RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-29_03:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.50 18.0140 0.612039
2 to 25 15.75 19.4642 0.697453
3 to 26 15.78 16.7755 0.530329
4 to 27 15.62 17.4321 0.574517
5 to 28 15.63 17.6941 0.591621
6 to 29 15.82 14.3685 0.359130
7 to 30 15.91 15.0493 0.408068
8 to 31 15.71 8.5188 0.045839
9 to 32 15.49 17.5163 0.580047
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.291975
Tough bday spacings test for dh-ranFile-2018-06-29_03:31: 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 34 70 106 98 65 72 30 16 2 2
(O-E)^2/E 1.9 0.2 0.1 0.7 0.0 2.2 7.6 0.0 0.1 3.2 1.0
Birthday Spacings: Sum(O-E)^2/E= 17.101, p= 0.928
RESULTS OF GCD FOR dh-ranFile-2018-06-29_03:31
Euclid's algorithm:
p-value, steps to gcd: 0.609700
p-value, dist. of gcd's: 0.562730
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-29_03:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.883 0.615 0.171 0.517 0.661 0.166 0.027 0.286
Bits 8 to 15---> 0.148 0.491 0.536 0.080 0.519 0.292 0.426 0.508
Bits 16 to 23---> 0.367 0.101 0.382 0.988 0.755 0.900 0.823 0.540
Bits 24 to 31---> 0.286 0.420 0.590 0.412 0.570 0.974 0.131 0.395
KS test for the above 32 p values: 0.449
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-29_03:31,
p-values for 5 runs: 0.3829, 0.3238, 0.4710, 0.8205, 0.6862
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-29_03:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 236 211.4 2.858 2.858
r= 29 5134 5134.0 0.000 2.858
r= 30 23119 23103.0 0.011 2.869
r= 31 11511 11551.5 0.142 3.011
chi-square = 3.011 with df = 3; p-value = 0.610
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-29_03:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 227 211.4 1.148 1.148
r= 30 5153 5134.0 0.070 1.219
r= 31 23044 23103.0 0.151 1.370
r= 32 11576 11551.5 0.052 1.421
chi-square = 1.421 with df = 3; p-value = 0.299
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-29_03:31
b-rank test for bits 1 to 8, p=0.76439
b-rank test for bits 2 to 9, p=0.84150
b-rank test for bits 3 to 10, p=0.01486
b-rank test for bits 4 to 11, p=0.56968
b-rank test for bits 5 to 12, p=0.79504
b-rank test for bits 6 to 13, p=0.71049
b-rank test for bits 7 to 14, p=0.13983
b-rank test for bits 8 to 15, p=0.63041
b-rank test for bits 9 to 16, p=0.37336
b-rank test for bits 10 to 17, p=0.31796
b-rank test for bits 11 to 18, p=0.63146
b-rank test for bits 12 to 19, p=0.70514
b-rank test for bits 13 to 20, p=0.66776
b-rank test for bits 14 to 21, p=0.91941
b-rank test for bits 15 to 22, p=0.23369
b-rank test for bits 16 to 23, p=0.42130
b-rank test for bits 17 to 24, p=0.50313
b-rank test for bits 18 to 25, p=0.33441
b-rank test for bits 19 to 26, p=0.54771
b-rank test for bits 20 to 27, p=0.26332
b-rank test for bits 21 to 28, p=0.75952
b-rank test for bits 22 to 29, p=0.06133
b-rank test for bits 23 to 30, p=0.18817
b-rank test for bits 24 to 31, p=0.07963
b-rank test for bits 25 to 32, p=0.23310
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 = 0.806881
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-29_03:31
(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 141960 0.12 0.547120
2 141949 0.09 0.536924
3 141672 -0.55 0.289615
4 141691 -0.51 0.304985
5 140972 -2.19 0.014261
6 141589 -0.75 0.227099
7 141839 -0.16 0.434739
8 142215 0.71 0.762443
9 142222 0.73 0.767469
10 142402 1.15 0.875154
11 141569 -0.80 0.213259
12 142100 0.45 0.672017
13 141962 0.12 0.548971
14 141775 -0.31 0.376816
15 141405 -1.18 0.119330
16 141044 -2.02 0.021599
17 141924 0.03 0.513671
18 142307 0.93 0.823591
19 142069 0.37 0.645448
20 141939 0.07 0.527634
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-29_03:31
Bits used No. missing words z-score p-value
23 to 32 141913 0.0127 0.505049
22 to 31 141825 -0.2908 0.385605
21 to 30 142064 0.5333 0.703103
20 to 29 142163 0.8747 0.809138
19 to 28 142018 0.3747 0.646067
18 to 27 142331 1.4540 0.927032
17 to 26 141669 -0.8287 0.203630
16 to 25 141846 -0.2184 0.413567
15 to 24 141376 -1.8391 0.032953
14 to 23 142005 0.3299 0.629261
13 to 22 142393 1.6678 0.952325
12 to 21 142355 1.5368 0.937828
11 to 20 141668 -0.8322 0.202656
10 to 19 141904 -0.0184 0.492668
9 to 18 142444 1.8437 0.967386
8 to 17 142449 1.8609 0.968623
7 to 16 142108 0.6851 0.753350
6 to 15 142080 0.5885 0.721907
5 to 14 141789 -0.4149 0.339096
4 to 13 141239 -2.3115 0.010403
3 to 12 141425 -1.6701 0.047449
2 to 11 142362 1.5609 0.940730
1 to 10 141856 -0.1839 0.427047
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-29_03:31
Bits used No. missing words z-score p-value
28 to 32 141915 0.0192 0.507667
27 to 31 142153 0.8260 0.795598
26 to 30 142044 0.4565 0.675988
25 to 29 141750 -0.5401 0.294564
24 to 28 141460 -1.5232 0.063860
23 to 27 141031 -2.9774 0.001454
22 to 26 142345 1.4768 0.930142
21 to 25 142252 1.1616 0.877300
20 to 24 141956 0.1582 0.562852
19 to 23 141668 -0.8181 0.206659
18 to 22 142033 0.4192 0.662473
17 to 21 141842 -0.2282 0.409731
16 to 20 142196 0.9718 0.834416
15 to 19 141672 -0.8045 0.210552
14 to 18 141909 -0.0011 0.499554
13 to 17 142183 0.9277 0.823217
12 to 16 142155 0.8328 0.797516
11 to 15 141916 0.0226 0.509019
10 to 14 141659 -0.8486 0.198059
9 to 13 141698 -0.7164 0.236881
8 to 12 141944 0.1175 0.546778
7 to 11 141972 0.2124 0.584118
6 to 10 141276 -2.1469 0.015901
5 to 9 142203 0.9955 0.840251
4 to 8 142755 2.8667 0.997926
3 to 7 141880 -0.0994 0.460401
2 to 6 142176 0.9040 0.816993
1 to 5 141816 -0.3164 0.375860
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-29_03:31
Bits used No. missing words z-score p-value
31 to 32 141490 -1.2370 0.108051
30 to 31 141812 -0.2871 0.387014
29 to 30 141014 -2.6411 0.004132
28 to 29 141630 -0.8240 0.204975
27 to 28 142259 1.0315 0.848841
26 to 27 141458 -1.3314 0.091536
25 to 26 141924 0.0433 0.517259
24 to 25 141715 -0.5732 0.283240
23 to 24 141731 -0.5260 0.299428
22 to 23 141719 -0.5614 0.287247
21 to 22 141665 -0.7207 0.235536
20 to 21 141538 -1.0954 0.136678
19 to 20 141570 -1.0010 0.158420
18 to 19 142411 1.4799 0.930544
17 to 18 142177 0.7896 0.785116
16 to 17 141644 -0.7827 0.216906
15 to 16 141576 -0.9833 0.162736
14 to 15 142044 0.3973 0.654411
13 to 14 142025 0.3412 0.633527
12 to 13 141478 -1.2724 0.101623
11 to 12 141173 -2.1721 0.014925
10 to 11 141799 -0.3255 0.372418
9 to 10 142242 0.9813 0.836784
8 to 9 142056 0.4327 0.667367
7 to 8 142402 1.4533 0.926930
6 to 7 142073 0.4828 0.685382
5 to 6 142168 0.7630 0.777280
4 to 5 141487 -1.2458 0.106417
3 to 4 141854 -0.1632 0.435174
2 to 3 141749 -0.4729 0.318125
1 to 2 141514 -1.1662 0.121774
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-29_03:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2456.03 -0.622 0.267026
Test results for specific bytes for dh-ranFile-2018-06-29_03:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2513.19 0.187 0.573985
2 to 9 2400.33 -1.409 0.079344
3 to 10 2457.05 -0.607 0.271814
4 to 11 2574.77 1.057 0.854832
5 to 12 2455.70 -0.627 0.265481
6 to 13 2538.85 0.549 0.708635
7 to 14 2521.05 0.298 0.617056
8 to 15 2499.47 -0.008 0.496988
9 to 16 2566.38 0.939 0.826085
10 to 17 2543.42 0.614 0.730425
11 to 18 2600.77 1.425 0.922937
12 to 19 2459.67 -0.570 0.284242
13 to 20 2423.49 -1.082 0.139631
14 to 21 2607.60 1.522 0.935955
15 to 22 2477.14 -0.323 0.373261
16 to 23 2552.56 0.743 0.771364
17 to 24 2414.85 -1.204 0.114254
18 to 25 2413.01 -1.230 0.109300
19 to 26 2513.15 0.186 0.573768
20 to 27 2440.73 -0.838 0.200954
21 to 28 2497.37 -0.037 0.485167
22 to 29 2511.78 0.167 0.566165
23 to 30 2594.91 1.342 0.910240
24 to 31 2580.87 1.144 0.873626
25 to 32 2640.62 1.989 0.976630
CDPARK for dh-ranFile-2018-06-29_03:31: 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
3533 0.4566 0.676028
3526 0.1370 0.554479
3482 -1.8721 0.030593
3525 0.0913 0.536383
3538 0.6849 0.753306
3530 0.3196 0.625377
3513 -0.4566 0.323972
3563 1.8265 0.966111
3507 -0.7306 0.232514
3506 -0.7763 0.218799
Square side=100, avg. no. parked=3522.30 sample std.=20.76
p-value of the KSTEST for those 10 p-values: 0.973473
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-29_03:31
0.2756,0.6271,0.4021,0.1191,0.9469,0.2293,0.6533,0.9415,0.2198,0.1784,
The KS test for those 10 p-values: 0.647233
The 3DSPHERES test for dh-ranFile-2018-06-29_03:31
sample no r^3 equiv. uni.
1 3.603 0.113176
2 1.200 0.039225
3 1.059 0.034684
4 20.790 0.499927
5 34.941 0.687980
6 102.202 0.966851
7 15.162 0.396728
8 18.851 0.466532
9 0.634 0.020924
10 22.951 0.534681
11 0.637 0.020997
12 0.979 0.032101
13 40.306 0.739077
14 16.910 0.430878
15 230.809 0.999544
16 8.810 0.254477
17 112.263 0.976296
18 28.223 0.609677
19 0.690 0.022751
20 39.561 0.732517
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.035301
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-29_03:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -1.2 1.3 0.0 0.7 0.8
-0.9 -0.1 -2.0 -0.4 -0.5 0.1
-0.2 -0.6 -0.4 -1.4 0.3 1.7
0.0 1.0 -0.4 -0.2 -0.5 1.8
0.3 2.3 -1.1 -0.8 0.8 -0.1
-0.4 0.9 0.5 -1.8 -0.2 -1.9
0.3 -0.1 -0.8 1.0 -1.3 -1.0
1.8
Chi-square with 42 degrees of freedom:43.482230
z-score=0.161725, p-value=0.591914
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-29_03:31
Test no p-value
1 0.374343
2 0.582805
3 0.322801
4 0.900055
5 0.005803
6 0.294607
7 0.264882
8 0.036227
9 0.875550
10 0.983422
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.456235
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-29_03:31:
(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 66750 0.10 66560 0.17
3 25000.00 25003 0.00 25092 0.34
4 6666.67 6609 0.50 6718 0.40
5 1388.89 1383 0.02 1342 1.58
6 238.10 217 1.87 247 0.33
7 34.72 34 0.01 37 0.15
8 4.96 3 0.77 3 0.77
p=0.22792 p=0.28883
Number of rngs required: 687828, p-value: 0.253
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-29_03:31
No. of wins: Observed Expected
98843 98585.9
z-score= 1.150, pvalue=0.87495
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66575 66666.7 0.126 0.126
2 37588 37654.3 0.117 0.243
3 27078 26954.7 0.564 0.807
4 19540 19313.5 2.657 3.464
5 13837 13851.4 0.015 3.479
6 9938 9943.5 0.003 3.482
7 7031 7145.0 1.820 5.302
8 5009 5139.1 3.292 8.594
9 3780 3699.9 1.736 10.329
10 2662 2666.3 0.007 10.336
11 1914 1923.3 0.045 10.382
12 1404 1388.7 0.168 10.549
13 1018 1003.7 0.203 10.753
14 743 726.1 0.391 11.144
15 529 525.8 0.019 11.163
16 372 381.2 0.220 11.383
17 264 276.5 0.569 11.951
18 197 200.8 0.073 12.024
19 125 146.0 3.016 15.041
20 96 106.2 0.982 16.023
21 300 287.1 0.578 16.602
Chisq= 16.60 for 20 degrees of freedom, p= 0.32132
SUMMARY of craptest
p-value for no. of wins: 0.874946
p-value for throws/game: 0.321323
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-29_03:31
No. of wins: Observed Expected
98631 98585.9
z-score= 0.202, pvalue=0.58000
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66626 66666.7 0.025 0.025
2 37634 37654.3 0.011 0.036
3 27019 26954.7 0.153 0.189
4 19366 19313.5 0.143 0.332
5 13772 13851.4 0.455 0.787
6 9988 9943.5 0.199 0.986
7 7072 7145.0 0.746 1.732
8 5188 5139.1 0.466 2.198
9 3712 3699.9 0.040 2.238
10 2573 2666.3 3.265 5.503
11 1900 1923.3 0.283 5.786
12 1396 1388.7 0.038 5.824
13 1021 1003.7 0.298 6.121
14 739 726.1 0.228 6.349
15 504 525.8 0.907 7.256
16 416 381.2 3.186 10.442
17 274 276.5 0.023 10.465
18 227 200.8 3.410 13.876
19 169 146.0 3.629 17.504
20 124 106.2 2.978 20.482
21 280 287.1 0.176 20.658
Chisq= 20.66 for 20 degrees of freedom, p= 0.58252
SUMMARY of craptest
p-value for no. of wins: 0.580002
p-value for throws/game: 0.582520
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0015,0.0041,0.0058,0.0104,0.0143,0.0149,0.0149,0.0159,0.0209,0.0210,
0.0216,0.0228,0.0272,0.0306,0.0321,0.0330,0.0347,0.0353,0.0362,0.0392,
0.0458,0.0474,0.0613,0.0639,0.0793,0.0796,0.0801,0.0915,0.1007,0.1016,
0.1064,0.1081,0.1093,0.1132,0.1143,0.1191,0.1193,0.1218,0.1311,0.1367,
0.1396,0.1398,0.1477,0.1584,0.1627,0.1663,0.1710,0.1784,0.1882,0.1981,
0.2010,0.2027,0.2036,0.2050,0.2067,0.2106,0.2133,0.2169,0.2188,0.2198,
0.2271,0.2279,0.2293,0.2325,0.2331,0.2337,0.2355,0.2369,0.2535,0.2545,
0.2633,0.2649,0.2655,0.2670,0.2718,0.2756,0.2832,0.2842,0.2861,0.2863,
0.2872,0.2888,0.2896,0.2916,0.2920,0.2946,0.2946,0.2994,0.2995,0.3050,
0.3180,0.3181,0.3213,0.3228,0.3238,0.3240,0.3344,0.3391,0.3591,0.3666,
0.3724,0.3733,0.3734,0.3743,0.3759,0.3768,0.3823,0.3829,0.3856,0.3870,
0.3946,0.3967,0.4021,0.4081,0.4097,0.4124,0.4136,0.4205,0.4213,0.4264,
0.4270,0.4309,0.4347,0.4352,0.4486,0.4562,0.4604,0.4665,0.4710,0.4852,
0.4910,0.4927,0.4970,0.4996,0.4999,0.5031,0.5050,0.5077,0.5083,0.5090,
0.5137,0.5167,0.5173,0.5190,0.5276,0.5303,0.5347,0.5361,0.5364,0.5369,
0.5399,0.5468,0.5471,0.5477,0.5490,0.5545,0.5627,0.5629,0.5662,0.5696,
0.5697,0.5738,0.5740,0.5745,0.5800,0.5800,0.5825,0.5828,0.5841,0.5903,
0.5916,0.5919,0.6097,0.6097,0.6101,0.6120,0.6154,0.6171,0.6254,0.6271,
0.6293,0.6304,0.6315,0.6335,0.6454,0.6461,0.6472,0.6533,0.6544,0.6612,
0.6625,0.6674,0.6678,0.6720,0.6760,0.6760,0.6854,0.6862,0.6880,0.6975,
0.7031,0.7051,0.7086,0.7105,0.7219,0.7304,0.7325,0.7391,0.7533,0.7533,
0.7551,0.7595,0.7624,0.7644,0.7675,0.7714,0.7773,0.7851,0.7950,0.7956,
0.7975,0.8069,0.8091,0.8170,0.8205,0.8228,0.8232,0.8236,0.8261,0.8344,
0.8368,0.8403,0.8415,0.8488,0.8548,0.8736,0.8749,0.8752,0.8755,0.8773,
0.8829,0.8999,0.9001,0.9102,0.9194,0.9229,0.9269,0.9270,0.9278,0.9301,
0.9305,0.9360,0.9378,0.9407,0.9415,0.9469,0.9523,0.9661,0.9669,0.9674,
0.9686,0.9735,0.9738,0.9763,0.9766,0.9834,0.9880,0.9979,0.9995,
Overall p-value after applying KStest on 269 p-values = 0.428146
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.