RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-08_06:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.64 17.6506 0.588804
2 to 25 15.78 10.2517 0.107273
3 to 26 15.54 29.4877 0.969715
4 to 27 15.78 16.1527 0.486966
5 to 28 15.77 10.1579 0.103143
6 to 29 15.61 22.3476 0.828283
7 to 30 15.55 19.1869 0.682089
8 to 31 15.98 14.9280 0.399332
9 to 32 15.97 11.7292 0.183750
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.981808
Tough bday spacings test for dh-ranFile-2018-07-08_06:31: 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 10 28 75 99 98 86 57 31 7 5 4
(O-E)^2/E 0.1 2.0 0.0 0.0 0.0 0.8 0.5 0.1 4.2 0.4 0.0
Birthday Spacings: Sum(O-E)^2/E= 8.045, p= 0.376
RESULTS OF GCD FOR dh-ranFile-2018-07-08_06:31
Euclid's algorithm:
p-value, steps to gcd: 0.765937
p-value, dist. of gcd's: 0.346783
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-08_06:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.684 0.715 0.289 0.855 0.188 0.502 0.389 0.536
Bits 8 to 15---> 0.819 0.747 0.446 0.347 0.965 0.822 0.622 0.765
Bits 16 to 23---> 0.582 0.106 0.247 0.250 0.857 0.949 0.415 0.104
Bits 24 to 31---> 0.146 0.752 0.592 0.073 0.325 0.662 0.270 0.718
KS test for the above 32 p values: 0.169
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-08_06:31,
p-values for 5 runs: 0.5400, 0.3705, 0.3342, 0.1600, 0.7687
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-08_06:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 211 211.4 0.001 0.001
r= 29 5078 5134.0 0.611 0.612
r= 30 23182 23103.0 0.270 0.882
r= 31 11529 11551.5 0.044 0.926
chi-square = 0.926 with df = 3; p-value = 0.181
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-08_06:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 210 211.4 0.010 0.010
r= 30 5083 5134.0 0.507 0.516
r= 31 23164 23103.0 0.161 0.677
r= 32 11543 11551.5 0.006 0.683
chi-square = 0.683 with df = 3; p-value = 0.123
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-08_06:31
b-rank test for bits 1 to 8, p=0.87665
b-rank test for bits 2 to 9, p=0.39067
b-rank test for bits 3 to 10, p=0.96715
b-rank test for bits 4 to 11, p=0.71301
b-rank test for bits 5 to 12, p=0.12188
b-rank test for bits 6 to 13, p=0.39775
b-rank test for bits 7 to 14, p=0.29069
b-rank test for bits 8 to 15, p=0.37259
b-rank test for bits 9 to 16, p=0.76155
b-rank test for bits 10 to 17, p=0.80458
b-rank test for bits 11 to 18, p=0.99055
b-rank test for bits 12 to 19, p=0.30976
b-rank test for bits 13 to 20, p=0.99277
b-rank test for bits 14 to 21, p=0.43735
b-rank test for bits 15 to 22, p=0.89458
b-rank test for bits 16 to 23, p=0.54801
b-rank test for bits 17 to 24, p=0.51202
b-rank test for bits 18 to 25, p=0.71522
b-rank test for bits 19 to 26, p=0.88022
b-rank test for bits 20 to 27, p=0.93609
b-rank test for bits 21 to 28, p=0.32024
b-rank test for bits 22 to 29, p=0.72388
b-rank test for bits 23 to 30, p=0.47997
b-rank test for bits 24 to 31, p=0.91077
b-rank test for bits 25 to 32, p=0.76798
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 = 0.015094
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-08_06:31
(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 141303 -1.42 0.078291
2 142077 0.39 0.652379
3 141297 -1.43 0.076261
4 141628 -0.66 0.255490
5 142363 1.06 0.855422
6 141631 -0.65 0.257748
7 142738 1.94 0.973575
8 142614 1.65 0.950162
9 141693 -0.51 0.306624
10 142590 1.59 0.944122
11 142262 0.82 0.795029
12 141583 -0.76 0.222895
13 140899 -2.36 0.009123
14 141613 -0.69 0.244356
15 142156 0.58 0.717805
16 142113 0.48 0.682915
17 142141 0.54 0.705844
18 142613 1.64 0.949921
19 141597 -0.73 0.232774
20 141796 -0.26 0.395586
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-08_06:31
Bits used No. missing words z-score p-value
23 to 32 142257 1.1989 0.884709
22 to 31 142150 0.8299 0.796701
21 to 30 142154 0.8437 0.800579
20 to 29 142074 0.5678 0.714924
19 to 28 141991 0.2816 0.610883
18 to 27 141637 -0.9391 0.173848
17 to 26 141669 -0.8287 0.203630
16 to 25 141617 -1.0080 0.156719
15 to 24 141884 -0.0873 0.465199
14 to 23 141514 -1.3632 0.086409
13 to 22 142282 1.2851 0.900616
12 to 21 141679 -0.7942 0.213528
11 to 20 142015 0.3644 0.642213
10 to 19 141831 -0.2701 0.393540
9 to 18 141883 -0.0908 0.463829
8 to 17 142608 2.4092 0.992006
7 to 16 141876 -0.1149 0.454250
6 to 15 141585 -1.1184 0.131703
5 to 14 141854 -0.1908 0.424344
4 to 13 142071 0.5575 0.711401
3 to 12 141784 -0.4322 0.332808
2 to 11 141770 -0.4804 0.315454
1 to 10 141435 -1.6356 0.050960
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-08_06:31
Bits used No. missing words z-score p-value
28 to 32 141657 -0.8554 0.196177
27 to 31 142035 0.4260 0.664946
26 to 30 142059 0.5074 0.694048
25 to 29 141822 -0.2960 0.383602
24 to 28 141702 -0.7028 0.241086
23 to 27 142026 0.3955 0.653760
22 to 26 142511 2.0396 0.979303
21 to 25 142067 0.5345 0.703493
20 to 24 141466 -1.5028 0.066444
19 to 23 142147 0.8057 0.789781
18 to 22 141854 -0.1876 0.425611
17 to 21 141737 -0.5842 0.279553
16 to 20 141475 -1.4723 0.070469
15 to 19 142032 0.4158 0.661233
14 to 18 141688 -0.7503 0.226546
13 to 17 142003 0.3175 0.624578
12 to 16 142083 0.5887 0.721973
11 to 15 141554 -1.2045 0.114197
10 to 14 141372 -1.8215 0.034269
9 to 13 142005 0.3243 0.627147
8 to 12 141704 -0.6960 0.243204
7 to 11 142229 1.0836 0.860735
6 to 10 141466 -1.5028 0.066444
5 to 9 142003 0.3175 0.624578
4 to 8 141463 -1.5130 0.065142
3 to 7 142016 0.3616 0.641172
2 to 6 141976 0.2260 0.589399
1 to 5 142227 1.0768 0.859226
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-08_06:31
Bits used No. missing words z-score p-value
31 to 32 142100 0.5624 0.713095
30 to 31 141796 -0.3343 0.369074
29 to 30 141930 0.0610 0.524310
28 to 29 142144 0.6922 0.755607
27 to 28 142087 0.5241 0.699896
26 to 27 141681 -0.6735 0.250302
25 to 26 141814 -0.2812 0.389275
24 to 25 141729 -0.5319 0.297381
23 to 24 140466 -4.2576 0.000010
22 to 23 141506 -1.1898 0.117070
21 to 22 141719 -0.5614 0.287247
20 to 21 142129 0.6480 0.741506
19 to 20 141726 -0.5408 0.294324
18 to 19 141848 -0.1809 0.428217
17 to 18 142163 0.7483 0.772857
16 to 17 142137 0.6716 0.749079
15 to 16 141746 -0.4818 0.314974
14 to 15 141447 -1.3638 0.086314
13 to 14 141649 -0.7679 0.221263
12 to 13 141828 -0.2399 0.405199
11 to 12 142128 0.6450 0.740551
10 to 11 141730 -0.5290 0.298404
9 to 10 141429 -1.4169 0.078256
8 to 9 141440 -1.3845 0.083110
7 to 8 142288 1.1170 0.868007
6 to 7 142440 1.5654 0.941255
5 to 6 141907 -0.0069 0.497258
4 to 5 142087 0.5241 0.699896
3 to 4 141570 -1.0010 0.158420
2 to 3 141637 -0.8033 0.210891
1 to 2 142122 0.6273 0.734784
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-08_06:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2534.27 0.485 0.686061
Test results for specific bytes for dh-ranFile-2018-07-08_06:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2457.34 -0.603 0.273146
2 to 9 2577.76 1.100 0.864256
3 to 10 2482.59 -0.246 0.402762
4 to 11 2576.15 1.077 0.859253
5 to 12 2517.77 0.251 0.599193
6 to 13 2544.04 0.623 0.733315
7 to 14 2495.65 -0.062 0.475459
8 to 15 2537.10 0.525 0.700083
9 to 16 2556.85 0.804 0.789296
10 to 17 2404.61 -1.349 0.088668
11 to 18 2408.15 -1.299 0.096979
12 to 19 2510.05 0.142 0.556538
13 to 20 2374.81 -1.770 0.038329
14 to 21 2629.14 1.826 0.966093
15 to 22 2609.47 1.548 0.939202
16 to 23 2484.13 -0.224 0.411188
17 to 24 2514.70 0.208 0.582316
18 to 25 2587.20 1.233 0.891251
19 to 26 2475.48 -0.347 0.364374
20 to 27 2457.66 -0.599 0.274646
21 to 28 2465.78 -0.484 0.314222
22 to 29 2543.83 0.620 0.732306
23 to 30 2463.05 -0.523 0.300658
24 to 31 2476.19 -0.337 0.368158
25 to 32 2514.86 0.210 0.583222
CDPARK for dh-ranFile-2018-07-08_06:31: 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
3508 -0.6849 0.246694
3538 0.6849 0.753306
3534 0.5023 0.692266
3500 -1.0502 0.146807
3551 1.2785 0.899470
3520 -0.1370 0.445521
3488 -1.5982 0.055002
3531 0.3653 0.642555
3552 1.3242 0.907282
3525 0.0913 0.536383
Square side=100, avg. no. parked=3524.70 sample std.=20.00
p-value of the KSTEST for those 10 p-values: 0.976003
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-08_06:31
0.0592,0.4296,0.7696,0.0352,0.9686,0.1106,0.1766,0.7701,0.3172,0.0738,
The KS test for those 10 p-values: 0.125235
The 3DSPHERES test for dh-ranFile-2018-07-08_06:31
sample no r^3 equiv. uni.
1 3.156 0.099868
2 22.526 0.528039
3 24.938 0.564495
4 18.854 0.466599
5 7.358 0.217497
6 10.176 0.287666
7 22.077 0.520925
8 39.944 0.735907
9 32.391 0.660299
10 15.182 0.397138
11 10.285 0.290239
12 70.142 0.903486
13 6.324 0.190072
14 2.404 0.076995
15 2.091 0.067314
16 121.416 0.982529
17 46.943 0.790860
18 15.925 0.411893
19 11.670 0.322263
20 26.918 0.592315
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.763621
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-08_06:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -0.3 0.1 -0.3 -0.3 -0.4
-1.6 0.4 0.5 -0.4 -1.9 2.0
-0.3 -1.6 2.2 -0.4 -0.3 1.0
0.6 -1.7 0.2 2.2 -0.8 0.4
-1.9 0.8 0.1 0.1 -0.9 -1.7
-0.2 1.1 0.8 0.9 -1.2 -0.1
-0.5 0.8 -1.6 1.0 -0.6 0.0
-1.1
Chi-square with 42 degrees of freedom:47.195865
z-score=0.566915, p-value=0.731447
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-08_06:31
Test no p-value
1 0.188842
2 0.451316
3 0.167641
4 0.150399
5 0.323994
6 0.286444
7 0.742259
8 0.286685
9 0.758859
10 0.897552
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.477581
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-08_06:31:
(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 66777 0.18 66747 0.10
3 25000.00 24923 0.24 24863 0.75
4 6666.67 6604 0.59 6683 0.04
5 1388.89 1432 1.34 1414 0.45
6 238.10 230 0.28 254 1.06
7 34.72 29 0.94 33 0.09
8 4.96 4 0.19 5 0.00
p=0.28959 p=0.13036
Number of rngs required: 688659, p-value: 0.616
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-08_06:31
No. of wins: Observed Expected
98822 98585.9
z-score= 1.056, pvalue=0.85455
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66635 66666.7 0.015 0.015
2 37687 37654.3 0.028 0.043
3 26917 26954.7 0.053 0.096
4 19483 19313.5 1.488 1.584
5 13789 13851.4 0.281 1.866
6 9973 9943.5 0.087 1.953
7 7134 7145.0 0.017 1.970
8 5133 5139.1 0.007 1.977
9 3659 3699.9 0.451 2.429
10 2615 2666.3 0.987 3.415
11 1954 1923.3 0.489 3.905
12 1380 1388.7 0.055 3.960
13 1031 1003.7 0.742 4.701
14 743 726.1 0.391 5.093
15 505 525.8 0.826 5.918
16 363 381.2 0.864 6.783
17 284 276.5 0.201 6.984
18 204 200.8 0.050 7.034
19 136 146.0 0.683 7.717
20 107 106.2 0.006 7.723
21 268 287.1 1.272 8.995
Chisq= 9.00 for 20 degrees of freedom, p= 0.01704
SUMMARY of craptest
p-value for no. of wins: 0.854553
p-value for throws/game: 0.017036
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-08_06:31
No. of wins: Observed Expected
98771 98585.9
z-score= 0.828, pvalue=0.79618
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66912 66666.7 0.903 0.903
2 37718 37654.3 0.108 1.011
3 26847 26954.7 0.431 1.441
4 19197 19313.5 0.702 2.143
5 13813 13851.4 0.107 2.250
6 9938 9943.5 0.003 2.253
7 7135 7145.0 0.014 2.267
8 5140 5139.1 0.000 2.267
9 3729 3699.9 0.229 2.497
10 2696 2666.3 0.331 2.828
11 1872 1923.3 1.370 4.197
12 1457 1388.7 3.355 7.553
13 986 1003.7 0.313 7.865
14 714 726.1 0.203 8.068
15 464 525.8 7.272 15.340
16 386 381.2 0.062 15.402
17 277 276.5 0.001 15.402
18 174 200.8 3.584 18.987
19 145 146.0 0.007 18.993
20 113 106.2 0.433 19.427
21 287 287.1 0.000 19.427
Chisq= 19.43 for 20 degrees of freedom, p= 0.50573
SUMMARY of craptest
p-value for no. of wins: 0.796182
p-value for throws/game: 0.505734
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0000,0.0091,0.0151,0.0170,0.0343,0.0352,0.0383,0.0510,0.0550,0.0592,
0.0651,0.0664,0.0664,0.0673,0.0705,0.0727,0.0738,0.0763,0.0770,0.0783,
0.0783,0.0831,0.0863,0.0864,0.0887,0.0970,0.0999,0.1031,0.1037,0.1058,
0.1073,0.1106,0.1142,0.1171,0.1219,0.1229,0.1252,0.1304,0.1317,0.1464,
0.1468,0.1504,0.1567,0.1584,0.1600,0.1676,0.1687,0.1738,0.1766,0.1808,
0.1837,0.1880,0.1888,0.1901,0.1962,0.2036,0.2109,0.2135,0.2175,0.2213,
0.2229,0.2265,0.2328,0.2411,0.2432,0.2444,0.2467,0.2472,0.2503,0.2503,
0.2555,0.2577,0.2704,0.2731,0.2746,0.2796,0.2864,0.2867,0.2872,0.2877,
0.2885,0.2896,0.2902,0.2907,0.2943,0.2974,0.2984,0.3007,0.3066,0.3098,
0.3142,0.3150,0.3155,0.3172,0.3202,0.3223,0.3240,0.3249,0.3328,0.3342,
0.3465,0.3468,0.3644,0.3682,0.3691,0.3705,0.3726,0.3756,0.3836,0.3886,
0.3893,0.3907,0.3935,0.3956,0.3971,0.3978,0.3993,0.4028,0.4052,0.4112,
0.4119,0.4155,0.4243,0.4256,0.4282,0.4296,0.4373,0.4455,0.4455,0.4513,
0.4542,0.4638,0.4652,0.4666,0.4755,0.4776,0.4800,0.4870,0.4973,0.5015,
0.5057,0.5120,0.5209,0.5243,0.5280,0.5360,0.5364,0.5400,0.5480,0.5565,
0.5645,0.5816,0.5823,0.5832,0.5888,0.5894,0.5923,0.5923,0.5992,0.6109,
0.6159,0.6221,0.6246,0.6246,0.6271,0.6412,0.6422,0.6426,0.6524,0.6538,
0.6603,0.6612,0.6622,0.6649,0.6821,0.6829,0.6841,0.6861,0.6923,0.6940,
0.6999,0.6999,0.7001,0.7035,0.7058,0.7114,0.7130,0.7131,0.7148,0.7149,
0.7152,0.7177,0.7178,0.7220,0.7239,0.7314,0.7323,0.7333,0.7348,0.7359,
0.7406,0.7415,0.7423,0.7470,0.7491,0.7519,0.7533,0.7556,0.7589,0.7616,
0.7636,0.7650,0.7659,0.7680,0.7687,0.7696,0.7701,0.7729,0.7893,0.7898,
0.7909,0.7950,0.7962,0.7967,0.8006,0.8046,0.8189,0.8217,0.8283,0.8546,
0.8551,0.8554,0.8569,0.8592,0.8593,0.8607,0.8643,0.8680,0.8766,0.8802,
0.8847,0.8913,0.8946,0.8976,0.8995,0.9006,0.9035,0.9073,0.9108,0.9361,
0.9392,0.9413,0.9441,0.9492,0.9499,0.9502,0.9647,0.9661,0.9672,0.9686,
0.9697,0.9736,0.9760,0.9793,0.9818,0.9825,0.9905,0.9920,0.9928,
Overall p-value after applying KStest on 269 p-values = 0.678818
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.