RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-10_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 15.69 16.9642 0.543208
2 to 25 15.56 23.7867 0.874654
3 to 26 15.45 24.0047 0.880693
4 to 27 15.51 27.5059 0.948947
5 to 28 15.73 11.1531 0.151507
6 to 29 15.77 29.9405 0.973222
7 to 30 15.81 7.0082 0.016557
8 to 31 15.63 28.6727 0.962334
9 to 32 15.51 17.9017 0.604934
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.036938
Tough bday spacings test for dh-ranFile-2018-07-10_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 8 46 65 99 99 79 50 32 15 3 4
(O-E)^2/E 0.1 2.4 0.9 0.0 0.0 0.0 0.1 0.2 0.0 2.0 0.0
Birthday Spacings: Sum(O-E)^2/E= 5.749, p= 0.164
RESULTS OF GCD FOR dh-ranFile-2018-07-10_21:31
Euclid's algorithm:
p-value, steps to gcd: 0.116148
p-value, dist. of gcd's: 0.852613
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-10_21:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.686 0.858 0.272 0.836 0.565 0.316 0.595 0.751
Bits 8 to 15---> 0.478 0.201 0.137 0.107 0.114 0.114 0.327 0.458
Bits 16 to 23---> 0.471 0.523 0.246 0.746 0.840 0.742 0.857 0.829
Bits 24 to 31---> 0.859 0.530 0.584 0.127 0.034 0.812 0.508 0.377
KS test for the above 32 p values: 0.295
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-10_21:31,
p-values for 5 runs: 0.3008, 0.6986, 0.0029, 0.5348, 0.2086
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-10_21:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 228 211.4 1.301 1.301
r= 29 5183 5134.0 0.467 1.768
r= 30 23167 23103.0 0.177 1.945
r= 31 11422 11551.5 1.452 3.397
chi-square = 3.397 with df = 3; p-value = 0.666
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-10_21:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 215 211.4 0.061 0.061
r= 30 5118 5134.0 0.050 0.111
r= 31 23023 23103.0 0.277 0.388
r= 32 11644 11551.5 0.740 1.128
chi-square = 1.128 with df = 3; p-value = 0.230
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-10_21:31
b-rank test for bits 1 to 8, p=0.90782
b-rank test for bits 2 to 9, p=0.80444
b-rank test for bits 3 to 10, p=0.06314
b-rank test for bits 4 to 11, p=0.09022
b-rank test for bits 5 to 12, p=0.68621
b-rank test for bits 6 to 13, p=0.30175
b-rank test for bits 7 to 14, p=0.93612
b-rank test for bits 8 to 15, p=0.60329
b-rank test for bits 9 to 16, p=0.91471
b-rank test for bits 10 to 17, p=0.21344
b-rank test for bits 11 to 18, p=0.93449
b-rank test for bits 12 to 19, p=0.34787
b-rank test for bits 13 to 20, p=0.14975
b-rank test for bits 14 to 21, p=0.86306
b-rank test for bits 15 to 22, p=0.14350
b-rank test for bits 16 to 23, p=0.59609
b-rank test for bits 17 to 24, p=0.67675
b-rank test for bits 18 to 25, p=0.95397
b-rank test for bits 19 to 26, p=0.46814
b-rank test for bits 20 to 27, p=0.33721
b-rank test for bits 21 to 28, p=0.45842
b-rank test for bits 22 to 29, p=0.12526
b-rank test for bits 23 to 30, p=0.70431
b-rank test for bits 24 to 31, p=0.54794
b-rank test for bits 25 to 32, p=0.43748
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 = 0.848386
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-10_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 142311 0.94 0.826001
2 142364 1.06 0.855953
3 141744 -0.39 0.349643
4 141616 -0.69 0.246561
5 141402 -1.19 0.117939
6 141912 0.01 0.502489
7 142425 1.20 0.885867
8 141493 -0.97 0.165343
9 141964 0.13 0.550820
10 141811 -0.23 0.409146
11 141476 -1.01 0.155661
12 142456 1.28 0.899246
13 141706 -0.48 0.317369
14 141999 0.21 0.582975
15 142334 0.99 0.839455
16 142176 0.62 0.733378
17 142037 0.30 0.617261
18 141329 -1.36 0.087564
19 141779 -0.30 0.380370
20 141674 -0.55 0.291216
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-10_21:31
Bits used No. missing words z-score p-value
23 to 32 142100 0.6575 0.744565
22 to 31 142113 0.7023 0.758757
21 to 30 142016 0.3678 0.643499
20 to 29 141955 0.1575 0.562568
19 to 28 142092 0.6299 0.735619
18 to 27 141612 -1.0253 0.152617
17 to 26 141696 -0.7356 0.230981
16 to 25 141702 -0.7149 0.237326
15 to 24 141861 -0.1667 0.433821
14 to 23 141917 0.0264 0.510550
13 to 22 142111 0.6954 0.756602
12 to 21 141886 -0.0804 0.467940
11 to 20 142121 0.7299 0.767273
10 to 19 141857 -0.1804 0.428400
9 to 18 141964 0.1885 0.574764
8 to 17 141688 -0.7632 0.222670
7 to 16 141970 0.2092 0.582857
6 to 15 141974 0.2230 0.588232
5 to 14 141381 -1.8218 0.034241
4 to 13 142055 0.5023 0.692275
3 to 12 141863 -0.1598 0.436536
2 to 11 141927 0.0609 0.524293
1 to 10 141961 0.1782 0.570706
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-10_21:31
Bits used No. missing words z-score p-value
28 to 32 142370 1.5616 0.940808
27 to 31 141490 -1.4215 0.077592
26 to 30 141595 -1.0655 0.143319
25 to 29 142020 0.3752 0.646227
24 to 28 141641 -0.9096 0.181519
23 to 27 142002 0.3141 0.623291
22 to 26 141664 -0.8316 0.202810
21 to 25 141980 0.2396 0.594664
20 to 24 141736 -0.5876 0.278414
19 to 23 141670 -0.8113 0.208600
18 to 22 142266 1.2091 0.886678
17 to 21 142199 0.9819 0.836933
16 to 20 141555 -1.2011 0.114853
15 to 19 141836 -0.2486 0.401844
14 to 18 142000 0.3074 0.620714
13 to 17 142010 0.3413 0.633544
12 to 16 141642 -0.9062 0.182414
11 to 15 141950 0.1379 0.554826
10 to 14 141603 -1.0384 0.149540
9 to 13 141960 0.1718 0.568188
8 to 12 141650 -0.8791 0.189678
7 to 11 141977 0.2294 0.590717
6 to 10 141498 -1.3943 0.081608
5 to 9 142561 2.2091 0.986414
4 to 8 141813 -0.3265 0.372007
3 to 7 141791 -0.4011 0.344166
2 to 6 141564 -1.1706 0.120878
1 to 5 142343 1.4701 0.929228
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-10_21:31
Bits used No. missing words z-score p-value
31 to 32 141526 -1.1308 0.129077
30 to 31 142499 1.7394 0.959021
29 to 30 141923 0.0403 0.516083
28 to 29 141789 -0.3550 0.361311
27 to 28 141595 -0.9272 0.176904
26 to 27 141959 0.1465 0.558244
25 to 26 141792 -0.3461 0.364632
24 to 25 141342 -1.6735 0.047111
23 to 24 141437 -1.3933 0.081764
22 to 23 141418 -1.4494 0.073620
21 to 22 142172 0.7748 0.780782
20 to 21 142290 1.1229 0.869264
19 to 20 141819 -0.2665 0.394942
18 to 19 142101 0.5654 0.714099
17 to 18 141751 -0.4671 0.320232
16 to 17 142382 1.3943 0.918388
15 to 16 142158 0.7335 0.768385
14 to 15 141852 -0.1691 0.432853
13 to 14 141957 0.1406 0.555915
12 to 13 142106 0.5801 0.719092
11 to 12 141650 -0.7650 0.222140
10 to 11 141742 -0.4936 0.310795
9 to 10 142195 0.8427 0.800298
8 to 9 141905 -0.0128 0.494905
7 to 8 142189 0.8250 0.795310
6 to 7 141792 -0.3461 0.364632
5 to 6 141968 0.1731 0.568701
4 to 5 141864 -0.1337 0.446813
3 to 4 141661 -0.7325 0.231921
2 to 3 141948 0.1141 0.545409
1 to 2 142283 1.1023 0.864828
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-10_21:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2483.55 -0.233 0.407998
Test results for specific bytes for dh-ranFile-2018-07-10_21:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2540.03 0.566 0.714354
2 to 9 2537.55 0.531 0.702296
3 to 10 2579.52 1.125 0.869630
4 to 11 2457.41 -0.602 0.273469
5 to 12 2455.91 -0.623 0.266486
6 to 13 2530.12 0.426 0.664938
7 to 14 2514.43 0.204 0.580851
8 to 15 2407.43 -1.309 0.095240
9 to 16 2610.22 1.559 0.940476
10 to 17 2485.61 -0.204 0.419365
11 to 18 2370.98 -1.825 0.034028
12 to 19 2502.61 0.037 0.514728
13 to 20 2519.75 0.279 0.609981
14 to 21 2458.49 -0.587 0.278586
15 to 22 2604.36 1.476 0.930017
16 to 23 2508.11 0.115 0.545662
17 to 24 2413.13 -1.228 0.109632
18 to 25 2459.56 -0.572 0.283689
19 to 26 2573.77 1.043 0.851594
20 to 27 2591.93 1.300 0.903215
21 to 28 2436.13 -0.903 0.183184
22 to 29 2588.08 1.246 0.893559
23 to 30 2550.64 0.716 0.763073
24 to 31 2358.64 -1.999 0.022794
25 to 32 2538.76 0.548 0.708209
CDPARK for dh-ranFile-2018-07-10_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
3525 0.0913 0.536383
3560 1.6895 0.954438
3527 0.1826 0.572463
3523 0.0000 0.500000
3531 0.3653 0.642555
3527 0.1826 0.572463
3517 -0.2740 0.392053
3537 0.6393 0.738676
3544 0.9589 0.831196
3508 -0.6849 0.246694
Square side=100, avg. no. parked=3529.90 sample std.=13.75
p-value of the KSTEST for those 10 p-values: 0.305265
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-10_21:31
0.2265,0.7491,0.9892,0.1966,0.8967,0.9080,0.7302,0.4855,0.0407,0.6481,
The KS test for those 10 p-values: 0.469592
The 3DSPHERES test for dh-ranFile-2018-07-10_21:31
sample no r^3 equiv. uni.
1 8.926 0.257362
2 13.367 0.359529
3 37.650 0.714928
4 5.822 0.176410
5 9.586 0.273505
6 22.859 0.533257
7 69.691 0.902025
8 7.037 0.209099
9 17.248 0.437250
10 61.706 0.872145
11 1.369 0.044612
12 15.230 0.398104
13 33.117 0.668422
14 2.448 0.078354
15 5.180 0.158587
16 27.432 0.599248
17 6.243 0.187866
18 9.796 0.278571
19 1.997 0.064385
20 15.280 0.399111
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.101866
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-10_21:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -0.3 0.3 0.3 0.6 -2.0
-0.5 1.2 -0.8 -1.2 0.9 0.8
-0.6 0.3 -0.7 -1.1 0.1 -0.0
1.3 0.3 0.4 -0.8 0.7 -0.3
0.3 -0.4 -0.8 -0.8 0.4 3.0
-1.2 -0.7 0.2 -1.2 3.3 0.4
-0.5 1.1 0.5 1.0 0.1 0.0
1.8
Chi-square with 42 degrees of freedom:45.895306
z-score=0.425013, p-value=0.686097
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-10_21:31
Test no p-value
1 0.373360
2 0.014323
3 0.000333
4 0.486346
5 0.067027
6 0.109722
7 0.180240
8 0.042078
9 0.135771
10 0.688823
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000562
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-10_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 66698 0.01 66584 0.10
3 25000.00 25129 0.67 24915 0.29
4 6666.67 6591 0.86 6798 2.59
5 1388.89 1318 3.62 1411 0.35
6 238.10 223 0.96 257 1.50
7 34.72 36 0.05 30 0.64
8 4.96 4 0.19 4 0.19
p=0.61460 p=0.53756
Number of rngs required: 687590, p-value: 0.173
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-10_21:31
No. of wins: Observed Expected
98735 98585.9
z-score= 0.667, pvalue=0.74763
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66654 66666.7 0.002 0.002
2 37526 37654.3 0.437 0.440
3 27198 26954.7 2.195 2.635
4 19369 19313.5 0.160 2.795
5 13841 13851.4 0.008 2.803
6 9771 9943.5 2.994 5.797
7 7070 7145.0 0.788 6.585
8 5200 5139.1 0.722 7.307
9 3681 3699.9 0.096 7.403
10 2653 2666.3 0.066 7.469
11 1951 1923.3 0.398 7.868
12 1337 1388.7 1.928 9.795
13 1040 1003.7 1.312 11.107
14 709 726.1 0.405 11.512
15 567 525.8 3.222 14.734
16 368 381.2 0.454 15.188
17 270 276.5 0.155 15.342
18 206 200.8 0.133 15.475
19 160 146.0 1.346 16.821
20 116 106.2 0.901 17.722
21 313 287.1 2.334 20.056
Chisq= 20.06 for 20 degrees of freedom, p= 0.54559
SUMMARY of craptest
p-value for no. of wins: 0.747629
p-value for throws/game: 0.545589
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-10_21:31
No. of wins: Observed Expected
98619 98585.9
z-score= 0.148, pvalue=0.55892
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67091 66666.7 2.701 2.701
2 37597 37654.3 0.087 2.788
3 27018 26954.7 0.148 2.937
4 19479 19313.5 1.419 4.355
5 13677 13851.4 2.196 6.552
6 10002 9943.5 0.344 6.895
7 7056 7145.0 1.109 8.005
8 5020 5139.1 2.759 10.764
9 3690 3699.9 0.026 10.790
10 2553 2666.3 4.814 15.604
11 1924 1923.3 0.000 15.604
12 1348 1388.7 1.195 16.800
13 993 1003.7 0.114 16.914
14 727 726.1 0.001 16.915
15 477 525.8 4.536 21.451
16 360 381.2 1.174 22.624
17 259 276.5 1.112 23.737
18 196 200.8 0.116 23.853
19 143 146.0 0.061 23.914
20 105 106.2 0.014 23.928
21 285 287.1 0.016 23.943
Chisq= 23.94 for 20 degrees of freedom, p= 0.75512
SUMMARY of craptest
p-value for no. of wins: 0.558918
p-value for throws/game: 0.755122
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0003,0.0006,0.0029,0.0143,0.0166,0.0228,0.0340,0.0341,0.0342,0.0369,
0.0407,0.0421,0.0446,0.0471,0.0631,0.0644,0.0670,0.0736,0.0776,0.0784,
0.0816,0.0818,0.0876,0.0902,0.0952,0.1019,0.1070,0.1096,0.1097,0.1142,
0.1142,0.1149,0.1161,0.1179,0.1209,0.1253,0.1270,0.1291,0.1358,0.1374,
0.1433,0.1435,0.1495,0.1498,0.1515,0.1526,0.1557,0.1586,0.1641,0.1653,
0.1733,0.1764,0.1769,0.1802,0.1815,0.1824,0.1832,0.1879,0.1897,0.1966,
0.2012,0.2028,0.2086,0.2086,0.2091,0.2134,0.2221,0.2227,0.2265,0.2298,
0.2310,0.2319,0.2373,0.2464,0.2466,0.2467,0.2574,0.2665,0.2721,0.2735,
0.2735,0.2784,0.2786,0.2786,0.2837,0.2912,0.2951,0.3008,0.3018,0.3053,
0.3108,0.3163,0.3174,0.3202,0.3268,0.3372,0.3442,0.3479,0.3496,0.3595,
0.3613,0.3646,0.3646,0.3720,0.3734,0.3765,0.3804,0.3921,0.3949,0.3981,
0.3991,0.4018,0.4080,0.4091,0.4194,0.4284,0.4329,0.4338,0.4365,0.4373,
0.4375,0.4468,0.4578,0.4584,0.4679,0.4681,0.4696,0.4707,0.4779,0.4855,
0.4863,0.4949,0.5000,0.5025,0.5077,0.5106,0.5147,0.5161,0.5230,0.5243,
0.5300,0.5333,0.5348,0.5364,0.5376,0.5432,0.5454,0.5456,0.5457,0.5479,
0.5508,0.5548,0.5559,0.5582,0.5589,0.5626,0.5653,0.5682,0.5687,0.5707,
0.5725,0.5725,0.5748,0.5809,0.5829,0.5830,0.5842,0.5882,0.5907,0.5946,
0.5947,0.5961,0.5992,0.6033,0.6049,0.6100,0.6146,0.6173,0.6207,0.6233,
0.6335,0.6426,0.6435,0.6462,0.6481,0.6649,0.6657,0.6684,0.6768,0.6856,
0.6861,0.6862,0.6888,0.6923,0.6986,0.7023,0.7043,0.7082,0.7141,0.7144,
0.7149,0.7191,0.7302,0.7334,0.7356,0.7387,0.7420,0.7446,0.7463,0.7476,
0.7491,0.7509,0.7551,0.7566,0.7588,0.7631,0.7673,0.7684,0.7808,0.7953,
0.8003,0.8044,0.8119,0.8260,0.8293,0.8312,0.8361,0.8369,0.8395,0.8400,
0.8484,0.8516,0.8526,0.8560,0.8568,0.8577,0.8586,0.8631,0.8648,0.8693,
0.8696,0.8721,0.8747,0.8807,0.8859,0.8867,0.8936,0.8967,0.8992,0.9020,
0.9032,0.9078,0.9080,0.9147,0.9184,0.9292,0.9300,0.9345,0.9361,0.9405,
0.9408,0.9489,0.9540,0.9544,0.9590,0.9623,0.9732,0.9864,0.9892,
Overall p-value after applying KStest on 269 p-values = 0.413819
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.