RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-02_17:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.77 18.5408 0.644481
2 to 25 16.21 16.9420 0.541698
3 to 26 15.80 23.5941 0.869111
4 to 27 15.75 17.7312 0.594015
5 to 28 15.58 15.3069 0.426612
6 to 29 15.54 21.0828 0.777390
7 to 30 15.68 25.8554 0.922865
8 to 31 15.83 28.4008 0.959532
9 to 32 15.72 16.2661 0.494946
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.071792
Tough bday spacings test for dh-ranFile-2018-07-02_17:31: 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 33 80 103 91 80 53 26 17 4 3
(O-E)^2/E 0.1 0.4 0.6 0.3 0.5 0.0 0.0 0.5 0.3 1.0 0.3
Birthday Spacings: Sum(O-E)^2/E= 3.955, p= 0.051
RESULTS OF GCD FOR dh-ranFile-2018-07-02_17:31
Euclid's algorithm:
p-value, steps to gcd: 0.662804
p-value, dist. of gcd's: 0.772709
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-02_17:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.292 0.754 0.352 0.475 0.004 0.851 0.190 0.256
Bits 8 to 15---> 0.862 0.509 0.572 0.866 0.915 0.723 0.066 0.582
Bits 16 to 23---> 0.096 0.063 0.615 0.069 0.918 0.438 0.321 0.517
Bits 24 to 31---> 0.359 0.775 0.070 0.918 0.812 0.557 0.294 0.973
KS test for the above 32 p values: 0.083
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-02_17:31,
p-values for 5 runs: 0.0122, 0.6382, 0.4314, 0.2034, 0.7323
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-02_17:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 224 211.4 0.749 0.749
r= 29 5204 5134.0 0.954 1.703
r= 30 22790 23103.0 4.242 5.945
r= 31 11782 11551.5 4.598 10.543
chi-square = 10.543 with df = 3; p-value = 0.986
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-02_17:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 221 211.4 0.434 0.434
r= 30 5233 5134.0 1.909 2.343
r= 31 22872 23103.0 2.311 4.654
r= 32 11674 11551.5 1.299 5.952
chi-square = 5.952 with df = 3; p-value = 0.886
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-02_17:31
b-rank test for bits 1 to 8, p=0.59984
b-rank test for bits 2 to 9, p=0.36558
b-rank test for bits 3 to 10, p=0.15839
b-rank test for bits 4 to 11, p=0.84766
b-rank test for bits 5 to 12, p=0.83245
b-rank test for bits 6 to 13, p=0.79315
b-rank test for bits 7 to 14, p=0.21536
b-rank test for bits 8 to 15, p=0.37811
b-rank test for bits 9 to 16, p=0.77946
b-rank test for bits 10 to 17, p=0.69514
b-rank test for bits 11 to 18, p=0.86342
b-rank test for bits 12 to 19, p=0.61412
b-rank test for bits 13 to 20, p=0.59851
b-rank test for bits 14 to 21, p=0.84927
b-rank test for bits 15 to 22, p=0.81982
b-rank test for bits 16 to 23, p=0.41196
b-rank test for bits 17 to 24, p=0.84777
b-rank test for bits 18 to 25, p=0.82590
b-rank test for bits 19 to 26, p=0.78258
b-rank test for bits 20 to 27, p=0.33453
b-rank test for bits 21 to 28, p=0.27981
b-rank test for bits 22 to 29, p=0.32286
b-rank test for bits 23 to 30, p=0.08795
b-rank test for bits 24 to 31, p=0.74382
b-rank test for bits 25 to 32, p=0.56182
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 = 0.104622
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-02_17:31
(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 141858 -0.12 0.452269
2 142446 1.25 0.895061
3 142208 0.70 0.757357
4 141537 -0.87 0.192169
5 141810 -0.23 0.408238
6 141811 -0.23 0.409146
7 142013 0.24 0.595695
8 142035 0.29 0.615476
9 141470 -1.03 0.152335
10 141908 -0.00 0.498760
11 141548 -0.84 0.199271
12 141428 -1.12 0.130379
13 141462 -1.05 0.147974
14 141633 -0.65 0.259259
15 142299 0.91 0.818706
16 142606 1.63 0.948209
17 142082 0.40 0.656686
18 142733 1.92 0.972852
19 141086 -1.92 0.027198
20 142367 1.07 0.857538
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-02_17:31
Bits used No. missing words z-score p-value
23 to 32 141549 -1.2425 0.107023
22 to 31 141673 -0.8149 0.207556
21 to 30 141780 -0.4460 0.327811
20 to 29 142161 0.8678 0.807256
19 to 28 142533 2.1506 0.984246
18 to 27 141808 -0.3494 0.363389
17 to 26 142172 0.9058 0.817468
16 to 25 141864 -0.1563 0.437894
15 to 24 141777 -0.4563 0.324083
14 to 23 141993 0.2885 0.613525
13 to 22 142101 0.6609 0.745672
12 to 21 141622 -0.9908 0.160893
11 to 20 142231 1.1092 0.866330
10 to 19 141624 -0.9839 0.162583
9 to 18 141963 0.1851 0.573413
8 to 17 142403 1.7023 0.955651
7 to 16 142138 0.7885 0.784803
6 to 15 141928 0.0644 0.525666
5 to 14 141926 0.0575 0.522920
4 to 13 142010 0.3471 0.635756
3 to 12 141940 0.1058 0.542113
2 to 11 141908 -0.0046 0.498170
1 to 10 141456 -1.5632 0.059002
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-02_17:31
Bits used No. missing words z-score p-value
28 to 32 141548 -1.2248 0.110316
27 to 31 142262 1.1955 0.884053
26 to 30 142534 2.1175 0.982892
25 to 29 141754 -0.5265 0.299256
24 to 28 141898 -0.0384 0.484682
23 to 27 141795 -0.3876 0.349171
22 to 26 142178 0.9107 0.818785
21 to 25 141850 -0.2011 0.420303
20 to 24 141315 -2.0147 0.021969
19 to 23 141489 -1.4248 0.077101
18 to 22 142039 0.4396 0.669872
17 to 21 141601 -1.0452 0.147968
16 to 20 142193 0.9616 0.831873
15 to 19 141762 -0.4994 0.308741
14 to 18 141991 0.2768 0.609051
13 to 17 142098 0.6396 0.738770
12 to 16 141949 0.1345 0.553486
11 to 15 142445 1.8158 0.965302
10 to 14 142079 0.5752 0.717406
9 to 13 141568 -1.1571 0.123626
8 to 12 142056 0.4972 0.690471
7 to 11 141839 -0.2384 0.405783
6 to 10 141792 -0.3977 0.345415
5 to 9 141860 -0.1672 0.433598
4 to 8 142219 1.0497 0.853079
3 to 7 141755 -0.5232 0.300434
2 to 6 141879 -0.1028 0.459056
1 to 5 141458 -1.5299 0.063017
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-02_17:31
Bits used No. missing words z-score p-value
31 to 32 141894 -0.0452 0.481966
30 to 31 142199 0.8545 0.803582
29 to 30 141939 0.0875 0.534872
28 to 29 141520 -1.1485 0.125388
27 to 28 141562 -1.0246 0.152783
26 to 27 142493 1.7217 0.957442
25 to 26 142303 1.1613 0.877234
24 to 25 142216 0.9046 0.817170
23 to 24 142259 1.0315 0.848841
22 to 23 141683 -0.6676 0.252182
21 to 22 141654 -0.7532 0.225669
20 to 21 141160 -2.2104 0.013538
19 to 20 141950 0.1200 0.547747
18 to 19 141734 -0.5172 0.302509
17 to 18 141435 -1.3992 0.080876
16 to 17 142410 1.4769 0.930149
15 to 16 141913 0.0108 0.504319
14 to 15 141800 -0.3225 0.373534
13 to 14 142330 1.2409 0.892681
12 to 13 141802 -0.3166 0.375771
11 to 12 142144 0.6922 0.755607
10 to 11 142202 0.8633 0.806023
9 to 10 141736 -0.5113 0.304571
8 to 9 142358 1.3235 0.907167
7 to 8 141322 -1.7325 0.041589
6 to 7 141938 0.0846 0.533699
5 to 6 142172 0.7748 0.780782
4 to 5 142051 0.4179 0.661992
3 to 4 141208 -2.0688 0.019281
2 to 3 141621 -0.8505 0.197515
1 to 2 142132 0.6568 0.744359
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-02_17:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2592.64 1.310 0.904926
Test results for specific bytes for dh-ranFile-2018-07-02_17:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2623.41 1.745 0.959530
2 to 9 2518.57 0.263 0.603579
3 to 10 2547.54 0.672 0.749310
4 to 11 2610.63 1.565 0.941154
5 to 12 2588.59 1.253 0.894861
6 to 13 2519.79 0.280 0.610197
7 to 14 2496.52 -0.049 0.480394
8 to 15 2330.54 -2.397 0.008276
9 to 16 2454.09 -0.649 0.258087
10 to 17 2565.27 0.923 0.822012
11 to 18 2507.88 0.111 0.544386
12 to 19 2435.64 -0.910 0.181363
13 to 20 2486.23 -0.195 0.422804
14 to 21 2534.93 0.494 0.689329
15 to 22 2408.69 -1.291 0.098298
16 to 23 2394.22 -1.496 0.067331
17 to 24 2385.55 -1.619 0.052767
18 to 25 2402.68 -1.376 0.084367
19 to 26 2422.59 -1.095 0.136817
20 to 27 2427.06 -1.032 0.151153
21 to 28 2502.11 0.030 0.511876
22 to 29 2614.73 1.623 0.947653
23 to 30 2434.28 -0.929 0.176351
24 to 31 2445.95 -0.764 0.222302
25 to 32 2451.25 -0.689 0.245259
CDPARK for dh-ranFile-2018-07-02_17:31: 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
3565 1.9178 0.972432
3537 0.6393 0.738676
3550 1.2329 0.891189
3503 -0.9132 0.180558
3522 -0.0457 0.481790
3530 0.3196 0.625377
3532 0.4110 0.659449
3554 1.4155 0.921543
3553 1.3699 0.914635
3547 1.0959 0.863437
Square side=100, avg. no. parked=3539.30 sample std.=17.32
p-value of the KSTEST for those 10 p-values: 0.017847
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-02_17:31
0.8565,0.8322,0.7286,0.8027,0.2350,0.8605,0.9893,0.1629,0.5118,0.3897,
The KS test for those 10 p-values: 0.187271
The 3DSPHERES test for dh-ranFile-2018-07-02_17:31
sample no r^3 equiv. uni.
1 17.151 0.435430
2 48.339 0.800375
3 18.380 0.458100
4 0.425 0.014077
5 13.663 0.365836
6 59.583 0.862769
7 49.043 0.805005
8 0.924 0.030317
9 9.907 0.281249
10 52.525 0.826370
11 1.930 0.062303
12 6.691 0.199919
13 7.933 0.232360
14 7.092 0.210541
15 66.369 0.890551
16 38.280 0.720845
17 23.487 0.542915
18 5.981 0.180758
19 81.216 0.933276
20 8.783 0.253792
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.598462
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-02_17:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 -1.2 1.5 -1.3 0.8 1.3
-0.3 1.5 -0.3 0.2 0.4 -0.5
-0.9 -0.4 0.6 1.1 -0.4 0.5
-0.5 -0.3 0.5 -1.6 0.1 0.5
-0.0 0.1 -1.0 1.2 -0.5 -1.9
0.2 1.0 0.1 0.2 -0.1 0.6
1.7 -0.4 -0.8 -0.1 -0.6 0.0
0.8
Chi-square with 42 degrees of freedom:31.053472
z-score=-1.194364, p-value=0.106944
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-02_17:31
Test no p-value
1 0.671498
2 0.350656
3 0.012651
4 0.238603
5 0.909926
6 0.028365
7 0.403853
8 0.228479
9 0.139651
10 0.198600
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.058874
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-02_17:31:
(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 66555 0.19 66609 0.05
3 25000.00 25116 0.54 24924 0.23
4 6666.67 6669 0.00 6810 3.08
5 1388.89 1391 0.00 1377 0.10
6 238.10 225 0.72 240 0.02
7 34.72 36 0.05 30 0.64
8 4.96 7 0.84 9 3.29
p=0.11362 p=0.71556
Number of rngs required: 688551, p-value: 0.568
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-02_17:31
No. of wins: Observed Expected
98779 98585.9
z-score= 0.864, pvalue=0.80616
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66813 66666.7 0.321 0.321
2 37724 37654.3 0.129 0.450
3 26787 26954.7 1.044 1.494
4 19328 19313.5 0.011 1.505
5 13743 13851.4 0.849 2.353
6 9961 9943.5 0.031 2.384
7 7133 7145.0 0.020 2.404
8 5052 5139.1 1.475 3.880
9 3720 3699.9 0.110 3.989
10 2669 2666.3 0.003 3.992
11 2001 1923.3 3.137 7.129
12 1401 1388.7 0.108 7.237
13 958 1003.7 2.082 9.319
14 692 726.1 1.605 10.924
15 553 525.8 1.403 12.327
16 388 381.2 0.123 12.450
17 276 276.5 0.001 12.452
18 221 200.8 2.026 14.477
19 145 146.0 0.007 14.484
20 104 106.2 0.046 14.530
21 331 287.1 6.708 21.238
Chisq= 21.24 for 20 degrees of freedom, p= 0.61677
SUMMARY of craptest
p-value for no. of wins: 0.806162
p-value for throws/game: 0.616767
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-02_17:31
No. of wins: Observed Expected
98400 98585.9
z-score=-0.831, pvalue=0.20291
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66569 66666.7 0.143 0.143
2 37619 37654.3 0.033 0.176
3 27091 26954.7 0.689 0.865
4 19267 19313.5 0.112 0.977
5 13926 13851.4 0.402 1.378
6 9783 9943.5 2.592 3.970
7 7252 7145.0 1.602 5.572
8 5129 5139.1 0.020 5.592
9 3658 3699.9 0.474 6.066
10 2734 2666.3 1.719 7.785
11 1938 1923.3 0.112 7.897
12 1424 1388.7 0.895 8.792
13 1043 1003.7 1.538 10.329
14 687 726.1 2.110 12.439
15 529 525.8 0.019 12.458
16 361 381.2 1.065 13.523
17 249 276.5 2.743 16.266
18 211 200.8 0.515 16.781
19 136 146.0 0.683 17.464
20 98 106.2 0.635 18.099
21 296 287.1 0.275 18.374
Chisq= 18.37 for 20 degrees of freedom, p= 0.43724
SUMMARY of craptest
p-value for no. of wins: 0.202911
p-value for throws/game: 0.437238
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0041,0.0083,0.0122,0.0127,0.0135,0.0141,0.0178,0.0193,0.0220,0.0272,
0.0284,0.0303,0.0416,0.0506,0.0528,0.0589,0.0590,0.0623,0.0630,0.0631,
0.0656,0.0673,0.0693,0.0704,0.0718,0.0771,0.0809,0.0831,0.0844,0.0880,
0.0961,0.0983,0.1046,0.1069,0.1070,0.1103,0.1136,0.1236,0.1254,0.1304,
0.1368,0.1397,0.1480,0.1480,0.1512,0.1523,0.1528,0.1584,0.1609,0.1626,
0.1629,0.1764,0.1806,0.1808,0.1814,0.1873,0.1897,0.1922,0.1975,0.1986,
0.1993,0.1999,0.2029,0.2034,0.2076,0.2105,0.2154,0.2223,0.2257,0.2285,
0.2324,0.2350,0.2386,0.2453,0.2522,0.2538,0.2557,0.2581,0.2593,0.2798,
0.2812,0.2920,0.2936,0.2993,0.3004,0.3025,0.3046,0.3087,0.3209,0.3229,
0.3241,0.3278,0.3345,0.3454,0.3492,0.3507,0.3525,0.3592,0.3634,0.3656,
0.3658,0.3735,0.3758,0.3781,0.3897,0.4039,0.4058,0.4082,0.4091,0.4120,
0.4203,0.4228,0.4266,0.4314,0.4336,0.4354,0.4372,0.4379,0.4381,0.4523,
0.4581,0.4591,0.4747,0.4804,0.4818,0.4820,0.4847,0.4949,0.4982,0.4988,
0.5043,0.5088,0.5118,0.5119,0.5169,0.5229,0.5257,0.5337,0.5349,0.5417,
0.5421,0.5429,0.5444,0.5477,0.5535,0.5567,0.5618,0.5676,0.5718,0.5734,
0.5819,0.5940,0.5957,0.5985,0.5985,0.5998,0.6036,0.6091,0.6102,0.6135,
0.6141,0.6154,0.6155,0.6168,0.6254,0.6358,0.6382,0.6445,0.6567,0.6594,
0.6620,0.6628,0.6699,0.6715,0.6893,0.6905,0.6951,0.7156,0.7174,0.7208,
0.7233,0.7286,0.7323,0.7387,0.7388,0.7438,0.7444,0.7457,0.7493,0.7535,
0.7556,0.7574,0.7727,0.7750,0.7774,0.7795,0.7808,0.7826,0.7848,0.7931,
0.8004,0.8027,0.8036,0.8050,0.8060,0.8062,0.8073,0.8123,0.8172,0.8175,
0.8187,0.8188,0.8198,0.8220,0.8259,0.8264,0.8319,0.8322,0.8325,0.8477,
0.8478,0.8488,0.8493,0.8505,0.8531,0.8565,0.8575,0.8605,0.8621,0.8628,
0.8634,0.8634,0.8663,0.8663,0.8691,0.8772,0.8841,0.8860,0.8906,0.8912,
0.8927,0.8949,0.8951,0.9049,0.9072,0.9099,0.9146,0.9149,0.9175,0.9184,
0.9215,0.9229,0.9301,0.9333,0.9412,0.9477,0.9482,0.9557,0.9574,0.9595,
0.9595,0.9653,0.9724,0.9729,0.9729,0.9829,0.9842,0.9855,0.9893,
Overall p-value after applying KStest on 269 p-values = 0.379413
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.