RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-14_16:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.74 29.5108 0.969903
2 to 25 15.80 11.9619 0.197562
3 to 26 15.91 25.5438 0.916817
4 to 27 15.37 26.2720 0.930354
5 to 28 15.60 14.2652 0.351752
6 to 29 15.74 19.4273 0.695439
7 to 30 16.12 9.7334 0.085584
8 to 31 16.20 16.6192 0.519558
9 to 32 15.45 33.5561 0.990425
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.105200
Tough bday spacings test for dh-ranFile-2018-06-14_16:31: 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 30 79 103 97 82 52 30 10 6 3
(O-E)^2/E 0.1 1.2 0.4 0.3 0.0 0.2 0.0 0.0 1.6 0.1 0.3
Birthday Spacings: Sum(O-E)^2/E= 4.222, p= 0.063
RESULTS OF GCD FOR dh-ranFile-2018-06-14_16:31
Euclid's algorithm:
p-value, steps to gcd: 0.736559
p-value, dist. of gcd's: 0.022466
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-14_16:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.232 0.674 0.250 0.657 0.957 0.516 0.350 0.947
Bits 8 to 15---> 0.075 0.965 0.387 0.470 0.514 0.098 0.413 0.474
Bits 16 to 23---> 0.852 0.927 0.384 0.678 0.847 0.721 0.006 0.611
Bits 24 to 31---> 0.187 0.918 0.879 0.713 0.397 0.038 0.296 0.079
KS test for the above 32 p values: 0.071
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-14_16:31,
p-values for 5 runs: 0.2155, 0.0175, 0.9027, 0.4215, 0.1983
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-14_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 200 211.4 0.617 0.617
r= 29 5265 5134.0 3.342 3.959
r= 30 22996 23103.0 0.496 4.455
r= 31 11539 11551.5 0.014 4.468
chi-square = 4.468 with df = 3; p-value = 0.785
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-14_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 217 211.4 0.147 0.147
r= 30 5089 5134.0 0.395 0.542
r= 31 23045 23103.0 0.146 0.688
r= 32 11649 11551.5 0.823 1.510
chi-square = 1.510 with df = 3; p-value = 0.320
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-14_16:31
b-rank test for bits 1 to 8, p=0.65823
b-rank test for bits 2 to 9, p=0.96271
b-rank test for bits 3 to 10, p=0.39638
b-rank test for bits 4 to 11, p=0.48779
b-rank test for bits 5 to 12, p=0.64342
b-rank test for bits 6 to 13, p=0.69881
b-rank test for bits 7 to 14, p=0.13689
b-rank test for bits 8 to 15, p=0.40823
b-rank test for bits 9 to 16, p=0.26805
b-rank test for bits 10 to 17, p=0.68639
b-rank test for bits 11 to 18, p=0.60316
b-rank test for bits 12 to 19, p=0.80036
b-rank test for bits 13 to 20, p=0.29323
b-rank test for bits 14 to 21, p=0.03406
b-rank test for bits 15 to 22, p=0.40935
b-rank test for bits 16 to 23, p=0.68483
b-rank test for bits 17 to 24, p=0.91217
b-rank test for bits 18 to 25, p=0.67286
b-rank test for bits 19 to 26, p=0.08535
b-rank test for bits 20 to 27, p=0.20144
b-rank test for bits 21 to 28, p=0.34087
b-rank test for bits 22 to 29, p=0.55949
b-rank test for bits 23 to 30, p=0.27587
b-rank test for bits 24 to 31, p=0.77886
b-rank test for bits 25 to 32, p=0.35965
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 = 0.789313
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-14_16:31
(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 142495 1.37 0.914405
2 141776 -0.31 0.377703
3 142809 2.10 0.982225
4 141679 -0.54 0.295235
5 142178 0.63 0.734911
6 142080 0.40 0.654966
7 142492 1.36 0.913303
8 142370 1.08 0.859111
9 142277 0.86 0.804841
10 142484 1.34 0.910313
11 141795 -0.27 0.394686
12 142159 0.58 0.720168
13 141344 -1.32 0.093273
14 141670 -0.56 0.288019
15 141856 -0.12 0.450419
16 141716 -0.45 0.325741
17 142038 0.30 0.618152
18 142000 0.21 0.583886
19 142523 1.43 0.924187
20 142102 0.45 0.673704
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-14_16:31
Bits used No. missing words z-score p-value
23 to 32 142409 1.7230 0.957556
22 to 31 141622 -0.9908 0.160893
21 to 30 141588 -1.1080 0.133923
20 to 29 141797 -0.3873 0.349251
19 to 28 141906 -0.0115 0.495419
18 to 27 141620 -0.9977 0.159215
17 to 26 141633 -0.9529 0.170330
16 to 25 141933 0.0816 0.532526
15 to 24 141824 -0.2942 0.384287
14 to 23 141779 -0.4494 0.326567
13 to 22 142021 0.3851 0.649907
12 to 21 141573 -1.1598 0.123074
11 to 20 141902 -0.0253 0.489918
10 to 19 141959 0.1713 0.567997
9 to 18 142080 0.5885 0.721907
8 to 17 142011 0.3506 0.637051
7 to 16 142131 0.7644 0.777679
6 to 15 141674 -0.8115 0.208544
5 to 14 142327 1.4402 0.925100
4 to 13 142258 1.2023 0.885378
3 to 12 141720 -0.6529 0.256923
2 to 11 142039 0.4471 0.672612
1 to 10 142297 1.3368 0.909355
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-14_16:31
Bits used No. missing words z-score p-value
28 to 32 141950 0.1379 0.554826
27 to 31 141437 -1.6011 0.054675
26 to 30 142364 1.5413 0.938373
25 to 29 141539 -1.2554 0.104675
24 to 28 141887 -0.0757 0.469831
23 to 27 141707 -0.6859 0.246399
22 to 26 141541 -1.2486 0.105910
21 to 25 141712 -0.6689 0.251775
20 to 24 141505 -1.3706 0.085248
19 to 23 141366 -1.8418 0.032752
18 to 22 141904 -0.0181 0.492792
17 to 21 141661 -0.8418 0.199951
16 to 20 141647 -0.8893 0.186933
15 to 19 141819 -0.3062 0.379725
14 to 18 141722 -0.6350 0.262709
13 to 17 141778 -0.4452 0.328093
12 to 16 141796 -0.3842 0.350426
11 to 15 142120 0.7141 0.762428
10 to 14 141818 -0.3096 0.378435
9 to 13 142079 0.5752 0.717406
8 to 12 141848 -0.2079 0.417654
7 to 11 141820 -0.3028 0.381016
6 to 10 141492 -1.4147 0.078581
5 to 9 142398 1.6565 0.951191
4 to 8 141416 -1.6723 0.047232
3 to 7 142012 0.3480 0.636093
2 to 6 142377 1.5853 0.943553
1 to 5 142023 0.3853 0.650001
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-14_16:31
Bits used No. missing words z-score p-value
31 to 32 141812 -0.2871 0.387014
30 to 31 142224 0.9282 0.823356
29 to 30 141683 -0.6676 0.252182
28 to 29 141577 -0.9803 0.163463
27 to 28 141455 -1.3402 0.090089
26 to 27 141696 -0.6293 0.264579
25 to 26 142003 0.2763 0.608846
24 to 25 141786 -0.3638 0.358002
23 to 24 141282 -1.8505 0.032119
22 to 23 141819 -0.2665 0.394942
21 to 22 142066 0.4622 0.678014
20 to 21 142085 0.5182 0.697841
19 to 20 142023 0.3353 0.631304
18 to 19 142090 0.5329 0.702966
17 to 18 141599 -0.9154 0.179984
16 to 17 141719 -0.5614 0.287247
15 to 16 142017 0.3176 0.624610
14 to 15 142583 1.9872 0.976551
13 to 14 141644 -0.7827 0.216906
12 to 13 141640 -0.7945 0.213457
11 to 12 142297 1.1436 0.873599
10 to 11 142376 1.3766 0.915683
9 to 10 141816 -0.2753 0.391539
8 to 9 141612 -0.8771 0.190222
7 to 8 141835 -0.2193 0.413223
6 to 7 142126 0.6391 0.738636
5 to 6 141705 -0.6027 0.273340
4 to 5 142307 1.1731 0.879616
3 to 4 142281 1.0964 0.863542
2 to 3 141782 -0.3756 0.353605
1 to 2 142043 0.3943 0.653323
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-14_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2501.40 0.020 0.507895
Test results for specific bytes for dh-ranFile-2018-06-14_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2500.85 0.012 0.504811
2 to 9 2537.41 0.529 0.701593
3 to 10 2465.40 -0.489 0.312325
4 to 11 2460.61 -0.557 0.288738
5 to 12 2443.21 -0.803 0.210931
6 to 13 2402.22 -1.383 0.083359
7 to 14 2469.22 -0.435 0.331656
8 to 15 2526.83 0.379 0.647801
9 to 16 2475.27 -0.350 0.363249
10 to 17 2619.65 1.692 0.954690
11 to 18 2602.07 1.443 0.925554
12 to 19 2484.36 -0.221 0.412473
13 to 20 2468.84 -0.441 0.329710
14 to 21 2318.88 -2.561 0.005212
15 to 22 2460.88 -0.553 0.290029
16 to 23 2493.14 -0.097 0.461369
17 to 24 2465.61 -0.486 0.313349
18 to 25 2430.18 -0.987 0.161735
19 to 26 2557.67 0.816 0.792628
20 to 27 2422.59 -1.095 0.136817
21 to 28 2483.92 -0.227 0.410080
22 to 29 2515.29 0.216 0.585581
23 to 30 2405.17 -1.341 0.089951
24 to 31 2423.24 -1.086 0.138836
25 to 32 2467.33 -0.462 0.322055
CDPARK for dh-ranFile-2018-06-14_16:31: 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
3479 -2.0091 0.022262
3547 1.0959 0.863437
3503 -0.9132 0.180558
3513 -0.4566 0.323972
3505 -0.8219 0.205562
3525 0.0913 0.536383
3535 0.5479 0.708135
3525 0.0913 0.536383
3510 -0.5936 0.276387
3538 0.6849 0.753306
Square side=100, avg. no. parked=3518.00 sample std.=19.06
p-value of the KSTEST for those 10 p-values: 0.833593
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-14_16:31
0.6941,0.4836,0.5396,0.2734,0.1797,0.4875,0.5866,0.5296,0.3299,0.0864,
The KS test for those 10 p-values: 0.301388
The 3DSPHERES test for dh-ranFile-2018-06-14_16:31
sample no r^3 equiv. uni.
1 46.624 0.788626
2 107.642 0.972349
3 16.463 0.422337
4 37.211 0.710718
5 28.198 0.609347
6 42.596 0.758255
7 1.910 0.061697
8 13.911 0.371047
9 19.357 0.475455
10 42.037 0.753703
11 1.648 0.053463
12 14.620 0.385734
13 3.750 0.117492
14 26.726 0.589704
15 0.566 0.018694
16 16.986 0.432322
17 0.686 0.022599
18 123.108 0.983487
19 33.652 0.674290
20 31.538 0.650510
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.579744
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-14_16:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 -1.2 0.3 -0.7 0.6 -0.4
-0.6 1.5 2.2 -0.8 -2.3 0.2
-0.7 0.1 -1.3 0.9 0.7 0.4
-2.4 -0.4 0.4 0.1 -0.4 -0.9
2.8 1.6 0.3 1.7 0.4 -0.5
0.6 1.7 -0.9 0.7 -0.5 -0.8
-0.2 -1.0 -1.6 0.4 0.1 0.0
-0.1
Chi-square with 42 degrees of freedom:52.047686
z-score=1.096292, p-value=0.862325
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-14_16:31
Test no p-value
1 0.039304
2 0.727847
3 0.035161
4 0.284292
5 0.134943
6 0.714785
7 0.249808
8 0.050498
9 0.028790
10 0.927027
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.017340
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-14_16:31:
(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 66609 0.05 66635 0.02
3 25000.00 25073 0.21 25045 0.08
4 6666.67 6626 0.25 6653 0.03
5 1388.89 1412 0.38 1385 0.01
6 238.10 247 0.33 239 0.00
7 34.72 28 1.30 36 0.05
8 4.96 4 0.19 6 0.22
p=0.15635 p=0.00118
Number of rngs required: 687977, p-value: 0.312
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-14_16:31
No. of wins: Observed Expected
98631 98585.9
z-score= 0.202, pvalue=0.58000
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66691 66666.7 0.009 0.009
2 37603 37654.3 0.070 0.079
3 26928 26954.7 0.027 0.105
4 19244 19313.5 0.250 0.355
5 13886 13851.4 0.086 0.441
6 9966 9943.5 0.051 0.492
7 7191 7145.0 0.296 0.788
8 5178 5139.1 0.295 1.083
9 3748 3699.9 0.626 1.709
10 2686 2666.3 0.146 1.855
11 1868 1923.3 1.592 3.446
12 1364 1388.7 0.441 3.887
13 958 1003.7 2.082 5.969
14 719 726.1 0.070 6.040
15 575 525.8 4.597 10.636
16 390 381.2 0.205 10.842
17 260 276.5 0.989 11.831
18 214 200.8 0.864 12.695
19 135 146.0 0.827 13.521
20 96 106.2 0.982 14.504
21 300 287.1 0.578 15.082
Chisq= 15.08 for 20 degrees of freedom, p= 0.22829
SUMMARY of craptest
p-value for no. of wins: 0.580002
p-value for throws/game: 0.228294
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-14_16:31
No. of wins: Observed Expected
99057 98585.9
z-score= 2.107, pvalue=0.98245
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66690 66666.7 0.008 0.008
2 37570 37654.3 0.189 0.197
3 27104 26954.7 0.827 1.024
4 19387 19313.5 0.280 1.304
5 14092 13851.4 4.179 5.482
6 9868 9943.5 0.574 6.056
7 6999 7145.0 2.984 9.040
8 5176 5139.1 0.265 9.306
9 3658 3699.9 0.474 9.779
10 2666 2666.3 0.000 9.780
11 1842 1923.3 3.439 13.219
12 1382 1388.7 0.033 13.251
13 985 1003.7 0.349 13.600
14 721 726.1 0.036 13.637
15 508 525.8 0.605 14.242
16 370 381.2 0.326 14.568
17 267 276.5 0.329 14.897
18 195 200.8 0.169 15.066
19 154 146.0 0.440 15.506
20 104 106.2 0.046 15.552
21 262 287.1 2.197 17.749
Chisq= 17.75 for 20 degrees of freedom, p= 0.39607
SUMMARY of craptest
p-value for no. of wins: 0.982451
p-value for throws/game: 0.396074
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0012,0.0052,0.0057,0.0173,0.0175,0.0187,0.0223,0.0225,0.0226,0.0288,
0.0321,0.0328,0.0341,0.0352,0.0377,0.0393,0.0472,0.0505,0.0535,0.0547,
0.0617,0.0632,0.0715,0.0747,0.0786,0.0790,0.0834,0.0852,0.0853,0.0856,
0.0864,0.0900,0.0901,0.0933,0.0979,0.1047,0.1052,0.1059,0.1175,0.1231,
0.1339,0.1349,0.1368,0.1369,0.1388,0.1563,0.1592,0.1609,0.1617,0.1635,
0.1703,0.1797,0.1800,0.1806,0.1869,0.1873,0.1902,0.1976,0.1983,0.2000,
0.2014,0.2056,0.2085,0.2109,0.2135,0.2155,0.2169,0.2283,0.2325,0.2464,
0.2498,0.2501,0.2518,0.2522,0.2569,0.2627,0.2646,0.2680,0.2733,0.2734,
0.2759,0.2764,0.2843,0.2872,0.2880,0.2887,0.2900,0.2932,0.2952,0.2956,
0.3014,0.3117,0.3123,0.3133,0.3201,0.3221,0.3240,0.3257,0.3266,0.3281,
0.3297,0.3299,0.3317,0.3409,0.3493,0.3498,0.3504,0.3518,0.3536,0.3580,
0.3597,0.3632,0.3710,0.3777,0.3784,0.3797,0.3810,0.3843,0.3843,0.3857,
0.3869,0.3870,0.3915,0.3947,0.3949,0.3961,0.3964,0.3969,0.4082,0.4094,
0.4101,0.4125,0.4127,0.4132,0.4177,0.4215,0.4223,0.4323,0.4504,0.4614,
0.4698,0.4700,0.4735,0.4755,0.4836,0.4875,0.4878,0.4899,0.4928,0.4954,
0.5048,0.5079,0.5142,0.5160,0.5196,0.5296,0.5325,0.5364,0.5364,0.5396,
0.5548,0.5595,0.5680,0.5797,0.5800,0.5839,0.5856,0.5866,0.5897,0.6032,
0.6088,0.6093,0.6107,0.6182,0.6246,0.6313,0.6361,0.6371,0.6434,0.6478,
0.6499,0.6500,0.6505,0.6533,0.6550,0.6567,0.6582,0.6726,0.6729,0.6735,
0.6737,0.6743,0.6780,0.6782,0.6848,0.6864,0.6941,0.6954,0.6978,0.6988,
0.7016,0.7030,0.7081,0.7107,0.7127,0.7148,0.7174,0.7202,0.7211,0.7219,
0.7278,0.7349,0.7366,0.7386,0.7533,0.7537,0.7583,0.7624,0.7777,0.7789,
0.7849,0.7886,0.7893,0.7926,0.8004,0.8048,0.8234,0.8336,0.8466,0.8515,
0.8591,0.8623,0.8634,0.8635,0.8736,0.8789,0.8796,0.8854,0.9027,0.9094,
0.9103,0.9122,0.9133,0.9144,0.9157,0.9168,0.9182,0.9242,0.9251,0.9256,
0.9270,0.9272,0.9304,0.9384,0.9436,0.9473,0.9512,0.9547,0.9567,0.9576,
0.9627,0.9651,0.9699,0.9723,0.9766,0.9822,0.9825,0.9835,0.9904,
Overall p-value after applying KStest on 269 p-values = 0.119632
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.