RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-09_09:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.59 19.8792 0.719547
2 to 25 15.94 7.4420 0.022929
3 to 26 15.88 13.1630 0.274792
4 to 27 16.02 24.0788 0.882690
5 to 28 15.98 27.7725 0.952332
6 to 29 15.68 20.8595 0.767361
7 to 30 15.45 16.0508 0.479762
8 to 31 15.17 42.5596 0.999443
9 to 32 15.40 33.0154 0.988779
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.020609
Tough bday spacings test for dh-ranFile-2018-07-09_09:31: 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 4 40 78 113 92 83 43 24 20 3 0
(O-E)^2/E 2.9 0.3 0.3 2.4 0.3 0.3 1.6 1.1 1.8 2.0 4.1
Birthday Spacings: Sum(O-E)^2/E= 17.062, p= 0.927
RESULTS OF GCD FOR dh-ranFile-2018-07-09_09:31
Euclid's algorithm:
p-value, steps to gcd: 0.299014
p-value, dist. of gcd's: 0.468342
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-09_09:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.472 0.441 0.122 0.984 0.092 0.876 0.807 0.245
Bits 8 to 15---> 0.690 0.346 0.351 0.833 0.728 0.290 0.946 0.074
Bits 16 to 23---> 0.657 0.945 0.047 0.605 0.261 0.750 0.483 0.482
Bits 24 to 31---> 0.522 0.012 0.680 0.571 0.671 0.132 0.859 0.754
KS test for the above 32 p values: 0.033
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-09_09:31,
p-values for 5 runs: 0.7937, 0.8177, 0.6025, 0.3272, 0.4432
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-09_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 222 211.4 0.530 0.530
r= 29 5010 5134.0 2.995 3.525
r= 30 23298 23103.0 1.645 5.170
r= 31 11470 11551.5 0.575 5.746
chi-square = 5.746 with df = 3; p-value = 0.875
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-09_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 240 211.4 3.864 3.864
r= 30 5100 5134.0 0.225 4.089
r= 31 23227 23103.0 0.665 4.754
r= 32 11433 11551.5 1.216 5.970
chi-square = 5.970 with df = 3; p-value = 0.887
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-09_09:31
b-rank test for bits 1 to 8, p=0.26098
b-rank test for bits 2 to 9, p=0.80792
b-rank test for bits 3 to 10, p=0.41052
b-rank test for bits 4 to 11, p=0.80877
b-rank test for bits 5 to 12, p=0.10747
b-rank test for bits 6 to 13, p=0.88302
b-rank test for bits 7 to 14, p=0.96624
b-rank test for bits 8 to 15, p=0.74079
b-rank test for bits 9 to 16, p=0.64297
b-rank test for bits 10 to 17, p=0.53827
b-rank test for bits 11 to 18, p=0.23977
b-rank test for bits 12 to 19, p=0.27089
b-rank test for bits 13 to 20, p=0.15582
b-rank test for bits 14 to 21, p=0.46978
b-rank test for bits 15 to 22, p=0.39678
b-rank test for bits 16 to 23, p=0.35094
b-rank test for bits 17 to 24, p=0.59248
b-rank test for bits 18 to 25, p=0.28078
b-rank test for bits 19 to 26, p=0.02377
b-rank test for bits 20 to 27, p=0.82211
b-rank test for bits 21 to 28, p=0.61852
b-rank test for bits 22 to 29, p=0.81247
b-rank test for bits 23 to 30, p=0.46553
b-rank test for bits 24 to 31, p=0.27196
b-rank test for bits 25 to 32, p=0.41427
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 = 0.861757
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-09_09:31
(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 142137 0.53 0.702616
2 142216 0.72 0.763164
3 142154 0.57 0.716223
4 141829 -0.19 0.425561
5 141542 -0.86 0.195378
6 141606 -0.71 0.239251
7 141879 -0.07 0.471753
8 141620 -0.68 0.249519
9 141939 0.07 0.527634
10 141171 -1.73 0.042257
11 142218 0.72 0.764604
12 142669 1.77 0.962045
13 142408 1.17 0.878014
14 141564 -0.81 0.209878
15 141270 -1.49 0.067619
16 141071 -1.96 0.025073
17 142393 1.13 0.870777
18 141327 -1.36 0.086823
19 141244 -1.55 0.060031
20 142070 0.38 0.646317
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-09_09:31
Bits used No. missing words z-score p-value
23 to 32 141798 -0.3839 0.350528
22 to 31 141754 -0.5356 0.296110
21 to 30 141472 -1.5080 0.065773
20 to 29 141828 -0.2804 0.389567
19 to 28 141987 0.2678 0.605584
18 to 27 141707 -0.6977 0.242686
17 to 26 141492 -1.4391 0.075066
16 to 25 141459 -1.5529 0.060228
15 to 24 142047 0.4747 0.682508
14 to 23 142463 1.9092 0.971882
13 to 22 142026 0.4023 0.656272
12 to 21 142321 1.4196 0.922131
11 to 20 142093 0.6333 0.736746
10 to 19 141596 -1.0804 0.139971
9 to 18 141586 -1.1149 0.132440
8 to 17 142275 1.2609 0.896333
7 to 16 142315 1.3989 0.919073
6 to 15 141898 -0.0391 0.484418
5 to 14 142016 0.3678 0.643499
4 to 13 142148 0.8230 0.794746
3 to 12 142283 1.2885 0.901217
2 to 11 141911 0.0058 0.502297
1 to 10 142081 0.5920 0.723063
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-09_09:31
Bits used No. missing words z-score p-value
28 to 32 141920 0.0362 0.514426
27 to 31 141554 -1.2045 0.114197
26 to 30 142029 0.4057 0.657504
25 to 29 141624 -0.9672 0.166717
24 to 28 141836 -0.2486 0.401844
23 to 27 141602 -1.0418 0.148753
22 to 26 142296 1.3107 0.905028
21 to 25 141725 -0.6248 0.266036
20 to 24 141994 0.2870 0.612950
19 to 23 142007 0.3311 0.629710
18 to 22 141978 0.2328 0.592034
17 to 21 141496 -1.4011 0.080589
16 to 20 142031 0.4124 0.659992
15 to 19 142193 0.9616 0.831873
14 to 18 141689 -0.7469 0.227568
13 to 17 142019 0.3718 0.644965
12 to 16 142481 1.9379 0.973680
11 to 15 142336 1.4463 0.925959
10 to 14 141938 0.0972 0.538711
9 to 13 141757 -0.5164 0.302797
8 to 12 142122 0.7209 0.764519
7 to 11 141649 -0.8825 0.188760
6 to 10 141719 -0.6452 0.259403
5 to 9 142103 0.6565 0.744252
4 to 8 142274 1.2362 0.891802
3 to 7 141830 -0.2689 0.393998
2 to 6 141837 -0.2452 0.403156
1 to 5 141954 0.1514 0.560179
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-09_09:31
Bits used No. missing words z-score p-value
31 to 32 141659 -0.7384 0.230125
30 to 31 141756 -0.4523 0.325526
29 to 30 141422 -1.4376 0.075281
28 to 29 141944 0.1023 0.540729
27 to 28 141220 -2.0334 0.021005
26 to 27 142407 1.4681 0.928955
25 to 26 142078 0.4976 0.690600
24 to 25 141764 -0.4287 0.334070
23 to 24 141452 -1.3491 0.088660
22 to 23 142091 0.5359 0.703986
21 to 22 140987 -2.7207 0.003257
20 to 21 142147 0.7011 0.758377
19 to 20 142587 1.9990 0.977197
18 to 19 142176 0.7866 0.784253
17 to 18 142031 0.3589 0.640168
16 to 17 142000 0.2675 0.605444
15 to 16 141216 -2.0452 0.020417
14 to 15 141912 0.0079 0.503142
13 to 14 141851 -0.1721 0.431693
12 to 13 141748 -0.4759 0.317073
11 to 12 141663 -0.7266 0.233724
10 to 11 141817 -0.2724 0.392673
9 to 10 142547 1.8810 0.970016
8 to 9 141835 -0.2193 0.413223
7 to 8 141752 -0.4641 0.321288
6 to 7 142264 1.0462 0.852271
5 to 6 141927 0.0521 0.520785
4 to 5 141633 -0.8151 0.207498
3 to 4 141614 -0.8712 0.191828
2 to 3 141825 -0.2488 0.401773
1 to 2 141680 -0.6765 0.249365
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-09_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2549.89 0.706 0.759781
Test results for specific bytes for dh-ranFile-2018-07-09_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2519.54 0.276 0.608830
2 to 9 2389.88 -1.557 0.059691
3 to 10 2450.16 -0.705 0.240450
4 to 11 2482.33 -0.250 0.401339
5 to 12 2493.02 -0.099 0.460681
6 to 13 2564.51 0.912 0.819198
7 to 14 2527.00 0.382 0.648734
8 to 15 2584.39 1.193 0.883654
9 to 16 2621.92 1.724 0.957663
10 to 17 2497.37 -0.037 0.485150
11 to 18 2354.71 -2.055 0.019953
12 to 19 2455.07 -0.635 0.262599
13 to 20 2569.95 0.989 0.838719
14 to 21 2556.39 0.797 0.787409
15 to 22 2467.59 -0.458 0.323333
16 to 23 2453.01 -0.665 0.253165
17 to 24 2472.97 -0.382 0.351121
18 to 25 2560.02 0.849 0.802003
19 to 26 2462.49 -0.531 0.297878
20 to 27 2421.12 -1.116 0.132300
21 to 28 2425.23 -1.057 0.145175
22 to 29 2526.86 0.380 0.647967
23 to 30 2527.79 0.393 0.652828
24 to 31 2413.21 -1.227 0.109849
25 to 32 2423.64 -1.080 0.140106
CDPARK for dh-ranFile-2018-07-09_09:31: 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
3511 -0.5479 0.291865
3537 0.6393 0.738676
3533 0.4566 0.676028
3518 -0.2283 0.409702
3522 -0.0457 0.481790
3505 -0.8219 0.205562
3486 -1.6895 0.045562
3513 -0.4566 0.323972
3504 -0.8676 0.192812
3493 -1.3699 0.085365
Square side=100, avg. no. parked=3512.20 sample std.=15.34
p-value of the KSTEST for those 10 p-values: 0.157305
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-09_09:31
0.9382,0.7835,0.7676,0.2902,0.0817,0.8027,0.4500,0.0972,0.6520,0.5744,
The KS test for those 10 p-values: 0.877738
The 3DSPHERES test for dh-ranFile-2018-07-09_09:31
sample no r^3 equiv. uni.
1 62.936 0.877283
2 79.533 0.929426
3 12.514 0.341061
4 7.663 0.225414
5 1.423 0.046337
6 46.314 0.786432
7 55.615 0.843366
8 6.007 0.181447
9 4.265 0.132529
10 27.098 0.594755
11 34.217 0.680364
12 33.386 0.671383
13 81.329 0.933527
14 12.040 0.330581
15 10.047 0.284583
16 19.535 0.478556
17 0.384 0.012713
18 14.680 0.386962
19 38.975 0.727241
20 5.929 0.179317
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.978385
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-09_09:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -1.6 0.8 0.3 0.2 -1.1
0.1 1.6 -0.0 0.8 -0.8 0.3
-0.0 -1.0 -0.9 -0.6 -0.5 0.6
-0.6 -0.2 -0.5 0.6 0.6 0.8
0.8 0.4 0.8 1.2 0.4 0.6
-1.5 0.3 -1.0 -0.4 0.9 0.2
0.5 2.7 1.3 -0.7 0.9 0.0
-1.1
Chi-square with 42 degrees of freedom:32.819635
z-score=-1.001660, p-value=0.155911
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-09_09:31
Test no p-value
1 0.129657
2 0.609418
3 0.475309
4 0.410354
5 0.201790
6 0.485996
7 0.690885
8 0.160917
9 0.320380
10 0.935430
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.714878
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-09_09:31:
(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 66673 0.00 66568 0.15
3 25000.00 24939 0.15 25011 0.00
4 6666.67 6675 0.01 6743 0.87
5 1388.89 1415 0.49 1402 0.12
6 238.10 255 1.20 239 0.00
7 34.72 37 0.15 35 0.00
8 4.96 5 0.00 1 3.16
p=0.08039 p=0.36599
Number of rngs required: 689380, p-value: 0.872
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-09_09:31
No. of wins: Observed Expected
98784 98585.9
z-score= 0.886, pvalue=0.81225
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66833 66666.7 0.415 0.415
2 37566 37654.3 0.207 0.622
3 27040 26954.7 0.270 0.892
4 19090 19313.5 2.586 3.477
5 13748 13851.4 0.772 4.250
6 9830 9943.5 1.297 5.546
7 7226 7145.0 0.918 6.464
8 5200 5139.1 0.722 7.186
9 3787 3699.9 2.052 9.238
10 2703 2666.3 0.505 9.743
11 1882 1923.3 0.888 10.632
12 1441 1388.7 1.967 12.598
13 988 1003.7 0.246 12.844
14 767 726.1 2.299 15.143
15 497 525.8 1.581 16.725
16 383 381.2 0.009 16.734
17 277 276.5 0.001 16.734
18 178 200.8 2.595 19.330
19 147 146.0 0.007 19.337
20 108 106.2 0.030 19.367
21 309 287.1 1.668 21.035
Chisq= 21.03 for 20 degrees of freedom, p= 0.60492
SUMMARY of craptest
p-value for no. of wins: 0.812246
p-value for throws/game: 0.604925
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-09_09:31
No. of wins: Observed Expected
98389 98585.9
z-score=-0.880, pvalue=0.18930
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66505 66666.7 0.392 0.392
2 37578 37654.3 0.155 0.547
3 27173 26954.7 1.767 2.314
4 19283 19313.5 0.048 2.362
5 13890 13851.4 0.107 2.470
6 9978 9943.5 0.119 2.589
7 7298 7145.0 3.275 5.864
8 5110 5139.1 0.164 6.029
9 3588 3699.9 3.382 9.411
10 2707 2666.3 0.621 10.032
11 1861 1923.3 2.020 12.052
12 1357 1388.7 0.725 12.778
13 988 1003.7 0.246 13.024
14 726 726.1 0.000 13.024
15 541 525.8 0.437 13.461
16 387 381.2 0.090 13.551
17 262 276.5 0.764 14.315
18 224 200.8 2.673 16.988
19 149 146.0 0.062 17.051
20 110 106.2 0.135 17.186
21 285 287.1 0.016 17.201
Chisq= 17.20 for 20 degrees of freedom, p= 0.36012
SUMMARY of craptest
p-value for no. of wins: 0.189303
p-value for throws/game: 0.360120
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0033,0.0122,0.0127,0.0200,0.0204,0.0206,0.0210,0.0229,0.0238,0.0251,
0.0330,0.0423,0.0456,0.0463,0.0469,0.0597,0.0600,0.0602,0.0658,0.0676,
0.0737,0.0751,0.0753,0.0804,0.0806,0.0817,0.0854,0.0868,0.0887,0.0919,
0.0972,0.1075,0.1098,0.1142,0.1221,0.1297,0.1319,0.1323,0.1324,0.1325,
0.1400,0.1401,0.1452,0.1488,0.1558,0.1559,0.1573,0.1609,0.1667,0.1793,
0.1814,0.1888,0.1893,0.1918,0.1928,0.1954,0.2018,0.2056,0.2075,0.2099,
0.2254,0.2276,0.2301,0.2337,0.2393,0.2398,0.2405,0.2427,0.2454,0.2494,
0.2495,0.2532,0.2594,0.2610,0.2615,0.2626,0.2660,0.2709,0.2720,0.2748,
0.2808,0.2846,0.2902,0.2904,0.2919,0.2961,0.2979,0.2990,0.3028,0.3171,
0.3204,0.3213,0.3233,0.3240,0.3255,0.3272,0.3306,0.3341,0.3411,0.3463,
0.3505,0.3506,0.3509,0.3511,0.3601,0.3660,0.3870,0.3896,0.3927,0.3940,
0.3968,0.4013,0.4018,0.4018,0.4032,0.4097,0.4104,0.4105,0.4132,0.4143,
0.4256,0.4317,0.4406,0.4432,0.4500,0.4607,0.4655,0.4683,0.4698,0.4718,
0.4723,0.4753,0.4786,0.4798,0.4818,0.4823,0.4833,0.4844,0.4852,0.4860,
0.5023,0.5031,0.5144,0.5208,0.5221,0.5276,0.5383,0.5387,0.5407,0.5602,
0.5712,0.5744,0.5920,0.5925,0.5948,0.6025,0.6049,0.6053,0.6054,0.6056,
0.6088,0.6094,0.6130,0.6185,0.6297,0.6402,0.6430,0.6435,0.6450,0.6463,
0.6480,0.6487,0.6520,0.6528,0.6563,0.6574,0.6575,0.6600,0.6713,0.6714,
0.6760,0.6803,0.6804,0.6825,0.6900,0.6906,0.6909,0.7026,0.7040,0.7149,
0.7162,0.7195,0.7231,0.7272,0.7280,0.7367,0.7387,0.7408,0.7443,0.7499,
0.7541,0.7584,0.7598,0.7632,0.7645,0.7646,0.7674,0.7676,0.7835,0.7843,
0.7864,0.7874,0.7937,0.7947,0.8020,0.8027,0.8073,0.8079,0.8088,0.8122,
0.8125,0.8177,0.8192,0.8221,0.8319,0.8327,0.8387,0.8434,0.8523,0.8590,
0.8618,0.8708,0.8716,0.8753,0.8763,0.8773,0.8777,0.8780,0.8827,0.8830,
0.8837,0.8869,0.8918,0.8963,0.9012,0.9050,0.9191,0.9221,0.9260,0.9270,
0.9290,0.9294,0.9335,0.9354,0.9382,0.9445,0.9457,0.9523,0.9577,0.9620,
0.9662,0.9700,0.9719,0.9737,0.9772,0.9784,0.9837,0.9888,0.9994,
Overall p-value after applying KStest on 269 p-values = 0.951593
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.