RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-27_11:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.95 17.5437 0.581843
2 to 25 15.73 19.4024 0.694071
3 to 26 15.71 12.7906 0.249915
4 to 27 15.62 30.1180 0.974493
5 to 28 15.84 17.3802 0.571092
6 to 29 16.06 10.4328 0.115515
7 to 30 15.72 21.8204 0.808274
8 to 31 15.66 14.1822 0.345836
9 to 32 15.79 15.8050 0.462300
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.959773
Tough bday spacings test for dh-ranFile-2018-06-27_11:31: 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 13 31 73 114 103 67 45 31 12 7 4
(O-E)^2/E 1.6 0.9 0.0 2.7 0.3 1.6 1.0 0.1 0.6 0.0 0.0
Birthday Spacings: Sum(O-E)^2/E= 8.684, p= 0.438
RESULTS OF GCD FOR dh-ranFile-2018-06-27_11:31
Euclid's algorithm:
p-value, steps to gcd: 0.363647
p-value, dist. of gcd's: 0.815683
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-27_11:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.042 0.448 0.775 0.432 0.881 0.031 0.736 0.843
Bits 8 to 15---> 0.447 0.885 0.299 0.608 0.899 0.262 0.147 0.485
Bits 16 to 23---> 0.209 0.785 0.681 0.550 0.734 0.973 0.680 0.632
Bits 24 to 31---> 0.789 0.212 0.728 0.462 0.660 0.590 0.494 0.429
KS test for the above 32 p values: 0.704
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-27_11:31,
p-values for 5 runs: 0.6006, 0.8746, 0.9507, 0.4743, 0.9536
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-27_11:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 207 211.4 0.092 0.092
r= 29 5127 5134.0 0.010 0.102
r= 30 23173 23103.0 0.212 0.314
r= 31 11493 11551.5 0.297 0.610
chi-square = 0.610 with df = 3; p-value = 0.106
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-27_11:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 178 211.4 5.282 5.282
r= 30 5220 5134.0 1.440 6.722
r= 31 23082 23103.0 0.019 6.742
r= 32 11520 11551.5 0.086 6.828
chi-square = 6.828 with df = 3; p-value = 0.922
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-27_11:31
b-rank test for bits 1 to 8, p=0.46237
b-rank test for bits 2 to 9, p=0.75396
b-rank test for bits 3 to 10, p=0.64345
b-rank test for bits 4 to 11, p=0.65093
b-rank test for bits 5 to 12, p=0.50422
b-rank test for bits 6 to 13, p=0.83359
b-rank test for bits 7 to 14, p=0.58580
b-rank test for bits 8 to 15, p=0.41625
b-rank test for bits 9 to 16, p=0.75293
b-rank test for bits 10 to 17, p=0.43150
b-rank test for bits 11 to 18, p=0.60475
b-rank test for bits 12 to 19, p=0.23310
b-rank test for bits 13 to 20, p=0.13190
b-rank test for bits 14 to 21, p=0.76364
b-rank test for bits 15 to 22, p=0.58971
b-rank test for bits 16 to 23, p=0.25469
b-rank test for bits 17 to 24, p=0.08335
b-rank test for bits 18 to 25, p=0.54966
b-rank test for bits 19 to 26, p=0.68987
b-rank test for bits 20 to 27, p=0.54771
b-rank test for bits 21 to 28, p=0.88144
b-rank test for bits 22 to 29, p=0.79897
b-rank test for bits 23 to 30, p=0.20469
b-rank test for bits 24 to 31, p=0.35198
b-rank test for bits 25 to 32, p=0.79298
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 = 0.256868
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-27_11:31
(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 142302 0.92 0.820547
2 142368 1.07 0.858063
3 142215 0.71 0.762443
4 141061 -1.98 0.023735
5 142485 1.35 0.910691
6 141991 0.19 0.575666
7 142228 0.74 0.771730
8 141184 -1.69 0.045067
9 142543 1.48 0.930635
10 142092 0.43 0.665237
11 141918 0.02 0.508081
12 142345 1.02 0.845642
13 141302 -1.42 0.077950
14 141767 -0.33 0.369738
15 141571 -0.79 0.214621
16 141555 -0.83 0.203871
17 142583 1.57 0.942256
18 141235 -1.58 0.057566
19 141963 0.13 0.549895
20 142256 0.81 0.791023
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-27_11:31
Bits used No. missing words z-score p-value
23 to 32 142093 0.6333 0.736746
22 to 31 141852 -0.1977 0.421644
21 to 30 141349 -1.9322 0.026669
20 to 29 142160 0.8644 0.806310
19 to 28 141528 -1.3149 0.094267
18 to 27 141250 -2.2736 0.011496
17 to 26 142308 1.3747 0.915392
16 to 25 141940 0.1058 0.542113
15 to 24 141999 0.3092 0.621418
14 to 23 142334 1.4644 0.928455
13 to 22 141866 -0.1494 0.440614
12 to 21 142316 1.4023 0.919589
11 to 20 141508 -1.3839 0.083195
10 to 19 141911 0.0058 0.502297
9 to 18 141808 -0.3494 0.363389
8 to 17 142469 1.9299 0.973190
7 to 16 141898 -0.0391 0.484418
6 to 15 142140 0.7954 0.786814
5 to 14 141821 -0.3046 0.380341
4 to 13 142173 0.9092 0.818380
3 to 12 141615 -1.0149 0.155069
2 to 11 142051 0.4885 0.687408
1 to 10 141943 0.1161 0.546215
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-27_11:31
Bits used No. missing words z-score p-value
28 to 32 142219 1.0497 0.853079
27 to 31 141875 -0.1164 0.453679
26 to 30 141447 -1.5672 0.058532
25 to 29 141381 -1.7909 0.036651
24 to 28 141925 0.0531 0.521181
23 to 27 141625 -0.9638 0.167565
22 to 26 141982 0.2463 0.597290
21 to 25 141735 -0.5909 0.277277
20 to 24 142109 0.6768 0.750749
19 to 23 142050 0.4768 0.683265
18 to 22 141895 -0.0486 0.480629
17 to 21 141730 -0.6079 0.271628
16 to 20 142186 0.9379 0.825843
15 to 19 141687 -0.7537 0.225526
14 to 18 141879 -0.1028 0.459056
13 to 17 141549 -1.2215 0.110956
12 to 16 142110 0.6802 0.751823
11 to 15 141846 -0.2147 0.415009
10 to 14 141043 -2.9367 0.001659
9 to 13 141605 -1.0316 0.151123
8 to 12 141645 -0.8960 0.185117
7 to 11 142273 1.2328 0.891171
6 to 10 141906 -0.0113 0.495497
5 to 9 142321 1.3955 0.918566
4 to 8 141703 -0.6994 0.242144
3 to 7 141967 0.1955 0.577496
2 to 6 141765 -0.4893 0.312331
1 to 5 142109 0.6768 0.750749
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-27_11:31
Bits used No. missing words z-score p-value
31 to 32 141741 -0.4965 0.309754
30 to 31 141929 0.0580 0.523135
29 to 30 141462 -1.3196 0.093491
28 to 29 141855 -0.1603 0.436336
27 to 28 141603 -0.9036 0.183096
26 to 27 142430 1.5359 0.937719
25 to 26 142131 0.6539 0.743410
24 to 25 142457 1.6155 0.946904
23 to 24 142075 0.4887 0.687474
22 to 23 142005 0.2822 0.611110
21 to 22 142005 0.2822 0.611110
20 to 21 141840 -0.2045 0.418976
19 to 20 142000 0.2675 0.605444
18 to 19 142069 0.4710 0.681181
17 to 18 141650 -0.7650 0.222140
16 to 17 141704 -0.6057 0.272359
15 to 16 141656 -0.7473 0.227445
14 to 15 141467 -1.3048 0.095979
13 to 14 141513 -1.1691 0.121179
12 to 13 142024 0.3383 0.632416
11 to 12 142448 1.5890 0.943969
10 to 11 141986 0.2262 0.589464
9 to 10 141862 -0.1396 0.444482
8 to 9 142332 1.2468 0.893767
7 to 8 141526 -1.1308 0.129077
6 to 7 141950 0.1200 0.547747
5 to 6 142478 1.6775 0.953277
4 to 5 142130 0.6509 0.742459
3 to 4 141717 -0.5673 0.285240
2 to 3 141589 -0.9449 0.172348
1 to 2 141915 0.0167 0.506672
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-27_11:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2445.90 -0.765 0.222108
Test results for specific bytes for dh-ranFile-2018-06-27_11:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2456.30 -0.618 0.268269
2 to 9 2448.96 -0.722 0.235201
3 to 10 2542.03 0.594 0.723856
4 to 11 2457.36 -0.603 0.273262
5 to 12 2456.38 -0.617 0.268641
6 to 13 2470.17 -0.422 0.336575
7 to 14 2567.65 0.957 0.830631
8 to 15 2433.52 -0.940 0.173570
9 to 16 2532.30 0.457 0.676085
10 to 17 2611.94 1.583 0.943296
11 to 18 2577.50 1.096 0.863463
12 to 19 2636.88 1.936 0.973550
13 to 20 2454.29 -0.646 0.259006
14 to 21 2636.71 1.933 0.973402
15 to 22 2442.42 -0.814 0.207726
16 to 23 2496.22 -0.053 0.478709
17 to 24 2498.37 -0.023 0.490810
18 to 25 2525.36 0.359 0.640088
19 to 26 2552.07 0.736 0.769235
20 to 27 2506.81 0.096 0.538358
21 to 28 2545.27 0.640 0.738971
22 to 29 2445.87 -0.766 0.221964
23 to 30 2597.17 1.374 0.915303
24 to 31 2482.13 -0.253 0.400244
25 to 32 2525.16 0.356 0.639002
CDPARK for dh-ranFile-2018-06-27_11:31: 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
3521 -0.0913 0.463617
3532 0.4110 0.659449
3530 0.3196 0.625377
3496 -1.2329 0.108811
3487 -1.6438 0.050105
3558 1.5982 0.944998
3520 -0.1370 0.445521
3545 1.0046 0.842447
3513 -0.4566 0.323972
3484 -1.7808 0.037471
Square side=100, avg. no. parked=3518.60 sample std.=23.03
p-value of the KSTEST for those 10 p-values: 0.795168
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-27_11:31
0.3701,0.6822,0.7773,0.4366,0.8139,0.2242,0.9958,0.4310,0.6725,0.3844,
The KS test for those 10 p-values: 0.414818
The 3DSPHERES test for dh-ranFile-2018-06-27_11:31
sample no r^3 equiv. uni.
1 28.688 0.615674
2 7.495 0.221064
3 56.415 0.847487
4 3.949 0.123335
5 11.828 0.325837
6 9.148 0.262818
7 32.965 0.666737
8 56.958 0.850222
9 3.917 0.122393
10 184.963 0.997899
11 7.032 0.208960
12 7.184 0.212955
13 24.986 0.565201
14 2.739 0.087267
15 26.695 0.589275
16 6.977 0.207499
17 13.467 0.361680
18 38.523 0.723103
19 3.395 0.107004
20 14.555 0.384402
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.273012
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-27_11:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 -1.6 -0.1 0.2 0.5 -1.7
-1.1 0.4 -0.9 0.8 -0.1 -1.4
1.6 0.5 -0.1 -0.7 0.9 -0.7
0.2 0.8 0.7 -0.2 -0.1 -1.4
-1.1 1.3 -0.2 0.4 0.1 -0.4
-1.0 -0.3 1.0 -1.5 -1.7 1.7
-0.2 -0.4 2.1 -0.7 0.9 0.0
-0.1
Chi-square with 42 degrees of freedom:40.189955
z-score=-0.197492, p-value=0.449344
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-27_11:31
Test no p-value
1 0.000605
2 0.008826
3 0.751141
4 0.612901
5 0.231016
6 0.430805
7 0.985662
8 0.152190
9 0.016712
10 0.432828
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.031827
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-27_11:31:
(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 66396 1.10 66814 0.33
3 25000.00 25157 0.99 24823 1.25
4 6666.67 6745 0.92 6707 0.24
5 1388.89 1404 0.16 1406 0.21
6 238.10 252 0.81 212 2.86
7 34.72 39 0.53 30 0.64
8 4.96 6 0.22 7 0.84
p=0.42077 p=0.61740
Number of rngs required: 688368, p-value: 0.484
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-27_11:31
No. of wins: Observed Expected
98408 98585.9
z-score=-0.795, pvalue=0.21317
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66511 66666.7 0.363 0.363
2 37291 37654.3 3.506 3.869
3 26891 26954.7 0.151 4.020
4 19368 19313.5 0.154 4.174
5 14103 13851.4 4.569 8.743
6 9973 9943.5 0.087 8.830
7 7223 7145.0 0.851 9.681
8 5133 5139.1 0.007 9.689
9 3710 3699.9 0.028 9.716
10 2735 2666.3 1.770 11.487
11 2061 1923.3 9.854 21.341
12 1404 1388.7 0.168 21.509
13 997 1003.7 0.045 21.554
14 701 726.1 0.870 22.424
15 532 525.8 0.072 22.496
16 390 381.2 0.205 22.702
17 274 276.5 0.023 22.725
18 177 200.8 2.828 25.553
19 142 146.0 0.109 25.661
20 116 106.2 0.901 26.563
21 268 287.1 1.272 27.835
Chisq= 27.84 for 20 degrees of freedom, p= 0.88664
SUMMARY of craptest
p-value for no. of wins: 0.213165
p-value for throws/game: 0.886644
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-27_11:31
No. of wins: Observed Expected
98482 98585.9
z-score=-0.465, pvalue=0.32114
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66492 66666.7 0.458 0.458
2 37437 37654.3 1.254 1.712
3 27062 26954.7 0.427 2.139
4 19618 19313.5 4.802 6.941
5 13899 13851.4 0.163 7.104
6 9922 9943.5 0.047 7.151
7 7177 7145.0 0.143 7.294
8 5067 5139.1 1.011 8.305
9 3710 3699.9 0.028 8.332
10 2644 2666.3 0.186 8.519
11 1919 1923.3 0.010 8.529
12 1369 1388.7 0.281 8.809
13 1016 1003.7 0.150 8.960
14 790 726.1 5.616 14.576
15 515 525.8 0.223 14.799
16 351 381.2 2.385 17.184
17 283 276.5 0.151 17.335
18 222 200.8 2.232 19.567
19 140 146.0 0.245 19.812
20 118 106.2 1.308 21.119
21 249 287.1 5.060 26.179
Chisq= 26.18 for 20 degrees of freedom, p= 0.84002
SUMMARY of craptest
p-value for no. of wins: 0.321139
p-value for throws/game: 0.840019
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0006,0.0017,0.0088,0.0115,0.0167,0.0237,0.0267,0.0305,0.0318,0.0367,
0.0375,0.0418,0.0451,0.0501,0.0576,0.0585,0.0780,0.0832,0.0833,0.0873,
0.0935,0.0943,0.0960,0.1059,0.1070,0.1088,0.1110,0.1155,0.1212,0.1224,
0.1233,0.1291,0.1319,0.1467,0.1511,0.1522,0.1551,0.1676,0.1723,0.1736,
0.1831,0.1851,0.2039,0.2047,0.2075,0.2077,0.2089,0.2090,0.2115,0.2130,
0.2132,0.2146,0.2211,0.2220,0.2221,0.2221,0.2242,0.2255,0.2274,0.2310,
0.2331,0.2352,0.2421,0.2499,0.2547,0.2569,0.2590,0.2621,0.2628,0.2683,
0.2686,0.2716,0.2724,0.2730,0.2733,0.2773,0.2852,0.2991,0.3098,0.3123,
0.3211,0.3240,0.3258,0.3366,0.3458,0.3520,0.3617,0.3634,0.3636,0.3697,
0.3701,0.3803,0.3844,0.3844,0.4002,0.4148,0.4150,0.4162,0.4190,0.4208,
0.4216,0.4290,0.4308,0.4310,0.4315,0.4318,0.4328,0.4363,0.4366,0.4376,
0.4406,0.4445,0.4455,0.4467,0.4483,0.4493,0.4537,0.4591,0.4618,0.4623,
0.4624,0.4636,0.4743,0.4787,0.4806,0.4839,0.4844,0.4850,0.4908,0.4941,
0.4955,0.5023,0.5042,0.5067,0.5081,0.5212,0.5231,0.5384,0.5421,0.5462,
0.5477,0.5477,0.5497,0.5499,0.5501,0.5652,0.5711,0.5757,0.5775,0.5818,
0.5858,0.5893,0.5895,0.5897,0.5901,0.5973,0.6006,0.6047,0.6054,0.6085,
0.6111,0.6111,0.6129,0.6157,0.6174,0.6214,0.6254,0.6322,0.6324,0.6390,
0.6401,0.6435,0.6509,0.6594,0.6603,0.6652,0.6667,0.6725,0.6761,0.6798,
0.6808,0.6812,0.6822,0.6833,0.6874,0.6875,0.6899,0.6941,0.7039,0.7231,
0.7239,0.7283,0.7337,0.7362,0.7367,0.7390,0.7425,0.7434,0.7507,0.7507,
0.7511,0.7518,0.7529,0.7540,0.7624,0.7636,0.7692,0.7717,0.7747,0.7773,
0.7847,0.7868,0.7889,0.7910,0.7930,0.7952,0.7990,0.8063,0.8083,0.8139,
0.8157,0.8184,0.8205,0.8258,0.8306,0.8336,0.8400,0.8424,0.8433,0.8456,
0.8475,0.8502,0.8531,0.8581,0.8635,0.8746,0.8813,0.8814,0.8848,0.8866,
0.8912,0.8938,0.8990,0.9107,0.9153,0.9154,0.9186,0.9196,0.9224,0.9285,
0.9306,0.9377,0.9423,0.9433,0.9440,0.9450,0.9469,0.9507,0.9533,0.9536,
0.9598,0.9729,0.9732,0.9734,0.9736,0.9745,0.9857,0.9958,0.9979,
Overall p-value after applying KStest on 269 p-values = 0.685288
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.