RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-03_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 15.58 19.7102 0.710682
2 to 25 15.84 22.9356 0.848642
3 to 26 15.58 16.0623 0.480580
4 to 27 15.73 22.2280 0.823890
5 to 28 15.79 11.6411 0.178635
6 to 29 15.81 20.3020 0.740924
7 to 30 15.95 15.3010 0.426191
8 to 31 15.73 13.4123 0.291822
9 to 32 15.41 23.9384 0.878881
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.466686
Tough bday spacings test for dh-ranFile-2018-07-03_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 9 32 73 110 90 83 46 33 15 5 4
(O-E)^2/E 0.0 0.6 0.0 1.6 0.6 0.3 0.7 0.4 0.0 0.4 0.0
Birthday Spacings: Sum(O-E)^2/E= 4.509, p= 0.078
RESULTS OF GCD FOR dh-ranFile-2018-07-03_04:31
Euclid's algorithm:
p-value, steps to gcd: 0.289298
p-value, dist. of gcd's: 0.602465
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-03_04:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.132 0.137 0.240 0.720 0.463 0.199 0.021 0.683
Bits 8 to 15---> 0.571 0.454 0.829 0.932 0.584 0.487 0.930 0.057
Bits 16 to 23---> 0.538 0.413 0.154 0.870 0.603 0.764 0.531 0.860
Bits 24 to 31---> 0.216 0.328 0.485 0.485 0.877 0.840 0.456 0.640
KS test for the above 32 p values: 0.172
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-03_04:31,
p-values for 5 runs: 0.7872, 0.2191, 0.6556, 0.3506, 0.8278
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-03_04:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 185 211.4 3.301 3.301
r= 29 5040 5134.0 1.721 5.023
r= 30 23172 23103.0 0.206 5.228
r= 31 11603 11551.5 0.229 5.458
chi-square = 5.458 with df = 3; p-value = 0.859
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-03_04:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 210 211.4 0.010 0.010
r= 30 5136 5134.0 0.001 0.010
r= 31 22955 23103.0 0.949 0.959
r= 32 11699 11551.5 1.883 2.842
chi-square = 2.842 with df = 3; p-value = 0.583
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-03_04:31
b-rank test for bits 1 to 8, p=0.60442
b-rank test for bits 2 to 9, p=0.20208
b-rank test for bits 3 to 10, p=0.85928
b-rank test for bits 4 to 11, p=0.94057
b-rank test for bits 5 to 12, p=0.32368
b-rank test for bits 6 to 13, p=0.67180
b-rank test for bits 7 to 14, p=0.24426
b-rank test for bits 8 to 15, p=0.59133
b-rank test for bits 9 to 16, p=0.41541
b-rank test for bits 10 to 17, p=0.33196
b-rank test for bits 11 to 18, p=0.44722
b-rank test for bits 12 to 19, p=0.82599
b-rank test for bits 13 to 20, p=0.78377
b-rank test for bits 14 to 21, p=0.88612
b-rank test for bits 15 to 22, p=0.88022
b-rank test for bits 16 to 23, p=0.56396
b-rank test for bits 17 to 24, p=0.97103
b-rank test for bits 18 to 25, p=0.08926
b-rank test for bits 19 to 26, p=0.32498
b-rank test for bits 20 to 27, p=0.61367
b-rank test for bits 21 to 28, p=0.67612
b-rank test for bits 22 to 29, p=0.47110
b-rank test for bits 23 to 30, p=0.42100
b-rank test for bits 24 to 31, p=0.26432
b-rank test for bits 25 to 32, p=0.45932
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 = 0.426315
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-03_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 142096 0.44 0.668634
2 141946 0.09 0.534139
3 141998 0.21 0.582063
4 141640 -0.63 0.264584
5 141665 -0.57 0.284046
6 141536 -0.87 0.191532
7 141896 -0.03 0.487577
8 142126 0.51 0.693655
9 142025 0.27 0.606519
10 142522 1.43 0.923853
11 141340 -1.33 0.091725
12 141386 -1.22 0.110715
13 141455 -1.06 0.144227
14 141777 -0.31 0.378591
15 141983 0.17 0.568331
16 142229 0.75 0.772436
17 142249 0.79 0.786292
18 142136 0.53 0.701806
19 141879 -0.07 0.471753
20 142100 0.45 0.672017
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-03_04:31
Bits used No. missing words z-score p-value
23 to 32 142431 1.7989 0.963980
22 to 31 141626 -0.9770 0.164285
21 to 30 142184 0.9471 0.828216
20 to 29 141964 0.1885 0.574764
19 to 28 141591 -1.0977 0.136170
18 to 27 141881 -0.0977 0.461089
17 to 26 141856 -0.1839 0.427047
16 to 25 141919 0.0333 0.513300
15 to 24 142306 1.3678 0.914317
14 to 23 142321 1.4196 0.922131
13 to 22 141959 0.1713 0.567997
12 to 21 142279 1.2747 0.898797
11 to 20 142305 1.3644 0.913776
10 to 19 141884 -0.0873 0.465199
9 to 18 142210 1.0368 0.850084
8 to 17 141723 -0.6425 0.260269
7 to 16 141907 -0.0080 0.496795
6 to 15 141694 -0.7425 0.228887
5 to 14 142096 0.6437 0.740112
4 to 13 141686 -0.7701 0.220619
3 to 12 142354 1.5333 0.937405
2 to 11 142202 1.0092 0.843562
1 to 10 142005 0.3299 0.629261
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-03_04:31
Bits used No. missing words z-score p-value
28 to 32 141937 0.0938 0.537365
27 to 31 141923 0.0463 0.518480
26 to 30 141391 -1.7571 0.039455
25 to 29 141574 -1.1367 0.127829
24 to 28 142201 0.9887 0.838598
23 to 27 142293 1.3006 0.903298
22 to 26 141560 -1.1842 0.118173
21 to 25 141836 -0.2486 0.401844
20 to 24 142002 0.3141 0.623291
19 to 23 141877 -0.1096 0.456366
18 to 22 141509 -1.3571 0.087383
17 to 21 141692 -0.7367 0.230649
16 to 20 141256 -2.2147 0.013391
15 to 19 141421 -1.6554 0.048926
14 to 18 142394 1.6429 0.949803
13 to 17 141911 0.0057 0.502258
12 to 16 142246 1.1413 0.873118
11 to 15 142191 0.9548 0.830164
10 to 14 141564 -1.1706 0.120878
9 to 13 142098 0.6396 0.738770
8 to 12 141966 0.1921 0.576169
7 to 11 141817 -0.3130 0.377147
6 to 10 141531 -1.2825 0.099838
5 to 9 142324 1.4057 0.920088
4 to 8 142095 0.6294 0.735453
3 to 7 142374 1.5752 0.942389
2 to 6 141669 -0.8147 0.207628
1 to 5 141909 -0.0011 0.499554
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-03_04:31
Bits used No. missing words z-score p-value
31 to 32 141903 -0.0187 0.492551
30 to 31 141635 -0.8092 0.209191
29 to 30 142287 1.1141 0.867376
28 to 29 141475 -1.2812 0.100060
27 to 28 142316 1.1996 0.884856
26 to 27 142292 1.1288 0.870513
25 to 26 142442 1.5713 0.941943
24 to 25 142128 0.6450 0.740551
23 to 24 141999 0.2645 0.604308
22 to 23 141586 -0.9538 0.170099
21 to 22 141950 0.1200 0.547747
20 to 21 142470 1.6539 0.950925
19 to 20 141742 -0.4936 0.310795
18 to 19 141956 0.1377 0.554749
17 to 18 141774 -0.3992 0.344872
16 to 17 141504 -1.1957 0.115914
15 to 16 141697 -0.6263 0.265545
14 to 15 141062 -2.4995 0.006218
13 to 14 142634 2.1377 0.983728
12 to 13 141940 0.0905 0.536044
11 to 12 142118 0.6155 0.730903
10 to 11 142127 0.6421 0.739594
9 to 10 141884 -0.0747 0.470219
8 to 9 142418 1.5005 0.933258
7 to 8 141775 -0.3963 0.345959
6 to 7 142544 1.8722 0.969409
5 to 6 142150 0.7099 0.761130
4 to 5 142101 0.5654 0.714099
3 to 4 141579 -0.9744 0.164923
2 to 3 142295 1.1377 0.872371
1 to 2 141778 -0.3874 0.349229
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-03_04:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2462.70 -0.527 0.298931
Test results for specific bytes for dh-ranFile-2018-07-03_04:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2614.92 1.625 0.947942
2 to 9 2426.77 -1.036 0.150174
3 to 10 2331.70 -2.380 0.008652
4 to 11 2478.51 -0.304 0.380590
5 to 12 2473.88 -0.369 0.355941
6 to 13 2462.24 -0.534 0.296691
7 to 14 2351.37 -2.102 0.017778
8 to 15 2553.93 0.763 0.777195
9 to 16 2559.64 0.843 0.800520
10 to 17 2526.48 0.375 0.645988
11 to 18 2489.39 -0.150 0.440351
12 to 19 2458.94 -0.581 0.280744
13 to 20 2483.36 -0.235 0.406987
14 to 21 2407.40 -1.310 0.095166
15 to 22 2546.66 0.660 0.745332
16 to 23 2599.61 1.409 0.920528
17 to 24 2645.71 2.061 0.980329
18 to 25 2498.80 -0.017 0.493233
19 to 26 2550.65 0.716 0.763084
20 to 27 2443.52 -0.799 0.212208
21 to 28 2531.08 0.440 0.669889
22 to 29 2466.70 -0.471 0.318844
23 to 30 2631.81 1.864 0.968840
24 to 31 2443.09 -0.805 0.210458
25 to 32 2491.45 -0.121 0.451902
CDPARK for dh-ranFile-2018-07-03_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
3539 0.7306 0.767486
3522 -0.0457 0.481790
3497 -1.1872 0.117571
3499 -1.0959 0.136563
3542 0.8676 0.807188
3499 -1.0959 0.136563
3527 0.1826 0.572463
3508 -0.6849 0.246694
3520 -0.1370 0.445521
3542 0.8676 0.807188
Square side=100, avg. no. parked=3519.50 sample std.=17.13
p-value of the KSTEST for those 10 p-values: 0.737135
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-03_04:31
0.6345,0.2860,0.0102,0.2580,0.7615,0.7951,0.6291,0.2510,0.8481,0.1021,
The KS test for those 10 p-values: 0.752751
The 3DSPHERES test for dh-ranFile-2018-07-03_04:31
sample no r^3 equiv. uni.
1 73.494 0.913690
2 31.454 0.649526
3 10.181 0.287783
4 3.050 0.096679
5 98.344 0.962301
6 11.603 0.320753
7 1.921 0.062037
8 6.572 0.196734
9 54.353 0.836635
10 6.466 0.193876
11 24.692 0.560918
12 20.648 0.497546
13 48.195 0.799412
14 9.115 0.262008
15 1.547 0.050253
16 31.801 0.653554
17 2.603 0.083105
18 8.756 0.253130
19 7.130 0.211539
20 88.462 0.947594
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.423692
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-03_04:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 -2.4 -1.1 -1.7 1.3 -0.2
-0.6 1.1 -0.1 -0.3 0.4 -1.5
0.6 1.1 -1.5 0.7 0.6 -0.8
1.6 0.4 -0.1 0.1 -2.6 0.6
1.0 -1.4 0.3 1.5 -1.6 -0.1
-0.4 -0.1 0.3 0.7 -0.8 -1.6
0.5 -0.7 0.1 -0.7 0.1 -1.0
2.7
Chi-square with 42 degrees of freedom:54.052932
z-score=1.315083, p-value=0.899395
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-03_04:31
Test no p-value
1 0.584974
2 0.002805
3 0.475476
4 0.174132
5 0.699004
6 0.002296
7 0.189878
8 0.358191
9 0.000004
10 0.614295
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.002032
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-03_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 66575 0.13 66640 0.01
3 25000.00 24975 0.03 25061 0.15
4 6666.67 6751 1.07 6572 1.34
5 1388.89 1412 0.38 1452 2.87
6 238.10 248 0.41 236 0.02
7 34.72 36 0.05 31 0.40
8 4.96 2 1.77 7 0.84
p=0.30006 p=0.53383
Number of rngs required: 691101, p-value: 0.999
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-03_04:31
No. of wins: Observed Expected
98371 98585.9
z-score=-0.961, pvalue=0.16828
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66286 66666.7 2.174 2.174
2 38033 37654.3 3.808 5.982
3 26943 26954.7 0.005 5.987
4 19612 19313.5 4.615 10.602
5 13611 13851.4 4.173 14.775
6 9973 9943.5 0.087 14.862
7 7073 7145.0 0.726 15.588
8 5124 5139.1 0.044 15.632
9 3771 3699.9 1.368 17.000
10 2651 2666.3 0.088 17.088
11 1908 1923.3 0.122 17.210
12 1373 1388.7 0.178 17.388
13 1022 1003.7 0.333 17.721
14 748 726.1 0.658 18.379
15 497 525.8 1.581 19.961
16 374 381.2 0.134 20.095
17 237 276.5 5.653 25.748
18 201 200.8 0.000 25.748
19 158 146.0 0.989 26.737
20 107 106.2 0.006 26.743
21 298 287.1 0.413 27.156
Chisq= 27.16 for 20 degrees of freedom, p= 0.86906
SUMMARY of craptest
p-value for no. of wins: 0.168283
p-value for throws/game: 0.869062
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-03_04:31
No. of wins: Observed Expected
98091 98585.9
z-score=-2.213, pvalue=0.01344
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66280 66666.7 2.243 2.243
2 38237 37654.3 9.017 11.259
3 26931 26954.7 0.021 11.280
4 19184 19313.5 0.868 12.148
5 13631 13851.4 3.508 15.656
6 9962 9943.5 0.034 15.690
7 7271 7145.0 2.221 17.911
8 5217 5139.1 1.182 19.093
9 3672 3699.9 0.210 19.302
10 2678 2666.3 0.051 19.354
11 1883 1923.3 0.846 20.199
12 1402 1388.7 0.127 20.326
13 1011 1003.7 0.053 20.379
14 731 726.1 0.033 20.411
15 551 525.8 1.204 21.616
16 371 381.2 0.270 21.886
17 285 276.5 0.259 22.145
18 204 200.8 0.050 22.195
19 132 146.0 1.340 23.535
20 95 106.2 1.184 24.719
21 272 287.1 0.796 25.514
Chisq= 25.51 for 20 degrees of freedom, p= 0.81754
SUMMARY of craptest
p-value for no. of wins: 0.013439
p-value for throws/game: 0.817542
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0000,0.0020,0.0023,0.0028,0.0062,0.0087,0.0102,0.0134,0.0134,0.0178,
0.0207,0.0395,0.0489,0.0503,0.0567,0.0620,0.0785,0.0831,0.0874,0.0893,
0.0917,0.0952,0.0967,0.0998,0.1001,0.1021,0.1107,0.1159,0.1176,0.1182,
0.1209,0.1278,0.1323,0.1362,0.1366,0.1366,0.1367,0.1442,0.1502,0.1541,
0.1643,0.1649,0.1683,0.1701,0.1719,0.1741,0.1786,0.1899,0.1915,0.1939,
0.1967,0.1992,0.2021,0.2076,0.2092,0.2105,0.2115,0.2122,0.2158,0.2191,
0.2206,0.2289,0.2306,0.2401,0.2443,0.2467,0.2510,0.2531,0.2580,0.2603,
0.2620,0.2643,0.2646,0.2655,0.2807,0.2840,0.2860,0.2878,0.2893,0.2918,
0.2967,0.2989,0.3001,0.3108,0.3188,0.3208,0.3237,0.3250,0.3281,0.3320,
0.3449,0.3460,0.3492,0.3506,0.3559,0.3582,0.3771,0.3786,0.3806,0.4018,
0.4070,0.4134,0.4154,0.4210,0.4237,0.4262,0.4263,0.4270,0.4404,0.4455,
0.4472,0.4519,0.4539,0.4556,0.4564,0.4593,0.4611,0.4633,0.4652,0.4667,
0.4702,0.4711,0.4718,0.4755,0.4806,0.4818,0.4851,0.4854,0.4874,0.4876,
0.4926,0.4932,0.4968,0.4975,0.4996,0.5023,0.5133,0.5185,0.5313,0.5338,
0.5341,0.5360,0.5374,0.5378,0.5477,0.5547,0.5609,0.5640,0.5680,0.5683,
0.5706,0.5725,0.5748,0.5762,0.5821,0.5833,0.5844,0.5850,0.5913,0.6025,
0.6032,0.6043,0.6044,0.6065,0.6137,0.6143,0.6233,0.6291,0.6293,0.6345,
0.6404,0.6460,0.6495,0.6536,0.6556,0.6686,0.6699,0.6718,0.6720,0.6761,
0.6833,0.6937,0.6990,0.7018,0.7107,0.7141,0.7198,0.7309,0.7355,0.7371,
0.7388,0.7396,0.7401,0.7406,0.7409,0.7453,0.7528,0.7611,0.7615,0.7631,
0.7643,0.7675,0.7724,0.7772,0.7838,0.7863,0.7872,0.7951,0.7994,0.8005,
0.8072,0.8072,0.8175,0.8239,0.8260,0.8278,0.8282,0.8293,0.8302,0.8366,
0.8386,0.8401,0.8436,0.8481,0.8486,0.8501,0.8588,0.8593,0.8603,0.8674,
0.8691,0.8699,0.8705,0.8724,0.8731,0.8774,0.8789,0.8802,0.8849,0.8861,
0.8988,0.8994,0.9033,0.9137,0.9138,0.9143,0.9201,0.9205,0.9221,0.9239,
0.9296,0.9323,0.9333,0.9374,0.9406,0.9419,0.9424,0.9476,0.9479,0.9498,
0.9509,0.9623,0.9640,0.9688,0.9694,0.9710,0.9803,0.9837,0.9995,
Overall p-value after applying KStest on 269 p-values = 0.694416
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.