RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-30_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 15.56 20.8329 0.766147
2 to 25 15.83 27.4327 0.947980
3 to 26 15.73 11.6623 0.179862
4 to 27 15.63 27.3008 0.946199
5 to 28 15.65 20.1492 0.733330
6 to 29 15.78 19.9495 0.723182
7 to 30 15.98 16.0426 0.479183
8 to 31 15.50 26.5290 0.934653
9 to 32 15.63 12.9329 0.259335
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.106123
Tough bday spacings test for dh-ranFile-2018-06-30_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 13 32 71 101 97 70 58 34 14 6 4
(O-E)^2/E 1.6 0.6 0.1 0.1 0.0 0.8 0.7 0.6 0.1 0.1 0.0
Birthday Spacings: Sum(O-E)^2/E= 4.615, p= 0.085
RESULTS OF GCD FOR dh-ranFile-2018-06-30_03:31
Euclid's algorithm:
p-value, steps to gcd: 0.996108
p-value, dist. of gcd's: 0.551378
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-30_03:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.381 0.869 0.577 0.288 0.481 0.612 0.075 0.377
Bits 8 to 15---> 0.228 0.448 0.211 0.979 0.630 0.687 0.503 0.897
Bits 16 to 23---> 0.180 0.405 0.904 0.273 0.087 0.845 0.474 0.825
Bits 24 to 31---> 0.891 0.364 0.482 0.046 0.389 0.374 0.025 0.457
KS test for the above 32 p values: 0.299
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-30_03:31,
p-values for 5 runs: 0.0006, 0.7900, 0.6321, 0.7316, 0.7049
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-30_03:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 201 211.4 0.513 0.513
r= 29 5276 5134.0 3.927 4.440
r= 30 23092 23103.0 0.005 4.446
r= 31 11431 11551.5 1.257 5.703
chi-square = 5.703 with df = 3; p-value = 0.873
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-30_03:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 218 211.4 0.205 0.205
r= 30 5164 5134.0 0.175 0.380
r= 31 23002 23103.0 0.442 0.822
r= 32 11616 11551.5 0.360 1.182
chi-square = 1.182 with df = 3; p-value = 0.243
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-30_03:31
b-rank test for bits 1 to 8, p=0.96341
b-rank test for bits 2 to 9, p=0.92068
b-rank test for bits 3 to 10, p=0.89195
b-rank test for bits 4 to 11, p=0.05147
b-rank test for bits 5 to 12, p=0.53318
b-rank test for bits 6 to 13, p=0.81301
b-rank test for bits 7 to 14, p=0.79022
b-rank test for bits 8 to 15, p=0.97941
b-rank test for bits 9 to 16, p=0.83488
b-rank test for bits 10 to 17, p=0.41246
b-rank test for bits 11 to 18, p=0.59877
b-rank test for bits 12 to 19, p=0.59784
b-rank test for bits 13 to 20, p=0.20159
b-rank test for bits 14 to 21, p=0.90032
b-rank test for bits 15 to 22, p=0.01611
b-rank test for bits 16 to 23, p=0.70796
b-rank test for bits 17 to 24, p=0.76158
b-rank test for bits 18 to 25, p=0.86844
b-rank test for bits 19 to 26, p=0.51140
b-rank test for bits 20 to 27, p=0.36976
b-rank test for bits 21 to 28, p=0.30596
b-rank test for bits 22 to 29, p=0.19577
b-rank test for bits 23 to 30, p=0.17481
b-rank test for bits 24 to 31, p=0.75418
b-rank test for bits 25 to 32, p=0.91107
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 = 0.096381
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-30_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 142072 0.38 0.648053
2 142266 0.83 0.797674
3 142025 0.27 0.606519
4 141387 -1.22 0.111157
5 141913 0.01 0.503421
6 141330 -1.35 0.087936
7 141555 -0.83 0.203871
8 142308 0.93 0.824195
9 142452 1.27 0.897587
10 142230 0.75 0.773140
11 142042 0.31 0.621711
12 141429 -1.12 0.130875
13 141989 0.19 0.573834
14 142026 0.27 0.607417
15 142031 0.28 0.611900
16 141702 -0.48 0.314045
17 142485 1.35 0.910691
18 141578 -0.77 0.219425
19 141700 -0.49 0.312389
20 141770 -0.33 0.372387
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-30_03:31
Bits used No. missing words z-score p-value
23 to 32 142291 1.3161 0.905930
22 to 31 142092 0.6299 0.735619
21 to 30 141629 -0.9667 0.166858
20 to 29 141868 -0.1425 0.443336
19 to 28 142089 0.6196 0.732224
18 to 27 142102 0.6644 0.746776
17 to 26 141791 -0.4080 0.341624
16 to 25 142210 1.0368 0.850084
15 to 24 141932 0.0782 0.531155
14 to 23 141642 -0.9218 0.178309
13 to 22 141957 0.1644 0.565284
12 to 21 141978 0.2368 0.593591
11 to 20 142020 0.3816 0.648629
10 to 19 141863 -0.1598 0.436536
9 to 18 141818 -0.3149 0.376407
8 to 17 142181 0.9368 0.825568
7 to 16 141920 0.0368 0.514675
6 to 15 141891 -0.0632 0.474801
5 to 14 141542 -1.2667 0.102639
4 to 13 141631 -0.9598 0.168588
3 to 12 141793 -0.4011 0.344159
2 to 11 141314 -2.0529 0.020043
1 to 10 141829 -0.2770 0.390890
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-30_03:31
Bits used No. missing words z-score p-value
28 to 32 142001 0.3107 0.622003
27 to 31 142214 1.0328 0.849147
26 to 30 141851 -0.1977 0.421629
25 to 29 141803 -0.3604 0.359259
24 to 28 142191 0.9548 0.830164
23 to 27 141651 -0.8757 0.190598
22 to 26 141840 -0.2350 0.407098
21 to 25 142117 0.7040 0.759273
20 to 24 142214 1.0328 0.849147
19 to 23 142177 0.9074 0.817891
18 to 22 141632 -0.9401 0.173583
17 to 21 141661 -0.8418 0.199951
16 to 20 141829 -0.2723 0.392694
15 to 19 142339 1.4565 0.927374
14 to 18 141756 -0.5198 0.301615
13 to 17 142331 1.4294 0.923554
12 to 16 141724 -0.6282 0.264924
11 to 15 141800 -0.3706 0.355464
10 to 14 141582 -1.1096 0.133587
9 to 13 142295 1.3074 0.904454
8 to 12 142407 1.6870 0.954200
7 to 11 141823 -0.2926 0.384897
6 to 10 142011 0.3446 0.634819
5 to 9 142214 1.0328 0.849147
4 to 8 141749 -0.5435 0.293396
3 to 7 142191 0.9548 0.830164
2 to 6 141960 0.1718 0.568188
1 to 5 142322 1.3989 0.919076
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-30_03:31
Bits used No. missing words z-score p-value
31 to 32 141443 -1.3756 0.084472
30 to 31 141490 -1.2370 0.108051
29 to 30 141663 -0.7266 0.233724
28 to 29 141990 0.2380 0.594046
27 to 28 141453 -1.3461 0.089134
26 to 27 140926 -2.9007 0.001862
25 to 26 142048 0.4091 0.658751
24 to 25 142252 1.0108 0.843950
23 to 24 141535 -1.1042 0.134749
22 to 23 141306 -1.7797 0.037560
21 to 22 142052 0.4209 0.663070
20 to 21 141822 -0.2576 0.398354
19 to 20 142024 0.3383 0.632416
18 to 19 141201 -2.0895 0.018333
17 to 18 141773 -0.4022 0.343786
16 to 17 142081 0.5064 0.693713
15 to 16 142412 1.4828 0.930937
14 to 15 141753 -0.4612 0.322345
13 to 14 141724 -0.5467 0.292294
12 to 13 142363 1.3383 0.909594
11 to 12 141499 -1.2104 0.113060
10 to 11 141430 -1.4140 0.078688
9 to 10 141749 -0.4729 0.318125
8 to 9 141685 -0.6617 0.254069
7 to 8 141917 0.0226 0.509025
6 to 7 141485 -1.2517 0.105338
5 to 6 142451 1.5978 0.944961
4 to 5 141688 -0.6529 0.256913
3 to 4 141566 -1.0128 0.155584
2 to 3 142118 0.6155 0.730903
1 to 2 142013 0.3058 0.620126
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-30_03:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2483.58 -0.232 0.408164
Test results for specific bytes for dh-ranFile-2018-06-30_03:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2519.42 0.275 0.608200
2 to 9 2556.40 0.798 0.787436
3 to 10 2552.45 0.742 0.770872
4 to 11 2565.66 0.929 0.823440
5 to 12 2541.51 0.587 0.721418
6 to 13 2620.54 1.705 0.955871
7 to 14 2435.65 -0.910 0.181416
8 to 15 2413.84 -1.219 0.111515
9 to 16 2440.53 -0.841 0.200165
10 to 17 2433.06 -0.947 0.171918
11 to 18 2464.38 -0.504 0.307201
12 to 19 2520.07 0.284 0.611706
13 to 20 2525.91 0.366 0.642979
14 to 21 2680.70 2.556 0.994699
15 to 22 2568.56 0.970 0.833859
16 to 23 2451.23 -0.690 0.245193
17 to 24 2464.90 -0.496 0.309809
18 to 25 2544.07 0.623 0.733427
19 to 26 2580.61 1.140 0.872869
20 to 27 2505.05 0.071 0.528494
21 to 28 2428.31 -1.014 0.155318
22 to 29 2531.22 0.442 0.670575
23 to 30 2502.55 0.036 0.514411
24 to 31 2459.31 -0.575 0.282519
25 to 32 2552.09 0.737 0.769325
CDPARK for dh-ranFile-2018-06-30_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
3524 0.0457 0.518210
3509 -0.6393 0.261324
3524 0.0457 0.518210
3540 0.7763 0.781201
3522 -0.0457 0.481790
3517 -0.2740 0.392053
3529 0.2740 0.607947
3510 -0.5936 0.276387
3480 -1.9635 0.024796
3525 0.0913 0.536383
Square side=100, avg. no. parked=3518.00 sample std.=15.27
p-value of the KSTEST for those 10 p-values: 0.379570
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-30_03:31
0.3858,0.4838,0.2594,0.5731,0.8318,0.8721,0.6218,0.0812,0.7413,0.8438,
The KS test for those 10 p-values: 0.694033
The 3DSPHERES test for dh-ranFile-2018-06-30_03:31
sample no r^3 equiv. uni.
1 49.866 0.810278
2 5.115 0.156768
3 13.200 0.355965
4 11.655 0.321933
5 1.554 0.050486
6 47.720 0.796213
7 2.484 0.079461
8 76.995 0.923197
9 19.503 0.477999
10 27.974 0.606423
11 26.979 0.593144
12 20.309 0.491847
13 23.859 0.548548
14 55.353 0.841990
15 24.069 0.551701
16 91.041 0.951911
17 29.180 0.621932
18 25.245 0.568939
19 5.331 0.162803
20 82.896 0.936910
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.758995
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-30_03:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -1.2 2.0 -0.7 0.8 -0.4
-1.9 -0.4 0.8 1.1 -0.3 0.1
-0.2 1.3 1.2 0.5 0.2 0.2
0.3 -0.9 0.1 0.1 -0.8 0.2
-1.1 -1.7 -1.0 -0.9 -1.0 0.4
0.3 -1.3 0.8 -0.6 0.9 -0.5
0.7 2.7 0.9 1.0 -0.6 -1.0
0.8
Chi-square with 42 degrees of freedom:40.231241
z-score=-0.192987, p-value=0.451177
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-30_03:31
Test no p-value
1 0.291600
2 0.800357
3 0.413839
4 0.252762
5 0.319187
6 0.616995
7 0.251606
8 0.715480
9 0.422301
10 0.007161
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.361868
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-30_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 66817 0.34 66791 0.23
3 25000.00 24893 0.46 24945 0.12
4 6666.67 6656 0.02 6596 0.75
5 1388.89 1368 0.31 1399 0.07
6 238.10 237 0.01 230 0.28
7 34.72 21 5.42 32 0.21
8 4.96 7 0.84 6 0.22
p=0.71405 p=0.06977
Number of rngs required: 687962, p-value: 0.306
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-30_03:31
No. of wins: Observed Expected
98274 98585.9
z-score=-1.395, pvalue=0.08154
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66627 66666.7 0.024 0.024
2 37597 37654.3 0.087 0.111
3 26897 26954.7 0.124 0.235
4 19461 19313.5 1.127 1.362
5 13881 13851.4 0.063 1.425
6 9893 9943.5 0.257 1.682
7 7052 7145.0 1.211 2.893
8 5140 5139.1 0.000 2.893
9 3726 3699.9 0.185 3.078
10 2608 2666.3 1.275 4.352
11 1918 1923.3 0.015 4.367
12 1454 1388.7 3.067 7.434
13 1049 1003.7 2.043 9.477
14 755 726.1 1.147 10.624
15 523 525.8 0.015 10.639
16 379 381.2 0.012 10.651
17 256 276.5 1.526 12.177
18 196 200.8 0.116 12.293
19 146 146.0 0.000 12.293
20 99 106.2 0.490 12.783
21 343 287.1 10.878 23.661
Chisq= 23.66 for 20 degrees of freedom, p= 0.74249
SUMMARY of craptest
p-value for no. of wins: 0.081536
p-value for throws/game: 0.742491
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-30_03:31
No. of wins: Observed Expected
98181 98585.9
z-score=-1.811, pvalue=0.03509
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66726 66666.7 0.053 0.053
2 37626 37654.3 0.021 0.074
3 27020 26954.7 0.158 0.232
4 19238 19313.5 0.295 0.527
5 13953 13851.4 0.745 1.272
6 10029 9943.5 0.734 2.006
7 7163 7145.0 0.045 2.052
8 5107 5139.1 0.200 2.252
9 3604 3699.9 2.484 4.736
10 2565 2666.3 3.848 8.584
11 1973 1923.3 1.283 9.867
12 1382 1388.7 0.033 9.900
13 1047 1003.7 1.867 11.766
14 719 726.1 0.070 11.836
15 490 525.8 2.442 14.279
16 378 381.2 0.026 14.305
17 276 276.5 0.001 14.306
18 181 200.8 1.958 16.264
19 131 146.0 1.538 17.802
20 89 106.2 2.790 20.592
21 303 287.1 0.879 21.471
Chisq= 21.47 for 20 degrees of freedom, p= 0.63011
SUMMARY of craptest
p-value for no. of wins: 0.035089
p-value for throws/game: 0.630111
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0006,0.0019,0.0072,0.0161,0.0183,0.0200,0.0248,0.0248,0.0351,0.0376,
0.0465,0.0505,0.0515,0.0698,0.0750,0.0787,0.0795,0.0812,0.0815,0.0845,
0.0846,0.0867,0.0879,0.0891,0.0964,0.1026,0.1053,0.1061,0.1081,0.1112,
0.1115,0.1131,0.1309,0.1336,0.1347,0.1553,0.1556,0.1568,0.1628,0.1669,
0.1686,0.1719,0.1736,0.1748,0.1783,0.1799,0.1801,0.1814,0.1906,0.1958,
0.2000,0.2002,0.2016,0.2039,0.2107,0.2194,0.2278,0.2337,0.2427,0.2452,
0.2516,0.2528,0.2541,0.2569,0.2593,0.2594,0.2613,0.2649,0.2731,0.2764,
0.2825,0.2875,0.2916,0.2923,0.2934,0.2986,0.3016,0.3056,0.3060,0.3072,
0.3098,0.3124,0.3140,0.3181,0.3192,0.3219,0.3223,0.3416,0.3438,0.3442,
0.3555,0.3560,0.3593,0.3619,0.3637,0.3698,0.3724,0.3742,0.3764,0.3773,
0.3796,0.3807,0.3849,0.3858,0.3892,0.3909,0.3921,0.3927,0.3984,0.4047,
0.4071,0.4082,0.4125,0.4138,0.4216,0.4223,0.4365,0.4433,0.4482,0.4512,
0.4565,0.4736,0.4748,0.4780,0.4792,0.4812,0.4818,0.4823,0.4838,0.4918,
0.5027,0.5034,0.5090,0.5114,0.5144,0.5147,0.5182,0.5182,0.5285,0.5312,
0.5332,0.5364,0.5485,0.5514,0.5517,0.5653,0.5682,0.5689,0.5731,0.5738,
0.5772,0.5931,0.5936,0.5940,0.5978,0.5988,0.6064,0.6065,0.6074,0.6079,
0.6082,0.6117,0.6119,0.6120,0.6170,0.6201,0.6217,0.6218,0.6219,0.6220,
0.6299,0.6301,0.6321,0.6324,0.6348,0.6430,0.6481,0.6486,0.6588,0.6631,
0.6706,0.6869,0.6937,0.6940,0.7049,0.7080,0.7141,0.7155,0.7214,0.7232,
0.7309,0.7316,0.7322,0.7333,0.7334,0.7356,0.7413,0.7425,0.7468,0.7542,
0.7590,0.7593,0.7616,0.7661,0.7693,0.7709,0.7731,0.7812,0.7874,0.7900,
0.7902,0.7962,0.7977,0.8004,0.8103,0.8130,0.8179,0.8234,0.8242,0.8247,
0.8256,0.8302,0.8302,0.8318,0.8339,0.8349,0.8420,0.8438,0.8440,0.8445,
0.8491,0.8491,0.8491,0.8501,0.8684,0.8686,0.8721,0.8729,0.8730,0.8906,
0.8919,0.8972,0.8976,0.9003,0.9043,0.9045,0.9059,0.9096,0.9107,0.9111,
0.9191,0.9207,0.9232,0.9236,0.9274,0.9309,0.9347,0.9369,0.9450,0.9462,
0.9480,0.9519,0.9542,0.9559,0.9634,0.9792,0.9794,0.9947,0.9961,
Overall p-value after applying KStest on 269 p-values = 0.855979
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.