RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-15_07:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.77 18.2072 0.624115
2 to 25 16.20 13.5418 0.300772
3 to 26 15.48 24.6958 0.898271
4 to 27 15.82 17.3445 0.568729
5 to 28 15.80 13.6798 0.310379
6 to 29 15.91 19.6967 0.709966
7 to 30 15.75 13.7785 0.317284
8 to 31 15.81 19.8284 0.716902
9 to 32 16.00 23.6767 0.871510
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.441337
Tough bday spacings test for dh-ranFile-2018-06-15_07:31: 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 9 38 76 99 98 74 55 28 12 9 2
(O-E)^2/E 0.0 0.1 0.1 0.0 0.0 0.2 0.2 0.1 0.6 0.9 1.0
Birthday Spacings: Sum(O-E)^2/E= 3.130, p= 0.022
RESULTS OF GCD FOR dh-ranFile-2018-06-15_07:31
Euclid's algorithm:
p-value, steps to gcd: 0.518773
p-value, dist. of gcd's: 0.817313
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-15_07:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.387 0.212 0.457 0.900 0.010 0.701 0.302 0.576
Bits 8 to 15---> 0.711 0.187 0.444 0.506 0.665 0.489 0.104 0.306
Bits 16 to 23---> 0.167 0.592 0.240 0.956 0.807 0.329 0.041 0.523
Bits 24 to 31---> 0.910 0.298 0.142 0.476 0.161 0.120 0.702 0.502
KS test for the above 32 p values: 0.677
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-15_07:31,
p-values for 5 runs: 0.8658, 0.8976, 0.4777, 0.5805, 0.2964
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-15_07:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 200 211.4 0.617 0.617
r= 29 5136 5134.0 0.001 0.617
r= 30 22981 23103.0 0.645 1.262
r= 31 11683 11551.5 1.496 2.759
chi-square = 2.759 with df = 3; p-value = 0.570
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-15_07:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 184 211.4 3.556 3.556
r= 30 5192 5134.0 0.655 4.211
r= 31 23095 23103.0 0.003 4.214
r= 32 11529 11551.5 0.044 4.257
chi-square = 4.257 with df = 3; p-value = 0.765
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-15_07:31
b-rank test for bits 1 to 8, p=0.99845
b-rank test for bits 2 to 9, p=0.67736
b-rank test for bits 3 to 10, p=0.70175
b-rank test for bits 4 to 11, p=0.13423
b-rank test for bits 5 to 12, p=0.36183
b-rank test for bits 6 to 13, p=0.25330
b-rank test for bits 7 to 14, p=0.64269
b-rank test for bits 8 to 15, p=0.21552
b-rank test for bits 9 to 16, p=0.76971
b-rank test for bits 10 to 17, p=0.81811
b-rank test for bits 11 to 18, p=0.33058
b-rank test for bits 12 to 19, p=0.09481
b-rank test for bits 13 to 20, p=0.07165
b-rank test for bits 14 to 21, p=0.36104
b-rank test for bits 15 to 22, p=0.59815
b-rank test for bits 16 to 23, p=0.06728
b-rank test for bits 17 to 24, p=0.67772
b-rank test for bits 18 to 25, p=0.67770
b-rank test for bits 19 to 26, p=0.64826
b-rank test for bits 20 to 27, p=0.04998
b-rank test for bits 21 to 28, p=0.07626
b-rank test for bits 22 to 29, p=0.88114
b-rank test for bits 23 to 30, p=0.08088
b-rank test for bits 24 to 31, p=0.96406
b-rank test for bits 25 to 32, p=0.47804
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 = 0.471892
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-15_07:31
(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 141809 -0.23 0.407331
2 142099 0.44 0.671173
3 141547 -0.85 0.198619
4 141466 -1.04 0.150144
5 141485 -0.99 0.160739
6 141924 0.03 0.513671
7 141922 0.03 0.511808
8 141842 -0.16 0.437499
9 142429 1.21 0.887661
10 142027 0.27 0.608315
11 141400 -1.19 0.117019
12 141764 -0.34 0.367095
13 141409 -1.17 0.121203
14 141955 0.11 0.542489
15 141865 -0.10 0.458753
16 142182 0.64 0.737963
17 141779 -0.30 0.380370
18 141245 -1.55 0.060310
19 141296 -1.43 0.075927
20 141885 -0.06 0.477334
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-15_07:31
Bits used No. missing words z-score p-value
23 to 32 142063 0.5299 0.701908
22 to 31 141542 -1.2667 0.102639
21 to 30 141747 -0.5598 0.287822
20 to 29 141961 0.1782 0.570706
19 to 28 142459 1.8954 0.970981
18 to 27 142236 1.1264 0.870012
17 to 26 142163 0.8747 0.809138
16 to 25 141413 -1.7115 0.043496
15 to 24 141995 0.2954 0.616161
14 to 23 141611 -1.0287 0.151805
13 to 22 142162 0.8713 0.808198
12 to 21 142104 0.6713 0.748978
11 to 20 142009 0.3437 0.634460
10 to 19 142227 1.0954 0.863332
9 to 18 141810 -0.3425 0.365981
8 to 17 142259 1.2058 0.886045
7 to 16 141554 -1.2253 0.110236
6 to 15 141640 -0.9287 0.176516
5 to 14 142122 0.7333 0.768326
4 to 13 141958 0.1678 0.566641
3 to 12 141588 -1.1080 0.133923
2 to 11 141682 -0.7839 0.216550
1 to 10 141771 -0.4770 0.316681
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-15_07:31
Bits used No. missing words z-score p-value
28 to 32 142211 1.0226 0.846754
27 to 31 142540 2.1379 0.983736
26 to 30 141990 0.2735 0.607749
25 to 29 141874 -0.1198 0.452336
24 to 28 141444 -1.5774 0.057353
23 to 27 141945 0.1209 0.548121
22 to 26 142370 1.5616 0.940808
21 to 25 142193 0.9616 0.831873
20 to 24 141792 -0.3977 0.345415
19 to 23 141738 -0.5808 0.280695
18 to 22 141598 -1.0554 0.145631
17 to 21 141546 -1.2316 0.109044
16 to 20 141615 -0.9977 0.159205
15 to 19 141965 0.1887 0.574841
14 to 18 141351 -1.8926 0.029203
13 to 17 142118 0.7074 0.760327
12 to 16 142036 0.4294 0.666180
11 to 15 141650 -0.8791 0.189678
10 to 14 141939 0.1006 0.540057
9 to 13 142179 0.9141 0.819677
8 to 12 142568 2.2328 0.987218
7 to 11 142245 1.1379 0.872411
6 to 10 141734 -0.5943 0.276143
5 to 9 141624 -0.9672 0.166717
4 to 8 141945 0.1209 0.548121
3 to 7 142520 2.0701 0.980777
2 to 6 141763 -0.4960 0.309935
1 to 5 141855 -0.1842 0.426940
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-15_07:31
Bits used No. missing words z-score p-value
31 to 32 141707 -0.5968 0.275306
30 to 31 142384 1.4002 0.919274
29 to 30 142191 0.8309 0.796981
28 to 29 142437 1.5565 0.940211
27 to 28 141828 -0.2399 0.405199
26 to 27 141788 -0.3579 0.360207
25 to 26 141609 -0.8859 0.187828
24 to 25 142707 2.3530 0.990689
23 to 24 142211 0.8899 0.813235
22 to 23 141517 -1.1573 0.123572
21 to 22 141776 -0.3933 0.347048
20 to 21 141465 -1.3107 0.094978
19 to 20 141569 -1.0039 0.157708
18 to 19 142274 1.0757 0.858974
17 to 18 141423 -1.4346 0.075700
16 to 17 141940 0.0905 0.536044
15 to 16 141916 0.0197 0.507849
14 to 15 141841 -0.2016 0.420129
13 to 14 141207 -2.0718 0.019143
12 to 13 141978 0.2026 0.580263
11 to 12 141934 0.0728 0.529007
10 to 11 142069 0.4710 0.681181
9 to 10 141882 -0.0806 0.467872
8 to 9 142245 0.9902 0.838956
7 to 8 141925 0.0462 0.518434
6 to 7 141189 -2.1249 0.016799
5 to 6 142192 0.8338 0.797813
4 to 5 141792 -0.3461 0.364632
3 to 4 141553 -1.0511 0.146602
2 to 3 141880 -0.0865 0.465527
1 to 2 142522 1.8073 0.964641
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-15_07:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2587.58 1.239 0.892259
Test results for specific bytes for dh-ranFile-2018-06-15_07:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2441.82 -0.823 0.205332
2 to 9 2545.21 0.639 0.738727
3 to 10 2646.83 2.076 0.981076
4 to 11 2469.53 -0.431 0.333271
5 to 12 2527.38 0.387 0.650704
6 to 13 2442.59 -0.812 0.208429
7 to 14 2470.93 -0.411 0.340492
8 to 15 2465.13 -0.493 0.310975
9 to 16 2422.44 -1.097 0.136361
10 to 17 2545.10 0.638 0.738179
11 to 18 2639.30 1.970 0.975578
12 to 19 2543.59 0.616 0.731215
13 to 20 2482.40 -0.249 0.401713
14 to 21 2467.49 -0.460 0.322833
15 to 22 2571.51 1.011 0.844066
16 to 23 2557.27 0.810 0.791007
17 to 24 2625.79 1.779 0.962376
18 to 25 2488.25 -0.166 0.434014
19 to 26 2613.48 1.605 0.945735
20 to 27 2534.14 0.483 0.685375
21 to 28 2603.43 1.463 0.928228
22 to 29 2490.58 -0.133 0.446992
23 to 30 2479.59 -0.289 0.386426
24 to 31 2544.72 0.632 0.736444
25 to 32 2593.80 1.327 0.907669
CDPARK for dh-ranFile-2018-06-15_07:31: 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
3552 1.3242 0.907282
3508 -0.6849 0.246694
3533 0.4566 0.676028
3522 -0.0457 0.481790
3532 0.4110 0.659449
3533 0.4566 0.676028
3516 -0.3196 0.374623
3550 1.2329 0.891189
3532 0.4110 0.659449
3500 -1.0502 0.146807
Square side=100, avg. no. parked=3527.80 sample std.=15.83
p-value of the KSTEST for those 10 p-values: 0.579484
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-15_07:31
0.6415,0.7469,0.3353,0.0806,0.1264,0.2886,0.3540,0.9294,0.1917,0.0730,
The KS test for those 10 p-values: 0.273753
The 3DSPHERES test for dh-ranFile-2018-06-15_07:31
sample no r^3 equiv. uni.
1 9.294 0.266413
2 78.004 0.925736
3 6.826 0.203511
4 5.653 0.171732
5 5.101 0.156365
6 22.516 0.527884
7 7.624 0.224407
8 8.405 0.244352
9 0.273 0.009065
10 61.366 0.870687
11 189.787 0.998211
12 31.586 0.651069
13 73.749 0.914419
14 54.127 0.835401
15 0.169 0.005618
16 60.887 0.868606
17 46.030 0.784400
18 2.848 0.090559
19 30.177 0.634288
20 12.085 0.331572
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.347055
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-15_07:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 0.9 0.1 -1.3 -0.5 -0.2
0.5 -0.9 1.4 -0.7 0.5 0.1
-1.6 -1.5 0.2 -0.8 -0.3 -0.7
2.1 0.2 -0.3 0.4 0.5 0.3
1.0 -0.5 -0.1 1.6 1.3 -0.7
0.7 -0.1 -1.9 -1.0 0.8 -0.3
-0.2 1.8 0.5 2.1 1.6 -1.0
-0.1
Chi-square with 42 degrees of freedom:41.557580
z-score=-0.048272, p-value=0.509750
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-15_07:31
Test no p-value
1 0.440123
2 0.161416
3 0.533778
4 0.527654
5 0.008052
6 0.000053
7 0.688677
8 0.260563
9 0.051851
10 0.185467
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.009426
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-15_07:31:
(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 66568 0.15 66527 0.29
3 25000.00 25194 1.51 25145 0.84
4 6666.67 6596 0.75 6620 0.33
5 1388.89 1362 0.52 1420 0.70
6 238.10 234 0.07 258 1.66
7 34.72 39 0.53 27 1.72
8 4.96 6 0.22 2 1.77
p=0.28783 p=0.70637
Number of rngs required: 688285, p-value: 0.446
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-15_07:31
No. of wins: Observed Expected
98575 98585.9
z-score=-0.049, pvalue=0.48063
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66720 66666.7 0.043 0.043
2 37506 37654.3 0.584 0.627
3 26973 26954.7 0.012 0.639
4 19195 19313.5 0.727 1.366
5 13878 13851.4 0.051 1.417
6 10006 9943.5 0.392 1.809
7 7123 7145.0 0.068 1.877
8 5117 5139.1 0.095 1.972
9 3769 3699.9 1.292 3.264
10 2702 2666.3 0.478 3.742
11 1985 1923.3 1.977 5.719
12 1389 1388.7 0.000 5.719
13 1055 1003.7 2.620 8.340
14 715 726.1 0.171 8.511
15 488 525.8 2.722 11.233
16 402 381.2 1.140 12.374
17 245 276.5 3.597 15.971
18 173 200.8 3.857 19.827
19 142 146.0 0.109 19.936
20 111 106.2 0.216 20.151
21 306 287.1 1.242 21.394
Chisq= 21.39 for 20 degrees of freedom, p= 0.62571
SUMMARY of craptest
p-value for no. of wins: 0.480633
p-value for throws/game: 0.625709
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-15_07:31
No. of wins: Observed Expected
98525 98585.9
z-score=-0.272, pvalue=0.39274
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66708 66666.7 0.026 0.026
2 37441 37654.3 1.209 1.234
3 26963 26954.7 0.003 1.237
4 19407 19313.5 0.453 1.690
5 13922 13851.4 0.360 2.049
6 9991 9943.5 0.226 2.276
7 7111 7145.0 0.162 2.438
8 5097 5139.1 0.344 2.782
9 3692 3699.9 0.017 2.799
10 2672 2666.3 0.012 2.811
11 1921 1923.3 0.003 2.814
12 1364 1388.7 0.441 3.255
13 1027 1003.7 0.540 3.795
14 730 726.1 0.021 3.815
15 528 525.8 0.009 3.824
16 365 381.2 0.684 4.509
17 268 276.5 0.264 4.772
18 209 200.8 0.332 5.105
19 173 146.0 4.999 10.104
20 114 106.2 0.571 10.675
21 297 287.1 0.340 11.015
Chisq= 11.02 for 20 degrees of freedom, p= 0.05417
SUMMARY of craptest
p-value for no. of wins: 0.392736
p-value for throws/game: 0.054174
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0001,0.0056,0.0081,0.0091,0.0094,0.0104,0.0168,0.0191,0.0218,0.0292,
0.0412,0.0435,0.0500,0.0519,0.0542,0.0574,0.0603,0.0673,0.0717,0.0730,
0.0757,0.0759,0.0763,0.0806,0.0809,0.0906,0.0948,0.0950,0.1026,0.1039,
0.1090,0.1102,0.1170,0.1203,0.1212,0.1236,0.1264,0.1339,0.1342,0.1364,
0.1417,0.1456,0.1466,0.1468,0.1501,0.1518,0.1564,0.1577,0.1592,0.1607,
0.1609,0.1614,0.1666,0.1667,0.1717,0.1765,0.1855,0.1868,0.1878,0.1897,
0.1917,0.1986,0.2035,0.2053,0.2084,0.2124,0.2155,0.2166,0.2244,0.2400,
0.2444,0.2467,0.2533,0.2606,0.2664,0.2738,0.2753,0.2761,0.2807,0.2878,
0.2878,0.2886,0.2964,0.2977,0.3008,0.3024,0.3058,0.3099,0.3104,0.3110,
0.3167,0.3173,0.3228,0.3294,0.3306,0.3316,0.3333,0.3353,0.3405,0.3454,
0.3470,0.3471,0.3540,0.3602,0.3610,0.3618,0.3646,0.3660,0.3671,0.3746,
0.3804,0.3864,0.3871,0.3927,0.4017,0.4052,0.4073,0.4201,0.4269,0.4340,
0.4375,0.4401,0.4413,0.4441,0.4460,0.4470,0.4523,0.4566,0.4588,0.4655,
0.4679,0.4719,0.4763,0.4773,0.4777,0.4780,0.4806,0.4818,0.4885,0.5022,
0.5062,0.5078,0.5097,0.5118,0.5137,0.5184,0.5188,0.5228,0.5277,0.5279,
0.5290,0.5338,0.5360,0.5401,0.5425,0.5481,0.5481,0.5666,0.5687,0.5696,
0.5707,0.5748,0.5755,0.5795,0.5803,0.5805,0.5920,0.5982,0.6077,0.6083,
0.6162,0.6241,0.6257,0.6343,0.6345,0.6415,0.6427,0.6483,0.6507,0.6511,
0.6594,0.6594,0.6652,0.6662,0.6712,0.6760,0.6760,0.6773,0.6774,0.6777,
0.6777,0.6812,0.6854,0.6887,0.7008,0.7018,0.7019,0.7023,0.7064,0.7100,
0.7114,0.7169,0.7312,0.7364,0.7380,0.7382,0.7387,0.7469,0.7490,0.7603,
0.7650,0.7683,0.7697,0.7844,0.7910,0.7970,0.7978,0.8071,0.8082,0.8091,
0.8132,0.8173,0.8181,0.8197,0.8319,0.8354,0.8390,0.8441,0.8468,0.8590,
0.8633,0.8658,0.8686,0.8700,0.8707,0.8715,0.8724,0.8811,0.8860,0.8877,
0.8912,0.8923,0.8976,0.8983,0.9004,0.9073,0.9077,0.9096,0.9144,0.9193,
0.9257,0.9282,0.9294,0.9402,0.9408,0.9457,0.9559,0.9624,0.9641,0.9646,
0.9710,0.9756,0.9808,0.9811,0.9837,0.9872,0.9907,0.9982,0.9985,
Overall p-value after applying KStest on 269 p-values = 0.716616
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.