RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-28_20:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.73 14.8385 0.392887
2 to 25 15.91 21.2098 0.782956
3 to 26 15.98 14.2795 0.352773
4 to 27 15.85 21.7282 0.804602
5 to 28 16.03 15.9470 0.472404
6 to 29 15.84 20.6875 0.759419
7 to 30 16.12 16.6895 0.524414
8 to 31 15.97 12.3999 0.224657
9 to 32 16.07 17.4213 0.573805
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.516404
Tough bday spacings test for dh-ranFile-2018-06-28_20:31: 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 4 44 75 92 83 88 60 28 14 5 7
(O-E)^2/E 2.9 1.5 0.0 0.3 2.2 1.2 1.2 0.1 0.1 0.4 2.1
Birthday Spacings: Sum(O-E)^2/E= 12.077, p= 0.720
RESULTS OF GCD FOR dh-ranFile-2018-06-28_20:31
Euclid's algorithm:
p-value, steps to gcd: 0.685596
p-value, dist. of gcd's: 0.805929
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-28_20:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.206 0.549 0.605 0.432 0.152 0.235 0.934 0.622
Bits 8 to 15---> 0.085 0.053 0.898 0.827 0.006 0.840 0.624 0.456
Bits 16 to 23---> 0.111 0.035 0.880 0.826 0.703 0.652 0.874 0.005
Bits 24 to 31---> 0.964 0.008 0.505 0.902 0.246 0.368 0.055 0.524
KS test for the above 32 p values: 0.798
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-28_20:31,
p-values for 5 runs: 0.4494, 0.6698, 0.8712, 0.6183, 0.6300
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-28_20:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 212 211.4 0.002 0.002
r= 29 5075 5134.0 0.678 0.680
r= 30 23206 23103.0 0.459 1.139
r= 31 11507 11551.5 0.172 1.310
chi-square = 1.310 with df = 3; p-value = 0.273
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-28_20:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 223 211.4 0.634 0.634
r= 30 5121 5134.0 0.033 0.667
r= 31 23069 23103.0 0.050 0.718
r= 32 11587 11551.5 0.109 0.827
chi-square = 0.827 with df = 3; p-value = 0.157
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-28_20:31
b-rank test for bits 1 to 8, p=0.58664
b-rank test for bits 2 to 9, p=0.84352
b-rank test for bits 3 to 10, p=0.92851
b-rank test for bits 4 to 11, p=0.38838
b-rank test for bits 5 to 12, p=0.64718
b-rank test for bits 6 to 13, p=0.81729
b-rank test for bits 7 to 14, p=0.58726
b-rank test for bits 8 to 15, p=0.27217
b-rank test for bits 9 to 16, p=0.23985
b-rank test for bits 10 to 17, p=0.60402
b-rank test for bits 11 to 18, p=0.67419
b-rank test for bits 12 to 19, p=0.34807
b-rank test for bits 13 to 20, p=0.03161
b-rank test for bits 14 to 21, p=0.61542
b-rank test for bits 15 to 22, p=0.77549
b-rank test for bits 16 to 23, p=0.71099
b-rank test for bits 17 to 24, p=0.96229
b-rank test for bits 18 to 25, p=0.29069
b-rank test for bits 19 to 26, p=0.50102
b-rank test for bits 20 to 27, p=0.40673
b-rank test for bits 21 to 28, p=0.45128
b-rank test for bits 22 to 29, p=0.87077
b-rank test for bits 23 to 30, p=0.80999
b-rank test for bits 24 to 31, p=0.09620
b-rank test for bits 25 to 32, p=0.58190
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 = 0.396928
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-28_20:31
(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 141882 -0.06 0.474543
2 142311 0.94 0.826001
3 142521 1.43 0.923517
4 142302 0.92 0.820547
5 141890 -0.05 0.481989
6 141175 -1.72 0.043106
7 142280 0.87 0.806769
8 141726 -0.43 0.334201
9 142192 0.66 0.745516
10 141744 -0.39 0.349643
11 142724 1.90 0.971508
12 142880 2.27 0.988333
13 141474 -1.02 0.154547
14 141958 0.11 0.545268
15 141723 -0.44 0.331654
16 141363 -1.28 0.100894
17 141660 -0.58 0.280099
18 141988 0.18 0.572918
19 141735 -0.41 0.341889
20 141666 -0.57 0.284838
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-28_20:31
Bits used No. missing words z-score p-value
23 to 32 141890 -0.0667 0.473428
22 to 31 141643 -0.9184 0.179210
21 to 30 142017 0.3713 0.644784
20 to 29 142249 1.1713 0.879256
19 to 28 141666 -0.8391 0.200715
18 to 27 141651 -0.8908 0.186520
17 to 26 142147 0.8196 0.793764
16 to 25 142129 0.7575 0.775620
15 to 24 141733 -0.6080 0.271582
14 to 23 141917 0.0264 0.510550
13 to 22 141930 0.0713 0.528411
12 to 21 141986 0.2644 0.604256
11 to 20 141630 -0.9632 0.167722
10 to 19 142206 1.0230 0.846846
9 to 18 142282 1.2851 0.900616
8 to 17 141589 -1.1046 0.134669
7 to 16 141845 -0.2218 0.412224
6 to 15 141890 -0.0667 0.473428
5 to 14 142149 0.8264 0.795725
4 to 13 142365 1.5713 0.941941
3 to 12 141902 -0.0253 0.489918
2 to 11 141852 -0.1977 0.421644
1 to 10 141830 -0.2736 0.392215
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-28_20:31
Bits used No. missing words z-score p-value
28 to 32 141772 -0.4655 0.320778
27 to 31 141927 0.0599 0.523882
26 to 30 141794 -0.3909 0.347917
25 to 29 141598 -1.0554 0.145631
24 to 28 141411 -1.6893 0.045585
23 to 27 141722 -0.6350 0.262709
22 to 26 142485 1.9514 0.974497
21 to 25 142068 0.5379 0.704665
20 to 24 142233 1.0972 0.863720
19 to 23 141950 0.1379 0.554826
18 to 22 142483 1.9446 0.974091
17 to 21 141428 -1.6316 0.051379
16 to 20 142352 1.5006 0.933267
15 to 19 141828 -0.2757 0.391391
14 to 18 141757 -0.5164 0.302797
13 to 17 142246 1.1413 0.873118
12 to 16 141960 0.1718 0.568188
11 to 15 141865 -0.1503 0.440275
10 to 14 141789 -0.4079 0.341674
9 to 13 142161 0.8531 0.803203
8 to 12 141220 -2.3367 0.009727
7 to 11 141689 -0.7469 0.227568
6 to 10 141725 -0.6248 0.266036
5 to 9 141978 0.2328 0.592034
4 to 8 142297 1.3141 0.905600
3 to 7 141974 0.2192 0.586761
2 to 6 142014 0.3548 0.638635
1 to 5 141955 0.1548 0.561516
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-28_20:31
Bits used No. missing words z-score p-value
31 to 32 142648 2.1790 0.985333
30 to 31 141596 -0.9243 0.177671
29 to 30 141584 -0.9597 0.168609
28 to 29 142396 1.4356 0.924443
27 to 28 141890 -0.0570 0.477264
26 to 27 141196 -2.1042 0.017680
25 to 26 142324 1.2232 0.889376
24 to 25 141971 0.1819 0.572176
23 to 24 141550 -1.0600 0.144579
22 to 23 142653 2.1937 0.985872
21 to 22 142468 1.6480 0.950323
20 to 21 141986 0.2262 0.589464
19 to 20 141763 -0.4317 0.332997
18 to 19 142277 1.0846 0.860944
17 to 18 141755 -0.4553 0.324464
16 to 17 142180 0.7984 0.787691
15 to 16 141662 -0.7296 0.232821
14 to 15 141667 -0.7148 0.237355
13 to 14 141863 -0.1367 0.445647
12 to 13 142101 0.5654 0.714099
11 to 12 142071 0.4769 0.683284
10 to 11 141778 -0.3874 0.349229
9 to 10 141736 -0.5113 0.304571
8 to 9 141804 -0.3107 0.378011
7 to 8 141964 0.1613 0.564059
6 to 7 141701 -0.6145 0.269428
5 to 6 142432 1.5418 0.938439
4 to 5 141921 0.0344 0.513731
3 to 4 141464 -1.3137 0.094481
2 to 3 141747 -0.4788 0.316023
1 to 2 142171 0.7719 0.779910
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-28_20:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2391.84 -1.530 0.063062
Test results for specific bytes for dh-ranFile-2018-06-28_20:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2628.08 1.811 0.964952
2 to 9 2442.18 -0.818 0.206775
3 to 10 2522.90 0.324 0.626991
4 to 11 2401.38 -1.395 0.081564
5 to 12 2504.19 0.059 0.523623
6 to 13 2625.43 1.774 0.961953
7 to 14 2617.89 1.667 0.952257
8 to 15 2259.49 -3.401 0.000335
9 to 16 2466.09 -0.480 0.315761
10 to 17 2574.35 1.051 0.853469
11 to 18 2571.90 1.017 0.845386
12 to 19 2525.25 0.357 0.639506
13 to 20 2507.95 0.112 0.544781
14 to 21 2496.31 -0.052 0.479217
15 to 22 2493.81 -0.088 0.465117
16 to 23 2430.16 -0.988 0.161654
17 to 24 2465.24 -0.492 0.311503
18 to 25 2420.81 -1.120 0.131371
19 to 26 2457.22 -0.605 0.272579
20 to 27 2486.34 -0.193 0.423403
21 to 28 2413.78 -1.219 0.111346
22 to 29 2502.87 0.041 0.516201
23 to 30 2503.98 0.056 0.522451
24 to 31 2449.97 -0.708 0.239598
25 to 32 2496.12 -0.055 0.478107
CDPARK for dh-ranFile-2018-06-28_20:31: 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
3512 -0.5023 0.307734
3509 -0.6393 0.261324
3518 -0.2283 0.409702
3544 0.9589 0.831196
3501 -1.0046 0.157553
3509 -0.6393 0.261324
3569 2.1005 0.982156
3542 0.8676 0.807188
3540 0.7763 0.781201
3508 -0.6849 0.246694
Square side=100, avg. no. parked=3525.20 sample std.=20.99
p-value of the KSTEST for those 10 p-values: 0.642671
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-28_20:31
0.4026,0.9823,0.3905,0.1982,0.8874,0.4104,0.8819,0.2106,0.8009,0.7712,
The KS test for those 10 p-values: 0.391889
The 3DSPHERES test for dh-ranFile-2018-06-28_20:31
sample no r^3 equiv. uni.
1 11.687 0.322641
2 102.112 0.966752
3 11.156 0.310549
4 16.761 0.428046
5 7.149 0.212029
6 15.208 0.397665
7 65.280 0.886504
8 1.771 0.057330
9 47.954 0.797791
10 7.915 0.231909
11 25.823 0.577163
12 77.200 0.923718
13 27.206 0.596218
14 119.009 0.981069
15 55.367 0.842065
16 12.812 0.347577
17 3.988 0.124467
18 0.768 0.025261
19 29.191 0.622060
20 12.584 0.342609
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.907657
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-28_20:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 -0.7 1.1 -0.1 0.2 -1.0
0.0 2.0 -2.0 0.5 0.4 -1.3
-1.4 -0.3 0.1 1.6 1.3 -0.9
0.1 -0.7 0.5 -0.0 -0.9 0.8
0.5 1.0 0.5 -0.8 0.2 -2.6
0.5 1.8 -0.8 0.2 0.8 -0.8
-0.7 -0.1 -1.2 -0.7 0.9 -1.0
0.8
Chi-square with 42 degrees of freedom:43.288485
z-score=0.140585, p-value=0.583873
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-28_20:31
Test no p-value
1 0.252999
2 0.740222
3 0.052799
4 0.397610
5 0.684449
6 0.047694
7 0.825353
8 0.564867
9 0.023021
10 0.556507
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.357193
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-28_20:31:
(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 66701 0.02 66808 0.30
3 25000.00 25019 0.01 24950 0.10
4 6666.67 6632 0.18 6571 1.37
5 1388.89 1355 0.83 1409 0.29
6 238.10 252 0.81 231 0.21
7 34.72 31 0.40 25 2.72
8 4.96 9 3.29 5 0.00
p=0.52344 p=0.45575
Number of rngs required: 689276, p-value: 0.844
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-28_20:31
No. of wins: Observed Expected
98333 98585.9
z-score=-1.131, pvalue=0.12904
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66707 66666.7 0.024 0.024
2 37596 37654.3 0.090 0.115
3 27101 26954.7 0.794 0.908
4 19358 19313.5 0.103 1.011
5 13875 13851.4 0.040 1.051
6 9921 9943.5 0.051 1.102
7 7059 7145.0 1.036 2.138
8 5191 5139.1 0.525 2.663
9 3677 3699.9 0.141 2.804
10 2613 2666.3 1.065 3.870
11 1929 1923.3 0.017 3.886
12 1390 1388.7 0.001 3.887
13 955 1003.7 2.364 6.252
14 701 726.1 0.870 7.122
15 510 525.8 0.477 7.599
16 407 381.2 1.753 9.352
17 276 276.5 0.001 9.353
18 188 200.8 0.820 10.173
19 150 146.0 0.110 10.283
20 119 106.2 1.539 11.822
21 277 287.1 0.356 12.178
Chisq= 12.18 for 20 degrees of freedom, p= 0.09020
SUMMARY of craptest
p-value for no. of wins: 0.129042
p-value for throws/game: 0.090204
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-28_20:31
No. of wins: Observed Expected
98378 98585.9
z-score=-0.930, pvalue=0.17627
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66506 66666.7 0.387 0.387
2 37926 37654.3 1.960 2.347
3 26956 26954.7 0.000 2.347
4 19252 19313.5 0.196 2.543
5 13969 13851.4 0.998 3.541
6 9750 9943.5 3.767 7.308
7 7165 7145.0 0.056 7.364
8 5167 5139.1 0.152 7.516
9 3770 3699.9 1.329 8.845
10 2703 2666.3 0.505 9.351
11 1861 1923.3 2.020 11.371
12 1379 1388.7 0.068 11.439
13 988 1003.7 0.246 11.685
14 738 726.1 0.194 11.879
15 488 525.8 2.722 14.601
16 363 381.2 0.864 15.465
17 288 276.5 0.475 15.940
18 206 200.8 0.133 16.073
19 145 146.0 0.007 16.080
20 97 106.2 0.800 16.880
21 283 287.1 0.059 16.938
Chisq= 16.94 for 20 degrees of freedom, p= 0.34304
SUMMARY of craptest
p-value for no. of wins: 0.176272
p-value for throws/game: 0.343036
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0003,0.0049,0.0061,0.0083,0.0097,0.0177,0.0230,0.0253,0.0316,0.0351,
0.0431,0.0456,0.0477,0.0514,0.0528,0.0532,0.0553,0.0573,0.0631,0.0816,
0.0850,0.0902,0.0945,0.0962,0.1009,0.1106,0.1113,0.1245,0.1290,0.1314,
0.1347,0.1446,0.1456,0.1517,0.1545,0.1569,0.1576,0.1617,0.1677,0.1686,
0.1763,0.1777,0.1792,0.1865,0.1982,0.2007,0.2063,0.2068,0.2106,0.2120,
0.2247,0.2276,0.2319,0.2328,0.2353,0.2374,0.2396,0.2399,0.2458,0.2467,
0.2530,0.2613,0.2613,0.2627,0.2660,0.2694,0.2716,0.2722,0.2726,0.2733,
0.2801,0.2848,0.2907,0.3028,0.3046,0.3077,0.3105,0.3115,0.3158,0.3160,
0.3208,0.3226,0.3245,0.3317,0.3330,0.3342,0.3417,0.3419,0.3426,0.3430,
0.3476,0.3479,0.3481,0.3492,0.3496,0.3528,0.3572,0.3684,0.3780,0.3884,
0.3905,0.3914,0.3919,0.3922,0.3929,0.3969,0.3976,0.3977,0.4026,0.4067,
0.4097,0.4104,0.4122,0.4216,0.4234,0.4280,0.4324,0.4403,0.4456,0.4494,
0.4513,0.4557,0.4558,0.4651,0.4724,0.4734,0.4734,0.4745,0.4773,0.4781,
0.4792,0.4820,0.4899,0.5010,0.5048,0.5106,0.5137,0.5162,0.5164,0.5225,
0.5234,0.5236,0.5236,0.5239,0.5244,0.5284,0.5448,0.5453,0.5491,0.5548,
0.5565,0.5615,0.5641,0.5649,0.5682,0.5722,0.5729,0.5738,0.5772,0.5819,
0.5839,0.5866,0.5868,0.5873,0.5895,0.5920,0.5962,0.6040,0.6043,0.6046,
0.6154,0.6183,0.6216,0.6221,0.6236,0.6270,0.6300,0.6386,0.6395,0.6427,
0.6448,0.6472,0.6525,0.6698,0.6742,0.6833,0.6844,0.6856,0.7032,0.7047,
0.7110,0.7141,0.7200,0.7402,0.7455,0.7594,0.7712,0.7755,0.7756,0.7799,
0.7812,0.7830,0.7877,0.7938,0.7957,0.7978,0.7984,0.8009,0.8032,0.8046,
0.8059,0.8068,0.8072,0.8100,0.8173,0.8205,0.8254,0.8260,0.8260,0.8268,
0.8312,0.8402,0.8421,0.8435,0.8441,0.8454,0.8468,0.8535,0.8609,0.8637,
0.8708,0.8712,0.8731,0.8739,0.8793,0.8796,0.8819,0.8865,0.8874,0.8894,
0.8984,0.9006,0.9023,0.9056,0.9077,0.9235,0.9237,0.9244,0.9285,0.9333,
0.9341,0.9384,0.9419,0.9503,0.9523,0.9620,0.9623,0.9644,0.9650,0.9668,
0.9715,0.9741,0.9745,0.9811,0.9822,0.9823,0.9853,0.9859,0.9883,
Overall p-value after applying KStest on 269 p-values = 0.718406
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.