RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-19_01:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.44 26.3819 0.932221
2 to 25 15.55 28.1516 0.956802
3 to 26 15.60 13.7104 0.312514
4 to 27 15.76 12.6768 0.242463
5 to 28 15.74 16.8223 0.533534
6 to 29 15.56 21.8376 0.808953
7 to 30 15.74 16.5957 0.517935
8 to 31 15.91 12.4743 0.229397
9 to 32 15.92 15.3430 0.429210
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.703819
Tough bday spacings test for dh-ranFile-2018-06-19_01:31: 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 8 43 78 93 88 75 62 28 13 7 5
(O-E)^2/E 0.1 1.1 0.3 0.2 1.0 0.1 1.9 0.1 0.2 0.0 0.2
Birthday Spacings: Sum(O-E)^2/E= 5.334, p= 0.132
RESULTS OF GCD FOR dh-ranFile-2018-06-19_01:31
Euclid's algorithm:
p-value, steps to gcd: 0.519449
p-value, dist. of gcd's: 0.778696
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-19_01:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.570 0.207 0.688 0.236 0.303 0.757 0.200 0.756
Bits 8 to 15---> 0.250 0.722 0.896 0.409 0.495 0.944 0.349 0.289
Bits 16 to 23---> 0.229 0.187 0.598 0.031 0.202 0.951 0.851 0.698
Bits 24 to 31---> 0.024 0.142 0.469 0.821 0.272 0.054 0.787 0.911
KS test for the above 32 p values: 0.187
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-19_01:31,
p-values for 5 runs: 0.6712, 0.5634, 0.2428, 0.4456, 0.3195
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-19_01:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 222 211.4 0.530 0.530
r= 29 5092 5134.0 0.344 0.873
r= 30 23186 23103.0 0.298 1.171
r= 31 11500 11551.5 0.230 1.401
chi-square = 1.401 with df = 3; p-value = 0.295
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-19_01:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 208 211.4 0.055 0.055
r= 30 5149 5134.0 0.044 0.099
r= 31 23134 23103.0 0.041 0.140
r= 32 11509 11551.5 0.157 0.297
chi-square = 0.297 with df = 3; p-value = 0.039
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-19_01:31
b-rank test for bits 1 to 8, p=0.41268
b-rank test for bits 2 to 9, p=0.06558
b-rank test for bits 3 to 10, p=0.51090
b-rank test for bits 4 to 11, p=0.96847
b-rank test for bits 5 to 12, p=0.71284
b-rank test for bits 6 to 13, p=0.09059
b-rank test for bits 7 to 14, p=0.78626
b-rank test for bits 8 to 15, p=0.87142
b-rank test for bits 9 to 16, p=0.67489
b-rank test for bits 10 to 17, p=0.85105
b-rank test for bits 11 to 18, p=0.87028
b-rank test for bits 12 to 19, p=0.25602
b-rank test for bits 13 to 20, p=0.46608
b-rank test for bits 14 to 21, p=0.47377
b-rank test for bits 15 to 22, p=0.23188
b-rank test for bits 16 to 23, p=0.25213
b-rank test for bits 17 to 24, p=0.05943
b-rank test for bits 18 to 25, p=0.25229
b-rank test for bits 19 to 26, p=0.15600
b-rank test for bits 20 to 27, p=0.33074
b-rank test for bits 21 to 28, p=0.73110
b-rank test for bits 22 to 29, p=0.80816
b-rank test for bits 23 to 30, p=0.35444
b-rank test for bits 24 to 31, p=0.79338
b-rank test for bits 25 to 32, p=0.38692
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 = 0.953824
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-19_01:31
(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 143101 2.78 0.997318
2 141860 -0.12 0.454121
3 141582 -0.76 0.222198
4 142608 1.63 0.948703
5 142340 1.01 0.842850
6 141914 0.01 0.504353
7 141028 -2.06 0.019738
8 142129 0.51 0.696111
9 142894 2.30 0.989294
10 141964 0.13 0.550820
11 141623 -0.67 0.251749
12 141853 -0.13 0.447646
13 142392 1.13 0.870284
14 141692 -0.51 0.305804
15 141952 0.10 0.539707
16 142513 1.41 0.920796
17 141642 -0.62 0.266116
18 141907 -0.01 0.497828
19 141962 0.12 0.548971
20 142133 0.52 0.699371
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-19_01:31
Bits used No. missing words z-score p-value
23 to 32 142296 1.3333 0.908791
22 to 31 141583 -1.1253 0.130236
21 to 30 142128 0.7540 0.774586
20 to 29 141693 -0.7460 0.227844
19 to 28 141654 -0.8804 0.189308
18 to 27 142013 0.3575 0.639635
17 to 26 141957 0.1644 0.565284
16 to 25 141796 -0.3908 0.347975
15 to 24 141987 0.2678 0.605584
14 to 23 141479 -1.4839 0.068918
13 to 22 141755 -0.5322 0.297303
12 to 21 142018 0.3747 0.646067
11 to 20 141980 0.2437 0.596264
10 to 19 142159 0.8609 0.805362
9 to 18 142167 0.8885 0.812869
8 to 17 141491 -1.4425 0.074578
7 to 16 142143 0.8058 0.789809
6 to 15 142145 0.8127 0.791792
5 to 14 142234 1.1196 0.868548
4 to 13 141887 -0.0770 0.469312
3 to 12 142102 0.6644 0.746776
2 to 11 142155 0.8471 0.801541
1 to 10 142638 2.5127 0.994009
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-19_01:31
Bits used No. missing words z-score p-value
28 to 32 141381 -1.7909 0.036651
27 to 31 141903 -0.0215 0.491440
26 to 30 141817 -0.3130 0.377147
25 to 29 141416 -1.6723 0.047232
24 to 28 141461 -1.5198 0.064285
23 to 27 142070 0.5446 0.707001
22 to 26 141929 0.0667 0.526581
21 to 25 142088 0.6057 0.727630
20 to 24 142557 2.1955 0.985936
19 to 23 141454 -1.5435 0.061356
18 to 22 141436 -1.6045 0.054301
17 to 21 141684 -0.7638 0.222484
16 to 20 141512 -1.3469 0.089009
15 to 19 142024 0.3887 0.651255
14 to 18 141693 -0.7333 0.231681
13 to 17 142121 0.7175 0.763475
12 to 16 141781 -0.4350 0.331775
11 to 15 141691 -0.7401 0.229619
10 to 14 141845 -0.2181 0.413688
9 to 13 141687 -0.7537 0.225526
8 to 12 142205 1.0023 0.841894
7 to 11 141976 0.2260 0.589399
6 to 10 141933 0.0802 0.531976
5 to 9 141777 -0.4486 0.326869
4 to 8 141789 -0.4079 0.341674
3 to 7 142144 0.7955 0.786836
2 to 6 141971 0.2091 0.582796
1 to 5 141647 -0.8893 0.186933
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-19_01:31
Bits used No. missing words z-score p-value
31 to 32 141527 -1.1278 0.129699
30 to 31 141737 -0.5083 0.305605
29 to 30 141831 -0.2311 0.408633
28 to 29 141903 -0.0187 0.492551
27 to 28 142487 1.7040 0.955813
26 to 27 141803 -0.3137 0.376891
25 to 26 141140 -2.2694 0.011622
24 to 25 141333 -1.7001 0.044557
23 to 24 141835 -0.2193 0.413223
22 to 23 141983 0.2173 0.586019
21 to 22 141984 0.2203 0.587168
20 to 21 142235 0.9607 0.831643
19 to 20 142368 1.3530 0.911974
18 to 19 141692 -0.6411 0.260732
17 to 18 142041 0.3884 0.651143
16 to 17 141573 -0.9921 0.160569
15 to 16 141445 -1.3697 0.085390
14 to 15 142432 1.5418 0.938439
13 to 14 141885 -0.0718 0.471393
12 to 13 142037 0.3766 0.646767
11 to 12 142836 2.7335 0.996867
10 to 11 141489 -1.2399 0.107504
9 to 10 141603 -0.9036 0.183096
8 to 9 141661 -0.7325 0.231921
7 to 8 141191 -2.1190 0.017047
6 to 7 141781 -0.3786 0.352509
5 to 6 141285 -1.8417 0.032761
4 to 5 142270 1.0639 0.856318
3 to 4 141735 -0.5142 0.303539
2 to 3 141656 -0.7473 0.227445
1 to 2 141946 0.1082 0.543070
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-19_01:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2416.17 -1.186 0.117901
Test results for specific bytes for dh-ranFile-2018-06-19_01:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2516.58 0.235 0.592704
2 to 9 2366.56 -1.887 0.029569
3 to 10 2397.69 -1.447 0.073963
4 to 11 2566.91 0.946 0.827982
5 to 12 2540.88 0.578 0.718412
6 to 13 2448.01 -0.735 0.231074
7 to 14 2487.61 -0.175 0.430469
8 to 15 2390.87 -1.543 0.061378
9 to 16 2546.48 0.657 0.744529
10 to 17 2542.26 0.598 0.724947
11 to 18 2655.75 2.203 0.986188
12 to 19 2434.82 -0.922 0.178335
13 to 20 2606.88 1.512 0.934680
14 to 21 2674.76 2.472 0.993273
15 to 22 2520.77 0.294 0.615513
16 to 23 2400.04 -1.414 0.078722
17 to 24 2418.43 -1.154 0.124348
18 to 25 2530.64 0.433 0.667602
19 to 26 2553.43 0.756 0.775047
20 to 27 2459.97 -0.566 0.285668
21 to 28 2456.09 -0.621 0.267288
22 to 29 2375.24 -1.764 0.038834
23 to 30 2583.15 1.176 0.880200
24 to 31 2500.49 0.007 0.502782
25 to 32 2450.90 -0.694 0.243722
CDPARK for dh-ranFile-2018-06-19_01:31: 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
3518 -0.2283 0.409702
3498 -1.1416 0.126820
3523 0.0000 0.500000
3529 0.2740 0.607947
3506 -0.7763 0.218799
3567 2.0091 0.977738
3517 -0.2740 0.392053
3501 -1.0046 0.157553
3535 0.5479 0.708135
3494 -1.3242 0.092718
Square side=100, avg. no. parked=3518.80 sample std.=20.59
p-value of the KSTEST for those 10 p-values: 0.588587
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-19_01:31
0.0920,0.6041,0.5109,0.8424,0.0447,0.0953,0.5929,0.4172,0.9804,0.6976,
The KS test for those 10 p-values: 0.838321
The 3DSPHERES test for dh-ranFile-2018-06-19_01:31
sample no r^3 equiv. uni.
1 10.866 0.303865
2 3.033 0.096153
3 48.092 0.798719
4 10.356 0.291932
5 2.183 0.070171
6 34.186 0.680032
7 2.747 0.087497
8 12.247 0.335183
9 24.944 0.564593
10 81.584 0.934090
11 27.893 0.605356
12 1.212 0.039606
13 61.407 0.870867
14 33.208 0.669425
15 0.422 0.013980
16 49.249 0.806338
17 91.281 0.952294
18 20.858 0.501061
19 2.274 0.072997
20 4.891 0.150443
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.324939
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-19_01:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 1.8 -0.8 -0.8 -0.9 -0.3
-0.6 0.6 -1.7 -0.0 0.3 -0.7
-0.2 1.0 -0.6 1.2 -0.6 2.0
-1.2 -2.3 0.7 0.3 2.3 0.0
-1.8 -0.1 0.4 -0.3 1.5 -0.4
-1.1 -0.1 0.7 -1.7 2.7 0.1
1.0 -0.1 -0.4 -0.1 0.9 -1.0
-1.1
Chi-square with 42 degrees of freedom:53.506940
z-score=1.255510, p-value=0.890197
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-19_01:31
Test no p-value
1 0.505931
2 0.299944
3 0.276816
4 0.871297
5 0.234483
6 0.811921
7 0.154582
8 0.354107
9 0.313494
10 0.241715
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.237699
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-19_01:31:
(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 66795 0.25 66980 1.47
3 25000.00 24779 1.95 24804 1.54
4 6666.67 6684 0.05 6583 1.05
5 1388.89 1468 4.51 1349 1.15
6 238.10 232 0.16 237 0.01
7 34.72 34 0.01 40 0.80
8 4.96 7 0.84 6 0.22
p=0.74392 p=0.60219
Number of rngs required: 687237, p-value: 0.087
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-19_01:31
No. of wins: Observed Expected
98740 98585.9
z-score= 0.689, pvalue=0.75472
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66999 66666.7 1.657 1.657
2 37626 37654.3 0.021 1.678
3 26911 26954.7 0.071 1.749
4 19173 19313.5 1.022 2.770
5 13805 13851.4 0.156 2.926
6 9864 9943.5 0.636 3.562
7 7115 7145.0 0.126 3.689
8 5139 5139.1 0.000 3.689
9 3668 3699.9 0.274 3.963
10 2653 2666.3 0.066 4.029
11 1890 1923.3 0.578 4.607
12 1412 1388.7 0.390 4.996
13 977 1003.7 0.711 5.707
14 749 726.1 0.720 6.427
15 557 525.8 1.847 8.274
16 388 381.2 0.123 8.397
17 284 276.5 0.201 8.598
18 229 200.8 3.951 12.550
19 161 146.0 1.544 14.094
20 96 106.2 0.982 15.077
21 304 287.1 0.993 16.070
Chisq= 16.07 for 20 degrees of freedom, p= 0.28772
SUMMARY of craptest
p-value for no. of wins: 0.754717
p-value for throws/game: 0.287717
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-19_01:31
No. of wins: Observed Expected
98406 98585.9
z-score=-0.804, pvalue=0.21057
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66577 66666.7 0.121 0.121
2 37750 37654.3 0.243 0.364
3 27105 26954.7 0.838 1.201
4 19322 19313.5 0.004 1.205
5 13767 13851.4 0.515 1.720
6 9902 9943.5 0.174 1.893
7 7225 7145.0 0.895 2.788
8 5092 5139.1 0.431 3.220
9 3685 3699.9 0.060 3.279
10 2608 2666.3 1.275 4.554
11 1886 1923.3 0.725 5.278
12 1405 1388.7 0.190 5.469
13 985 1003.7 0.349 5.818
14 724 726.1 0.006 5.824
15 532 525.8 0.072 5.896
16 386 381.2 0.062 5.958
17 287 276.5 0.396 6.354
18 213 200.8 0.737 7.091
19 154 146.0 0.440 7.531
20 104 106.2 0.046 7.578
21 291 287.1 0.053 7.630
Chisq= 7.63 for 20 degrees of freedom, p= 0.00595
SUMMARY of craptest
p-value for no. of wins: 0.210574
p-value for throws/game: 0.005955
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0060,0.0116,0.0140,0.0170,0.0197,0.0237,0.0296,0.0305,0.0328,0.0367,
0.0388,0.0394,0.0396,0.0446,0.0447,0.0472,0.0543,0.0545,0.0594,0.0614,
0.0614,0.0643,0.0656,0.0689,0.0702,0.0730,0.0740,0.0746,0.0787,0.0854,
0.0871,0.0875,0.0890,0.0906,0.0920,0.0927,0.0953,0.0962,0.1075,0.1179,
0.1243,0.1268,0.1297,0.1302,0.1322,0.1420,0.1504,0.1546,0.1560,0.1576,
0.1606,0.1783,0.1831,0.1866,0.1869,0.1874,0.1893,0.2002,0.2023,0.2068,
0.2106,0.2188,0.2222,0.2225,0.2255,0.2274,0.2278,0.2291,0.2294,0.2296,
0.2311,0.2317,0.2319,0.2319,0.2345,0.2364,0.2377,0.2417,0.2425,0.2428,
0.2437,0.2501,0.2517,0.2521,0.2523,0.2560,0.2607,0.2661,0.2673,0.2716,
0.2768,0.2857,0.2877,0.2895,0.2919,0.2947,0.2973,0.2999,0.3026,0.3035,
0.3039,0.3056,0.3058,0.3125,0.3135,0.3195,0.3249,0.3269,0.3307,0.3318,
0.3352,0.3417,0.3480,0.3488,0.3525,0.3541,0.3544,0.3769,0.3771,0.3869,
0.3921,0.4086,0.4091,0.4097,0.4127,0.4132,0.4137,0.4172,0.4292,0.4305,
0.4456,0.4476,0.4541,0.4661,0.4690,0.4693,0.4714,0.4738,0.4914,0.4926,
0.4945,0.4978,0.5000,0.5011,0.5028,0.5044,0.5059,0.5109,0.5109,0.5179,
0.5194,0.5266,0.5320,0.5335,0.5397,0.5431,0.5490,0.5508,0.5634,0.5646,
0.5653,0.5703,0.5828,0.5860,0.5872,0.5886,0.5894,0.5927,0.5929,0.5963,
0.5978,0.6022,0.6041,0.6054,0.6056,0.6079,0.6155,0.6396,0.6461,0.6468,
0.6511,0.6513,0.6676,0.6694,0.6712,0.6749,0.6800,0.6883,0.6961,0.6976,
0.6977,0.6994,0.7038,0.7070,0.7081,0.7128,0.7184,0.7225,0.7249,0.7276,
0.7311,0.7439,0.7445,0.7468,0.7547,0.7559,0.7568,0.7635,0.7746,0.7750,
0.7787,0.7863,0.7868,0.7870,0.7898,0.7918,0.7934,0.7987,0.8015,0.8054,
0.8063,0.8082,0.8090,0.8119,0.8129,0.8211,0.8280,0.8316,0.8383,0.8419,
0.8424,0.8428,0.8510,0.8510,0.8563,0.8685,0.8703,0.8703,0.8709,0.8713,
0.8714,0.8802,0.8902,0.8956,0.9088,0.9112,0.9120,0.9208,0.9322,0.9341,
0.9347,0.9384,0.9438,0.9487,0.9514,0.9523,0.9538,0.9558,0.9568,0.9685,
0.9777,0.9804,0.9859,0.9862,0.9893,0.9933,0.9940,0.9969,0.9973,
Overall p-value after applying KStest on 269 p-values = 0.145099
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.