RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-26_01:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.92 13.6064 0.305261
2 to 25 15.84 24.5615 0.895037
3 to 26 15.70 22.9230 0.848226
4 to 27 15.82 13.0385 0.266395
5 to 28 15.67 15.8844 0.467954
6 to 29 15.54 34.7553 0.993302
7 to 30 15.60 18.4029 0.636139
8 to 31 15.92 21.0254 0.774845
9 to 32 15.89 8.6595 0.049657
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.593708
Tough bday spacings test for dh-ranFile-2018-06-26_01:31: 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 17 33 76 101 89 73 57 31 16 5 2
(O-E)^2/E 6.7 0.4 0.1 0.1 0.8 0.3 0.5 0.1 0.1 0.4 1.0
Birthday Spacings: Sum(O-E)^2/E= 10.441, p= 0.597
RESULTS OF GCD FOR dh-ranFile-2018-06-26_01:31
Euclid's algorithm:
p-value, steps to gcd: 0.026213
p-value, dist. of gcd's: 0.446696
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-26_01:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.435 0.500 0.516 0.233 0.240 0.181 0.433 0.214
Bits 8 to 15---> 0.746 0.977 0.787 0.196 0.847 0.988 0.483 0.051
Bits 16 to 23---> 0.018 0.252 0.436 0.666 0.412 0.122 0.217 0.467
Bits 24 to 31---> 0.979 0.599 0.697 0.394 0.797 0.851 0.624 0.780
KS test for the above 32 p values: 0.097
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-26_01:31,
p-values for 5 runs: 0.4243, 0.4745, 0.4894, 0.1374, 0.2888
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-26_01:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 195 211.4 1.275 1.275
r= 29 5120 5134.0 0.038 1.313
r= 30 23082 23103.0 0.019 1.332
r= 31 11603 11551.5 0.229 1.562
chi-square = 1.562 with df = 3; p-value = 0.332
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-26_01:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 202 211.4 0.420 0.420
r= 30 5113 5134.0 0.086 0.506
r= 31 23138 23103.0 0.053 0.558
r= 32 11547 11551.5 0.002 0.560
chi-square = 0.560 with df = 3; p-value = 0.095
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-26_01:31
b-rank test for bits 1 to 8, p=0.24416
b-rank test for bits 2 to 9, p=0.77046
b-rank test for bits 3 to 10, p=0.86894
b-rank test for bits 4 to 11, p=0.24755
b-rank test for bits 5 to 12, p=0.23806
b-rank test for bits 6 to 13, p=0.88617
b-rank test for bits 7 to 14, p=0.27071
b-rank test for bits 8 to 15, p=0.19481
b-rank test for bits 9 to 16, p=0.37775
b-rank test for bits 10 to 17, p=0.30310
b-rank test for bits 11 to 18, p=0.51976
b-rank test for bits 12 to 19, p=0.27253
b-rank test for bits 13 to 20, p=0.82426
b-rank test for bits 14 to 21, p=0.62948
b-rank test for bits 15 to 22, p=0.97847
b-rank test for bits 16 to 23, p=0.83307
b-rank test for bits 17 to 24, p=0.97419
b-rank test for bits 18 to 25, p=0.31196
b-rank test for bits 19 to 26, p=0.01461
b-rank test for bits 20 to 27, p=0.41113
b-rank test for bits 21 to 28, p=0.22184
b-rank test for bits 22 to 29, p=0.40980
b-rank test for bits 23 to 30, p=0.46355
b-rank test for bits 24 to 31, p=0.89624
b-rank test for bits 25 to 32, p=0.85506
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 = 0.474949
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-26_01:31
(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 142101 0.45 0.672861
2 141965 0.13 0.551745
3 141582 -0.76 0.222198
4 141832 -0.18 0.428310
5 142023 0.27 0.604720
6 141359 -1.29 0.099253
7 141845 -0.15 0.440263
8 141300 -1.42 0.077271
9 141229 -1.59 0.055967
10 142391 1.13 0.869790
11 142006 0.23 0.589347
12 140859 -2.45 0.007063
13 142274 0.85 0.802902
14 141627 -0.66 0.254739
15 141840 -0.16 0.435658
16 141229 -1.59 0.055967
17 141664 -0.57 0.283254
18 141489 -0.98 0.163030
19 142269 0.84 0.799644
20 141698 -0.49 0.310737
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-26_01:31
Bits used No. missing words z-score p-value
23 to 32 142052 0.4920 0.688628
22 to 31 141734 -0.6046 0.272727
21 to 30 142601 2.3851 0.991462
20 to 29 142305 1.3644 0.913776
19 to 28 142332 1.4575 0.927508
18 to 27 141866 -0.1494 0.440614
17 to 26 142170 0.8989 0.815637
16 to 25 141655 -0.8770 0.190243
15 to 24 142144 0.8092 0.790802
14 to 23 141968 0.2023 0.580163
13 to 22 142091 0.6264 0.734490
12 to 21 142156 0.8506 0.802500
11 to 20 142187 0.9575 0.830838
10 to 19 142016 0.3678 0.643499
9 to 18 141670 -0.8253 0.204608
8 to 17 142010 0.3471 0.635756
7 to 16 142120 0.7264 0.766218
6 to 15 141926 0.0575 0.522920
5 to 14 141705 -0.7046 0.240534
4 to 13 142083 0.5989 0.725368
3 to 12 141789 -0.4149 0.339096
2 to 11 141684 -0.7770 0.218579
1 to 10 141739 -0.5873 0.278486
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-26_01:31
Bits used No. missing words z-score p-value
28 to 32 142193 0.9616 0.831873
27 to 31 141546 -1.2316 0.109044
26 to 30 141535 -1.2689 0.102236
25 to 29 141522 -1.3130 0.094594
24 to 28 141917 0.0260 0.510371
23 to 27 141523 -1.3096 0.095167
22 to 26 142049 0.4735 0.682057
21 to 25 141428 -1.6316 0.051379
20 to 24 142035 0.4260 0.664946
19 to 23 141686 -0.7571 0.224510
18 to 22 141730 -0.6079 0.271628
17 to 21 141778 -0.4452 0.328093
16 to 20 142039 0.4396 0.669872
15 to 19 142368 1.5548 0.940005
14 to 18 142068 0.5379 0.704665
13 to 17 141753 -0.5299 0.298080
12 to 16 141851 -0.1977 0.421629
11 to 15 142694 2.6599 0.996092
10 to 14 142175 0.9006 0.816093
9 to 13 142126 0.7345 0.768670
8 to 12 141783 -0.4282 0.334239
7 to 11 142598 2.3345 0.990215
6 to 10 141762 -0.4994 0.308741
5 to 9 142285 1.2735 0.898572
4 to 8 142017 0.3650 0.642438
3 to 7 141781 -0.4350 0.331775
2 to 6 141996 0.2938 0.615543
1 to 5 141554 -1.2045 0.114197
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-26_01:31
Bits used No. missing words z-score p-value
31 to 32 141988 0.2321 0.591756
30 to 31 141919 0.0285 0.511378
29 to 30 141235 -1.9892 0.023341
28 to 29 141577 -0.9803 0.163463
27 to 28 141912 0.0079 0.503142
26 to 27 141992 0.2439 0.596332
25 to 26 141622 -0.8476 0.198336
24 to 25 141778 -0.3874 0.349229
23 to 24 142297 1.1436 0.873599
22 to 23 141729 -0.5319 0.297381
21 to 22 142069 0.4710 0.681181
20 to 21 141704 -0.6057 0.272359
19 to 20 141854 -0.1632 0.435174
18 to 19 142018 0.3206 0.625728
17 to 18 141717 -0.5673 0.285240
16 to 17 141761 -0.4376 0.330856
15 to 16 142072 0.4799 0.684334
14 to 15 142168 0.7630 0.777280
13 to 14 142117 0.6126 0.729928
12 to 13 142321 1.2144 0.887696
11 to 12 142214 0.8987 0.815602
10 to 11 141884 -0.0747 0.470219
9 to 10 142395 1.4327 0.924022
8 to 9 141919 0.0285 0.511378
7 to 8 142153 0.7188 0.763865
6 to 7 141839 -0.2075 0.417824
5 to 6 141541 -1.0865 0.138625
4 to 5 141691 -0.6440 0.259774
3 to 4 141689 -0.6499 0.257865
2 to 3 141290 -1.8269 0.033855
1 to 2 141763 -0.4317 0.332997
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-26_01:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2562.29 0.881 0.810806
Test results for specific bytes for dh-ranFile-2018-06-26_01:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2426.01 -1.046 0.147690
2 to 9 2605.92 1.498 0.932923
3 to 10 2598.68 1.396 0.918582
4 to 11 2490.16 -0.139 0.444652
5 to 12 2506.51 0.092 0.536655
6 to 13 2568.53 0.969 0.833781
7 to 14 2377.26 -1.736 0.041298
8 to 15 2503.86 0.055 0.521771
9 to 16 2531.68 0.448 0.672926
10 to 17 2565.43 0.925 0.822584
11 to 18 2453.87 -0.652 0.257092
12 to 19 2525.02 0.354 0.638243
13 to 20 2501.42 0.020 0.507991
14 to 21 2479.18 -0.294 0.384204
15 to 22 2455.19 -0.634 0.263115
16 to 23 2433.66 -0.938 0.174085
17 to 24 2543.79 0.619 0.732124
18 to 25 2493.69 -0.089 0.464437
19 to 26 2558.33 0.825 0.795282
20 to 27 2491.56 -0.119 0.452486
21 to 28 2460.80 -0.554 0.289676
22 to 29 2695.52 2.765 0.997155
23 to 30 2566.84 0.945 0.827735
24 to 31 2605.66 1.494 0.932444
25 to 32 2494.95 -0.071 0.471508
CDPARK for dh-ranFile-2018-06-26_01:31: 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
3548 1.1416 0.873180
3550 1.2329 0.891189
3510 -0.5936 0.276387
3521 -0.0913 0.463617
3511 -0.5479 0.291865
3543 0.9132 0.819442
3493 -1.3699 0.085365
3529 0.2740 0.607947
3480 -1.9635 0.024796
3516 -0.3196 0.374623
Square side=100, avg. no. parked=3520.10 sample std.=21.96
p-value of the KSTEST for those 10 p-values: 0.938051
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-26_01:31
0.0780,0.7151,0.9204,0.3403,0.9249,0.6833,0.6973,0.1684,0.0208,0.0029,
The KS test for those 10 p-values: 0.233628
The 3DSPHERES test for dh-ranFile-2018-06-26_01:31
sample no r^3 equiv. uni.
1 2.987 0.094774
2 3.331 0.105098
3 1.553 0.050445
4 1.499 0.048723
5 20.193 0.489877
6 17.295 0.438144
7 43.835 0.768037
8 25.416 0.571380
9 0.089 0.002973
10 108.402 0.973040
11 57.714 0.853949
12 0.435 0.014389
13 26.489 0.586445
14 37.381 0.712357
15 27.780 0.603868
16 22.341 0.525119
17 6.535 0.195738
18 9.656 0.275197
19 59.369 0.861790
20 8.451 0.245488
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.204121
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-26_01:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 0.1 0.1 -0.1 -1.6 0.6
-0.6 1.5 -1.3 -0.1 2.0 0.9
0.4 -0.0 -0.6 -1.6 -1.5 1.3
-0.1 -1.2 0.2 0.4 1.2 0.3
0.4 -0.0 0.5 0.2 -0.4 0.4
0.5 -0.7 -0.3 -0.2 -0.4 -0.1
-0.7 -1.0 -0.8 0.4 -0.6 0.0
-0.1
Chi-square with 42 degrees of freedom:27.226150
z-score=-1.611959, p-value=0.037738
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-26_01:31
Test no p-value
1 0.175925
2 0.499870
3 0.001892
4 0.048000
5 0.560256
6 0.582605
7 0.214210
8 0.722701
9 0.105172
10 0.212054
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.046771
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-26_01:31:
(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 66661 0.00 66973 1.41
3 25000.00 25076 0.23 24885 0.53
4 6666.67 6629 0.21 6474 5.57
5 1388.89 1342 1.58 1344 1.45
6 238.10 250 0.60 270 4.28
7 34.72 35 0.00 47 4.34
8 4.96 6 0.22 6 0.22
p=0.17172 p=0.99323
Number of rngs required: 688158, p-value: 0.389
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-26_01:31
No. of wins: Observed Expected
98526 98585.9
z-score=-0.268, pvalue=0.39446
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66685 66666.7 0.005 0.005
2 37402 37654.3 1.691 1.696
3 26983 26954.7 0.030 1.725
4 19225 19313.5 0.405 2.131
5 13887 13851.4 0.091 2.222
6 9992 9943.5 0.236 2.458
7 7103 7145.0 0.247 2.705
8 5264 5139.1 3.037 5.742
9 3820 3699.9 3.901 9.643
10 2623 2666.3 0.703 10.346
11 1941 1923.3 0.162 10.509
12 1432 1388.7 1.348 11.856
13 964 1003.7 1.571 13.428
14 723 726.1 0.014 13.441
15 531 525.8 0.051 13.492
16 416 381.2 3.186 16.678
17 258 276.5 1.243 17.921
18 180 200.8 2.160 20.082
19 148 146.0 0.028 20.109
20 113 106.2 0.433 20.543
21 310 287.1 1.824 22.367
Chisq= 22.37 for 20 degrees of freedom, p= 0.67907
SUMMARY of craptest
p-value for no. of wins: 0.394456
p-value for throws/game: 0.679070
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-26_01:31
No. of wins: Observed Expected
98610 98585.9
z-score= 0.108, pvalue=0.54299
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66897 66666.7 0.796 0.796
2 37640 37654.3 0.005 0.801
3 27175 26954.7 1.800 2.601
4 19429 19313.5 0.691 3.292
5 13747 13851.4 0.787 4.080
6 9783 9943.5 2.592 6.672
7 7131 7145.0 0.028 6.699
8 4919 5139.1 9.424 16.123
9 3721 3699.9 0.121 16.244
10 2631 2666.3 0.467 16.711
11 1891 1923.3 0.543 17.255
12 1403 1388.7 0.146 17.401
13 1011 1003.7 0.053 17.454
14 704 726.1 0.675 18.129
15 518 525.8 0.117 18.246
16 388 381.2 0.123 18.369
17 276 276.5 0.001 18.370
18 191 200.8 0.481 18.851
19 154 146.0 0.440 19.291
20 98 106.2 0.635 19.927
21 293 287.1 0.121 20.047
Chisq= 20.05 for 20 degrees of freedom, p= 0.54503
SUMMARY of craptest
p-value for no. of wins: 0.542992
p-value for throws/game: 0.545033
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0019,0.0029,0.0030,0.0071,0.0144,0.0146,0.0178,0.0208,0.0233,0.0248,
0.0262,0.0339,0.0377,0.0413,0.0468,0.0480,0.0487,0.0497,0.0504,0.0508,
0.0514,0.0560,0.0560,0.0773,0.0780,0.0854,0.0945,0.0946,0.0948,0.0952,
0.0974,0.0993,0.1022,0.1051,0.1052,0.1090,0.1142,0.1220,0.1374,0.1386,
0.1477,0.1630,0.1635,0.1684,0.1717,0.1741,0.1759,0.1811,0.1902,0.1948,
0.1957,0.1959,0.1983,0.2041,0.2046,0.2121,0.2140,0.2142,0.2174,0.2186,
0.2218,0.2222,0.2245,0.2332,0.2336,0.2381,0.2395,0.2405,0.2442,0.2455,
0.2476,0.2517,0.2547,0.2571,0.2579,0.2598,0.2631,0.2664,0.2707,0.2716,
0.2724,0.2725,0.2727,0.2752,0.2764,0.2785,0.2833,0.2852,0.2888,0.2897,
0.2919,0.2974,0.2981,0.3031,0.3053,0.3087,0.3107,0.3120,0.3281,0.3309,
0.3318,0.3319,0.3330,0.3342,0.3391,0.3403,0.3492,0.3746,0.3777,0.3842,
0.3890,0.3942,0.3945,0.4098,0.4111,0.4122,0.4178,0.4216,0.4243,0.4283,
0.4327,0.4350,0.4352,0.4357,0.4361,0.4381,0.4403,0.4406,0.4447,0.4467,
0.4525,0.4636,0.4636,0.4644,0.4672,0.4680,0.4702,0.4715,0.4745,0.4749,
0.4832,0.4894,0.4899,0.4996,0.4999,0.5031,0.5080,0.5104,0.5114,0.5114,
0.5159,0.5198,0.5218,0.5229,0.5251,0.5367,0.5430,0.5450,0.5517,0.5603,
0.5714,0.5802,0.5826,0.5864,0.5893,0.5918,0.5937,0.5963,0.5973,0.5986,
0.6039,0.6047,0.6079,0.6155,0.6238,0.6257,0.6295,0.6358,0.6361,0.6382,
0.6424,0.6435,0.6649,0.6657,0.6699,0.6729,0.6729,0.6791,0.6812,0.6821,
0.6833,0.6843,0.6886,0.6968,0.6973,0.7047,0.7124,0.7151,0.7227,0.7254,
0.7299,0.7321,0.7345,0.7460,0.7639,0.7662,0.7680,0.7687,0.7705,0.7748,
0.7773,0.7796,0.7865,0.7908,0.7953,0.7972,0.7996,0.8025,0.8029,0.8108,
0.8156,0.8156,0.8161,0.8194,0.8226,0.8243,0.8277,0.8308,0.8319,0.8331,
0.8338,0.8470,0.8482,0.8513,0.8539,0.8551,0.8618,0.8689,0.8698,0.8732,
0.8736,0.8862,0.8877,0.8912,0.8950,0.8962,0.8986,0.9138,0.9186,0.9204,
0.9240,0.9249,0.9275,0.9324,0.9329,0.9381,0.9400,0.9730,0.9742,0.9771,
0.9785,0.9793,0.9877,0.9902,0.9915,0.9932,0.9933,0.9961,0.9972,
Overall p-value after applying KStest on 269 p-values = 0.431871
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.