RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-07_00:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.42 24.5051 0.893653
2 to 25 15.79 21.0375 0.775381
3 to 26 15.48 28.0283 0.955391
4 to 27 15.52 21.9224 0.812277
5 to 28 15.77 17.6972 0.591819
6 to 29 16.12 19.5091 0.699898
7 to 30 15.56 17.8128 0.599256
8 to 31 15.74 13.7095 0.312455
9 to 32 15.75 23.4049 0.863473
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.032770
Tough bday spacings test for dh-ranFile-2018-07-07_00:31: 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 12 27 80 99 101 74 51 29 21 4 2
(O-E)^2/E 0.9 2.5 0.6 0.0 0.1 0.2 0.0 0.0 2.5 1.0 1.0
Birthday Spacings: Sum(O-E)^2/E= 9.023, p= 0.470
RESULTS OF GCD FOR dh-ranFile-2018-07-07_00:31
Euclid's algorithm:
p-value, steps to gcd: 0.730644
p-value, dist. of gcd's: 0.728892
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-07_00:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.777 0.516 0.010 0.515 0.654 0.456 0.643 0.771
Bits 8 to 15---> 0.330 0.753 0.165 0.503 0.945 0.601 0.980 0.380
Bits 16 to 23---> 0.716 0.012 0.696 0.499 0.427 0.093 0.806 0.576
Bits 24 to 31---> 0.522 0.836 0.050 0.152 0.181 0.043 0.252 0.746
KS test for the above 32 p values: 0.273
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-07_00:31,
p-values for 5 runs: 0.4666, 0.9030, 0.0672, 0.1803, 0.8972
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-07_00:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 208 211.4 0.055 0.055
r= 29 5143 5134.0 0.016 0.071
r= 30 23010 23103.0 0.375 0.446
r= 31 11639 11551.5 0.662 1.108
chi-square = 1.108 with df = 3; p-value = 0.225
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-07_00:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 213 211.4 0.012 0.012
r= 30 5164 5134.0 0.175 0.187
r= 31 22879 23103.0 2.173 2.360
r= 32 11744 11551.5 3.207 5.567
chi-square = 5.567 with df = 3; p-value = 0.865
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-07_00:31
b-rank test for bits 1 to 8, p=0.33101
b-rank test for bits 2 to 9, p=0.71644
b-rank test for bits 3 to 10, p=0.66961
b-rank test for bits 4 to 11, p=0.70636
b-rank test for bits 5 to 12, p=0.34086
b-rank test for bits 6 to 13, p=0.04229
b-rank test for bits 7 to 14, p=0.09816
b-rank test for bits 8 to 15, p=0.90783
b-rank test for bits 9 to 16, p=0.22308
b-rank test for bits 10 to 17, p=0.43114
b-rank test for bits 11 to 18, p=0.61035
b-rank test for bits 12 to 19, p=0.98899
b-rank test for bits 13 to 20, p=0.67865
b-rank test for bits 14 to 21, p=0.39686
b-rank test for bits 15 to 22, p=0.55211
b-rank test for bits 16 to 23, p=0.61336
b-rank test for bits 17 to 24, p=0.68572
b-rank test for bits 18 to 25, p=0.66861
b-rank test for bits 19 to 26, p=0.13041
b-rank test for bits 20 to 27, p=0.80858
b-rank test for bits 21 to 28, p=0.19590
b-rank test for bits 22 to 29, p=0.95169
b-rank test for bits 23 to 30, p=0.98373
b-rank test for bits 24 to 31, p=0.69476
b-rank test for bits 25 to 32, p=0.88316
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 = 0.313634
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-07_00:31
(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 141243 -1.56 0.059754
2 141823 -0.20 0.420073
3 141515 -0.92 0.178439
4 141793 -0.27 0.392888
5 141692 -0.51 0.305804
6 141838 -0.17 0.433819
7 141817 -0.22 0.414601
8 141199 -1.66 0.048492
9 142414 1.18 0.880828
10 141331 -1.35 0.088310
11 141758 -0.35 0.361829
12 142014 0.24 0.596600
13 142216 0.72 0.763164
14 142000 0.21 0.583886
15 140889 -2.38 0.008564
16 141885 -0.06 0.477334
17 141847 -0.15 0.442106
18 142306 0.93 0.822985
19 141226 -1.60 0.055181
20 141628 -0.66 0.255490
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-07_00:31
Bits used No. missing words z-score p-value
23 to 32 141936 0.0920 0.536637
22 to 31 141961 0.1782 0.570706
21 to 30 142088 0.6161 0.731087
20 to 29 142560 2.2437 0.987574
19 to 28 141921 0.0402 0.516050
18 to 27 141647 -0.9046 0.182842
17 to 26 142196 0.9885 0.838550
16 to 25 142290 1.3127 0.905350
15 to 24 142041 0.4540 0.675098
14 to 23 142065 0.5368 0.704295
13 to 22 141883 -0.0908 0.463829
12 to 21 141928 0.0644 0.525666
11 to 20 141680 -0.7908 0.214532
10 to 19 141927 0.0609 0.524293
9 to 18 141895 -0.0494 0.480295
8 to 17 141365 -1.8770 0.030259
7 to 16 141448 -1.5908 0.055828
6 to 15 141695 -0.7391 0.229933
5 to 14 141642 -0.9218 0.178309
4 to 13 142216 1.0575 0.854854
3 to 12 141239 -2.3115 0.010403
2 to 11 141468 -1.5218 0.064026
1 to 10 142103 0.6678 0.747878
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-07_00:31
Bits used No. missing words z-score p-value
28 to 32 142257 1.1785 0.880710
27 to 31 142147 0.8057 0.789781
26 to 30 141800 -0.3706 0.355464
25 to 29 142284 1.2701 0.897970
24 to 28 142520 2.0701 0.980777
23 to 27 141874 -0.1198 0.452336
22 to 26 141724 -0.6282 0.264924
21 to 25 142462 1.8735 0.969497
20 to 24 141822 -0.2960 0.383602
19 to 23 141508 -1.3604 0.086845
18 to 22 142160 0.8497 0.802262
17 to 21 142394 1.6429 0.949803
16 to 20 141823 -0.2926 0.384897
15 to 19 142149 0.8124 0.791731
14 to 18 141716 -0.6554 0.256119
13 to 17 141572 -1.1435 0.126417
12 to 16 141855 -0.1842 0.426940
11 to 15 141632 -0.9401 0.173583
10 to 14 142017 0.3650 0.642438
9 to 13 142156 0.8362 0.798470
8 to 12 141708 -0.6825 0.247470
7 to 11 141641 -0.9096 0.181519
6 to 10 141906 -0.0113 0.495497
5 to 9 141871 -0.1299 0.448310
4 to 8 141549 -1.2215 0.110956
3 to 7 142591 2.3107 0.989577
2 to 6 141719 -0.6452 0.259403
1 to 5 142132 0.7548 0.774820
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-07_00:31
Bits used No. missing words z-score p-value
31 to 32 142036 0.3737 0.645671
30 to 31 141996 0.2557 0.600895
29 to 30 142021 0.3294 0.629077
28 to 29 141420 -1.4435 0.074447
27 to 28 141749 -0.4729 0.318125
26 to 27 141511 -1.1750 0.119994
25 to 26 141804 -0.3107 0.378011
24 to 25 142577 1.9695 0.975554
23 to 24 142147 0.7011 0.758377
22 to 23 142159 0.7365 0.769284
21 to 22 141528 -1.1249 0.130323
20 to 21 142039 0.3825 0.648958
19 to 20 141563 -1.0216 0.153480
18 to 19 141759 -0.4435 0.328720
17 to 18 142303 1.1613 0.877234
16 to 17 142234 0.9577 0.830900
15 to 16 141806 -0.3048 0.380256
14 to 15 141807 -0.3019 0.381380
13 to 14 142675 2.2586 0.988046
12 to 13 141486 -1.2488 0.105876
11 to 12 141869 -0.1190 0.452651
10 to 11 142095 0.5477 0.708051
9 to 10 141757 -0.4494 0.326589
8 to 9 141805 -0.3078 0.379133
7 to 8 141909 -0.0010 0.499612
6 to 7 142131 0.6539 0.743410
5 to 6 141914 0.0138 0.505496
4 to 5 142492 1.7188 0.957174
3 to 4 141964 0.1613 0.564059
2 to 3 142237 0.9666 0.833123
1 to 2 141795 -0.3373 0.367962
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-07_00:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2552.89 0.748 0.772760
Test results for specific bytes for dh-ranFile-2018-07-07_00:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2428.89 -1.006 0.157280
2 to 9 2521.92 0.310 0.621736
3 to 10 2420.82 -1.120 0.131399
4 to 11 2712.02 2.998 0.998643
5 to 12 2466.21 -0.478 0.316365
6 to 13 2567.67 0.957 0.830728
7 to 14 2414.73 -1.206 0.113916
8 to 15 2568.92 0.975 0.835131
9 to 16 2552.10 0.737 0.769382
10 to 17 2578.08 1.104 0.865246
11 to 18 2585.06 1.203 0.885511
12 to 19 2373.35 -1.791 0.036633
13 to 20 2368.22 -1.864 0.031180
14 to 21 2369.58 -1.844 0.032562
15 to 22 2513.56 0.192 0.576057
16 to 23 2499.63 -0.005 0.497906
17 to 24 2510.19 0.144 0.557287
18 to 25 2571.01 1.004 0.842367
19 to 26 2556.31 0.796 0.787077
20 to 27 2705.47 2.906 0.998168
21 to 28 2489.01 -0.155 0.438249
22 to 29 2447.81 -0.738 0.230254
23 to 30 2476.90 -0.327 0.371942
24 to 31 2516.79 0.237 0.593863
25 to 32 2391.98 -1.528 0.063302
CDPARK for dh-ranFile-2018-07-07_00:31: 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
3524 0.0457 0.518210
3475 -2.1918 0.014198
3526 0.1370 0.554479
3541 0.8219 0.794438
3516 -0.3196 0.374623
3497 -1.1872 0.117571
3516 -0.3196 0.374623
3512 -0.5023 0.307734
3501 -1.0046 0.157553
3531 0.3653 0.642555
Square side=100, avg. no. parked=3513.90 sample std.=18.04
p-value of the KSTEST for those 10 p-values: 0.354690
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-07_00:31
0.1117,0.4248,0.8760,0.9096,0.3617,0.9420,0.2469,0.6066,0.8318,0.3259,
The KS test for those 10 p-values: 0.674910
The 3DSPHERES test for dh-ranFile-2018-07-07_00:31
sample no r^3 equiv. uni.
1 44.268 0.771360
2 13.579 0.364041
3 19.148 0.471797
4 8.151 0.237916
5 38.148 0.719617
6 14.150 0.376036
7 116.340 0.979308
8 4.725 0.145718
9 15.894 0.411271
10 67.908 0.896024
11 9.854 0.279974
12 60.453 0.866692
13 2.279 0.073147
14 42.035 0.753687
15 65.557 0.887550
16 27.158 0.595569
17 0.280 0.009289
18 10.299 0.290580
19 34.819 0.686717
20 14.258 0.378276
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.987729
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-07_00:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 0.5 -0.8 -1.0 -0.1 0.3
0.1 -1.0 -1.0 0.2 0.3 0.1
0.8 0.7 -1.4 -0.5 1.5 -1.2
0.3 0.2 1.4 -0.5 1.3 -2.3
0.9 -1.4 0.6 0.4 -1.1 0.6
-0.8 0.0 -0.1 -1.3 0.2 0.2
1.7 0.8 0.5 1.5 -0.6 0.0
1.8
Chi-square with 42 degrees of freedom:37.844411
z-score=-0.453412, p-value=0.346105
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-07_00:31
Test no p-value
1 0.599698
2 0.371809
3 0.652815
4 0.035380
5 0.649077
6 0.862819
7 0.869728
8 0.220880
9 0.027738
10 0.038142
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.301503
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-07_00:31:
(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 66699 0.02 66889 0.74
3 25000.00 24906 0.35 24917 0.28
4 6666.67 6712 0.31 6491 4.63
5 1388.89 1382 0.03 1432 1.34
6 238.10 252 0.81 235 0.04
7 34.72 41 1.14 34 0.01
8 4.96 7 0.84 1 3.16
p=0.25583 p=0.88356
Number of rngs required: 687560, p-value: 0.164
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-07_00:31
No. of wins: Observed Expected
98512 98585.9
z-score=-0.330, pvalue=0.37057
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66340 66666.7 1.601 1.601
2 37720 37654.3 0.115 1.715
3 27257 26954.7 3.390 5.105
4 19180 19313.5 0.922 6.027
5 13922 13851.4 0.360 6.387
6 9845 9943.5 0.977 7.363
7 7181 7145.0 0.181 7.544
8 5176 5139.1 0.265 7.810
9 3771 3699.9 1.368 9.177
10 2737 2666.3 1.875 11.052
11 1931 1923.3 0.031 11.083
12 1398 1388.7 0.062 11.145
13 965 1003.7 1.493 12.638
14 719 726.1 0.070 12.708
15 509 525.8 0.539 13.247
16 371 381.2 0.270 13.518
17 255 276.5 1.678 15.195
18 202 200.8 0.007 15.202
19 130 146.0 1.750 16.952
20 107 106.2 0.006 16.958
21 284 287.1 0.034 16.992
Chisq= 16.99 for 20 degrees of freedom, p= 0.34649
SUMMARY of craptest
p-value for no. of wins: 0.370572
p-value for throws/game: 0.346494
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-07_00:31
No. of wins: Observed Expected
98490 98585.9
z-score=-0.429, pvalue=0.33406
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66595 66666.7 0.077 0.077
2 37712 37654.3 0.088 0.165
3 27000 26954.7 0.076 0.241
4 19294 19313.5 0.020 0.261
5 13715 13851.4 1.344 1.605
6 10085 9943.5 2.012 3.617
7 7084 7145.0 0.521 4.138
8 5162 5139.1 0.102 4.240
9 3725 3699.9 0.171 4.411
10 2633 2666.3 0.416 4.827
11 1906 1923.3 0.156 4.983
12 1407 1388.7 0.240 5.223
13 1006 1003.7 0.005 5.228
14 769 726.1 2.530 7.758
15 538 525.8 0.281 8.040
16 380 381.2 0.003 8.043
17 259 276.5 1.112 9.156
18 189 200.8 0.697 9.852
19 148 146.0 0.028 9.880
20 109 106.2 0.073 9.953
21 284 287.1 0.034 9.987
Chisq= 9.99 for 20 degrees of freedom, p= 0.03159
SUMMARY of craptest
p-value for no. of wins: 0.334058
p-value for throws/game: 0.031592
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0086,0.0093,0.0095,0.0104,0.0125,0.0142,0.0277,0.0303,0.0312,0.0316,
0.0326,0.0328,0.0354,0.0366,0.0381,0.0423,0.0428,0.0485,0.0498,0.0552,
0.0558,0.0598,0.0633,0.0640,0.0672,0.0731,0.0744,0.0868,0.0883,0.0927,
0.0982,0.1059,0.1110,0.1117,0.1139,0.1176,0.1200,0.1264,0.1303,0.1304,
0.1314,0.1457,0.1518,0.1535,0.1573,0.1576,0.1644,0.1655,0.1736,0.1783,
0.1784,0.1803,0.1809,0.1815,0.1828,0.1959,0.2145,0.2209,0.2231,0.2249,
0.2299,0.2303,0.2379,0.2469,0.2475,0.2517,0.2555,0.2558,0.2561,0.2594,
0.2649,0.2729,0.2800,0.2906,0.3015,0.3058,0.3077,0.3125,0.3136,0.3164,
0.3181,0.3259,0.3266,0.3287,0.3304,0.3310,0.3341,0.3409,0.3461,0.3465,
0.3547,0.3555,0.3617,0.3618,0.3640,0.3680,0.3706,0.3718,0.3719,0.3746,
0.3746,0.3760,0.3780,0.3783,0.3791,0.3802,0.3803,0.3814,0.3836,0.3849,
0.3929,0.3969,0.4113,0.4146,0.4201,0.4248,0.4266,0.4269,0.4311,0.4338,
0.4382,0.4421,0.4483,0.4523,0.4527,0.4560,0.4638,0.4666,0.4701,0.4718,
0.4773,0.4803,0.4955,0.4979,0.4988,0.4996,0.5027,0.5055,0.5147,0.5160,
0.5164,0.5182,0.5216,0.5243,0.5257,0.5366,0.5521,0.5545,0.5573,0.5641,
0.5707,0.5758,0.5761,0.5839,0.5918,0.5939,0.5956,0.5966,0.5993,0.5997,
0.6006,0.6009,0.6066,0.6104,0.6134,0.6217,0.6291,0.6424,0.6426,0.6428,
0.6457,0.6490,0.6491,0.6528,0.6539,0.6686,0.6696,0.6749,0.6751,0.6786,
0.6857,0.6867,0.6948,0.6960,0.6999,0.7043,0.7064,0.7081,0.7159,0.7164,
0.7196,0.7289,0.7306,0.7311,0.7434,0.7461,0.7479,0.7530,0.7537,0.7584,
0.7632,0.7693,0.7694,0.7714,0.7714,0.7728,0.7748,0.7754,0.7769,0.7871,
0.7898,0.7917,0.7944,0.7985,0.8023,0.8060,0.8086,0.8123,0.8230,0.8307,
0.8309,0.8318,0.8331,0.8351,0.8364,0.8386,0.8424,0.8549,0.8628,0.8635,
0.8652,0.8653,0.8667,0.8697,0.8760,0.8772,0.8807,0.8808,0.8832,0.8836,
0.8855,0.8876,0.8937,0.8960,0.8972,0.8980,0.9030,0.9054,0.9078,0.9096,
0.9420,0.9453,0.9498,0.9517,0.9554,0.9572,0.9695,0.9756,0.9793,0.9798,
0.9808,0.9837,0.9876,0.9877,0.9880,0.9890,0.9896,0.9982,0.9986,
Overall p-value after applying KStest on 269 p-values = 0.861061
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.