RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-15_03:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.62 22.6255 0.838154
2 to 25 15.86 21.2590 0.785080
3 to 26 15.63 19.8121 0.716046
4 to 27 15.71 24.1929 0.885712
5 to 28 15.78 20.1784 0.734793
6 to 29 15.71 20.5392 0.752416
7 to 30 15.77 13.3427 0.287040
8 to 31 15.61 14.1861 0.346109
9 to 32 15.66 19.5287 0.700955
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.069500
Tough bday spacings test for dh-ranFile-2018-06-15_03:31: 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 9 38 80 96 73 90 59 26 20 5 4
(O-E)^2/E 0.0 0.1 0.6 0.0 6.2 1.8 0.9 0.5 1.8 0.4 0.0
Birthday Spacings: Sum(O-E)^2/E= 12.283, p= 0.733
RESULTS OF GCD FOR dh-ranFile-2018-06-15_03:31
Euclid's algorithm:
p-value, steps to gcd: 0.935077
p-value, dist. of gcd's: 0.526094
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-15_03:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.500 0.745 0.348 0.331 0.765 0.808 0.493 0.956
Bits 8 to 15---> 0.565 0.003 0.977 0.120 0.779 0.568 0.508 0.098
Bits 16 to 23---> 0.081 0.499 0.677 0.355 0.832 0.102 0.371 0.945
Bits 24 to 31---> 0.179 0.389 0.824 0.296 0.945 0.693 0.068 0.753
KS test for the above 32 p values: 0.090
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-15_03:31,
p-values for 5 runs: 0.7647, 0.8577, 0.9975, 0.6328, 0.2819
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-15_03:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 225 211.4 0.873 0.873
r= 29 5132 5134.0 0.001 0.873
r= 30 22951 23103.0 1.001 1.874
r= 31 11692 11551.5 1.708 3.582
chi-square = 3.582 with df = 3; p-value = 0.690
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-15_03:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 191 211.4 1.972 1.972
r= 30 5149 5134.0 0.044 2.016
r= 31 23318 23103.0 2.000 4.016
r= 32 11342 11551.5 3.800 7.816
chi-square = 7.816 with df = 3; p-value = 0.950
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-15_03:31
b-rank test for bits 1 to 8, p=0.93595
b-rank test for bits 2 to 9, p=0.74107
b-rank test for bits 3 to 10, p=0.43986
b-rank test for bits 4 to 11, p=0.73863
b-rank test for bits 5 to 12, p=0.60521
b-rank test for bits 6 to 13, p=0.06999
b-rank test for bits 7 to 14, p=0.50551
b-rank test for bits 8 to 15, p=0.75442
b-rank test for bits 9 to 16, p=0.77599
b-rank test for bits 10 to 17, p=0.53495
b-rank test for bits 11 to 18, p=0.30388
b-rank test for bits 12 to 19, p=0.62642
b-rank test for bits 13 to 20, p=0.16771
b-rank test for bits 14 to 21, p=0.08662
b-rank test for bits 15 to 22, p=0.05149
b-rank test for bits 16 to 23, p=0.05506
b-rank test for bits 17 to 24, p=0.99857
b-rank test for bits 18 to 25, p=0.97697
b-rank test for bits 19 to 26, p=0.17771
b-rank test for bits 20 to 27, p=0.20776
b-rank test for bits 21 to 28, p=0.93950
b-rank test for bits 22 to 29, p=0.31716
b-rank test for bits 23 to 30, p=0.56031
b-rank test for bits 24 to 31, p=0.04428
b-rank test for bits 25 to 32, p=0.61755
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 = 0.630643
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-15_03:31
(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 142129 0.51 0.696111
2 141520 -0.91 0.181504
3 142006 0.23 0.589347
4 141666 -0.57 0.284838
5 141436 -1.11 0.134382
6 141857 -0.12 0.451344
7 141754 -0.36 0.358332
8 141747 -0.38 0.352242
9 142662 1.76 0.960675
10 141664 -0.57 0.283254
11 141789 -0.28 0.389300
12 141635 -0.64 0.260775
13 142160 0.59 0.720954
14 142118 0.49 0.687065
15 141463 -1.04 0.148514
16 141457 -1.06 0.145291
17 142069 0.37 0.645448
18 141388 -1.22 0.111600
19 142149 0.56 0.712252
20 142191 0.66 0.744765
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-15_03:31
Bits used No. missing words z-score p-value
23 to 32 141585 -1.1184 0.131703
22 to 31 141596 -1.0804 0.139971
21 to 30 141733 -0.6080 0.271582
20 to 29 141978 0.2368 0.593591
19 to 28 142234 1.1196 0.868548
18 to 27 142180 0.9333 0.824679
17 to 26 141606 -1.0460 0.147789
16 to 25 142263 1.2196 0.888683
15 to 24 142252 1.1816 0.881322
14 to 23 141693 -0.7460 0.227844
13 to 22 141758 -0.5218 0.300895
12 to 21 141966 0.1954 0.577466
11 to 20 142137 0.7851 0.783793
10 to 19 141769 -0.4839 0.314230
9 to 18 141948 0.1333 0.553040
8 to 17 142213 1.0471 0.852482
7 to 16 141923 0.0471 0.518798
6 to 15 141715 -0.6701 0.251396
5 to 14 142275 1.2609 0.896333
4 to 13 141874 -0.1218 0.451518
3 to 12 142057 0.5092 0.694696
2 to 11 141751 -0.5460 0.292545
1 to 10 141829 -0.2770 0.390890
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-15_03:31
Bits used No. missing words z-score p-value
28 to 32 141650 -0.8791 0.189678
27 to 31 141969 0.2023 0.580148
26 to 30 142171 0.8870 0.812465
25 to 29 141792 -0.3977 0.345415
24 to 28 141713 -0.6655 0.252857
23 to 27 141905 -0.0147 0.494145
22 to 26 141770 -0.4723 0.318355
21 to 25 142330 1.4260 0.923066
20 to 24 142095 0.6294 0.735453
19 to 23 141305 -2.0486 0.020252
18 to 22 141865 -0.1503 0.440275
17 to 21 141928 0.0633 0.525232
16 to 20 142136 0.7684 0.778867
15 to 19 141718 -0.6486 0.258306
14 to 18 141819 -0.3062 0.379725
13 to 17 142138 0.7752 0.780875
12 to 16 141913 0.0124 0.504963
11 to 15 141632 -0.9401 0.173583
10 to 14 141945 0.1209 0.548121
9 to 13 142237 1.1107 0.866661
8 to 12 141471 -1.4859 0.068658
7 to 11 142220 1.0531 0.853857
6 to 10 141896 -0.0452 0.481979
5 to 9 142194 0.9650 0.832723
4 to 8 142291 1.2938 0.902132
3 to 7 141891 -0.0621 0.475227
2 to 6 141922 0.0429 0.517129
1 to 5 142105 0.6633 0.746427
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-15_03:31
Bits used No. missing words z-score p-value
31 to 32 141625 -0.8387 0.200810
30 to 31 142191 0.8309 0.796981
29 to 30 141752 -0.4641 0.321288
28 to 29 142157 0.7306 0.767485
27 to 28 141713 -0.5791 0.281246
26 to 27 142476 1.6716 0.952698
25 to 26 141925 0.0462 0.518434
24 to 25 141546 -1.0718 0.141912
23 to 24 141959 0.1465 0.558244
22 to 23 142341 1.2734 0.898555
21 to 22 141685 -0.6617 0.254069
20 to 21 141819 -0.2665 0.394942
19 to 20 141861 -0.1426 0.443316
18 to 19 142728 2.4150 0.992131
17 to 18 141479 -1.2694 0.102147
16 to 17 141635 -0.8092 0.209191
15 to 16 141805 -0.3078 0.379133
14 to 15 141894 -0.0452 0.481966
13 to 14 141499 -1.2104 0.113060
12 to 13 142258 1.0285 0.848149
11 to 12 141778 -0.3874 0.349229
10 to 11 141712 -0.5821 0.280252
9 to 10 142104 0.5742 0.717100
8 to 9 142607 2.0580 0.980206
7 to 8 142219 0.9135 0.819505
6 to 7 141989 0.2350 0.592901
5 to 6 142292 1.1288 0.870513
4 to 5 141911 0.0049 0.501965
3 to 4 141964 0.1613 0.564059
2 to 3 141791 -0.3491 0.363524
1 to 2 141755 -0.4553 0.324464
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-15_03:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2477.35 -0.320 0.374380
Test results for specific bytes for dh-ranFile-2018-06-15_03:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2391.02 -1.541 0.061634
2 to 9 2376.76 -1.743 0.040677
3 to 10 2332.99 -2.362 0.009091
4 to 11 2559.20 0.837 0.798763
5 to 12 2526.69 0.378 0.647108
6 to 13 2445.52 -0.771 0.220500
7 to 14 2581.77 1.156 0.876251
8 to 15 2461.77 -0.541 0.294350
9 to 16 2487.17 -0.181 0.428012
10 to 17 2563.30 0.895 0.814671
11 to 18 2462.39 -0.532 0.297399
12 to 19 2500.64 0.009 0.503638
13 to 20 2567.14 0.949 0.828811
14 to 21 2481.73 -0.258 0.398074
15 to 22 2526.54 0.375 0.646314
16 to 23 2514.98 0.212 0.583892
17 to 24 2615.42 1.632 0.948696
18 to 25 2527.69 0.392 0.652298
19 to 26 2528.14 0.398 0.654684
20 to 27 2504.12 0.058 0.523223
21 to 28 2467.21 -0.464 0.321405
22 to 29 2539.36 0.557 0.711120
23 to 30 2418.14 -1.158 0.123503
24 to 31 2576.52 1.082 0.860412
25 to 32 2483.17 -0.238 0.405944
CDPARK for dh-ranFile-2018-06-15_03:31: 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
3476 -2.1461 0.015932
3537 0.6393 0.738676
3532 0.4110 0.659449
3485 -1.7352 0.041356
3550 1.2329 0.891189
3510 -0.5936 0.276387
3503 -0.9132 0.180558
3513 -0.4566 0.323972
3578 2.5114 0.993988
3536 0.5936 0.723613
Square side=100, avg. no. parked=3522.00 sample std.=29.18
p-value of the KSTEST for those 10 p-values: 0.602058
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-15_03:31
0.1201,0.3730,0.2552,0.8446,0.8268,0.4034,0.2734,0.0156,0.9616,0.1457,
The KS test for those 10 p-values: 0.473340
The 3DSPHERES test for dh-ranFile-2018-06-15_03:31
sample no r^3 equiv. uni.
1 37.049 0.709160
2 2.639 0.084194
3 12.025 0.330228
4 101.457 0.966017
5 57.079 0.850824
6 4.194 0.130457
7 27.448 0.599454
8 4.050 0.126290
9 11.126 0.309869
10 0.700 0.023055
11 96.377 0.959747
12 23.852 0.548454
13 0.457 0.015118
14 53.700 0.833042
15 3.366 0.106122
16 32.826 0.665196
17 15.450 0.402508
18 43.264 0.763576
19 25.348 0.570414
20 4.954 0.152209
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.547644
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-15_03:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 0.5 -0.8 -1.3 -1.0 -1.8
1.3 1.1 -0.2 0.8 1.1 0.1
0.4 -0.9 -0.1 -1.9 0.8 -1.4
1.9 1.7 1.4 -0.9 -0.7 -0.3
-0.6 0.5 0.3 -0.8 -1.0 -0.3
0.1 -2.2 0.3 -0.5 -2.9 -1.0
-1.2 -1.3 -0.8 -0.1 -0.6 -1.0
-0.1
Chi-square with 42 degrees of freedom:51.051091
z-score=0.987555, p-value=0.840371
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-15_03:31
Test no p-value
1 0.343137
2 0.031595
3 0.187650
4 0.195240
5 0.063858
6 0.242401
7 0.166616
8 0.288170
9 0.680146
10 0.932209
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.047081
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-15_03:31:
(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 66697 0.01 66900 0.82
3 25000.00 24922 0.24 24868 0.70
4 6666.67 6734 0.68 6601 0.65
5 1388.89 1382 0.03 1352 0.98
6 238.10 229 0.35 233 0.11
7 34.72 31 0.40 37 0.15
8 4.96 4 0.19 8 1.86
p=0.07161 p=0.48936
Number of rngs required: 687116, p-value: 0.066
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-15_03:31
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 66791 66666.7 0.232 0.232
2 37594 37654.3 0.097 0.329
3 26783 26954.7 1.094 1.423
4 19444 19313.5 0.882 2.305
5 13937 13851.4 0.529 2.834
6 9933 9943.5 0.011 2.845
7 7123 7145.0 0.068 2.913
8 5116 5139.1 0.104 3.016
9 3703 3699.9 0.003 3.019
10 2629 2666.3 0.522 3.541
11 1942 1923.3 0.181 3.722
12 1346 1388.7 1.315 5.037
13 1022 1003.7 0.333 5.370
14 736 726.1 0.134 5.504
15 543 525.8 0.560 6.065
16 357 381.2 1.530 7.595
17 278 276.5 0.008 7.603
18 200 200.8 0.003 7.606
19 138 146.0 0.437 8.043
20 87 106.2 3.476 11.519
21 298 287.1 0.413 11.932
Chisq= 11.93 for 20 degrees of freedom, p= 0.08159
SUMMARY of craptest
p-value for no. of wins: 0.509173
p-value for throws/game: 0.081591
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-15_03:31
No. of wins: Observed Expected
98921 98585.9
z-score= 1.499, pvalue=0.93306
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66364 66666.7 1.374 1.374
2 37770 37654.3 0.355 1.729
3 27031 26954.7 0.216 1.945
4 19473 19313.5 1.318 3.263
5 13922 13851.4 0.360 3.623
6 9958 9943.5 0.021 3.644
7 7085 7145.0 0.504 4.148
8 5144 5139.1 0.005 4.153
9 3751 3699.9 0.707 4.860
10 2661 2666.3 0.011 4.870
11 1962 1923.3 0.778 5.648
12 1315 1388.7 3.916 9.563
13 967 1003.7 1.343 10.906
14 743 726.1 0.391 11.298
15 534 525.8 0.127 11.424
16 362 381.2 0.962 12.387
17 255 276.5 1.678 14.064
18 192 200.8 0.388 14.452
19 132 146.0 1.340 15.792
20 89 106.2 2.790 18.582
21 290 287.1 0.029 18.611
Chisq= 18.61 for 20 degrees of freedom, p= 0.45279
SUMMARY of craptest
p-value for no. of wins: 0.933056
p-value for throws/game: 0.452793
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0032,0.0091,0.0151,0.0156,0.0159,0.0203,0.0231,0.0316,0.0407,0.0414,
0.0443,0.0471,0.0515,0.0551,0.0616,0.0639,0.0663,0.0678,0.0687,0.0695,
0.0700,0.0716,0.0814,0.0816,0.0842,0.0866,0.0899,0.0985,0.1021,0.1024,
0.1061,0.1116,0.1131,0.1197,0.1201,0.1235,0.1263,0.1305,0.1317,0.1344,
0.1400,0.1419,0.1453,0.1457,0.1478,0.1485,0.1522,0.1666,0.1677,0.1736,
0.1777,0.1794,0.1806,0.1815,0.1876,0.1897,0.1952,0.2008,0.2078,0.2092,
0.2205,0.2278,0.2424,0.2514,0.2529,0.2541,0.2552,0.2583,0.2608,0.2716,
0.2734,0.2764,0.2803,0.2812,0.2819,0.2833,0.2848,0.2870,0.2882,0.2925,
0.2944,0.2955,0.2974,0.3009,0.3039,0.3099,0.3142,0.3172,0.3184,0.3213,
0.3214,0.3240,0.3245,0.3302,0.3311,0.3431,0.3454,0.3461,0.3484,0.3492,
0.3522,0.3550,0.3583,0.3635,0.3714,0.3730,0.3744,0.3791,0.3797,0.3887,
0.3893,0.3909,0.3949,0.3981,0.4025,0.4034,0.4059,0.4280,0.4399,0.4403,
0.4433,0.4513,0.4515,0.4528,0.4733,0.4752,0.4820,0.4820,0.4894,0.4926,
0.4941,0.4993,0.5004,0.5020,0.5036,0.5050,0.5055,0.5081,0.5092,0.5171,
0.5184,0.5188,0.5232,0.5252,0.5261,0.5350,0.5476,0.5481,0.5485,0.5530,
0.5582,0.5603,0.5641,0.5652,0.5677,0.5704,0.5775,0.5801,0.5839,0.5893,
0.5929,0.5936,0.5995,0.6021,0.6052,0.6176,0.6264,0.6306,0.6328,0.6454,
0.6463,0.6471,0.6523,0.6547,0.6594,0.6652,0.6766,0.6801,0.6871,0.6898,
0.6930,0.6947,0.6961,0.7010,0.7092,0.7111,0.7123,0.7160,0.7171,0.7210,
0.7236,0.7334,0.7348,0.7355,0.7386,0.7387,0.7411,0.7448,0.7451,0.7464,
0.7524,0.7534,0.7544,0.7636,0.7647,0.7653,0.7675,0.7760,0.7789,0.7793,
0.7809,0.7838,0.7851,0.7970,0.7988,0.8077,0.8125,0.8147,0.8195,0.8244,
0.8247,0.8268,0.8288,0.8323,0.8327,0.8330,0.8382,0.8404,0.8446,0.8481,
0.8508,0.8525,0.8539,0.8577,0.8604,0.8667,0.8685,0.8705,0.8763,0.8813,
0.8857,0.8887,0.8912,0.8963,0.8986,0.9021,0.9231,0.9322,0.9331,0.9351,
0.9359,0.9395,0.9449,0.9453,0.9487,0.9500,0.9527,0.9561,0.9597,0.9607,
0.9616,0.9660,0.9765,0.9770,0.9802,0.9921,0.9940,0.9975,0.9986,
Overall p-value after applying KStest on 269 p-values = 0.988766
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.