RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-17_07:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.56 30.2222 0.975214
2 to 25 15.56 20.2927 0.740470
3 to 26 15.79 7.0000 0.016451
4 to 27 15.48 21.4281 0.792274
5 to 28 15.56 23.6780 0.871548
6 to 29 15.80 24.7119 0.898655
7 to 30 15.91 14.9082 0.397908
8 to 31 15.58 23.1541 0.855701
9 to 32 16.08 17.7197 0.593275
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.059392
Tough bday spacings test for dh-ranFile-2018-06-17_07:31: 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 11 30 78 86 100 77 45 41 19 8 5
(O-E)^2/E 0.4 1.2 0.3 1.4 0.1 0.0 1.0 4.2 1.1 0.3 0.2
Birthday Spacings: Sum(O-E)^2/E= 10.191, p= 0.576
RESULTS OF GCD FOR dh-ranFile-2018-06-17_07:31
Euclid's algorithm:
p-value, steps to gcd: 0.645531
p-value, dist. of gcd's: 0.517804
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-17_07:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.953 0.717 0.128 0.778 0.657 0.606 0.322 0.583
Bits 8 to 15---> 0.378 0.020 0.966 0.550 0.889 0.695 0.192 0.023
Bits 16 to 23---> 0.965 0.275 0.601 0.533 0.066 0.044 0.165 0.294
Bits 24 to 31---> 0.637 0.859 0.781 0.685 0.883 0.217 0.597 0.707
KS test for the above 32 p values: 0.258
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-17_07:31,
p-values for 5 runs: 0.2748, 0.7663, 0.1978, 0.8004, 0.3519
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-17_07:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 168 211.4 8.917 8.917
r= 29 5094 5134.0 0.312 9.228
r= 30 23096 23103.0 0.002 9.231
r= 31 11642 11551.5 0.709 9.939
chi-square = 9.939 with df = 3; p-value = 0.981
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-17_07:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 182 211.4 4.093 4.093
r= 30 5066 5134.0 0.901 4.994
r= 31 23170 23103.0 0.194 5.188
r= 32 11582 11551.5 0.080 5.269
chi-square = 5.269 with df = 3; p-value = 0.847
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-17_07:31
b-rank test for bits 1 to 8, p=0.60749
b-rank test for bits 2 to 9, p=0.56834
b-rank test for bits 3 to 10, p=0.16878
b-rank test for bits 4 to 11, p=0.40694
b-rank test for bits 5 to 12, p=0.69959
b-rank test for bits 6 to 13, p=0.68002
b-rank test for bits 7 to 14, p=0.77775
b-rank test for bits 8 to 15, p=0.62121
b-rank test for bits 9 to 16, p=0.34195
b-rank test for bits 10 to 17, p=0.32556
b-rank test for bits 11 to 18, p=0.62706
b-rank test for bits 12 to 19, p=0.42816
b-rank test for bits 13 to 20, p=0.14952
b-rank test for bits 14 to 21, p=0.72172
b-rank test for bits 15 to 22, p=0.08385
b-rank test for bits 16 to 23, p=0.27873
b-rank test for bits 17 to 24, p=0.44952
b-rank test for bits 18 to 25, p=0.91427
b-rank test for bits 19 to 26, p=0.75091
b-rank test for bits 20 to 27, p=0.94409
b-rank test for bits 21 to 28, p=0.53335
b-rank test for bits 22 to 29, p=0.46042
b-rank test for bits 23 to 30, p=0.63979
b-rank test for bits 24 to 31, p=0.70769
b-rank test for bits 25 to 32, p=0.51144
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 = 0.281424
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-17_07:31
(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 141189 -1.68 0.046186
2 141853 -0.13 0.447646
3 141222 -1.61 0.054147
4 141475 -1.01 0.155103
5 141409 -1.17 0.121203
6 141685 -0.52 0.300092
7 142180 0.63 0.736439
8 142174 0.62 0.731840
9 141341 -1.33 0.092110
10 142126 0.51 0.693655
11 141674 -0.55 0.291216
12 142041 0.31 0.620822
13 142152 0.57 0.714638
14 142514 1.41 0.921140
15 141715 -0.45 0.324899
16 142179 0.63 0.735676
17 142043 0.31 0.622599
18 141968 0.14 0.554516
19 141380 -1.24 0.108090
20 142604 1.62 0.947712
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-17_07:31
Bits used No. missing words z-score p-value
23 to 32 141980 0.2437 0.596264
22 to 31 141831 -0.2701 0.393540
21 to 30 142025 0.3989 0.655003
20 to 29 142425 1.7782 0.962312
19 to 28 141927 0.0609 0.524293
18 to 27 142031 0.4196 0.662594
17 to 26 141751 -0.5460 0.292545
16 to 25 141927 0.0609 0.524293
15 to 24 141707 -0.6977 0.242686
14 to 23 141986 0.2644 0.604256
13 to 22 142385 1.6402 0.949523
12 to 21 141622 -0.9908 0.160893
11 to 20 141997 0.3023 0.618792
10 to 19 142238 1.1333 0.871465
9 to 18 141642 -0.9218 0.178309
8 to 17 142092 0.6299 0.735619
7 to 16 141998 0.3058 0.620106
6 to 15 141986 0.2644 0.604256
5 to 14 141227 -2.3529 0.009315
4 to 13 141552 -1.2322 0.108942
3 to 12 141451 -1.5804 0.057002
2 to 11 142218 1.0644 0.856422
1 to 10 142408 1.7196 0.957243
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-17_07:31
Bits used No. missing words z-score p-value
28 to 32 141883 -0.0893 0.464440
27 to 31 141746 -0.5537 0.289905
26 to 30 141960 0.1718 0.568188
25 to 29 141721 -0.6384 0.261605
24 to 28 142009 0.3379 0.632267
23 to 27 142199 0.9819 0.836933
22 to 26 141877 -0.1096 0.456366
21 to 25 142318 1.3853 0.917023
20 to 24 141887 -0.0757 0.469831
19 to 23 141492 -1.4147 0.078581
18 to 22 141994 0.2870 0.612950
17 to 21 141561 -1.1808 0.118845
16 to 20 141872 -0.1265 0.449651
15 to 19 141762 -0.4994 0.308741
14 to 18 142144 0.7955 0.786836
13 to 17 142101 0.6497 0.742066
12 to 16 141941 0.1074 0.542747
11 to 15 141868 -0.1401 0.444290
10 to 14 142039 0.4396 0.669872
9 to 13 141957 0.1616 0.564187
8 to 12 142095 0.6294 0.735453
7 to 11 142036 0.4294 0.666180
6 to 10 141778 -0.4452 0.328093
5 to 9 142052 0.4836 0.685675
4 to 8 142391 1.6328 0.948742
3 to 7 142025 0.3921 0.652509
2 to 6 142156 0.8362 0.798470
1 to 5 141941 0.1074 0.542747
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-17_07:31
Bits used No. missing words z-score p-value
31 to 32 141745 -0.4847 0.313927
30 to 31 142661 2.2173 0.986699
29 to 30 142201 0.8604 0.805211
28 to 29 141870 -0.1160 0.453819
27 to 28 142470 1.6539 0.950925
26 to 27 142232 0.9518 0.829408
25 to 26 142220 0.9164 0.820280
24 to 25 142245 0.9902 0.838956
23 to 24 141442 -1.3786 0.084016
22 to 23 141640 -0.7945 0.213457
21 to 22 141523 -1.1396 0.127223
20 to 21 141470 -1.2960 0.097495
19 to 20 142085 0.5182 0.697841
18 to 19 141714 -0.5762 0.282242
17 to 18 141785 -0.3668 0.356901
16 to 17 142030 0.3560 0.639064
15 to 16 142206 0.8751 0.809249
14 to 15 142286 1.1111 0.866742
13 to 14 141611 -0.8800 0.189422
12 to 13 141829 -0.2370 0.406343
11 to 12 141562 -1.0246 0.152783
10 to 11 141815 -0.2783 0.390407
9 to 10 142026 0.3442 0.634637
8 to 9 142099 0.5595 0.712089
7 to 8 141620 -0.8535 0.196696
6 to 7 142243 0.9843 0.837510
5 to 6 142177 0.7896 0.785116
4 to 5 142078 0.4976 0.690600
3 to 4 142025 0.3412 0.633527
2 to 3 141660 -0.7355 0.231022
1 to 2 141768 -0.4169 0.338375
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-17_07:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2579.63 1.126 0.869960
Test results for specific bytes for dh-ranFile-2018-06-17_07:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2490.22 -0.138 0.445001
2 to 9 2378.82 -1.714 0.043289
3 to 10 2536.23 0.512 0.695806
4 to 11 2608.50 1.534 0.937536
5 to 12 2346.62 -2.169 0.015035
6 to 13 2497.49 -0.035 0.485868
7 to 14 2557.22 0.809 0.790804
8 to 15 2557.30 0.810 0.791136
9 to 16 2525.82 0.365 0.642508
10 to 17 2444.45 -0.786 0.216054
11 to 18 2502.16 0.031 0.512173
12 to 19 2442.53 -0.813 0.208192
13 to 20 2564.05 0.906 0.817469
14 to 21 2543.51 0.615 0.730813
15 to 22 2435.48 -0.912 0.180755
16 to 23 2456.37 -0.617 0.268628
17 to 24 2623.31 1.744 0.959403
18 to 25 2416.24 -1.185 0.118107
19 to 26 2545.83 0.648 0.741540
20 to 27 2558.54 0.828 0.796111
21 to 28 2485.21 -0.209 0.417160
22 to 29 2443.69 -0.796 0.212917
23 to 30 2560.97 0.862 0.805712
24 to 31 2389.54 -1.562 0.059130
25 to 32 2462.82 -0.526 0.299534
CDPARK for dh-ranFile-2018-06-17_07:31: 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
3505 -0.8219 0.205562
3524 0.0457 0.518210
3530 0.3196 0.625377
3485 -1.7352 0.041356
3531 0.3653 0.642555
3535 0.5479 0.708135
3489 -1.5525 0.060270
3508 -0.6849 0.246694
3540 0.7763 0.781201
3519 -0.1826 0.427537
Square side=100, avg. no. parked=3516.60 sample std.=18.17
p-value of the KSTEST for those 10 p-values: 0.608593
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-17_07:31
0.5792,0.3600,0.7251,0.3805,0.3563,0.6023,0.3085,0.9365,0.4668,0.6255,
The KS test for those 10 p-values: 0.386351
The 3DSPHERES test for dh-ranFile-2018-06-17_07:31
sample no r^3 equiv. uni.
1 23.665 0.545628
2 4.245 0.131945
3 14.641 0.386171
4 51.601 0.820942
5 96.746 0.960239
6 19.790 0.482978
7 9.671 0.275579
8 11.521 0.318902
9 10.302 0.290645
10 1.640 0.053202
11 26.952 0.592779
12 38.304 0.721069
13 12.293 0.336202
14 37.843 0.716751
15 36.099 0.699799
16 2.927 0.092965
17 5.533 0.168413
18 22.365 0.525502
19 30.867 0.642603
20 11.119 0.309713
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.653919
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-17_07:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 0.9 -0.4 1.8 -0.9 0.3
2.2 -0.1 -1.0 0.2 -0.9 -0.3
0.5 -1.2 -1.4 0.5 1.0 1.9
-1.5 -0.2 1.2 -0.8 0.4 -0.8
-0.0 0.0 1.6 0.5 0.6 -0.5
0.1 -0.5 -2.3 -0.9 1.3 1.1
-0.5 0.2 -1.2 -0.7 -0.6 -1.0
-0.1
Chi-square with 42 degrees of freedom:41.820788
z-score=-0.019554, p-value=0.521240
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-17_07:31
Test no p-value
1 0.220892
2 0.375177
3 0.007363
4 0.553926
5 0.229750
6 0.544004
7 0.021988
8 0.128761
9 0.878370
10 0.780793
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.208469
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-17_07:31:
(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 66654 0.00 66792 0.24
3 25000.00 25031 0.04 24877 0.61
4 6666.67 6606 0.55 6580 1.13
5 1388.89 1410 0.32 1457 3.34
6 238.10 245 0.20 238 0.00
7 34.72 46 3.66 49 5.87
8 4.96 7 0.84 6 0.22
p=0.53267 p=0.92320
Number of rngs required: 688638, p-value: 0.607
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-17_07:31
No. of wins: Observed Expected
98598 98585.9
z-score= 0.054, pvalue=0.52165
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66786 66666.7 0.214 0.214
2 37604 37654.3 0.067 0.281
3 27032 26954.7 0.221 0.502
4 19331 19313.5 0.016 0.518
5 13729 13851.4 1.082 1.600
6 9857 9943.5 0.753 2.353
7 7086 7145.0 0.488 2.841
8 5156 5139.1 0.056 2.897
9 3735 3699.9 0.334 3.230
10 2683 2666.3 0.105 3.335
11 1973 1923.3 1.283 4.618
12 1371 1388.7 0.227 4.845
13 996 1003.7 0.059 4.904
14 723 726.1 0.014 4.917
15 562 525.8 2.487 7.405
16 379 381.2 0.012 7.417
17 250 276.5 2.547 9.964
18 199 200.8 0.017 9.980
19 137 146.0 0.553 10.533
20 107 106.2 0.006 10.539
21 304 287.1 0.993 11.532
Chisq= 11.53 for 20 degrees of freedom, p= 0.06876
SUMMARY of craptest
p-value for no. of wins: 0.521653
p-value for throws/game: 0.068763
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-17_07:31
No. of wins: Observed Expected
98245 98585.9
z-score=-1.525, pvalue=0.06369
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66756 66666.7 0.120 0.120
2 37618 37654.3 0.035 0.155
3 26924 26954.7 0.035 0.190
4 19365 19313.5 0.138 0.327
5 13756 13851.4 0.657 0.985
6 10063 9943.5 1.435 2.420
7 7017 7145.0 2.294 4.714
8 5122 5139.1 0.057 4.770
9 3754 3699.9 0.792 5.563
10 2643 2666.3 0.204 5.766
11 1919 1923.3 0.010 5.776
12 1391 1388.7 0.004 5.780
13 1011 1003.7 0.053 5.832
14 739 726.1 0.228 6.060
15 531 525.8 0.051 6.111
16 383 381.2 0.009 6.120
17 284 276.5 0.201 6.321
18 185 200.8 1.248 7.569
19 152 146.0 0.248 7.817
20 105 106.2 0.014 7.831
21 282 287.1 0.091 7.922
Chisq= 7.92 for 20 degrees of freedom, p= 0.00763
SUMMARY of craptest
p-value for no. of wins: 0.063690
p-value for throws/game: 0.007627
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0074,0.0076,0.0093,0.0150,0.0165,0.0197,0.0220,0.0226,0.0414,0.0433,
0.0445,0.0462,0.0532,0.0541,0.0570,0.0591,0.0594,0.0603,0.0637,0.0659,
0.0688,0.0786,0.0839,0.0840,0.0921,0.0930,0.0975,0.1081,0.1089,0.1181,
0.1188,0.1212,0.1272,0.1280,0.1288,0.1319,0.1495,0.1528,0.1551,0.1609,
0.1645,0.1684,0.1688,0.1783,0.1808,0.1894,0.1919,0.1967,0.1978,0.2056,
0.2082,0.2085,0.2129,0.2135,0.2161,0.2171,0.2209,0.2298,0.2310,0.2427,
0.2467,0.2576,0.2616,0.2686,0.2748,0.2754,0.2756,0.2787,0.2814,0.2822,
0.2899,0.2906,0.2912,0.2925,0.2943,0.2995,0.3001,0.3085,0.3087,0.3097,
0.3139,0.3189,0.3219,0.3249,0.3256,0.3281,0.3362,0.3384,0.3420,0.3519,
0.3563,0.3569,0.3600,0.3752,0.3782,0.3805,0.3862,0.3864,0.3904,0.3935,
0.3979,0.4063,0.4069,0.4172,0.4275,0.4282,0.4443,0.4450,0.4476,0.4495,
0.4497,0.4538,0.4564,0.4604,0.4644,0.4668,0.4698,0.4830,0.4859,0.5114,
0.5122,0.5178,0.5182,0.5212,0.5217,0.5243,0.5243,0.5255,0.5327,0.5329,
0.5333,0.5427,0.5427,0.5440,0.5456,0.5495,0.5539,0.5545,0.5642,0.5682,
0.5683,0.5761,0.5792,0.5825,0.5928,0.5933,0.5963,0.5970,0.6008,0.6023,
0.6043,0.6043,0.6055,0.6066,0.6075,0.6086,0.6130,0.6188,0.6201,0.6208,
0.6212,0.6226,0.6254,0.6255,0.6271,0.6323,0.6335,0.6346,0.6368,0.6391,
0.6398,0.6425,0.6426,0.6426,0.6455,0.6525,0.6539,0.6550,0.6571,0.6626,
0.6662,0.6699,0.6800,0.6854,0.6857,0.6906,0.6937,0.6950,0.6958,0.6978,
0.6996,0.6998,0.7067,0.7077,0.7081,0.7121,0.7146,0.7168,0.7168,0.7211,
0.7217,0.7251,0.7308,0.7318,0.7355,0.7356,0.7357,0.7364,0.7405,0.7415,
0.7421,0.7509,0.7663,0.7778,0.7784,0.7808,0.7812,0.7812,0.7851,0.7868,
0.7908,0.7911,0.7923,0.7961,0.7985,0.8004,0.8052,0.8057,0.8092,0.8175,
0.8203,0.8209,0.8294,0.8369,0.8375,0.8390,0.8469,0.8557,0.8564,0.8589,
0.8667,0.8700,0.8715,0.8715,0.8784,0.8830,0.8889,0.8987,0.9143,0.9170,
0.9211,0.9232,0.9365,0.9375,0.9441,0.9477,0.9487,0.9495,0.9509,0.9534,
0.9572,0.9594,0.9602,0.9623,0.9650,0.9665,0.9752,0.9809,0.9867,
Overall p-value after applying KStest on 269 p-values = 0.290147
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.