RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-22_05:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.79 13.2791 0.282687
2 to 25 15.86 10.6182 0.124293
3 to 26 15.75 18.6175 0.649075
4 to 27 15.78 11.9227 0.195207
5 to 28 15.80 16.0647 0.480748
6 to 29 15.86 10.6777 0.127183
7 to 30 16.12 11.8096 0.188474
8 to 31 15.56 16.1809 0.488949
9 to 32 15.71 21.4617 0.793684
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.249321
Tough bday spacings test for dh-ranFile-2018-06-22_05:31: 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 49 70 90 103 73 42 32 21 7 3
(O-E)^2/E 0.1 4.2 0.1 0.6 0.3 0.3 2.0 0.2 2.5 0.0 0.3
Birthday Spacings: Sum(O-E)^2/E= 10.570, p= 0.608
RESULTS OF GCD FOR dh-ranFile-2018-06-22_05:31
Euclid's algorithm:
p-value, steps to gcd: 0.042802
p-value, dist. of gcd's: 0.292030
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-22_05:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.425 0.911 0.907 0.984 0.571 0.002 0.080 0.754
Bits 8 to 15---> 0.525 0.162 0.827 0.409 0.935 0.374 0.878 0.181
Bits 16 to 23---> 0.842 0.743 0.400 0.399 0.883 0.006 0.980 0.971
Bits 24 to 31---> 0.983 0.011 0.738 0.285 0.695 0.448 0.909 0.997
KS test for the above 32 p values: 0.990
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-22_05:31,
p-values for 5 runs: 0.3493, 0.3265, 0.5611, 0.6318, 0.2351
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-22_05:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 207 211.4 0.092 0.092
r= 29 5026 5134.0 2.272 2.365
r= 30 23313 23103.0 1.908 4.273
r= 31 11454 11551.5 0.823 5.096
chi-square = 5.096 with df = 3; p-value = 0.835
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-22_05:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 209 211.4 0.028 0.028
r= 30 5253 5134.0 2.758 2.785
r= 31 22979 23103.0 0.666 3.451
r= 32 11559 11551.5 0.005 3.456
chi-square = 3.456 with df = 3; p-value = 0.674
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-22_05:31
b-rank test for bits 1 to 8, p=0.02700
b-rank test for bits 2 to 9, p=0.39873
b-rank test for bits 3 to 10, p=0.01016
b-rank test for bits 4 to 11, p=0.14739
b-rank test for bits 5 to 12, p=0.04229
b-rank test for bits 6 to 13, p=0.74254
b-rank test for bits 7 to 14, p=0.98340
b-rank test for bits 8 to 15, p=0.72140
b-rank test for bits 9 to 16, p=0.12376
b-rank test for bits 10 to 17, p=0.59348
b-rank test for bits 11 to 18, p=0.15712
b-rank test for bits 12 to 19, p=0.90075
b-rank test for bits 13 to 20, p=0.80502
b-rank test for bits 14 to 21, p=0.89596
b-rank test for bits 15 to 22, p=0.66797
b-rank test for bits 16 to 23, p=0.15389
b-rank test for bits 17 to 24, p=0.03485
b-rank test for bits 18 to 25, p=0.23519
b-rank test for bits 19 to 26, p=0.27610
b-rank test for bits 20 to 27, p=0.92157
b-rank test for bits 21 to 28, p=0.38802
b-rank test for bits 22 to 29, p=0.03543
b-rank test for bits 23 to 30, p=0.82147
b-rank test for bits 24 to 31, p=0.72042
b-rank test for bits 25 to 32, p=0.79940
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 = 0.168392
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-22_05:31
(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 142179 0.63 0.735676
2 142087 0.42 0.660972
3 141715 -0.45 0.324899
4 142169 0.61 0.727977
5 141726 -0.43 0.334201
6 141748 -0.38 0.353109
7 142221 0.73 0.766755
8 142141 0.54 0.705844
9 141697 -0.50 0.309913
10 141195 -1.67 0.047559
11 141109 -1.87 0.030747
12 142031 0.28 0.611900
13 141613 -0.69 0.244356
14 141727 -0.43 0.335052
15 142307 0.93 0.823591
16 142332 0.99 0.838313
17 142017 0.25 0.599312
18 141390 -1.21 0.112491
19 141983 0.17 0.568331
20 142665 1.77 0.961267
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-22_05:31
Bits used No. missing words z-score p-value
23 to 32 142018 0.3747 0.646067
22 to 31 142132 0.7678 0.778705
21 to 30 142411 1.7299 0.958176
20 to 29 142272 1.2506 0.894457
19 to 28 141927 0.0609 0.524293
18 to 27 141760 -0.5149 0.303301
17 to 26 141594 -1.0873 0.138442
16 to 25 142038 0.4437 0.671367
15 to 24 141870 -0.1356 0.446061
14 to 23 141971 0.2127 0.584202
13 to 22 141549 -1.2425 0.107023
12 to 21 141586 -1.1149 0.132440
11 to 20 141960 0.1747 0.569352
10 to 19 141928 0.0644 0.525666
9 to 18 141839 -0.2425 0.404190
8 to 17 141788 -0.4184 0.337835
7 to 16 141770 -0.4804 0.315454
6 to 15 141331 -1.9942 0.023063
5 to 14 141861 -0.1667 0.433821
4 to 13 141741 -0.5804 0.280806
3 to 12 141797 -0.3873 0.349251
2 to 11 142010 0.3471 0.635756
1 to 10 142034 0.4299 0.666365
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-22_05:31
Bits used No. missing words z-score p-value
28 to 32 141901 -0.0282 0.488737
27 to 31 142548 2.1650 0.984806
26 to 30 141663 -0.8350 0.201854
25 to 29 141755 -0.5232 0.300434
24 to 28 141487 -1.4316 0.076125
23 to 27 141513 -1.3435 0.089556
22 to 26 141569 -1.1537 0.124320
21 to 25 142493 1.9785 0.976066
20 to 24 142348 1.4870 0.931495
19 to 23 141778 -0.4452 0.328093
18 to 22 141335 -1.9469 0.025774
17 to 21 141908 -0.0045 0.498201
16 to 20 141970 0.2057 0.581472
15 to 19 142249 1.1514 0.875221
14 to 18 141825 -0.2859 0.387491
13 to 17 141770 -0.4723 0.318355
12 to 16 142150 0.8158 0.792702
11 to 15 141408 -1.6994 0.044620
10 to 14 141868 -0.1401 0.444290
9 to 13 141697 -0.7198 0.235836
8 to 12 142341 1.4633 0.928306
7 to 11 142311 1.3616 0.913337
6 to 10 141710 -0.6757 0.249617
5 to 9 141870 -0.1333 0.446969
4 to 8 142601 2.3446 0.990477
3 to 7 141951 0.1413 0.556166
2 to 6 141923 0.0463 0.518480
1 to 5 142249 1.1514 0.875221
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-22_05:31
Bits used No. missing words z-score p-value
31 to 32 141798 -0.3284 0.371302
30 to 31 142106 0.5801 0.719092
29 to 30 142855 2.7896 0.997361
28 to 29 141797 -0.3314 0.370187
27 to 28 141661 -0.7325 0.231921
26 to 27 142193 0.8368 0.798643
25 to 26 142189 0.8250 0.795310
24 to 25 142032 0.3619 0.641271
23 to 24 141568 -1.0069 0.156998
22 to 23 141597 -0.9213 0.178440
21 to 22 141612 -0.8771 0.190222
20 to 21 141743 -0.4906 0.311837
19 to 20 141917 0.0226 0.509025
18 to 19 141495 -1.2222 0.110814
17 to 18 141780 -0.3815 0.351415
16 to 17 142264 1.0462 0.852271
15 to 16 142189 0.8250 0.795310
14 to 15 141592 -0.9361 0.174617
13 to 14 141649 -0.7679 0.221263
12 to 13 141920 0.0315 0.512555
11 to 12 142004 0.2793 0.609978
10 to 11 141788 -0.3579 0.360207
9 to 10 141927 0.0521 0.520785
8 to 9 141962 0.1554 0.561735
7 to 8 142599 2.0344 0.979046
6 to 7 141807 -0.3019 0.381380
5 to 6 142124 0.6332 0.736713
4 to 5 141328 -1.7148 0.043188
3 to 4 141839 -0.2075 0.417824
2 to 3 141555 -1.0452 0.147960
1 to 2 141797 -0.3314 0.370187
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-22_05:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2408.45 -1.295 0.097698
Test results for specific bytes for dh-ranFile-2018-06-22_05:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2626.38 1.787 0.963049
2 to 9 2424.88 -1.062 0.144036
3 to 10 2581.58 1.154 0.875706
4 to 11 2526.31 0.372 0.645081
5 to 12 2487.42 -0.178 0.429396
6 to 13 2370.65 -1.829 0.033681
7 to 14 2421.60 -1.109 0.133774
8 to 15 2473.91 -0.369 0.356071
9 to 16 2354.60 -2.056 0.019882
10 to 17 2362.50 -1.945 0.025914
11 to 18 2516.29 0.230 0.591087
12 to 19 2501.78 0.025 0.510026
13 to 20 2386.64 -1.603 0.054457
14 to 21 2475.82 -0.342 0.366199
15 to 22 2546.43 0.657 0.744287
16 to 23 2540.68 0.575 0.717476
17 to 24 2385.25 -1.623 0.052315
18 to 25 2493.57 -0.091 0.463782
19 to 26 2455.37 -0.631 0.263971
20 to 27 2345.36 -2.187 0.014375
21 to 28 2439.69 -0.853 0.196858
22 to 29 2458.37 -0.589 0.278004
23 to 30 2587.08 1.231 0.890922
24 to 31 2453.43 -0.659 0.255060
25 to 32 2598.08 1.387 0.917279
CDPARK for dh-ranFile-2018-06-22_05:31: 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
3535 0.5479 0.708135
3566 1.9635 0.975204
3516 -0.3196 0.374623
3523 0.0000 0.500000
3529 0.2740 0.607947
3532 0.4110 0.659449
3540 0.7763 0.781201
3526 0.1370 0.554479
3522 -0.0457 0.481790
3501 -1.0046 0.157553
Square side=100, avg. no. parked=3529.00 sample std.=16.07
p-value of the KSTEST for those 10 p-values: 0.431428
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-22_05:31
0.6299,0.6400,0.5801,0.7495,0.2497,0.7422,0.7004,0.2036,0.5040,0.5237,
The KS test for those 10 p-values: 0.272337
The 3DSPHERES test for dh-ranFile-2018-06-22_05:31
sample no r^3 equiv. uni.
1 36.860 0.707317
2 1.240 0.040490
3 54.418 0.836987
4 19.267 0.473878
5 114.356 0.977893
6 11.144 0.310282
7 10.478 0.294805
8 15.846 0.410337
9 6.748 0.201439
10 35.743 0.696219
11 38.288 0.720923
12 8.218 0.239629
13 18.226 0.455309
14 13.282 0.357722
15 7.568 0.222970
16 10.079 0.285362
17 106.864 0.971622
18 31.221 0.646787
19 24.380 0.556331
20 56.502 0.847927
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.865426
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-22_05:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 0.1 1.3 1.2 -0.2 -0.4
0.2 -0.6 0.5 1.3 0.4 -1.0
-1.2 -0.4 0.4 0.1 0.6 0.3
-0.7 -0.4 1.2 0.3 -0.3 1.2
-0.6 -1.1 -0.2 -1.2 0.5 -1.1
0.7 1.8 0.1 -1.3 1.5 0.6
1.0 0.5 -0.4 -1.3 0.9 2.0
-0.1
Chi-square with 42 degrees of freedom:34.943602
z-score=-0.769916, p-value=0.228458
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-22_05:31
Test no p-value
1 0.034494
2 0.400472
3 0.310995
4 0.714133
5 0.912289
6 0.490008
7 0.730378
8 0.006543
9 0.442918
10 0.899962
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.717050
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-22_05:31:
(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 66622 0.03 66460 0.64
3 25000.00 25170 1.16 25306 3.75
4 6666.67 6504 3.97 6510 3.68
5 1388.89 1443 2.11 1439 1.81
6 238.10 226 0.61 251 0.70
7 34.72 29 0.94 30 0.64
8 4.96 5 0.00 3 0.77
p=0.81606 p=0.93784
Number of rngs required: 687828, p-value: 0.253
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-22_05:31
No. of wins: Observed Expected
98883 98585.9
z-score= 1.329, pvalue=0.90807
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66637 66666.7 0.013 0.013
2 37342 37654.3 2.591 2.604
3 27044 26954.7 0.296 2.899
4 19461 19313.5 1.127 4.026
5 13891 13851.4 0.113 4.140
6 9932 9943.5 0.013 4.153
7 7073 7145.0 0.726 4.879
8 5167 5139.1 0.152 5.031
9 3663 3699.9 0.367 5.398
10 2697 2666.3 0.354 5.752
11 1930 1923.3 0.023 5.775
12 1466 1388.7 4.298 10.073
13 1039 1003.7 1.240 11.313
14 717 726.1 0.115 11.428
15 527 525.8 0.003 11.431
16 387 381.2 0.090 11.521
17 297 276.5 1.514 13.035
18 203 200.8 0.023 13.058
19 136 146.0 0.683 13.741
20 114 106.2 0.571 14.311
21 277 287.1 0.356 14.668
Chisq= 14.67 for 20 degrees of freedom, p= 0.20491
SUMMARY of craptest
p-value for no. of wins: 0.908074
p-value for throws/game: 0.204906
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-22_05:31
No. of wins: Observed Expected
99022 98585.9
z-score= 1.951, pvalue=0.97445
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66825 66666.7 0.376 0.376
2 37777 37654.3 0.400 0.776
3 26905 26954.7 0.092 0.867
4 19233 19313.5 0.335 1.203
5 13770 13851.4 0.479 1.681
6 10012 9943.5 0.471 2.153
7 7070 7145.0 0.788 2.940
8 5069 5139.1 0.955 3.896
9 3659 3699.9 0.451 4.347
10 2668 2666.3 0.001 4.348
11 1937 1923.3 0.097 4.445
12 1435 1388.7 1.541 5.986
13 1006 1003.7 0.005 5.992
14 735 726.1 0.108 6.100
15 516 525.8 0.184 6.284
16 391 381.2 0.255 6.538
17 256 276.5 1.526 8.064
18 184 200.8 1.410 9.474
19 167 146.0 3.025 12.499
20 103 106.2 0.097 12.597
21 282 287.1 0.091 12.688
Chisq= 12.69 for 20 degrees of freedom, p= 0.10963
SUMMARY of craptest
p-value for no. of wins: 0.974452
p-value for throws/game: 0.109629
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0020,0.0062,0.0065,0.0102,0.0106,0.0144,0.0199,0.0231,0.0258,0.0259,
0.0270,0.0307,0.0337,0.0345,0.0348,0.0354,0.0405,0.0423,0.0428,0.0432,
0.0446,0.0476,0.0523,0.0545,0.0761,0.0801,0.0896,0.0977,0.1070,0.1096,
0.1108,0.1125,0.1238,0.1243,0.1243,0.1272,0.1324,0.1338,0.1384,0.1440,
0.1474,0.1480,0.1539,0.1570,0.1571,0.1576,0.1620,0.1684,0.1746,0.1784,
0.1806,0.1885,0.1902,0.1952,0.1969,0.2014,0.2019,0.2036,0.2049,0.2213,
0.2230,0.2285,0.2319,0.2351,0.2352,0.2358,0.2396,0.2444,0.2493,0.2496,
0.2497,0.2535,0.2551,0.2640,0.2723,0.2761,0.2780,0.2808,0.2827,0.2852,
0.2854,0.2920,0.2948,0.3004,0.3033,0.3099,0.3103,0.3110,0.3118,0.3155,
0.3184,0.3249,0.3265,0.3281,0.3342,0.3351,0.3378,0.3493,0.3493,0.3514,
0.3531,0.3561,0.3577,0.3602,0.3662,0.3702,0.3702,0.3713,0.3735,0.3746,
0.3814,0.3875,0.3880,0.3987,0.3991,0.3999,0.4005,0.4042,0.4094,0.4103,
0.4178,0.4254,0.4294,0.4314,0.4338,0.4429,0.4443,0.4461,0.4470,0.4481,
0.4553,0.4638,0.4739,0.4807,0.4818,0.4887,0.4889,0.4900,0.4982,0.5000,
0.5040,0.5090,0.5100,0.5126,0.5185,0.5208,0.5237,0.5243,0.5250,0.5257,
0.5545,0.5562,0.5563,0.5611,0.5617,0.5683,0.5694,0.5707,0.5801,0.5815,
0.5842,0.5911,0.5935,0.5993,0.6079,0.6080,0.6100,0.6119,0.6299,0.6318,
0.6358,0.6400,0.6413,0.6451,0.6461,0.6468,0.6491,0.6594,0.6610,0.6664,
0.6680,0.6714,0.6735,0.6952,0.6962,0.7004,0.7058,0.7073,0.7081,0.7141,
0.7170,0.7175,0.7191,0.7204,0.7209,0.7214,0.7280,0.7304,0.7357,0.7367,
0.7381,0.7422,0.7425,0.7429,0.7443,0.7495,0.7541,0.7668,0.7787,0.7812,
0.7927,0.7937,0.7953,0.7953,0.7986,0.7994,0.8050,0.8161,0.8215,0.8236,
0.8266,0.8351,0.8370,0.8383,0.8418,0.8479,0.8523,0.8654,0.8752,0.8752,
0.8757,0.8779,0.8832,0.8909,0.8945,0.8960,0.9000,0.9008,0.9067,0.9081,
0.9093,0.9111,0.9123,0.9133,0.9173,0.9216,0.9283,0.9315,0.9348,0.9378,
0.9582,0.9613,0.9630,0.9711,0.9716,0.9745,0.9752,0.9761,0.9779,0.9790,
0.9803,0.9833,0.9834,0.9838,0.9848,0.9896,0.9905,0.9965,0.9974,
Overall p-value after applying KStest on 269 p-values = 0.622073
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.