RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-07_09:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.88 18.7881 0.659171
2 to 25 15.62 15.4731 0.438555
3 to 26 15.61 23.4907 0.866053
4 to 27 15.35 25.7531 0.920921
5 to 28 15.61 10.6206 0.124404
6 to 29 15.86 16.8087 0.532602
7 to 30 15.71 17.7190 0.593227
8 to 31 15.80 17.0819 0.551166
9 to 32 15.60 18.4697 0.640192
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.402306
Tough bday spacings test for dh-ranFile-2018-07-07_09:31: 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 15 42 66 103 111 80 42 25 7 6 3
(O-E)^2/E 3.7 0.8 0.7 0.3 1.8 0.0 2.0 0.8 4.2 0.1 0.3
Birthday Spacings: Sum(O-E)^2/E= 14.618, p= 0.853
RESULTS OF GCD FOR dh-ranFile-2018-07-07_09:31
Euclid's algorithm:
p-value, steps to gcd: 0.465564
p-value, dist. of gcd's: 0.322364
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-07_09:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.977 0.206 0.590 0.987 0.042 0.716 0.528 0.192
Bits 8 to 15---> 0.040 0.571 0.719 0.750 0.288 0.028 0.206 0.599
Bits 16 to 23---> 0.526 0.772 0.927 0.044 0.491 0.973 0.486 0.275
Bits 24 to 31---> 0.347 0.608 0.727 0.866 0.403 0.910 0.417 0.529
KS test for the above 32 p values: 0.229
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-07_09:31,
p-values for 5 runs: 0.7863, 0.3153, 0.8093, 0.3948, 0.9130
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-07_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 234 211.4 2.412 2.412
r= 29 5123 5134.0 0.024 2.436
r= 30 23029 23103.0 0.237 2.673
r= 31 11614 11551.5 0.338 3.011
chi-square = 3.011 with df = 3; p-value = 0.610
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-07_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 209 211.4 0.028 0.028
r= 30 5101 5134.0 0.212 0.240
r= 31 23117 23103.0 0.008 0.248
r= 32 11573 11551.5 0.040 0.288
chi-square = 0.288 with df = 3; p-value = 0.038
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-07_09:31
b-rank test for bits 1 to 8, p=0.89769
b-rank test for bits 2 to 9, p=0.59100
b-rank test for bits 3 to 10, p=0.37801
b-rank test for bits 4 to 11, p=0.33889
b-rank test for bits 5 to 12, p=0.71650
b-rank test for bits 6 to 13, p=0.63230
b-rank test for bits 7 to 14, p=0.95092
b-rank test for bits 8 to 15, p=0.41375
b-rank test for bits 9 to 16, p=0.00789
b-rank test for bits 10 to 17, p=0.94419
b-rank test for bits 11 to 18, p=0.58475
b-rank test for bits 12 to 19, p=0.19082
b-rank test for bits 13 to 20, p=0.49132
b-rank test for bits 14 to 21, p=0.92507
b-rank test for bits 15 to 22, p=0.77395
b-rank test for bits 16 to 23, p=0.96058
b-rank test for bits 17 to 24, p=0.54223
b-rank test for bits 18 to 25, p=0.49762
b-rank test for bits 19 to 26, p=0.30304
b-rank test for bits 20 to 27, p=0.64216
b-rank test for bits 21 to 28, p=0.21249
b-rank test for bits 22 to 29, p=0.38604
b-rank test for bits 23 to 30, p=0.05987
b-rank test for bits 24 to 31, p=0.53924
b-rank test for bits 25 to 32, p=0.42437
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 = 0.623566
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-07_09:31
(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 142468 1.31 0.904105
2 142001 0.21 0.584798
3 142177 0.63 0.734145
4 142313 0.94 0.827199
5 141696 -0.50 0.309089
6 141486 -0.99 0.161310
7 142218 0.72 0.764604
8 141795 -0.27 0.394686
9 141729 -0.42 0.336756
10 141828 -0.19 0.424645
11 141400 -1.19 0.117019
12 141713 -0.46 0.323219
13 142341 1.01 0.843411
14 142038 0.30 0.618152
15 141469 -1.03 0.151785
16 141965 0.13 0.551745
17 141585 -0.76 0.224291
18 142228 0.74 0.771730
19 141610 -0.70 0.242161
20 142325 0.97 0.834274
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-07_09:31
Bits used No. missing words z-score p-value
23 to 32 141622 -0.9908 0.160893
22 to 31 141891 -0.0632 0.474801
21 to 30 142106 0.6782 0.751169
20 to 29 142169 0.8954 0.814717
19 to 28 142421 1.7644 0.961166
18 to 27 141749 -0.5529 0.290179
17 to 26 142044 0.4644 0.678812
16 to 25 142398 1.6851 0.954012
15 to 24 142067 0.5437 0.706673
14 to 23 141223 -2.3667 0.008975
13 to 22 142098 0.6506 0.742343
12 to 21 142223 1.0816 0.860289
11 to 20 141823 -0.2977 0.382970
10 to 19 141997 0.3023 0.618792
9 to 18 142470 1.9333 0.973403
8 to 17 141644 -0.9149 0.180114
7 to 16 141834 -0.2598 0.397525
6 to 15 141895 -0.0494 0.480295
5 to 14 141620 -0.9977 0.159215
4 to 13 141609 -1.0356 0.150190
3 to 12 142212 1.0437 0.851686
2 to 11 141675 -0.8080 0.209535
1 to 10 141701 -0.7184 0.236262
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-07_09:31
Bits used No. missing words z-score p-value
28 to 32 142011 0.3446 0.634819
27 to 31 142403 1.6735 0.952881
26 to 30 141970 0.2057 0.581472
25 to 29 142300 1.3243 0.907299
24 to 28 141771 -0.4689 0.319565
23 to 27 141775 -0.4554 0.324427
22 to 26 142038 0.4362 0.668643
21 to 25 142084 0.5921 0.723109
20 to 24 142460 1.8667 0.969027
19 to 23 141538 -1.2587 0.104061
18 to 22 141551 -1.2147 0.112244
17 to 21 141812 -0.3299 0.370726
16 to 20 142269 1.2192 0.888620
15 to 19 142495 1.9853 0.976446
14 to 18 141929 0.0667 0.526581
13 to 17 141343 -1.9198 0.027444
12 to 16 142726 2.7684 0.997183
11 to 15 142155 0.8328 0.797516
10 to 14 142043 0.4531 0.674768
9 to 13 141667 -0.8215 0.205693
8 to 12 141930 0.0701 0.527930
7 to 11 141715 -0.6587 0.255030
6 to 10 141624 -0.9672 0.166717
5 to 9 141578 -1.1232 0.130686
4 to 8 141829 -0.2723 0.392694
3 to 7 142353 1.5040 0.933705
2 to 6 141987 0.2633 0.603836
1 to 5 141660 -0.8452 0.199003
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-07_09:31
Bits used No. missing words z-score p-value
31 to 32 142015 0.3117 0.622370
30 to 31 141886 -0.0688 0.472566
29 to 30 141991 0.2409 0.595189
28 to 29 142344 1.2822 0.900116
27 to 28 142255 1.0197 0.846059
26 to 27 142081 0.5064 0.693713
25 to 26 141361 -1.6175 0.052886
24 to 25 141980 0.2085 0.582568
23 to 24 141664 -0.7237 0.234629
22 to 23 142564 1.9312 0.973270
21 to 22 142506 1.7601 0.960804
20 to 21 142244 0.9872 0.838234
19 to 20 142040 0.3855 0.650051
18 to 19 141701 -0.6145 0.269428
17 to 18 142132 0.6568 0.744359
16 to 17 141788 -0.3579 0.360207
15 to 16 141039 -2.5673 0.005124
14 to 15 141591 -0.9390 0.173859
13 to 14 141868 -0.1219 0.451482
12 to 13 141425 -1.4287 0.076545
11 to 12 142183 0.8073 0.790249
10 to 11 142914 2.9636 0.998480
9 to 10 141777 -0.3904 0.348137
8 to 9 142292 1.1288 0.870513
7 to 8 142617 2.0875 0.981580
6 to 7 141898 -0.0334 0.486669
5 to 6 142255 1.0197 0.846059
4 to 5 141318 -1.7443 0.040550
3 to 4 141927 0.0521 0.520785
2 to 3 142040 0.3855 0.650051
1 to 2 142728 2.4150 0.992131
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-07_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2485.25 -0.209 0.417370
Test results for specific bytes for dh-ranFile-2018-07-07_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2560.17 0.851 0.802598
2 to 9 2506.57 0.093 0.537019
3 to 10 2468.63 -0.444 0.328668
4 to 11 2509.11 0.129 0.551272
5 to 12 2589.53 1.266 0.897274
6 to 13 2520.37 0.288 0.613340
7 to 14 2459.10 -0.578 0.281496
8 to 15 2466.59 -0.472 0.318305
9 to 16 2342.79 -2.223 0.013097
10 to 17 2469.31 -0.434 0.332115
11 to 18 2519.06 0.270 0.606265
12 to 19 2569.29 0.980 0.836424
13 to 20 2456.02 -0.622 0.267002
14 to 21 2524.36 0.345 0.634779
15 to 22 2356.24 -2.033 0.021022
16 to 23 2427.87 -1.020 0.153860
17 to 24 2497.71 -0.032 0.487057
18 to 25 2519.57 0.277 0.608999
19 to 26 2455.36 -0.631 0.263923
20 to 27 2601.65 1.438 0.924716
21 to 28 2576.43 1.081 0.860133
22 to 29 2460.85 -0.554 0.289920
23 to 30 2498.14 -0.026 0.489522
24 to 31 2556.62 0.801 0.788355
25 to 32 2421.06 -1.116 0.132134
CDPARK for dh-ranFile-2018-07-07_09:31: 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
3487 -1.6438 0.050105
3519 -0.1826 0.427537
3498 -1.1416 0.126820
3527 0.1826 0.572463
3499 -1.0959 0.136563
3531 0.3653 0.642555
3546 1.0502 0.853193
3530 0.3196 0.625377
3516 -0.3196 0.374623
3481 -1.9178 0.027568
Square side=100, avg. no. parked=3513.40 sample std.=20.16
p-value of the KSTEST for those 10 p-values: 0.298238
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-07_09:31
0.7380,0.6012,0.0004,0.8141,0.8251,0.1976,0.7756,0.9719,0.0999,0.3016,
The KS test for those 10 p-values: 0.422949
The 3DSPHERES test for dh-ranFile-2018-07-07_09:31
sample no r^3 equiv. uni.
1 5.204 0.159247
2 0.495 0.016354
3 21.834 0.517023
4 21.296 0.508286
5 31.894 0.654634
6 58.797 0.859125
7 2.288 0.073426
8 63.986 0.881503
9 22.280 0.524158
10 40.088 0.737179
11 24.845 0.563144
12 12.518 0.341149
13 5.016 0.153980
14 24.151 0.552929
15 30.630 0.639767
16 4.381 0.135874
17 40.005 0.736450
18 2.480 0.079329
19 2.263 0.072672
20 1.670 0.054139
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.169461
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-07_09:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -1.6 -1.1 -0.5 0.0 0.1
-0.6 0.2 -1.9 -0.1 0.0 1.7
-0.3 0.7 3.5 -1.1 -2.3 0.7
-0.8 0.9 -1.6 0.4 1.5 -0.5
-0.9 0.3 0.1 -0.5 0.7 -1.0
0.8 -2.6 0.3 -1.9 -1.3 -0.1
-0.5 -0.7 -0.4 -0.7 0.1 1.0
-1.1
Chi-square with 42 degrees of freedom:57.006098
z-score=1.637300, p-value=0.938930
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-07_09:31
Test no p-value
1 0.155909
2 0.724457
3 0.021251
4 0.131509
5 0.591242
6 0.633870
7 0.106587
8 0.027129
9 0.098936
10 0.811776
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.036610
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-07_09:31:
(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 66646 0.01 66369 1.33
3 25000.00 24891 0.48 25385 5.93
4 6666.67 6758 1.25 6534 2.64
5 1388.89 1430 1.22 1433 1.40
6 238.10 228 0.43 241 0.04
7 34.72 41 1.14 31 0.40
8 4.96 5 0.00 6 0.22
p=0.39251 p=0.93694
Number of rngs required: 688451, p-value: 0.522
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-07_09:31
No. of wins: Observed Expected
98730 98585.9
z-score= 0.645, pvalue=0.74043
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66698 66666.7 0.015 0.015
2 37395 37654.3 1.786 1.801
3 27001 26954.7 0.079 1.880
4 19451 19313.5 0.979 2.860
5 13842 13851.4 0.006 2.866
6 9845 9943.5 0.977 3.843
7 7115 7145.0 0.126 3.969
8 5107 5139.1 0.200 4.169
9 3730 3699.9 0.245 4.414
10 2765 2666.3 3.654 8.068
11 1952 1923.3 0.427 8.496
12 1411 1388.7 0.357 8.852
13 1004 1003.7 0.000 8.852
14 750 726.1 0.784 9.636
15 505 525.8 0.826 10.462
16 397 381.2 0.659 11.121
17 279 276.5 0.022 11.143
18 222 200.8 2.232 13.375
19 132 146.0 1.340 14.714
20 105 106.2 0.014 14.728
21 294 287.1 0.165 14.893
Chisq= 14.89 for 20 degrees of freedom, p= 0.21751
SUMMARY of craptest
p-value for no. of wins: 0.740434
p-value for throws/game: 0.217514
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-07_09:31
No. of wins: Observed Expected
98749 98585.9
z-score= 0.730, pvalue=0.76720
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66827 66666.7 0.386 0.386
2 37274 37654.3 3.841 4.227
3 26960 26954.7 0.001 4.228
4 19544 19313.5 2.752 6.980
5 13754 13851.4 0.685 7.665
6 10132 9943.5 3.572 11.237
7 7023 7145.0 2.084 13.321
8 5079 5139.1 0.702 14.023
9 3748 3699.9 0.626 14.649
10 2666 2666.3 0.000 14.649
11 1889 1923.3 0.613 15.262
12 1422 1388.7 0.797 16.059
13 998 1003.7 0.033 16.091
14 735 726.1 0.108 16.199
15 509 525.8 0.539 16.738
16 396 381.2 0.579 17.317
17 281 276.5 0.072 17.389
18 202 200.8 0.007 17.396
19 146 146.0 0.000 17.396
20 117 106.2 1.095 18.491
21 298 287.1 0.413 18.903
Chisq= 18.90 for 20 degrees of freedom, p= 0.47188
SUMMARY of craptest
p-value for no. of wins: 0.767202
p-value for throws/game: 0.471881
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0004,0.0051,0.0079,0.0090,0.0131,0.0164,0.0210,0.0213,0.0271,0.0274,
0.0276,0.0284,0.0366,0.0378,0.0404,0.0406,0.0418,0.0436,0.0501,0.0529,
0.0541,0.0599,0.0727,0.0734,0.0765,0.0793,0.0989,0.0999,0.1041,0.1066,
0.1122,0.1170,0.1244,0.1268,0.1307,0.1315,0.1321,0.1359,0.1366,0.1502,
0.1518,0.1539,0.1540,0.1559,0.1592,0.1592,0.1609,0.1613,0.1667,0.1695,
0.1739,0.1801,0.1908,0.1917,0.1976,0.1990,0.2057,0.2060,0.2063,0.2095,
0.2125,0.2175,0.2243,0.2294,0.2346,0.2363,0.2422,0.2550,0.2639,0.2670,
0.2694,0.2747,0.2815,0.2884,0.2899,0.2902,0.2982,0.3016,0.3030,0.3091,
0.3153,0.3183,0.3196,0.3224,0.3232,0.3244,0.3287,0.3321,0.3368,0.3389,
0.3411,0.3467,0.3481,0.3602,0.3707,0.3746,0.3780,0.3830,0.3860,0.3925,
0.3927,0.3947,0.3948,0.3975,0.4023,0.4027,0.4138,0.4172,0.4174,0.4229,
0.4244,0.4246,0.4275,0.4386,0.4515,0.4656,0.4719,0.4726,0.4748,0.4803,
0.4863,0.4867,0.4871,0.4895,0.4913,0.4914,0.4976,0.5083,0.5170,0.5208,
0.5220,0.5242,0.5257,0.5266,0.5279,0.5279,0.5294,0.5326,0.5370,0.5392,
0.5422,0.5512,0.5513,0.5517,0.5529,0.5631,0.5708,0.5725,0.5815,0.5826,
0.5848,0.5848,0.5896,0.5910,0.5912,0.5932,0.5952,0.5987,0.6012,0.6038,
0.6063,0.6079,0.6090,0.6100,0.6133,0.6182,0.6188,0.6224,0.6236,0.6254,
0.6323,0.6339,0.6348,0.6348,0.6398,0.6402,0.6422,0.6426,0.6501,0.6501,
0.6546,0.6592,0.6686,0.6748,0.6788,0.6937,0.7067,0.7161,0.7165,0.7195,
0.7231,0.7245,0.7266,0.7341,0.7364,0.7372,0.7380,0.7404,0.7423,0.7444,
0.7497,0.7512,0.7646,0.7672,0.7715,0.7717,0.7739,0.7756,0.7863,0.7884,
0.7902,0.7975,0.8026,0.8093,0.8118,0.8141,0.8147,0.8251,0.8272,0.8343,
0.8364,0.8382,0.8434,0.8461,0.8461,0.8517,0.8532,0.8534,0.8591,0.8601,
0.8603,0.8660,0.8661,0.8705,0.8815,0.8886,0.8973,0.8977,0.9001,0.9041,
0.9073,0.9102,0.9130,0.9209,0.9247,0.9251,0.9272,0.9337,0.9369,0.9389,
0.9442,0.9509,0.9529,0.9540,0.9606,0.9608,0.9612,0.9690,0.9719,0.9726,
0.9733,0.9734,0.9764,0.9769,0.9816,0.9874,0.9921,0.9972,0.9985,
Overall p-value after applying KStest on 269 p-values = 0.829506
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.