RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-17_14:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.93 10.1520 0.102884
2 to 25 15.59 29.3062 0.968195
3 to 26 15.72 15.6868 0.453866
4 to 27 15.81 16.9882 0.544837
5 to 28 15.69 15.7374 0.457479
6 to 29 15.82 14.2855 0.353203
7 to 30 15.85 16.4345 0.506735
8 to 31 15.84 14.1462 0.343275
9 to 32 15.79 14.3850 0.360312
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.366787
Tough bday spacings test for dh-ranFile-2018-06-17_14:31: 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 10 50 58 91 104 74 52 29 18 7 7
(O-E)^2/E 0.1 4.9 3.2 0.5 0.4 0.2 0.0 0.0 0.7 0.0 2.1
Birthday Spacings: Sum(O-E)^2/E= 12.033, p= 0.717
RESULTS OF GCD FOR dh-ranFile-2018-06-17_14:31
Euclid's algorithm:
p-value, steps to gcd: 0.393015
p-value, dist. of gcd's: 0.908980
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-17_14:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.945 0.546 0.447 0.492 0.263 0.976 0.039 0.887
Bits 8 to 15---> 0.572 0.401 0.981 0.332 0.682 0.415 0.289 0.413
Bits 16 to 23---> 0.218 0.034 0.393 0.518 0.540 0.176 0.909 0.090
Bits 24 to 31---> 0.466 0.360 0.865 0.480 0.217 0.014 0.958 0.357
KS test for the above 32 p values: 0.550
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-17_14:31,
p-values for 5 runs: 0.7486, 0.7447, 0.5341, 0.8192, 0.3334
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-17_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 197 211.4 0.983 0.983
r= 29 5080 5134.0 0.568 1.551
r= 30 23242 23103.0 0.836 2.387
r= 31 11481 11551.5 0.431 2.818
chi-square = 2.818 with df = 3; p-value = 0.579
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-17_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 203 211.4 0.335 0.335
r= 30 5093 5134.0 0.328 0.663
r= 31 23121 23103.0 0.014 0.677
r= 32 11583 11551.5 0.086 0.762
chi-square = 0.762 with df = 3; p-value = 0.142
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-17_14:31
b-rank test for bits 1 to 8, p=0.79421
b-rank test for bits 2 to 9, p=0.45577
b-rank test for bits 3 to 10, p=0.01722
b-rank test for bits 4 to 11, p=0.84160
b-rank test for bits 5 to 12, p=0.14134
b-rank test for bits 6 to 13, p=0.82304
b-rank test for bits 7 to 14, p=0.76361
b-rank test for bits 8 to 15, p=0.49723
b-rank test for bits 9 to 16, p=0.91183
b-rank test for bits 10 to 17, p=0.24343
b-rank test for bits 11 to 18, p=0.44505
b-rank test for bits 12 to 19, p=0.84974
b-rank test for bits 13 to 20, p=0.15388
b-rank test for bits 14 to 21, p=0.90487
b-rank test for bits 15 to 22, p=0.62694
b-rank test for bits 16 to 23, p=0.21821
b-rank test for bits 17 to 24, p=0.67539
b-rank test for bits 18 to 25, p=0.89261
b-rank test for bits 19 to 26, p=0.39195
b-rank test for bits 20 to 27, p=0.91379
b-rank test for bits 21 to 28, p=0.74949
b-rank test for bits 22 to 29, p=0.83183
b-rank test for bits 23 to 30, p=0.72526
b-rank test for bits 24 to 31, p=0.75507
b-rank test for bits 25 to 32, p=0.12508
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 = 0.116043
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-17_14:31
(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 140876 -2.41 0.007882
2 142165 0.60 0.724866
3 142103 0.45 0.674546
4 141886 -0.05 0.478265
5 141426 -1.13 0.129391
6 142412 1.17 0.879895
7 142050 0.33 0.628797
8 141788 -0.28 0.388404
9 141687 -0.52 0.301719
10 141753 -0.37 0.357460
11 141835 -0.17 0.431063
12 141496 -0.97 0.167091
13 142089 0.42 0.662681
14 141874 -0.08 0.467106
15 141778 -0.31 0.379480
16 142079 0.40 0.654104
17 141870 -0.09 0.463392
18 142141 0.54 0.705844
19 142128 0.51 0.695293
20 142398 1.14 0.873222
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-17_14:31
Bits used No. missing words z-score p-value
23 to 32 141743 -0.5736 0.283136
22 to 31 142166 0.8851 0.811940
21 to 30 142133 0.7713 0.779728
20 to 29 141972 0.2161 0.585547
19 to 28 142198 0.9954 0.840233
18 to 27 141885 -0.0839 0.466569
17 to 26 141517 -1.3529 0.088050
16 to 25 142135 0.7782 0.781766
15 to 24 141772 -0.4736 0.317910
14 to 23 141855 -0.1873 0.425695
13 to 22 142191 0.9713 0.834295
12 to 21 141807 -0.3529 0.362096
11 to 20 141724 -0.6391 0.261389
10 to 19 141825 -0.2908 0.385605
9 to 18 142109 0.6885 0.754436
8 to 17 142051 0.4885 0.687408
7 to 16 141703 -0.7115 0.238393
6 to 15 142407 1.7161 0.956928
5 to 14 141842 -0.2322 0.408202
4 to 13 142265 1.2264 0.889985
3 to 12 142257 1.1989 0.884709
2 to 11 142092 0.6299 0.735619
1 to 10 142098 0.6506 0.742343
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-17_14:31
Bits used No. missing words z-score p-value
28 to 32 141493 -1.4113 0.079080
27 to 31 142399 1.6599 0.951533
26 to 30 142449 1.8294 0.966329
25 to 29 142342 1.4667 0.928768
24 to 28 141979 0.2362 0.593349
23 to 27 141697 -0.7198 0.235836
22 to 26 142043 0.4531 0.674768
21 to 25 141861 -0.1638 0.434932
20 to 24 141761 -0.5028 0.307548
19 to 23 141659 -0.8486 0.198059
18 to 22 141641 -0.9096 0.181519
17 to 21 141861 -0.1638 0.434932
16 to 20 141757 -0.5164 0.302797
15 to 19 141984 0.2531 0.599912
14 to 18 142001 0.3107 0.622003
13 to 17 142049 0.4735 0.682057
12 to 16 141720 -0.6418 0.260503
11 to 15 141797 -0.3808 0.351683
10 to 14 142308 1.3514 0.911720
9 to 13 142179 0.9141 0.819677
8 to 12 141989 0.2701 0.606446
7 to 11 141638 -0.9198 0.178848
6 to 10 142332 1.4328 0.924040
5 to 9 142390 1.6294 0.948385
4 to 8 142240 1.1209 0.868838
3 to 7 141870 -0.1333 0.446969
2 to 6 141741 -0.5706 0.284132
1 to 5 142542 2.1446 0.984009
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-17_14:31
Bits used No. missing words z-score p-value
31 to 32 141784 -0.3697 0.355801
30 to 31 142232 0.9518 0.829408
29 to 30 141518 -1.1544 0.124175
28 to 29 141739 -0.5024 0.307676
27 to 28 141686 -0.6588 0.255015
26 to 27 141757 -0.4494 0.326589
25 to 26 142451 1.5978 0.944961
24 to 25 142604 2.0492 0.979777
23 to 24 142293 1.1318 0.871134
22 to 23 142069 0.4710 0.681181
21 to 22 141633 -0.8151 0.207498
20 to 21 141644 -0.7827 0.216906
19 to 20 141837 -0.2134 0.415522
18 to 19 141768 -0.4169 0.338375
17 to 18 141757 -0.4494 0.326589
16 to 17 141758 -0.4464 0.327654
15 to 16 142020 0.3265 0.627962
14 to 15 141706 -0.5998 0.274322
13 to 14 142359 1.3265 0.907656
12 to 13 141964 0.1613 0.564059
11 to 12 141735 -0.5142 0.303539
10 to 11 141980 0.2085 0.582568
9 to 10 141994 0.2498 0.598615
8 to 9 142087 0.5241 0.699896
7 to 8 141810 -0.2930 0.384758
6 to 7 142575 1.9636 0.975213
5 to 6 142188 0.8220 0.794472
4 to 5 142112 0.5978 0.725029
3 to 4 141842 -0.1986 0.421283
2 to 3 142453 1.6037 0.945615
1 to 2 141217 -2.0423 0.020562
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-17_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2616.74 1.651 0.950621
Test results for specific bytes for dh-ranFile-2018-06-17_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2590.57 1.281 0.899884
2 to 9 2492.52 -0.106 0.457877
3 to 10 2522.51 0.318 0.624899
4 to 11 2554.15 0.766 0.778089
5 to 12 2471.01 -0.410 0.340927
6 to 13 2529.62 0.419 0.662357
7 to 14 2519.71 0.279 0.609765
8 to 15 2432.49 -0.955 0.169842
9 to 16 2476.94 -0.326 0.372147
10 to 17 2444.79 -0.781 0.217456
11 to 18 2398.84 -1.431 0.076268
12 to 19 2450.16 -0.705 0.240451
13 to 20 2618.22 1.672 0.952725
14 to 21 2469.39 -0.433 0.332533
15 to 22 2596.73 1.368 0.914338
16 to 23 2401.61 -1.391 0.082042
17 to 24 2511.11 0.157 0.562438
18 to 25 2481.10 -0.267 0.394602
19 to 26 2536.96 0.523 0.699429
20 to 27 2570.98 1.004 0.842270
21 to 28 2424.45 -1.068 0.142674
22 to 29 2439.60 -0.854 0.196505
23 to 30 2492.03 -0.113 0.455137
24 to 31 2510.43 0.148 0.558646
25 to 32 2551.58 0.730 0.767156
CDPARK for dh-ranFile-2018-06-17_14:31: 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
3532 0.4110 0.659449
3551 1.2785 0.899470
3517 -0.2740 0.392053
3557 1.5525 0.939730
3496 -1.2329 0.108811
3535 0.5479 0.708135
3547 1.0959 0.863437
3507 -0.7306 0.232514
3497 -1.1872 0.117571
3565 1.9178 0.972432
Square side=100, avg. no. parked=3530.40 sample std.=23.78
p-value of the KSTEST for those 10 p-values: 0.344531
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-17_14:31
0.6958,0.0323,0.9245,0.8191,0.1668,0.8430,0.5478,0.5672,0.0505,0.0022,
The KS test for those 10 p-values: 0.243716
The 3DSPHERES test for dh-ranFile-2018-06-17_14:31
sample no r^3 equiv. uni.
1 43.968 0.769060
2 10.854 0.303579
3 42.283 0.755722
4 17.464 0.441288
5 67.595 0.894934
6 22.188 0.522689
7 98.792 0.962861
8 33.140 0.668674
9 10.310 0.290842
10 39.581 0.732695
11 55.892 0.844804
12 13.016 0.352011
13 15.122 0.395927
14 57.402 0.852422
15 9.308 0.266756
16 27.576 0.601157
17 63.923 0.881254
18 45.807 0.782792
19 15.519 0.403875
20 3.471 0.109246
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.224548
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-17_14:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -0.7 -1.1 -0.3 0.4 0.2
0.1 1.9 0.4 -0.7 -2.7 -0.3
-1.2 0.1 0.6 0.6 -0.8 0.3
-0.8 -0.5 1.6 2.5 0.6 -0.8
-0.9 0.1 -1.3 0.8 1.2 -0.7
1.3 -2.6 0.8 0.3 -1.0 0.2
-0.7 0.2 0.9 2.6 -1.3 0.0
0.8
Chi-square with 42 degrees of freedom:53.916440
z-score=1.300190, p-value=0.897156
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-17_14:31
Test no p-value
1 0.689542
2 0.184996
3 0.432794
4 0.533108
5 0.557238
6 0.613619
7 0.449180
8 0.061695
9 0.027555
10 0.493733
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.279333
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-17_14:31:
(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 66610 0.05 66757 0.12
3 25000.00 25007 0.00 24857 0.82
4 6666.67 6719 0.41 6780 1.93
5 1388.89 1369 0.28 1345 1.39
6 238.10 256 1.35 223 0.96
7 34.72 33 0.09 31 0.40
8 4.96 5 0.00 6 0.22
p=0.09735 p=0.55722
Number of rngs required: 688203, p-value: 0.409
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-17_14:31
No. of wins: Observed Expected
98524 98585.9
z-score=-0.277, pvalue=0.39102
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66885 66666.7 0.715 0.715
2 37447 37654.3 1.141 1.857
3 26988 26954.7 0.041 1.898
4 19312 19313.5 0.000 1.898
5 13879 13851.4 0.055 1.953
6 9875 9943.5 0.472 2.425
7 7197 7145.0 0.378 2.803
8 5164 5139.1 0.121 2.924
9 3649 3699.9 0.699 3.623
10 2617 2666.3 0.911 4.535
11 1945 1923.3 0.244 4.779
12 1354 1388.7 0.869 5.648
13 998 1003.7 0.033 5.681
14 758 726.1 1.398 7.078
15 539 525.8 0.330 7.408
16 394 381.2 0.433 7.841
17 292 276.5 0.864 8.706
18 168 200.8 5.367 14.072
19 146 146.0 0.000 14.072
20 102 106.2 0.167 14.240
21 291 287.1 0.053 14.292
Chisq= 14.29 for 20 degrees of freedom, p= 0.18462
SUMMARY of craptest
p-value for no. of wins: 0.391018
p-value for throws/game: 0.184620
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-17_14:31
No. of wins: Observed Expected
98671 98585.9
z-score= 0.381, pvalue=0.64832
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67046 66666.7 2.158 2.158
2 37689 37654.3 0.032 2.190
3 26963 26954.7 0.003 2.193
4 19337 19313.5 0.029 2.222
5 13777 13851.4 0.400 2.621
6 9778 9943.5 2.756 5.377
7 7205 7145.0 0.503 5.881
8 5080 5139.1 0.679 6.560
9 3708 3699.9 0.018 6.578
10 2560 2666.3 4.238 10.815
11 1887 1923.3 0.686 11.502
12 1353 1388.7 0.920 12.422
13 1024 1003.7 0.410 12.831
14 717 726.1 0.115 12.947
15 514 525.8 0.266 13.213
16 391 381.2 0.255 13.467
17 261 276.5 0.873 14.341
18 208 200.8 0.256 14.597
19 135 146.0 0.827 15.423
20 90 106.2 2.475 17.899
21 277 287.1 0.356 18.255
Chisq= 18.25 for 20 degrees of freedom, p= 0.42938
SUMMARY of craptest
p-value for no. of wins: 0.648325
p-value for throws/game: 0.429380
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0022,0.0079,0.0141,0.0172,0.0206,0.0276,0.0323,0.0340,0.0394,0.0505,
0.0617,0.0763,0.0791,0.0820,0.0880,0.0899,0.0973,0.1029,0.1088,0.1092,
0.1160,0.1176,0.1242,0.1251,0.1294,0.1413,0.1416,0.1427,0.1539,0.1668,
0.1671,0.1698,0.1764,0.1788,0.1815,0.1846,0.1850,0.1965,0.1981,0.2075,
0.2169,0.2175,0.2175,0.2182,0.2182,0.2245,0.2325,0.2358,0.2384,0.2405,
0.2434,0.2437,0.2550,0.2605,0.2614,0.2626,0.2668,0.2743,0.2793,0.2831,
0.2841,0.2886,0.2908,0.3017,0.3028,0.3035,0.3036,0.3075,0.3077,0.3179,
0.3266,0.3266,0.3277,0.3318,0.3325,0.3334,0.3384,0.3409,0.3433,0.3445,
0.3517,0.3520,0.3532,0.3558,0.3571,0.3575,0.3596,0.3603,0.3621,0.3668,
0.3721,0.3795,0.3848,0.3856,0.3884,0.3910,0.3920,0.3921,0.3928,0.3930,
0.3946,0.3959,0.4010,0.4039,0.4082,0.4090,0.4129,0.4152,0.4155,0.4213,
0.4257,0.4294,0.4311,0.4328,0.4349,0.4349,0.4413,0.4450,0.4467,0.4470,
0.4492,0.4539,0.4551,0.4558,0.4575,0.4579,0.4634,0.4663,0.4666,0.4671,
0.4783,0.4803,0.4917,0.4937,0.4972,0.5067,0.5177,0.5227,0.5331,0.5341,
0.5400,0.5448,0.5461,0.5478,0.5505,0.5572,0.5572,0.5586,0.5624,0.5641,
0.5672,0.5718,0.5794,0.5826,0.5855,0.5933,0.5986,0.5999,0.6012,0.6064,
0.6098,0.6136,0.6220,0.6249,0.6269,0.6280,0.6288,0.6483,0.6541,0.6594,
0.6624,0.6627,0.6687,0.6745,0.6748,0.6754,0.6812,0.6818,0.6821,0.6874,
0.6895,0.6953,0.6958,0.6994,0.6999,0.7058,0.7081,0.7171,0.7249,0.7250,
0.7253,0.7327,0.7356,0.7423,0.7447,0.7486,0.7495,0.7544,0.7551,0.7557,
0.7636,0.7672,0.7691,0.7781,0.7797,0.7818,0.7828,0.7942,0.7945,0.8119,
0.8191,0.8192,0.8197,0.8230,0.8294,0.8318,0.8343,0.8402,0.8416,0.8423,
0.8430,0.8448,0.8497,0.8524,0.8634,0.8655,0.8688,0.8711,0.8732,0.8799,
0.8813,0.8847,0.8871,0.8900,0.8926,0.8949,0.8972,0.8995,0.8999,0.9049,
0.9077,0.9090,0.9091,0.9117,0.9118,0.9138,0.9143,0.9240,0.9245,0.9288,
0.9397,0.9446,0.9450,0.9456,0.9484,0.9506,0.9515,0.9527,0.9569,0.9582,
0.9629,0.9663,0.9682,0.9724,0.9752,0.9763,0.9798,0.9806,0.9840,
Overall p-value after applying KStest on 269 p-values = 0.120262
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.