RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-08_01:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.70 14.4129 0.362308
2 to 25 15.69 17.4567 0.576139
3 to 26 15.38 36.4440 0.996000
4 to 27 15.55 24.9108 0.903276
5 to 28 15.66 19.7793 0.714325
6 to 29 15.62 13.9693 0.330724
7 to 30 15.72 15.9834 0.474986
8 to 31 15.73 16.9308 0.540938
9 to 32 15.73 15.7553 0.458757
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.290712
Tough bday spacings test for dh-ranFile-2018-07-08_01:31: 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 9 33 60 91 88 105 54 32 20 5 3
(O-E)^2/E 0.0 0.4 2.4 0.5 1.0 9.2 0.1 0.2 1.8 0.4 0.3
Birthday Spacings: Sum(O-E)^2/E= 16.076, p= 0.903
RESULTS OF GCD FOR dh-ranFile-2018-07-08_01:31
Euclid's algorithm:
p-value, steps to gcd: 0.347534
p-value, dist. of gcd's: 0.871131
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-08_01:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.793 0.402 0.543 0.976 0.441 0.556 0.513 0.736
Bits 8 to 15---> 0.435 0.513 0.165 0.404 0.292 0.407 0.003 0.492
Bits 16 to 23---> 0.610 0.152 0.195 0.935 0.697 0.035 0.549 0.056
Bits 24 to 31---> 0.742 0.407 0.095 0.619 0.731 0.269 0.055 0.343
KS test for the above 32 p values: 0.697
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-08_01:31,
p-values for 5 runs: 0.1972, 0.8430, 0.9896, 0.3125, 0.0820
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-08_01:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 204 211.4 0.260 0.260
r= 29 5213 5134.0 1.215 1.476
r= 30 22964 23103.0 0.837 2.312
r= 31 11619 11551.5 0.394 2.707
chi-square = 2.707 with df = 3; p-value = 0.561
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-08_01:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 216 211.4 0.099 0.099
r= 30 5208 5134.0 1.066 1.166
r= 31 22930 23103.0 1.296 2.462
r= 32 11646 11551.5 0.773 3.234
chi-square = 3.234 with df = 3; p-value = 0.643
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-08_01:31
b-rank test for bits 1 to 8, p=0.61380
b-rank test for bits 2 to 9, p=0.44994
b-rank test for bits 3 to 10, p=0.58467
b-rank test for bits 4 to 11, p=0.77680
b-rank test for bits 5 to 12, p=0.37942
b-rank test for bits 6 to 13, p=0.42017
b-rank test for bits 7 to 14, p=0.42807
b-rank test for bits 8 to 15, p=0.59233
b-rank test for bits 9 to 16, p=0.35036
b-rank test for bits 10 to 17, p=0.63388
b-rank test for bits 11 to 18, p=0.43391
b-rank test for bits 12 to 19, p=0.00374
b-rank test for bits 13 to 20, p=0.74140
b-rank test for bits 14 to 21, p=0.33297
b-rank test for bits 15 to 22, p=0.32004
b-rank test for bits 16 to 23, p=0.82417
b-rank test for bits 17 to 24, p=0.02752
b-rank test for bits 18 to 25, p=0.35149
b-rank test for bits 19 to 26, p=0.67750
b-rank test for bits 20 to 27, p=0.24096
b-rank test for bits 21 to 28, p=0.18586
b-rank test for bits 22 to 29, p=0.19956
b-rank test for bits 23 to 30, p=0.66300
b-rank test for bits 24 to 31, p=0.30780
b-rank test for bits 25 to 32, p=0.28908
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 = 0.130364
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-08_01:31
(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 141690 -0.51 0.304167
2 142370 1.08 0.859111
3 141841 -0.16 0.436579
4 142501 1.38 0.916577
5 141940 0.07 0.528563
6 141418 -1.15 0.125491
7 142773 2.02 0.978200
8 141063 -1.98 0.023998
9 142027 0.27 0.608315
10 141238 -1.57 0.058379
11 141484 -0.99 0.160169
12 141995 0.20 0.579324
13 142264 0.83 0.796354
14 142247 0.79 0.784929
15 140825 -2.53 0.005647
16 141891 -0.04 0.482920
17 142147 0.56 0.710657
18 142224 0.74 0.768894
19 141833 -0.18 0.429228
20 141432 -1.12 0.132370
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-08_01:31
Bits used No. missing words z-score p-value
23 to 32 141816 -0.3218 0.373792
22 to 31 142027 0.4058 0.657540
21 to 30 142035 0.4333 0.667618
20 to 29 141670 -0.8253 0.204608
19 to 28 141850 -0.2046 0.418948
18 to 27 141592 -1.0942 0.136925
17 to 26 141604 -1.0529 0.146202
16 to 25 142357 1.5437 0.938668
15 to 24 141630 -0.9632 0.167722
14 to 23 141480 -1.4804 0.069377
13 to 22 141981 0.2471 0.597599
12 to 21 141723 -0.6425 0.260269
11 to 20 142216 1.0575 0.854854
10 to 19 141992 0.2851 0.612204
9 to 18 142021 0.3851 0.649907
8 to 17 142029 0.4127 0.660070
7 to 16 141919 0.0333 0.513300
6 to 15 141900 -0.0322 0.487167
5 to 14 142054 0.4989 0.691062
4 to 13 142197 0.9920 0.839393
3 to 12 141997 0.3023 0.618792
2 to 11 141935 0.0885 0.535267
1 to 10 142083 0.5989 0.725368
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-08_01:31
Bits used No. missing words z-score p-value
28 to 32 141659 -0.8486 0.198059
27 to 31 141362 -1.8554 0.031773
26 to 30 141912 0.0091 0.503611
25 to 29 142150 0.8158 0.792702
24 to 28 142165 0.8667 0.806941
23 to 27 141888 -0.0723 0.471180
22 to 26 141956 0.1582 0.562852
21 to 25 142008 0.3345 0.630989
20 to 24 142347 1.4836 0.931046
19 to 23 141599 -1.0520 0.146408
18 to 22 142094 0.6260 0.734343
17 to 21 142207 1.0091 0.843525
16 to 20 142325 1.4091 0.920590
15 to 19 142122 0.7209 0.764519
14 to 18 141583 -1.1062 0.134319
13 to 17 141878 -0.1062 0.457711
12 to 16 142261 1.1921 0.883389
11 to 15 141965 0.1887 0.574841
10 to 14 142121 0.7175 0.763475
9 to 13 141698 -0.7164 0.236881
8 to 12 141698 -0.7164 0.236881
7 to 11 141876 -0.1130 0.455022
6 to 10 141675 -0.7943 0.213499
5 to 9 142309 1.3548 0.912262
4 to 8 141853 -0.1909 0.424283
3 to 7 142089 0.6091 0.728755
2 to 6 141937 0.0938 0.537365
1 to 5 141743 -0.5638 0.286435
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-08_01:31
Bits used No. missing words z-score p-value
31 to 32 141887 -0.0659 0.473741
30 to 31 141812 -0.2871 0.387014
29 to 30 142331 1.2439 0.893225
28 to 29 142075 0.4887 0.687474
27 to 28 141999 0.2645 0.604308
26 to 27 142314 1.1937 0.883706
25 to 26 142127 0.6421 0.739594
24 to 25 141836 -0.2163 0.414372
23 to 24 141548 -1.0659 0.143241
22 to 23 141805 -0.3078 0.379133
21 to 22 142190 0.8279 0.796146
20 to 21 142045 0.4002 0.655498
19 to 20 141672 -0.7001 0.241936
18 to 19 141713 -0.5791 0.281246
17 to 18 142146 0.6981 0.757456
16 to 17 141554 -1.0482 0.147280
15 to 16 141623 -0.8446 0.199158
14 to 15 141653 -0.7561 0.224784
13 to 14 141682 -0.6706 0.251241
12 to 13 141682 -0.6706 0.251241
11 to 12 141542 -1.0836 0.139278
10 to 11 141874 -0.1042 0.458498
9 to 10 141413 -1.4641 0.071583
8 to 9 142254 1.0167 0.845358
7 to 8 142382 1.3943 0.918388
6 to 7 141726 -0.5408 0.294324
5 to 6 141761 -0.4376 0.330856
4 to 5 141536 -1.1013 0.135390
3 to 4 141505 -1.1927 0.116491
2 to 3 142363 1.3383 0.909594
1 to 2 141632 -0.8181 0.206655
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-08_01:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2583.31 1.178 0.880625
Test results for specific bytes for dh-ranFile-2018-07-08_01:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2560.95 0.862 0.805644
2 to 9 2562.86 0.889 0.813007
3 to 10 2498.35 -0.023 0.490680
4 to 11 2427.39 -1.027 0.152252
5 to 12 2565.67 0.929 0.823478
6 to 13 2367.58 -1.873 0.030550
7 to 14 2546.09 0.652 0.742723
8 to 15 2543.49 0.615 0.730721
9 to 16 2527.12 0.384 0.649348
10 to 17 2486.22 -0.195 0.422718
11 to 18 2579.09 1.119 0.868325
12 to 19 2420.00 -1.131 0.128959
13 to 20 2459.91 -0.567 0.285369
14 to 21 2431.23 -0.973 0.165387
15 to 22 2543.50 0.615 0.730767
16 to 23 2628.29 1.814 0.965189
17 to 24 2539.81 0.563 0.713304
18 to 25 2516.66 0.236 0.593132
19 to 26 2412.32 -1.240 0.107490
20 to 27 2580.55 1.139 0.872666
21 to 28 2357.03 -2.022 0.021594
22 to 29 2370.56 -1.831 0.033585
23 to 30 2407.10 -1.314 0.094447
24 to 31 2432.13 -0.960 0.168560
25 to 32 2456.11 -0.621 0.267384
CDPARK for dh-ranFile-2018-07-08_01:31: 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
3528 0.2283 0.590298
3552 1.3242 0.907282
3531 0.3653 0.642555
3536 0.5936 0.723613
3552 1.3242 0.907282
3550 1.2329 0.891189
3523 0.0000 0.500000
3475 -2.1918 0.014198
3568 2.0548 0.980051
3488 -1.5982 0.055002
Square side=100, avg. no. parked=3530.30 sample std.=27.73
p-value of the KSTEST for those 10 p-values: 0.130938
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-08_01:31
0.1673,0.9126,0.3779,0.7845,0.5910,0.8330,0.8630,0.1392,0.4663,0.8465,
The KS test for those 10 p-values: 0.398907
The 3DSPHERES test for dh-ranFile-2018-07-08_01:31
sample no r^3 equiv. uni.
1 27.640 0.602010
2 22.113 0.521504
3 60.042 0.864853
4 54.487 0.837365
5 59.375 0.861815
6 23.387 0.541395
7 12.927 0.350084
8 10.282 0.290174
9 9.172 0.263409
10 0.388 0.012859
11 22.898 0.533853
12 26.323 0.584155
13 7.036 0.209064
14 10.852 0.303525
15 11.604 0.320784
16 9.043 0.260251
17 24.996 0.565341
18 4.475 0.138561
19 102.464 0.967139
20 8.571 0.248509
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.585117
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-08_01:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 0.9 -1.1 0.3 -0.4 0.5
-0.7 0.3 -1.3 -0.0 0.5 0.2
-0.8 -2.0 -1.8 -0.8 1.2 2.0
1.2 0.6 -0.0 0.1 -0.0 -0.8
0.4 1.1 0.7 -0.5 -0.0 -0.8
-0.3 0.4 -0.5 -0.3 0.5 0.2
0.3 -1.0 0.1 -1.3 0.1 0.0
0.8
Chi-square with 42 degrees of freedom:30.747398
z-score=-1.227760, p-value=0.099575
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-08_01:31
Test no p-value
1 0.179296
2 0.827561
3 0.015747
4 0.298834
5 0.601068
6 0.081355
7 0.165375
8 0.652919
9 0.367592
10 0.020441
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.058835
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-08_01:31:
(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 66680 0.00 66542 0.23
3 25000.00 25184 1.35 25036 0.05
4 6666.67 6543 2.29 6781 1.96
5 1388.89 1320 3.42 1360 0.60
6 238.10 232 0.16 236 0.02
7 34.72 34 0.01 37 0.15
8 4.96 6 0.22 7 0.84
p=0.71936 p=0.30355
Number of rngs required: 688149, p-value: 0.385
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-08_01:31
No. of wins: Observed Expected
98659 98585.9
z-score= 0.327, pvalue=0.62822
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66561 66666.7 0.167 0.167
2 37456 37654.3 1.045 1.212
3 27162 26954.7 1.594 2.806
4 19331 19313.5 0.016 2.822
5 13820 13851.4 0.071 2.893
6 9955 9943.5 0.013 2.906
7 7136 7145.0 0.011 2.918
8 5164 5139.1 0.121 3.039
9 3687 3699.9 0.045 3.083
10 2632 2666.3 0.441 3.524
11 1973 1923.3 1.283 4.807
12 1398 1388.7 0.062 4.869
13 1021 1003.7 0.298 5.167
14 741 726.1 0.304 5.471
15 484 525.8 3.328 8.799
16 427 381.2 5.515 14.314
17 268 276.5 0.264 14.578
18 223 200.8 2.447 17.026
19 160 146.0 1.346 18.371
20 111 106.2 0.216 18.587
21 290 287.1 0.029 18.616
Chisq= 18.62 for 20 degrees of freedom, p= 0.45309
SUMMARY of craptest
p-value for no. of wins: 0.628216
p-value for throws/game: 0.453086
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-08_01:31
No. of wins: Observed Expected
98636 98585.9
z-score= 0.224, pvalue=0.58872
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66729 66666.7 0.058 0.058
2 37315 37654.3 3.058 3.116
3 26923 26954.7 0.037 3.153
4 19305 19313.5 0.004 3.157
5 14003 13851.4 1.659 4.816
6 10035 9943.5 0.841 5.657
7 7212 7145.0 0.628 6.285
8 5164 5139.1 0.121 6.406
9 3732 3699.9 0.279 6.685
10 2650 2666.3 0.100 6.785
11 1897 1923.3 0.360 7.145
12 1377 1388.7 0.099 7.244
13 997 1003.7 0.045 7.289
14 723 726.1 0.014 7.303
15 534 525.8 0.127 7.429
16 389 381.2 0.162 7.591
17 284 276.5 0.201 7.792
18 175 200.8 3.322 11.115
19 137 146.0 0.553 11.667
20 110 106.2 0.135 11.802
21 309 287.1 1.668 13.471
Chisq= 13.47 for 20 degrees of freedom, p= 0.14371
SUMMARY of craptest
p-value for no. of wins: 0.588723
p-value for throws/game: 0.143709
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0026,0.0037,0.0056,0.0129,0.0142,0.0157,0.0204,0.0216,0.0240,0.0275,
0.0306,0.0318,0.0336,0.0346,0.0550,0.0551,0.0556,0.0584,0.0588,0.0694,
0.0716,0.0814,0.0820,0.0944,0.0954,0.0996,0.1075,0.1165,0.1255,0.1290,
0.1304,0.1309,0.1324,0.1343,0.1354,0.1369,0.1386,0.1392,0.1393,0.1432,
0.1437,0.1462,0.1464,0.1473,0.1516,0.1523,0.1602,0.1652,0.1654,0.1654,
0.1673,0.1677,0.1686,0.1793,0.1859,0.1950,0.1972,0.1981,0.1992,0.1996,
0.2046,0.2067,0.2091,0.2135,0.2248,0.2369,0.2369,0.2410,0.2419,0.2485,
0.2512,0.2512,0.2603,0.2603,0.2634,0.2674,0.2687,0.2812,0.2854,0.2864,
0.2891,0.2902,0.2907,0.2915,0.2943,0.2988,0.3035,0.3035,0.3042,0.3078,
0.3125,0.3200,0.3208,0.3307,0.3309,0.3330,0.3426,0.3475,0.3501,0.3504,
0.3515,0.3623,0.3676,0.3738,0.3779,0.3791,0.3794,0.3850,0.3870,0.3989,
0.4015,0.4044,0.4066,0.4072,0.4144,0.4189,0.4202,0.4227,0.4243,0.4281,
0.4292,0.4339,0.4348,0.4366,0.4411,0.4499,0.4531,0.4550,0.4577,0.4585,
0.4588,0.4663,0.4712,0.4737,0.4750,0.4829,0.4872,0.4907,0.4923,0.5000,
0.5036,0.5125,0.5129,0.5133,0.5215,0.5286,0.5339,0.5353,0.5374,0.5409,
0.5414,0.5430,0.5489,0.5559,0.5609,0.5629,0.5653,0.5748,0.5761,0.5793,
0.5842,0.5847,0.5851,0.5887,0.5903,0.5910,0.5923,0.5931,0.5976,0.6011,
0.6020,0.6043,0.6083,0.6097,0.6122,0.6138,0.6187,0.6188,0.6282,0.6310,
0.6339,0.6426,0.6431,0.6493,0.6499,0.6529,0.6555,0.6575,0.6601,0.6630,
0.6676,0.6775,0.6875,0.6911,0.6968,0.6972,0.7107,0.7133,0.7143,0.7194,
0.7236,0.7254,0.7288,0.7307,0.7308,0.7314,0.7343,0.7356,0.7396,0.7414,
0.7423,0.7427,0.7575,0.7635,0.7645,0.7689,0.7768,0.7845,0.7849,0.7927,
0.7929,0.7961,0.7964,0.8056,0.8069,0.8130,0.8235,0.8242,0.8276,0.8330,
0.8374,0.8394,0.8430,0.8435,0.8454,0.8465,0.8549,0.8591,0.8618,0.8630,
0.8649,0.8683,0.8711,0.8727,0.8806,0.8834,0.8837,0.8912,0.8932,0.9025,
0.9033,0.9073,0.9073,0.9096,0.9123,0.9126,0.9166,0.9184,0.9206,0.9310,
0.9347,0.9387,0.9652,0.9671,0.9758,0.9782,0.9801,0.9896,0.9960,
Overall p-value after applying KStest on 269 p-values = 0.390587
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.