RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-09-04_08:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 16.07 23.1268 0.854831
2 to 25 16.11 18.7658 0.657863
3 to 26 15.89 17.7754 0.596857
4 to 27 15.71 18.9281 0.667323
5 to 28 15.59 21.1729 0.781347
6 to 29 15.65 17.8467 0.601426
7 to 30 15.83 14.6620 0.380184
8 to 31 15.86 16.4615 0.508616
9 to 32 15.90 15.2097 0.419621
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.171747
Tough bday spacings test for dh-ranFile-2018-09-04_08:31: 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 10 37 65 109 113 66 49 28 17 4 2
(O-E)^2/E 0.1 0.0 0.9 1.3 2.4 1.9 0.2 0.1 0.3 1.0 1.0
Birthday Spacings: Sum(O-E)^2/E= 9.288, p= 0.495
RESULTS OF GCD FOR dh-ranFile-2018-09-04_08:31
Euclid's algorithm:
p-value, steps to gcd: 0.967831
p-value, dist. of gcd's: 0.274492
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-09-04_08:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.122 0.054 0.257 0.743 0.086 0.216 0.351 0.051
Bits 8 to 15---> 0.785 0.135 0.367 0.874 0.741 0.628 0.349 0.348
Bits 16 to 23---> 0.983 0.734 0.195 0.257 0.383 0.553 0.553 0.422
Bits 24 to 31---> 0.588 0.481 0.183 0.115 0.284 0.800 0.494 0.673
KS test for the above 32 p values: 0.725
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-09-04_08:31,
p-values for 5 runs: 0.8114, 0.4396, 0.7884, 0.7278, 0.0209
Rank test for binary matrices (31x31) for dh-ranFile-2018-09-04_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 199 211.4 0.729 0.729
r= 29 5122 5134.0 0.028 0.757
r= 30 23114 23103.0 0.005 0.763
r= 31 11565 11551.5 0.016 0.778
chi-square = 0.778 with df = 3; p-value = 0.145
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-09-04_08:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 207 211.4 0.092 0.092
r= 30 5012 5134.0 2.900 2.992
r= 31 23244 23103.0 0.860 3.852
r= 32 11537 11551.5 0.018 3.870
chi-square = 3.870 with df = 3; p-value = 0.724
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-09-04_08:31
b-rank test for bits 1 to 8, p=0.35605
b-rank test for bits 2 to 9, p=0.02980
b-rank test for bits 3 to 10, p=0.35241
b-rank test for bits 4 to 11, p=0.96941
b-rank test for bits 5 to 12, p=0.71644
b-rank test for bits 6 to 13, p=0.47951
b-rank test for bits 7 to 14, p=0.00031
b-rank test for bits 8 to 15, p=0.79495
b-rank test for bits 9 to 16, p=0.62072
b-rank test for bits 10 to 17, p=0.84842
b-rank test for bits 11 to 18, p=0.12833
b-rank test for bits 12 to 19, p=0.73067
b-rank test for bits 13 to 20, p=0.64484
b-rank test for bits 14 to 21, p=0.65512
b-rank test for bits 15 to 22, p=0.37183
b-rank test for bits 16 to 23, p=0.60942
b-rank test for bits 17 to 24, p=0.66049
b-rank test for bits 18 to 25, p=0.46080
b-rank test for bits 19 to 26, p=0.58995
b-rank test for bits 20 to 27, p=0.47242
b-rank test for bits 21 to 28, p=0.84766
b-rank test for bits 22 to 29, p=0.05821
b-rank test for bits 23 to 30, p=0.18290
b-rank test for bits 24 to 31, p=0.71817
b-rank test for bits 25 to 32, p=0.38570
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 = 0.569291
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-09-04_08:31
(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 141522 -0.90 0.182739
2 141717 -0.45 0.326583
3 142383 1.11 0.865789
4 141707 -0.47 0.318202
5 141970 0.14 0.556362
6 142229 0.75 0.772436
7 142601 1.62 0.946958
8 142108 0.46 0.678741
9 141729 -0.42 0.336756
10 141657 -0.59 0.277744
11 142189 0.65 0.743262
12 141370 -1.26 0.103814
13 141950 0.10 0.537852
14 141830 -0.19 0.426477
15 141558 -0.82 0.205862
16 141883 -0.06 0.475473
17 142065 0.36 0.641965
18 142208 0.70 0.757357
19 142153 0.57 0.715431
20 142304 0.92 0.821769
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-09-04_08:31
Bits used No. missing words z-score p-value
23 to 32 141812 -0.3356 0.368579
22 to 31 141665 -0.8425 0.199749
21 to 30 142069 0.5506 0.709041
20 to 29 142478 1.9609 0.975056
19 to 28 141732 -0.6115 0.270440
18 to 27 141959 0.1713 0.567997
17 to 26 142391 1.6609 0.951636
16 to 25 141816 -0.3218 0.373792
15 to 24 142168 0.8920 0.813794
14 to 23 142068 0.5471 0.707858
13 to 22 141994 0.2920 0.614844
12 to 21 141830 -0.2736 0.392215
11 to 20 141624 -0.9839 0.162583
10 to 19 142110 0.6920 0.755521
9 to 18 141696 -0.7356 0.230981
8 to 17 141579 -1.1391 0.127337
7 to 16 141389 -1.7942 0.036387
6 to 15 141970 0.2092 0.582857
5 to 14 142084 0.6023 0.726516
4 to 13 141821 -0.3046 0.380341
3 to 12 141730 -0.6184 0.268163
2 to 11 141484 -1.4667 0.071235
1 to 10 141414 -1.7080 0.043815
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-09-04_08:31
Bits used No. missing words z-score p-value
28 to 32 141815 -0.3198 0.374574
27 to 31 142475 1.9175 0.972414
26 to 30 141915 0.0192 0.507667
25 to 29 141622 -0.9740 0.165028
24 to 28 141681 -0.7740 0.219465
23 to 27 142320 1.3921 0.918054
22 to 26 141882 -0.0926 0.463093
21 to 25 141873 -0.1232 0.450993
20 to 24 141980 0.2396 0.594664
19 to 23 141527 -1.2960 0.097482
18 to 22 141802 -0.3638 0.357992
17 to 21 142024 0.3887 0.651255
16 to 20 142076 0.5650 0.713957
15 to 19 141543 -1.2418 0.107156
14 to 18 141748 -0.5469 0.292230
13 to 17 141926 0.0565 0.522532
12 to 16 141668 -0.8181 0.206659
11 to 15 141688 -0.7503 0.226546
10 to 14 141415 -1.6757 0.046899
9 to 13 141924 0.0497 0.519831
8 to 12 142595 2.3243 0.989945
7 to 11 141794 -0.3909 0.347917
6 to 10 141936 0.0904 0.536018
5 to 9 141994 0.2870 0.612950
4 to 8 141988 0.2667 0.605141
3 to 7 141851 -0.1977 0.421629
2 to 6 142003 0.3175 0.624578
1 to 5 141869 -0.1367 0.445629
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-09-04_08:31
Bits used No. missing words z-score p-value
31 to 32 141634 -0.8122 0.208343
30 to 31 141527 -1.1278 0.129699
29 to 30 141973 0.1878 0.574490
28 to 29 141653 -0.7561 0.224784
27 to 28 141858 -0.1514 0.439824
26 to 27 141858 -0.1514 0.439824
25 to 26 141988 0.2321 0.591756
24 to 25 141875 -0.1013 0.459669
23 to 24 142681 2.2763 0.988586
22 to 23 142139 0.6775 0.750953
21 to 22 142057 0.4356 0.668438
20 to 21 141829 -0.2370 0.406343
19 to 20 142017 0.3176 0.624610
18 to 19 141996 0.2557 0.600895
17 to 18 141735 -0.5142 0.303539
16 to 17 141776 -0.3933 0.347048
15 to 16 141469 -1.2989 0.096988
14 to 15 141206 -2.0747 0.019006
13 to 14 141976 0.1967 0.577956
12 to 13 142015 0.3117 0.622370
11 to 12 141393 -1.5231 0.063867
10 to 11 141507 -1.1868 0.117650
9 to 10 142209 0.8840 0.811647
8 to 9 142182 0.8043 0.789399
7 to 8 142016 0.3147 0.623490
6 to 7 141878 -0.0924 0.463183
5 to 6 141932 0.0669 0.526659
4 to 5 142128 0.6450 0.740551
3 to 4 142014 0.3088 0.621248
2 to 3 141799 -0.3255 0.372418
1 to 2 142150 0.7099 0.761130
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-09-04_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2543.96 0.622 0.732927
Test results for specific bytes for dh-ranFile-2018-09-04_08:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2516.98 0.240 0.594900
2 to 9 2558.16 0.822 0.794587
3 to 10 2457.86 -0.596 0.275585
4 to 11 2602.25 1.446 0.925920
5 to 12 2506.18 0.087 0.534817
6 to 13 2554.43 0.770 0.779257
7 to 14 2563.17 0.893 0.814164
8 to 15 2635.11 1.911 0.971983
9 to 16 2443.63 -0.797 0.212660
10 to 17 2315.87 -2.604 0.004606
11 to 18 2614.46 1.619 0.947248
12 to 19 2341.92 -2.236 0.012688
13 to 20 2452.45 -0.672 0.250645
14 to 21 2371.81 -1.813 0.034928
15 to 22 2414.30 -1.212 0.112764
16 to 23 2622.36 1.730 0.958227
17 to 24 2478.98 -0.297 0.383123
18 to 25 2573.58 1.041 0.850970
19 to 26 2577.90 1.102 0.864700
20 to 27 2520.27 0.287 0.612827
21 to 28 2473.74 -0.371 0.355174
22 to 29 2466.66 -0.471 0.318642
23 to 30 2561.14 0.865 0.806390
24 to 31 2532.56 0.460 0.677416
25 to 32 2458.80 -0.583 0.280081
CDPARK for dh-ranFile-2018-09-04_08:31: 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
3564 1.8721 0.969407
3526 0.1370 0.554479
3534 0.5023 0.692266
3527 0.1826 0.572463
3504 -0.8676 0.192812
3529 0.2740 0.607947
3510 -0.5936 0.276387
3499 -1.0959 0.136563
3523 0.0000 0.500000
3490 -1.5068 0.065925
Square side=100, avg. no. parked=3520.60 sample std.=20.00
p-value of the KSTEST for those 10 p-values: 0.851436
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-09-04_08:31
0.4005,0.0275,0.7025,0.4318,0.8114,0.4603,0.8525,0.3159,0.9401,0.9634,
The KS test for those 10 p-values: 0.485115
The 3DSPHERES test for dh-ranFile-2018-09-04_08:31
sample no r^3 equiv. uni.
1 23.019 0.535731
2 4.151 0.129222
3 10.686 0.299665
4 88.808 0.948195
5 9.899 0.281054
6 6.543 0.195953
7 9.756 0.277609
8 5.141 0.157492
9 0.236 0.007830
10 54.933 0.839764
11 24.405 0.556697
12 2.472 0.079093
13 16.738 0.427618
14 20.325 0.492107
15 49.031 0.804925
16 68.548 0.898220
17 66.205 0.889951
18 26.670 0.588930
19 45.719 0.782150
20 4.585 0.141716
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.857676
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-09-04_08:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 1.3 -1.1 0.2 1.8 -0.3
0.4 0.5 0.0 -0.8 1.4 -2.5
-0.6 -0.4 1.6 0.7 0.5 -0.6
0.5 0.1 0.1 -0.2 -2.4 1.1
-1.2 0.8 0.8 -0.8 0.6 0.9
-0.3 1.3 -0.5 -0.2 -1.3 0.4
-0.7 -2.0 0.9 -0.1 0.1 0.0
1.8
Chi-square with 42 degrees of freedom:44.819761
z-score=0.307661, p-value=0.645596
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-09-04_08:31
Test no p-value
1 0.273482
2 0.000289
3 0.886428
4 0.812493
5 0.489769
6 0.191675
7 0.022894
8 0.219660
9 0.666981
10 0.542580
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.257371
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-09-04_08:31:
(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 66615 0.04 66839 0.45
3 25000.00 25091 0.33 25011 0.00
4 6666.67 6615 0.40 6582 1.08
5 1388.89 1396 0.04 1317 3.72
6 238.10 246 0.26 211 3.08
7 34.72 34 0.01 35 0.00
8 4.96 2 1.77 4 0.19
p=0.17282 p=0.79746
Number of rngs required: 688410, p-value: 0.503
RESULTS OF CRAPS TEST for dh-ranFile-2018-09-04_08:31
No. of wins: Observed Expected
98554 98585.9
z-score=-0.142, pvalue=0.44335
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66761 66666.7 0.133 0.133
2 37665 37654.3 0.003 0.137
3 26946 26954.7 0.003 0.139
4 19234 19313.5 0.327 0.466
5 13817 13851.4 0.086 0.552
6 9968 9943.5 0.060 0.612
7 7227 7145.0 0.940 1.552
8 5064 5139.1 1.097 2.649
9 3723 3699.9 0.145 2.794
10 2661 2666.3 0.011 2.804
11 1975 1923.3 1.388 4.192
12 1390 1388.7 0.001 4.194
13 961 1003.7 1.818 6.011
14 718 726.1 0.091 6.103
15 493 525.8 2.050 8.153
16 394 381.2 0.433 8.586
17 289 276.5 0.561 9.148
18 199 200.8 0.017 9.164
19 129 146.0 1.976 11.140
20 90 106.2 2.475 13.616
21 296 287.1 0.275 13.891
Chisq= 13.89 for 20 degrees of freedom, p= 0.16402
SUMMARY of craptest
p-value for no. of wins: 0.443346
p-value for throws/game: 0.164019
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-09-04_08:31
No. of wins: Observed Expected
98563 98585.9
z-score=-0.102, pvalue=0.45928
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66805 66666.7 0.287 0.287
2 37648 37654.3 0.001 0.288
3 27099 26954.7 0.772 1.060
4 19388 19313.5 0.288 1.348
5 13717 13851.4 1.304 2.652
6 9909 9943.5 0.120 2.772
7 7106 7145.0 0.213 2.986
8 5135 5139.1 0.003 2.989
9 3621 3699.9 1.681 4.670
10 2627 2666.3 0.579 5.249
11 1971 1923.3 1.182 6.431
12 1341 1388.7 1.641 8.072
13 990 1003.7 0.187 8.259
14 680 726.1 2.932 11.191
15 519 525.8 0.089 11.280
16 420 381.2 3.960 15.240
17 286 276.5 0.324 15.563
18 212 200.8 0.621 16.185
19 122 146.0 3.940 20.125
20 105 106.2 0.014 20.139
21 299 287.1 0.492 20.631
Chisq= 20.63 for 20 degrees of freedom, p= 0.58087
SUMMARY of craptest
p-value for no. of wins: 0.459284
p-value for throws/game: 0.580872
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0003,0.0003,0.0046,0.0078,0.0127,0.0190,0.0209,0.0229,0.0275,0.0298,
0.0349,0.0364,0.0438,0.0469,0.0509,0.0545,0.0582,0.0639,0.0659,0.0712,
0.0791,0.0863,0.0970,0.0975,0.1038,0.1072,0.1128,0.1146,0.1177,0.1224,
0.1273,0.1283,0.1292,0.1297,0.1345,0.1366,0.1417,0.1454,0.1575,0.1626,
0.1640,0.1650,0.1717,0.1728,0.1827,0.1827,0.1829,0.1917,0.1928,0.1949,
0.1960,0.1997,0.2059,0.2067,0.2083,0.2127,0.2162,0.2195,0.2197,0.2248,
0.2265,0.2310,0.2506,0.2568,0.2574,0.2574,0.2682,0.2704,0.2735,0.2745,
0.2756,0.2764,0.2776,0.2777,0.2801,0.2811,0.2840,0.2922,0.2997,0.3035,
0.3159,0.3182,0.3186,0.3266,0.3368,0.3470,0.3479,0.3479,0.3491,0.3511,
0.3524,0.3552,0.3560,0.3580,0.3675,0.3686,0.3718,0.3724,0.3738,0.3746,
0.3802,0.3803,0.3830,0.3831,0.3857,0.3922,0.4005,0.4063,0.4196,0.4216,
0.4220,0.4265,0.4276,0.4318,0.4396,0.4398,0.4398,0.4433,0.4456,0.4510,
0.4593,0.4597,0.4603,0.4608,0.4631,0.4632,0.4724,0.4755,0.4795,0.4808,
0.4851,0.4898,0.4921,0.4940,0.4950,0.5000,0.5032,0.5077,0.5086,0.5198,
0.5225,0.5267,0.5348,0.5357,0.5360,0.5379,0.5426,0.5533,0.5533,0.5545,
0.5564,0.5567,0.5680,0.5693,0.5725,0.5745,0.5780,0.5809,0.5829,0.5881,
0.5889,0.5899,0.5918,0.5947,0.5949,0.5969,0.6009,0.6014,0.6051,0.6079,
0.6094,0.6128,0.6130,0.6148,0.6207,0.6212,0.6224,0.6235,0.6246,0.6246,
0.6283,0.6420,0.6448,0.6456,0.6513,0.6551,0.6579,0.6605,0.6670,0.6673,
0.6684,0.6732,0.6774,0.6787,0.6923,0.7025,0.7079,0.7090,0.7140,0.7154,
0.7164,0.7182,0.7242,0.7251,0.7265,0.7278,0.7307,0.7329,0.7335,0.7406,
0.7406,0.7433,0.7433,0.7510,0.7555,0.7574,0.7611,0.7724,0.7793,0.7813,
0.7822,0.7851,0.7884,0.7894,0.7946,0.7949,0.7975,0.7996,0.8049,0.8064,
0.8114,0.8114,0.8116,0.8125,0.8138,0.8142,0.8218,0.8398,0.8477,0.8484,
0.8510,0.8514,0.8525,0.8548,0.8577,0.8647,0.8658,0.8743,0.8864,0.8900,
0.8982,0.9181,0.9259,0.9401,0.9470,0.9472,0.9482,0.9516,0.9582,0.9634,
0.9678,0.9694,0.9694,0.9720,0.9724,0.9751,0.9826,0.9886,0.9899,
Overall p-value after applying KStest on 269 p-values = 0.346057
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.