RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-21_19:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.64 18.8277 0.661489
2 to 25 16.00 29.6849 0.971291
3 to 26 15.65 24.6292 0.896678
4 to 27 16.01 10.1467 0.102654
5 to 28 15.84 16.0245 0.477901
6 to 29 16.02 17.6752 0.590395
7 to 30 16.05 22.6704 0.839708
8 to 31 16.00 20.8799 0.768291
9 to 32 15.89 10.8456 0.135525
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.460178
Tough bday spacings test for dh-ranFile-2018-06-21_19:31: 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 6 39 69 104 96 99 39 23 15 8 2
(O-E)^2/E 1.1 0.2 0.2 0.4 0.0 5.6 3.3 1.5 0.0 0.3 1.0
Birthday Spacings: Sum(O-E)^2/E= 13.665, p= 0.811
RESULTS OF GCD FOR dh-ranFile-2018-06-21_19:31
Euclid's algorithm:
p-value, steps to gcd: 0.111061
p-value, dist. of gcd's: 0.875007
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-21_19:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.103 0.381 0.280 0.640 0.682 0.203 0.258 0.024
Bits 8 to 15---> 0.661 0.405 0.413 0.044 0.105 0.207 0.716 0.398
Bits 16 to 23---> 0.075 0.302 0.764 0.717 0.848 0.323 0.856 0.814
Bits 24 to 31---> 0.831 0.761 0.388 0.485 0.656 0.808 0.130 0.454
KS test for the above 32 p values: 0.472
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-21_19:31,
p-values for 5 runs: 0.2217, 0.9439, 0.5652, 0.8502, 0.3453
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-21_19:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 219 211.4 0.272 0.272
r= 29 5085 5134.0 0.468 0.740
r= 30 23205 23103.0 0.450 1.190
r= 31 11491 11551.5 0.317 1.507
chi-square = 1.507 with df = 3; p-value = 0.319
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-21_19:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 219 211.4 0.272 0.272
r= 30 5105 5134.0 0.164 0.436
r= 31 23289 23103.0 1.497 1.933
r= 32 11387 11551.5 2.343 4.276
chi-square = 4.276 with df = 3; p-value = 0.767
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-21_19:31
b-rank test for bits 1 to 8, p=0.51676
b-rank test for bits 2 to 9, p=0.65365
b-rank test for bits 3 to 10, p=0.02495
b-rank test for bits 4 to 11, p=0.44935
b-rank test for bits 5 to 12, p=0.04580
b-rank test for bits 6 to 13, p=0.78745
b-rank test for bits 7 to 14, p=0.81122
b-rank test for bits 8 to 15, p=0.90078
b-rank test for bits 9 to 16, p=0.69782
b-rank test for bits 10 to 17, p=0.04965
b-rank test for bits 11 to 18, p=0.35492
b-rank test for bits 12 to 19, p=0.37394
b-rank test for bits 13 to 20, p=0.57674
b-rank test for bits 14 to 21, p=0.73822
b-rank test for bits 15 to 22, p=0.50108
b-rank test for bits 16 to 23, p=0.30465
b-rank test for bits 17 to 24, p=0.61574
b-rank test for bits 18 to 25, p=0.52720
b-rank test for bits 19 to 26, p=0.02912
b-rank test for bits 20 to 27, p=0.16431
b-rank test for bits 21 to 28, p=0.38806
b-rank test for bits 22 to 29, p=0.22167
b-rank test for bits 23 to 30, p=0.83175
b-rank test for bits 24 to 31, p=0.17411
b-rank test for bits 25 to 32, p=0.16696
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 = 0.409833
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-21_19:31
(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 141301 -1.42 0.077610
2 141401 -1.19 0.117478
3 141978 0.16 0.563734
4 141836 -0.17 0.431981
5 141434 -1.11 0.133374
6 141677 -0.54 0.293624
7 142642 1.71 0.956537
8 141933 0.06 0.522052
9 140858 -2.46 0.007017
10 142051 0.33 0.629680
11 140971 -2.19 0.014177
12 142099 0.44 0.671173
13 141836 -0.17 0.431981
14 141775 -0.31 0.376816
15 142273 0.85 0.802253
16 141295 -1.44 0.075594
17 141676 -0.55 0.292821
18 142789 2.06 0.980075
19 141499 -0.96 0.168851
20 142576 1.56 0.940341
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-21_19:31
Bits used No. missing words z-score p-value
23 to 32 141900 -0.0322 0.487167
22 to 31 141264 -2.2253 0.013031
21 to 30 142217 1.0609 0.855639
20 to 29 141750 -0.5494 0.291361
19 to 28 142037 0.4402 0.670119
18 to 27 141968 0.2023 0.580163
17 to 26 141917 0.0264 0.510550
16 to 25 142231 1.1092 0.866330
15 to 24 141653 -0.8839 0.188376
14 to 23 141746 -0.5632 0.286647
13 to 22 141833 -0.2632 0.396196
12 to 21 142316 1.4023 0.919589
11 to 20 142562 2.2506 0.987794
10 to 19 141897 -0.0425 0.483043
9 to 18 141837 -0.2494 0.401520
8 to 17 141741 -0.5804 0.280806
7 to 16 142122 0.7333 0.768326
6 to 15 141839 -0.2425 0.404190
5 to 14 142122 0.7333 0.768326
4 to 13 141809 -0.3460 0.364684
3 to 12 141373 -1.8494 0.032199
2 to 11 141679 -0.7942 0.213528
1 to 10 141699 -0.7253 0.234141
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-21_19:31
Bits used No. missing words z-score p-value
28 to 32 142177 0.9074 0.817891
27 to 31 141274 -2.1537 0.015633
26 to 30 141941 0.1074 0.542747
25 to 29 141394 -1.7469 0.040329
24 to 28 142371 1.5650 0.941207
23 to 27 142221 1.0565 0.854632
22 to 26 142148 0.8091 0.790757
21 to 25 142515 2.0531 0.979969
20 to 24 142556 2.1921 0.985814
19 to 23 142079 0.5752 0.717406
18 to 22 141719 -0.6452 0.259403
17 to 21 141781 -0.4350 0.331775
16 to 20 141929 0.0667 0.526581
15 to 19 141969 0.2023 0.580148
14 to 18 142060 0.5107 0.695236
13 to 17 142022 0.3819 0.648744
12 to 16 141963 0.1819 0.572182
11 to 15 141922 0.0429 0.517129
10 to 14 141793 -0.3943 0.346665
9 to 13 142260 1.1887 0.882723
8 to 12 142231 1.0904 0.862233
7 to 11 142143 0.7921 0.785849
6 to 10 141714 -0.6621 0.253942
5 to 9 141874 -0.1198 0.452336
4 to 8 141864 -0.1537 0.438939
3 to 7 142262 1.1955 0.884053
2 to 6 141985 0.2565 0.601221
1 to 5 142029 0.4057 0.657504
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-21_19:31
Bits used No. missing words z-score p-value
31 to 32 142195 0.8427 0.800298
30 to 31 141414 -1.4612 0.071987
29 to 30 142017 0.3176 0.624610
28 to 29 141926 0.0492 0.519610
27 to 28 141944 0.1023 0.540729
26 to 27 141893 -0.0482 0.480790
25 to 26 141901 -0.0246 0.490198
24 to 25 142100 0.5624 0.713095
23 to 24 142155 0.7247 0.765679
22 to 23 141992 0.2439 0.596332
21 to 22 141734 -0.5172 0.302509
20 to 21 142190 0.8279 0.796146
19 to 20 141972 0.1849 0.573333
18 to 19 141803 -0.3137 0.376891
17 to 18 142296 1.1406 0.872986
16 to 17 141942 0.0964 0.538387
15 to 16 142213 0.8958 0.814815
14 to 15 141899 -0.0305 0.487845
13 to 14 142072 0.4799 0.684334
12 to 13 141691 -0.6440 0.259774
11 to 12 141763 -0.4317 0.332997
10 to 11 141485 -1.2517 0.105338
9 to 10 142091 0.5359 0.703986
8 to 9 142474 1.6657 0.952113
7 to 8 141590 -0.9420 0.173102
6 to 7 142018 0.3206 0.625728
5 to 6 141463 -1.3166 0.093985
4 to 5 141635 -0.8092 0.209191
3 to 4 141536 -1.1013 0.135390
2 to 3 141646 -0.7768 0.218643
1 to 2 142446 1.5831 0.943300
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-21_19:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2482.83 -0.243 0.404086
Test results for specific bytes for dh-ranFile-2018-06-21_19:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2498.41 -0.023 0.491004
2 to 9 2480.20 -0.280 0.389710
3 to 10 2464.63 -0.500 0.308489
4 to 11 2712.77 3.009 0.998689
5 to 12 2470.22 -0.421 0.336836
6 to 13 2497.46 -0.036 0.485695
7 to 14 2439.89 -0.850 0.197655
8 to 15 2392.45 -1.521 0.064138
9 to 16 2453.75 -0.654 0.256545
10 to 17 2382.77 -1.658 0.048675
11 to 18 2562.30 0.881 0.810841
12 to 19 2645.55 2.058 0.980220
13 to 20 2494.84 -0.073 0.470933
14 to 21 2578.89 1.116 0.867715
15 to 22 2548.82 0.690 0.755020
16 to 23 2576.82 1.086 0.861363
17 to 24 2511.28 0.160 0.563384
18 to 25 2522.44 0.317 0.624495
19 to 26 2437.29 -0.887 0.187596
20 to 27 2548.70 0.689 0.754484
21 to 28 2460.19 -0.563 0.286742
22 to 29 2509.90 0.140 0.555658
23 to 30 2567.30 0.952 0.829385
24 to 31 2461.11 -0.550 0.291186
25 to 32 2474.66 -0.358 0.360042
CDPARK for dh-ranFile-2018-06-21_19:31: 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
3512 -0.5023 0.307734
3518 -0.2283 0.409702
3502 -0.9589 0.168804
3499 -1.0959 0.136563
3548 1.1416 0.873180
3498 -1.1416 0.126820
3497 -1.1872 0.117571
3533 0.4566 0.676028
3535 0.5479 0.708135
3530 0.3196 0.625377
Square side=100, avg. no. parked=3517.20 sample std.=17.45
p-value of the KSTEST for those 10 p-values: 0.486025
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-21_19:31
0.8098,0.9420,0.3710,0.6539,0.2036,0.9244,0.3560,0.5284,0.4028,0.0145,
The KS test for those 10 p-values: 0.937830
The 3DSPHERES test for dh-ranFile-2018-06-21_19:31
sample no r^3 equiv. uni.
1 8.603 0.249308
2 26.518 0.586852
3 14.394 0.381099
4 39.879 0.735342
5 28.571 0.614178
6 12.904 0.349587
7 14.924 0.391929
8 3.606 0.113251
9 13.033 0.352372
10 35.299 0.691682
11 7.126 0.211437
12 54.539 0.837645
13 73.964 0.915030
14 0.182 0.006037
15 57.147 0.851164
16 29.673 0.628083
17 23.338 0.540647
18 45.282 0.778960
19 3.343 0.105442
20 3.355 0.105817
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.910403
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-21_19:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 0.9 -0.1 0.0 -0.4 2.0
0.1 0.4 -0.2 -1.2 -1.9 0.1
2.5 -0.5 -0.9 -0.5 0.1 -0.8
-0.5 1.5 -0.8 0.7 -0.7 1.6
-2.5 1.9 0.4 -0.2 0.8 0.6
1.6 0.1 0.6 0.5 0.9 0.1
-0.2 -0.1 0.5 -0.1 0.1 -1.0
-1.1
Chi-square with 42 degrees of freedom:42.410401
z-score=0.044778, p-value=0.546727
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-21_19:31
Test no p-value
1 0.370055
2 0.116363
3 0.089315
4 0.022627
5 0.152989
6 0.960423
7 0.008170
8 0.811248
9 0.460413
10 0.358305
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.053915
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-21_19:31:
(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 66681 0.00 66747 0.10
3 25000.00 24895 0.44 25150 0.90
4 6666.67 6746 0.94 6444 7.44
5 1388.89 1401 0.11 1369 0.28
6 238.10 233 0.11 257 1.50
7 34.72 36 0.05 29 0.94
8 4.96 7 0.84 3 0.77
p=0.13029 p=0.93661
Number of rngs required: 689303, p-value: 0.852
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-21_19:31
No. of wins: Observed Expected
98365 98585.9
z-score=-0.988, pvalue=0.16162
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66767 66666.7 0.151 0.151
2 37467 37654.3 0.932 1.083
3 26949 26954.7 0.001 1.084
4 19294 19313.5 0.020 1.104
5 13923 13851.4 0.370 1.474
6 9832 9943.5 1.251 2.725
7 7195 7145.0 0.350 3.074
8 5167 5139.1 0.152 3.226
9 3680 3699.9 0.107 3.333
10 2658 2666.3 0.026 3.359
11 1988 1923.3 2.175 5.533
12 1425 1388.7 0.947 6.480
13 1028 1003.7 0.588 7.067
14 751 726.1 0.851 7.919
15 487 525.8 2.868 10.787
16 403 381.2 1.253 12.039
17 267 276.5 0.329 12.368
18 193 200.8 0.305 12.674
19 159 146.0 1.160 13.834
20 103 106.2 0.097 13.931
21 264 287.1 1.861 15.792
Chisq= 15.79 for 20 degrees of freedom, p= 0.27057
SUMMARY of craptest
p-value for no. of wins: 0.161623
p-value for throws/game: 0.270570
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-21_19:31
No. of wins: Observed Expected
98715 98585.9
z-score= 0.578, pvalue=0.71823
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66547 66666.7 0.215 0.215
2 37489 37654.3 0.726 0.941
3 26953 26954.7 0.000 0.941
4 19437 19313.5 0.790 1.731
5 13913 13851.4 0.274 2.005
6 9928 9943.5 0.024 2.029
7 7140 7145.0 0.004 2.033
8 5146 5139.1 0.009 2.042
9 3729 3699.9 0.229 2.271
10 2728 2666.3 1.428 3.699
11 1919 1923.3 0.010 3.709
12 1386 1388.7 0.005 3.714
13 981 1003.7 0.514 4.228
14 751 726.1 0.851 5.080
15 544 525.8 0.627 5.707
16 386 381.2 0.062 5.769
17 292 276.5 0.864 6.633
18 203 200.8 0.023 6.656
19 167 146.0 3.025 9.682
20 96 106.2 0.982 10.664
21 265 287.1 1.703 12.368
Chisq= 12.37 for 20 degrees of freedom, p= 0.09715
SUMMARY of craptest
p-value for no. of wins: 0.718231
p-value for throws/game: 0.097155
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0060,0.0070,0.0082,0.0130,0.0142,0.0145,0.0156,0.0226,0.0240,0.0249,
0.0291,0.0322,0.0403,0.0442,0.0458,0.0487,0.0497,0.0539,0.0641,0.0720,
0.0749,0.0756,0.0776,0.0893,0.0940,0.0972,0.1027,0.1032,0.1052,0.1053,
0.1054,0.1058,0.1111,0.1133,0.1164,0.1175,0.1176,0.1268,0.1301,0.1303,
0.1334,0.1354,0.1355,0.1366,0.1530,0.1616,0.1643,0.1670,0.1688,0.1689,
0.1731,0.1741,0.1876,0.1884,0.1977,0.2029,0.2036,0.2071,0.2092,0.2114,
0.2135,0.2186,0.2217,0.2217,0.2341,0.2493,0.2539,0.2565,0.2580,0.2594,
0.2598,0.2706,0.2804,0.2808,0.2866,0.2867,0.2912,0.2914,0.2928,0.2936,
0.3019,0.3025,0.3046,0.3077,0.3085,0.3193,0.3227,0.3318,0.3330,0.3368,
0.3453,0.3467,0.3496,0.3524,0.3549,0.3560,0.3583,0.3600,0.3647,0.3701,
0.3710,0.3739,0.3768,0.3769,0.3811,0.3815,0.3881,0.3883,0.3897,0.3919,
0.3962,0.3978,0.4015,0.4028,0.4041,0.4042,0.4054,0.4097,0.4098,0.4127,
0.4320,0.4320,0.4389,0.4494,0.4523,0.4545,0.4602,0.4604,0.4709,0.4719,
0.4779,0.4808,0.4830,0.4854,0.4857,0.4860,0.4872,0.4878,0.4902,0.4910,
0.5011,0.5106,0.5168,0.5171,0.5196,0.5221,0.5266,0.5272,0.5284,0.5384,
0.5406,0.5407,0.5427,0.5467,0.5557,0.5634,0.5637,0.5652,0.5722,0.5733,
0.5767,0.5801,0.5802,0.5869,0.5904,0.5963,0.6012,0.6142,0.6157,0.6245,
0.6246,0.6254,0.6257,0.6281,0.6297,0.6403,0.6487,0.6536,0.6539,0.6562,
0.6575,0.6605,0.6615,0.6701,0.6712,0.6760,0.6822,0.6843,0.6917,0.6952,
0.6978,0.7040,0.7081,0.7131,0.7161,0.7174,0.7174,0.7182,0.7353,0.7382,
0.7545,0.7550,0.7608,0.7640,0.7657,0.7668,0.7683,0.7683,0.7683,0.7790,
0.7858,0.7874,0.7908,0.7961,0.8003,0.8023,0.8079,0.8098,0.8108,0.8112,
0.8112,0.8112,0.8144,0.8148,0.8179,0.8294,0.8313,0.8318,0.8376,0.8397,
0.8476,0.8502,0.8512,0.8516,0.8546,0.8555,0.8556,0.8614,0.8622,0.8663,
0.8677,0.8730,0.8732,0.8750,0.8827,0.8841,0.8967,0.9008,0.9104,0.9150,
0.9196,0.9244,0.9366,0.9378,0.9403,0.9412,0.9420,0.9433,0.9439,0.9521,
0.9565,0.9604,0.9713,0.9800,0.9801,0.9802,0.9858,0.9878,0.9987,
Overall p-value after applying KStest on 269 p-values = 0.903697
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.