RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-05_14:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.53 17.8970 0.604635
2 to 25 15.55 19.7404 0.712275
3 to 26 15.66 17.8706 0.602951
4 to 27 15.81 14.3640 0.358809
5 to 28 15.59 30.6946 0.978250
6 to 29 15.49 24.5128 0.893841
7 to 30 15.62 18.1279 0.619186
8 to 31 15.64 38.3631 0.997810
9 to 32 16.01 30.0275 0.973853
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.005825
Tough bday spacings test for dh-ranFile-2018-07-05_14:31: 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 14 36 69 99 104 67 55 24 24 5 3
(O-E)^2/E 2.6 0.0 0.2 0.0 0.4 1.6 0.2 1.1 5.6 0.4 0.3
Birthday Spacings: Sum(O-E)^2/E= 12.371, p= 0.739
RESULTS OF GCD FOR dh-ranFile-2018-07-05_14:31
Euclid's algorithm:
p-value, steps to gcd: 0.276743
p-value, dist. of gcd's: 0.807555
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-05_14:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.021 0.825 0.099 0.219 0.379 0.162 0.942 0.493
Bits 8 to 15---> 0.753 0.668 0.798 0.851 0.864 0.430 0.687 0.514
Bits 16 to 23---> 0.443 0.715 0.890 0.987 0.292 0.134 0.541 0.301
Bits 24 to 31---> 0.426 0.226 0.393 0.838 0.963 0.522 0.698 0.503
KS test for the above 32 p values: 0.371
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-05_14:31,
p-values for 5 runs: 0.8800, 0.6676, 0.7659, 0.4530, 0.7880
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-05_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 253 211.4 8.178 8.178
r= 29 5066 5134.0 0.901 9.079
r= 30 23209 23103.0 0.486 9.565
r= 31 11472 11551.5 0.547 10.113
chi-square = 10.113 with df = 3; p-value = 0.982
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-05_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 213 211.4 0.012 0.012
r= 30 5047 5134.0 1.475 1.486
r= 31 23113 23103.0 0.004 1.491
r= 32 11627 11551.5 0.493 1.984
chi-square = 1.984 with df = 3; p-value = 0.424
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-05_14:31
b-rank test for bits 1 to 8, p=0.05343
b-rank test for bits 2 to 9, p=0.22287
b-rank test for bits 3 to 10, p=0.08662
b-rank test for bits 4 to 11, p=0.44681
b-rank test for bits 5 to 12, p=0.96463
b-rank test for bits 6 to 13, p=0.25602
b-rank test for bits 7 to 14, p=0.30598
b-rank test for bits 8 to 15, p=0.28890
b-rank test for bits 9 to 16, p=0.76501
b-rank test for bits 10 to 17, p=0.95416
b-rank test for bits 11 to 18, p=0.36802
b-rank test for bits 12 to 19, p=0.45858
b-rank test for bits 13 to 20, p=0.52311
b-rank test for bits 14 to 21, p=0.88922
b-rank test for bits 15 to 22, p=0.04845
b-rank test for bits 16 to 23, p=0.72743
b-rank test for bits 17 to 24, p=0.31288
b-rank test for bits 18 to 25, p=0.39909
b-rank test for bits 19 to 26, p=0.53525
b-rank test for bits 20 to 27, p=0.54325
b-rank test for bits 21 to 28, p=0.68527
b-rank test for bits 22 to 29, p=0.62921
b-rank test for bits 23 to 30, p=0.50632
b-rank test for bits 24 to 31, p=0.60498
b-rank test for bits 25 to 32, p=0.45517
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 = 0.698130
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-05_14:31
(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 142378 1.10 0.863247
2 142090 0.42 0.663534
3 141166 -1.74 0.041215
4 141492 -0.98 0.164763
5 142364 1.06 0.855953
6 142287 0.88 0.811222
7 142643 1.71 0.956752
8 141799 -0.26 0.398288
9 141867 -0.10 0.460608
10 141452 -1.07 0.142641
11 141798 -0.26 0.397387
12 141692 -0.51 0.305804
13 142176 0.62 0.733378
14 141209 -1.64 0.050890
15 141125 -1.83 0.033435
16 142505 1.39 0.918001
17 141889 -0.05 0.481057
18 141967 0.13 0.553593
19 142040 0.31 0.619933
20 140885 -2.39 0.008349
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-05_14:31
Bits used No. missing words z-score p-value
23 to 32 141690 -0.7563 0.224732
22 to 31 141674 -0.8115 0.208544
21 to 30 141377 -1.8356 0.033207
20 to 29 141834 -0.2598 0.397525
19 to 28 141955 0.1575 0.562568
18 to 27 141944 0.1196 0.547581
17 to 26 141994 0.2920 0.614844
16 to 25 141915 0.0196 0.507800
15 to 24 141987 0.2678 0.605584
14 to 23 142083 0.5989 0.725368
13 to 22 142124 0.7402 0.770423
12 to 21 141729 -0.6218 0.267028
11 to 20 141498 -1.4184 0.078040
10 to 19 141550 -1.2391 0.107660
9 to 18 141713 -0.6770 0.249203
8 to 17 141774 -0.4667 0.320373
7 to 16 141737 -0.5942 0.276175
6 to 15 141661 -0.8563 0.195913
5 to 14 141371 -1.8563 0.031705
4 to 13 141873 -0.1253 0.450153
3 to 12 141363 -1.8839 0.029789
2 to 11 142346 1.5058 0.933935
1 to 10 142254 1.1885 0.882685
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-05_14:31
Bits used No. missing words z-score p-value
28 to 32 141804 -0.3571 0.360527
27 to 31 141473 -1.4791 0.069559
26 to 30 141964 0.1853 0.573512
25 to 29 142192 0.9582 0.831020
24 to 28 141911 0.0057 0.502258
23 to 27 141345 -1.9130 0.027875
22 to 26 141963 0.1819 0.572182
21 to 25 141927 0.0599 0.523882
20 to 24 141748 -0.5469 0.292230
19 to 23 141708 -0.6825 0.247470
18 to 22 141561 -1.1808 0.118845
17 to 21 141394 -1.7469 0.040329
16 to 20 142265 1.2057 0.886026
15 to 19 141708 -0.6825 0.247470
14 to 18 142063 0.5209 0.698787
13 to 17 141838 -0.2418 0.404469
12 to 16 141947 0.1277 0.550805
11 to 15 141801 -0.3672 0.356727
10 to 14 141965 0.1887 0.574841
9 to 13 142257 1.1785 0.880710
8 to 12 141782 -0.4316 0.333006
7 to 11 141638 -0.9198 0.178848
6 to 10 142238 1.1141 0.867390
5 to 9 141797 -0.3808 0.351683
4 to 8 141877 -0.1096 0.456366
3 to 7 142531 2.1074 0.982457
2 to 6 141581 -1.1130 0.132858
1 to 5 141596 -1.0621 0.144087
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-05_14:31
Bits used No. missing words z-score p-value
31 to 32 142623 2.1052 0.982364
30 to 31 142057 0.4356 0.668438
29 to 30 141812 -0.2871 0.387014
28 to 29 142382 1.3943 0.918388
27 to 28 141894 -0.0452 0.481966
26 to 27 141869 -0.1190 0.452651
25 to 26 141941 0.0934 0.537216
24 to 25 142195 0.8427 0.800298
23 to 24 141923 0.0403 0.516083
22 to 23 141404 -1.4906 0.068027
21 to 22 142586 1.9961 0.977037
20 to 21 141795 -0.3373 0.367962
19 to 20 142395 1.4327 0.924022
18 to 19 142275 1.0787 0.859633
17 to 18 141538 -1.0954 0.136678
16 to 17 142290 1.1229 0.869264
15 to 16 142236 0.9636 0.832384
14 to 15 142159 0.7365 0.769284
13 to 14 142000 0.2675 0.605444
12 to 13 142211 0.8899 0.813235
11 to 12 141171 -2.1780 0.014704
10 to 11 141665 -0.7207 0.235536
9 to 10 142444 1.5772 0.942625
8 to 9 141384 -1.5496 0.060613
7 to 8 142263 1.0433 0.851589
6 to 7 141595 -0.9272 0.176904
5 to 6 141815 -0.2783 0.390407
4 to 5 141872 -0.1101 0.456158
3 to 4 142001 0.2704 0.606579
2 to 3 141724 -0.5467 0.292294
1 to 2 142173 0.7778 0.781653
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-05_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2571.79 1.015 0.845026
Test results for specific bytes for dh-ranFile-2018-07-05_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2415.15 -1.200 0.115070
2 to 9 2600.48 1.421 0.922348
3 to 10 2504.61 0.065 0.525996
4 to 11 2487.06 -0.183 0.427383
5 to 12 2481.13 -0.267 0.394806
6 to 13 2563.09 0.892 0.813856
7 to 14 2568.75 0.972 0.834532
8 to 15 2486.75 -0.187 0.425695
9 to 16 2482.93 -0.241 0.404621
10 to 17 2483.54 -0.233 0.407978
11 to 18 2552.27 0.739 0.770092
12 to 19 2516.53 0.234 0.592428
13 to 20 2590.68 1.282 0.900149
14 to 21 2459.16 -0.578 0.281768
15 to 22 2359.95 -1.981 0.023817
16 to 23 2443.52 -0.799 0.212221
17 to 24 2539.87 0.564 0.713548
18 to 25 2482.29 -0.251 0.401093
19 to 26 2552.90 0.748 0.772801
20 to 27 2549.77 0.704 0.759230
21 to 28 2499.83 -0.002 0.499017
22 to 29 2568.38 0.967 0.833237
23 to 30 2466.47 -0.474 0.317695
24 to 31 2597.53 1.379 0.916107
25 to 32 2534.15 0.483 0.685415
CDPARK for dh-ranFile-2018-07-05_14:31: 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
3519 -0.1826 0.427537
3524 0.0457 0.518210
3484 -1.7808 0.037471
3531 0.3653 0.642555
3533 0.4566 0.676028
3489 -1.5525 0.060270
3508 -0.6849 0.246694
3536 0.5936 0.723613
3489 -1.5525 0.060270
3534 0.5023 0.692266
Square side=100, avg. no. parked=3514.70 sample std.=19.60
p-value of the KSTEST for those 10 p-values: 0.299195
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-05_14:31
0.5595,0.9518,0.0150,0.9375,0.8921,0.6167,0.1001,0.1870,0.0306,0.7249,
The KS test for those 10 p-values: 0.325511
The 3DSPHERES test for dh-ranFile-2018-07-05_14:31
sample no r^3 equiv. uni.
1 3.224 0.101892
2 0.372 0.012321
3 6.833 0.203690
4 10.799 0.302298
5 42.578 0.758110
6 0.527 0.017397
7 5.250 0.160547
8 12.090 0.331695
9 56.438 0.847602
10 18.291 0.456479
11 49.883 0.810385
12 8.260 0.240672
13 1.479 0.048109
14 24.145 0.552837
15 28.617 0.614761
16 3.690 0.115736
17 18.427 0.458952
18 4.643 0.143378
19 5.621 0.170858
20 38.147 0.719611
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.032014
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-05_14:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 0.9 -2.3 0.6 1.7 1.1
0.9 -0.8 -0.7 2.3 1.0 0.6
-1.1 1.2 1.2 -1.3 -1.9 1.2
0.6 -2.5 0.2 -0.5 1.1 -0.0
-0.9 -1.2 2.0 -0.6 -0.4 -0.7
-0.7 0.9 0.9 0.9 -1.6 1.7
-0.9 0.5 3.8 -0.7 0.9 -1.0
-1.1
Chi-square with 42 degrees of freedom:74.618793
z-score=3.559002, p-value=0.998564
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-05_14:31
Test no p-value
1 0.825530
2 0.157132
3 0.711490
4 0.157330
5 0.686867
6 0.315637
7 0.589695
8 0.469922
9 0.120856
10 0.151151
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.479516
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-05_14:31:
(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 66722 0.05 66956 1.26
3 25000.00 24917 0.28 24787 1.81
4 6666.67 6675 0.01 6651 0.04
5 1388.89 1396 0.04 1327 2.76
6 238.10 250 0.60 240 0.02
7 34.72 37 0.15 31 0.40
8 4.96 2 1.77 7 0.84
p=0.17621 p=0.68993
Number of rngs required: 687534, p-value: 0.157
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-05_14:31
No. of wins: Observed Expected
98417 98585.9
z-score=-0.755, pvalue=0.22505
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66636 66666.7 0.014 0.014
2 37677 37654.3 0.014 0.028
3 27101 26954.7 0.794 0.821
4 19308 19313.5 0.002 0.823
5 13789 13851.4 0.281 1.104
6 9938 9943.5 0.003 1.107
7 7296 7145.0 3.190 4.297
8 5170 5139.1 0.186 4.484
9 3578 3699.9 4.014 8.498
10 2626 2666.3 0.609 9.107
11 1948 1923.3 0.316 9.423
12 1338 1388.7 1.854 11.277
13 1023 1003.7 0.371 11.647
14 671 726.1 4.187 15.835
15 505 525.8 0.826 16.660
16 386 381.2 0.062 16.722
17 265 276.5 0.482 17.203
18 195 200.8 0.169 17.373
19 146 146.0 0.000 17.373
20 111 106.2 0.216 17.588
21 293 287.1 0.121 17.709
Chisq= 17.71 for 20 degrees of freedom, p= 0.39343
SUMMARY of craptest
p-value for no. of wins: 0.225054
p-value for throws/game: 0.393425
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-05_14:31
No. of wins: Observed Expected
98395 98585.9
z-score=-0.854, pvalue=0.19665
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66495 66666.7 0.442 0.442
2 37771 37654.3 0.362 0.804
3 26862 26954.7 0.319 1.123
4 19243 19313.5 0.257 1.380
5 13836 13851.4 0.017 1.397
6 10069 9943.5 1.583 2.980
7 7288 7145.0 2.861 5.841
8 5186 5139.1 0.429 6.269
9 3709 3699.9 0.023 6.292
10 2665 2666.3 0.001 6.292
11 1864 1923.3 1.830 8.123
12 1346 1388.7 1.315 9.438
13 1036 1003.7 1.038 10.476
14 776 726.1 3.424 13.900
15 524 525.8 0.006 13.906
16 367 381.2 0.525 14.432
17 249 276.5 2.743 17.174
18 199 200.8 0.017 17.191
19 144 146.0 0.027 17.218
20 107 106.2 0.006 17.224
21 264 287.1 1.861 19.084
Chisq= 19.08 for 20 degrees of freedom, p= 0.48366
SUMMARY of craptest
p-value for no. of wins: 0.196655
p-value for throws/game: 0.483658
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0058,0.0083,0.0123,0.0147,0.0150,0.0174,0.0205,0.0238,0.0279,0.0298,
0.0306,0.0317,0.0320,0.0332,0.0334,0.0375,0.0403,0.0412,0.0481,0.0485,
0.0509,0.0534,0.0603,0.0603,0.0606,0.0680,0.0696,0.0780,0.0866,0.0993,
0.1001,0.1019,0.1077,0.1151,0.1157,0.1188,0.1209,0.1329,0.1339,0.1367,
0.1426,0.1434,0.1441,0.1512,0.1570,0.1571,0.1573,0.1605,0.1619,0.1648,
0.1709,0.1762,0.1769,0.1788,0.1870,0.1959,0.1967,0.2037,0.2085,0.2122,
0.2193,0.2229,0.2247,0.2251,0.2255,0.2355,0.2407,0.2467,0.2475,0.2475,
0.2492,0.2560,0.2670,0.2762,0.2767,0.2818,0.2889,0.2920,0.2922,0.2923,
0.2992,0.3015,0.3023,0.3058,0.3060,0.3129,0.3156,0.3177,0.3204,0.3255,
0.3317,0.3330,0.3517,0.3567,0.3588,0.3605,0.3680,0.3680,0.3711,0.3794,
0.3870,0.3904,0.3931,0.3934,0.3948,0.3974,0.3975,0.3983,0.3991,0.4011,
0.4045,0.4046,0.4080,0.4242,0.4257,0.4258,0.4274,0.4275,0.4298,0.4428,
0.4468,0.4502,0.4527,0.4530,0.4552,0.4562,0.4564,0.4565,0.4586,0.4590,
0.4606,0.4699,0.4795,0.4811,0.4820,0.4837,0.4935,0.4990,0.5023,0.5034,
0.5063,0.5078,0.5144,0.5161,0.5182,0.5222,0.5231,0.5239,0.5260,0.5352,
0.5372,0.5415,0.5433,0.5476,0.5508,0.5528,0.5536,0.5595,0.5626,0.5722,
0.5735,0.5748,0.5897,0.5924,0.6030,0.6046,0.6050,0.6054,0.6056,0.6066,
0.6148,0.6148,0.6167,0.6192,0.6199,0.6292,0.6426,0.6635,0.6676,0.6678,
0.6684,0.6760,0.6853,0.6854,0.6869,0.6873,0.6899,0.6923,0.6981,0.6984,
0.6988,0.7115,0.7123,0.7135,0.7152,0.7196,0.7236,0.7249,0.7254,0.7274,
0.7334,0.7390,0.7534,0.7581,0.7592,0.7650,0.7659,0.7693,0.7701,0.7704,
0.7728,0.7817,0.7880,0.7978,0.8003,0.8076,0.8104,0.8112,0.8132,0.8139,
0.8249,0.8255,0.8310,0.8324,0.8332,0.8345,0.8382,0.8450,0.8476,0.8515,
0.8516,0.8560,0.8596,0.8632,0.8640,0.8674,0.8693,0.8800,0.8807,0.8827,
0.8860,0.8892,0.8896,0.8921,0.8938,0.9001,0.9161,0.9180,0.9184,0.9223,
0.9240,0.9339,0.9375,0.9425,0.9426,0.9518,0.9542,0.9568,0.9631,0.9646,
0.9739,0.9770,0.9783,0.9824,0.9824,0.9825,0.9869,0.9978,0.9986,
Overall p-value after applying KStest on 269 p-values = 0.883098
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.