RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-18_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 15.98 22.9437 0.848907
2 to 25 15.68 25.9625 0.924854
3 to 26 15.55 17.4092 0.573008
4 to 27 16.01 16.3951 0.503982
5 to 28 15.74 22.6388 0.838616
6 to 29 15.62 25.5061 0.916058
7 to 30 15.49 18.7765 0.658489
8 to 31 16.00 12.0089 0.200402
9 to 32 16.12 18.9228 0.667019
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.091067
Tough bday spacings test for dh-ranFile-2018-06-18_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 9 40 82 101 104 82 38 28 10 3 3
(O-E)^2/E 0.0 0.3 1.0 0.1 0.4 0.2 3.8 0.1 1.6 2.0 0.3
Birthday Spacings: Sum(O-E)^2/E= 9.845, p= 0.546
RESULTS OF GCD FOR dh-ranFile-2018-06-18_09:31
Euclid's algorithm:
p-value, steps to gcd: 0.395190
p-value, dist. of gcd's: 0.698201
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-18_09:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.444 0.861 0.807 0.152 0.647 0.125 0.272 0.408
Bits 8 to 15---> 0.132 0.224 0.081 0.063 0.031 0.360 0.128 0.273
Bits 16 to 23---> 0.229 0.101 0.593 0.575 0.436 0.743 0.613 0.895
Bits 24 to 31---> 0.502 0.321 0.721 0.384 0.675 0.542 0.376 0.731
KS test for the above 32 p values: 0.826
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-18_09:31,
p-values for 5 runs: 0.7361, 0.0762, 0.7459, 0.0355, 0.5534
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-18_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 222 211.4 0.530 0.530
r= 29 5079 5134.0 0.589 1.119
r= 30 23067 23103.0 0.056 1.175
r= 31 11632 11551.5 0.561 1.736
chi-square = 1.736 with df = 3; p-value = 0.371
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-18_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 223 211.4 0.634 0.634
r= 30 5260 5134.0 3.092 3.726
r= 31 23002 23103.0 0.442 4.168
r= 32 11515 11551.5 0.115 4.284
chi-square = 4.284 with df = 3; p-value = 0.768
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-18_09:31
b-rank test for bits 1 to 8, p=0.40953
b-rank test for bits 2 to 9, p=0.04291
b-rank test for bits 3 to 10, p=0.22709
b-rank test for bits 4 to 11, p=0.96066
b-rank test for bits 5 to 12, p=0.99133
b-rank test for bits 6 to 13, p=0.99486
b-rank test for bits 7 to 14, p=0.98083
b-rank test for bits 8 to 15, p=0.50165
b-rank test for bits 9 to 16, p=0.15579
b-rank test for bits 10 to 17, p=0.20256
b-rank test for bits 11 to 18, p=0.81110
b-rank test for bits 12 to 19, p=0.00190
b-rank test for bits 13 to 20, p=0.55270
b-rank test for bits 14 to 21, p=0.58692
b-rank test for bits 15 to 22, p=0.37892
b-rank test for bits 16 to 23, p=0.64132
b-rank test for bits 17 to 24, p=0.29904
b-rank test for bits 18 to 25, p=0.04722
b-rank test for bits 19 to 26, p=0.92219
b-rank test for bits 20 to 27, p=0.68671
b-rank test for bits 21 to 28, p=0.45650
b-rank test for bits 22 to 29, p=0.31632
b-rank test for bits 23 to 30, p=0.74307
b-rank test for bits 24 to 31, p=0.48613
b-rank test for bits 25 to 32, p=0.39792
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 = 0.480138
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-18_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 140780 -2.64 0.004162
2 142451 1.27 0.897169
3 142277 0.86 0.804841
4 142221 0.73 0.766755
5 142077 0.39 0.652379
6 141107 -1.87 0.030424
7 142193 0.66 0.746264
8 141955 0.11 0.542489
9 142474 1.32 0.906469
10 141845 -0.15 0.440263
11 142000 0.21 0.583886
12 142004 0.22 0.587528
13 141636 -0.64 0.261535
14 140893 -2.37 0.008784
15 142064 0.36 0.641092
16 141781 -0.30 0.382151
17 142038 0.30 0.618152
18 141034 -2.05 0.020419
19 142046 0.32 0.625259
20 142456 1.28 0.899246
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-18_09:31
Bits used No. missing words z-score p-value
23 to 32 141481 -1.4770 0.069838
22 to 31 142086 0.6092 0.728806
21 to 30 142230 1.1058 0.865585
20 to 29 142291 1.3161 0.905930
19 to 28 142132 0.7678 0.778705
18 to 27 141963 0.1851 0.573413
17 to 26 141297 -2.1115 0.017365
16 to 25 141714 -0.6736 0.250298
15 to 24 142063 0.5299 0.701908
14 to 23 141618 -1.0046 0.157548
13 to 22 142187 0.9575 0.830838
12 to 21 142067 0.5437 0.706673
11 to 20 142267 1.2333 0.891276
10 to 19 142083 0.5989 0.725368
9 to 18 141676 -0.8046 0.210529
8 to 17 142208 1.0299 0.848471
7 to 16 141920 0.0368 0.514675
6 to 15 142395 1.6747 0.953006
5 to 14 142353 1.5299 0.936979
4 to 13 141813 -0.3322 0.369880
3 to 12 141905 -0.0149 0.494044
2 to 11 141763 -0.5046 0.306925
1 to 10 142215 1.0540 0.854066
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-18_09:31
Bits used No. missing words z-score p-value
28 to 32 141584 -1.1028 0.135054
27 to 31 141928 0.0633 0.525232
26 to 30 141946 0.1243 0.549463
25 to 29 141454 -1.5435 0.061356
24 to 28 141885 -0.0825 0.467135
23 to 27 141958 0.1650 0.565521
22 to 26 142069 0.5413 0.705834
21 to 25 141966 0.1921 0.576169
20 to 24 141438 -1.5977 0.055052
19 to 23 141898 -0.0384 0.484682
18 to 22 141969 0.2023 0.580148
17 to 21 142130 0.7480 0.772780
16 to 20 141699 -0.7130 0.237928
15 to 19 141812 -0.3299 0.370726
14 to 18 142512 2.0429 0.979471
13 to 17 141870 -0.1333 0.446969
12 to 16 141894 -0.0520 0.479278
11 to 15 141754 -0.5265 0.299256
10 to 14 141845 -0.2181 0.413688
9 to 13 141709 -0.6791 0.248542
8 to 12 141599 -1.0520 0.146408
7 to 11 141954 0.1514 0.560179
6 to 10 141788 -0.4113 0.340431
5 to 9 141429 -1.6282 0.051737
4 to 8 142240 1.1209 0.868838
3 to 7 142133 0.7582 0.775835
2 to 6 141294 -2.0859 0.018495
1 to 5 141905 -0.0147 0.494145
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-18_09:31
Bits used No. missing words z-score p-value
31 to 32 141734 -0.5172 0.302509
30 to 31 141834 -0.2222 0.412074
29 to 30 141746 -0.4818 0.314974
28 to 29 141940 0.0905 0.536044
27 to 28 142436 1.5536 0.939860
26 to 27 141963 0.1583 0.562897
25 to 26 141688 -0.6529 0.256913
24 to 25 141336 -1.6912 0.045396
23 to 24 141596 -0.9243 0.177671
22 to 23 141716 -0.5703 0.284239
21 to 22 142521 1.8043 0.964411
20 to 21 142026 0.3442 0.634637
19 to 20 141911 0.0049 0.501965
18 to 19 141789 -0.3550 0.361311
17 to 18 142281 1.0964 0.863542
16 to 17 142316 1.1996 0.884856
15 to 16 141987 0.2291 0.590610
14 to 15 142181 0.8014 0.788546
13 to 14 141552 -1.0541 0.145925
12 to 13 142507 1.7630 0.961053
11 to 12 141782 -0.3756 0.353605
10 to 11 142261 1.0374 0.850219
9 to 10 142062 0.4504 0.673772
8 to 9 141891 -0.0541 0.478439
7 to 8 141502 -1.2016 0.114766
6 to 7 142145 0.6952 0.756532
5 to 6 141827 -0.2429 0.404056
4 to 5 141845 -0.1898 0.424747
3 to 4 141620 -0.8535 0.196696
2 to 3 141971 0.1819 0.572176
1 to 2 141485 -1.2517 0.105338
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-18_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2591.59 1.295 0.902380
Test results for specific bytes for dh-ranFile-2018-06-18_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2425.90 -1.048 0.147331
2 to 9 2508.86 0.125 0.549844
3 to 10 2567.96 0.961 0.831741
4 to 11 2407.83 -1.304 0.096193
5 to 12 2554.22 0.767 0.778393
6 to 13 2552.47 0.742 0.770951
7 to 14 2514.79 0.209 0.582856
8 to 15 2519.01 0.269 0.605949
9 to 16 2454.86 -0.638 0.261608
10 to 17 2350.60 -2.113 0.017308
11 to 18 2366.22 -1.892 0.029248
12 to 19 2562.24 0.880 0.810639
13 to 20 2660.55 2.270 0.988411
14 to 21 2461.58 -0.543 0.293445
15 to 22 2405.63 -1.335 0.090993
16 to 23 2482.25 -0.251 0.400896
17 to 24 2556.27 0.796 0.786906
18 to 25 2402.21 -1.383 0.083329
19 to 26 2488.77 -0.159 0.436908
20 to 27 2500.71 0.010 0.504023
21 to 28 2483.81 -0.229 0.409427
22 to 29 2551.08 0.722 0.764958
23 to 30 2429.43 -0.998 0.159130
24 to 31 2445.17 -0.775 0.219050
25 to 32 2520.63 0.292 0.614745
CDPARK for dh-ranFile-2018-06-18_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
3515 -0.3653 0.357445
3522 -0.0457 0.481790
3522 -0.0457 0.481790
3524 0.0457 0.518210
3529 0.2740 0.607947
3511 -0.5479 0.291865
3536 0.5936 0.723613
3513 -0.4566 0.323972
3516 -0.3196 0.374623
3498 -1.1416 0.126820
Square side=100, avg. no. parked=3518.60 sample std.=9.98
p-value of the KSTEST for those 10 p-values: 0.234866
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-18_09:31
0.3267,0.3540,0.4712,0.4419,0.0465,0.5993,0.4874,0.3850,0.7597,0.2840,
The KS test for those 10 p-values: 0.247922
The 3DSPHERES test for dh-ranFile-2018-06-18_09:31
sample no r^3 equiv. uni.
1 47.266 0.793103
2 19.628 0.480177
3 0.919 0.030163
4 117.990 0.980415
5 36.909 0.707792
6 40.101 0.737288
7 4.051 0.126321
8 185.006 0.997902
9 1.782 0.057665
10 104.349 0.969141
11 8.316 0.242106
12 16.164 0.416547
13 3.266 0.103151
14 0.285 0.009440
15 6.586 0.197105
16 20.685 0.498165
17 0.007 0.000219
18 7.043 0.209255
19 35.315 0.691848
20 11.762 0.324332
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.086888
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-18_09:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -0.7 -0.6 0.3 -0.5 -1.4
0.9 -0.7 1.1 0.6 0.2 -0.5
-0.7 0.0 2.5 0.0 0.4 -0.3
-0.2 -1.0 0.1 -0.9 0.8 -2.0
0.4 -0.3 0.7 1.2 -0.4 0.5
-0.4 0.6 -1.6 -0.5 0.2 -1.0
-0.7 -0.1 0.1 -0.1 -1.3 0.0
-1.1
Chi-square with 42 degrees of freedom:30.316848
z-score=-1.274736, p-value=0.089770
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-18_09:31
Test no p-value
1 0.038478
2 0.670012
3 0.066595
4 0.004197
5 0.714451
6 0.236716
7 0.084131
8 0.022321
9 0.208841
10 0.574929
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.003727
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-18_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 66872 0.63 66513 0.35
3 25000.00 24786 1.83 25155 0.96
4 6666.67 6626 0.25 6675 0.01
5 1388.89 1431 1.28 1388 0.00
6 238.10 252 0.81 230 0.28
7 34.72 25 2.72 29 0.94
8 4.96 7 0.84 9 3.29
p=0.78719 p=0.55801
Number of rngs required: 687705, p-value: 0.210
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-18_09:31
No. of wins: Observed Expected
99095 98585.9
z-score= 2.277, pvalue=0.98861
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66698 66666.7 0.015 0.015
2 37672 37654.3 0.008 0.023
3 26866 26954.7 0.292 0.315
4 19486 19313.5 1.541 1.857
5 13670 13851.4 2.376 4.233
6 9947 9943.5 0.001 4.234
7 7184 7145.0 0.213 4.446
8 5114 5139.1 0.122 4.569
9 3688 3699.9 0.038 4.607
10 2698 2666.3 0.377 4.984
11 1910 1923.3 0.092 5.076
12 1420 1388.7 0.704 5.780
13 1010 1003.7 0.039 5.819
14 742 726.1 0.346 6.166
15 501 525.8 1.173 7.339
16 378 381.2 0.026 7.365
17 310 276.5 4.049 11.413
18 191 200.8 0.481 11.894
19 138 146.0 0.437 12.331
20 109 106.2 0.073 12.404
21 268 287.1 1.272 13.677
Chisq= 13.68 for 20 degrees of freedom, p= 0.15349
SUMMARY of craptest
p-value for no. of wins: 0.988612
p-value for throws/game: 0.153490
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-18_09:31
No. of wins: Observed Expected
98330 98585.9
z-score=-1.144, pvalue=0.12624
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66572 66666.7 0.134 0.134
2 37722 37654.3 0.122 0.256
3 26782 26954.7 1.107 1.363
4 19278 19313.5 0.065 1.428
5 13911 13851.4 0.256 1.684
6 10084 9943.5 1.984 3.668
7 7069 7145.0 0.809 4.477
8 5246 5139.1 2.225 6.702
9 3646 3699.9 0.784 7.486
10 2633 2666.3 0.416 7.902
11 2021 1923.3 4.960 12.862
12 1400 1388.7 0.091 12.953
13 1020 1003.7 0.264 13.218
14 691 726.1 1.701 14.918
15 530 525.8 0.033 14.951
16 386 381.2 0.062 15.013
17 290 276.5 0.655 15.668
18 175 200.8 3.322 18.990
19 160 146.0 1.346 20.336
20 104 106.2 0.046 20.382
21 280 287.1 0.176 20.558
Chisq= 20.56 for 20 degrees of freedom, p= 0.57647
SUMMARY of craptest
p-value for no. of wins: 0.126240
p-value for throws/game: 0.576472
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0002,0.0019,0.0037,0.0042,0.0042,0.0088,0.0094,0.0173,0.0174,0.0185,
0.0204,0.0223,0.0292,0.0302,0.0304,0.0310,0.0355,0.0385,0.0429,0.0454,
0.0465,0.0472,0.0517,0.0551,0.0577,0.0614,0.0634,0.0666,0.0698,0.0762,
0.0807,0.0833,0.0841,0.0869,0.0898,0.0910,0.0911,0.0962,0.1013,0.1032,
0.1053,0.1148,0.1245,0.1262,0.1263,0.1268,0.1281,0.1318,0.1351,0.1459,
0.1464,0.1473,0.1523,0.1535,0.1558,0.1575,0.1591,0.1777,0.1967,0.1971,
0.2004,0.2026,0.2088,0.2093,0.2099,0.2105,0.2191,0.2239,0.2271,0.2293,
0.2349,0.2367,0.2379,0.2421,0.2479,0.2485,0.2503,0.2569,0.2615,0.2616,
0.2717,0.2729,0.2840,0.2842,0.2919,0.2934,0.2990,0.2993,0.3025,0.3069,
0.3150,0.3163,0.3215,0.3240,0.3243,0.3267,0.3404,0.3536,0.3540,0.3574,
0.3599,0.3613,0.3699,0.3707,0.3710,0.3746,0.3763,0.3789,0.3822,0.3840,
0.3850,0.3952,0.3979,0.4009,0.4041,0.4084,0.4094,0.4095,0.4121,0.4137,
0.4165,0.4247,0.4359,0.4369,0.4403,0.4419,0.4438,0.4470,0.4565,0.4671,
0.4712,0.4784,0.4793,0.4801,0.4802,0.4818,0.4818,0.4847,0.4861,0.4874,
0.4940,0.4941,0.4982,0.5017,0.5020,0.5022,0.5040,0.5040,0.5147,0.5182,
0.5252,0.5360,0.5420,0.5425,0.5458,0.5495,0.5498,0.5527,0.5534,0.5580,
0.5602,0.5629,0.5655,0.5722,0.5730,0.5734,0.5749,0.5749,0.5762,0.5765,
0.5801,0.5829,0.5839,0.5869,0.5875,0.5906,0.5930,0.5993,0.6059,0.6079,
0.6134,0.6147,0.6182,0.6253,0.6346,0.6411,0.6413,0.6470,0.6524,0.6585,
0.6670,0.6700,0.6738,0.6748,0.6867,0.6918,0.6982,0.7019,0.7058,0.7067,
0.7078,0.7145,0.7214,0.7236,0.7254,0.7288,0.7305,0.7361,0.7373,0.7431,
0.7432,0.7459,0.7463,0.7565,0.7597,0.7650,0.7668,0.7676,0.7710,0.7728,
0.7758,0.7784,0.7787,0.7869,0.7872,0.7885,0.7931,0.8048,0.8068,0.8106,
0.8111,0.8256,0.8308,0.8317,0.8386,0.8485,0.8489,0.8502,0.8541,0.8608,
0.8635,0.8656,0.8688,0.8849,0.8913,0.8946,0.8972,0.8992,0.9024,0.9059,
0.9065,0.9161,0.9222,0.9249,0.9370,0.9399,0.9530,0.9607,0.9611,0.9644,
0.9691,0.9795,0.9804,0.9808,0.9884,0.9886,0.9913,0.9949,0.9979,
Overall p-value after applying KStest on 269 p-values = 0.085864
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.