RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-09_17:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.77 12.6391 0.240010
2 to 25 15.69 11.0574 0.146434
3 to 26 15.61 15.4602 0.437629
4 to 27 15.76 8.4485 0.044007
5 to 28 15.86 21.9580 0.813659
6 to 29 15.63 11.8217 0.189186
7 to 30 15.67 16.8976 0.538677
8 to 31 15.94 12.2030 0.212311
9 to 32 15.78 13.9305 0.327988
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.116447
Tough bday spacings test for dh-ranFile-2018-07-09_17:31: 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 10 36 76 100 109 78 44 25 14 6 2
(O-E)^2/E 0.1 0.0 0.1 0.1 1.3 0.0 1.3 0.8 0.1 0.1 1.0
Birthday Spacings: Sum(O-E)^2/E= 4.740, p= 0.092
RESULTS OF GCD FOR dh-ranFile-2018-07-09_17:31
Euclid's algorithm:
p-value, steps to gcd: 0.957956
p-value, dist. of gcd's: 0.889079
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-09_17:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.871 0.049 0.780 0.633 0.576 0.819 0.877 0.007
Bits 8 to 15---> 0.591 0.729 0.418 0.537 0.014 0.712 0.881 0.677
Bits 16 to 23---> 0.240 0.472 0.108 0.829 0.666 0.721 0.087 0.741
Bits 24 to 31---> 0.817 0.388 0.386 0.260 0.727 0.511 0.249 0.384
KS test for the above 32 p values: 0.554
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-09_17:31,
p-values for 5 runs: 0.4075, 0.2370, 0.0809, 0.8029, 0.2933
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-09_17:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 182 211.4 4.093 4.093
r= 29 5122 5134.0 0.028 4.122
r= 30 23291 23103.0 1.529 5.651
r= 31 11405 11551.5 1.859 7.509
chi-square = 7.509 with df = 3; p-value = 0.943
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-09_17:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 210 211.4 0.010 0.010
r= 30 5142 5134.0 0.012 0.022
r= 31 23101 23103.0 0.000 0.022
r= 32 11547 11551.5 0.002 0.024
chi-square = 0.024 with df = 3; p-value = 0.001
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-09_17:31
b-rank test for bits 1 to 8, p=0.25044
b-rank test for bits 2 to 9, p=0.01593
b-rank test for bits 3 to 10, p=0.35094
b-rank test for bits 4 to 11, p=0.47034
b-rank test for bits 5 to 12, p=0.75075
b-rank test for bits 6 to 13, p=0.80061
b-rank test for bits 7 to 14, p=0.74232
b-rank test for bits 8 to 15, p=0.77357
b-rank test for bits 9 to 16, p=0.25667
b-rank test for bits 10 to 17, p=0.11329
b-rank test for bits 11 to 18, p=0.12063
b-rank test for bits 12 to 19, p=0.04427
b-rank test for bits 13 to 20, p=0.95007
b-rank test for bits 14 to 21, p=0.48633
b-rank test for bits 15 to 22, p=0.16844
b-rank test for bits 16 to 23, p=0.94551
b-rank test for bits 17 to 24, p=0.36855
b-rank test for bits 18 to 25, p=0.81861
b-rank test for bits 19 to 26, p=0.86325
b-rank test for bits 20 to 27, p=0.58002
b-rank test for bits 21 to 28, p=0.15781
b-rank test for bits 22 to 29, p=0.10407
b-rank test for bits 23 to 30, p=0.88812
b-rank test for bits 24 to 31, p=0.47557
b-rank test for bits 25 to 32, p=0.76767
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 = 0.841481
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-09_17:31
(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 141855 -0.13 0.449494
2 142083 0.41 0.657545
3 141966 0.13 0.552669
4 141642 -0.62 0.266116
5 141355 -1.30 0.097632
6 141513 -0.93 0.177222
7 142668 1.77 0.961852
8 141587 -0.75 0.225693
9 141646 -0.62 0.269193
10 141553 -0.83 0.202550
11 142642 1.71 0.956537
12 142032 0.29 0.612795
13 141641 -0.63 0.265350
14 141771 -0.32 0.373272
15 142009 0.23 0.592070
16 141535 -0.87 0.190895
17 142227 0.74 0.771023
18 141722 -0.44 0.330807
19 142396 1.14 0.872247
20 141658 -0.59 0.278528
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-09_17:31
Bits used No. missing words z-score p-value
23 to 32 142112 0.6989 0.757681
22 to 31 141835 -0.2563 0.398856
21 to 30 141466 -1.5287 0.063166
20 to 29 141984 0.2575 0.601597
19 to 28 141874 -0.1218 0.451518
18 to 27 141835 -0.2563 0.398856
17 to 26 141984 0.2575 0.601597
16 to 25 141912 0.0092 0.503673
15 to 24 142167 0.8885 0.812869
14 to 23 142017 0.3713 0.644784
13 to 22 141812 -0.3356 0.368579
12 to 21 142439 1.8264 0.966109
11 to 20 141415 -1.7046 0.044136
10 to 19 141940 0.1058 0.542113
9 to 18 141577 -1.1460 0.125905
8 to 17 141684 -0.7770 0.218579
7 to 16 141852 -0.1977 0.421644
6 to 15 141474 -1.5011 0.066660
5 to 14 142166 0.8851 0.811940
4 to 13 141929 0.0678 0.527039
3 to 12 142091 0.6264 0.734490
2 to 11 141943 0.1161 0.546215
1 to 10 142093 0.6333 0.736746
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-09_17:31
Bits used No. missing words z-score p-value
28 to 32 141307 -2.0418 0.020586
27 to 31 141470 -1.4893 0.068210
26 to 30 141555 -1.2011 0.114853
25 to 29 141606 -1.0282 0.151919
24 to 28 141456 -1.5367 0.062182
23 to 27 142270 1.2226 0.889262
22 to 26 141906 -0.0113 0.495497
21 to 25 142045 0.4599 0.677205
20 to 24 141676 -0.7909 0.214487
19 to 23 142248 1.1480 0.874523
18 to 22 141865 -0.1503 0.440275
17 to 21 141927 0.0599 0.523882
16 to 20 141821 -0.2994 0.382308
15 to 19 142512 2.0429 0.979471
14 to 18 141371 -1.8248 0.034012
13 to 17 141547 -1.2282 0.109679
12 to 16 142498 1.9955 0.977005
11 to 15 142082 0.5853 0.720834
10 to 14 141410 -1.6926 0.045262
9 to 13 141169 -2.5096 0.006044
8 to 12 142165 0.8667 0.806941
7 to 11 142127 0.7379 0.769702
6 to 10 141948 0.1311 0.552146
5 to 9 141998 0.3006 0.618131
4 to 8 142005 0.3243 0.627147
3 to 7 141814 -0.3232 0.373290
2 to 6 142018 0.3684 0.643702
1 to 5 142014 0.3548 0.638635
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-09_17:31
Bits used No. missing words z-score p-value
31 to 32 141726 -0.5408 0.294324
30 to 31 141759 -0.4435 0.328720
29 to 30 142075 0.4887 0.687474
28 to 29 142372 1.3648 0.913843
27 to 28 142396 1.4356 0.924443
26 to 27 141434 -1.4022 0.080435
25 to 26 141792 -0.3461 0.364632
24 to 25 141784 -0.3697 0.355801
23 to 24 141798 -0.3284 0.371302
22 to 23 142793 2.6067 0.995429
21 to 22 142011 0.2999 0.617878
20 to 21 141633 -0.8151 0.207498
19 to 20 141508 -1.1839 0.118233
18 to 19 142163 0.7483 0.772857
17 to 18 142711 2.3648 0.990980
16 to 17 141179 -2.1544 0.015606
15 to 16 141363 -1.6116 0.053525
14 to 15 141526 -1.1308 0.129077
13 to 14 141543 -1.0806 0.139933
12 to 13 141831 -0.2311 0.408633
11 to 12 141809 -0.2960 0.383631
10 to 11 142236 0.9636 0.832384
9 to 10 141296 -1.8092 0.035207
8 to 9 141800 -0.3225 0.373534
7 to 8 141551 -1.0570 0.145251
6 to 7 141386 -1.5437 0.061325
5 to 6 141516 -1.1603 0.122970
4 to 5 141919 0.0285 0.511378
3 to 4 142081 0.5064 0.693713
2 to 3 141949 0.1170 0.546578
1 to 2 142066 0.4622 0.678014
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-09_17:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2533.47 0.473 0.682019
Test results for specific bytes for dh-ranFile-2018-07-09_17:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2539.19 0.554 0.710280
2 to 9 2454.17 -0.648 0.258453
3 to 10 2467.10 -0.465 0.320848
4 to 11 2520.45 0.289 0.613813
5 to 12 2506.78 0.096 0.538208
6 to 13 2511.65 0.165 0.565411
7 to 14 2551.53 0.729 0.766937
8 to 15 2483.67 -0.231 0.408677
9 to 16 2487.61 -0.175 0.430459
10 to 17 2354.68 -2.055 0.019930
11 to 18 2350.24 -2.118 0.017089
12 to 19 2557.71 0.816 0.792772
13 to 20 2568.29 0.966 0.832926
14 to 21 2551.27 0.725 0.765813
15 to 22 2399.80 -1.417 0.078236
16 to 23 2435.03 -0.919 0.179103
17 to 24 2441.69 -0.825 0.204773
18 to 25 2321.66 -2.522 0.005833
19 to 26 2395.44 -1.479 0.069605
20 to 27 2539.09 0.553 0.709812
21 to 28 2504.94 0.070 0.527859
22 to 29 2412.07 -1.243 0.106845
23 to 30 2466.11 -0.479 0.315879
24 to 31 2448.18 -0.733 0.231843
25 to 32 2532.58 0.461 0.677512
CDPARK for dh-ranFile-2018-07-09_17:31: 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
3510 -0.5936 0.276387
3542 0.8676 0.807188
3540 0.7763 0.781201
3543 0.9132 0.819442
3525 0.0913 0.536383
3557 1.5525 0.939730
3524 0.0457 0.518210
3554 1.4155 0.921543
3533 0.4566 0.676028
3508 -0.6849 0.246694
Square side=100, avg. no. parked=3533.60 sample std.=15.94
p-value of the KSTEST for those 10 p-values: 0.155930
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-09_17:31
0.3744,0.4531,0.1374,0.6491,0.8041,0.1645,0.4545,0.8057,0.7743,0.8559,
The KS test for those 10 p-values: 0.727708
The 3DSPHERES test for dh-ranFile-2018-07-09_17:31
sample no r^3 equiv. uni.
1 34.424 0.682556
2 13.330 0.358745
3 26.800 0.590706
4 5.701 0.173062
5 21.142 0.505767
6 34.511 0.683478
7 210.035 0.999089
8 51.848 0.822406
9 4.962 0.152454
10 33.497 0.672597
11 21.078 0.504702
12 75.208 0.918483
13 10.171 0.287548
14 23.566 0.544130
15 4.823 0.148523
16 21.069 0.504557
17 6.374 0.191403
18 47.579 0.795254
19 6.321 0.189978
20 7.633 0.224648
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.690381
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-09_17:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -0.7 -1.1 -1.0 -0.5 0.1
-1.3 1.1 1.6 0.5 0.4 -1.7
0.1 2.3 -0.1 -0.4 -0.6 0.4
0.5 1.2 -1.2 -1.4 0.0 -1.0
0.0 0.9 -0.1 -0.7 0.2 -1.3
-0.9 -1.3 2.8 0.7 2.6 -0.8
-0.5 -1.0 -0.4 -1.3 0.1 0.0
-0.1
Chi-square with 42 degrees of freedom:48.004096
z-score=0.655101, p-value=0.757489
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-09_17:31
Test no p-value
1 0.919583
2 0.097971
3 0.591126
4 0.833363
5 0.584881
6 0.108810
7 0.879437
8 0.869371
9 0.056136
10 0.273302
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.566026
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-09_17:31:
(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 66889 0.74 66690 0.01
3 25000.00 24795 1.68 25002 0.00
4 6666.67 6596 0.75 6679 0.02
5 1388.89 1444 2.19 1356 0.78
6 238.10 239 0.00 244 0.15
7 34.72 31 0.40 26 2.19
8 4.96 5 0.00 2 1.77
p=0.54947 p=0.44497
Number of rngs required: 687078, p-value: 0.061
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-09_17:31
No. of wins: Observed Expected
98337 98585.9
z-score=-1.113, pvalue=0.13285
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66832 66666.7 0.410 0.410
2 37663 37654.3 0.002 0.412
3 26785 26954.7 1.069 1.481
4 19095 19313.5 2.471 3.952
5 13866 13851.4 0.015 3.967
6 9982 9943.5 0.149 4.116
7 7151 7145.0 0.005 4.121
8 5214 5139.1 1.092 5.213
9 3767 3699.9 1.218 6.432
10 2587 2666.3 2.358 8.790
11 1930 1923.3 0.023 8.813
12 1427 1388.7 1.054 9.867
13 984 1003.7 0.387 10.254
14 757 726.1 1.311 11.566
15 523 525.8 0.015 11.581
16 398 381.2 0.745 12.326
17 260 276.5 0.989 13.315
18 207 200.8 0.190 13.505
19 155 146.0 0.557 14.062
20 106 106.2 0.000 14.062
21 311 287.1 1.987 16.049
Chisq= 16.05 for 20 degrees of freedom, p= 0.28643
SUMMARY of craptest
p-value for no. of wins: 0.132845
p-value for throws/game: 0.286432
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-09_17:31
No. of wins: Observed Expected
98775 98585.9
z-score= 0.846, pvalue=0.80121
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66846 66666.7 0.482 0.482
2 37654 37654.3 0.000 0.482
3 26918 26954.7 0.050 0.532
4 19221 19313.5 0.443 0.975
5 13937 13851.4 0.529 1.504
6 9799 9943.5 2.101 3.605
7 7198 7145.0 0.393 3.998
8 5112 5139.1 0.143 4.140
9 3623 3699.9 1.597 5.737
10 2704 2666.3 0.533 6.270
11 1892 1923.3 0.510 6.781
12 1480 1388.7 5.997 12.778
13 1007 1003.7 0.011 12.788
14 723 726.1 0.014 12.802
15 505 525.8 0.826 13.628
16 395 381.2 0.503 14.131
17 258 276.5 1.243 15.374
18 205 200.8 0.087 15.460
19 145 146.0 0.007 15.467
20 107 106.2 0.006 15.473
21 271 287.1 0.904 16.377
Chisq= 16.38 for 20 degrees of freedom, p= 0.30704
SUMMARY of craptest
p-value for no. of wins: 0.801210
p-value for throws/game: 0.307036
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0010,0.0058,0.0060,0.0072,0.0143,0.0156,0.0159,0.0171,0.0199,0.0206,
0.0340,0.0352,0.0440,0.0441,0.0443,0.0453,0.0487,0.0535,0.0561,0.0607,
0.0613,0.0622,0.0632,0.0667,0.0682,0.0696,0.0782,0.0804,0.0809,0.0874,
0.0921,0.0976,0.0980,0.1041,0.1068,0.1083,0.1088,0.1097,0.1133,0.1149,
0.1164,0.1182,0.1206,0.1230,0.1259,0.1291,0.1328,0.1374,0.1399,0.1453,
0.1464,0.1485,0.1519,0.1525,0.1559,0.1578,0.1645,0.1684,0.1731,0.1772,
0.1791,0.1892,0.1900,0.1909,0.1914,0.2026,0.2048,0.2075,0.2123,0.2145,
0.2186,0.2246,0.2257,0.2318,0.2370,0.2400,0.2400,0.2467,0.2486,0.2504,
0.2567,0.2585,0.2595,0.2653,0.2661,0.2692,0.2733,0.2764,0.2785,0.2864,
0.2875,0.2933,0.2943,0.3070,0.3159,0.3208,0.3280,0.3287,0.3308,0.3509,
0.3558,0.3587,0.3646,0.3686,0.3686,0.3713,0.3733,0.3733,0.3735,0.3744,
0.3823,0.3836,0.3843,0.3856,0.3883,0.3989,0.3989,0.4075,0.4086,0.4087,
0.4178,0.4216,0.4305,0.4376,0.4403,0.4450,0.4495,0.4515,0.4531,0.4545,
0.4703,0.4716,0.4756,0.4863,0.4955,0.5037,0.5046,0.5047,0.5058,0.5114,
0.5114,0.5182,0.5239,0.5270,0.5279,0.5364,0.5371,0.5382,0.5387,0.5421,
0.5441,0.5462,0.5466,0.5495,0.5521,0.5527,0.5544,0.5654,0.5660,0.5765,
0.5800,0.5849,0.5907,0.5911,0.5913,0.5921,0.6016,0.6016,0.6128,0.6138,
0.6179,0.6181,0.6271,0.6334,0.6386,0.6437,0.6448,0.6491,0.6575,0.6657,
0.6726,0.6760,0.6771,0.6772,0.6775,0.6780,0.6820,0.6826,0.6835,0.6875,
0.6904,0.6937,0.7098,0.7103,0.7120,0.7208,0.7212,0.7269,0.7277,0.7295,
0.7345,0.7367,0.7409,0.7423,0.7508,0.7575,0.7577,0.7658,0.7669,0.7677,
0.7697,0.7710,0.7729,0.7736,0.7743,0.7799,0.7812,0.7928,0.7953,0.8006,
0.8012,0.8029,0.8041,0.8057,0.8069,0.8072,0.8119,0.8129,0.8137,0.8172,
0.8186,0.8194,0.8195,0.8224,0.8293,0.8324,0.8329,0.8334,0.8415,0.8559,
0.8633,0.8694,0.8707,0.8722,0.8745,0.8769,0.8794,0.8814,0.8881,0.8891,
0.8893,0.9138,0.9185,0.9196,0.9215,0.9244,0.9397,0.9427,0.9455,0.9501,
0.9565,0.9580,0.9619,0.9661,0.9770,0.9795,0.9910,0.9954,0.9991,
Overall p-value after applying KStest on 269 p-values = 0.193322
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.