RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-06_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 15.78 19.1476 0.679872
2 to 25 15.58 23.7472 0.873532
3 to 26 16.04 10.9708 0.141922
4 to 27 15.71 14.9195 0.398720
5 to 28 16.15 22.7187 0.841365
6 to 29 15.87 9.7264 0.085312
7 to 30 15.95 22.8165 0.844678
8 to 31 16.05 16.8187 0.533288
9 to 32 15.88 30.4202 0.976531
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.455274
Tough bday spacings test for dh-ranFile-2018-07-06_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 7 32 72 95 80 86 60 34 20 6 8
(O-E)^2/E 0.5 0.6 0.0 0.1 3.2 0.8 1.2 0.6 1.8 0.1 3.8
Birthday Spacings: Sum(O-E)^2/E= 12.600, p= 0.753
RESULTS OF GCD FOR dh-ranFile-2018-07-06_20:31
Euclid's algorithm:
p-value, steps to gcd: 0.469441
p-value, dist. of gcd's: 0.540488
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-06_20:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.898 0.167 0.858 0.377 0.151 0.532 0.607 0.470
Bits 8 to 15---> 0.053 0.085 0.655 0.526 0.838 0.146 0.688 0.202
Bits 16 to 23---> 0.488 0.150 0.849 0.570 0.664 0.140 0.397 0.406
Bits 24 to 31---> 0.004 0.375 0.579 0.085 0.343 0.270 0.213 0.314
KS test for the above 32 p values: 0.886
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-06_20:31,
p-values for 5 runs: 0.3724, 0.0217, 0.9888, 0.5063, 0.3272
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-06_20:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 204 211.4 0.260 0.260
r= 29 5107 5134.0 0.142 0.402
r= 30 22963 23103.0 0.849 1.251
r= 31 11726 11551.5 2.635 3.887
chi-square = 3.887 with df = 3; p-value = 0.726
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-06_20:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 194 211.4 1.435 1.435
r= 30 5174 5134.0 0.311 1.746
r= 31 22978 23103.0 0.677 2.423
r= 32 11654 11551.5 0.909 3.332
chi-square = 3.332 with df = 3; p-value = 0.657
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-06_20:31
b-rank test for bits 1 to 8, p=0.83398
b-rank test for bits 2 to 9, p=0.42001
b-rank test for bits 3 to 10, p=0.41418
b-rank test for bits 4 to 11, p=0.56853
b-rank test for bits 5 to 12, p=0.27322
b-rank test for bits 6 to 13, p=0.93638
b-rank test for bits 7 to 14, p=0.45824
b-rank test for bits 8 to 15, p=0.25803
b-rank test for bits 9 to 16, p=0.29496
b-rank test for bits 10 to 17, p=0.47214
b-rank test for bits 11 to 18, p=0.60553
b-rank test for bits 12 to 19, p=0.77071
b-rank test for bits 13 to 20, p=0.72547
b-rank test for bits 14 to 21, p=0.94401
b-rank test for bits 15 to 22, p=0.25128
b-rank test for bits 16 to 23, p=0.73162
b-rank test for bits 17 to 24, p=0.39763
b-rank test for bits 18 to 25, p=0.73674
b-rank test for bits 19 to 26, p=0.05320
b-rank test for bits 20 to 27, p=0.74686
b-rank test for bits 21 to 28, p=0.47375
b-rank test for bits 22 to 29, p=0.32407
b-rank test for bits 23 to 30, p=0.20087
b-rank test for bits 24 to 31, p=0.79367
b-rank test for bits 25 to 32, p=0.86477
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 = 0.499161
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-06_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 141869 -0.09 0.462464
2 142175 0.62 0.732610
3 141230 -1.59 0.056231
4 141663 -0.58 0.282464
5 142187 0.65 0.741754
6 141265 -1.51 0.066105
7 141770 -0.33 0.372387
8 141802 -0.25 0.400996
9 141785 -0.29 0.385720
10 141948 0.09 0.535996
11 141714 -0.46 0.324059
12 142024 0.27 0.605620
13 142561 1.52 0.936070
14 141244 -1.55 0.060031
15 142505 1.39 0.918001
16 141724 -0.43 0.332502
17 142149 0.56 0.712252
18 141376 -1.25 0.106364
19 141677 -0.54 0.293624
20 141116 -1.85 0.031900
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-06_20:31
Bits used No. missing words z-score p-value
23 to 32 141838 -0.2460 0.402855
22 to 31 141894 -0.0529 0.478921
21 to 30 142345 1.5023 0.933492
20 to 29 141732 -0.6115 0.270440
19 to 28 141924 0.0506 0.520172
18 to 27 142076 0.5747 0.717261
17 to 26 142638 2.5127 0.994009
16 to 25 142336 1.4713 0.929392
15 to 24 142118 0.7196 0.764100
14 to 23 141914 0.0161 0.506424
13 to 22 141968 0.2023 0.580163
12 to 21 141766 -0.4942 0.310568
11 to 20 142318 1.4092 0.920613
10 to 19 141810 -0.3425 0.365981
9 to 18 142259 1.2058 0.886045
8 to 17 142127 0.7506 0.773549
7 to 16 141945 0.1230 0.548947
6 to 15 142546 2.1954 0.985933
5 to 14 141952 0.1471 0.558488
4 to 13 142548 2.2023 0.986178
3 to 12 142140 0.7954 0.786814
2 to 11 142084 0.6023 0.726516
1 to 10 141763 -0.5046 0.306925
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-06_20:31
Bits used No. missing words z-score p-value
28 to 32 142139 0.7785 0.781875
27 to 31 142245 1.1379 0.872411
26 to 30 141277 -2.1435 0.016037
25 to 29 141339 -1.9333 0.026598
24 to 28 141935 0.0870 0.534671
23 to 27 141993 0.2836 0.611652
22 to 26 142619 2.4057 0.991928
21 to 25 141982 0.2463 0.597290
20 to 24 142199 0.9819 0.836933
19 to 23 142148 0.8091 0.790757
18 to 22 142160 0.8497 0.802262
17 to 21 141813 -0.3265 0.372007
16 to 20 141836 -0.2486 0.401844
15 to 19 141462 -1.5164 0.064713
14 to 18 141951 0.1413 0.556166
13 to 17 141819 -0.3062 0.379725
12 to 16 142213 1.0294 0.848352
11 to 15 141701 -0.7062 0.240031
10 to 14 141683 -0.7672 0.221475
9 to 13 141960 0.1718 0.568188
8 to 12 141687 -0.7537 0.225526
7 to 11 141847 -0.2113 0.416331
6 to 10 141921 0.0396 0.515778
5 to 9 142137 0.7718 0.779873
4 to 8 141827 -0.2791 0.390090
3 to 7 141738 -0.5808 0.280695
2 to 6 141465 -1.5062 0.066008
1 to 5 141452 -1.5503 0.060538
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-06_20:31
Bits used No. missing words z-score p-value
31 to 32 142666 2.2321 0.987195
30 to 31 142446 1.5831 0.943300
29 to 30 142004 0.2793 0.609978
28 to 29 142010 0.2970 0.616752
27 to 28 141700 -0.6175 0.268455
26 to 27 142176 0.7866 0.784253
25 to 26 141714 -0.5762 0.282242
24 to 25 141861 -0.1426 0.443316
23 to 24 141739 -0.5024 0.307676
22 to 23 141933 0.0698 0.527833
21 to 22 142327 1.2321 0.891038
20 to 21 142528 1.8250 0.965998
19 to 20 141987 0.2291 0.590610
18 to 19 141807 -0.3019 0.381380
17 to 18 142308 1.1760 0.880206
16 to 17 141435 -1.3992 0.080876
15 to 16 142179 0.7955 0.786835
14 to 15 142235 0.9607 0.831643
13 to 14 141620 -0.8535 0.196696
12 to 13 141905 -0.0128 0.494905
11 to 12 142102 0.5683 0.715101
10 to 11 141848 -0.1809 0.428217
9 to 10 141902 -0.0216 0.491375
8 to 9 141911 0.0049 0.501965
7 to 8 141908 -0.0039 0.498435
6 to 7 141946 0.1082 0.543070
5 to 6 141980 0.2085 0.582568
4 to 5 141993 0.2468 0.597474
3 to 4 141708 -0.5939 0.276292
2 to 3 141653 -0.7561 0.224784
1 to 2 141912 0.0079 0.503142
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-06_20:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2575.52 1.068 0.857259
Test results for specific bytes for dh-ranFile-2018-07-06_20:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2402.36 -1.381 0.083668
2 to 9 2551.01 0.721 0.764671
3 to 10 2491.16 -0.125 0.450228
4 to 11 2537.76 0.534 0.703329
5 to 12 2495.45 -0.064 0.474373
6 to 13 2475.42 -0.348 0.364042
7 to 14 2454.43 -0.644 0.259645
8 to 15 2608.31 1.532 0.937200
9 to 16 2503.27 0.046 0.518447
10 to 17 2522.86 0.323 0.626755
11 to 18 2500.83 0.012 0.504660
12 to 19 2487.30 -0.180 0.428747
13 to 20 2456.54 -0.615 0.269382
14 to 21 2580.82 1.143 0.873475
15 to 22 2604.55 1.479 0.930379
16 to 23 2507.55 0.107 0.542519
17 to 24 2586.40 1.222 0.889127
18 to 25 2507.70 0.109 0.543350
19 to 26 2373.85 -1.784 0.037209
20 to 27 2411.71 -1.249 0.105909
21 to 28 2569.86 0.988 0.838426
22 to 29 2475.31 -0.349 0.363489
23 to 30 2476.83 -0.328 0.371604
24 to 31 2448.21 -0.732 0.231938
25 to 32 2364.29 -1.919 0.027479
CDPARK for dh-ranFile-2018-07-06_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
3542 0.8676 0.807188
3530 0.3196 0.625377
3555 1.4612 0.928018
3513 -0.4566 0.323972
3550 1.2329 0.891189
3516 -0.3196 0.374623
3541 0.8219 0.794438
3500 -1.0502 0.146807
3504 -0.8676 0.192812
3530 0.3196 0.625377
Square side=100, avg. no. parked=3528.10 sample std.=18.21
p-value of the KSTEST for those 10 p-values: 0.726938
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-06_20:31
0.5723,0.0195,0.6148,0.0367,0.2487,0.4898,0.2159,0.4823,0.9168,0.4761,
The KS test for those 10 p-values: 0.399396
The 3DSPHERES test for dh-ranFile-2018-07-06_20:31
sample no r^3 equiv. uni.
1 71.073 0.906434
2 116.221 0.979226
3 1.800 0.058220
4 30.098 0.633320
5 52.116 0.823986
6 19.831 0.483685
7 6.594 0.197317
8 7.632 0.224612
9 7.587 0.223460
10 9.411 0.269251
11 87.867 0.946544
12 13.902 0.370868
13 3.652 0.114606
14 108.700 0.973307
15 5.804 0.175898
16 94.692 0.957422
17 6.022 0.181881
18 17.703 0.445726
19 41.961 0.753080
20 7.528 0.221930
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.301374
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-06_20:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
2.0 0.1 0.8 0.5 1.5 -1.4
0.7 0.9 0.8 -0.0 -0.4 -0.6
-0.6 0.0 -1.7 -0.3 0.1 0.9
0.3 -0.9 0.3 0.0 1.0 0.6
-0.7 0.1 -0.1 0.9 -0.4 1.8
-0.7 -0.5 2.9 -1.8 -0.8 1.5
1.2 -0.7 0.9 1.5 2.4 1.0
0.8
Chi-square with 42 degrees of freedom:51.118667
z-score=0.994928, p-value=0.841938
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-06_20:31
Test no p-value
1 0.801824
2 0.874446
3 0.009325
4 0.029591
5 0.501415
6 0.754512
7 0.978209
8 0.074243
9 0.143112
10 0.116079
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.126996
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-06_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 66428 0.85 66851 0.51
3 25000.00 25263 2.77 24842 1.00
4 6666.67 6617 0.37 6666 0.00
5 1388.89 1422 0.79 1392 0.01
6 238.10 224 0.83 211 3.08
7 34.72 43 1.97 32 0.21
8 4.96 2 1.77 5 0.00
p=0.84548 p=0.43187
Number of rngs required: 688565, p-value: 0.574
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-06_20:31
No. of wins: Observed Expected
98474 98585.9
z-score=-0.500, pvalue=0.30843
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66578 66666.7 0.118 0.118
2 37683 37654.3 0.022 0.140
3 26886 26954.7 0.175 0.315
4 19209 19313.5 0.565 0.880
5 13920 13851.4 0.340 1.220
6 10167 9943.5 5.022 6.241
7 7106 7145.0 0.213 6.454
8 5167 5139.1 0.152 6.606
9 3714 3699.9 0.054 6.660
10 2708 2666.3 0.652 7.312
11 1914 1923.3 0.045 7.358
12 1356 1388.7 0.772 8.130
13 1000 1003.7 0.014 8.143
14 769 726.1 2.530 10.673
15 493 525.8 2.050 12.723
16 353 381.2 2.079 14.803
17 272 276.5 0.075 14.877
18 179 200.8 2.373 17.250
19 126 146.0 2.736 19.986
20 116 106.2 0.901 20.887
21 284 287.1 0.034 20.921
Chisq= 20.92 for 20 degrees of freedom, p= 0.59820
SUMMARY of craptest
p-value for no. of wins: 0.308433
p-value for throws/game: 0.598197
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-06_20:31
No. of wins: Observed Expected
98313 98585.9
z-score=-1.220, pvalue=0.11116
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66879 66666.7 0.676 0.676
2 37168 37654.3 6.281 6.957
3 27057 26954.7 0.388 7.345
4 19321 19313.5 0.003 7.348
5 13858 13851.4 0.003 7.351
6 10072 9943.5 1.659 9.011
7 7157 7145.0 0.020 9.031
8 5131 5139.1 0.013 9.044
9 3718 3699.9 0.089 9.133
10 2631 2666.3 0.467 9.600
11 1900 1923.3 0.283 9.883
12 1417 1388.7 0.575 10.458
13 1030 1003.7 0.688 11.146
14 721 726.1 0.036 11.183
15 527 525.8 0.003 11.185
16 405 381.2 1.492 12.677
17 272 276.5 0.075 12.752
18 186 200.8 1.095 13.847
19 155 146.0 0.557 14.404
20 99 106.2 0.490 14.894
21 296 287.1 0.275 15.169
Chisq= 15.17 for 20 degrees of freedom, p= 0.23334
SUMMARY of craptest
p-value for no. of wins: 0.111160
p-value for throws/game: 0.233341
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0042,0.0093,0.0160,0.0195,0.0217,0.0266,0.0275,0.0296,0.0319,0.0367,
0.0372,0.0532,0.0532,0.0562,0.0582,0.0600,0.0605,0.0647,0.0660,0.0661,
0.0742,0.0809,0.0837,0.0847,0.0849,0.0853,0.1059,0.1064,0.1112,0.1146,
0.1161,0.1270,0.1403,0.1419,0.1431,0.1461,0.1468,0.1504,0.1507,0.1668,
0.1759,0.1819,0.1928,0.1967,0.1973,0.2009,0.2022,0.2129,0.2159,0.2215,
0.2219,0.2235,0.2246,0.2248,0.2255,0.2319,0.2333,0.2400,0.2487,0.2513,
0.2580,0.2596,0.2685,0.2693,0.2694,0.2697,0.2704,0.2732,0.2763,0.2807,
0.2822,0.2825,0.2936,0.2950,0.3014,0.3069,0.3077,0.3084,0.3106,0.3138,
0.3240,0.3241,0.3241,0.3272,0.3325,0.3429,0.3635,0.3640,0.3660,0.3709,
0.3716,0.3720,0.3724,0.3724,0.3745,0.3746,0.3772,0.3797,0.3814,0.3857,
0.3901,0.3966,0.3976,0.3987,0.3994,0.4010,0.4018,0.4029,0.4063,0.4142,
0.4163,0.4200,0.4282,0.4287,0.4319,0.4433,0.4457,0.4502,0.4553,0.4582,
0.4625,0.4694,0.4697,0.4721,0.4737,0.4744,0.4761,0.4789,0.4823,0.4837,
0.4878,0.4898,0.4914,0.4949,0.4984,0.4992,0.5014,0.5020,0.5031,0.5047,
0.5063,0.5064,0.5158,0.5184,0.5202,0.5262,0.5278,0.5321,0.5333,0.5347,
0.5360,0.5405,0.5425,0.5431,0.5434,0.5489,0.5562,0.5585,0.5682,0.5685,
0.5697,0.5723,0.5739,0.5791,0.5802,0.5826,0.5906,0.5973,0.5975,0.5982,
0.6055,0.6056,0.6070,0.6100,0.6117,0.6148,0.6168,0.6254,0.6254,0.6268,
0.6333,0.6553,0.6568,0.6639,0.6799,0.6877,0.7033,0.7123,0.7151,0.7173,
0.7255,0.7260,0.7265,0.7269,0.7316,0.7326,0.7367,0.7418,0.7469,0.7531,
0.7531,0.7545,0.7641,0.7647,0.7707,0.7735,0.7799,0.7819,0.7843,0.7868,
0.7868,0.7908,0.7937,0.7944,0.8018,0.8023,0.8072,0.8240,0.8316,0.8340,
0.8369,0.8378,0.8384,0.8414,0.8419,0.8447,0.8455,0.8484,0.8488,0.8573,
0.8582,0.8648,0.8724,0.8735,0.8735,0.8744,0.8802,0.8856,0.8860,0.8891,
0.8910,0.8912,0.8981,0.9064,0.9168,0.9180,0.9206,0.9280,0.9294,0.9304,
0.9335,0.9361,0.9364,0.9372,0.9433,0.9440,0.9465,0.9574,0.9660,0.9733,
0.9765,0.9782,0.9792,0.9859,0.9862,0.9872,0.9888,0.9919,0.9940,
Overall p-value after applying KStest on 269 p-values = 0.751848
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.