RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-08-31_16:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.76 22.8905 0.847150
2 to 25 15.61 37.3621 0.996995
3 to 26 15.98 7.2352 0.019707
4 to 27 15.85 19.0807 0.676080
5 to 28 15.73 15.2032 0.419155
6 to 29 15.61 14.1966 0.346857
7 to 30 15.84 17.8174 0.599554
8 to 31 15.84 17.5300 0.580946
9 to 32 15.93 27.4203 0.947816
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.317951
Tough bday spacings test for dh-ranFile-2018-08-31_16:31: 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 7 44 73 101 94 78 50 28 15 5 5
(O-E)^2/E 0.5 1.5 0.0 0.1 0.1 0.0 0.1 0.1 0.0 0.4 0.2
Birthday Spacings: Sum(O-E)^2/E= 3.043, p= 0.020
RESULTS OF GCD FOR dh-ranFile-2018-08-31_16:31
Euclid's algorithm:
p-value, steps to gcd: 0.555484
p-value, dist. of gcd's: 0.411447
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-08-31_16:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.475 0.633 0.259 0.955 0.194 0.730 0.749 0.743
Bits 8 to 15---> 0.770 0.702 0.089 0.208 0.073 0.890 0.453 0.436
Bits 16 to 23---> 0.173 0.336 0.868 0.528 0.207 0.700 0.976 0.113
Bits 24 to 31---> 0.341 0.381 0.607 0.799 0.129 0.016 0.961 0.276
KS test for the above 32 p values: 0.007
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-08-31_16:31,
p-values for 5 runs: 0.0335, 0.8269, 0.4012, 0.3503, 0.0633
Rank test for binary matrices (31x31) for dh-ranFile-2018-08-31_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 226 211.4 1.006 1.006
r= 29 5027 5134.0 2.230 3.236
r= 30 23182 23103.0 0.270 3.506
r= 31 11565 11551.5 0.016 3.522
chi-square = 3.522 with df = 3; p-value = 0.682
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-08-31_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 209 211.4 0.028 0.028
r= 30 5123 5134.0 0.024 0.051
r= 31 23120 23103.0 0.012 0.064
r= 32 11548 11551.5 0.001 0.065
chi-square = 0.065 with df = 3; p-value = 0.004
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-08-31_16:31
b-rank test for bits 1 to 8, p=0.57377
b-rank test for bits 2 to 9, p=0.64404
b-rank test for bits 3 to 10, p=0.14021
b-rank test for bits 4 to 11, p=0.15010
b-rank test for bits 5 to 12, p=0.60747
b-rank test for bits 6 to 13, p=0.11815
b-rank test for bits 7 to 14, p=0.24489
b-rank test for bits 8 to 15, p=0.93272
b-rank test for bits 9 to 16, p=0.71264
b-rank test for bits 10 to 17, p=0.57787
b-rank test for bits 11 to 18, p=0.41992
b-rank test for bits 12 to 19, p=0.63084
b-rank test for bits 13 to 20, p=0.59206
b-rank test for bits 14 to 21, p=0.68692
b-rank test for bits 15 to 22, p=0.61040
b-rank test for bits 16 to 23, p=0.69699
b-rank test for bits 17 to 24, p=0.33188
b-rank test for bits 18 to 25, p=0.74672
b-rank test for bits 19 to 26, p=0.91299
b-rank test for bits 20 to 27, p=0.24507
b-rank test for bits 21 to 28, p=0.03585
b-rank test for bits 22 to 29, p=0.22763
b-rank test for bits 23 to 30, p=0.27672
b-rank test for bits 24 to 31, p=0.77070
b-rank test for bits 25 to 32, p=0.48794
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 = 0.635015
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-08-31_16:31
(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 141902 -0.02 0.493168
2 141325 -1.37 0.086086
3 141660 -0.58 0.280099
4 142780 2.03 0.979038
5 141460 -1.05 0.146897
6 141953 0.10 0.540635
7 141586 -0.76 0.224991
8 141872 -0.09 0.465249
9 142017 0.25 0.599312
10 141255 -1.53 0.063156
11 142028 0.28 0.609212
12 141967 0.13 0.553593
13 142160 0.59 0.720954
14 141335 -1.34 0.089815
15 141812 -0.23 0.410054
16 142099 0.44 0.671173
17 141866 -0.10 0.459681
18 141529 -0.89 0.187103
19 141732 -0.41 0.339319
20 141206 -1.64 0.050161
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-08-31_16:31
Bits used No. missing words z-score p-value
23 to 32 141722 -0.6460 0.259151
22 to 31 141743 -0.5736 0.283136
21 to 30 141600 -1.0667 0.143064
20 to 29 141100 -2.7908 0.002629
19 to 28 142338 1.4782 0.930319
18 to 27 141298 -2.1080 0.017514
17 to 26 141856 -0.1839 0.427047
16 to 25 141709 -0.6908 0.244848
15 to 24 141331 -1.9942 0.023063
14 to 23 141631 -0.9598 0.168588
13 to 22 141515 -1.3598 0.086953
12 to 21 141859 -0.1736 0.431109
11 to 20 141312 -2.0598 0.019711
10 to 19 141929 0.0678 0.527039
9 to 18 141893 -0.0563 0.477547
8 to 17 141538 -1.2804 0.100194
7 to 16 141790 -0.4115 0.340359
6 to 15 142218 1.0644 0.856422
5 to 14 142278 1.2713 0.898185
4 to 13 141675 -0.8080 0.209535
3 to 12 141351 -1.9253 0.027097
2 to 11 142304 1.3609 0.913232
1 to 10 141924 0.0506 0.520172
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-08-31_16:31
Bits used No. missing words z-score p-value
28 to 32 141413 -1.6825 0.046238
27 to 31 141940 0.1040 0.541402
26 to 30 141762 -0.4994 0.308741
25 to 29 142073 0.5548 0.710489
24 to 28 142113 0.6904 0.755031
23 to 27 141922 0.0429 0.517129
22 to 26 141835 -0.2520 0.400534
21 to 25 142062 0.5175 0.697605
20 to 24 141796 -0.3842 0.350426
19 to 23 141865 -0.1503 0.440275
18 to 22 142069 0.5413 0.705834
17 to 21 141613 -1.0045 0.157567
16 to 20 141395 -1.7435 0.040624
15 to 19 142096 0.6328 0.736561
14 to 18 142027 0.3989 0.655010
13 to 17 141715 -0.6587 0.255030
12 to 16 142292 1.2972 0.902717
11 to 15 142134 0.7616 0.776849
10 to 14 142272 1.2294 0.890537
9 to 13 142172 0.8904 0.813376
8 to 12 141192 -2.4316 0.007516
7 to 11 141214 -2.3571 0.009210
6 to 10 141719 -0.6452 0.259403
5 to 9 142183 0.9277 0.823217
4 to 8 142338 1.4531 0.926905
3 to 7 142171 0.8870 0.812465
2 to 6 142492 1.9752 0.975875
1 to 5 142011 0.3446 0.634819
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-08-31_16:31
Bits used No. missing words z-score p-value
31 to 32 141548 -1.0659 0.143241
30 to 31 141680 -0.6765 0.249365
29 to 30 141802 -0.3166 0.375771
28 to 29 141844 -0.1927 0.423592
27 to 28 141883 -0.0777 0.469045
26 to 27 141892 -0.0511 0.479615
25 to 26 142342 1.2763 0.899078
24 to 25 142138 0.6745 0.750017
23 to 24 142017 0.3176 0.624610
22 to 23 141975 0.1937 0.576801
21 to 22 142067 0.4651 0.679071
20 to 21 141609 -0.8859 0.187828
19 to 20 141614 -0.8712 0.191828
18 to 19 142257 1.0256 0.847454
17 to 18 141344 -1.6676 0.047694
16 to 17 141804 -0.3107 0.378011
15 to 16 142064 0.4563 0.675896
14 to 15 141758 -0.4464 0.327654
13 to 14 141007 -2.6617 0.003887
12 to 13 141643 -0.7856 0.216041
11 to 12 141871 -0.1131 0.454988
10 to 11 142217 0.9076 0.817950
9 to 10 141842 -0.1986 0.421283
8 to 9 142027 0.3471 0.635745
7 to 8 142055 0.4297 0.666295
6 to 7 142002 0.2734 0.607713
5 to 6 141599 -0.9154 0.179984
4 to 5 141835 -0.2193 0.413223
3 to 4 141351 -1.6470 0.049780
2 to 3 141880 -0.0865 0.465527
1 to 2 142257 1.0256 0.847454
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-08-31_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2648.60 2.102 0.982204
Test results for specific bytes for dh-ranFile-2018-08-31_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2448.76 -0.725 0.234333
2 to 9 2658.11 2.236 0.987323
3 to 10 2400.11 -1.413 0.078886
4 to 11 2473.61 -0.373 0.354486
5 to 12 2515.96 0.226 0.589284
6 to 13 2436.92 -0.892 0.186177
7 to 14 2431.61 -0.967 0.166726
8 to 15 2623.92 1.753 0.960160
9 to 16 2475.18 -0.351 0.362772
10 to 17 2463.53 -0.516 0.303011
11 to 18 2504.59 0.065 0.525858
12 to 19 2538.95 0.551 0.709132
13 to 20 2465.60 -0.487 0.313297
14 to 21 2471.76 -0.399 0.344801
15 to 22 2475.95 -0.340 0.366900
16 to 23 2522.18 0.314 0.623095
17 to 24 2448.63 -0.726 0.233785
18 to 25 2500.45 0.006 0.502546
19 to 26 2410.05 -1.272 0.101669
20 to 27 2456.43 -0.616 0.268881
21 to 28 2534.86 0.493 0.688981
22 to 29 2361.55 -1.958 0.025115
23 to 30 2603.35 1.462 0.928083
24 to 31 2421.32 -1.113 0.132913
25 to 32 2466.45 -0.474 0.317578
CDPARK for dh-ranFile-2018-08-31_16:31: 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
3587 2.9224 0.998263
3496 -1.2329 0.108811
3519 -0.1826 0.427537
3508 -0.6849 0.246694
3511 -0.5479 0.291865
3550 1.2329 0.891189
3545 1.0046 0.842447
3508 -0.6849 0.246694
3518 -0.2283 0.409702
3531 0.3653 0.642555
Square side=100, avg. no. parked=3527.30 sample std.=25.60
p-value of the KSTEST for those 10 p-values: 0.673186
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-08-31_16:31
0.2557,0.6988,0.8440,0.7282,0.1270,0.2485,0.8616,0.3104,0.5341,0.3459,
The KS test for those 10 p-values: 0.892939
The 3DSPHERES test for dh-ranFile-2018-08-31_16:31
sample no r^3 equiv. uni.
1 7.512 0.221515
2 0.200 0.006636
3 37.122 0.709867
4 3.408 0.107380
5 51.419 0.819848
6 31.786 0.653379
7 38.247 0.720540
8 30.957 0.643671
9 76.835 0.922786
10 7.547 0.222419
11 0.678 0.022348
12 55.874 0.844710
13 1.582 0.051362
14 17.883 0.449044
15 68.468 0.897949
16 28.329 0.611044
17 20.865 0.501183
18 0.117 0.003899
19 30.479 0.637946
20 17.044 0.433409
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.308308
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-08-31_16:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 0.5 -1.3 -0.8 -1.4 -0.3
-1.9 0.1 -1.4 0.0 -0.3 0.1
1.3 0.5 -1.5 -1.3 -2.1 0.5
2.3 0.1 1.5 -2.1 0.8 2.1
-0.8 -1.1 0.5 1.1 1.0 -0.8
-0.3 1.4 1.0 1.4 -0.9 0.2
0.7 -0.1 -1.6 0.4 -0.6 1.0
-1.1
Chi-square with 42 degrees of freedom:56.246127
z-score=1.554380, p-value=0.930274
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-08-31_16:31
Test no p-value
1 0.331623
2 0.030510
3 0.000245
4 0.700508
5 0.692853
6 0.421460
7 0.472634
8 0.354044
9 0.174802
10 0.015752
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.025410
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-08-31_16:31:
(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 66365 1.37 66779 0.19
3 25000.00 25211 1.78 25002 0.00
4 6666.67 6754 1.14 6597 0.73
5 1388.89 1401 0.11 1359 0.64
6 238.10 219 1.53 229 0.35
7 34.72 39 0.53 29 0.94
8 4.96 10 5.12 4 0.19
p=0.92787 p=0.19573
Number of rngs required: 687745, p-value: 0.224
RESULTS OF CRAPS TEST for dh-ranFile-2018-08-31_16:31
No. of wins: Observed Expected
98688 98585.9
z-score= 0.457, pvalue=0.67611
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66925 66666.7 1.001 1.001
2 37231 37654.3 4.759 5.760
3 27093 26954.7 0.709 6.469
4 19349 19313.5 0.065 6.535
5 13914 13851.4 0.283 6.818
6 9790 9943.5 2.371 9.188
7 7186 7145.0 0.235 9.423
8 5148 5139.1 0.016 9.439
9 3731 3699.9 0.262 9.701
10 2575 2666.3 3.126 12.827
11 1969 1923.3 1.084 13.912
12 1349 1388.7 1.137 15.049
13 1003 1003.7 0.001 15.049
14 753 726.1 0.994 16.043
15 508 525.8 0.605 16.648
16 435 381.2 7.608 24.256
17 302 276.5 2.344 26.600
18 215 200.8 1.000 27.600
19 126 146.0 2.736 30.335
20 111 106.2 0.216 30.551
21 287 287.1 0.000 30.551
Chisq= 30.55 for 20 degrees of freedom, p= 0.93860
SUMMARY of craptest
p-value for no. of wins: 0.676106
p-value for throws/game: 0.938595
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-08-31_16:31
No. of wins: Observed Expected
99041 98585.9
z-score= 2.036, pvalue=0.97911
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66366 66666.7 1.356 1.356
2 37520 37654.3 0.479 1.835
3 27107 26954.7 0.860 2.695
4 19339 19313.5 0.034 2.729
5 13844 13851.4 0.004 2.733
6 10091 9943.5 2.187 4.920
7 7296 7145.0 3.190 8.110
8 5142 5139.1 0.002 8.112
9 3620 3699.9 1.724 9.835
10 2686 2666.3 0.146 9.981
11 1964 1923.3 0.860 10.841
12 1377 1388.7 0.099 10.940
13 964 1003.7 1.571 12.512
14 729 726.1 0.011 12.523
15 478 525.8 4.352 16.875
16 389 381.2 0.162 17.036
17 277 276.5 0.001 17.037
18 221 200.8 2.026 19.063
19 140 146.0 0.245 19.308
20 133 106.2 6.754 26.063
21 317 287.1 3.111 29.174
Chisq= 29.17 for 20 degrees of freedom, p= 0.91560
SUMMARY of craptest
p-value for no. of wins: 0.979108
p-value for throws/game: 0.915602
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0002,0.0026,0.0039,0.0039,0.0043,0.0066,0.0071,0.0075,0.0092,0.0158,
0.0158,0.0175,0.0196,0.0197,0.0197,0.0223,0.0231,0.0251,0.0254,0.0271,
0.0305,0.0335,0.0359,0.0406,0.0462,0.0477,0.0498,0.0502,0.0514,0.0632,
0.0633,0.0725,0.0789,0.0861,0.0870,0.0894,0.0898,0.1002,0.1017,0.1074,
0.1088,0.1125,0.1182,0.1270,0.1291,0.1329,0.1402,0.1431,0.1432,0.1469,
0.1501,0.1576,0.1667,0.1686,0.1727,0.1748,0.1800,0.1862,0.1871,0.1878,
0.1918,0.1935,0.1957,0.2068,0.2078,0.2095,0.2160,0.2215,0.2224,0.2236,
0.2250,0.2276,0.2338,0.2343,0.2448,0.2449,0.2451,0.2467,0.2467,0.2485,
0.2494,0.2550,0.2557,0.2586,0.2592,0.2594,0.2689,0.2756,0.2767,0.2801,
0.2831,0.2919,0.3030,0.3083,0.3087,0.3104,0.3133,0.3176,0.3180,0.3277,
0.3316,0.3319,0.3358,0.3393,0.3404,0.3407,0.3448,0.3459,0.3469,0.3503,
0.3504,0.3540,0.3545,0.3628,0.3669,0.3758,0.3780,0.3815,0.4005,0.4012,
0.4097,0.4101,0.4114,0.4132,0.4192,0.4199,0.4213,0.4215,0.4236,0.4270,
0.4275,0.4311,0.4334,0.4365,0.4403,0.4490,0.4530,0.4550,0.4597,0.4652,
0.4655,0.4690,0.4726,0.4749,0.4775,0.4796,0.4879,0.4932,0.5012,0.5025,
0.5171,0.5202,0.5259,0.5270,0.5279,0.5341,0.5406,0.5414,0.5536,0.5555,
0.5738,0.5768,0.5779,0.5809,0.5893,0.5921,0.5993,0.5996,0.6074,0.6075,
0.6077,0.6092,0.6104,0.6110,0.6231,0.6246,0.6308,0.6330,0.6348,0.6350,
0.6357,0.6379,0.6426,0.6437,0.6440,0.6534,0.6550,0.6663,0.6712,0.6732,
0.6759,0.6761,0.6761,0.6791,0.6820,0.6869,0.6890,0.6929,0.6970,0.6976,
0.6988,0.7003,0.7005,0.7015,0.7058,0.7091,0.7099,0.7105,0.7126,0.7205,
0.7210,0.7282,0.7298,0.7366,0.7426,0.7467,0.7494,0.7500,0.7550,0.7704,
0.7707,0.7768,0.7993,0.8125,0.8134,0.8180,0.8198,0.8232,0.8269,0.8424,
0.8440,0.8447,0.8472,0.8475,0.8475,0.8564,0.8616,0.8677,0.8903,0.8905,
0.8912,0.8929,0.8979,0.8982,0.8991,0.9027,0.9130,0.9132,0.9156,0.9228,
0.9269,0.9279,0.9281,0.9303,0.9303,0.9327,0.9386,0.9478,0.9553,0.9602,
0.9607,0.9759,0.9763,0.9790,0.9791,0.9822,0.9873,0.9970,0.9983,
Overall p-value after applying KStest on 269 p-values = 0.025963
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.