RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-02_08:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.57 20.6949 0.759763
2 to 25 15.98 20.1238 0.732052
3 to 26 15.63 20.8726 0.767957
4 to 27 15.50 15.6143 0.448674
5 to 28 15.73 18.5849 0.647127
6 to 29 15.87 8.8312 0.054591
7 to 30 15.96 18.4747 0.640497
8 to 31 15.78 24.7669 0.899951
9 to 32 15.59 21.1116 0.778662
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.141044
Tough bday spacings test for dh-ranFile-2018-07-02_08:31: 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 47 84 91 100 73 44 23 16 8 3
(O-E)^2/E 0.4 2.9 1.6 0.5 0.1 0.3 1.3 1.5 0.1 0.3 0.3
Birthday Spacings: Sum(O-E)^2/E= 9.181, p= 0.485
RESULTS OF GCD FOR dh-ranFile-2018-07-02_08:31
Euclid's algorithm:
p-value, steps to gcd: 0.763267
p-value, dist. of gcd's: 0.554232
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-02_08:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.997 0.875 0.334 0.247 0.602 0.947 0.930 0.223
Bits 8 to 15---> 0.219 0.203 0.973 0.877 0.752 0.902 0.290 0.384
Bits 16 to 23---> 0.044 0.498 0.160 0.433 0.615 0.574 0.835 0.519
Bits 24 to 31---> 0.256 0.577 0.131 0.700 0.271 0.707 0.624 0.699
KS test for the above 32 p values: 0.401
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-02_08:31,
p-values for 5 runs: 0.5571, 0.1634, 0.6418, 0.7653, 0.4439
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-02_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 230 211.4 1.633 1.633
r= 29 5133 5134.0 0.000 1.633
r= 30 23077 23103.0 0.029 1.663
r= 31 11560 11551.5 0.006 1.669
chi-square = 1.669 with df = 3; p-value = 0.356
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-02_08:31
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 23111 23103.0 0.003 0.011
r= 32 11550 11551.5 0.000 0.011
chi-square = 0.011 with df = 3; p-value = 0.000
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-02_08:31
b-rank test for bits 1 to 8, p=0.86172
b-rank test for bits 2 to 9, p=0.83381
b-rank test for bits 3 to 10, p=0.54824
b-rank test for bits 4 to 11, p=0.86462
b-rank test for bits 5 to 12, p=0.37195
b-rank test for bits 6 to 13, p=0.89769
b-rank test for bits 7 to 14, p=0.43039
b-rank test for bits 8 to 15, p=0.62130
b-rank test for bits 9 to 16, p=0.23829
b-rank test for bits 10 to 17, p=0.30282
b-rank test for bits 11 to 18, p=0.64977
b-rank test for bits 12 to 19, p=0.18944
b-rank test for bits 13 to 20, p=0.77376
b-rank test for bits 14 to 21, p=0.81412
b-rank test for bits 15 to 22, p=0.23614
b-rank test for bits 16 to 23, p=0.14722
b-rank test for bits 17 to 24, p=0.55831
b-rank test for bits 18 to 25, p=0.84807
b-rank test for bits 19 to 26, p=0.22423
b-rank test for bits 20 to 27, p=0.37257
b-rank test for bits 21 to 28, p=0.75684
b-rank test for bits 22 to 29, p=0.94759
b-rank test for bits 23 to 30, p=0.22058
b-rank test for bits 24 to 31, p=0.62364
b-rank test for bits 25 to 32, p=0.55850
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 = 0.391632
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-02_08:31
(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 141718 -0.45 0.327426
2 141473 -1.02 0.153992
3 142415 1.18 0.881292
4 142104 0.45 0.675387
5 142410 1.17 0.878957
6 142503 1.39 0.917291
7 142152 0.57 0.714638
8 141535 -0.87 0.190895
9 142507 1.40 0.918707
10 142492 1.36 0.913303
11 142420 1.19 0.883596
12 142911 2.34 0.990367
13 141883 -0.06 0.475473
14 142248 0.79 0.785611
15 141679 -0.54 0.295235
16 141977 0.16 0.562814
17 141937 0.06 0.525774
18 142154 0.57 0.716223
19 142397 1.14 0.872735
20 141615 -0.69 0.245825
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-02_08:31
Bits used No. missing words z-score p-value
23 to 32 142108 0.6851 0.753350
22 to 31 141984 0.2575 0.601597
21 to 30 141789 -0.4149 0.339096
20 to 29 142031 0.4196 0.662594
19 to 28 141948 0.1333 0.553040
18 to 27 141739 -0.5873 0.278486
17 to 26 142107 0.6816 0.752261
16 to 25 141725 -0.6356 0.262512
15 to 24 141598 -1.0736 0.141512
14 to 23 141682 -0.7839 0.216550
13 to 22 141782 -0.4391 0.330306
12 to 21 142188 0.9609 0.831707
11 to 20 141941 0.1092 0.543481
10 to 19 142149 0.8264 0.795725
9 to 18 141956 0.1609 0.563926
8 to 17 141724 -0.6391 0.261389
7 to 16 142160 0.8644 0.806310
6 to 15 141565 -1.1873 0.117546
5 to 14 142223 1.0816 0.860289
4 to 13 142025 0.3989 0.655003
3 to 12 141640 -0.9287 0.176516
2 to 11 141876 -0.1149 0.454250
1 to 10 142146 0.8161 0.792780
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-02_08:31
Bits used No. missing words z-score p-value
28 to 32 141717 -0.6520 0.257212
27 to 31 142623 2.4192 0.992223
26 to 30 142244 1.1345 0.871702
25 to 29 142189 0.9480 0.828444
24 to 28 141698 -0.7164 0.236881
23 to 27 141737 -0.5842 0.279553
22 to 26 141815 -0.3198 0.374574
21 to 25 142286 1.2768 0.899172
20 to 24 141838 -0.2418 0.404469
19 to 23 141829 -0.2723 0.392694
18 to 22 142090 0.6124 0.729877
17 to 21 141691 -0.7401 0.229619
16 to 20 141782 -0.4316 0.333006
15 to 19 142287 1.2802 0.899769
14 to 18 142269 1.2192 0.888620
13 to 17 141582 -1.1096 0.133587
12 to 16 142056 0.4972 0.690471
11 to 15 141987 0.2633 0.603836
10 to 14 142215 1.0362 0.849938
9 to 13 141831 -0.2655 0.395302
8 to 12 141725 -0.6248 0.266036
7 to 11 141522 -1.3130 0.094594
6 to 10 141856 -0.1808 0.428270
5 to 9 141692 -0.7367 0.230649
4 to 8 141950 0.1379 0.554826
3 to 7 142254 1.1684 0.878672
2 to 6 141486 -1.4350 0.075641
1 to 5 141697 -0.7198 0.235836
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-02_08:31
Bits used No. missing words z-score p-value
31 to 32 141913 0.0108 0.504319
30 to 31 142006 0.2852 0.612240
29 to 30 141950 0.1200 0.547747
28 to 29 141777 -0.3904 0.348137
27 to 28 142175 0.7837 0.783388
26 to 27 141689 -0.6499 0.257865
25 to 26 142115 0.6067 0.727974
24 to 25 142056 0.4327 0.667367
23 to 24 141757 -0.4494 0.326589
22 to 23 142146 0.6981 0.757456
21 to 22 142030 0.3560 0.639064
20 to 21 141800 -0.3225 0.373534
19 to 20 141116 -2.3402 0.009637
18 to 19 142242 0.9813 0.836784
17 to 18 141698 -0.6234 0.266513
16 to 17 142352 1.3058 0.904192
15 to 16 142009 0.2940 0.615626
14 to 15 142128 0.6450 0.740551
13 to 14 142050 0.4150 0.660913
12 to 13 141201 -2.0895 0.018333
11 to 12 141845 -0.1898 0.424747
10 to 11 141590 -0.9420 0.173102
9 to 10 141710 -0.5880 0.278268
8 to 9 142036 0.3737 0.645671
7 to 8 142454 1.6067 0.945939
6 to 7 142485 1.6981 0.955259
5 to 6 142135 0.6657 0.747196
4 to 5 142113 0.6008 0.726012
3 to 4 142016 0.3147 0.623490
2 to 3 142032 0.3619 0.641271
1 to 2 142342 1.2763 0.899078
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-02_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2368.84 -1.855 0.031809
Test results for specific bytes for dh-ranFile-2018-07-02_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2380.93 -1.684 0.046095
2 to 9 2396.80 -1.459 0.072220
3 to 10 2600.12 1.416 0.921591
4 to 11 2556.69 0.802 0.788633
5 to 12 2568.94 0.975 0.835218
6 to 13 2529.07 0.411 0.659490
7 to 14 2527.56 0.390 0.651659
8 to 15 2611.71 1.580 0.942924
9 to 16 2535.16 0.497 0.690470
10 to 17 2461.64 -0.542 0.293763
11 to 18 2498.22 -0.025 0.489938
12 to 19 2420.20 -1.129 0.129546
13 to 20 2396.00 -1.471 0.070683
14 to 21 2518.61 0.263 0.603812
15 to 22 2513.42 0.190 0.575238
16 to 23 2437.16 -0.889 0.187094
17 to 24 2466.33 -0.476 0.316989
18 to 25 2401.63 -1.391 0.082082
19 to 26 2364.47 -1.917 0.027635
20 to 27 2459.11 -0.578 0.281547
21 to 28 2491.86 -0.115 0.454175
22 to 29 2503.99 0.056 0.522523
23 to 30 2540.70 0.576 0.717547
24 to 31 2545.38 0.642 0.739481
25 to 32 2441.84 -0.823 0.205382
CDPARK for dh-ranFile-2018-07-02_08:31: 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
3524 0.0457 0.518210
3515 -0.3653 0.357445
3489 -1.5525 0.060270
3514 -0.4110 0.340551
3533 0.4566 0.676028
3513 -0.4566 0.323972
3542 0.8676 0.807188
3493 -1.3699 0.085365
3513 -0.4566 0.323972
3499 -1.0959 0.136563
Square side=100, avg. no. parked=3513.50 sample std.=15.93
p-value of the KSTEST for those 10 p-values: 0.207587
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-02_08:31
0.4166,0.7111,0.1797,0.1790,0.7208,0.2243,0.8021,0.7487,0.9887,0.1241,
The KS test for those 10 p-values: 0.755578
The 3DSPHERES test for dh-ranFile-2018-07-02_08:31
sample no r^3 equiv. uni.
1 19.963 0.485957
2 5.909 0.178773
3 38.628 0.724070
4 31.394 0.648820
5 20.145 0.489053
6 62.501 0.875489
7 32.129 0.657324
8 1.505 0.048936
9 59.837 0.863929
10 2.017 0.065020
11 59.980 0.864572
12 7.754 0.227755
13 0.849 0.027903
14 4.013 0.125203
15 56.496 0.847899
16 7.568 0.222958
17 10.514 0.295638
18 38.008 0.718304
19 3.539 0.111275
20 17.155 0.435506
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.524281
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-02_08:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 0.1 -0.8 -0.8 2.0 0.5
1.7 0.8 -1.3 0.4 0.0 0.3
0.2 -1.2 0.1 0.3 -1.9 -0.1
-0.2 -0.2 0.0 1.8 0.5 -0.9
0.5 0.7 0.7 -0.3 -0.8 -1.0
2.2 -2.3 0.7 1.6 -0.2 2.6
2.4 -2.0 1.3 1.5 -0.6 -1.0
1.8
Chi-square with 42 degrees of freedom:61.622697
z-score=2.141012, p-value=0.974228
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-02_08:31
Test no p-value
1 0.923347
2 0.003951
3 0.073760
4 0.683423
5 0.369704
6 0.783367
7 0.453469
8 0.548018
9 0.251772
10 0.125787
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.613627
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-02_08:31:
(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 66525 0.30 66782 0.20
3 25000.00 25012 0.01 24834 1.10
4 6666.67 6776 1.79 6714 0.34
5 1388.89 1429 1.16 1397 0.05
6 238.10 215 2.24 231 0.21
7 34.72 35 0.00 34 0.01
8 4.96 7 0.84 7 0.84
p=0.61376 p=0.16056
Number of rngs required: 688121, p-value: 0.373
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-02_08:31
No. of wins: Observed Expected
98653 98585.9
z-score= 0.300, pvalue=0.61802
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66517 66666.7 0.336 0.336
2 37867 37654.3 1.201 1.537
3 26844 26954.7 0.455 1.992
4 19379 19313.5 0.222 2.215
5 13885 13851.4 0.081 2.296
6 9875 9943.5 0.472 2.768
7 7237 7145.0 1.184 3.952
8 5080 5139.1 0.679 4.631
9 3651 3699.9 0.645 5.277
10 2717 2666.3 0.964 6.241
11 1945 1923.3 0.244 6.485
12 1388 1388.7 0.000 6.486
13 1056 1003.7 2.724 9.209
14 684 726.1 2.446 11.655
15 504 525.8 0.907 12.561
16 358 381.2 1.406 13.968
17 282 276.5 0.108 14.075
18 182 200.8 1.765 15.841
19 157 146.0 0.831 16.672
20 107 106.2 0.006 16.678
21 285 287.1 0.016 16.693
Chisq= 16.69 for 20 degrees of freedom, p= 0.32722
SUMMARY of craptest
p-value for no. of wins: 0.618024
p-value for throws/game: 0.327221
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-02_08:31
No. of wins: Observed Expected
98797 98585.9
z-score= 0.944, pvalue=0.82750
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66708 66666.7 0.026 0.026
2 37607 37654.3 0.059 0.085
3 26569 26954.7 5.520 5.605
4 19524 19313.5 2.295 7.900
5 13905 13851.4 0.207 8.107
6 9947 9943.5 0.001 8.109
7 7133 7145.0 0.020 8.129
8 5233 5139.1 1.717 9.846
9 3689 3699.9 0.032 9.878
10 2700 2666.3 0.426 10.304
11 2002 1923.3 3.218 13.521
12 1326 1388.7 2.834 16.356
13 969 1003.7 1.201 17.557
14 704 726.1 0.675 18.232
15 540 525.8 0.382 18.613
16 379 381.2 0.012 18.625
17 271 276.5 0.111 18.736
18 185 200.8 1.248 19.984
19 166 146.0 2.744 22.728
20 128 106.2 4.468 27.196
21 315 287.1 2.708 29.905
Chisq= 29.90 for 20 degrees of freedom, p= 0.92859
SUMMARY of craptest
p-value for no. of wins: 0.827504
p-value for throws/game: 0.928590
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0003,0.0040,0.0096,0.0183,0.0276,0.0279,0.0318,0.0436,0.0461,0.0489,
0.0546,0.0603,0.0650,0.0707,0.0722,0.0738,0.0756,0.0821,0.0854,0.0946,
0.1113,0.1175,0.1241,0.1252,0.1258,0.1295,0.1307,0.1336,0.1366,0.1410,
0.1415,0.1472,0.1540,0.1599,0.1606,0.1634,0.1731,0.1765,0.1788,0.1790,
0.1797,0.1871,0.1894,0.1909,0.2035,0.2054,0.2076,0.2166,0.2189,0.2206,
0.2228,0.2230,0.2242,0.2243,0.2278,0.2296,0.2306,0.2358,0.2361,0.2369,
0.2383,0.2458,0.2472,0.2518,0.2560,0.2572,0.2579,0.2614,0.2625,0.2660,
0.2665,0.2708,0.2783,0.2785,0.2796,0.2815,0.2902,0.2938,0.2952,0.2956,
0.3028,0.3170,0.3240,0.3240,0.3266,0.3272,0.3274,0.3303,0.3330,0.3335,
0.3391,0.3406,0.3481,0.3562,0.3574,0.3697,0.3720,0.3726,0.3727,0.3735,
0.3746,0.3838,0.3916,0.3927,0.3953,0.4009,0.4045,0.4166,0.4247,0.4283,
0.4304,0.4332,0.4355,0.4439,0.4487,0.4535,0.4542,0.4542,0.4755,0.4850,
0.4860,0.4891,0.4899,0.4983,0.5043,0.5182,0.5186,0.5225,0.5243,0.5258,
0.5435,0.5477,0.5480,0.5482,0.5530,0.5542,0.5548,0.5571,0.5583,0.5585,
0.5628,0.5639,0.5741,0.5752,0.5766,0.6016,0.6021,0.6038,0.6038,0.6122,
0.6136,0.6138,0.6147,0.6156,0.6180,0.6213,0.6235,0.6236,0.6238,0.6391,
0.6405,0.6413,0.6418,0.6457,0.6471,0.6488,0.6498,0.6517,0.6550,0.6573,
0.6595,0.6609,0.6626,0.6674,0.6754,0.6760,0.6834,0.6905,0.6905,0.6993,
0.7002,0.7075,0.7111,0.7146,0.7162,0.7175,0.7183,0.7208,0.7241,0.7260,
0.7280,0.7299,0.7321,0.7395,0.7406,0.7472,0.7487,0.7515,0.7523,0.7533,
0.7556,0.7568,0.7575,0.7598,0.7633,0.7653,0.7680,0.7738,0.7787,0.7834,
0.7834,0.7856,0.7886,0.7928,0.7957,0.8021,0.8063,0.8072,0.8141,0.8275,
0.8284,0.8317,0.8338,0.8349,0.8352,0.8368,0.8479,0.8481,0.8499,0.8603,
0.8617,0.8639,0.8646,0.8646,0.8717,0.8727,0.8754,0.8755,0.8773,0.8787,
0.8790,0.8813,0.8836,0.8886,0.8977,0.8991,0.8992,0.8998,0.9000,0.9021,
0.9042,0.9133,0.9173,0.9187,0.9216,0.9233,0.9286,0.9301,0.9429,0.9459,
0.9468,0.9476,0.9553,0.9734,0.9742,0.9887,0.9904,0.9922,0.9967,
Overall p-value after applying KStest on 269 p-values = 0.291250
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.