1375 0.14
6 238.10 199 6.42 245 0.20
7 34.72 26 2.19 33 0.09
8 4.96 2 1.77 3 0.77
p=0.93034 p=0.11168
Number of rngs required: 689217, p-value: 0.827
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-15_15:31
No. of wins: Observed Expected
98401 98585.9
z-score=-0.827, pvalue=0.20418
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66447 66666.7 0.724 0.724
2 37912 37654.3 1.763 2.487
3 27016 26954.7 0.139 2.626
4 19389 19313.5 0.295 2.922
5 13754 13851.4 0.685 3.607
6 10058 9943.5 1.317 4.925
7 7155 7145.0 0.014 4.938
8 5132 5139.1 0.010 4.948
9 3627 3699.9 1.435 6.383
10 2654 2666.3 0.057 6.440
11 1882 1923.3 0.888 7.328
12 1357 1388.7 0.725 8.053
13 1026 1003.7 0.495 8.548
14 715 726.1 0.171 8.719
15 503 525.8 0.992 9.711
16 408 381.2 1.891 11.602
17 243 276.5 4.068 15.670
18 188 200.8 0.820 16.490
19 143 146.0 0.061 16.551
20 118 106.2 1.308 17.858
21 273 287.1 0.694 18.552
Chisq= 18.55 for 20 degrees of freedom, p= 0.44890
SUMMARY of craptest
p-value for no. of wins: 0.204177
p-value for throws/game: 0.448903
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-15_15:31
No. of wins: Observed Expected
98666 98585.9
z-score= 0.358, pvalue=0.63999
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66693 66666.7 0.010 0.010
2 37540 37654.3 0.347 0.357
3 27091 26954.7 0.689 1.046
4 19327 19313.5 0.009 1.056
5 13740 13851.4 0.896 1.952
6 9858 9943.5 0.736 2.688
7 7156 7145.0 0.017 2.705
8 5156 5139.1 0.056 2.761
9 3738 3699.9 0.393 3.154
10 2676 2666.3 0.035 3.189
11 1943 1923.3 0.201 3.390
12 1401 1388.7 0.108 3.498
13 1012 1003.7 0.068 3.567
14 752 726.1 0.921 4.488
15 501 525.8 1.173 5.661
16 407 381.2 1.753 7.414
17 303 276.5 2.532 9.946
18 188 200.8 0.820 10.765
19 137 146.0 0.553 11.318
20 96 106.2 0.982 12.301
21 285 287.1 0.016 12.316
Chisq= 12.32 for 20 degrees of freedom, p= 0.09524
SUMMARY of craptest
p-value for no. of wins: 0.639993
p-value for throws/game: 0.095240
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0016,0.0102,0.0234,0.0245,0.0255,0.0257,0.0368,0.0452,0.0456,0.0460,
0.0462,0.0510,0.0524,0.0550,0.0611,0.0624,0.0635,0.0678,0.0680,0.0708,
0.0832,0.0883,0.0905,0.0916,0.0938,0.0952,0.0955,0.1003,0.1051,0.1117,
0.1142,0.1216,0.1236,0.1268,0.1303,0.1320,0.1354,0.1378,0.1380,0.1442,
0.1482,0.1573,0.1576,0.1583,0.1592,0.1606,0.1610,0.1613,0.1659,0.1678,
0.1699,0.1727,0.1747,0.1756,0.1778,0.1928,0.1934,0.1975,0.2002,0.2035,
0.2042,0.2147,0.2248,0.2255,0.2264,0.2283,0.2296,0.2299,0.2317,0.2325,
0.2429,0.2458,0.2466,0.2467,0.2485,0.2517,0.2531,0.2557,0.2579,0.2648,
0.2694,0.2773,0.2784,0.2784,0.2814,0.2827,0.2853,0.2871,0.2893,0.2985,
0.3010,0.3011,0.3066,0.3094,0.3111,0.3230,0.3287,0.3292,0.3299,0.3395,
0.3406,0.3519,0.3535,0.3547,0.3547,0.3593,0.3614,0.3669,0.3693,0.3763,
0.3786,0.3888,0.3940,0.3962,0.3978,0.4029,0.4040,0.4121,0.4137,0.4256,
0.4257,0.4338,0.4341,0.4391,0.4402,0.4455,0.4461,0.4480,0.4489,0.4491,
0.4519,0.4519,0.4534,0.4537,0.4555,0.4597,0.4690,0.4714,0.4716,0.4734,
0.4770,0.4803,0.4858,0.4874,0.4950,0.5025,0.5077,0.5232,0.5261,0.5314,
0.5349,0.5419,0.5442,0.5491,0.5528,0.5545,0.5622,0.5654,0.5656,0.5669,
0.5694,0.5709,0.5745,0.5768,0.5780,0.5791,0.5814,0.5831,0.5871,0.5882,
0.5959,0.6103,0.6119,0.6131,0.6146,0.6208,0.6238,0.6280,0.6306,0.6400,
0.6403,0.6428,0.6475,0.6481,0.6538,0.6573,0.6575,0.6582,0.6590,0.6653,
0.6680,0.6721,0.6760,0.6763,0.6775,0.6846,0.6855,0.6885,0.6896,0.6923,
0.6936,0.7008,0.7090,0.7101,0.7154,0.7156,0.7295,0.7355,0.7356,0.7464,
0.7522,0.7581,0.7597,0.7640,0.7648,0.7658,0.7683,0.7689,0.7728,0.7809,
0.7885,0.7919,0.7996,0.8006,0.8022,0.8106,0.8148,0.8190,0.8203,0.8227,
0.8270,0.8382,0.8418,0.8419,0.8484,0.8527,0.8708,0.8799,0.8908,0.8911,
0.8924,0.8947,0.8966,0.8981,0.9137,0.9224,0.9303,0.9319,0.9355,0.9423,
0.9476,0.9515,0.9544,0.9548,0.9580,0.9620,0.9643,0.9697,0.9705,0.9706,
0.9724,0.9770,0.9774,0.9806,0.9884,0.9921,0.9931,0.9946,0.9998,
Overall p-value after applying KStest on 269 p-values = 0.330263
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.