RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-03-08_19:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.81 29.6052 0.970663
2 to 25 15.86 16.6447 0.521326
3 to 26 15.74 10.0854 0.100008
4 to 27 16.04 18.8109 0.660509
5 to 28 16.18 7.2374 0.019739
6 to 29 16.06 11.4143 0.165767
7 to 30 15.57 20.8596 0.767368
8 to 31 15.72 7.7877 0.029121
9 to 32 15.74 23.5204 0.866936
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.337335
Tough bday spacings test for dh-ranFile-2017-03-08_19:31: 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 9 37 71 99 87 84 50 41 12 6 4
(O-E)^2/E 0.0 0.0 0.1 0.0 1.2 0.4 0.1 4.2 0.6 0.1 0.0
Birthday Spacings: Sum(O-E)^2/E= 6.639, p= 0.241
RESULTS OF GCD FOR dh-ranFile-2017-03-08_19:31
Euclid's algorithm:
p-value, steps to gcd: 0.987139
p-value, dist. of gcd's: 0.647548
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-03-08_19:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.661 0.183 0.400 0.954 0.209 0.667 0.003 0.271
Bits 8 to 15---> 0.891 0.320 0.582 0.239 0.837 0.304 0.857 0.524
Bits 16 to 23---> 0.905 0.430 0.957 0.924 0.882 0.524 0.013 0.011
Bits 24 to 31---> 0.972 0.462 0.239 0.803 0.645 0.143 0.862 0.492
KS test for the above 32 p values: 0.597
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-03-08_19:31,
p-values for 5 runs: 0.1489, 0.8235, 0.6044, 0.7345, 0.7628
Rank test for binary matrices (31x31) for dh-ranFile-2017-03-08_19:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 234 211.4 2.412 2.412
r= 29 5198 5134.0 0.798 3.210
r= 30 23213 23103.0 0.523 3.733
r= 31 11355 11551.5 3.343 7.076
chi-square = 7.076 with df = 3; p-value = 0.930
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2017-03-08_19:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 225 211.4 0.873 0.873
r= 30 5236 5134.0 2.026 2.899
r= 31 23016 23103.0 0.328 3.227
r= 32 11523 11551.5 0.070 3.297
chi-square = 3.297 with df = 3; p-value = 0.652
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2017-03-08_19:31
b-rank test for bits 1 to 8, p=0.49479
b-rank test for bits 2 to 9, p=0.97196
b-rank test for bits 3 to 10, p=0.62744
b-rank test for bits 4 to 11, p=0.28657
b-rank test for bits 5 to 12, p=0.02686
b-rank test for bits 6 to 13, p=0.88691
b-rank test for bits 7 to 14, p=0.50357
b-rank test for bits 8 to 15, p=0.68910
b-rank test for bits 9 to 16, p=0.15051
b-rank test for bits 10 to 17, p=0.58363
b-rank test for bits 11 to 18, p=0.23403
b-rank test for bits 12 to 19, p=0.79793
b-rank test for bits 13 to 20, p=0.41793
b-rank test for bits 14 to 21, p=0.87881
b-rank test for bits 15 to 22, p=0.93644
b-rank test for bits 16 to 23, p=0.68041
b-rank test for bits 17 to 24, p=0.59293
b-rank test for bits 18 to 25, p=0.03867
b-rank test for bits 19 to 26, p=0.09317
b-rank test for bits 20 to 27, p=0.03297
b-rank test for bits 21 to 28, p=0.20251
b-rank test for bits 22 to 29, p=0.27166
b-rank test for bits 23 to 30, p=0.64699
b-rank test for bits 24 to 31, p=0.84646
b-rank test for bits 25 to 32, p=0.72037
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 = 0.946336
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-03-08_19:31
(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 142821 2.13 0.983417
2 142992 2.53 0.994290
3 142337 1.00 0.841158
4 142018 0.25 0.600214
5 142474 1.32 0.906469
6 141756 -0.36 0.360079
7 141741 -0.39 0.347051
8 141918 0.02 0.508081
9 142154 0.57 0.716223
10 142082 0.40 0.656686
11 141908 -0.00 0.498760
12 142551 1.50 0.933093
13 141983 0.17 0.568331
14 141215 -1.62 0.052373
15 142445 1.25 0.894636
16 142624 1.67 0.952520
17 141993 0.20 0.577496
18 141863 -0.11 0.456900
19 141417 -1.15 0.125009
20 141635 -0.64 0.260775
----------------------------------------------------------------
OPSO test for dh-ranFile-2017-03-08_19:31
Bits used No. missing words z-score p-value
23 to 32 142016 0.3678 0.643499
22 to 31 141807 -0.3529 0.362096
21 to 30 142173 0.9092 0.818380
20 to 29 142245 1.1575 0.876462
19 to 28 141593 -1.0908 0.137682
18 to 27 141629 -0.9667 0.166858
17 to 26 142338 1.4782 0.930319
16 to 25 141606 -1.0460 0.147789
15 to 24 142385 1.6402 0.949523
14 to 23 141984 0.2575 0.601597
13 to 22 142775 2.9851 0.998582
12 to 21 142188 0.9609 0.831707
11 to 20 142210 1.0368 0.850084
10 to 19 141519 -1.3460 0.089157
9 to 18 142104 0.6713 0.748978
8 to 17 142415 1.7437 0.959393
7 to 16 142295 1.3299 0.908224
6 to 15 141635 -0.9460 0.172083
5 to 14 141714 -0.6736 0.250298
4 to 13 142150 0.8299 0.796701
3 to 12 142009 0.3437 0.634460
2 to 11 141938 0.0989 0.539376
1 to 10 141991 0.2816 0.610883
-----------------------------------------------------------------
OQSO test for dh-ranFile-2017-03-08_19:31
Bits used No. missing words z-score p-value
28 to 32 141802 -0.3638 0.357992
27 to 31 142092 0.6192 0.732114
26 to 30 142122 0.7209 0.764519
25 to 29 142185 0.9345 0.824970
24 to 28 142042 0.4497 0.673547
23 to 27 141548 -1.2248 0.110316
22 to 26 141243 -2.2587 0.011950
21 to 25 141929 0.0667 0.526581
20 to 24 142172 0.8904 0.813376
19 to 23 141903 -0.0215 0.491440
18 to 22 141810 -0.3367 0.368167
17 to 21 142617 2.3989 0.991777
16 to 20 142222 1.0599 0.855405
15 to 19 141971 0.2091 0.582796
14 to 18 141943 0.1141 0.545435
13 to 17 142104 0.6599 0.745341
12 to 16 141496 -1.4011 0.080589
11 to 15 141492 -1.4147 0.078581
10 to 14 141608 -1.0215 0.153519
9 to 13 142286 1.2768 0.899172
8 to 12 142060 0.5107 0.695236
7 to 11 141780 -0.4384 0.330546
6 to 10 142297 1.3141 0.905600
5 to 9 141753 -0.5299 0.298080
4 to 8 141936 0.0904 0.536018
3 to 7 142158 0.8429 0.800372
2 to 6 141805 -0.3537 0.361797
1 to 5 142194 0.9650 0.832723
-----------------------------------------------------------------
DNA test for dh-ranFile-2017-03-08_19:31
Bits used No. missing words z-score p-value
31 to 32 141841 -0.2016 0.420129
30 to 31 142004 0.2793 0.609978
29 to 30 142448 1.5890 0.943969
28 to 29 141438 -1.3904 0.082211
27 to 28 142259 1.0315 0.848841
26 to 27 142187 0.8191 0.793631
25 to 26 142149 0.7070 0.760214
24 to 25 141532 -1.1131 0.132840
23 to 24 141223 -2.0246 0.021456
22 to 23 142148 0.7040 0.759297
21 to 22 141796 -0.3343 0.369074
20 to 21 141492 -1.2311 0.109150
19 to 20 141877 -0.0954 0.462011
18 to 19 141723 -0.5496 0.291281
17 to 18 141974 0.1908 0.575646
16 to 17 141912 0.0079 0.503142
15 to 16 141880 -0.0865 0.465527
14 to 15 141680 -0.6765 0.249365
13 to 14 141858 -0.1514 0.439824
12 to 13 142414 1.4887 0.931717
11 to 12 141858 -0.1514 0.439824
10 to 11 142289 1.1200 0.868637
9 to 10 141383 -1.5526 0.060260
8 to 9 142299 1.1495 0.874819
7 to 8 142060 0.4445 0.671643
6 to 7 142130 0.6509 0.742459
5 to 6 141724 -0.5467 0.292294
4 to 5 142046 0.4032 0.656583
3 to 4 141976 0.1967 0.577956
2 to 3 142354 1.3117 0.905191
1 to 2 142051 0.4179 0.661992
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2017-03-08_19:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2547.89 0.677 0.750870
Test results for specific bytes for dh-ranFile-2017-03-08_19:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2520.73 0.293 0.615320
2 to 9 2466.21 -0.478 0.316361
3 to 10 2483.14 -0.238 0.405789
4 to 11 2524.03 0.340 0.633023
5 to 12 2552.59 0.744 0.771486
6 to 13 2557.52 0.813 0.792031
7 to 14 2590.98 1.287 0.900897
8 to 15 2464.79 -0.498 0.309280
9 to 16 2447.13 -0.748 0.227315
10 to 17 2570.76 1.001 0.841527
11 to 18 2427.48 -1.026 0.152560
12 to 19 2504.64 0.066 0.526141
13 to 20 2561.18 0.865 0.806558
14 to 21 2491.39 -0.122 0.451519
15 to 22 2545.84 0.648 0.741587
16 to 23 2483.41 -0.235 0.407234
17 to 24 2473.72 -0.372 0.355051
18 to 25 2507.29 0.103 0.541049
19 to 26 2585.35 1.207 0.886284
20 to 27 2522.55 0.319 0.625095
21 to 28 2464.28 -0.505 0.306728
22 to 29 2612.43 1.590 0.944075
23 to 30 2396.08 -1.470 0.070835
24 to 31 2518.95 0.268 0.605666
25 to 32 2390.35 -1.551 0.060481
CDPARK for dh-ranFile-2017-03-08_19:31: 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
3541 0.8219 0.794438
3517 -0.2740 0.392053
3549 1.1872 0.882429
3539 0.7306 0.767486
3522 -0.0457 0.481790
3515 -0.3653 0.357445
3535 0.5479 0.708135
3485 -1.7352 0.041356
3531 0.3653 0.642555
3544 0.9589 0.831196
Square side=100, avg. no. parked=3527.80 sample std.=17.94
p-value of the KSTEST for those 10 p-values: 0.440560
Results for the MINIMUM DISTANCE test for dh-ranFile-2017-03-08_19:31
0.6832,0.8495,0.8133,0.3854,0.2711,0.7560,0.8880,0.4437,0.6261,0.4889,
The KS test for those 10 p-values: 0.248544
The 3DSPHERES test for dh-ranFile-2017-03-08_19:31
sample no r^3 equiv. uni.
1 5.488 0.167177
2 7.616 0.224213
3 158.010 0.994841
4 25.234 0.568774
5 23.297 0.540020
6 11.434 0.316909
7 11.717 0.323316
8 15.035 0.394178
9 10.409 0.293182
10 34.051 0.678591
11 12.991 0.351469
12 28.077 0.607773
13 57.392 0.852374
14 64.892 0.885027
15 28.523 0.613556
16 9.320 0.267052
17 2.640 0.084238
18 20.970 0.502920
19 16.382 0.420771
20 29.302 0.623462
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.548413
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-03-08_19:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 0.1 0.3 -0.4 -0.4 2.4
0.2 -1.3 -0.8 -0.6 -0.2 0.0
0.2 -0.1 -0.4 0.2 0.4 -1.2
-0.6 0.6 -0.3 -1.4 -0.7 1.0
2.3 1.3 0.2 1.5 -0.1 0.6
0.6 -0.2 -0.2 0.4 -0.4 -0.3
0.5 -0.4 -0.4 -0.7 0.1 -1.0
1.8
Chi-square with 42 degrees of freedom:31.163614
z-score=-1.182347, p-value=0.109678
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2017-03-08_19:31
Test no p-value
1 0.223802
2 0.171122
3 0.651699
4 0.170400
5 0.049368
6 0.121015
7 0.775763
8 0.015188
9 0.019529
10 0.000140
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000340
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-03-08_19:31:
(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 66783 0.20 66925 1.00
3 25000.00 24954 0.08 24742 2.66
4 6666.67 6589 0.90 6656 0.02
5 1388.89 1419 0.65 1394 0.02
6 238.10 224 0.83 247 0.33
7 34.72 25 2.72 30 0.64
8 4.96 5 0.00 5 0.00
p=0.50652 p=0.41381
Number of rngs required: 688670, p-value: 0.621
RESULTS OF CRAPS TEST for dh-ranFile-2017-03-08_19:31
No. of wins: Observed Expected
98454 98585.9
z-score=-0.590, pvalue=0.27768
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66872 66666.7 0.632 0.632
2 37453 37654.3 1.076 1.709
3 26915 26954.7 0.059 1.767
4 19319 19313.5 0.002 1.769
5 13980 13851.4 1.194 2.963
6 10017 9943.5 0.543 3.505
7 7036 7145.0 1.664 5.169
8 5059 5139.1 1.248 6.416
9 3642 3699.9 0.905 7.321
10 2730 2666.3 1.522 8.843
11 1939 1923.3 0.128 8.971
12 1334 1388.7 2.158 11.129
13 1017 1003.7 0.176 11.305
14 738 726.1 0.194 11.498
15 548 525.8 0.934 12.433
16 349 381.2 2.712 15.144
17 259 276.5 1.112 16.257
18 219 200.8 1.644 17.901
19 159 146.0 1.160 19.061
20 112 106.2 0.315 19.376
21 303 287.1 0.879 20.255
Chisq= 20.26 for 20 degrees of freedom, p= 0.55794
SUMMARY of craptest
p-value for no. of wins: 0.277680
p-value for throws/game: 0.557937
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2017-03-08_19:31
No. of wins: Observed Expected
98686 98585.9
z-score= 0.448, pvalue=0.67288
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66760 66666.7 0.131 0.131
2 37620 37654.3 0.031 0.162
3 26907 26954.7 0.085 0.246
4 19286 19313.5 0.039 0.286
5 13805 13851.4 0.156 0.441
6 10043 9943.5 0.995 1.436
7 7094 7145.0 0.364 1.800
8 5133 5139.1 0.007 1.807
9 3687 3699.9 0.045 1.852
10 2675 2666.3 0.028 1.881
11 1971 1923.3 1.182 3.062
12 1378 1388.7 0.083 3.145
13 984 1003.7 0.387 3.532
14 712 726.1 0.275 3.808
15 534 525.8 0.127 3.935
16 389 381.2 0.162 4.096
17 258 276.5 1.243 5.339
18 207 200.8 0.190 5.529
19 160 146.0 1.346 6.874
20 96 106.2 0.982 7.857
21 301 287.1 0.672 8.528
Chisq= 8.53 for 20 degrees of freedom, p= 0.01225
SUMMARY of craptest
p-value for no. of wins: 0.672884
p-value for throws/game: 0.012245
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0001,0.0003,0.0030,0.0113,0.0119,0.0122,0.0130,0.0152,0.0195,0.0197,
0.0215,0.0269,0.0291,0.0330,0.0387,0.0414,0.0494,0.0524,0.0603,0.0605,
0.0708,0.0786,0.0806,0.0822,0.0842,0.0892,0.0932,0.1000,0.1091,0.1097,
0.1103,0.1210,0.1250,0.1328,0.1377,0.1431,0.1478,0.1489,0.1505,0.1526,
0.1535,0.1658,0.1669,0.1672,0.1704,0.1711,0.1721,0.1827,0.2025,0.2092,
0.2238,0.2242,0.2273,0.2340,0.2387,0.2391,0.2410,0.2485,0.2494,0.2503,
0.2608,0.2671,0.2711,0.2715,0.2717,0.2777,0.2866,0.2913,0.2923,0.2932,
0.2981,0.3040,0.3067,0.3093,0.3164,0.3169,0.3195,0.3233,0.3305,0.3373,
0.3471,0.3515,0.3551,0.3574,0.3580,0.3601,0.3618,0.3621,0.3682,0.3691,
0.3854,0.3921,0.3942,0.4002,0.4058,0.4072,0.4138,0.4179,0.4201,0.4208,
0.4300,0.4398,0.4398,0.4406,0.4437,0.4515,0.4569,0.4619,0.4620,0.4655,
0.4818,0.4889,0.4914,0.4919,0.4948,0.4988,0.5029,0.5031,0.5036,0.5065,
0.5081,0.5213,0.5235,0.5239,0.5261,0.5266,0.5360,0.5394,0.5400,0.5410,
0.5454,0.5484,0.5579,0.5683,0.5688,0.5756,0.5775,0.5780,0.5816,0.5828,
0.5836,0.5929,0.5968,0.6002,0.6016,0.6044,0.6057,0.6078,0.6100,0.6109,
0.6136,0.6153,0.6207,0.6235,0.6251,0.6261,0.6274,0.6330,0.6345,0.6426,
0.6435,0.6448,0.6470,0.6475,0.6517,0.6519,0.6566,0.6567,0.6605,0.6614,
0.6620,0.6667,0.6716,0.6729,0.6735,0.6786,0.6804,0.6832,0.6891,0.6952,
0.7081,0.7162,0.7204,0.7321,0.7345,0.7416,0.7425,0.7453,0.7490,0.7509,
0.7560,0.7593,0.7602,0.7628,0.7645,0.7674,0.7675,0.7715,0.7758,0.7920,
0.7936,0.7944,0.7967,0.7979,0.8004,0.8027,0.8066,0.8133,0.8134,0.8184,
0.8235,0.8250,0.8312,0.8317,0.8327,0.8374,0.8412,0.8415,0.8465,0.8488,
0.8495,0.8501,0.8524,0.8554,0.8570,0.8620,0.8669,0.8686,0.8748,0.8765,
0.8788,0.8822,0.8824,0.8850,0.8863,0.8869,0.8880,0.8913,0.8946,0.8992,
0.9009,0.9052,0.9055,0.9056,0.9065,0.9082,0.9239,0.9303,0.9305,0.9317,
0.9331,0.9364,0.9440,0.9441,0.9463,0.9495,0.9525,0.9535,0.9566,0.9594,
0.9707,0.9720,0.9725,0.9834,0.9871,0.9918,0.9943,0.9948,0.9986,
Overall p-value after applying KStest on 269 p-values = 0.082446
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.