RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-15_05:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.73 17.3720 0.570548
2 to 25 15.74 23.6239 0.869980
3 to 26 15.60 22.6080 0.837546
4 to 27 15.92 15.3492 0.429657
5 to 28 15.80 24.8837 0.902656
6 to 29 15.85 20.7248 0.761158
7 to 30 15.41 24.3833 0.890612
8 to 31 15.53 22.1126 0.819574
9 to 32 16.04 11.5813 0.175200
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.047843
Tough bday spacings test for dh-ranFile-2018-06-15_05:31: 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 5 46 81 94 90 73 53 36 12 6 4
(O-E)^2/E 1.9 2.4 0.8 0.1 0.6 0.3 0.0 1.3 0.6 0.1 0.0
Birthday Spacings: Sum(O-E)^2/E= 8.120, p= 0.383
RESULTS OF GCD FOR dh-ranFile-2018-06-15_05:31
Euclid's algorithm:
p-value, steps to gcd: 0.357761
p-value, dist. of gcd's: 0.337097
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-15_05:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.096 0.727 0.373 0.970 0.724 0.772 0.876 0.268
Bits 8 to 15---> 0.779 0.672 0.555 0.938 0.176 0.591 0.494 0.931
Bits 16 to 23---> 0.185 0.948 0.262 0.843 0.393 0.708 0.688 0.518
Bits 24 to 31---> 0.209 0.539 0.446 0.306 0.880 0.875 0.174 0.060
KS test for the above 32 p values: 0.591
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-15_05:31,
p-values for 5 runs: 0.5959, 0.3276, 0.4065, 0.9287, 0.7550
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-15_05:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 234 211.4 2.412 2.412
r= 29 5089 5134.0 0.395 2.807
r= 30 23104 23103.0 0.000 2.807
r= 31 11573 11551.5 0.040 2.847
chi-square = 2.847 with df = 3; p-value = 0.584
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-15_05:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 232 211.4 2.004 2.004
r= 30 5175 5134.0 0.327 2.331
r= 31 23205 23103.0 0.450 2.781
r= 32 11388 11551.5 2.315 5.096
chi-square = 5.096 with df = 3; p-value = 0.835
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-15_05:31
b-rank test for bits 1 to 8, p=0.80093
b-rank test for bits 2 to 9, p=0.57970
b-rank test for bits 3 to 10, p=0.77248
b-rank test for bits 4 to 11, p=0.62762
b-rank test for bits 5 to 12, p=0.13706
b-rank test for bits 6 to 13, p=0.83677
b-rank test for bits 7 to 14, p=0.98863
b-rank test for bits 8 to 15, p=0.24337
b-rank test for bits 9 to 16, p=0.55243
b-rank test for bits 10 to 17, p=0.20039
b-rank test for bits 11 to 18, p=0.26090
b-rank test for bits 12 to 19, p=0.90674
b-rank test for bits 13 to 20, p=0.76281
b-rank test for bits 14 to 21, p=0.15373
b-rank test for bits 15 to 22, p=0.05365
b-rank test for bits 16 to 23, p=0.31549
b-rank test for bits 17 to 24, p=0.85700
b-rank test for bits 18 to 25, p=0.63621
b-rank test for bits 19 to 26, p=0.22346
b-rank test for bits 20 to 27, p=0.53690
b-rank test for bits 21 to 28, p=0.25569
b-rank test for bits 22 to 29, p=0.52499
b-rank test for bits 23 to 30, p=0.94866
b-rank test for bits 24 to 31, p=0.77886
b-rank test for bits 25 to 32, p=0.02686
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 = 0.926053
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-15_05:31
(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 141341 -1.33 0.092110
2 142343 1.01 0.844529
3 141185 -1.69 0.045289
4 141642 -0.62 0.266116
5 141690 -0.51 0.304167
6 141736 -0.40 0.342747
7 142359 1.05 0.853286
8 142069 0.37 0.645448
9 142124 0.50 0.692013
10 141970 0.14 0.556362
11 142018 0.25 0.600214
12 142563 1.53 0.936653
13 141838 -0.17 0.433819
14 142074 0.38 0.649786
15 142222 0.73 0.767469
16 142162 0.59 0.722522
17 142538 1.47 0.929064
18 141966 0.13 0.552669
19 140969 -2.20 0.014009
20 141401 -1.19 0.117478
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-15_05:31
Bits used No. missing words z-score p-value
23 to 32 141621 -0.9942 0.160053
22 to 31 141722 -0.6460 0.259151
21 to 30 141387 -1.8011 0.035841
20 to 29 141962 0.1816 0.572060
19 to 28 141807 -0.3529 0.362096
18 to 27 141920 0.0368 0.514675
17 to 26 141725 -0.6356 0.262512
16 to 25 141543 -1.2632 0.103257
15 to 24 141889 -0.0701 0.472056
14 to 23 141845 -0.2218 0.412224
13 to 22 141698 -0.7287 0.233085
12 to 21 141938 0.0989 0.539376
11 to 20 142278 1.2713 0.898185
10 to 19 141661 -0.8563 0.195913
9 to 18 141752 -0.5425 0.293731
8 to 17 141703 -0.7115 0.238393
7 to 16 141908 -0.0046 0.498170
6 to 15 142355 1.5368 0.937828
5 to 14 141790 -0.4115 0.340359
4 to 13 141527 -1.3184 0.093688
3 to 12 141836 -0.2529 0.400187
2 to 11 141839 -0.2425 0.404190
1 to 10 142048 0.4782 0.683736
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-15_05:31
Bits used No. missing words z-score p-value
28 to 32 142117 0.7040 0.759273
27 to 31 142571 2.2429 0.987550
26 to 30 141460 -1.5232 0.063860
25 to 29 141842 -0.2282 0.409731
24 to 28 141367 -1.8384 0.033001
23 to 27 142273 1.2328 0.891171
22 to 26 141096 -2.7571 0.002916
21 to 25 142258 1.1819 0.881384
20 to 24 142009 0.3379 0.632267
19 to 23 142429 1.7616 0.960931
18 to 22 141985 0.2565 0.601221
17 to 21 142549 2.1684 0.984935
16 to 20 141726 -0.6215 0.267149
15 to 19 142013 0.3514 0.637365
14 to 18 142393 1.6396 0.949452
13 to 17 141515 -1.3367 0.090658
12 to 16 142394 1.6429 0.949803
11 to 15 142006 0.3277 0.628429
10 to 14 141908 -0.0045 0.498201
9 to 13 141855 -0.1842 0.426940
8 to 12 142099 0.6429 0.739872
7 to 11 142192 0.9582 0.831020
6 to 10 141984 0.2531 0.599912
5 to 9 141702 -0.7028 0.241086
4 to 8 141620 -0.9808 0.163351
3 to 7 141690 -0.7435 0.228592
2 to 6 141720 -0.6418 0.260503
1 to 5 141930 0.0701 0.527930
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-15_05:31
Bits used No. missing words z-score p-value
31 to 32 141890 -0.0570 0.477264
30 to 31 141853 -0.1662 0.434014
29 to 30 142690 2.3029 0.989357
28 to 29 142030 0.3560 0.639064
27 to 28 142211 0.8899 0.813235
26 to 27 142056 0.4327 0.667367
25 to 26 142306 1.1701 0.879023
24 to 25 141922 0.0374 0.514907
23 to 24 142049 0.4120 0.659832
22 to 23 141380 -1.5614 0.059209
21 to 22 142373 1.3678 0.914306
20 to 21 141266 -1.8977 0.028866
19 to 20 141294 -1.8151 0.034752
18 to 19 142310 1.1819 0.881381
17 to 18 142223 0.9253 0.822590
16 to 17 142293 1.1318 0.871134
15 to 16 141808 -0.2989 0.382505
14 to 15 141807 -0.3019 0.381380
13 to 14 141986 0.2262 0.589464
12 to 13 142225 0.9312 0.824120
11 to 12 141934 0.0728 0.529007
10 to 11 142063 0.4533 0.674835
9 to 10 141429 -1.4169 0.078256
8 to 9 141824 -0.2517 0.400632
7 to 8 141846 -0.1868 0.425903
6 to 7 141991 0.2409 0.595189
5 to 6 141510 -1.1780 0.119405
4 to 5 141878 -0.0924 0.463183
3 to 4 141790 -0.3520 0.362417
2 to 3 141697 -0.6263 0.265545
1 to 2 141894 -0.0452 0.481966
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-15_05:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2507.91 0.112 0.544527
Test results for specific bytes for dh-ranFile-2018-06-15_05:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2526.03 0.368 0.643604
2 to 9 2347.28 -2.160 0.015397
3 to 10 2452.41 -0.673 0.250465
4 to 11 2567.58 0.956 0.830379
5 to 12 2483.44 -0.234 0.407432
6 to 13 2473.44 -0.376 0.353615
7 to 14 2356.76 -2.026 0.021394
8 to 15 2507.65 0.108 0.543088
9 to 16 2574.09 1.048 0.852648
10 to 17 2557.55 0.814 0.792131
11 to 18 2396.45 -1.464 0.071548
12 to 19 2392.08 -1.526 0.063473
13 to 20 2513.94 0.197 0.578139
14 to 21 2466.02 -0.481 0.315417
15 to 22 2467.33 -0.462 0.322020
16 to 23 2518.49 0.261 0.603126
17 to 24 2676.29 2.493 0.993669
18 to 25 2464.36 -0.504 0.307145
19 to 26 2446.15 -0.762 0.223149
20 to 27 2348.85 -2.138 0.016278
21 to 28 2445.09 -0.777 0.218710
22 to 29 2529.34 0.415 0.660909
23 to 30 2544.53 0.630 0.735588
24 to 31 2392.10 -1.526 0.063514
25 to 32 2575.59 1.069 0.857471
CDPARK for dh-ranFile-2018-06-15_05:31: 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
3522 -0.0457 0.481790
3511 -0.5479 0.291865
3555 1.4612 0.928018
3531 0.3653 0.642555
3513 -0.4566 0.323972
3523 0.0000 0.500000
3522 -0.0457 0.481790
3527 0.1826 0.572463
3495 -1.2785 0.100530
3517 -0.2740 0.392053
Square side=100, avg. no. parked=3521.60 sample std.=14.66
p-value of the KSTEST for those 10 p-values: 0.534893
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-15_05:31
0.5246,0.6200,0.4806,0.3563,0.8793,0.3323,0.4415,0.5212,0.4822,0.8214,
The KS test for those 10 p-values: 0.263637
The 3DSPHERES test for dh-ranFile-2018-06-15_05:31
sample no r^3 equiv. uni.
1 38.787 0.725524
2 86.746 0.944510
3 5.545 0.168767
4 130.445 0.987069
5 10.984 0.306589
6 36.784 0.706572
7 55.889 0.844791
8 183.336 0.997782
9 5.185 0.158735
10 5.194 0.158967
11 95.742 0.958886
12 5.787 0.175436
13 1.934 0.062430
14 1.952 0.062992
15 23.581 0.544349
16 15.953 0.412432
17 75.850 0.920208
18 47.100 0.791954
19 21.811 0.516652
20 26.312 0.584004
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.248087
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-15_05:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 2.2 -0.6 0.0 0.5 -1.8
-1.3 0.7 1.9 -0.2 -0.2 0.4
-1.3 -2.3 -2.3 0.4 0.6 -0.6
0.5 1.9 -0.3 0.2 0.3 0.7
0.8 1.0 0.2 -0.8 0.3 0.3
1.6 2.0 -1.7 -0.6 0.1 -1.4
0.7 0.2 -0.8 -1.8 0.1 0.0
0.8
Chi-square with 42 degrees of freedom:52.724083
z-score=1.170093, p-value=0.875856
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-15_05:31
Test no p-value
1 0.625397
2 0.001054
3 0.011335
4 0.477643
5 0.961925
6 0.046296
7 0.893157
8 0.792144
9 0.403617
10 0.006715
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.023032
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-15_05:31:
(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 66667 0.00 66617 0.04
3 25000.00 24878 0.60 24959 0.07
4 6666.67 6735 0.70 6743 0.87
5 1388.89 1442 2.03 1406 0.21
6 238.10 227 0.52 230 0.28
7 34.72 43 1.97 41 1.14
8 4.96 7 0.84 3 0.77
p=0.64629 p=0.23943
Number of rngs required: 688725, p-value: 0.645
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-15_05:31
No. of wins: Observed Expected
98824 98585.9
z-score= 1.065, pvalue=0.85659
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66873 66666.7 0.639 0.639
2 37420 37654.3 1.458 2.097
3 26989 26954.7 0.044 2.140
4 19131 19313.5 1.724 3.864
5 13918 13851.4 0.320 4.184
6 9966 9943.5 0.051 4.235
7 7094 7145.0 0.364 4.599
8 5119 5139.1 0.078 4.678
9 3816 3699.9 3.645 8.323
10 2729 2666.3 1.475 9.798
11 1938 1923.3 0.112 9.910
12 1374 1388.7 0.156 10.066
13 1006 1003.7 0.005 10.071
14 662 726.1 5.666 15.737
15 504 525.8 0.907 16.644
16 396 381.2 0.579 17.222
17 264 276.5 0.569 17.791
18 230 200.8 4.237 22.028
19 156 146.0 0.687 22.715
20 107 106.2 0.006 22.720
21 308 287.1 1.519 24.240
Chisq= 24.24 for 20 degrees of freedom, p= 0.76793
SUMMARY of craptest
p-value for no. of wins: 0.856586
p-value for throws/game: 0.767926
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-15_05:31
No. of wins: Observed Expected
98709 98585.9
z-score= 0.551, pvalue=0.70910
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66631 66666.7 0.019 0.019
2 37635 37654.3 0.010 0.029
3 26851 26954.7 0.399 0.428
4 19333 19313.5 0.020 0.448
5 13862 13851.4 0.008 0.456
6 10051 9943.5 1.161 1.617
7 7241 7145.0 1.289 2.906
8 5143 5139.1 0.003 2.909
9 3692 3699.9 0.017 2.926
10 2599 2666.3 1.699 4.625
11 1956 1923.3 0.555 5.180
12 1439 1388.7 1.819 6.999
13 999 1003.7 0.022 7.021
14 709 726.1 0.405 7.425
15 496 525.8 1.693 9.118
16 377 381.2 0.045 9.164
17 273 276.5 0.045 9.209
18 199 200.8 0.017 9.225
19 155 146.0 0.557 9.782
20 99 106.2 0.490 10.272
21 260 287.1 2.561 12.833
Chisq= 12.83 for 20 degrees of freedom, p= 0.11556
SUMMARY of craptest
p-value for no. of wins: 0.709101
p-value for throws/game: 0.115564
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0011,0.0029,0.0067,0.0113,0.0140,0.0154,0.0163,0.0214,0.0230,0.0269,
0.0289,0.0330,0.0348,0.0358,0.0453,0.0463,0.0478,0.0536,0.0592,0.0599,
0.0624,0.0630,0.0635,0.0635,0.0639,0.0715,0.0783,0.0907,0.0921,0.0937,
0.0956,0.1005,0.1033,0.1156,0.1175,0.1194,0.1371,0.1537,0.1587,0.1590,
0.1601,0.1634,0.1688,0.1741,0.1752,0.1754,0.1764,0.1846,0.1959,0.2004,
0.2092,0.2187,0.2231,0.2235,0.2286,0.2331,0.2384,0.2394,0.2411,0.2434,
0.2481,0.2505,0.2557,0.2592,0.2605,0.2609,0.2624,0.2625,0.2636,0.2655,
0.2661,0.2671,0.2681,0.2919,0.2937,0.3042,0.3061,0.3066,0.3071,0.3154,
0.3155,0.3220,0.3240,0.3276,0.3323,0.3371,0.3404,0.3427,0.3536,0.3563,
0.3578,0.3621,0.3624,0.3730,0.3814,0.3825,0.3829,0.3921,0.3933,0.4002,
0.4006,0.4036,0.4042,0.4065,0.4074,0.4097,0.4122,0.4124,0.4259,0.4269,
0.4297,0.4338,0.4340,0.4415,0.4465,0.4632,0.4721,0.4773,0.4776,0.4806,
0.4818,0.4818,0.4820,0.4822,0.4944,0.4982,0.4982,0.5000,0.5147,0.5149,
0.5167,0.5182,0.5212,0.5246,0.5250,0.5279,0.5290,0.5349,0.5369,0.5388,
0.5394,0.5431,0.5443,0.5445,0.5524,0.5527,0.5548,0.5564,0.5705,0.5721,
0.5725,0.5781,0.5797,0.5840,0.5841,0.5895,0.5907,0.5907,0.5952,0.5959,
0.5999,0.6002,0.6012,0.6031,0.6200,0.6254,0.6276,0.6284,0.6323,0.6362,
0.6374,0.6391,0.6426,0.6436,0.6446,0.6454,0.6463,0.6498,0.6598,0.6609,
0.6674,0.6723,0.6748,0.6837,0.6879,0.6920,0.7066,0.7080,0.7091,0.7225,
0.7245,0.7255,0.7273,0.7356,0.7399,0.7550,0.7593,0.7612,0.7628,0.7675,
0.7679,0.7723,0.7725,0.7787,0.7789,0.7920,0.7921,0.7921,0.8009,0.8132,
0.8196,0.8214,0.8226,0.8241,0.8304,0.8310,0.8351,0.8368,0.8375,0.8430,
0.8445,0.8448,0.8526,0.8533,0.8566,0.8570,0.8575,0.8700,0.8711,0.8754,
0.8759,0.8761,0.8790,0.8793,0.8803,0.8814,0.8814,0.8906,0.8912,0.8932,
0.8982,0.9027,0.9067,0.9143,0.9202,0.9261,0.9280,0.9287,0.9291,0.9312,
0.9367,0.9378,0.9382,0.9445,0.9481,0.9487,0.9495,0.9498,0.9589,0.9609,
0.9619,0.9696,0.9849,0.9871,0.9875,0.9886,0.9894,0.9937,0.9978,
Overall p-value after applying KStest on 269 p-values = 0.668555
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.