RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-19_23:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.67 9.0878 0.062533
2 to 25 15.62 14.6734 0.381009
3 to 26 15.88 17.0345 0.547966
4 to 27 16.01 18.6896 0.653365
5 to 28 16.03 19.8697 0.719053
6 to 29 15.83 20.6055 0.755566
7 to 30 15.97 12.2403 0.214628
8 to 31 15.79 13.4483 0.294301
9 to 32 15.34 29.7269 0.971617
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.995954
Tough bday spacings test for dh-ranFile-2018-06-19_23:31: 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 34 82 95 83 86 57 21 22 4 7
(O-E)^2/E 0.0 0.2 1.0 0.1 2.2 0.8 0.5 2.6 3.4 1.0 2.1
Birthday Spacings: Sum(O-E)^2/E= 13.901, p= 0.822
RESULTS OF GCD FOR dh-ranFile-2018-06-19_23:31
Euclid's algorithm:
p-value, steps to gcd: 0.115989
p-value, dist. of gcd's: 0.473069
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-19_23:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.745 0.499 0.838 0.076 0.068 0.869 0.152 0.142
Bits 8 to 15---> 0.855 0.765 0.670 0.498 0.025 0.204 0.901 0.566
Bits 16 to 23---> 0.913 0.834 0.797 0.907 0.778 0.333 0.027 0.917
Bits 24 to 31---> 0.655 0.042 0.695 0.494 0.787 0.790 0.870 0.567
KS test for the above 32 p values: 0.930
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-19_23:31,
p-values for 5 runs: 0.7053, 0.2825, 0.8030, 0.1931, 0.4665
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-19_23:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 202 211.4 0.420 0.420
r= 29 5208 5134.0 1.066 1.486
r= 30 22944 23103.0 1.095 2.581
r= 31 11646 11551.5 0.773 3.353
chi-square = 3.353 with df = 3; p-value = 0.660
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-19_23:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 217 211.4 0.147 0.147
r= 30 5093 5134.0 0.328 0.475
r= 31 23174 23103.0 0.218 0.693
r= 32 11516 11551.5 0.109 0.802
chi-square = 0.802 with df = 3; p-value = 0.151
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-19_23:31
b-rank test for bits 1 to 8, p=0.41196
b-rank test for bits 2 to 9, p=0.57874
b-rank test for bits 3 to 10, p=0.90449
b-rank test for bits 4 to 11, p=0.34302
b-rank test for bits 5 to 12, p=0.49869
b-rank test for bits 6 to 13, p=0.18717
b-rank test for bits 7 to 14, p=0.35090
b-rank test for bits 8 to 15, p=0.28108
b-rank test for bits 9 to 16, p=0.75672
b-rank test for bits 10 to 17, p=0.45565
b-rank test for bits 11 to 18, p=0.01754
b-rank test for bits 12 to 19, p=0.21628
b-rank test for bits 13 to 20, p=0.69496
b-rank test for bits 14 to 21, p=0.13114
b-rank test for bits 15 to 22, p=0.95043
b-rank test for bits 16 to 23, p=0.97127
b-rank test for bits 17 to 24, p=0.10787
b-rank test for bits 18 to 25, p=0.50614
b-rank test for bits 19 to 26, p=0.48435
b-rank test for bits 20 to 27, p=0.52338
b-rank test for bits 21 to 28, p=0.42951
b-rank test for bits 22 to 29, p=0.31582
b-rank test for bits 23 to 30, p=0.11320
b-rank test for bits 24 to 31, p=0.31985
b-rank test for bits 25 to 32, p=0.86083
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 = 0.595429
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-19_23:31
(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 142048 0.32 0.627029
3 141511 -0.93 0.176010
4 142324 0.97 0.833691
5 141126 -1.83 0.033609
6 142286 0.88 0.810589
7 142158 0.58 0.719381
8 142121 0.49 0.689543
9 141847 -0.15 0.442106
10 142667 1.77 0.961658
11 142043 0.31 0.622599
12 141882 -0.06 0.474543
13 142315 0.95 0.828391
14 141989 0.19 0.573834
15 142367 1.07 0.857538
16 141262 -1.51 0.065209
17 142060 0.35 0.637593
18 141589 -0.75 0.227099
19 142234 0.76 0.775947
20 142383 1.11 0.865789
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-19_23:31
Bits used No. missing words z-score p-value
23 to 32 141952 0.1471 0.558488
22 to 31 141972 0.2161 0.585547
21 to 30 141778 -0.4529 0.325324
20 to 29 142469 1.9299 0.973190
19 to 28 141780 -0.4460 0.327811
18 to 27 141883 -0.0908 0.463829
17 to 26 142180 0.9333 0.824679
16 to 25 141979 0.2402 0.594928
15 to 24 141939 0.1023 0.540745
14 to 23 141815 -0.3253 0.372486
13 to 22 141832 -0.2667 0.394867
12 to 21 141937 0.0954 0.538007
11 to 20 142024 0.3954 0.653731
10 to 19 141933 0.0816 0.532526
9 to 18 141773 -0.4701 0.319141
8 to 17 141750 -0.5494 0.291361
7 to 16 141846 -0.2184 0.413567
6 to 15 142031 0.4196 0.662594
5 to 14 141661 -0.8563 0.195913
4 to 13 141681 -0.7873 0.215540
3 to 12 142125 0.7437 0.771468
2 to 11 141805 -0.3598 0.359514
1 to 10 142154 0.8437 0.800579
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-19_23:31
Bits used No. missing words z-score p-value
28 to 32 141970 0.2057 0.581472
27 to 31 141805 -0.3537 0.361797
26 to 30 141744 -0.5604 0.287589
25 to 29 141534 -1.2723 0.101632
24 to 28 141853 -0.1909 0.424283
23 to 27 141816 -0.3164 0.375860
22 to 26 141900 -0.0316 0.487385
21 to 25 141902 -0.0248 0.490088
20 to 24 142320 1.3921 0.918054
19 to 23 142335 1.4429 0.925483
18 to 22 142106 0.6667 0.747511
17 to 21 142076 0.5650 0.713957
16 to 20 141591 -1.0791 0.140275
15 to 19 141143 -2.5977 0.004692
14 to 18 142231 1.0904 0.862233
13 to 17 141832 -0.2621 0.396609
12 to 16 142007 0.3311 0.629710
11 to 15 141805 -0.3537 0.361797
10 to 14 141590 -1.0825 0.139521
9 to 13 141808 -0.3435 0.365614
8 to 12 142129 0.7446 0.771757
7 to 11 142205 1.0023 0.841894
6 to 10 142172 0.8904 0.813376
5 to 9 142054 0.4904 0.688077
4 to 8 141765 -0.4893 0.312331
3 to 7 142326 1.4124 0.921090
2 to 6 141878 -0.1062 0.457711
1 to 5 141545 -1.2350 0.108412
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-19_23:31
Bits used No. missing words z-score p-value
31 to 32 142166 0.7571 0.775517
30 to 31 142418 1.5005 0.933258
29 to 30 141742 -0.4936 0.310795
28 to 29 142023 0.3353 0.631304
27 to 28 142214 0.8987 0.815602
26 to 27 142174 0.7807 0.782522
25 to 26 142297 1.1436 0.873599
24 to 25 141838 -0.2104 0.416673
23 to 24 141592 -0.9361 0.174617
22 to 23 141521 -1.1455 0.125998
21 to 22 141952 0.1259 0.550083
20 to 21 142188 0.8220 0.794472
19 to 20 142498 1.7365 0.958761
18 to 19 142177 0.7896 0.785116
17 to 18 142185 0.8132 0.791944
16 to 17 141524 -1.1367 0.127839
15 to 16 142349 1.2970 0.902678
14 to 15 141774 -0.3992 0.344872
13 to 14 142751 2.4828 0.993482
12 to 13 142285 1.1082 0.866106
11 to 12 141400 -1.5024 0.066491
10 to 11 142155 0.7247 0.765679
9 to 10 142121 0.6244 0.733816
8 to 9 141847 -0.1839 0.427060
7 to 8 141773 -0.4022 0.343786
6 to 7 141729 -0.5319 0.297381
5 to 6 141923 0.0403 0.516083
4 to 5 142130 0.6509 0.742459
3 to 4 142061 0.4474 0.672708
2 to 3 142063 0.4533 0.674835
1 to 2 142308 1.1760 0.880206
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-19_23:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2482.89 -0.242 0.404394
Test results for specific bytes for dh-ranFile-2018-06-19_23:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2560.65 0.858 0.804469
2 to 9 2572.87 1.030 0.848611
3 to 10 2511.02 0.156 0.561944
4 to 11 2480.75 -0.272 0.392737
5 to 12 2568.68 0.971 0.834280
6 to 13 2516.82 0.238 0.594033
7 to 14 2536.19 0.512 0.695603
8 to 15 2476.25 -0.336 0.368509
9 to 16 2485.60 -0.204 0.419303
10 to 17 2628.28 1.814 0.965168
11 to 18 2468.41 -0.447 0.327549
12 to 19 2573.87 1.045 0.851909
13 to 20 2515.12 0.214 0.584655
14 to 21 2463.41 -0.517 0.302410
15 to 22 2435.28 -0.915 0.180031
16 to 23 2470.64 -0.415 0.338985
17 to 24 2508.46 0.120 0.547637
18 to 25 2499.80 -0.003 0.498848
19 to 26 2524.73 0.350 0.636744
20 to 27 2472.95 -0.383 0.351016
21 to 28 2300.41 -2.823 0.002382
22 to 29 2366.82 -1.883 0.029822
23 to 30 2502.75 0.039 0.515483
24 to 31 2473.68 -0.372 0.354843
25 to 32 2619.25 1.686 0.954142
CDPARK for dh-ranFile-2018-06-19_23:31: 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
3522 -0.0457 0.481790
3541 0.8219 0.794438
3582 2.6941 0.996471
3551 1.2785 0.899470
3515 -0.3653 0.357445
3513 -0.4566 0.323972
3474 -2.2374 0.012629
3530 0.3196 0.625377
3539 0.7306 0.767486
3522 -0.0457 0.481790
Square side=100, avg. no. parked=3528.90 sample std.=26.67
p-value of the KSTEST for those 10 p-values: 0.533390
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-19_23:31
0.0656,0.7923,0.6108,0.7103,0.1410,0.4107,0.9050,0.1884,0.8369,0.3633,
The KS test for those 10 p-values: 0.994230
The 3DSPHERES test for dh-ranFile-2018-06-19_23:31
sample no r^3 equiv. uni.
1 18.540 0.460977
2 8.676 0.251136
3 16.425 0.421601
4 25.891 0.578115
5 1.657 0.053734
6 24.642 0.560191
7 23.344 0.540736
8 32.722 0.664030
9 14.476 0.382779
10 7.955 0.232916
11 47.849 0.797084
12 20.042 0.487309
13 4.861 0.149589
14 73.036 0.912362
15 6.813 0.203160
16 13.729 0.367224
17 0.178 0.005907
18 108.466 0.973097
19 22.326 0.524893
20 13.176 0.355448
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.520720
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-19_23:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 0.5 1.5 0.2 1.1 0.1
1.2 0.9 0.8 0.3 0.4 -1.7
0.0 -2.0 -0.9 -0.2 0.0 0.2
0.8 -1.3 0.4 1.8 0.9 0.3
0.7 0.4 0.7 -0.2 -0.8 -0.6
-0.4 -0.5 -1.1 -1.5 0.5 2.2
-1.4 -0.7 0.1 0.4 0.1 -1.0
0.8
Chi-square with 42 degrees of freedom:39.153895
z-score=-0.310536, p-value=0.403382
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-19_23:31
Test no p-value
1 0.179736
2 0.096262
3 0.229010
4 0.236806
5 0.376935
6 0.549401
7 0.116761
8 0.013800
9 0.022925
10 0.853244
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.011632
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-19_23:31:
(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 66719 0.04 66668 0.00
3 25000.00 25022 0.02 24995 0.00
4 6666.67 6569 1.43 6683 0.04
5 1388.89 1418 0.61 1381 0.04
6 238.10 240 0.02 227 0.52
7 34.72 25 2.72 37 0.15
8 4.96 6 0.22 8 1.86
p=0.46334 p=0.14471
Number of rngs required: 687902, p-value: 0.282
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-19_23:31
No. of wins: Observed Expected
98513 98585.9
z-score=-0.326, pvalue=0.37226
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66589 66666.7 0.090 0.090
2 37344 37654.3 2.557 2.648
3 27187 26954.7 2.001 4.649
4 19232 19313.5 0.344 4.993
5 13966 13851.4 0.948 5.941
6 9935 9943.5 0.007 5.948
7 7104 7145.0 0.236 6.184
8 5228 5139.1 1.539 7.723
9 3710 3699.9 0.028 7.750
10 2706 2666.3 0.591 8.341
11 1919 1923.3 0.010 8.351
12 1415 1388.7 0.497 8.848
13 1014 1003.7 0.105 8.953
14 735 726.1 0.108 9.061
15 512 525.8 0.364 9.425
16 392 381.2 0.309 9.734
17 305 276.5 2.929 12.663
18 201 200.8 0.000 12.663
19 137 146.0 0.553 13.216
20 111 106.2 0.216 13.432
21 258 287.1 2.952 16.384
Chisq= 16.38 for 20 degrees of freedom, p= 0.30747
SUMMARY of craptest
p-value for no. of wins: 0.372263
p-value for throws/game: 0.307467
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-19_23:31
No. of wins: Observed Expected
99225 98585.9
z-score= 2.859, pvalue=0.99787
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67059 66666.7 2.309 2.309
2 37700 37654.3 0.055 2.364
3 26816 26954.7 0.714 3.078
4 19147 19313.5 1.435 4.513
5 13760 13851.4 0.603 5.116
6 9847 9943.5 0.937 6.054
7 7134 7145.0 0.017 6.071
8 5225 5139.1 1.437 7.508
9 3671 3699.9 0.225 7.733
10 2627 2666.3 0.579 8.312
11 1958 1923.3 0.625 8.937
12 1357 1388.7 0.725 9.662
13 997 1003.7 0.045 9.707
14 744 726.1 0.439 10.147
15 481 525.8 3.823 13.970
16 400 381.2 0.932 14.902
17 288 276.5 0.475 15.377
18 192 200.8 0.388 15.765
19 144 146.0 0.027 15.792
20 127 106.2 4.067 19.859
21 326 287.1 5.267 25.126
Chisq= 25.13 for 20 degrees of freedom, p= 0.80334
SUMMARY of craptest
p-value for no. of wins: 0.997873
p-value for throws/game: 0.803337
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0024,0.0047,0.0059,0.0116,0.0126,0.0138,0.0175,0.0229,0.0253,0.0271,
0.0298,0.0336,0.0417,0.0537,0.0625,0.0652,0.0656,0.0665,0.0679,0.0761,
0.0963,0.1016,0.1079,0.1084,0.1132,0.1160,0.1168,0.1260,0.1278,0.1311,
0.1395,0.1403,0.1410,0.1416,0.1447,0.1496,0.1510,0.1521,0.1746,0.1760,
0.1797,0.1800,0.1872,0.1884,0.1931,0.1959,0.2032,0.2036,0.2146,0.2155,
0.2163,0.2271,0.2290,0.2329,0.2368,0.2511,0.2811,0.2817,0.2825,0.2876,
0.2914,0.2943,0.2974,0.3024,0.3075,0.3108,0.3123,0.3158,0.3191,0.3199,
0.3240,0.3253,0.3275,0.3278,0.3334,0.3390,0.3430,0.3438,0.3449,0.3509,
0.3510,0.3548,0.3554,0.3574,0.3595,0.3618,0.3618,0.3633,0.3656,0.3672,
0.3685,0.3723,0.3725,0.3759,0.3769,0.3810,0.3828,0.3927,0.3949,0.3966,
0.4034,0.4044,0.4107,0.4120,0.4136,0.4167,0.4193,0.4216,0.4243,0.4271,
0.4295,0.4421,0.4557,0.4577,0.4610,0.4633,0.4638,0.4665,0.4731,0.4745,
0.4818,0.4818,0.4843,0.4873,0.4874,0.4901,0.4944,0.4985,0.4987,0.4988,
0.4994,0.5061,0.5155,0.5161,0.5207,0.5234,0.5249,0.5325,0.5334,0.5380,
0.5407,0.5407,0.5476,0.5480,0.5494,0.5501,0.5585,0.5602,0.5619,0.5664,
0.5667,0.5738,0.5781,0.5787,0.5815,0.5847,0.5855,0.5940,0.5949,0.5954,
0.6108,0.6226,0.6254,0.6270,0.6297,0.6313,0.6367,0.6376,0.6534,0.6537,
0.6545,0.6597,0.6626,0.6640,0.6705,0.6727,0.6748,0.6881,0.6895,0.6950,
0.6953,0.6956,0.7053,0.7103,0.7140,0.7191,0.7194,0.7338,0.7425,0.7450,
0.7475,0.7556,0.7567,0.7654,0.7657,0.7675,0.7715,0.7718,0.7755,0.7759,
0.7785,0.7825,0.7851,0.7866,0.7900,0.7919,0.7923,0.7944,0.7945,0.7966,
0.7971,0.8006,0.8030,0.8033,0.8045,0.8106,0.8134,0.8156,0.8205,0.8224,
0.8247,0.8284,0.8337,0.8341,0.8343,0.8369,0.8376,0.8419,0.8486,0.8519,
0.8532,0.8548,0.8575,0.8608,0.8622,0.8658,0.8661,0.8694,0.8699,0.8736,
0.8802,0.8995,0.9013,0.9027,0.9045,0.9050,0.9067,0.9124,0.9131,0.9166,
0.9181,0.9211,0.9255,0.9295,0.9333,0.9504,0.9541,0.9588,0.9617,0.9652,
0.9713,0.9716,0.9731,0.9732,0.9935,0.9942,0.9960,0.9965,0.9979,
Overall p-value after applying KStest on 269 p-values = 0.268281
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.