RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-26_00:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.51 22.6040 0.837409
2 to 25 15.86 7.4807 0.023571
3 to 26 15.71 11.9062 0.194214
4 to 27 15.63 15.3454 0.429381
5 to 28 15.76 13.5689 0.302654
6 to 29 15.64 34.5014 0.992771
7 to 30 15.77 26.5132 0.934395
8 to 31 15.63 16.1427 0.486261
9 to 32 15.85 10.5964 0.123240
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.624785
Tough bday spacings test for dh-ranFile-2018-06-26_00:31: 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 41 72 96 92 78 46 26 22 12 6
(O-E)^2/E 0.0 0.5 0.0 0.0 0.3 0.0 0.7 0.5 3.4 4.4 0.9
Birthday Spacings: Sum(O-E)^2/E= 10.800, p= 0.627
RESULTS OF GCD FOR dh-ranFile-2018-06-26_00:31
Euclid's algorithm:
p-value, steps to gcd: 0.964093
p-value, dist. of gcd's: 0.089910
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-26_00:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.733 0.623 0.152 0.729 0.345 0.576 0.142 0.863
Bits 8 to 15---> 0.850 0.209 0.113 0.880 0.871 0.800 0.854 0.352
Bits 16 to 23---> 0.194 0.998 0.725 0.023 0.234 0.798 0.623 0.302
Bits 24 to 31---> 0.984 0.479 0.887 0.533 0.076 0.934 0.938 0.977
KS test for the above 32 p values: 0.929
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-26_00:31,
p-values for 5 runs: 0.1969, 0.6169, 0.3196, 0.8301, 0.0496
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-26_00:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 224 211.4 0.749 0.749
r= 29 5188 5134.0 0.568 1.317
r= 30 22977 23103.0 0.688 2.004
r= 31 11611 11551.5 0.306 2.310
chi-square = 2.310 with df = 3; p-value = 0.489
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-26_00:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 225 211.4 0.873 0.873
r= 30 5237 5134.0 2.066 2.939
r= 31 23121 23103.0 0.014 2.952
r= 32 11417 11551.5 1.567 4.519
chi-square = 4.519 with df = 3; p-value = 0.789
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-26_00:31
b-rank test for bits 1 to 8, p=0.48271
b-rank test for bits 2 to 9, p=0.38049
b-rank test for bits 3 to 10, p=0.15044
b-rank test for bits 4 to 11, p=0.57569
b-rank test for bits 5 to 12, p=0.92819
b-rank test for bits 6 to 13, p=0.87378
b-rank test for bits 7 to 14, p=0.39129
b-rank test for bits 8 to 15, p=0.13894
b-rank test for bits 9 to 16, p=0.62322
b-rank test for bits 10 to 17, p=0.03121
b-rank test for bits 11 to 18, p=0.42058
b-rank test for bits 12 to 19, p=0.58458
b-rank test for bits 13 to 20, p=0.75745
b-rank test for bits 14 to 21, p=0.13853
b-rank test for bits 15 to 22, p=0.90917
b-rank test for bits 16 to 23, p=0.96992
b-rank test for bits 17 to 24, p=0.12319
b-rank test for bits 18 to 25, p=0.34173
b-rank test for bits 19 to 26, p=0.18586
b-rank test for bits 20 to 27, p=0.54410
b-rank test for bits 21 to 28, p=0.48739
b-rank test for bits 22 to 29, p=0.50385
b-rank test for bits 23 to 30, p=0.27982
b-rank test for bits 24 to 31, p=0.04877
b-rank test for bits 25 to 32, p=0.53958
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 = 0.672249
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-26_00:31
(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 141315 -1.39 0.082474
2 141683 -0.53 0.298469
3 141932 0.05 0.521121
4 141962 0.12 0.548971
5 141654 -0.60 0.275399
6 141464 -1.04 0.149056
7 140984 -2.16 0.015310
8 141879 -0.07 0.471753
9 141513 -0.93 0.177222
10 141755 -0.36 0.359205
11 141978 0.16 0.563734
12 142274 0.85 0.802902
13 142145 0.55 0.709057
14 141835 -0.17 0.431063
15 141651 -0.60 0.273063
16 142392 1.13 0.870284
17 142270 0.84 0.800298
18 142187 0.65 0.741754
19 141821 -0.21 0.418248
20 141674 -0.55 0.291216
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-26_00:31
Bits used No. missing words z-score p-value
23 to 32 141790 -0.4115 0.340359
22 to 31 142110 0.6920 0.755521
21 to 30 141506 -1.3908 0.082144
20 to 29 141919 0.0333 0.513300
19 to 28 142095 0.6402 0.738992
18 to 27 142488 1.9954 0.977001
17 to 26 141490 -1.4460 0.074093
16 to 25 141508 -1.3839 0.083195
15 to 24 141877 -0.1115 0.455617
14 to 23 142038 0.4437 0.671367
13 to 22 142488 1.9954 0.977001
12 to 21 142177 0.9230 0.821996
11 to 20 141938 0.0989 0.539376
10 to 19 141789 -0.4149 0.339096
9 to 18 141508 -1.3839 0.083195
8 to 17 141433 -1.6425 0.050241
7 to 16 141945 0.1230 0.548947
6 to 15 141981 0.2471 0.597599
5 to 14 141902 -0.0253 0.489918
4 to 13 142032 0.4230 0.663852
3 to 12 142055 0.5023 0.692275
2 to 11 141897 -0.0425 0.483043
1 to 10 142421 1.7644 0.961166
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-26_00:31
Bits used No. missing words z-score p-value
28 to 32 142294 1.3040 0.903877
27 to 31 141793 -0.3943 0.346665
26 to 30 141968 0.1989 0.578822
25 to 29 141655 -0.8621 0.194306
24 to 28 141989 0.2701 0.606446
23 to 27 141547 -1.2282 0.109679
22 to 26 142371 1.5650 0.941207
21 to 25 142467 1.8904 0.970648
20 to 24 142151 0.8192 0.793670
19 to 23 142367 1.5514 0.939600
18 to 22 141846 -0.2147 0.415009
17 to 21 141520 -1.3198 0.093457
16 to 20 141743 -0.5638 0.286435
15 to 19 142123 0.7243 0.765561
14 to 18 142046 0.4633 0.678421
13 to 17 141739 -0.5774 0.281838
12 to 16 142050 0.4768 0.683265
11 to 15 141760 -0.5062 0.306357
10 to 14 141419 -1.6621 0.048243
9 to 13 142008 0.3345 0.630989
8 to 12 141594 -1.0689 0.142554
7 to 11 142145 0.7989 0.787820
6 to 10 142118 0.7074 0.760327
5 to 9 141829 -0.2723 0.392694
4 to 8 142080 0.5785 0.718551
3 to 7 141521 -1.3164 0.094024
2 to 6 141673 -0.8011 0.211532
1 to 5 141594 -1.0689 0.142554
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-26_00:31
Bits used No. missing words z-score p-value
31 to 32 142533 1.8397 0.967096
30 to 31 141348 -1.6558 0.048877
29 to 30 141593 -0.9331 0.175377
28 to 29 142113 0.6008 0.726012
27 to 28 142404 1.4592 0.927745
26 to 27 141587 -0.9508 0.170846
25 to 26 142399 1.4445 0.925694
24 to 25 142318 1.2055 0.885998
23 to 24 141636 -0.8063 0.210040
22 to 23 142259 1.0315 0.848841
21 to 22 141808 -0.2989 0.382505
20 to 21 141741 -0.4965 0.309754
19 to 20 142485 1.6981 0.955259
18 to 19 142284 1.1052 0.865468
17 to 18 141517 -1.1573 0.123572
16 to 17 142318 1.2055 0.885998
15 to 16 141864 -0.1337 0.446813
14 to 15 141967 0.1701 0.567541
13 to 14 142554 1.9017 0.971394
12 to 13 141844 -0.1927 0.423592
11 to 12 142165 0.7542 0.774632
10 to 11 141991 0.2409 0.595189
9 to 10 141406 -1.4847 0.068805
8 to 9 141509 -1.1809 0.118818
7 to 8 141993 0.2468 0.597474
6 to 7 141692 -0.6411 0.260732
5 to 6 141820 -0.2635 0.396079
4 to 5 142350 1.2999 0.903184
3 to 4 141815 -0.2783 0.390407
2 to 3 141987 0.2291 0.590610
1 to 2 142013 0.3058 0.620126
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-26_00:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2512.60 0.178 0.570720
Test results for specific bytes for dh-ranFile-2018-06-26_00:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2444.08 -0.791 0.214539
2 to 9 2601.61 1.437 0.924630
3 to 10 2655.33 2.197 0.985979
4 to 11 2370.50 -1.831 0.033524
5 to 12 2305.99 -2.744 0.003037
6 to 13 2554.75 0.774 0.780629
7 to 14 2472.67 -0.386 0.349586
8 to 15 2501.58 0.022 0.508926
9 to 16 2449.13 -0.719 0.235954
10 to 17 2473.24 -0.378 0.352538
11 to 18 2410.62 -1.264 0.103118
12 to 19 2393.03 -1.513 0.065159
13 to 20 2469.64 -0.429 0.333843
14 to 21 2522.35 0.316 0.624052
15 to 22 2378.37 -1.720 0.042701
16 to 23 2411.64 -1.250 0.105728
17 to 24 2432.93 -0.948 0.171447
18 to 25 2493.33 -0.094 0.462415
19 to 26 2583.68 1.183 0.881670
20 to 27 2595.40 1.349 0.911347
21 to 28 2421.24 -1.114 0.132672
22 to 29 2455.53 -0.629 0.264729
23 to 30 2482.82 -0.243 0.403994
24 to 31 2492.32 -0.109 0.456771
25 to 32 2421.43 -1.111 0.133250
CDPARK for dh-ranFile-2018-06-26_00:31: 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
3537 0.6393 0.738676
3580 2.6027 0.995376
3507 -0.7306 0.232514
3556 1.5068 0.934075
3503 -0.9132 0.180558
3546 1.0502 0.853193
3511 -0.5479 0.291865
3512 -0.5023 0.307734
3515 -0.3653 0.357445
3513 -0.4566 0.323972
Square side=100, avg. no. parked=3528.00 sample std.=24.29
p-value of the KSTEST for those 10 p-values: 0.441517
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-26_00:31
0.3038,0.8234,0.5744,0.8954,0.0361,0.0250,0.5612,0.9939,0.3228,0.3464,
The KS test for those 10 p-values: 0.670730
The 3DSPHERES test for dh-ranFile-2018-06-26_00:31
sample no r^3 equiv. uni.
1 8.446 0.245371
2 106.443 0.971221
3 63.101 0.877953
4 4.955 0.152235
5 149.359 0.993117
6 8.307 0.241879
7 110.906 0.975199
8 29.738 0.628898
9 95.015 0.957877
10 15.396 0.401422
11 58.545 0.857939
12 11.426 0.316729
13 17.284 0.437927
14 19.668 0.480873
15 11.425 0.316697
16 40.799 0.743334
17 10.169 0.287494
18 26.479 0.586306
19 88.277 0.947269
20 72.912 0.912000
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.039346
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-26_00:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -0.3 0.3 0.3 -0.3 0.3
1.2 2.2 0.4 1.7 0.6 0.8
-0.6 0.1 -0.9 -0.5 -0.7 0.4
-1.3 -0.2 0.9 -1.3 -0.7 1.0
1.5 -0.1 -0.4 1.2 -1.2 -0.7
-0.5 1.9 -0.4 0.4 -0.4 0.1
-0.2 0.8 1.3 -1.3 0.1 0.0
-1.1
Chi-square with 42 degrees of freedom:33.744027
z-score=-0.900800, p-value=0.185769
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-26_00:31
Test no p-value
1 0.297781
2 0.038428
3 0.159931
4 0.105120
5 0.936743
6 0.044254
7 0.021184
8 0.407210
9 0.113835
10 0.484796
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.005951
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-26_00:31:
(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 66815 0.33 66687 0.01
3 25000.00 24814 1.38 24967 0.04
4 6666.67 6722 0.46 6639 0.11
5 1388.89 1363 0.48 1477 5.59
6 238.10 244 0.15 190 9.72
7 34.72 35 0.00 37 0.15
8 4.96 6 0.22 2 1.77
p=0.19398 p=0.99203
Number of rngs required: 688192, p-value: 0.404
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-26_00:31
No. of wins: Observed Expected
98299 98585.9
z-score=-1.283, pvalue=0.09975
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66643 66666.7 0.008 0.008
2 37918 37654.3 1.846 1.855
3 26827 26954.7 0.605 2.460
4 19089 19313.5 2.609 5.069
5 14025 13851.4 2.175 7.244
6 9986 9943.5 0.181 7.425
7 7048 7145.0 1.318 8.743
8 5081 5139.1 0.656 9.399
9 3615 3699.9 1.947 11.346
10 2697 2666.3 0.354 11.699
11 1963 1923.3 0.818 12.518
12 1464 1388.7 4.079 16.596
13 998 1003.7 0.033 16.629
14 734 726.1 0.085 16.714
15 481 525.8 3.823 20.537
16 386 381.2 0.062 20.598
17 273 276.5 0.045 20.644
18 214 200.8 0.864 21.507
19 150 146.0 0.110 21.618
20 94 106.2 1.405 23.023
21 314 287.1 2.518 25.540
Chisq= 25.54 for 20 degrees of freedom, p= 0.81846
SUMMARY of craptest
p-value for no. of wins: 0.099746
p-value for throws/game: 0.818461
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-26_00:31
No. of wins: Observed Expected
98463 98585.9
z-score=-0.549, pvalue=0.29133
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66504 66666.7 0.397 0.397
2 37561 37654.3 0.231 0.628
3 26998 26954.7 0.069 0.698
4 19487 19313.5 1.559 2.257
5 13791 13851.4 0.264 2.520
6 10036 9943.5 0.860 3.380
7 7144 7145.0 0.000 3.380
8 5057 5139.1 1.311 4.691
9 3851 3699.9 6.174 10.865
10 2620 2666.3 0.804 11.669
11 1917 1923.3 0.021 11.689
12 1414 1388.7 0.459 12.149
13 998 1003.7 0.033 12.181
14 738 726.1 0.194 12.375
15 554 525.8 1.508 13.884
16 373 381.2 0.174 14.058
17 237 276.5 5.653 19.711
18 202 200.8 0.007 19.718
19 128 146.0 2.216 21.934
20 109 106.2 0.073 22.007
21 281 287.1 0.130 22.137
Chisq= 22.14 for 20 degrees of freedom, p= 0.66687
SUMMARY of craptest
p-value for no. of wins: 0.291333
p-value for throws/game: 0.666868
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0030,0.0060,0.0153,0.0212,0.0225,0.0236,0.0250,0.0312,0.0335,0.0361,
0.0384,0.0393,0.0427,0.0443,0.0482,0.0488,0.0489,0.0496,0.0502,0.0652,
0.0688,0.0741,0.0760,0.0821,0.0825,0.0832,0.0832,0.0899,0.0935,0.0940,
0.0997,0.1031,0.1051,0.1057,0.1097,0.1132,0.1138,0.1188,0.1232,0.1232,
0.1236,0.1327,0.1332,0.1385,0.1389,0.1421,0.1426,0.1426,0.1491,0.1504,
0.1516,0.1522,0.1599,0.1708,0.1714,0.1754,0.1772,0.1806,0.1858,0.1859,
0.1940,0.1940,0.1942,0.1943,0.1969,0.2093,0.2100,0.2115,0.2145,0.2325,
0.2337,0.2360,0.2419,0.2454,0.2607,0.2647,0.2731,0.2754,0.2798,0.2818,
0.2864,0.2875,0.2912,0.2913,0.2919,0.2978,0.2985,0.3025,0.3027,0.3038,
0.3064,0.3077,0.3098,0.3167,0.3167,0.3196,0.3228,0.3240,0.3338,0.3391,
0.3404,0.3417,0.3453,0.3464,0.3467,0.3496,0.3516,0.3525,0.3574,0.3592,
0.3805,0.3825,0.3904,0.3913,0.3927,0.3961,0.4014,0.4040,0.4041,0.4072,
0.4150,0.4182,0.4206,0.4236,0.4294,0.4311,0.4379,0.4415,0.4468,0.4556,
0.4568,0.4624,0.4718,0.4792,0.4809,0.4827,0.4830,0.4848,0.4863,0.4874,
0.4895,0.4899,0.5038,0.5089,0.5133,0.5211,0.5333,0.5394,0.5396,0.5441,
0.5489,0.5490,0.5612,0.5637,0.5675,0.5707,0.5744,0.5757,0.5765,0.5788,
0.5846,0.5863,0.5906,0.5952,0.5975,0.5976,0.6064,0.6169,0.6201,0.6231,
0.6232,0.6235,0.6241,0.6248,0.6267,0.6289,0.6310,0.6639,0.6669,0.6707,
0.6714,0.6722,0.6784,0.6833,0.6923,0.7091,0.7186,0.7253,0.7260,0.7292,
0.7328,0.7387,0.7390,0.7418,0.7433,0.7555,0.7575,0.7603,0.7656,0.7746,
0.7806,0.7878,0.7894,0.7937,0.7983,0.8001,0.8003,0.8029,0.8185,0.8220,
0.8234,0.8301,0.8374,0.8488,0.8498,0.8532,0.8535,0.8579,0.8626,0.8655,
0.8703,0.8707,0.8738,0.8780,0.8804,0.8817,0.8860,0.8860,0.8872,0.8954,
0.9032,0.9039,0.9092,0.9113,0.9120,0.9246,0.9257,0.9277,0.9282,0.9293,
0.9340,0.9341,0.9344,0.9367,0.9380,0.9396,0.9412,0.9473,0.9553,0.9579,
0.9612,0.9641,0.9671,0.9699,0.9706,0.9712,0.9714,0.9752,0.9766,0.9770,
0.9770,0.9843,0.9860,0.9920,0.9928,0.9931,0.9939,0.9954,0.9983,
Overall p-value after applying KStest on 269 p-values = 0.138420
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.