RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-28_12:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 16.06 13.0402 0.266509
2 to 25 15.70 28.5388 0.960977
3 to 26 15.41 26.9365 0.940995
4 to 27 16.00 13.7149 0.312831
5 to 28 15.77 20.0366 0.727636
6 to 29 16.08 13.2254 0.279032
7 to 30 15.71 22.8172 0.844704
8 to 31 15.41 20.9052 0.769442
9 to 32 15.74 29.1909 0.967194
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.058584
Tough bday spacings test for dh-ranFile-2018-06-28_12:31: 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 6 33 79 93 115 82 40 22 17 7 6
(O-E)^2/E 1.1 0.4 0.4 0.2 3.1 0.2 2.8 2.0 0.3 0.0 0.9
Birthday Spacings: Sum(O-E)^2/E= 11.462, p= 0.677
RESULTS OF GCD FOR dh-ranFile-2018-06-28_12:31
Euclid's algorithm:
p-value, steps to gcd: 0.521971
p-value, dist. of gcd's: 0.869543
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-28_12:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.504 0.557 0.456 0.268 0.142 0.496 0.690 0.251
Bits 8 to 15---> 0.417 0.436 0.836 0.894 0.689 0.080 0.738 0.524
Bits 16 to 23---> 0.279 0.236 0.828 0.391 0.488 0.521 0.466 0.639
Bits 24 to 31---> 0.978 0.532 0.771 0.887 0.987 0.709 0.232 0.804
KS test for the above 32 p values: 0.725
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-28_12:31,
p-values for 5 runs: 0.4920, 0.8311, 0.8415, 0.9803, 0.5759
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-28_12:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 222 211.4 0.530 0.530
r= 29 5197 5134.0 0.773 1.302
r= 30 23081 23103.0 0.021 1.324
r= 31 11500 11551.5 0.230 1.553
chi-square = 1.553 with df = 3; p-value = 0.330
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-28_12:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 214 211.4 0.032 0.032
r= 30 5088 5134.0 0.412 0.444
r= 31 23127 23103.0 0.025 0.469
r= 32 11571 11551.5 0.033 0.502
chi-square = 0.502 with df = 3; p-value = 0.081
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-28_12:31
b-rank test for bits 1 to 8, p=0.98708
b-rank test for bits 2 to 9, p=0.55660
b-rank test for bits 3 to 10, p=0.20907
b-rank test for bits 4 to 11, p=0.05971
b-rank test for bits 5 to 12, p=0.97148
b-rank test for bits 6 to 13, p=0.54010
b-rank test for bits 7 to 14, p=0.79345
b-rank test for bits 8 to 15, p=0.11713
b-rank test for bits 9 to 16, p=0.84234
b-rank test for bits 10 to 17, p=0.94983
b-rank test for bits 11 to 18, p=0.65763
b-rank test for bits 12 to 19, p=0.54049
b-rank test for bits 13 to 20, p=0.96102
b-rank test for bits 14 to 21, p=0.64804
b-rank test for bits 15 to 22, p=0.15734
b-rank test for bits 16 to 23, p=0.53285
b-rank test for bits 17 to 24, p=0.74335
b-rank test for bits 18 to 25, p=0.60148
b-rank test for bits 19 to 26, p=0.92495
b-rank test for bits 20 to 27, p=0.61665
b-rank test for bits 21 to 28, p=0.74188
b-rank test for bits 22 to 29, p=0.32540
b-rank test for bits 23 to 30, p=0.93408
b-rank test for bits 24 to 31, p=0.18587
b-rank test for bits 25 to 32, p=0.44449
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 = 0.100140
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-28_12:31
(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 141891 -0.04 0.482920
2 141655 -0.59 0.276180
3 142243 0.78 0.782188
4 141774 -0.32 0.375929
5 142282 0.87 0.808048
6 141679 -0.54 0.295235
7 142205 0.69 0.755160
8 141741 -0.39 0.347051
9 141918 0.02 0.508081
10 142424 1.20 0.885415
11 141051 -2.01 0.022458
12 142595 1.60 0.945426
13 142132 0.52 0.698558
14 142075 0.39 0.650651
15 142336 1.00 0.840592
16 141883 -0.06 0.475473
17 141805 -0.24 0.403708
18 142213 0.71 0.760996
19 141874 -0.08 0.467106
20 141839 -0.16 0.434739
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-28_12:31
Bits used No. missing words z-score p-value
23 to 32 142205 1.0196 0.846029
22 to 31 141593 -1.0908 0.137682
21 to 30 141457 -1.5598 0.059408
20 to 29 141794 -0.3977 0.345430
19 to 28 141702 -0.7149 0.237326
18 to 27 142385 1.6402 0.949523
17 to 26 141916 0.0230 0.509175
16 to 25 142040 0.4506 0.673856
15 to 24 141962 0.1816 0.572060
14 to 23 142243 1.1506 0.875049
13 to 22 141887 -0.0770 0.469312
12 to 21 141743 -0.5736 0.283136
11 to 20 141786 -0.4253 0.335318
10 to 19 142210 1.0368 0.850084
9 to 18 141371 -1.8563 0.031705
8 to 17 141805 -0.3598 0.359514
7 to 16 141603 -1.0563 0.145413
6 to 15 142133 0.7713 0.779728
5 to 14 142221 1.0747 0.858751
4 to 13 142033 0.4264 0.665109
3 to 12 142281 1.2816 0.900012
2 to 11 141743 -0.5736 0.283136
1 to 10 141994 0.2920 0.614844
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-28_12:31
Bits used No. missing words z-score p-value
28 to 32 142378 1.5887 0.943937
27 to 31 142219 1.0497 0.853079
26 to 30 142056 0.4972 0.690471
25 to 29 141791 -0.4011 0.344166
24 to 28 141604 -1.0350 0.150331
23 to 27 141884 -0.0859 0.465787
22 to 26 142461 1.8701 0.969263
21 to 25 141456 -1.5367 0.062182
20 to 24 141917 0.0260 0.510371
19 to 23 141496 -1.4011 0.080589
18 to 22 141765 -0.4893 0.312331
17 to 21 141961 0.1752 0.569520
16 to 20 141729 -0.6113 0.270504
15 to 19 141787 -0.4147 0.339189
14 to 18 141856 -0.1808 0.428270
13 to 17 142317 1.3819 0.916504
12 to 16 142092 0.6192 0.732114
11 to 15 141855 -0.1842 0.426940
10 to 14 141992 0.2802 0.610352
9 to 13 141468 -1.4960 0.067322
8 to 12 141625 -0.9638 0.167565
7 to 11 142165 0.8667 0.806941
6 to 10 142069 0.5413 0.705834
5 to 9 141774 -0.4587 0.323208
4 to 8 142192 0.9582 0.831020
3 to 7 140933 -3.3096 0.000467
2 to 6 142077 0.5684 0.715109
1 to 5 142173 0.8938 0.814285
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-28_12:31
Bits used No. missing words z-score p-value
31 to 32 142537 1.8515 0.967954
30 to 31 141433 -1.4051 0.079995
29 to 30 141998 0.2616 0.603171
28 to 29 142396 1.4356 0.924443
27 to 28 141572 -0.9951 0.159850
26 to 27 141837 -0.2134 0.415522
25 to 26 141908 -0.0039 0.498435
24 to 25 141513 -1.1691 0.121179
23 to 24 141585 -0.9567 0.169353
22 to 23 141745 -0.4847 0.313927
21 to 22 141957 0.1406 0.555915
20 to 21 142193 0.8368 0.798643
19 to 20 142553 1.8987 0.971200
18 to 19 141619 -0.8564 0.195880
17 to 18 141522 -1.1426 0.126609
16 to 17 141488 -1.2429 0.106959
15 to 16 142503 1.7512 0.960048
14 to 15 141828 -0.2399 0.405199
13 to 14 141824 -0.2517 0.400632
12 to 13 142130 0.6509 0.742459
11 to 12 141438 -1.3904 0.082211
10 to 11 141684 -0.6647 0.253124
9 to 10 142019 0.3235 0.626846
8 to 9 142624 2.1082 0.982492
7 to 8 142350 1.2999 0.903184
6 to 7 142242 0.9813 0.836784
5 to 6 141555 -1.0452 0.147960
4 to 5 141883 -0.0777 0.469045
3 to 4 141921 0.0344 0.513731
2 to 3 142162 0.7453 0.771967
1 to 2 141681 -0.6735 0.250302
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-28_12:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2525.80 0.365 0.642369
Test results for specific bytes for dh-ranFile-2018-06-28_12:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2393.81 -1.502 0.066585
2 to 9 2405.99 -1.330 0.091834
3 to 10 2366.37 -1.890 0.029392
4 to 11 2591.34 1.292 0.901788
5 to 12 2609.39 1.547 0.939061
6 to 13 2518.88 0.267 0.605284
7 to 14 2485.73 -0.202 0.420048
8 to 15 2474.01 -0.368 0.356580
9 to 16 2432.46 -0.955 0.169735
10 to 17 2540.86 0.578 0.718321
11 to 18 2539.54 0.559 0.711970
12 to 19 2452.08 -0.678 0.249003
13 to 20 2562.01 0.877 0.809752
14 to 21 2495.64 -0.062 0.475416
15 to 22 2514.38 0.203 0.580575
16 to 23 2453.03 -0.664 0.253277
17 to 24 2628.07 1.811 0.964948
18 to 25 2519.53 0.276 0.608780
19 to 26 2663.38 2.311 0.989570
20 to 27 2494.93 -0.072 0.471420
21 to 28 2534.82 0.492 0.688805
22 to 29 2445.34 -0.773 0.219769
23 to 30 2512.17 0.172 0.568305
24 to 31 2572.32 1.023 0.846780
25 to 32 2584.98 1.202 0.885293
CDPARK for dh-ranFile-2018-06-28_12:31: 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
3551 1.2785 0.899470
3472 -2.3288 0.009936
3555 1.4612 0.928018
3510 -0.5936 0.276387
3546 1.0502 0.853193
3503 -0.9132 0.180558
3525 0.0913 0.536383
3529 0.2740 0.607947
3524 0.0457 0.518210
Square side=100, avg. no. parked=3524.30 sample std.=23.57
p-value of the KSTEST for those 10 p-values: 0.815188
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-28_12:31
0.8625,0.9909,0.4121,0.5005,0.4032,0.8519,0.2278,0.4116,0.0157,0.1809,
The KS test for those 10 p-values: 0.764473
The 3DSPHERES test for dh-ranFile-2018-06-28_12:31
sample no r^3 equiv. uni.
1 2.320 0.074412
2 33.460 0.672197
3 3.167 0.100196
4 17.638 0.444528
5 50.673 0.815312
6 14.949 0.392445
7 19.669 0.480892
8 4.575 0.141448
9 1.559 0.050650
10 74.387 0.916221
11 4.083 0.127256
12 16.497 0.423002
13 12.369 0.337872
14 3.685 0.115596
15 23.139 0.537584
16 4.164 0.129595
17 0.265 0.008784
18 29.047 0.620250
19 14.457 0.382383
20 48.526 0.801612
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.082277
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-28_12:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 0.5 0.6 1.5 0.7 -1.6
1.5 1.0 -0.0 1.2 1.2 -0.1
-2.3 -0.6 0.3 0.6 -0.8 -2.8
0.2 0.1 -0.3 1.2 0.0 -0.2
-0.3 1.3 1.7 0.7 0.9 0.8
2.7 0.3 -0.1 -0.2 -0.6 1.3
-2.3 0.5 0.5 0.4 -1.3 -1.0
-1.1
Chi-square with 42 degrees of freedom:55.056128
z-score=1.424540, p-value=0.914674
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-28_12:31
Test no p-value
1 0.079871
2 0.820632
3 0.873125
4 0.468680
5 0.631597
6 0.470194
7 0.975492
8 0.441120
9 0.326200
10 0.040014
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.952153
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-28_12:31:
(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 66601 0.06 66717 0.04
3 25000.00 24982 0.01 24987 0.01
4 6666.67 6769 1.57 6625 0.26
5 1388.89 1377 0.10 1385 0.01
6 238.10 227 0.52 242 0.06
7 34.72 39 0.53 39 0.53
8 4.96 4 0.19 4 0.19
p=0.18872 p=0.01818
Number of rngs required: 689785, p-value: 0.947
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-28_12:31
No. of wins: Observed Expected
98837 98585.9
z-score= 1.123, pvalue=0.86933
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66602 66666.7 0.063 0.063
2 37487 37654.3 0.744 0.806
3 27026 26954.7 0.188 0.995
4 19313 19313.5 0.000 0.995
5 14034 13851.4 2.407 3.401
6 9952 9943.5 0.007 3.409
7 7221 7145.0 0.808 4.216
8 4996 5139.1 3.983 8.200
9 3705 3699.9 0.007 8.207
10 2675 2666.3 0.028 8.235
11 1917 1923.3 0.021 8.256
12 1417 1388.7 0.575 8.831
13 964 1003.7 1.571 10.402
14 753 726.1 0.994 11.396
15 524 525.8 0.006 11.402
16 384 381.2 0.021 11.424
17 260 276.5 0.989 12.413
18 194 200.8 0.232 12.645
19 165 146.0 2.477 15.122
20 109 106.2 0.073 15.195
21 302 287.1 0.772 15.967
Chisq= 15.97 for 20 degrees of freedom, p= 0.28132
SUMMARY of craptest
p-value for no. of wins: 0.869335
p-value for throws/game: 0.281319
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-28_12:31
No. of wins: Observed Expected
98542 98585.9
z-score=-0.196, pvalue=0.42224
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66653 66666.7 0.003 0.003
2 37933 37654.3 2.062 2.065
3 26909 26954.7 0.078 2.143
4 19091 19313.5 2.562 4.705
5 13776 13851.4 0.411 5.116
6 9961 9943.5 0.031 5.147
7 7196 7145.0 0.364 5.510
8 5145 5139.1 0.007 5.517
9 3739 3699.9 0.414 5.931
10 2643 2666.3 0.204 6.135
11 1860 1923.3 2.085 8.220
12 1374 1388.7 0.156 8.376
13 1039 1003.7 1.240 9.617
14 702 726.1 0.803 10.419
15 505 525.8 0.826 11.245
16 385 381.2 0.039 11.284
17 276 276.5 0.001 11.285
18 212 200.8 0.621 11.906
19 156 146.0 0.687 12.593
20 127 106.2 4.067 16.661
21 318 287.1 3.323 19.983
Chisq= 19.98 for 20 degrees of freedom, p= 0.54101
SUMMARY of craptest
p-value for no. of wins: 0.422242
p-value for throws/game: 0.541010
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0005,0.0088,0.0099,0.0157,0.0182,0.0225,0.0294,0.0317,0.0400,0.0507,
0.0586,0.0594,0.0597,0.0622,0.0666,0.0673,0.0744,0.0797,0.0799,0.0800,
0.0806,0.0814,0.0822,0.0823,0.0918,0.1001,0.1002,0.1070,0.1156,0.1171,
0.1212,0.1266,0.1273,0.1296,0.1377,0.1414,0.1419,0.1454,0.1480,0.1503,
0.1573,0.1599,0.1676,0.1694,0.1697,0.1806,0.1809,0.1859,0.1887,0.1959,
0.2091,0.2198,0.2278,0.2323,0.2359,0.2373,0.2490,0.2503,0.2511,0.2531,
0.2533,0.2665,0.2682,0.2705,0.2762,0.2764,0.2790,0.2793,0.2813,0.2831,
0.2831,0.2952,0.3123,0.3128,0.3139,0.3232,0.3254,0.3262,0.3300,0.3353,
0.3379,0.3392,0.3442,0.3454,0.3471,0.3566,0.3595,0.3759,0.3824,0.3912,
0.3924,0.4006,0.4032,0.4037,0.4052,0.4116,0.4121,0.4155,0.4174,0.4200,
0.4222,0.4230,0.4269,0.4283,0.4347,0.4362,0.4411,0.4445,0.4445,0.4556,
0.4658,0.4664,0.4671,0.4687,0.4690,0.4693,0.4702,0.4714,0.4754,0.4755,
0.4809,0.4829,0.4880,0.4920,0.4955,0.4984,0.5005,0.5037,0.5081,0.5092,
0.5104,0.5137,0.5182,0.5212,0.5220,0.5238,0.5321,0.5329,0.5364,0.5376,
0.5401,0.5405,0.5410,0.5559,0.5566,0.5567,0.5683,0.5695,0.5721,0.5759,
0.5806,0.5903,0.6015,0.6032,0.6053,0.6079,0.6088,0.6104,0.6148,0.6167,
0.6202,0.6268,0.6316,0.6386,0.6424,0.6480,0.6507,0.6576,0.6651,0.6722,
0.6739,0.6774,0.6888,0.6889,0.6898,0.6905,0.6986,0.7058,0.7088,0.7120,
0.7151,0.7183,0.7250,0.7276,0.7321,0.7377,0.7419,0.7425,0.7434,0.7552,
0.7610,0.7645,0.7694,0.7710,0.7720,0.7797,0.7822,0.7934,0.7986,0.8016,
0.8036,0.8069,0.8080,0.8098,0.8143,0.8152,0.8153,0.8206,0.8275,0.8310,
0.8311,0.8358,0.8368,0.8406,0.8415,0.8423,0.8447,0.8460,0.8468,0.8501,
0.8519,0.8531,0.8532,0.8588,0.8625,0.8693,0.8695,0.8731,0.8750,0.8853,
0.8854,0.8870,0.8942,0.8995,0.9000,0.9018,0.9032,0.9147,0.9162,0.9165,
0.9244,0.9250,0.9280,0.9341,0.9391,0.9410,0.9439,0.9454,0.9472,0.9495,
0.9498,0.9522,0.9600,0.9610,0.9610,0.9649,0.9672,0.9680,0.9693,0.9712,
0.9715,0.9755,0.9779,0.9803,0.9825,0.9866,0.9871,0.9896,0.9909,
Overall p-value after applying KStest on 269 p-values = 0.125661
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.