RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-25_09:31
(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 23.5491 0.867785
2 to 25 15.50 19.6258 0.706184
3 to 26 15.67 21.9876 0.814803
4 to 27 15.97 17.8247 0.600018
5 to 28 15.90 8.0250 0.033991
6 to 29 15.94 13.0240 0.265420
7 to 30 15.85 16.8384 0.534632
8 to 31 15.80 17.1123 0.553219
9 to 32 15.43 27.1937 0.944713
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.581914
Tough bday spacings test for dh-ranFile-2018-06-25_09:31: 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 11 34 87 86 91 99 36 32 17 3 4
(O-E)^2/E 0.4 0.2 2.6 1.4 0.5 5.6 5.0 0.2 0.3 2.0 0.0
Birthday Spacings: Sum(O-E)^2/E= 17.973, p= 0.945
RESULTS OF GCD FOR dh-ranFile-2018-06-25_09:31
Euclid's algorithm:
p-value, steps to gcd: 0.545233
p-value, dist. of gcd's: 0.539432
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-25_09:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.245 0.266 0.944 0.289 0.192 0.184 0.534 0.937
Bits 8 to 15---> 0.442 0.409 0.106 0.840 0.681 0.513 0.128 0.260
Bits 16 to 23---> 0.553 0.953 0.809 0.714 0.478 0.226 0.511 0.105
Bits 24 to 31---> 0.668 0.839 0.757 0.121 0.461 0.571 0.690 0.749
KS test for the above 32 p values: 0.129
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-25_09:31,
p-values for 5 runs: 0.5269, 0.9917, 0.0869, 0.1259, 0.6675
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-25_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 220 211.4 0.348 0.348
r= 29 5164 5134.0 0.175 0.524
r= 30 22892 23103.0 1.928 2.451
r= 31 11724 11551.5 2.575 5.027
chi-square = 5.027 with df = 3; p-value = 0.830
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-25_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 195 211.4 1.275 1.275
r= 30 5046 5134.0 1.509 2.784
r= 31 23262 23103.0 1.094 3.877
r= 32 11497 11551.5 0.257 4.135
chi-square = 4.135 with df = 3; p-value = 0.753
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-25_09:31
b-rank test for bits 1 to 8, p=0.74941
b-rank test for bits 2 to 9, p=0.91521
b-rank test for bits 3 to 10, p=0.86952
b-rank test for bits 4 to 11, p=0.35640
b-rank test for bits 5 to 12, p=0.58054
b-rank test for bits 6 to 13, p=0.04914
b-rank test for bits 7 to 14, p=0.07714
b-rank test for bits 8 to 15, p=0.10489
b-rank test for bits 9 to 16, p=0.10579
b-rank test for bits 10 to 17, p=0.65143
b-rank test for bits 11 to 18, p=0.96920
b-rank test for bits 12 to 19, p=0.78444
b-rank test for bits 13 to 20, p=0.30157
b-rank test for bits 14 to 21, p=0.71648
b-rank test for bits 15 to 22, p=0.75818
b-rank test for bits 16 to 23, p=0.44857
b-rank test for bits 17 to 24, p=0.27198
b-rank test for bits 18 to 25, p=0.07026
b-rank test for bits 19 to 26, p=0.93066
b-rank test for bits 20 to 27, p=0.50389
b-rank test for bits 21 to 28, p=0.38353
b-rank test for bits 22 to 29, p=0.57048
b-rank test for bits 23 to 30, p=0.53471
b-rank test for bits 24 to 31, p=0.64119
b-rank test for bits 25 to 32, p=0.20646
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 = 0.995543
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-25_09:31
(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 141907 -0.01 0.497828
2 142027 0.27 0.608315
3 141323 -1.37 0.085354
4 141714 -0.46 0.324059
5 141604 -0.71 0.237803
6 140847 -2.48 0.006531
7 141630 -0.65 0.256994
8 141902 -0.02 0.493168
9 141214 -1.62 0.052124
10 141654 -0.60 0.275399
11 141260 -1.52 0.064617
12 141302 -1.42 0.077950
13 142411 1.17 0.879427
14 142400 1.15 0.874190
15 141816 -0.22 0.413691
16 141952 0.10 0.539707
17 141001 -2.12 0.016908
18 142322 0.96 0.832523
19 142031 0.28 0.611900
20 141900 -0.02 0.491304
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-25_09:31
Bits used No. missing words z-score p-value
23 to 32 141676 -0.8046 0.210529
22 to 31 141941 0.1092 0.543481
21 to 30 141934 0.0851 0.533897
20 to 29 142052 0.4920 0.688628
19 to 28 141842 -0.2322 0.408202
18 to 27 142099 0.6540 0.743455
17 to 26 142057 0.5092 0.694696
16 to 25 141722 -0.6460 0.259151
15 to 24 141690 -0.7563 0.224732
14 to 23 141793 -0.4011 0.344159
13 to 22 142108 0.6851 0.753350
12 to 21 141661 -0.8563 0.195913
11 to 20 141754 -0.5356 0.296110
10 to 19 142048 0.4782 0.683736
9 to 18 141778 -0.4529 0.325324
8 to 17 141807 -0.3529 0.362096
7 to 16 142083 0.5989 0.725368
6 to 15 141794 -0.3977 0.345430
5 to 14 142110 0.6920 0.755521
4 to 13 142197 0.9920 0.839393
3 to 12 141597 -1.0770 0.140740
2 to 11 142215 1.0540 0.854066
1 to 10 142757 2.9230 0.998267
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-25_09:31
Bits used No. missing words z-score p-value
28 to 32 141822 -0.2960 0.383602
27 to 31 141619 -0.9842 0.162516
26 to 30 142347 1.4836 0.931046
25 to 29 142067 0.5345 0.703493
24 to 28 142459 1.8633 0.968789
23 to 27 141797 -0.3808 0.351683
22 to 26 141785 -0.4215 0.336711
21 to 25 141248 -2.2418 0.012487
20 to 24 142357 1.5175 0.935433
19 to 23 142170 0.8836 0.811551
18 to 22 142252 1.1616 0.877300
17 to 21 141489 -1.4248 0.077101
16 to 20 141759 -0.5096 0.305168
15 to 19 141774 -0.4587 0.323208
14 to 18 141632 -0.9401 0.173583
13 to 17 141921 0.0396 0.515778
12 to 16 142485 1.9514 0.974497
11 to 15 141573 -1.1401 0.127122
10 to 14 142103 0.6565 0.744252
9 to 13 141643 -0.9028 0.183312
8 to 12 142495 1.9853 0.976446
7 to 11 142310 1.3582 0.912800
6 to 10 142436 1.7853 0.962895
5 to 9 141945 0.1209 0.548121
4 to 8 141430 -1.6248 0.052098
3 to 7 142128 0.7413 0.770730
2 to 6 141915 0.0192 0.507667
1 to 5 142663 2.5548 0.994688
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-25_09:31
Bits used No. missing words z-score p-value
31 to 32 142253 1.0138 0.844655
30 to 31 142283 1.1023 0.864828
29 to 30 142084 0.5153 0.696811
28 to 29 141551 -1.0570 0.145251
27 to 28 142308 1.1760 0.880206
26 to 27 142279 1.0905 0.862247
25 to 26 142059 0.4415 0.670576
24 to 25 142375 1.3737 0.915226
23 to 24 142175 0.7837 0.783388
22 to 23 141638 -0.8004 0.211744
21 to 22 142566 1.9371 0.973632
20 to 21 141583 -0.9626 0.167868
19 to 20 141855 -0.1603 0.436336
18 to 19 141925 0.0462 0.518434
17 to 18 141483 -1.2576 0.104266
16 to 17 141842 -0.1986 0.421283
15 to 16 141819 -0.2665 0.394942
14 to 15 142025 0.3412 0.633527
13 to 14 142028 0.3501 0.636853
12 to 13 141792 -0.3461 0.364632
11 to 12 141656 -0.7473 0.227445
10 to 11 141894 -0.0452 0.481966
9 to 10 141801 -0.3196 0.374652
8 to 9 141615 -0.8682 0.192634
7 to 8 141314 -1.7561 0.039533
6 to 7 142408 1.4710 0.929355
5 to 6 142242 0.9813 0.836784
4 to 5 142674 2.2557 0.987954
3 to 4 142369 1.3560 0.912444
2 to 3 141712 -0.5821 0.280252
1 to 2 141391 -1.5290 0.063133
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-25_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2409.59 -1.279 0.100516
Test results for specific bytes for dh-ranFile-2018-06-25_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2433.51 -0.940 0.173537
2 to 9 2639.14 1.968 0.975447
3 to 10 2584.33 1.193 0.883479
4 to 11 2418.90 -1.147 0.125716
5 to 12 2455.18 -0.634 0.263069
6 to 13 2683.81 2.599 0.995332
7 to 14 2510.63 0.150 0.559742
8 to 15 2703.27 2.875 0.997978
9 to 16 2481.08 -0.268 0.394523
10 to 17 2423.66 -1.080 0.140146
11 to 18 2526.04 0.368 0.643651
12 to 19 2394.12 -1.497 0.067151
13 to 20 2502.45 0.035 0.513806
14 to 21 2630.95 1.852 0.967982
15 to 22 2400.33 -1.409 0.079346
16 to 23 2487.34 -0.179 0.428950
17 to 24 2497.04 -0.042 0.483300
18 to 25 2568.61 0.970 0.834067
19 to 26 2540.09 0.567 0.714611
20 to 27 2573.84 1.044 0.851822
21 to 28 2725.01 3.182 0.999269
22 to 29 2435.69 -0.910 0.181541
23 to 30 2386.62 -1.603 0.054426
24 to 31 2563.12 0.893 0.813971
25 to 32 2486.91 -0.185 0.426560
CDPARK for dh-ranFile-2018-06-25_09:31: 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
3505 -0.8219 0.205562
3542 0.8676 0.807188
3505 -0.8219 0.205562
3515 -0.3653 0.357445
3506 -0.7763 0.218799
3554 1.4155 0.921543
3512 -0.5023 0.307734
3533 0.4566 0.676028
3545 1.0046 0.842447
3530 0.3196 0.625377
Square side=100, avg. no. parked=3524.70 sample std.=17.46
p-value of the KSTEST for those 10 p-values: 0.843927
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-25_09:31
0.9459,0.4885,0.9071,0.8135,0.5862,0.9179,0.2901,0.3468,0.4854,0.2117,
The KS test for those 10 p-values: 0.393818
The 3DSPHERES test for dh-ranFile-2018-06-25_09:31
sample no r^3 equiv. uni.
1 6.084 0.183551
2 10.401 0.292992
3 9.123 0.262221
4 21.410 0.510162
5 4.408 0.136645
6 41.248 0.747144
7 84.828 0.940845
8 8.408 0.244423
9 31.377 0.648623
10 13.650 0.365547
11 21.024 0.503814
12 46.440 0.787326
13 8.679 0.251200
14 52.298 0.825053
15 0.626 0.020661
16 23.144 0.537665
17 29.227 0.622523
18 4.987 0.153149
19 87.208 0.945357
20 8.153 0.237968
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.790152
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-25_09:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 0.1 0.3 -1.0 -0.1 -2.2
-0.2 0.5 1.0 -0.0 -0.8 -0.5
-0.3 -0.8 0.5 1.0 -0.1 1.3
0.6 -0.8 -1.7 1.0 -0.3 -0.3
1.2 -0.1 -1.1 0.4 0.1 0.1
-0.2 -0.8 1.3 1.3 0.2 -2.1
1.4 -0.7 1.3 -0.1 0.9 -1.0
-0.1
Chi-square with 42 degrees of freedom:34.453678
z-score=-0.823371, p-value=0.210516
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-25_09:31
Test no p-value
1 0.163078
2 0.031251
3 0.265582
4 0.465306
5 0.205106
6 0.332207
7 0.049255
8 0.793750
9 0.828926
10 0.735383
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.335151
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-25_09:31:
(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 66798 0.26 66873 0.64
3 25000.00 24737 2.77 24897 0.42
4 6666.67 6729 0.58 6544 2.26
5 1388.89 1435 1.53 1394 0.02
6 238.10 258 1.66 242 0.06
7 34.72 35 0.00 42 1.53
8 4.96 7 0.84 7 0.84
p=0.73467 p=0.55038
Number of rngs required: 687879, p-value: 0.273
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-25_09:31
No. of wins: Observed Expected
98620 98585.9
z-score= 0.153, pvalue=0.56068
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66582 66666.7 0.108 0.108
2 37717 37654.3 0.104 0.212
3 26774 26954.7 1.212 1.424
4 19187 19313.5 0.828 2.252
5 13958 13851.4 0.820 3.072
6 10050 9943.5 1.140 4.212
7 7083 7145.0 0.538 4.750
8 5204 5139.1 0.820 5.570
9 3724 3699.9 0.157 5.728
10 2662 2666.3 0.007 5.735
11 1904 1923.3 0.194 5.929
12 1464 1388.7 4.079 10.007
13 1029 1003.7 0.637 10.644
14 721 726.1 0.036 10.681
15 556 525.8 1.730 12.411
16 384 381.2 0.021 12.432
17 279 276.5 0.022 12.454
18 178 200.8 2.595 15.050
19 143 146.0 0.061 15.111
20 101 106.2 0.256 15.367
21 300 287.1 0.578 15.945
Chisq= 15.95 for 20 degrees of freedom, p= 0.27997
SUMMARY of craptest
p-value for no. of wins: 0.560683
p-value for throws/game: 0.279971
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-25_09:31
No. of wins: Observed Expected
98906 98585.9
z-score= 1.432, pvalue=0.92391
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66692 66666.7 0.010 0.010
2 37694 37654.3 0.042 0.051
3 26901 26954.7 0.107 0.159
4 19130 19313.5 1.743 1.901
5 13793 13851.4 0.246 2.148
6 9769 9943.5 3.064 5.212
7 7142 7145.0 0.001 5.213
8 5222 5139.1 1.338 6.551
9 3835 3699.9 4.936 11.487
10 2670 2666.3 0.005 11.492
11 1985 1923.3 1.977 13.469
12 1393 1388.7 0.013 13.482
13 1059 1003.7 3.045 16.527
14 785 726.1 4.771 21.298
15 568 525.8 3.381 24.679
16 365 381.2 0.684 25.364
17 258 276.5 1.243 26.607
18 225 200.8 2.909 29.516
19 130 146.0 1.750 31.266
20 104 106.2 0.046 31.312
21 280 287.1 0.176 31.488
Chisq= 31.49 for 20 degrees of freedom, p= 0.95093
SUMMARY of craptest
p-value for no. of wins: 0.923908
p-value for throws/game: 0.950934
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0065,0.0125,0.0169,0.0207,0.0313,0.0340,0.0395,0.0491,0.0493,0.0521,
0.0521,0.0544,0.0631,0.0646,0.0672,0.0703,0.0771,0.0771,0.0780,0.0793,
0.0854,0.0869,0.1005,0.1043,0.1048,0.1049,0.1058,0.1061,0.1205,0.1257,
0.1259,0.1271,0.1276,0.1289,0.1366,0.1401,0.1407,0.1453,0.1531,0.1625,
0.1631,0.1679,0.1735,0.1736,0.1815,0.1833,0.1835,0.1836,0.1921,0.1926,
0.1959,0.2051,0.2056,0.2056,0.2065,0.2105,0.2105,0.2117,0.2117,0.2188,
0.2247,0.2257,0.2274,0.2378,0.2380,0.2444,0.2449,0.2512,0.2570,0.2592,
0.2602,0.2622,0.2631,0.2654,0.2656,0.2663,0.2720,0.2728,0.2754,0.2800,
0.2803,0.2894,0.2901,0.2930,0.2961,0.3016,0.3052,0.3077,0.3232,0.3241,
0.3253,0.3322,0.3352,0.3367,0.3442,0.3454,0.3468,0.3517,0.3564,0.3574,
0.3621,0.3646,0.3655,0.3747,0.3835,0.3836,0.3938,0.3945,0.3949,0.4082,
0.4088,0.4137,0.4213,0.4266,0.4289,0.4363,0.4416,0.4486,0.4615,0.4653,
0.4784,0.4820,0.4833,0.4854,0.4885,0.4913,0.4932,0.4978,0.5038,0.5039,
0.5077,0.5102,0.5112,0.5133,0.5138,0.5158,0.5184,0.5269,0.5339,0.5344,
0.5346,0.5347,0.5377,0.5394,0.5397,0.5435,0.5452,0.5481,0.5504,0.5531,
0.5532,0.5597,0.5607,0.5705,0.5713,0.5805,0.5819,0.5862,0.6000,0.6083,
0.6119,0.6225,0.6254,0.6335,0.6369,0.6412,0.6437,0.6486,0.6514,0.6675,
0.6675,0.6706,0.6760,0.6813,0.6837,0.6886,0.6896,0.6947,0.6968,0.7035,
0.7062,0.7139,0.7146,0.7165,0.7254,0.7347,0.7354,0.7435,0.7443,0.7471,
0.7492,0.7494,0.7527,0.7533,0.7555,0.7572,0.7582,0.7707,0.7834,0.7844,
0.7873,0.7902,0.7937,0.8072,0.8086,0.8116,0.8135,0.8140,0.8148,0.8251,
0.8289,0.8301,0.8325,0.8341,0.8368,0.8391,0.8394,0.8404,0.8424,0.8439,
0.8447,0.8518,0.8541,0.8622,0.8648,0.8678,0.8695,0.8742,0.8773,0.8794,
0.8802,0.8835,0.9071,0.9124,0.9128,0.9152,0.9152,0.9179,0.9215,0.9239,
0.9294,0.9307,0.9310,0.9354,0.9374,0.9408,0.9443,0.9446,0.9447,0.9454,
0.9459,0.9509,0.9532,0.9629,0.9680,0.9688,0.9692,0.9736,0.9745,0.9754,
0.9764,0.9880,0.9917,0.9947,0.9953,0.9955,0.9980,0.9983,0.9993,
Overall p-value after applying KStest on 269 p-values = 0.274084
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.