RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-20_11:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 16.09 22.8458 0.845660
2 to 25 15.80 18.1053 0.617773
3 to 26 15.47 25.8815 0.923353
4 to 27 15.60 10.8624 0.136373
5 to 28 15.61 22.5485 0.835467
6 to 29 15.72 10.8719 0.136854
7 to 30 15.73 17.5017 0.579094
8 to 31 15.79 11.2534 0.156910
9 to 32 16.14 16.3629 0.501731
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.829963
Tough bday spacings test for dh-ranFile-2018-06-20_11:31: 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 33 55 90 109 84 60 35 10 13 3
(O-E)^2/E 0.1 0.4 4.6 0.6 1.3 0.4 1.2 0.9 1.6 6.2 0.3
Birthday Spacings: Sum(O-E)^2/E= 17.574, p= 0.937
RESULTS OF GCD FOR dh-ranFile-2018-06-20_11:31
Euclid's algorithm:
p-value, steps to gcd: 0.164387
p-value, dist. of gcd's: 0.031705
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-20_11:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.194 0.887 0.980 0.747 0.346 0.419 0.590 0.648
Bits 8 to 15---> 0.340 0.822 0.253 0.759 0.375 0.332 0.227 0.153
Bits 16 to 23---> 0.327 0.350 0.606 0.152 0.947 0.194 0.917 0.543
Bits 24 to 31---> 0.946 0.205 0.327 0.001 0.601 0.429 0.321 0.857
KS test for the above 32 p values: 0.420
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-20_11:31,
p-values for 5 runs: 0.2575, 0.8024, 0.4538, 0.0115, 0.5421
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-20_11:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 255 211.4 8.984 8.984
r= 29 5056 5134.0 1.185 10.169
r= 30 23122 23103.0 0.016 10.185
r= 31 11567 11551.5 0.021 10.206
chi-square = 10.206 with df = 3; p-value = 0.983
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-20_11:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 213 211.4 0.012 0.012
r= 30 5089 5134.0 0.395 0.406
r= 31 23223 23103.0 0.623 1.029
r= 32 11475 11551.5 0.507 1.536
chi-square = 1.536 with df = 3; p-value = 0.326
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-20_11:31
b-rank test for bits 1 to 8, p=0.60892
b-rank test for bits 2 to 9, p=0.00504
b-rank test for bits 3 to 10, p=0.44090
b-rank test for bits 4 to 11, p=0.34456
b-rank test for bits 5 to 12, p=0.79251
b-rank test for bits 6 to 13, p=0.69582
b-rank test for bits 7 to 14, p=0.98600
b-rank test for bits 8 to 15, p=0.90834
b-rank test for bits 9 to 16, p=0.94669
b-rank test for bits 10 to 17, p=0.62127
b-rank test for bits 11 to 18, p=0.90450
b-rank test for bits 12 to 19, p=0.83584
b-rank test for bits 13 to 20, p=0.71319
b-rank test for bits 14 to 21, p=0.73832
b-rank test for bits 15 to 22, p=0.62896
b-rank test for bits 16 to 23, p=0.87633
b-rank test for bits 17 to 24, p=0.88254
b-rank test for bits 18 to 25, p=0.52598
b-rank test for bits 19 to 26, p=0.58682
b-rank test for bits 20 to 27, p=0.33125
b-rank test for bits 21 to 28, p=0.51205
b-rank test for bits 22 to 29, p=0.25030
b-rank test for bits 23 to 30, p=0.88701
b-rank test for bits 24 to 31, p=0.36560
b-rank test for bits 25 to 32, p=0.03139
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 = 0.059018
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-20_11:31
(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 141231 -1.58 0.056496
2 141733 -0.41 0.340175
3 142746 1.95 0.974699
4 141633 -0.65 0.259259
5 141457 -1.06 0.145291
6 141889 -0.05 0.481057
7 142258 0.81 0.792364
8 141263 -1.51 0.065507
9 142103 0.45 0.674546
10 142064 0.36 0.641092
11 141824 -0.20 0.420987
12 142021 0.26 0.602920
13 142517 1.42 0.922166
14 141294 -1.44 0.075261
15 141616 -0.69 0.246561
16 141281 -1.47 0.071044
17 141642 -0.62 0.266116
18 141641 -0.63 0.265350
19 142244 0.78 0.782875
20 141624 -0.67 0.252495
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-20_11:31
Bits used No. missing words z-score p-value
23 to 32 142229 1.1023 0.864837
22 to 31 141456 -1.5632 0.059002
21 to 30 142697 2.7161 0.996697
20 to 29 142215 1.0540 0.854066
19 to 28 142687 2.6816 0.996337
18 to 27 141859 -0.1736 0.431109
17 to 26 142175 0.9161 0.820194
16 to 25 142461 1.9023 0.971435
15 to 24 141988 0.2713 0.606911
14 to 23 142334 1.4644 0.928455
13 to 22 142533 2.1506 0.984246
12 to 21 142016 0.3678 0.643499
11 to 20 141409 -1.7253 0.042239
10 to 19 142994 3.7402 0.999908
9 to 18 142059 0.5161 0.697109
8 to 17 142022 0.3885 0.651183
7 to 16 141454 -1.5701 0.058196
6 to 15 142157 0.8540 0.803457
5 to 14 141829 -0.2770 0.390890
4 to 13 141134 -2.6736 0.003753
3 to 12 141719 -0.6563 0.255812
2 to 11 142188 0.9609 0.831707
1 to 10 141751 -0.5460 0.292545
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-20_11:31
Bits used No. missing words z-score p-value
28 to 32 142358 1.5209 0.935859
27 to 31 141923 0.0463 0.518480
26 to 30 141926 0.0565 0.522532
25 to 29 141474 -1.4757 0.070013
24 to 28 141852 -0.1943 0.422955
23 to 27 141756 -0.5198 0.301615
22 to 26 142376 1.5819 0.943167
21 to 25 142701 2.6836 0.996359
20 to 24 141865 -0.1503 0.440275
19 to 23 142152 0.8226 0.794635
18 to 22 142207 1.0091 0.843525
17 to 21 141955 0.1548 0.561516
16 to 20 142050 0.4768 0.683265
15 to 19 141495 -1.4045 0.080084
14 to 18 142487 1.9582 0.974897
13 to 17 141973 0.2158 0.585440
12 to 16 141947 0.1277 0.550805
11 to 15 141559 -1.1876 0.117504
10 to 14 142129 0.7446 0.771757
9 to 13 141915 0.0192 0.507667
8 to 12 142103 0.6565 0.744252
7 to 11 141334 -1.9503 0.025572
6 to 10 141438 -1.5977 0.055052
5 to 9 142118 0.7074 0.760327
4 to 8 141675 -0.7943 0.213499
3 to 7 142356 1.5141 0.935004
2 to 6 142147 0.8057 0.789781
1 to 5 142048 0.4701 0.680847
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-20_11:31
Bits used No. missing words z-score p-value
31 to 32 142077 0.4946 0.689559
30 to 31 142109 0.5890 0.722068
29 to 30 141986 0.2262 0.589464
28 to 29 142299 1.1495 0.874819
27 to 28 141569 -1.0039 0.157708
26 to 27 141120 -2.3284 0.009945
25 to 26 142052 0.4209 0.663070
24 to 25 142092 0.5388 0.705005
23 to 24 141876 -0.0983 0.460840
22 to 23 141940 0.0905 0.536044
21 to 22 141840 -0.2045 0.418976
20 to 21 142373 1.3678 0.914306
19 to 20 142320 1.2114 0.887132
18 to 19 142156 0.7276 0.766583
17 to 18 141465 -1.3107 0.094978
16 to 17 142122 0.6273 0.734784
15 to 16 141651 -0.7620 0.223019
14 to 15 142238 0.9695 0.833859
13 to 14 141873 -0.1072 0.457328
12 to 13 142033 0.3648 0.642373
11 to 12 141349 -1.6529 0.049177
10 to 11 142124 0.6332 0.736713
9 to 10 142265 1.0492 0.852951
8 to 9 141697 -0.6263 0.265545
7 to 8 142339 1.2675 0.897505
6 to 7 142436 1.5536 0.939860
5 to 6 142314 1.1937 0.883706
4 to 5 142178 0.7925 0.785976
3 to 4 141471 -1.2930 0.098004
2 to 3 142441 1.5683 0.941600
1 to 2 141474 -1.2842 0.099543
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-20_11:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2560.26 0.852 0.802949
Test results for specific bytes for dh-ranFile-2018-06-20_11:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2417.41 -1.168 0.121409
2 to 9 2469.88 -0.426 0.335054
3 to 10 2574.25 1.050 0.853145
4 to 11 2472.87 -0.384 0.350591
5 to 12 2493.07 -0.098 0.460955
6 to 13 2397.77 -1.446 0.074133
7 to 14 2511.08 0.157 0.562277
8 to 15 2645.21 2.054 0.979992
9 to 16 2492.11 -0.112 0.455599
10 to 17 2481.99 -0.255 0.399468
11 to 18 2534.24 0.484 0.685902
12 to 19 2477.76 -0.314 0.376583
13 to 20 2507.09 0.100 0.539949
14 to 21 2454.31 -0.646 0.259100
15 to 22 2483.45 -0.234 0.407468
16 to 23 2478.84 -0.299 0.382364
17 to 24 2467.70 -0.457 0.323934
18 to 25 2561.02 0.863 0.805918
19 to 26 2499.32 -0.010 0.496164
20 to 27 2504.55 0.064 0.525678
21 to 28 2563.94 0.904 0.817077
22 to 29 2422.59 -1.095 0.136813
23 to 30 2500.46 0.007 0.502607
24 to 31 2471.50 -0.403 0.343437
25 to 32 2649.02 2.108 0.982463
CDPARK for dh-ranFile-2018-06-20_11:31: 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
3540 0.7763 0.781201
3521 -0.0913 0.463617
3514 -0.4110 0.340551
3513 -0.4566 0.323972
3519 -0.1826 0.427537
3510 -0.5936 0.276387
3494 -1.3242 0.092718
3513 -0.4566 0.323972
3535 0.5479 0.708135
3533 0.4566 0.676028
Square side=100, avg. no. parked=3519.20 sample std.=13.04
p-value of the KSTEST for those 10 p-values: 0.456511
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-20_11:31
0.8571,0.5101,0.2686,0.4825,0.1809,0.5415,0.8246,0.0709,0.2644,0.7179,
The KS test for those 10 p-values: 0.950301
The 3DSPHERES test for dh-ranFile-2018-06-20_11:31
sample no r^3 equiv. uni.
1 5.208 0.159367
2 16.535 0.423727
3 4.947 0.152024
4 93.387 0.955528
5 18.285 0.456375
6 7.945 0.232667
7 14.036 0.373660
8 9.490 0.271188
9 27.448 0.599451
10 7.401 0.218631
11 19.011 0.469368
12 10.633 0.298433
13 6.661 0.199118
14 55.036 0.840313
15 59.819 0.863848
16 13.503 0.362435
17 6.334 0.190338
18 11.490 0.318198
19 10.305 0.290710
20 96.020 0.959265
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.148496
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-20_11:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
2.7 -1.2 -1.3 1.6 -0.7 0.3
0.3 1.5 -0.7 -0.9 -1.1 0.1
0.1 -0.4 -0.1 1.3 0.1 -1.5
-0.1 0.8 -0.8 1.3 0.8 -1.0
0.8 0.0 0.5 -0.4 -0.5 0.3
-0.4 0.0 0.8 -2.3 -1.6 -0.1
0.3 -0.4 0.5 -0.7 0.9 0.0
-0.1
Chi-square with 42 degrees of freedom:38.757457
z-score=-0.353790, p-value=0.385896
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-20_11:31
Test no p-value
1 0.165479
2 0.055514
3 0.059843
4 0.013038
5 0.088096
6 0.364553
7 0.033812
8 0.000055
9 0.902091
10 0.553394
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000218
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-20_11:31:
(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 66615 0.04 66706 0.02
3 25000.00 25050 0.10 24965 0.05
4 6666.67 6725 0.51 6698 0.15
5 1388.89 1318 3.62 1339 1.79
6 238.10 255 1.20 239 0.00
7 34.72 33 0.09 44 2.48
8 4.96 3 0.77 8 1.86
p=0.61260 p=0.61575
Number of rngs required: 688526, p-value: 0.556
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-20_11:31
No. of wins: Observed Expected
98600 98585.9
z-score= 0.063, pvalue=0.52522
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67225 66666.7 4.676 4.676
2 37803 37654.3 0.587 5.263
3 26740 26954.7 1.711 6.974
4 19329 19313.5 0.013 6.986
5 13651 13851.4 2.900 9.886
6 9837 9943.5 1.142 11.028
7 7070 7145.0 0.788 11.816
8 5103 5139.1 0.253 12.069
9 3656 3699.9 0.520 12.589
10 2715 2666.3 0.890 13.478
11 1894 1923.3 0.447 13.926
12 1375 1388.7 0.136 14.062
13 1020 1003.7 0.264 14.326
14 731 726.1 0.033 14.358
15 498 525.8 1.474 15.832
16 368 381.2 0.454 16.286
17 289 276.5 0.561 16.847
18 183 200.8 1.583 18.430
19 138 146.0 0.437 18.867
20 116 106.2 0.901 19.768
21 259 287.1 2.753 22.521
Chisq= 22.52 for 20 degrees of freedom, p= 0.68708
SUMMARY of craptest
p-value for no. of wins: 0.525216
p-value for throws/game: 0.687079
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-20_11:31
No. of wins: Observed Expected
98667 98585.9
z-score= 0.363, pvalue=0.64166
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66653 66666.7 0.003 0.003
2 37672 37654.3 0.008 0.011
3 27086 26954.7 0.639 0.650
4 19089 19313.5 2.609 3.259
5 13826 13851.4 0.047 3.306
6 10057 9943.5 1.295 4.600
7 7181 7145.0 0.181 4.781
8 5093 5139.1 0.413 5.194
9 3693 3699.9 0.013 5.207
10 2744 2666.3 2.264 7.472
11 1929 1923.3 0.017 7.488
12 1384 1388.7 0.016 7.505
13 911 1003.7 8.564 16.069
14 752 726.1 0.921 16.990
15 495 525.8 1.808 18.798
16 386 381.2 0.062 18.860
17 299 276.5 1.824 20.684
18 184 200.8 1.410 22.094
19 167 146.0 3.025 25.120
20 99 106.2 0.490 25.610
21 300 287.1 0.578 26.188
Chisq= 26.19 for 20 degrees of freedom, p= 0.84031
SUMMARY of craptest
p-value for no. of wins: 0.641665
p-value for throws/game: 0.840312
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0001,0.0002,0.0008,0.0038,0.0050,0.0099,0.0115,0.0130,0.0256,0.0314,
0.0317,0.0338,0.0422,0.0492,0.0551,0.0555,0.0565,0.0582,0.0590,0.0590,
0.0598,0.0655,0.0700,0.0709,0.0710,0.0741,0.0753,0.0801,0.0881,0.0927,
0.0950,0.0980,0.0995,0.1175,0.1214,0.1364,0.1368,0.1369,0.1453,0.1485,
0.1520,0.1522,0.1532,0.1569,0.1577,0.1594,0.1644,0.1655,0.1809,0.1903,
0.1935,0.1940,0.1991,0.2050,0.2135,0.2186,0.2230,0.2273,0.2327,0.2466,
0.2503,0.2525,0.2530,0.2558,0.2575,0.2591,0.2593,0.2644,0.2653,0.2655,
0.2661,0.2686,0.2712,0.2764,0.2907,0.2925,0.2984,0.3016,0.3182,0.3211,
0.3239,0.3240,0.3240,0.3261,0.3268,0.3272,0.3312,0.3320,0.3351,0.3402,
0.3404,0.3406,0.3434,0.3446,0.3464,0.3498,0.3506,0.3624,0.3646,0.3656,
0.3737,0.3750,0.3766,0.3824,0.3859,0.3909,0.3995,0.4075,0.4187,0.4190,
0.4197,0.4210,0.4230,0.4237,0.4275,0.4293,0.4311,0.4403,0.4409,0.4538,
0.4556,0.4564,0.4565,0.4573,0.4608,0.4610,0.4636,0.4694,0.4811,0.4825,
0.4962,0.5017,0.5026,0.5077,0.5101,0.5120,0.5185,0.5225,0.5252,0.5257,
0.5260,0.5360,0.5399,0.5415,0.5421,0.5426,0.5508,0.5534,0.5563,0.5615,
0.5623,0.5791,0.5854,0.5868,0.5895,0.5898,0.5995,0.6014,0.6029,0.6060,
0.6069,0.6089,0.6126,0.6158,0.6178,0.6213,0.6290,0.6411,0.6417,0.6424,
0.6435,0.6482,0.6512,0.6631,0.6745,0.6760,0.6808,0.6833,0.6859,0.6871,
0.6896,0.6958,0.6971,0.7050,0.7081,0.7132,0.7179,0.7221,0.7348,0.7367,
0.7383,0.7443,0.7475,0.7588,0.7603,0.7666,0.7718,0.7812,0.7829,0.7860,
0.7898,0.7924,0.7925,0.7946,0.8024,0.8029,0.8035,0.8059,0.8171,0.8202,
0.8218,0.8246,0.8300,0.8317,0.8339,0.8355,0.8358,0.8403,0.8403,0.8435,
0.8457,0.8530,0.8531,0.8541,0.8571,0.8575,0.8638,0.8648,0.8748,0.8763,
0.8825,0.8837,0.8870,0.8871,0.8871,0.8975,0.9021,0.9045,0.9083,0.9143,
0.9172,0.9222,0.9234,0.9285,0.9350,0.9359,0.9374,0.9399,0.9416,0.9432,
0.9460,0.9467,0.9473,0.9503,0.9555,0.9593,0.9714,0.9747,0.9749,0.9800,
0.9803,0.9825,0.9831,0.9842,0.9860,0.9963,0.9964,0.9967,0.9999,
Overall p-value after applying KStest on 269 p-values = 0.449311
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.