RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-17_21:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.84 17.2092 0.559720
2 to 25 15.73 12.2972 0.218186
3 to 26 15.89 12.9512 0.260554
4 to 27 15.80 20.6726 0.758723
5 to 28 15.60 22.8534 0.845917
6 to 29 15.73 16.4434 0.507354
7 to 30 15.91 21.5246 0.796300
8 to 31 15.94 13.9865 0.331944
9 to 32 15.90 20.2460 0.738159
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.638120
Tough bday spacings test for dh-ranFile-2018-06-17_21:31: 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 11 26 79 110 90 85 50 25 14 8 2
(O-E)^2/E 0.4 3.1 0.4 1.6 0.6 0.6 0.1 0.8 0.1 0.3 1.0
Birthday Spacings: Sum(O-E)^2/E= 8.905, p= 0.459
RESULTS OF GCD FOR dh-ranFile-2018-06-17_21:31
Euclid's algorithm:
p-value, steps to gcd: 0.660962
p-value, dist. of gcd's: 0.169911
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-17_21:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.704 0.902 0.202 0.047 0.528 0.976 0.853 0.350
Bits 8 to 15---> 0.817 0.784 0.197 0.868 0.075 0.465 0.945 0.546
Bits 16 to 23---> 0.989 0.493 0.900 0.544 0.768 0.230 0.170 0.703
Bits 24 to 31---> 0.894 0.703 0.180 0.207 0.182 0.723 0.496 0.935
KS test for the above 32 p values: 0.825
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-17_21:31,
p-values for 5 runs: 0.8766, 0.6607, 0.1976, 0.7469, 0.2993
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-17_21:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 209 211.4 0.028 0.028
r= 29 5075 5134.0 0.678 0.706
r= 30 23047 23103.0 0.136 0.842
r= 31 11669 11551.5 1.195 2.037
chi-square = 2.037 with df = 3; p-value = 0.435
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-17_21:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 211 211.4 0.001 0.001
r= 30 5128 5134.0 0.007 0.008
r= 31 23105 23103.0 0.000 0.008
r= 32 11556 11551.5 0.002 0.010
chi-square = 0.010 with df = 3; p-value = 0.000
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-17_21:31
b-rank test for bits 1 to 8, p=0.66968
b-rank test for bits 2 to 9, p=0.16326
b-rank test for bits 3 to 10, p=0.50374
b-rank test for bits 4 to 11, p=0.01515
b-rank test for bits 5 to 12, p=0.20815
b-rank test for bits 6 to 13, p=0.36527
b-rank test for bits 7 to 14, p=0.20804
b-rank test for bits 8 to 15, p=0.90917
b-rank test for bits 9 to 16, p=0.97902
b-rank test for bits 10 to 17, p=0.70142
b-rank test for bits 11 to 18, p=0.23404
b-rank test for bits 12 to 19, p=0.66118
b-rank test for bits 13 to 20, p=0.61571
b-rank test for bits 14 to 21, p=0.33578
b-rank test for bits 15 to 22, p=0.67145
b-rank test for bits 16 to 23, p=0.14043
b-rank test for bits 17 to 24, p=0.30227
b-rank test for bits 18 to 25, p=0.74524
b-rank test for bits 19 to 26, p=0.46682
b-rank test for bits 20 to 27, p=0.61041
b-rank test for bits 21 to 28, p=0.77186
b-rank test for bits 22 to 29, p=0.35683
b-rank test for bits 23 to 30, p=0.65425
b-rank test for bits 24 to 31, p=0.27871
b-rank test for bits 25 to 32, p=0.85297
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 = 0.855054
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-17_21:31
(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 141452 -1.07 0.142641
2 141782 -0.30 0.383042
3 141727 -0.43 0.335052
4 142035 0.29 0.615476
5 141647 -0.61 0.269964
6 142290 0.89 0.813110
7 143099 2.78 0.997279
8 142167 0.60 0.726424
9 141573 -0.79 0.215987
10 141827 -0.19 0.423730
11 141956 0.11 0.543415
12 141913 0.01 0.503421
13 142324 0.97 0.833691
14 141871 -0.09 0.464320
15 141364 -1.27 0.101308
16 141742 -0.39 0.347914
17 142432 1.22 0.888993
18 141223 -1.60 0.054404
19 141912 0.01 0.502489
20 141655 -0.59 0.276180
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-17_21:31
Bits used No. missing words z-score p-value
23 to 32 141610 -1.0322 0.150996
22 to 31 141603 -1.0563 0.145413
21 to 30 141572 -1.1632 0.122373
20 to 29 141662 -0.8529 0.196868
19 to 28 141660 -0.8598 0.194961
18 to 27 141358 -1.9011 0.028642
17 to 26 142150 0.8299 0.796701
16 to 25 141741 -0.5804 0.280806
15 to 24 141699 -0.7253 0.234141
14 to 23 141977 0.2333 0.592253
13 to 22 141929 0.0678 0.527039
12 to 21 141661 -0.8563 0.195913
11 to 20 141725 -0.6356 0.262512
10 to 19 142048 0.4782 0.683736
9 to 18 142190 0.9678 0.833435
8 to 17 141550 -1.2391 0.107660
7 to 16 142260 1.2092 0.886708
6 to 15 141947 0.1299 0.551676
5 to 14 141625 -0.9804 0.163432
4 to 13 142091 0.6264 0.734490
3 to 12 142065 0.5368 0.704295
2 to 11 141876 -0.1149 0.454250
1 to 10 141711 -0.6839 0.247020
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-17_21:31
Bits used No. missing words z-score p-value
28 to 32 141807 -0.3469 0.364340
27 to 31 141446 -1.5706 0.058137
26 to 30 141939 0.1006 0.540057
25 to 29 141716 -0.6554 0.256119
24 to 28 141898 -0.0384 0.484682
23 to 27 141070 -2.8452 0.002219
22 to 26 141612 -1.0079 0.156752
21 to 25 141800 -0.3706 0.355464
20 to 24 142291 1.2938 0.902132
19 to 23 142008 0.3345 0.630989
18 to 22 141906 -0.0113 0.495497
17 to 21 141729 -0.6113 0.270504
16 to 20 141628 -0.9537 0.170128
15 to 19 141601 -1.0452 0.147968
14 to 18 141687 -0.7537 0.225526
13 to 17 142185 0.9345 0.824970
12 to 16 142511 2.0396 0.979303
11 to 15 141754 -0.5265 0.299256
10 to 14 142104 0.6599 0.745341
9 to 13 141406 -1.7062 0.043985
8 to 12 142519 2.0667 0.980618
7 to 11 142522 2.0768 0.981092
6 to 10 141788 -0.4113 0.340431
5 to 9 141393 -1.7503 0.040036
4 to 8 141973 0.2158 0.585440
3 to 7 142456 1.8531 0.968067
2 to 6 142254 1.1684 0.878672
1 to 5 141971 0.2091 0.582796
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-17_21:31
Bits used No. missing words z-score p-value
31 to 32 141232 -1.9980 0.022857
30 to 31 141441 -1.3815 0.083562
29 to 30 141910 0.0020 0.500789
28 to 29 142072 0.4799 0.684334
27 to 28 142086 0.5212 0.698869
26 to 27 141906 -0.0098 0.496081
25 to 26 142496 1.7306 0.958238
24 to 25 142685 2.2881 0.988935
23 to 24 141947 0.1111 0.544240
22 to 23 142076 0.4917 0.688517
21 to 22 142099 0.5595 0.712089
20 to 21 141599 -0.9154 0.179984
19 to 20 141912 0.0079 0.503142
18 to 19 141370 -1.5909 0.055811
17 to 18 141861 -0.1426 0.443316
16 to 17 141839 -0.2075 0.417824
15 to 16 141600 -0.9125 0.180759
14 to 15 142107 0.5831 0.720086
13 to 14 142099 0.5595 0.712089
12 to 13 141699 -0.6204 0.267483
11 to 12 142236 0.9636 0.832384
10 to 11 142270 1.0639 0.856318
9 to 10 141929 0.0580 0.523135
8 to 9 141765 -0.4258 0.335144
7 to 8 142095 0.5477 0.708051
6 to 7 142286 1.1111 0.866742
5 to 6 142412 1.4828 0.930937
4 to 5 142378 1.3825 0.916592
3 to 4 141893 -0.0482 0.480790
2 to 3 142366 1.3471 0.911027
1 to 2 141947 0.1111 0.544240
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-17_21:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2436.44 -0.899 0.184348
Test results for specific bytes for dh-ranFile-2018-06-17_21:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2436.53 -0.898 0.184716
2 to 9 2493.88 -0.087 0.465532
3 to 10 2574.62 1.055 0.854337
4 to 11 2646.12 2.066 0.980605
5 to 12 2454.21 -0.648 0.258641
6 to 13 2597.58 1.380 0.916209
7 to 14 2388.24 -1.581 0.056996
8 to 15 2532.20 0.455 0.675580
9 to 16 2492.53 -0.106 0.457912
10 to 17 2481.51 -0.261 0.396869
11 to 18 2580.50 1.138 0.872519
12 to 19 2429.49 -0.997 0.159348
13 to 20 2550.07 0.708 0.760550
14 to 21 2586.14 1.218 0.888438
15 to 22 2521.63 0.306 0.620141
16 to 23 2521.95 0.310 0.621901
17 to 24 2506.26 0.089 0.535263
18 to 25 2542.69 0.604 0.726986
19 to 26 2435.72 -0.909 0.181650
20 to 27 2445.20 -0.775 0.219193
21 to 28 2511.76 0.166 0.566049
22 to 29 2572.72 1.028 0.848134
23 to 30 2362.43 -1.946 0.025855
24 to 31 2496.37 -0.051 0.479529
25 to 32 2545.56 0.644 0.740292
CDPARK for dh-ranFile-2018-06-17_21:31: 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
3536 0.5936 0.723613
3552 1.3242 0.907282
3537 0.6393 0.738676
3516 -0.3196 0.374623
3546 1.0502 0.853193
3538 0.6849 0.753306
3572 2.2374 0.987371
3507 -0.7306 0.232514
3524 0.0457 0.518210
3479 -2.0091 0.022262
Square side=100, avg. no. parked=3530.70 sample std.=24.52
p-value of the KSTEST for those 10 p-values: 0.333128
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-17_21:31
0.4026,0.9847,0.2876,0.1634,0.0419,0.1734,0.8450,0.1371,0.8206,0.5801,
The KS test for those 10 p-values: 0.633076
The 3DSPHERES test for dh-ranFile-2018-06-17_21:31
sample no r^3 equiv. uni.
1 101.440 0.965998
2 87.902 0.946607
3 11.695 0.322833
4 35.713 0.695909
5 26.949 0.592739
6 17.036 0.433262
7 7.001 0.208124
8 223.121 0.999411
9 44.524 0.773302
10 91.345 0.952396
11 16.908 0.430834
12 21.862 0.517476
13 116.266 0.979257
14 21.193 0.506602
15 16.267 0.418561
16 19.365 0.475605
17 9.236 0.264995
18 10.163 0.287360
19 17.685 0.445398
20 11.757 0.324236
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.090625
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-17_21:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 0.1 1.1 -0.7 -1.6 1.2
-1.2 0.3 0.4 -1.5 1.9 -0.6
0.3 0.1 0.4 0.6 -0.2 -1.4
-0.3 0.1 0.1 -1.0 0.7 0.8
-0.2 -0.4 0.1 0.2 1.2 1.5
0.0 -0.6 -1.5 0.9 -0.9 -1.4
-0.7 0.2 -0.4 -0.1 0.1 -1.0
-1.1
Chi-square with 42 degrees of freedom:31.558303
z-score=-1.139283, p-value=0.119825
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-17_21:31
Test no p-value
1 0.346261
2 0.040543
3 0.823541
4 0.829658
5 0.682428
6 0.960641
7 0.020255
8 0.074865
9 0.331401
10 0.466941
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.556739
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-17_21:31:
(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 66776 0.18 66857 0.54
3 25000.00 25000 0.00 24825 1.23
4 6666.67 6605 0.57 6623 0.29
5 1388.89 1342 1.58 1405 0.19
6 238.10 225 0.72 252 0.81
7 34.72 46 3.66 29 0.94
8 4.96 5 0.00 8 1.86
p=0.65229 p=0.56082
Number of rngs required: 687237, p-value: 0.087
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-17_21:31
No. of wins: Observed Expected
98408 98585.9
z-score=-0.795, pvalue=0.21317
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66538 66666.7 0.248 0.248
2 37685 37654.3 0.025 0.273
3 26717 26954.7 2.097 2.370
4 19316 19313.5 0.000 2.370
5 14047 13851.4 2.762 5.132
6 9918 9943.5 0.066 5.198
7 7124 7145.0 0.062 5.259
8 5228 5139.1 1.539 6.798
9 3624 3699.9 1.556 8.354
10 2717 2666.3 0.964 9.318
11 2055 1923.3 9.014 18.332
12 1409 1388.7 0.296 18.628
13 1009 1003.7 0.028 18.656
14 691 726.1 1.701 20.356
15 524 525.8 0.006 20.363
16 373 381.2 0.174 20.537
17 288 276.5 0.475 21.012
18 199 200.8 0.017 21.029
19 152 146.0 0.248 21.276
20 101 106.2 0.256 21.532
21 285 287.1 0.016 21.548
Chisq= 21.55 for 20 degrees of freedom, p= 0.63447
SUMMARY of craptest
p-value for no. of wins: 0.213165
p-value for throws/game: 0.634469
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-17_21:31
No. of wins: Observed Expected
98726 98585.9
z-score= 0.627, pvalue=0.73460
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66869 66666.7 0.614 0.614
2 37559 37654.3 0.241 0.855
3 27059 26954.7 0.403 1.259
4 19297 19313.5 0.014 1.273
5 13802 13851.4 0.176 1.449
6 9939 9943.5 0.002 1.451
7 7164 7145.0 0.050 1.502
8 5001 5139.1 3.710 5.211
9 3585 3699.9 3.566 8.777
10 2774 2666.3 4.351 13.128
11 1883 1923.3 0.846 13.973
12 1393 1388.7 0.013 13.986
13 992 1003.7 0.137 14.123
14 694 726.1 1.423 15.546
15 516 525.8 0.184 15.730
16 425 381.2 5.045 20.774
17 297 276.5 1.514 22.288
18 193 200.8 0.305 22.594
19 159 146.0 1.160 23.754
20 103 106.2 0.097 23.851
21 296 287.1 0.275 24.126
Chisq= 24.13 for 20 degrees of freedom, p= 0.76308
SUMMARY of craptest
p-value for no. of wins: 0.734603
p-value for throws/game: 0.763082
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0003,0.0022,0.0152,0.0203,0.0223,0.0229,0.0259,0.0286,0.0400,0.0405,
0.0419,0.0440,0.0473,0.0544,0.0558,0.0570,0.0581,0.0749,0.0749,0.0836,
0.0871,0.0906,0.1013,0.1077,0.1198,0.1224,0.1371,0.1404,0.1426,0.1454,
0.1480,0.1510,0.1568,0.1593,0.1633,0.1634,0.1634,0.1699,0.1700,0.1701,
0.1734,0.1797,0.1800,0.1808,0.1817,0.1818,0.1843,0.1847,0.1950,0.1959,
0.1968,0.1969,0.1976,0.2021,0.2065,0.2080,0.2081,0.2082,0.2132,0.2160,
0.2182,0.2192,0.2255,0.2296,0.2325,0.2340,0.2341,0.2470,0.2561,0.2586,
0.2606,0.2625,0.2650,0.2675,0.2700,0.2705,0.2762,0.2787,0.2808,0.2874,
0.2876,0.2993,0.2993,0.3023,0.3228,0.3242,0.3314,0.3319,0.3331,0.3351,
0.3351,0.3358,0.3404,0.3463,0.3479,0.3497,0.3555,0.3568,0.3643,0.3653,
0.3746,0.3830,0.3969,0.4026,0.4178,0.4186,0.4237,0.4308,0.4333,0.4352,
0.4433,0.4454,0.4542,0.4579,0.4588,0.4643,0.4655,0.4655,0.4668,0.4669,
0.4756,0.4795,0.4808,0.4847,0.4935,0.4955,0.4961,0.4965,0.5008,0.5025,
0.5031,0.5034,0.5037,0.5066,0.5074,0.5175,0.5182,0.5231,0.5270,0.5281,
0.5353,0.5401,0.5434,0.5442,0.5442,0.5444,0.5462,0.5517,0.5567,0.5597,
0.5608,0.5660,0.5801,0.5828,0.5854,0.5923,0.5927,0.6104,0.6155,0.6157,
0.6201,0.6219,0.6310,0.6331,0.6345,0.6381,0.6523,0.6543,0.6607,0.6610,
0.6612,0.6697,0.6715,0.6756,0.6824,0.6837,0.6843,0.6885,0.6959,0.6989,
0.7014,0.7027,0.7031,0.7043,0.7045,0.7081,0.7121,0.7121,0.7201,0.7231,
0.7236,0.7264,0.7270,0.7345,0.7346,0.7382,0.7387,0.7403,0.7452,0.7453,
0.7469,0.7533,0.7587,0.7606,0.7631,0.7685,0.7719,0.7733,0.7841,0.7963,
0.7967,0.8131,0.8168,0.8206,0.8235,0.8250,0.8251,0.8297,0.8324,0.8334,
0.8337,0.8450,0.8459,0.8481,0.8526,0.8530,0.8532,0.8543,0.8551,0.8563,
0.8667,0.8677,0.8725,0.8766,0.8787,0.8867,0.8884,0.8890,0.8935,0.9000,
0.9021,0.9024,0.9073,0.9092,0.9110,0.9162,0.9166,0.9309,0.9347,0.9451,
0.9466,0.9524,0.9582,0.9606,0.9660,0.9681,0.9761,0.9790,0.9793,0.9793,
0.9806,0.9806,0.9811,0.9847,0.9874,0.9889,0.9891,0.9973,0.9994,
Overall p-value after applying KStest on 269 p-values = 0.626231
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.