RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-30_12:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.55 23.4885 0.865988
2 to 25 15.58 15.2222 0.420516
3 to 26 16.00 6.2431 0.008602
4 to 27 16.01 8.9315 0.057612
5 to 28 15.94 18.2705 0.628030
6 to 29 15.92 18.2535 0.626982
7 to 30 15.79 15.2901 0.425408
8 to 31 15.72 44.9930 0.999756
9 to 32 15.73 16.2147 0.491335
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.364486
Tough bday spacings test for dh-ranFile-2018-06-30_12:31: 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 15 32 62 93 104 78 54 34 12 12 4
(O-E)^2/E 3.7 0.6 1.7 0.2 0.4 0.0 0.1 0.6 0.6 4.4 0.0
Birthday Spacings: Sum(O-E)^2/E= 12.290, p= 0.734
RESULTS OF GCD FOR dh-ranFile-2018-06-30_12:31
Euclid's algorithm:
p-value, steps to gcd: 0.572860
p-value, dist. of gcd's: 0.101604
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-30_12:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.828 0.588 0.760 0.564 0.254 0.049 0.766 0.337
Bits 8 to 15---> 0.239 0.132 0.343 0.180 0.183 0.971 0.982 0.496
Bits 16 to 23---> 0.547 0.300 0.185 0.306 0.489 0.051 0.907 0.446
Bits 24 to 31---> 0.734 0.431 0.042 0.637 0.593 0.679 0.258 0.666
KS test for the above 32 p values: 0.198
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-30_12:31,
p-values for 5 runs: 0.2428, 0.4352, 0.9939, 0.3973, 0.7322
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-30_12:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 236 211.4 2.858 2.858
r= 29 5211 5134.0 1.155 4.013
r= 30 23090 23103.0 0.007 4.020
r= 31 11463 11551.5 0.678 4.698
chi-square = 4.698 with df = 3; p-value = 0.805
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-30_12:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 201 211.4 0.513 0.513
r= 30 5110 5134.0 0.112 0.626
r= 31 23041 23103.0 0.167 0.792
r= 32 11648 11551.5 0.806 1.598
chi-square = 1.598 with df = 3; p-value = 0.340
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-30_12:31
b-rank test for bits 1 to 8, p=0.22809
b-rank test for bits 2 to 9, p=0.39950
b-rank test for bits 3 to 10, p=0.58791
b-rank test for bits 4 to 11, p=0.52735
b-rank test for bits 5 to 12, p=0.12973
b-rank test for bits 6 to 13, p=0.62130
b-rank test for bits 7 to 14, p=0.48873
b-rank test for bits 8 to 15, p=0.62822
b-rank test for bits 9 to 16, p=0.68118
b-rank test for bits 10 to 17, p=0.21740
b-rank test for bits 11 to 18, p=0.69978
b-rank test for bits 12 to 19, p=0.22083
b-rank test for bits 13 to 20, p=0.85124
b-rank test for bits 14 to 21, p=0.66572
b-rank test for bits 15 to 22, p=0.75905
b-rank test for bits 16 to 23, p=0.58704
b-rank test for bits 17 to 24, p=0.54659
b-rank test for bits 18 to 25, p=0.23079
b-rank test for bits 19 to 26, p=0.65792
b-rank test for bits 20 to 27, p=0.69154
b-rank test for bits 21 to 28, p=0.93752
b-rank test for bits 22 to 29, p=0.89420
b-rank test for bits 23 to 30, p=0.36402
b-rank test for bits 24 to 31, p=0.39837
b-rank test for bits 25 to 32, p=0.94369
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 = 0.246407
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-30_12:31
(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 142568 1.54 0.938092
2 141749 -0.37 0.353978
3 142529 1.45 0.926167
4 141993 0.20 0.577496
5 142308 0.93 0.824195
6 142125 0.50 0.692835
7 141953 0.10 0.540635
8 142171 0.61 0.729526
9 142200 0.68 0.751474
10 141746 -0.38 0.351375
11 142199 0.68 0.750733
12 141821 -0.21 0.418248
13 142041 0.31 0.620822
14 141634 -0.64 0.260017
15 141874 -0.08 0.467106
16 141884 -0.06 0.476404
17 142152 0.57 0.714638
18 141956 0.11 0.543415
19 142563 1.53 0.936653
20 141712 -0.46 0.322381
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-30_12:31
Bits used No. missing words z-score p-value
23 to 32 141419 -1.6908 0.045438
22 to 31 141771 -0.4770 0.316681
21 to 30 142394 1.6713 0.952666
20 to 29 142106 0.6782 0.751169
19 to 28 141610 -1.0322 0.150996
18 to 27 142319 1.4127 0.921121
17 to 26 141860 -0.1701 0.432464
16 to 25 142043 0.4609 0.677576
15 to 24 142476 1.9540 0.974651
14 to 23 141775 -0.4632 0.321608
13 to 22 142041 0.4540 0.675098
12 to 21 141734 -0.6046 0.272727
11 to 20 142031 0.4196 0.662594
10 to 19 142124 0.7402 0.770423
9 to 18 141649 -0.8977 0.184676
8 to 17 141835 -0.2563 0.398856
7 to 16 141684 -0.7770 0.218579
6 to 15 141756 -0.5287 0.298498
5 to 14 141504 -1.3977 0.081103
4 to 13 142336 1.4713 0.929392
3 to 12 142167 0.8885 0.812869
2 to 11 142365 1.5713 0.941941
1 to 10 141814 -0.3287 0.371182
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-30_12:31
Bits used No. missing words z-score p-value
28 to 32 142054 0.4904 0.688077
27 to 31 141731 -0.6045 0.272753
26 to 30 141812 -0.3299 0.370726
25 to 29 141663 -0.8350 0.201854
24 to 28 141774 -0.4587 0.323208
23 to 27 141510 -1.3537 0.087922
22 to 26 141379 -1.7977 0.036110
21 to 25 141542 -1.2452 0.106532
20 to 24 141940 0.1040 0.541402
19 to 23 141735 -0.5909 0.277277
18 to 22 142086 0.5989 0.725374
17 to 21 141757 -0.5164 0.302797
16 to 20 142444 1.8124 0.965041
15 to 19 141859 -0.1706 0.432265
14 to 18 141761 -0.5028 0.307548
13 to 17 141884 -0.0859 0.465787
12 to 16 142276 1.2429 0.893057
11 to 15 141950 0.1379 0.554826
10 to 14 141855 -0.1842 0.426940
9 to 13 141695 -0.7265 0.233753
8 to 12 142209 1.0158 0.845145
7 to 11 141755 -0.5232 0.300434
6 to 10 141142 -2.6011 0.004646
5 to 9 142197 0.9752 0.835258
4 to 8 141670 -0.8113 0.208600
3 to 7 141703 -0.6994 0.242144
2 to 6 141997 0.2972 0.616838
1 to 5 141809 -0.3401 0.366890
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-30_12:31
Bits used No. missing words z-score p-value
31 to 32 142030 0.3560 0.639064
30 to 31 141734 -0.5172 0.302509
29 to 30 141856 -0.1573 0.437498
28 to 29 141878 -0.0924 0.463183
27 to 28 142120 0.6214 0.732847
26 to 27 141906 -0.0098 0.496081
25 to 26 142161 0.7424 0.771074
24 to 25 141678 -0.6824 0.247496
23 to 24 141884 -0.0747 0.470219
22 to 23 142076 0.4917 0.688517
21 to 22 141712 -0.5821 0.280252
20 to 21 141705 -0.6027 0.273340
19 to 20 142163 0.7483 0.772857
18 to 19 141473 -1.2871 0.099028
17 to 18 141876 -0.0983 0.460840
16 to 17 141860 -0.1455 0.442152
15 to 16 142025 0.3412 0.633527
14 to 15 141644 -0.7827 0.216906
13 to 14 142083 0.5123 0.695780
12 to 13 142178 0.7925 0.785976
11 to 12 141903 -0.0187 0.492551
10 to 11 141623 -0.8446 0.199158
9 to 10 142335 1.2557 0.895381
8 to 9 141790 -0.3520 0.362417
7 to 8 142091 0.5359 0.703986
6 to 7 142209 0.8840 0.811647
5 to 6 141820 -0.2635 0.396079
4 to 5 142231 0.9489 0.828659
3 to 4 142281 1.0964 0.863542
2 to 3 142262 1.0403 0.850905
1 to 2 141864 -0.1337 0.446813
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-30_12:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2532.05 0.453 0.674838
Test results for specific bytes for dh-ranFile-2018-06-30_12:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2485.61 -0.204 0.419345
2 to 9 2576.92 1.088 0.861650
3 to 10 2584.06 1.189 0.882725
4 to 11 2501.13 0.016 0.506353
5 to 12 2501.81 0.026 0.510233
6 to 13 2410.73 -1.263 0.103381
7 to 14 2486.34 -0.193 0.423408
8 to 15 2518.35 0.260 0.602405
9 to 16 2452.93 -0.666 0.252821
10 to 17 2528.14 0.398 0.654646
11 to 18 2522.44 0.317 0.624522
12 to 19 2507.62 0.108 0.542929
13 to 20 2435.71 -0.909 0.181636
14 to 21 2491.06 -0.126 0.449691
15 to 22 2402.24 -1.383 0.083406
16 to 23 2559.25 0.838 0.798973
17 to 24 2500.68 0.010 0.503836
18 to 25 2466.75 -0.470 0.319104
19 to 26 2526.26 0.371 0.644796
20 to 27 2437.92 -0.878 0.189974
21 to 28 2548.83 0.691 0.755089
22 to 29 2445.40 -0.772 0.220028
23 to 30 2480.15 -0.281 0.389481
24 to 31 2509.24 0.131 0.551966
25 to 32 2538.11 0.539 0.705036
CDPARK for dh-ranFile-2018-06-30_12:31: 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
3490 -1.5068 0.065925
3545 1.0046 0.842447
3566 1.9635 0.975204
3521 -0.0913 0.463617
3496 -1.2329 0.108811
3522 -0.0457 0.481790
3504 -0.8676 0.192812
3500 -1.0502 0.146807
3503 -0.9132 0.180558
3544 0.9589 0.831196
Square side=100, avg. no. parked=3519.10 sample std.=23.95
p-value of the KSTEST for those 10 p-values: 0.426589
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-30_12:31
0.9739,0.2265,0.8589,0.9437,0.5525,0.4160,0.3806,0.5585,0.5797,0.8812,
The KS test for those 10 p-values: 0.188816
The 3DSPHERES test for dh-ranFile-2018-06-30_12:31
sample no r^3 equiv. uni.
1 31.209 0.646656
2 16.780 0.428405
3 61.523 0.871365
4 0.813 0.026746
5 22.415 0.526292
6 47.008 0.791319
7 8.766 0.253376
8 73.980 0.915076
9 77.516 0.924518
10 0.231 0.007682
11 14.456 0.382377
12 9.973 0.282829
13 49.480 0.807821
14 47.759 0.796473
15 0.646 0.021308
16 4.847 0.149191
17 19.899 0.484847
18 60.795 0.868202
19 19.009 0.469335
20 17.392 0.439950
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.665857
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-30_12:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 0.1 0.1 -0.4 0.7 2.0
0.1 -0.6 -0.2 2.0 -0.1 0.0
2.5 -0.6 0.0 -2.0 -1.4 -1.0
1.6 1.1 -0.6 -1.2 -0.2 -0.8
-0.9 2.0 0.7 2.0 -0.2 0.7
-0.0 -1.2 -0.5 -0.3 -0.5 0.2
-0.7 -0.1 -0.8 1.0 2.4 -1.0
-1.1
Chi-square with 42 degrees of freedom:50.662138
z-score=0.945117, p-value=0.831130
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-30_12:31
Test no p-value
1 0.109724
2 0.894339
3 0.928628
4 0.788271
5 0.302656
6 0.403029
7 0.030969
8 0.062424
9 0.304106
10 0.011643
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.118867
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-30_12:31:
(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 66756 0.12 66687 0.01
3 25000.00 25061 0.15 24976 0.02
4 6666.67 6493 4.52 6597 0.73
5 1388.89 1395 0.03 1464 4.06
6 238.10 256 1.35 232 0.16
7 34.72 32 0.21 38 0.31
8 4.96 6 0.22 5 0.00
p=0.64029 p=0.49224
Number of rngs required: 691324, p-value: 1.000
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-30_12:31
No. of wins: Observed Expected
98598 98585.9
z-score= 0.054, pvalue=0.52165
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66617 66666.7 0.037 0.037
2 37717 37654.3 0.104 0.141
3 27198 26954.7 2.195 2.337
4 19139 19313.5 1.576 3.913
5 13905 13851.4 0.207 4.120
6 9910 9943.5 0.113 4.233
7 7086 7145.0 0.488 4.721
8 5158 5139.1 0.070 4.791
9 3719 3699.9 0.099 4.889
10 2647 2666.3 0.140 5.029
11 1911 1923.3 0.079 5.108
12 1362 1388.7 0.515 5.623
13 963 1003.7 1.652 7.275
14 708 726.1 0.453 7.728
15 549 525.8 1.020 8.748
16 367 381.2 0.525 9.274
17 287 276.5 0.396 9.669
18 205 200.8 0.087 9.756
19 134 146.0 0.984 10.740
20 99 106.2 0.490 11.230
21 319 287.1 3.541 14.771
Chisq= 14.77 for 20 degrees of freedom, p= 0.21064
SUMMARY of craptest
p-value for no. of wins: 0.521653
p-value for throws/game: 0.210645
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-30_12:31
No. of wins: Observed Expected
98499 98585.9
z-score=-0.388, pvalue=0.34883
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66717 66666.7 0.038 0.038
2 37379 37654.3 2.013 2.051
3 27128 26954.7 1.114 3.165
4 19416 19313.5 0.544 3.709
5 13941 13851.4 0.579 4.289
6 9994 9943.5 0.256 4.545
7 7096 7145.0 0.336 4.881
8 5026 5139.1 2.488 7.369
9 3758 3699.9 0.913 8.282
10 2651 2666.3 0.088 8.370
11 1918 1923.3 0.015 8.385
12 1413 1388.7 0.424 8.809
13 1032 1003.7 0.797 9.606
14 680 726.1 2.932 12.538
15 514 525.8 0.266 12.804
16 374 381.2 0.134 12.938
17 276 276.5 0.001 12.939
18 187 200.8 0.952 13.892
19 147 146.0 0.007 13.899
20 92 106.2 1.902 15.801
21 261 287.1 2.375 18.176
Chisq= 18.18 for 20 degrees of freedom, p= 0.42421
SUMMARY of craptest
p-value for no. of wins: 0.348830
p-value for throws/game: 0.424206
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0046,0.0077,0.0086,0.0116,0.0213,0.0267,0.0310,0.0361,0.0416,0.0454,
0.0495,0.0509,0.0576,0.0624,0.0659,0.0811,0.0834,0.0879,0.0990,0.1016,
0.1034,0.1065,0.1088,0.1097,0.1189,0.1297,0.1322,0.1468,0.1492,0.1510,
0.1799,0.1806,0.1816,0.1834,0.1847,0.1849,0.1888,0.1900,0.1928,0.1985,
0.1992,0.2019,0.2086,0.2106,0.2169,0.2174,0.2186,0.2200,0.2208,0.2265,
0.2281,0.2308,0.2338,0.2387,0.2421,0.2428,0.2464,0.2475,0.2528,0.2534,
0.2545,0.2584,0.2600,0.2727,0.2728,0.2733,0.2773,0.2803,0.2828,0.2985,
0.2999,0.3004,0.3025,0.3027,0.3028,0.3041,0.3063,0.3075,0.3167,0.3191,
0.3216,0.3224,0.3232,0.3367,0.3402,0.3431,0.3488,0.3514,0.3540,0.3624,
0.3640,0.3645,0.3669,0.3707,0.3712,0.3806,0.3824,0.3895,0.3961,0.3973,
0.3984,0.3989,0.3995,0.4030,0.4160,0.4182,0.4193,0.4205,0.4234,0.4242,
0.4254,0.4266,0.4269,0.4284,0.4315,0.4323,0.4325,0.4352,0.4375,0.4399,
0.4422,0.4455,0.4468,0.4497,0.4608,0.4632,0.4636,0.4658,0.4671,0.4693,
0.4702,0.4764,0.4818,0.4848,0.4887,0.4888,0.4913,0.4922,0.4926,0.4957,
0.4961,0.5038,0.5064,0.5102,0.5217,0.5263,0.5273,0.5406,0.5414,0.5429,
0.5434,0.5466,0.5466,0.5520,0.5525,0.5548,0.5585,0.5639,0.5729,0.5775,
0.5797,0.5870,0.5879,0.5880,0.5933,0.6024,0.6168,0.6208,0.6213,0.6245,
0.6270,0.6280,0.6282,0.6335,0.6373,0.6391,0.6403,0.6448,0.6467,0.6546,
0.6579,0.6626,0.6657,0.6657,0.6659,0.6748,0.6751,0.6776,0.6786,0.6812,
0.6881,0.6885,0.6915,0.6928,0.6958,0.6998,0.7040,0.7050,0.7146,0.7254,
0.7295,0.7322,0.7328,0.7339,0.7340,0.7507,0.7512,0.7515,0.7551,0.7590,
0.7603,0.7657,0.7704,0.7711,0.7729,0.7860,0.7883,0.7913,0.7965,0.7990,
0.8047,0.8078,0.8116,0.8129,0.8242,0.8279,0.8287,0.8311,0.8312,0.8353,
0.8424,0.8451,0.8509,0.8512,0.8589,0.8617,0.8635,0.8660,0.8682,0.8714,
0.8812,0.8827,0.8931,0.8942,0.8943,0.8954,0.9072,0.9151,0.9211,0.9245,
0.9262,0.9286,0.9294,0.9367,0.9375,0.9381,0.9419,0.9437,0.9437,0.9527,
0.9650,0.9711,0.9739,0.9747,0.9752,0.9820,0.9939,0.9998,0.9998,
Overall p-value after applying KStest on 269 p-values = 0.330003
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.