RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-24_06:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.49 21.5661 0.798013
2 to 25 15.90 16.2376 0.492939
3 to 26 15.87 11.0848 0.147876
4 to 27 15.62 28.8076 0.963658
5 to 28 15.83 21.1678 0.781124
6 to 29 16.08 11.9094 0.194407
7 to 30 15.84 9.3383 0.070952
8 to 31 15.86 15.4615 0.437722
9 to 32 15.24 30.8569 0.979212
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.623212
Tough bday spacings test for dh-ranFile-2018-06-24_06:31: 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 7 31 95 94 87 85 53 30 8 7 3
(O-E)^2/E 0.5 0.9 6.4 0.1 1.2 0.6 0.0 0.0 3.2 0.0 0.3
Birthday Spacings: Sum(O-E)^2/E= 13.236, p= 0.789
RESULTS OF GCD FOR dh-ranFile-2018-06-24_06:31
Euclid's algorithm:
p-value, steps to gcd: 0.289727
p-value, dist. of gcd's: 0.385368
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-24_06:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.957 0.351 0.155 0.746 0.554 0.675 0.804 0.915
Bits 8 to 15---> 0.044 0.956 0.261 0.183 0.615 0.658 0.963 0.626
Bits 16 to 23---> 0.386 0.339 0.624 0.989 0.463 0.706 0.381 0.177
Bits 24 to 31---> 0.699 0.805 0.322 0.946 0.518 0.407 0.318 0.708
KS test for the above 32 p values: 0.770
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-24_06:31,
p-values for 5 runs: 0.0382, 0.4685, 0.2641, 0.4851, 0.7626
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-24_06:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 227 211.4 1.148 1.148
r= 29 5171 5134.0 0.267 1.415
r= 30 22858 23103.0 2.599 4.014
r= 31 11744 11551.5 3.207 7.221
chi-square = 7.221 with df = 3; p-value = 0.935
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-24_06:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 196 211.4 1.124 1.124
r= 30 5205 5134.0 0.982 2.106
r= 31 23031 23103.0 0.225 2.331
r= 32 11568 11551.5 0.024 2.354
chi-square = 2.354 with df = 3; p-value = 0.498
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-24_06:31
b-rank test for bits 1 to 8, p=0.53186
b-rank test for bits 2 to 9, p=0.72903
b-rank test for bits 3 to 10, p=0.89726
b-rank test for bits 4 to 11, p=0.95120
b-rank test for bits 5 to 12, p=0.99996
b-rank test for bits 6 to 13, p=0.24453
b-rank test for bits 7 to 14, p=0.53457
b-rank test for bits 8 to 15, p=0.83615
b-rank test for bits 9 to 16, p=0.49592
b-rank test for bits 10 to 17, p=0.63650
b-rank test for bits 11 to 18, p=0.17499
b-rank test for bits 12 to 19, p=0.62901
b-rank test for bits 13 to 20, p=0.28878
b-rank test for bits 14 to 21, p=0.62008
b-rank test for bits 15 to 22, p=0.37868
b-rank test for bits 16 to 23, p=0.98857
b-rank test for bits 17 to 24, p=0.21021
b-rank test for bits 18 to 25, p=0.64342
b-rank test for bits 19 to 26, p=0.57886
b-rank test for bits 20 to 27, p=0.08832
b-rank test for bits 21 to 28, p=0.13858
b-rank test for bits 22 to 29, p=0.23767
b-rank test for bits 23 to 30, p=0.17989
b-rank test for bits 24 to 31, p=0.80195
b-rank test for bits 25 to 32, p=0.45117
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 = 0.533103
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-24_06:31
(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 141542 -0.86 0.195378
2 141807 -0.24 0.405518
3 141906 -0.01 0.496896
4 141592 -0.74 0.229218
5 142281 0.87 0.807409
6 141941 0.07 0.529493
7 142344 1.02 0.845086
8 141998 0.21 0.582063
9 141468 -1.03 0.151236
10 142123 0.50 0.691191
11 141845 -0.15 0.440263
12 142452 1.27 0.897587
13 141976 0.16 0.561893
14 141375 -1.25 0.105936
15 141940 0.07 0.528563
16 141288 -1.45 0.073292
17 142038 0.30 0.618152
18 141620 -0.68 0.249519
19 141801 -0.25 0.400093
20 141325 -1.37 0.086086
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-24_06:31
Bits used No. missing words z-score p-value
23 to 32 142226 1.0920 0.862576
22 to 31 142271 1.2471 0.893827
21 to 30 142518 2.0989 0.982085
20 to 29 141725 -0.6356 0.262512
19 to 28 142198 0.9954 0.840233
18 to 27 141702 -0.7149 0.237326
17 to 26 141477 -1.4908 0.068008
16 to 25 141758 -0.5218 0.300895
15 to 24 141843 -0.2287 0.409542
14 to 23 141651 -0.8908 0.186520
13 to 22 142297 1.3368 0.909355
12 to 21 141869 -0.1391 0.444698
11 to 20 141831 -0.2701 0.393540
10 to 19 142276 1.2644 0.896953
9 to 18 141733 -0.6080 0.271582
8 to 17 141582 -1.1287 0.129507
7 to 16 141508 -1.3839 0.083195
6 to 15 141544 -1.2598 0.103878
5 to 14 141654 -0.8804 0.189308
4 to 13 142158 0.8575 0.804411
3 to 12 141913 0.0127 0.505049
2 to 11 141781 -0.4425 0.329058
1 to 10 141535 -1.2908 0.098388
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-24_06:31
Bits used No. missing words z-score p-value
28 to 32 142446 1.8192 0.965561
27 to 31 141750 -0.5401 0.294564
26 to 30 141268 -2.1740 0.014853
25 to 29 141471 -1.4859 0.068658
24 to 28 141530 -1.2859 0.099245
23 to 27 141635 -0.9299 0.176203
22 to 26 142340 1.4599 0.927841
21 to 25 141869 -0.1367 0.445629
20 to 24 141515 -1.3367 0.090658
19 to 23 141802 -0.3638 0.357992
18 to 22 142267 1.2124 0.887328
17 to 21 141751 -0.5367 0.295733
16 to 20 141695 -0.7265 0.233753
15 to 19 141483 -1.4452 0.074203
14 to 18 141530 -1.2859 0.099245
13 to 17 142210 1.0192 0.845951
12 to 16 141880 -0.0994 0.460401
11 to 15 142877 3.2802 0.999481
10 to 14 142097 0.6362 0.737667
9 to 13 142065 0.5277 0.701145
8 to 12 142155 0.8328 0.797516
7 to 11 142131 0.7514 0.773801
6 to 10 142150 0.8158 0.792702
5 to 9 141899 -0.0350 0.486033
4 to 8 141694 -0.7299 0.232716
3 to 7 141614 -1.0011 0.158385
2 to 6 141865 -0.1503 0.440275
1 to 5 141348 -1.9028 0.028532
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-24_06:31
Bits used No. missing words z-score p-value
31 to 32 141478 -1.2724 0.101623
30 to 31 141871 -0.1131 0.454988
29 to 30 141772 -0.4051 0.342701
28 to 29 142287 1.1141 0.867376
27 to 28 142085 0.5182 0.697841
26 to 27 142452 1.6008 0.945289
25 to 26 142116 0.6096 0.728952
24 to 25 141550 -1.0600 0.144579
23 to 24 141928 0.0551 0.521960
22 to 23 141541 -1.0865 0.138625
21 to 22 142265 1.0492 0.852951
20 to 21 142039 0.3825 0.648958
19 to 20 142272 1.0698 0.857651
18 to 19 141810 -0.2930 0.384758
17 to 18 141971 0.1819 0.572176
16 to 17 141906 -0.0098 0.496081
15 to 16 142270 1.0639 0.856318
14 to 15 141845 -0.1898 0.424747
13 to 14 141780 -0.3815 0.351415
12 to 13 141325 -1.7237 0.042382
11 to 12 141973 0.1878 0.574490
10 to 11 141621 -0.8505 0.197515
9 to 10 142169 0.7660 0.778158
8 to 9 141825 -0.2488 0.401773
7 to 8 141342 -1.6735 0.047111
6 to 7 141415 -1.4582 0.072393
5 to 6 142063 0.4533 0.674835
4 to 5 141937 0.0816 0.532527
3 to 4 142384 1.4002 0.919274
2 to 3 141855 -0.1603 0.436336
1 to 2 142048 0.4091 0.658751
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-24_06:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2502.38 0.034 0.513439
Test results for specific bytes for dh-ranFile-2018-06-24_06:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2467.22 -0.464 0.321470
2 to 9 2601.66 1.438 0.924729
3 to 10 2536.12 0.511 0.695258
4 to 11 2532.07 0.454 0.674924
5 to 12 2572.99 1.032 0.849010
6 to 13 2544.21 0.625 0.734073
7 to 14 2502.68 0.038 0.515092
8 to 15 2540.15 0.568 0.714897
9 to 16 2413.09 -1.229 0.109529
10 to 17 2362.90 -1.939 0.026256
11 to 18 2451.90 -0.680 0.248186
12 to 19 2341.12 -2.247 0.012325
13 to 20 2461.47 -0.545 0.292919
14 to 21 2430.79 -0.979 0.163836
15 to 22 2511.07 0.157 0.562185
16 to 23 2459.85 -0.568 0.285074
17 to 24 2574.92 1.059 0.855311
18 to 25 2508.67 0.123 0.548793
19 to 26 2457.68 -0.598 0.274756
20 to 27 2495.92 -0.058 0.476977
21 to 28 2441.22 -0.831 0.202918
22 to 29 2405.17 -1.341 0.089949
23 to 30 2496.52 -0.049 0.480358
24 to 31 2459.36 -0.575 0.282752
25 to 32 2376.49 -1.747 0.040344
CDPARK for dh-ranFile-2018-06-24_06:31: 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
3573 2.2831 0.988788
3549 1.1872 0.882429
3533 0.4566 0.676028
3527 0.1826 0.572463
3546 1.0502 0.853193
3543 0.9132 0.819442
3495 -1.2785 0.100530
3572 2.2374 0.987371
3533 0.4566 0.676028
3509 -0.6393 0.261324
Square side=100, avg. no. parked=3538.00 sample std.=23.35
p-value of the KSTEST for those 10 p-values: 0.043712
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-24_06:31
0.7701,0.2731,0.3050,0.2804,0.8691,0.9096,0.3551,0.6832,0.4355,0.7572,
The KS test for those 10 p-values: 0.567039
The 3DSPHERES test for dh-ranFile-2018-06-24_06:31
sample no r^3 equiv. uni.
1 7.629 0.224544
2 6.682 0.199674
3 27.262 0.596967
4 6.869 0.204633
5 3.159 0.099959
6 5.649 0.171637
7 19.348 0.475311
8 16.293 0.419058
9 31.092 0.645274
10 16.112 0.415536
11 18.735 0.464479
12 9.147 0.262798
13 63.357 0.878994
14 9.975 0.282877
15 32.845 0.665400
16 14.094 0.374866
17 11.398 0.316084
18 16.625 0.425447
19 0.436 0.014439
20 15.341 0.400329
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.048615
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-24_06:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 0.1 0.6 1.2 -1.2 1.3
0.0 1.0 -0.4 -0.7 -0.3 -1.4
-0.9 0.8 -0.5 -0.3 1.0 0.3
0.2 -0.6 -0.3 -0.0 0.5 0.7
-0.1 0.1 0.4 -0.4 0.3 0.4
0.0 1.0 0.7 0.7 0.8 -1.0
-0.2 -1.3 0.1 1.0 1.6 1.0
0.8
Chi-square with 42 degrees of freedom:24.057027
z-score=-1.957739, p-value=0.011876
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-24_06:31
Test no p-value
1 0.481796
2 0.527964
3 0.030625
4 0.091035
5 0.712083
6 0.135512
7 0.208080
8 0.389300
9 0.254303
10 0.251140
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.061897
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-24_06:31:
(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 66498 0.43 66654 0.00
3 25000.00 25070 0.20 24841 1.01
4 6666.67 6728 0.56 6811 3.12
5 1388.89 1414 0.45 1422 0.79
6 238.10 245 0.20 229 0.35
7 34.72 39 0.53 38 0.31
8 4.96 5 0.00 4 0.19
p=0.11718 p=0.55064
Number of rngs required: 688972, p-value: 0.744
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-24_06:31
No. of wins: Observed Expected
98591 98585.9
z-score= 0.023, pvalue=0.50917
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66098 66666.7 4.851 4.851
2 37624 37654.3 0.024 4.875
3 27179 26954.7 1.866 6.741
4 19177 19313.5 0.964 7.705
5 13916 13851.4 0.301 8.006
6 10035 9943.5 0.841 8.848
7 7209 7145.0 0.573 9.420
8 5206 5139.1 0.872 10.292
9 3724 3699.9 0.157 10.449
10 2727 2666.3 1.382 11.831
11 1962 1923.3 0.778 12.609
12 1455 1388.7 3.161 15.770
13 1025 1003.7 0.451 16.222
14 697 726.1 1.169 17.391
15 597 525.8 9.631 27.022
16 376 381.2 0.070 27.092
17 265 276.5 0.482 27.573
18 194 200.8 0.232 27.806
19 155 146.0 0.557 28.362
20 111 106.2 0.216 28.578
21 268 287.1 1.272 29.850
Chisq= 29.85 for 20 degrees of freedom, p= 0.92768
SUMMARY of craptest
p-value for no. of wins: 0.509173
p-value for throws/game: 0.927685
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-24_06:31
No. of wins: Observed Expected
98668 98585.9
z-score= 0.367, pvalue=0.64333
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67083 66666.7 2.600 2.600
2 37620 37654.3 0.031 2.631
3 26899 26954.7 0.115 2.747
4 19281 19313.5 0.055 2.801
5 13935 13851.4 0.504 3.305
6 9926 9943.5 0.031 3.336
7 6917 7145.0 7.277 10.614
8 5036 5139.1 2.067 12.681
9 3673 3699.9 0.195 12.876
10 2725 2666.3 1.292 14.168
11 1875 1923.3 1.214 15.383
12 1406 1388.7 0.215 15.597
13 969 1003.7 1.201 16.798
14 700 726.1 0.941 17.739
15 557 525.8 1.847 19.586
16 375 381.2 0.099 19.685
17 277 276.5 0.001 19.686
18 195 200.8 0.169 19.855
19 140 146.0 0.245 20.100
20 114 106.2 0.571 20.671
21 297 287.1 0.340 21.011
Chisq= 21.01 for 20 degrees of freedom, p= 0.60354
SUMMARY of craptest
p-value for no. of wins: 0.643334
p-value for throws/game: 0.603542
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0119,0.0123,0.0144,0.0149,0.0263,0.0285,0.0306,0.0382,0.0403,0.0424,
0.0437,0.0445,0.0471,0.0486,0.0619,0.0680,0.0687,0.0710,0.0724,0.0733,
0.0742,0.0832,0.0861,0.0883,0.0899,0.0907,0.0910,0.0984,0.0992,0.0992,
0.1000,0.1005,0.1016,0.1039,0.1059,0.1095,0.1172,0.1295,0.1355,0.1386,
0.1386,0.1446,0.1479,0.1512,0.1546,0.1584,0.1638,0.1716,0.1750,0.1762,
0.1766,0.1799,0.1834,0.1865,0.1893,0.1944,0.1954,0.1975,0.1997,0.2029,
0.2046,0.2081,0.2102,0.2245,0.2292,0.2327,0.2338,0.2373,0.2377,0.2445,
0.2482,0.2495,0.2511,0.2543,0.2609,0.2613,0.2625,0.2628,0.2641,0.2716,
0.2731,0.2748,0.2804,0.2828,0.2829,0.2851,0.2888,0.2897,0.2929,0.2946,
0.2957,0.3009,0.3050,0.3161,0.3177,0.3215,0.3222,0.3291,0.3390,0.3427,
0.3509,0.3514,0.3551,0.3580,0.3749,0.3787,0.3808,0.3848,0.3854,0.3862,
0.3893,0.3935,0.4001,0.4003,0.4018,0.4055,0.4075,0.4095,0.4155,0.4191,
0.4247,0.4254,0.4355,0.4363,0.4377,0.4403,0.4403,0.4447,0.4456,0.4512,
0.4550,0.4604,0.4632,0.4645,0.4685,0.4753,0.4770,0.4804,0.4818,0.4851,
0.4860,0.4929,0.4959,0.4961,0.4969,0.4978,0.5050,0.5092,0.5134,0.5151,
0.5182,0.5220,0.5280,0.5286,0.5295,0.5319,0.5325,0.5331,0.5346,0.5488,
0.5506,0.5541,0.5619,0.5622,0.5670,0.5722,0.5725,0.5745,0.5789,0.5821,
0.5970,0.6035,0.6149,0.6182,0.6201,0.6232,0.6237,0.6262,0.6290,0.6365,
0.6433,0.6434,0.6453,0.6490,0.6584,0.6588,0.6654,0.6745,0.6748,0.6749,
0.6760,0.6760,0.6832,0.6912,0.6953,0.6978,0.6987,0.7011,0.7057,0.7082,
0.7121,0.7149,0.7290,0.7290,0.7341,0.7377,0.7443,0.7459,0.7572,0.7626,
0.7701,0.7705,0.7738,0.7782,0.7811,0.7892,0.7927,0.7975,0.7980,0.8020,
0.8039,0.8044,0.8055,0.8074,0.8194,0.8362,0.8402,0.8451,0.8460,0.8490,
0.8530,0.8532,0.8553,0.8563,0.8577,0.8626,0.8674,0.8691,0.8790,0.8824,
0.8873,0.8938,0.8970,0.8973,0.8976,0.9094,0.9096,0.9154,0.9193,0.9247,
0.9277,0.9278,0.9348,0.9453,0.9458,0.9512,0.9556,0.9571,0.9633,0.9637,
0.9656,0.9792,0.9821,0.9874,0.9886,0.9888,0.9890,0.9995,1.0000,
Overall p-value after applying KStest on 269 p-values = 0.470887
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.