RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2016-05-20_10:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.70 22.1505 0.820999
2 to 25 15.73 16.9157 0.539910
3 to 26 15.88 13.6458 0.308003
4 to 27 15.58 14.8447 0.393336
5 to 28 16.18 15.7736 0.460065
6 to 29 16.02 9.5316 0.077904
7 to 30 15.78 13.3785 0.289499
8 to 31 15.79 24.9873 0.905005
9 to 32 16.10 14.7629 0.387444
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.770151
Tough bday spacings test for dh-ranFile-2016-05-20_10:31: 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 12 34 86 88 113 58 58 32 5 7 7
(O-E)^2/E 0.9 0.2 2.2 1.0 2.4 5.2 0.7 0.2 6.6 0.0 2.1
Birthday Spacings: Sum(O-E)^2/E= 21.381, p= 0.981
RESULTS OF GCD FOR dh-ranFile-2016-05-20_10:31
Euclid's algorithm:
p-value, steps to gcd: 0.406339
p-value, dist. of gcd's: 0.424792
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2016-05-20_10:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.740 0.613 0.143 0.589 0.257 0.240 0.838 0.950
Bits 8 to 15---> 0.739 0.665 0.802 0.875 0.051 0.453 0.755 0.228
Bits 16 to 23---> 0.623 0.830 0.280 0.212 0.808 0.207 0.933 0.662
Bits 24 to 31---> 0.557 0.344 0.012 0.364 0.781 0.460 0.483 0.601
KS test for the above 32 p values: 0.332
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2016-05-20_10:31,
p-values for 5 runs: 0.5982, 0.0892, 0.1148, 0.3360, 0.5352
Rank test for binary matrices (31x31) for dh-ranFile-2016-05-20_10:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 208 211.4 0.055 0.055
r= 29 5096 5134.0 0.281 0.337
r= 30 23098 23103.0 0.001 0.338
r= 31 11598 11551.5 0.187 0.525
chi-square = 0.525 with df = 3; p-value = 0.087
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2016-05-20_10:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 204 211.4 0.260 0.260
r= 30 5227 5134.0 1.684 1.945
r= 31 23164 23103.0 0.161 2.105
r= 32 11405 11551.5 1.859 3.964
chi-square = 3.964 with df = 3; p-value = 0.735
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2016-05-20_10:31
b-rank test for bits 1 to 8, p=0.53186
b-rank test for bits 2 to 9, p=0.18043
b-rank test for bits 3 to 10, p=0.62202
b-rank test for bits 4 to 11, p=0.08638
b-rank test for bits 5 to 12, p=0.50036
b-rank test for bits 6 to 13, p=0.75681
b-rank test for bits 7 to 14, p=0.77994
b-rank test for bits 8 to 15, p=0.47532
b-rank test for bits 9 to 16, p=0.91528
b-rank test for bits 10 to 17, p=0.49525
b-rank test for bits 11 to 18, p=0.94922
b-rank test for bits 12 to 19, p=0.83207
b-rank test for bits 13 to 20, p=0.24752
b-rank test for bits 14 to 21, p=0.59937
b-rank test for bits 15 to 22, p=0.73344
b-rank test for bits 16 to 23, p=0.43875
b-rank test for bits 17 to 24, p=0.33086
b-rank test for bits 18 to 25, p=0.72856
b-rank test for bits 19 to 26, p=0.58712
b-rank test for bits 20 to 27, p=0.68022
b-rank test for bits 21 to 28, p=0.84902
b-rank test for bits 22 to 29, p=0.90729
b-rank test for bits 23 to 30, p=0.33370
b-rank test for bits 24 to 31, p=0.86768
b-rank test for bits 25 to 32, p=0.87079
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 = 0.073768
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2016-05-20_10:31
(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 142306 0.93 0.822985
2 141927 0.04 0.516466
3 141015 -2.09 0.018329
4 141892 -0.04 0.483851
5 141868 -0.10 0.461536
6 141913 0.01 0.503421
7 142833 2.16 0.984540
8 141724 -0.43 0.332502
9 142242 0.78 0.781499
10 142675 1.79 0.963188
11 142195 0.67 0.747759
12 142166 0.60 0.725646
13 142015 0.25 0.597504
14 142006 0.23 0.589347
15 141929 0.05 0.518328
16 142278 0.86 0.805485
17 141968 0.14 0.554516
18 142065 0.36 0.641965
19 141438 -1.10 0.135396
20 140702 -2.82 0.002395
----------------------------------------------------------------
OPSO test for dh-ranFile-2016-05-20_10:31
Bits used No. missing words z-score p-value
23 to 32 142126 0.7471 0.772510
22 to 31 142414 1.7402 0.959092
21 to 30 142337 1.4747 0.929857
20 to 29 141838 -0.2460 0.402855
19 to 28 141689 -0.7598 0.223699
18 to 27 141869 -0.1391 0.444698
17 to 26 141698 -0.7287 0.233085
16 to 25 141630 -0.9632 0.167722
15 to 24 142022 0.3885 0.651183
14 to 23 141938 0.0989 0.539376
13 to 22 141970 0.2092 0.582857
12 to 21 141884 -0.0873 0.465199
11 to 20 141980 0.2437 0.596264
10 to 19 141609 -1.0356 0.150190
9 to 18 141676 -0.8046 0.210529
8 to 17 142104 0.6713 0.748978
7 to 16 142051 0.4885 0.687408
6 to 15 142031 0.4196 0.662594
5 to 14 141888 -0.0736 0.470684
4 to 13 141507 -1.3873 0.082668
3 to 12 142033 0.4264 0.665109
2 to 11 142205 1.0196 0.846029
1 to 10 141848 -0.2115 0.416255
-----------------------------------------------------------------
OQSO test for dh-ranFile-2016-05-20_10:31
Bits used No. missing words z-score p-value
28 to 32 142538 2.1311 0.983459
27 to 31 142159 0.8463 0.801318
26 to 30 142166 0.8701 0.807868
25 to 29 141690 -0.7435 0.228592
24 to 28 141945 0.1209 0.548121
23 to 27 142565 2.2226 0.986879
22 to 26 141703 -0.6994 0.242144
21 to 25 142157 0.8396 0.799422
20 to 24 142415 1.7141 0.956748
19 to 23 142283 1.2667 0.897365
18 to 22 141803 -0.3604 0.359259
17 to 21 141838 -0.2418 0.404469
16 to 20 141682 -0.7706 0.220469
15 to 19 142309 1.3548 0.912262
14 to 18 141676 -0.7909 0.214487
13 to 17 141656 -0.8587 0.195240
12 to 16 141965 0.1887 0.574841
11 to 15 141949 0.1345 0.553486
10 to 14 142109 0.6768 0.750749
9 to 13 142219 1.0497 0.853079
8 to 12 141548 -1.2248 0.110316
7 to 11 142329 1.4226 0.922575
6 to 10 142219 1.0497 0.853079
5 to 9 142036 0.4294 0.666180
4 to 8 141733 -0.5977 0.275010
3 to 7 142148 0.8091 0.790757
2 to 6 141888 -0.0723 0.471180
1 to 5 141960 0.1718 0.568188
-----------------------------------------------------------------
DNA test for dh-ranFile-2016-05-20_10:31
Bits used No. missing words z-score p-value
31 to 32 141612 -0.8771 0.190222
30 to 31 142225 0.9312 0.824120
29 to 30 141625 -0.8387 0.200810
28 to 29 142117 0.6126 0.729928
27 to 28 141665 -0.7207 0.235536
26 to 27 142779 2.5654 0.994847
25 to 26 141648 -0.7709 0.220388
24 to 25 142303 1.1613 0.877234
23 to 24 141629 -0.8269 0.204138
22 to 23 142155 0.7247 0.765679
21 to 22 142406 1.4651 0.928554
20 to 21 142066 0.4622 0.678014
19 to 20 141690 -0.6470 0.258819
18 to 19 142137 0.6716 0.749079
17 to 18 142342 1.2763 0.899078
16 to 17 141745 -0.4847 0.313927
15 to 16 141899 -0.0305 0.487845
14 to 15 141235 -1.9892 0.023341
13 to 14 141587 -0.9508 0.170846
12 to 13 142128 0.6450 0.740551
11 to 12 142001 0.2704 0.606579
10 to 11 142335 1.2557 0.895381
9 to 10 141331 -1.7060 0.044005
8 to 9 141574 -0.9892 0.161289
7 to 8 142297 1.1436 0.873599
6 to 7 141866 -0.1278 0.449147
5 to 6 142277 1.0846 0.860944
4 to 5 141707 -0.5968 0.275306
3 to 4 142529 1.8279 0.966220
2 to 3 141837 -0.2134 0.415522
1 to 2 142138 0.6745 0.750017
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2016-05-20_10:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2477.92 -0.312 0.377401
Test results for specific bytes for dh-ranFile-2016-05-20_10:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2445.27 -0.774 0.219484
2 to 9 2484.77 -0.215 0.414727
3 to 10 2475.37 -0.348 0.363816
4 to 11 2486.68 -0.188 0.425267
5 to 12 2581.10 1.147 0.874297
6 to 13 2578.60 1.112 0.866851
7 to 14 2510.07 0.142 0.556628
8 to 15 2507.82 0.111 0.544003
9 to 16 2542.34 0.599 0.725335
10 to 17 2478.41 -0.305 0.380052
11 to 18 2477.49 -0.318 0.375090
12 to 19 2540.93 0.579 0.718651
13 to 20 2568.20 0.965 0.832612
14 to 21 2400.41 -1.408 0.079500
15 to 22 2519.78 0.280 0.610163
16 to 23 2469.03 -0.438 0.330715
17 to 24 2460.07 -0.565 0.286120
18 to 25 2482.56 -0.247 0.402585
19 to 26 2520.56 0.291 0.614408
20 to 27 2557.02 0.806 0.789972
21 to 28 2443.52 -0.799 0.212237
22 to 29 2455.36 -0.631 0.263942
23 to 30 2667.02 2.362 0.990914
24 to 31 2389.46 -1.563 0.059000
25 to 32 2486.64 -0.189 0.425096
CDPARK for dh-ranFile-2016-05-20_10:31: 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
3529 0.2740 0.607947
3528 0.2283 0.590298
3494 -1.3242 0.092718
3505 -0.8219 0.205562
3539 0.7306 0.767486
3510 -0.5936 0.276387
3517 -0.2740 0.392053
3524 0.0457 0.518210
3563 1.8265 0.966111
3558 1.5982 0.944998
Square side=100, avg. no. parked=3526.70 sample std.=20.92
p-value of the KSTEST for those 10 p-values: 0.941110
Results for the MINIMUM DISTANCE test for dh-ranFile-2016-05-20_10:31
0.1024,0.1688,0.2833,0.2561,0.6896,0.6619,0.4979,0.2282,0.9302,0.1510,
The KS test for those 10 p-values: 0.361652
The 3DSPHERES test for dh-ranFile-2016-05-20_10:31
sample no r^3 equiv. uni.
1 157.590 0.994768
2 10.712 0.300278
3 43.121 0.762450
4 51.398 0.819723
5 17.885 0.449073
6 9.725 0.276863
7 10.469 0.294592
8 17.426 0.440580
9 37.574 0.714204
10 1.170 0.038233
11 31.529 0.650406
12 40.718 0.742632
13 51.856 0.822453
14 34.280 0.681032
15 46.749 0.789504
16 19.235 0.473327
17 44.222 0.771010
18 15.290 0.399309
19 8.069 0.235842
20 86.177 0.943446
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.294943
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2016-05-20_10:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 0.9 -0.8 -1.1 -0.7 0.5
-0.9 -0.9 -0.9 -1.0 1.3 -0.6
-0.8 -0.0 -1.2 0.9 0.6 -0.1
-0.9 0.5 2.0 0.6 -1.7 0.4
1.2 -0.3 -1.7 1.3 -0.6 -0.1
1.5 1.3 -0.2 0.7 0.5 0.6
-1.2 -0.7 0.1 -1.8 0.1 1.0
-1.1
Chi-square with 42 degrees of freedom:40.003876
z-score=-0.217795, p-value=0.441080
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2016-05-20_10:31
Test no p-value
1 0.161141
2 0.515854
3 0.639958
4 0.785947
5 0.306526
6 0.033272
7 0.052310
8 0.870026
9 0.589393
10 0.349957
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.755124
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2016-05-20_10:31:
(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 66771 0.16
3 25000.00 24915 0.29 25010 0.00
4 6666.67 6785 2.10 6563 1.61
5 1388.89 1354 0.88 1355 0.83
6 238.10 237 0.01 265 3.04
7 34.72 39 0.53 29 0.94
8 4.96 8 1.86 6 0.22
p=0.53792 p=0.66093
Number of rngs required: 689151, p-value: 0.807
RESULTS OF CRAPS TEST for dh-ranFile-2016-05-20_10:31
No. of wins: Observed Expected
98693 98585.9
z-score= 0.479, pvalue=0.68410
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66519 66666.7 0.327 0.327
2 37499 37654.3 0.641 0.968
3 27115 26954.7 0.953 1.921
4 19257 19313.5 0.165 2.086
5 13822 13851.4 0.062 2.148
6 10101 9943.5 2.493 4.642
7 7257 7145.0 1.755 6.396
8 5161 5139.1 0.094 6.490
9 3706 3699.9 0.010 6.500
10 2730 2666.3 1.522 8.022
11 1956 1923.3 0.555 8.577
12 1359 1388.7 0.637 9.214
13 971 1003.7 1.066 10.280
14 680 726.1 2.932 13.212
15 518 525.8 0.117 13.329
16 407 381.2 1.753 15.082
17 258 276.5 1.243 16.325
18 173 200.8 3.857 20.181
19 140 146.0 0.245 20.427
20 114 106.2 0.571 20.997
21 257 287.1 3.159 24.156
Chisq= 24.16 for 20 degrees of freedom, p= 0.76435
SUMMARY of craptest
p-value for no. of wins: 0.684101
p-value for throws/game: 0.764349
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2016-05-20_10:31
No. of wins: Observed Expected
98227 98585.9
z-score=-1.605, pvalue=0.05424
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66348 66666.7 1.523 1.523
2 37560 37654.3 0.236 1.759
3 27032 26954.7 0.221 1.981
4 19400 19313.5 0.388 2.369
5 14004 13851.4 1.681 4.049
6 9976 9943.5 0.106 4.155
7 7122 7145.0 0.074 4.230
8 5216 5139.1 1.152 5.381
9 3701 3699.9 0.000 5.382
10 2602 2666.3 1.551 6.932
11 1917 1923.3 0.021 6.953
12 1405 1388.7 0.190 7.143
13 1018 1003.7 0.203 7.347
14 746 726.1 0.543 7.890
15 548 525.8 0.934 8.824
16 377 381.2 0.045 8.869
17 286 276.5 0.324 9.193
18 196 200.8 0.116 9.309
19 133 146.0 1.155 10.464
20 104 106.2 0.046 10.510
21 309 287.1 1.668 12.178
Chisq= 12.18 for 20 degrees of freedom, p= 0.09020
SUMMARY of craptest
p-value for no. of wins: 0.054244
p-value for throws/game: 0.090198
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0024,0.0117,0.0183,0.0233,0.0333,0.0382,0.0440,0.0506,0.0523,0.0542,
0.0590,0.0738,0.0779,0.0795,0.0827,0.0864,0.0866,0.0892,0.0902,0.0927,
0.1024,0.1103,0.1148,0.1354,0.1432,0.1502,0.1510,0.1611,0.1613,0.1677,
0.1688,0.1708,0.1804,0.1902,0.1952,0.2008,0.2041,0.2056,0.2074,0.2105,
0.2122,0.2124,0.2145,0.2195,0.2204,0.2205,0.2237,0.2276,0.2282,0.2286,
0.2331,0.2355,0.2358,0.2395,0.2421,0.2475,0.2561,0.2566,0.2588,0.2639,
0.2750,0.2753,0.2764,0.2769,0.2805,0.2833,0.2861,0.2895,0.2946,0.2949,
0.3003,0.3065,0.3080,0.3139,0.3307,0.3309,0.3317,0.3325,0.3337,0.3360,
0.3436,0.3500,0.3593,0.3617,0.3638,0.3645,0.3751,0.3774,0.3801,0.3874,
0.3921,0.3933,0.3993,0.4026,0.4029,0.4045,0.4063,0.4147,0.4155,0.4163,
0.4248,0.4251,0.4253,0.4387,0.4406,0.4411,0.4447,0.4491,0.4491,0.4528,
0.4601,0.4604,0.4615,0.4652,0.4707,0.4712,0.4733,0.4753,0.4830,0.4839,
0.4878,0.4952,0.4979,0.5004,0.5034,0.5159,0.5165,0.5182,0.5183,0.5319,
0.5352,0.5379,0.5394,0.5399,0.5440,0.5481,0.5535,0.5545,0.5566,0.5567,
0.5682,0.5748,0.5829,0.5871,0.5893,0.5894,0.5895,0.5903,0.5963,0.5975,
0.5982,0.5994,0.6014,0.6066,0.6079,0.6102,0.6130,0.6144,0.6220,0.6232,
0.6400,0.6420,0.6504,0.6512,0.6609,0.6619,0.6619,0.6626,0.6651,0.6653,
0.6662,0.6780,0.6802,0.6810,0.6841,0.6874,0.6896,0.7142,0.7187,0.7253,
0.7256,0.7286,0.7299,0.7334,0.7346,0.7392,0.7402,0.7406,0.7426,0.7478,
0.7490,0.7491,0.7500,0.7507,0.7551,0.7555,0.7568,0.7624,0.7643,0.7657,
0.7675,0.7702,0.7710,0.7725,0.7799,0.7814,0.7815,0.7859,0.7895,0.7900,
0.7908,0.7994,0.8013,0.8024,0.8055,0.8065,0.8079,0.8081,0.8197,0.8210,
0.8225,0.8230,0.8241,0.8303,0.8321,0.8326,0.8378,0.8460,0.8490,0.8531,
0.8531,0.8609,0.8669,0.8677,0.8700,0.8708,0.8736,0.8743,0.8752,0.8772,
0.8954,0.8974,0.8991,0.9050,0.9073,0.9123,0.9153,0.9226,0.9286,0.9299,
0.9302,0.9333,0.9411,0.9434,0.9450,0.9492,0.9503,0.9567,0.9591,0.9632,
0.9661,0.9662,0.9814,0.9835,0.9845,0.9869,0.9909,0.9948,0.9948,
Overall p-value after applying KStest on 269 p-values = 0.071074
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.