RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-01_06:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 16.04 22.8526 0.845890
2 to 25 15.99 12.8704 0.255181
3 to 26 15.67 11.2336 0.155832
4 to 27 15.69 15.9988 0.476081
5 to 28 15.89 25.4350 0.914612
6 to 29 15.62 16.8034 0.532238
7 to 30 15.61 19.4835 0.698503
8 to 31 15.91 24.2015 0.885938
9 to 32 15.83 25.2408 0.910551
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.253133
Tough bday spacings test for dh-ranFile-2018-07-01_06:31: 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 13 31 65 112 97 68 47 38 16 9 4
(O-E)^2/E 1.6 0.9 0.9 2.1 0.0 1.3 0.5 2.3 0.1 0.9 0.0
Birthday Spacings: Sum(O-E)^2/E= 10.548, p= 0.606
RESULTS OF GCD FOR dh-ranFile-2018-07-01_06:31
Euclid's algorithm:
p-value, steps to gcd: 0.305118
p-value, dist. of gcd's: 0.124515
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-01_06:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.727 0.632 0.734 0.439 0.288 0.385 0.776 0.554
Bits 8 to 15---> 0.590 0.226 0.237 0.298 0.486 0.641 0.504 0.876
Bits 16 to 23---> 0.257 0.808 0.729 0.041 0.020 0.392 0.279 0.102
Bits 24 to 31---> 0.774 0.846 0.068 0.116 0.754 0.927 0.262 0.287
KS test for the above 32 p values: 0.266
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-01_06:31,
p-values for 5 runs: 0.4611, 0.8567, 0.6425, 0.9779, 0.5205
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-01_06:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 208 211.4 0.055 0.055
r= 29 5166 5134.0 0.199 0.255
r= 30 23091 23103.0 0.006 0.261
r= 31 11535 11551.5 0.024 0.285
chi-square = 0.285 with df = 3; p-value = 0.037
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-01_06:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 215 211.4 0.061 0.061
r= 30 5093 5134.0 0.328 0.388
r= 31 23108 23103.0 0.001 0.389
r= 32 11584 11551.5 0.091 0.481
chi-square = 0.481 with df = 3; p-value = 0.077
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-01_06:31
b-rank test for bits 1 to 8, p=0.65474
b-rank test for bits 2 to 9, p=0.14957
b-rank test for bits 3 to 10, p=0.11864
b-rank test for bits 4 to 11, p=0.42807
b-rank test for bits 5 to 12, p=0.89647
b-rank test for bits 6 to 13, p=0.39439
b-rank test for bits 7 to 14, p=0.11756
b-rank test for bits 8 to 15, p=0.74641
b-rank test for bits 9 to 16, p=0.43964
b-rank test for bits 10 to 17, p=0.07199
b-rank test for bits 11 to 18, p=0.45138
b-rank test for bits 12 to 19, p=0.44348
b-rank test for bits 13 to 20, p=0.57856
b-rank test for bits 14 to 21, p=0.12091
b-rank test for bits 15 to 22, p=0.92134
b-rank test for bits 16 to 23, p=0.45559
b-rank test for bits 17 to 24, p=0.90926
b-rank test for bits 18 to 25, p=0.89032
b-rank test for bits 19 to 26, p=0.28786
b-rank test for bits 20 to 27, p=0.35973
b-rank test for bits 21 to 28, p=0.08468
b-rank test for bits 22 to 29, p=0.29168
b-rank test for bits 23 to 30, p=0.68744
b-rank test for bits 24 to 31, p=0.01180
b-rank test for bits 25 to 32, p=0.05435
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 = 0.249751
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-01_06:31
(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 141741 -0.39 0.347051
2 141474 -1.02 0.154547
3 141039 -2.03 0.021002
4 141974 0.15 0.560051
5 141878 -0.07 0.470823
6 142093 0.43 0.666088
7 141554 -0.83 0.203210
8 141434 -1.11 0.133374
9 141568 -0.80 0.212580
10 141761 -0.35 0.364459
11 142226 0.74 0.770315
12 141709 -0.47 0.319871
13 141937 0.06 0.525774
14 141944 0.08 0.532281
15 141793 -0.27 0.392888
16 141246 -1.55 0.060590
17 142460 1.29 0.900885
18 142176 0.62 0.733378
19 142133 0.52 0.699371
20 142288 0.88 0.811852
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-01_06:31
Bits used No. missing words z-score p-value
23 to 32 141945 0.1230 0.548947
22 to 31 142443 1.8402 0.967134
21 to 30 141496 -1.4253 0.077039
20 to 29 141944 0.1196 0.547581
19 to 28 141734 -0.6046 0.272727
18 to 27 141925 0.0540 0.521546
17 to 26 141776 -0.4598 0.322845
16 to 25 142830 3.1747 0.999250
15 to 24 142148 0.8230 0.794746
14 to 23 142264 1.2230 0.889335
13 to 22 142098 0.6506 0.742343
12 to 21 142024 0.3954 0.653731
11 to 20 141797 -0.3873 0.349251
10 to 19 141901 -0.0287 0.488542
9 to 18 141425 -1.6701 0.047449
8 to 17 141873 -0.1253 0.450153
7 to 16 141761 -0.5115 0.304507
6 to 15 141735 -0.6011 0.273874
5 to 14 141995 0.2954 0.616161
4 to 13 142174 0.9127 0.819288
3 to 12 141848 -0.2115 0.416255
2 to 11 141639 -0.9322 0.175624
1 to 10 141844 -0.2253 0.410882
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-01_06:31
Bits used No. missing words z-score p-value
28 to 32 142095 0.6294 0.735453
27 to 31 141947 0.1277 0.550805
26 to 30 141699 -0.7130 0.237928
25 to 29 141436 -1.6045 0.054301
24 to 28 142331 1.4294 0.923554
23 to 27 141872 -0.1265 0.449651
22 to 26 142446 1.8192 0.965561
21 to 25 142197 0.9752 0.835258
20 to 24 141685 -0.7604 0.223496
19 to 23 141975 0.2226 0.588081
18 to 22 141944 0.1175 0.546778
17 to 21 142095 0.6294 0.735453
16 to 20 141917 0.0260 0.510371
15 to 19 141975 0.2226 0.588081
14 to 18 141985 0.2565 0.601221
13 to 17 141883 -0.0893 0.464440
12 to 16 141813 -0.3265 0.372007
11 to 15 142224 1.0667 0.856941
10 to 14 141712 -0.6689 0.251775
9 to 13 141967 0.1955 0.577496
8 to 12 141927 0.0599 0.523882
7 to 11 141892 -0.0587 0.476577
6 to 10 141832 -0.2621 0.396609
5 to 9 141952 0.1446 0.557504
4 to 8 142316 1.3785 0.915982
3 to 7 141586 -1.0960 0.136532
2 to 6 141910 0.0023 0.500906
1 to 5 142266 1.2091 0.886678
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-01_06:31
Bits used No. missing words z-score p-value
31 to 32 142221 0.9194 0.821052
30 to 31 141497 -1.2163 0.111933
29 to 30 142956 3.0875 0.998991
28 to 29 141661 -0.7325 0.231921
27 to 28 142238 0.9695 0.833859
26 to 27 142217 0.9076 0.817950
25 to 26 141413 -1.4641 0.071583
24 to 25 142005 0.2822 0.611110
23 to 24 142109 0.5890 0.722068
22 to 23 142464 1.6362 0.949101
21 to 22 141495 -1.2222 0.110814
20 to 21 141894 -0.0452 0.481966
19 to 20 142191 0.8309 0.796981
18 to 19 141961 0.1524 0.560572
17 to 18 142112 0.5978 0.725029
16 to 17 141690 -0.6470 0.258819
15 to 16 142400 1.4474 0.926108
14 to 15 141561 -1.0275 0.152087
13 to 14 141946 0.1082 0.543070
12 to 13 141953 0.1288 0.551250
11 to 12 142544 1.8722 0.969409
10 to 11 142181 0.8014 0.788546
9 to 10 141756 -0.4523 0.325526
8 to 9 141736 -0.5113 0.304571
7 to 8 141860 -0.1455 0.442152
6 to 7 141783 -0.3727 0.354703
5 to 6 141913 0.0108 0.504319
4 to 5 141937 0.0816 0.532527
3 to 4 142232 0.9518 0.829408
2 to 3 142251 1.0079 0.843243
1 to 2 141615 -0.8682 0.192634
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-01_06:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2617.29 1.659 0.951419
Test results for specific bytes for dh-ranFile-2018-07-01_06:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2510.87 0.154 0.561085
2 to 9 2458.36 -0.589 0.277968
3 to 10 2389.48 -1.563 0.059031
4 to 11 2558.48 0.827 0.795906
5 to 12 2412.34 -1.240 0.107552
6 to 13 2408.06 -1.300 0.096762
7 to 14 2517.87 0.253 0.599773
8 to 15 2481.21 -0.266 0.395246
9 to 16 2470.66 -0.415 0.339117
10 to 17 2474.54 -0.360 0.359425
11 to 18 2545.05 0.637 0.737959
12 to 19 2568.35 0.967 0.833116
13 to 20 2406.33 -1.325 0.092648
14 to 21 2499.95 -0.001 0.499735
15 to 22 2447.23 -0.746 0.227745
16 to 23 2501.98 0.028 0.511160
17 to 24 2560.12 0.850 0.802409
18 to 25 2340.73 -2.252 0.012146
19 to 26 2516.00 0.226 0.589514
20 to 27 2389.57 -1.562 0.059174
21 to 28 2557.16 0.808 0.790563
22 to 29 2488.26 -0.166 0.434081
23 to 30 2661.50 2.284 0.988814
24 to 31 2489.66 -0.146 0.441860
25 to 32 2393.10 -1.512 0.065301
CDPARK for dh-ranFile-2018-07-01_06:31: 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
3511 -0.5479 0.291865
3520 -0.1370 0.445521
3530 0.3196 0.625377
3547 1.0959 0.863437
3530 0.3196 0.625377
3525 0.0913 0.536383
3529 0.2740 0.607947
3493 -1.3699 0.085365
3518 -0.2283 0.409702
3543 0.9132 0.819442
Square side=100, avg. no. parked=3524.60 sample std.=14.72
p-value of the KSTEST for those 10 p-values: 0.686337
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-01_06:31
0.7823,0.7988,0.8567,0.4573,0.1330,0.5813,0.2406,0.7047,0.8345,0.8740,
The KS test for those 10 p-values: 0.207650
The 3DSPHERES test for dh-ranFile-2018-07-01_06:31
sample no r^3 equiv. uni.
1 121.490 0.982572
2 27.085 0.594576
3 15.472 0.402940
4 7.880 0.231006
5 9.394 0.268836
6 20.279 0.491339
7 27.716 0.603014
8 34.173 0.679892
9 20.950 0.502589
10 31.027 0.644498
11 9.718 0.276706
12 15.874 0.410890
13 9.445 0.270100
14 2.891 0.091855
15 20.147 0.489091
16 8.943 0.257775
17 74.231 0.915784
18 23.847 0.548380
19 49.849 0.810174
20 14.140 0.375824
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.454388
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-01_06:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 0.1 -1.1 0.6 -1.3 0.7
-0.2 -0.9 -1.3 0.0 -0.6 0.9
0.6 -0.6 1.1 0.2 -0.3 0.3
-0.5 -1.9 1.1 -0.2 0.3 0.1
1.3 -0.7 -0.1 0.0 0.6 0.9
-0.5 0.6 -0.0 0.1 0.2 -1.4
0.0 -0.4 0.1 2.1 0.1 -1.0
-0.1
Chi-square with 42 degrees of freedom:26.469862
z-score=-1.694477, p-value=0.029429
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-01_06:31
Test no p-value
1 0.007102
2 0.785079
3 0.525895
4 0.694611
5 0.260899
6 0.031821
7 0.256751
8 0.421166
9 0.014411
10 0.062465
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.018552
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-01_06:31:
(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 66679 0.00 66764 0.14
3 25000.00 25015 0.01 24928 0.21
4 6666.67 6633 0.17 6649 0.05
5 1388.89 1395 0.03 1377 0.10
6 238.10 245 0.20 240 0.02
7 34.72 25 2.72 34 0.01
8 4.96 7 0.84 7 0.84
p=0.31908 p=0.03218
Number of rngs required: 688715, p-value: 0.640
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-01_06:31
No. of wins: Observed Expected
98272 98585.9
z-score=-1.404, pvalue=0.08020
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66260 66666.7 2.481 2.481
2 37628 37654.3 0.018 2.499
3 27067 26954.7 0.468 2.967
4 19418 19313.5 0.566 3.532
5 13894 13851.4 0.131 3.663
6 9853 9943.5 0.824 4.488
7 7278 7145.0 2.475 6.963
8 5175 5139.1 0.251 7.214
9 3743 3699.9 0.503 7.717
10 2694 2666.3 0.288 8.004
11 1848 1923.3 2.950 10.955
12 1417 1388.7 0.575 11.530
13 1024 1003.7 0.410 11.940
14 724 726.1 0.006 11.946
15 550 525.8 1.110 13.057
16 378 381.2 0.026 13.083
17 278 276.5 0.008 13.090
18 199 200.8 0.017 13.107
19 164 146.0 2.223 15.330
20 111 106.2 0.216 15.546
21 297 287.1 0.340 15.886
Chisq= 15.89 for 20 degrees of freedom, p= 0.27634
SUMMARY of craptest
p-value for no. of wins: 0.080195
p-value for throws/game: 0.276343
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-01_06:31
No. of wins: Observed Expected
98525 98585.9
z-score=-0.272, pvalue=0.39274
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66984 66666.7 1.511 1.511
2 37526 37654.3 0.437 1.948
3 26992 26954.7 0.052 1.999
4 19128 19313.5 1.781 3.780
5 13749 13851.4 0.757 4.538
6 9971 9943.5 0.076 4.613
7 7169 7145.0 0.080 4.694
8 5061 5139.1 1.186 5.880
9 3688 3699.9 0.038 5.918
10 2634 2666.3 0.391 6.309
11 2053 1923.3 8.742 15.052
12 1385 1388.7 0.010 15.062
13 1012 1003.7 0.068 15.130
14 674 726.1 3.744 18.874
15 536 525.8 0.196 19.070
16 388 381.2 0.123 19.194
17 301 276.5 2.164 21.357
18 219 200.8 1.644 23.001
19 150 146.0 0.110 23.112
20 91 106.2 2.180 25.291
21 289 287.1 0.012 25.304
Chisq= 25.30 for 20 degrees of freedom, p= 0.80994
SUMMARY of craptest
p-value for no. of wins: 0.392736
p-value for throws/game: 0.809935
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0071,0.0118,0.0121,0.0144,0.0186,0.0199,0.0210,0.0294,0.0318,0.0322,
0.0371,0.0406,0.0474,0.0543,0.0543,0.0590,0.0592,0.0606,0.0625,0.0653,
0.0679,0.0716,0.0720,0.0769,0.0770,0.0802,0.0847,0.0854,0.0919,0.0926,
0.0968,0.1020,0.1076,0.1108,0.1119,0.1156,0.1176,0.1186,0.1209,0.1245,
0.1330,0.1334,0.1365,0.1496,0.1521,0.1545,0.1558,0.1756,0.1926,0.2032,
0.2076,0.2126,0.2235,0.2255,0.2277,0.2310,0.2319,0.2368,0.2379,0.2406,
0.2498,0.2518,0.2531,0.2552,0.2565,0.2568,0.2578,0.2588,0.2609,0.2623,
0.2662,0.2688,0.2701,0.2727,0.2739,0.2763,0.2767,0.2780,0.2794,0.2872,
0.2879,0.2879,0.2917,0.2919,0.2980,0.3045,0.3046,0.3051,0.3191,0.3199,
0.3228,0.3255,0.3391,0.3471,0.3493,0.3547,0.3594,0.3597,0.3645,0.3720,
0.3758,0.3851,0.3924,0.3927,0.3929,0.3944,0.3952,0.3966,0.4029,0.4097,
0.4109,0.4109,0.4163,0.4212,0.4281,0.4341,0.4391,0.4396,0.4419,0.4422,
0.4435,0.4455,0.4497,0.4502,0.4514,0.4544,0.4556,0.4573,0.4611,0.4644,
0.4708,0.4761,0.4766,0.4820,0.4861,0.4885,0.4891,0.4913,0.4997,0.5009,
0.5026,0.5043,0.5043,0.5104,0.5112,0.5205,0.5215,0.5239,0.5258,0.5259,
0.5322,0.5323,0.5325,0.5364,0.5431,0.5468,0.5476,0.5484,0.5489,0.5508,
0.5513,0.5535,0.5575,0.5601,0.5606,0.5611,0.5775,0.5786,0.5813,0.5881,
0.5881,0.5895,0.5903,0.5946,0.5998,0.6012,0.6030,0.6062,0.6079,0.6111,
0.6162,0.6254,0.6254,0.6325,0.6403,0.6413,0.6425,0.6445,0.6537,0.6547,
0.6661,0.6799,0.6863,0.6874,0.6946,0.6985,0.6994,0.7047,0.7221,0.7250,
0.7273,0.7292,0.7334,0.7339,0.7355,0.7355,0.7380,0.7423,0.7464,0.7536,
0.7703,0.7739,0.7756,0.7823,0.7851,0.7885,0.7906,0.7947,0.7959,0.7970,
0.7988,0.8024,0.8080,0.8099,0.8102,0.8119,0.8180,0.8193,0.8194,0.8211,
0.8294,0.8331,0.8339,0.8345,0.8353,0.8432,0.8457,0.8459,0.8567,0.8567,
0.8569,0.8634,0.8740,0.8758,0.8859,0.8867,0.8893,0.8903,0.8965,0.9009,
0.9093,0.9106,0.9146,0.9158,0.9160,0.9213,0.9236,0.9261,0.9272,0.9491,
0.9514,0.9656,0.9671,0.9694,0.9779,0.9826,0.9888,0.9990,0.9993,
Overall p-value after applying KStest on 269 p-values = 0.358026
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.