RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2017-02-28_10:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.86 15.3186 0.427456
2 to 25 15.64 20.6448 0.757418
3 to 26 15.71 12.1860 0.211253
4 to 27 15.97 16.7733 0.530174
5 to 28 15.58 13.6085 0.305408
6 to 29 15.59 13.1551 0.274259
7 to 30 15.60 28.1445 0.956722
8 to 31 15.69 13.4526 0.294598
9 to 32 15.49 28.8414 0.963983
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.597144
Tough bday spacings test for dh-ranFile-2017-02-28_10:31: 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 38 77 97 102 70 57 28 13 10 1
(O-E)^2/E 0.5 0.1 0.2 0.0 0.2 0.8 0.5 0.1 0.2 1.7 2.3
Birthday Spacings: Sum(O-E)^2/E= 6.644, p= 0.241
RESULTS OF GCD FOR dh-ranFile-2017-02-28_10:31
Euclid's algorithm:
p-value, steps to gcd: 0.839433
p-value, dist. of gcd's: 0.210606
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2017-02-28_10:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.794 0.744 0.787 0.856 0.434 0.329 0.621 0.415
Bits 8 to 15---> 0.842 0.268 0.024 0.601 0.290 0.534 0.831 0.388
Bits 16 to 23---> 0.705 0.368 0.349 0.642 0.800 0.678 0.637 0.441
Bits 24 to 31---> 0.170 0.505 0.427 0.015 0.355 0.386 0.049 0.364
KS test for the above 32 p values: 0.691
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2017-02-28_10:31,
p-values for 5 runs: 0.1578, 0.3786, 0.0097, 0.9572, 0.2437
Rank test for binary matrices (31x31) for dh-ranFile-2017-02-28_10:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 233 211.4 2.203 2.203
r= 29 5161 5134.0 0.142 2.345
r= 30 23090 23103.0 0.007 2.352
r= 31 11516 11551.5 0.109 2.462
chi-square = 2.462 with df = 3; p-value = 0.518
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2017-02-28_10:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 229 211.4 1.462 1.462
r= 30 5085 5134.0 0.468 1.930
r= 31 23151 23103.0 0.100 2.030
r= 32 11535 11551.5 0.024 2.053
chi-square = 2.053 with df = 3; p-value = 0.439
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2017-02-28_10:31
b-rank test for bits 1 to 8, p=0.57353
b-rank test for bits 2 to 9, p=0.36368
b-rank test for bits 3 to 10, p=0.77171
b-rank test for bits 4 to 11, p=0.00141
b-rank test for bits 5 to 12, p=0.19306
b-rank test for bits 6 to 13, p=0.46538
b-rank test for bits 7 to 14, p=0.81190
b-rank test for bits 8 to 15, p=0.62425
b-rank test for bits 9 to 16, p=0.90257
b-rank test for bits 10 to 17, p=0.96116
b-rank test for bits 11 to 18, p=0.27431
b-rank test for bits 12 to 19, p=0.80664
b-rank test for bits 13 to 20, p=0.11999
b-rank test for bits 14 to 21, p=0.37966
b-rank test for bits 15 to 22, p=0.75145
b-rank test for bits 16 to 23, p=0.20039
b-rank test for bits 17 to 24, p=0.57606
b-rank test for bits 18 to 25, p=0.55126
b-rank test for bits 19 to 26, p=0.00395
b-rank test for bits 20 to 27, p=0.33510
b-rank test for bits 21 to 28, p=0.56834
b-rank test for bits 22 to 29, p=0.36521
b-rank test for bits 23 to 30, p=0.69117
b-rank test for bits 24 to 31, p=0.77046
b-rank test for bits 25 to 32, p=0.16752
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 = 0.741472
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2017-02-28_10:31
(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 142423 1.20 0.884962
2 142022 0.26 0.603820
3 141678 -0.54 0.294429
4 141644 -0.62 0.267652
5 141616 -0.69 0.246561
6 141742 -0.39 0.347914
7 141707 -0.47 0.318202
8 142928 2.38 0.991345
9 141476 -1.01 0.155661
10 141906 -0.01 0.496896
11 142376 1.09 0.862221
12 141789 -0.28 0.389300
13 142335 0.99 0.840024
14 142026 0.27 0.607417
15 141966 0.13 0.552669
16 141533 -0.88 0.189626
17 142243 0.78 0.782188
18 141191 -1.68 0.046640
19 141832 -0.18 0.428310
20 142373 1.08 0.860672
----------------------------------------------------------------
OPSO test for dh-ranFile-2017-02-28_10:31
Bits used No. missing words z-score p-value
23 to 32 141709 -0.6908 0.244848
22 to 31 142287 1.3023 0.903595
21 to 30 141919 0.0333 0.513300
20 to 29 141930 0.0713 0.528411
19 to 28 142453 1.8747 0.969585
18 to 27 142053 0.4954 0.689846
17 to 26 141964 0.1885 0.574764
16 to 25 141613 -1.0218 0.153431
15 to 24 141472 -1.5080 0.065773
14 to 23 141640 -0.9287 0.176516
13 to 22 142244 1.1540 0.875757
12 to 21 142681 2.6609 0.996104
11 to 20 141709 -0.6908 0.244848
10 to 19 141870 -0.1356 0.446061
9 to 18 142218 1.0644 0.856422
8 to 17 142439 1.8264 0.966109
7 to 16 142116 0.7127 0.761970
6 to 15 142198 0.9954 0.840233
5 to 14 141904 -0.0184 0.492668
4 to 13 141335 -1.9804 0.023827
3 to 12 141799 -0.3804 0.351806
2 to 11 141662 -0.8529 0.196868
1 to 10 141467 -1.5253 0.063595
-----------------------------------------------------------------
OQSO test for dh-ranFile-2017-02-28_10:31
Bits used No. missing words z-score p-value
28 to 32 141957 0.1616 0.564187
27 to 31 142044 0.4565 0.675988
26 to 30 141533 -1.2757 0.101032
25 to 29 141961 0.1752 0.569520
24 to 28 141956 0.1582 0.562852
23 to 27 141520 -1.3198 0.093457
22 to 26 141982 0.2463 0.597290
21 to 25 142099 0.6429 0.739872
20 to 24 141970 0.2057 0.581472
19 to 23 141929 0.0667 0.526581
18 to 22 141659 -0.8486 0.198059
17 to 21 142018 0.3684 0.643702
16 to 20 141873 -0.1232 0.450993
15 to 19 141649 -0.8825 0.188760
14 to 18 141583 -1.1062 0.134319
13 to 17 141733 -0.5977 0.275010
12 to 16 141646 -0.8926 0.186024
11 to 15 141877 -0.1096 0.456366
10 to 14 141955 0.1548 0.561516
9 to 13 142210 1.0192 0.845951
8 to 12 141693 -0.7333 0.231681
7 to 11 141780 -0.4384 0.330546
6 to 10 142100 0.6463 0.740970
5 to 9 142347 1.4836 0.931046
4 to 8 141816 -0.3164 0.375860
3 to 7 141675 -0.7943 0.213499
2 to 6 141925 0.0531 0.521181
1 to 5 141768 -0.4791 0.315939
-----------------------------------------------------------------
DNA test for dh-ranFile-2017-02-28_10:31
Bits used No. missing words z-score p-value
31 to 32 141863 -0.1367 0.445647
30 to 31 142222 0.9223 0.821822
29 to 30 141409 -1.4759 0.069985
28 to 29 141528 -1.1249 0.130323
27 to 28 141641 -0.7915 0.214316
26 to 27 142233 0.9548 0.830155
25 to 26 141796 -0.3343 0.369074
24 to 25 141996 0.2557 0.600895
23 to 24 141346 -1.6617 0.048282
22 to 23 141844 -0.1927 0.423592
21 to 22 142064 0.4563 0.675896
20 to 21 141770 -0.4110 0.340535
19 to 20 142149 0.7070 0.760214
18 to 19 141938 0.0846 0.533699
17 to 18 142102 0.5683 0.715101
16 to 17 142060 0.4445 0.671643
15 to 16 142247 0.9961 0.840394
14 to 15 142003 0.2763 0.608846
13 to 14 142382 1.3943 0.918388
12 to 13 142007 0.2881 0.613370
11 to 12 141383 -1.5526 0.060260
10 to 11 141807 -0.3019 0.381380
9 to 10 141662 -0.7296 0.232821
8 to 9 141996 0.2557 0.600895
7 to 8 141973 0.1878 0.574490
6 to 7 141762 -0.4346 0.331926
5 to 6 142516 1.7896 0.963240
4 to 5 142234 0.9577 0.830900
3 to 4 142726 2.4091 0.992003
2 to 3 141589 -0.9449 0.172348
1 to 2 141841 -0.2016 0.420129
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2017-02-28_10:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2439.00 -0.863 0.194153
Test results for specific bytes for dh-ranFile-2017-02-28_10:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2539.14 0.554 0.710048
2 to 9 2485.24 -0.209 0.417315
3 to 10 2431.68 -0.966 0.166982
4 to 11 2467.34 -0.462 0.322093
5 to 12 2531.95 0.452 0.674308
6 to 13 2624.71 1.764 0.961106
7 to 14 2524.73 0.350 0.636716
8 to 15 2528.32 0.400 0.655599
9 to 16 2594.96 1.343 0.910346
10 to 17 2587.17 1.233 0.891159
11 to 18 2348.89 -2.137 0.016298
12 to 19 2505.63 0.080 0.531752
13 to 20 2539.96 0.565 0.714011
14 to 21 2474.76 -0.357 0.360552
15 to 22 2496.03 -0.056 0.477605
16 to 23 2470.62 -0.416 0.338875
17 to 24 2445.88 -0.765 0.222034
18 to 25 2449.62 -0.712 0.238101
19 to 26 2635.88 1.922 0.972676
20 to 27 2456.33 -0.618 0.268443
21 to 28 2499.51 -0.007 0.497252
22 to 29 2534.78 0.492 0.688616
23 to 30 2557.91 0.819 0.793614
24 to 31 2627.77 1.807 0.964613
25 to 32 2562.45 0.883 0.811442
CDPARK for dh-ranFile-2017-02-28_10:31: 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
3518 -0.2283 0.409702
3511 -0.5479 0.291865
3494 -1.3242 0.092718
3472 -2.3288 0.009936
3509 -0.6393 0.261324
3470 -2.4201 0.007758
3517 -0.2740 0.392053
3524 0.0457 0.518210
3532 0.4110 0.659449
3544 0.9589 0.831196
Square side=100, avg. no. parked=3509.10 sample std.=22.90
p-value of the KSTEST for those 10 p-values: 0.094458
Results for the MINIMUM DISTANCE test for dh-ranFile-2017-02-28_10:31
0.6879,0.6950,0.4914,0.7256,0.3157,0.2774,0.6268,0.2222,0.2507,0.9626,
The KS test for those 10 p-values: 0.724788
The 3DSPHERES test for dh-ranFile-2017-02-28_10:31
sample no r^3 equiv. uni.
1 31.653 0.651846
2 17.324 0.438673
3 9.662 0.275341
4 18.284 0.456361
5 41.361 0.748093
6 62.622 0.875989
7 23.037 0.536015
8 21.616 0.513509
9 60.780 0.868139
10 101.829 0.966436
11 2.314 0.074246
12 10.700 0.299990
13 39.654 0.733341
14 46.646 0.788785
15 14.077 0.374526
16 3.710 0.116321
17 2.763 0.088000
18 4.058 0.126525
19 2.511 0.080291
20 12.281 0.335933
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.901141
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2017-02-28_10:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 1.3 -1.1 0.5 -2.5 0.8
0.9 -1.7 -0.2 1.2 1.1 0.8
0.6 -1.2 -0.3 -0.1 0.5 1.3
-0.0 0.2 -2.4 -0.3 -1.7 0.8
-0.4 0.9 0.3 -0.5 2.0 -0.8
-0.5 0.9 -0.5 0.1 0.8 -0.5
-0.9 -0.1 1.3 1.5 0.9 2.0
0.8
Chi-square with 42 degrees of freedom:49.478562
z-score=0.815978, p-value=0.800618
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2017-02-28_10:31
Test no p-value
1 0.056801
2 0.375434
3 0.432657
4 0.203604
5 0.295250
6 0.984560
7 0.180513
8 0.134195
9 0.952841
10 0.900547
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.338683
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2017-02-28_10:31:
(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 66654 0.00 66615 0.04
3 25000.00 25019 0.01 25074 0.22
4 6666.67 6680 0.03 6612 0.45
5 1388.89 1377 0.10 1389 0.00
6 238.10 233 0.11 268 3.76
7 34.72 33 0.09 35 0.00
8 4.96 3 0.77 6 0.22
p=0.01908 p=0.41504
Number of rngs required: 688475, p-value: 0.533
RESULTS OF CRAPS TEST for dh-ranFile-2017-02-28_10:31
No. of wins: Observed Expected
98260 98585.9
z-score=-1.457, pvalue=0.07250
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66444 66666.7 0.744 0.744
2 37817 37654.3 0.703 1.447
3 26935 26954.7 0.014 1.461
4 19273 19313.5 0.085 1.546
5 13822 13851.4 0.062 1.608
6 9844 9943.5 0.997 2.605
7 7155 7145.0 0.014 2.619
8 5188 5139.1 0.466 3.084
9 3730 3699.9 0.245 3.330
10 2677 2666.3 0.043 3.373
11 1975 1923.3 1.388 4.761
12 1367 1388.7 0.340 5.101
13 1077 1003.7 5.351 10.452
14 753 726.1 0.994 11.446
15 558 525.8 1.967 13.413
16 400 381.2 0.932 14.345
17 260 276.5 0.989 15.334
18 176 200.8 3.070 18.404
19 152 146.0 0.248 18.652
20 100 106.2 0.364 19.016
21 297 287.1 0.340 19.356
Chisq= 19.36 for 20 degrees of freedom, p= 0.50122
SUMMARY of craptest
p-value for no. of wins: 0.072499
p-value for throws/game: 0.501217
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2017-02-28_10:31
No. of wins: Observed Expected
98668 98585.9
z-score= 0.367, pvalue=0.64333
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66465 66666.7 0.610 0.610
2 37824 37654.3 0.765 1.375
3 26883 26954.7 0.191 1.566
4 19367 19313.5 0.148 1.714
5 13916 13851.4 0.301 2.015
6 9914 9943.5 0.088 2.103
7 7133 7145.0 0.020 2.123
8 5150 5139.1 0.023 2.146
9 3659 3699.9 0.451 2.598
10 2697 2666.3 0.354 2.951
11 1943 1923.3 0.201 3.152
12 1430 1388.7 1.226 4.378
13 1031 1003.7 0.742 5.120
14 714 726.1 0.203 5.323
15 507 525.8 0.675 5.998
16 376 381.2 0.070 6.067
17 249 276.5 2.743 8.810
18 189 200.8 0.697 9.507
19 160 146.0 1.346 10.852
20 119 106.2 1.539 12.391
21 274 287.1 0.599 12.990
Chisq= 12.99 for 20 degrees of freedom, p= 0.12219
SUMMARY of craptest
p-value for no. of wins: 0.643334
p-value for throws/game: 0.122190
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0014,0.0040,0.0078,0.0097,0.0099,0.0147,0.0163,0.0191,0.0238,0.0238,
0.0466,0.0483,0.0491,0.0568,0.0603,0.0636,0.0658,0.0700,0.0725,0.0742,
0.0803,0.0880,0.0927,0.0935,0.0945,0.1010,0.1163,0.1200,0.1222,0.1265,
0.1303,0.1342,0.1343,0.1534,0.1557,0.1578,0.1670,0.1675,0.1700,0.1723,
0.1765,0.1805,0.1860,0.1888,0.1896,0.1931,0.1942,0.1969,0.1981,0.2004,
0.2036,0.2106,0.2113,0.2135,0.2143,0.2220,0.2222,0.2317,0.2328,0.2381,
0.2414,0.2437,0.2448,0.2448,0.2466,0.2507,0.2613,0.2676,0.2677,0.2684,
0.2743,0.2743,0.2750,0.2753,0.2774,0.2898,0.2919,0.2944,0.2946,0.2953,
0.3000,0.3054,0.3157,0.3159,0.3182,0.3221,0.3287,0.3305,0.3319,0.3351,
0.3359,0.3387,0.3389,0.3405,0.3479,0.3492,0.3518,0.3546,0.3606,0.3637,
0.3637,0.3652,0.3683,0.3691,0.3745,0.3754,0.3759,0.3786,0.3797,0.3814,
0.3862,0.3884,0.3893,0.3921,0.4097,0.4150,0.4154,0.4173,0.4201,0.4236,
0.4271,0.4275,0.4283,0.4327,0.4343,0.4386,0.4387,0.4413,0.4456,0.4461,
0.4510,0.4564,0.4564,0.4654,0.4776,0.4914,0.4927,0.4969,0.4973,0.5012,
0.5053,0.5133,0.5135,0.5177,0.5182,0.5212,0.5266,0.5284,0.5302,0.5318,
0.5330,0.5337,0.5339,0.5360,0.5513,0.5527,0.5615,0.5629,0.5642,0.5683,
0.5695,0.5735,0.5745,0.5748,0.5761,0.5815,0.5971,0.5973,0.6009,0.6009,
0.6013,0.6038,0.6074,0.6088,0.6134,0.6207,0.6243,0.6268,0.6367,0.6373,
0.6418,0.6433,0.6437,0.6518,0.6556,0.6594,0.6716,0.6743,0.6759,0.6760,
0.6779,0.6879,0.6886,0.6898,0.6905,0.6912,0.6950,0.7049,0.7100,0.7140,
0.7151,0.7248,0.7256,0.7333,0.7399,0.7410,0.7415,0.7443,0.7481,0.7514,
0.7574,0.7602,0.7620,0.7705,0.7717,0.7822,0.7870,0.7888,0.7936,0.7942,
0.8000,0.8006,0.8066,0.8114,0.8119,0.8218,0.8302,0.8309,0.8312,0.8312,
0.8394,0.8400,0.8402,0.8404,0.8415,0.8460,0.8555,0.8564,0.8607,0.8622,
0.8681,0.8758,0.8760,0.8850,0.8912,0.9005,0.9011,0.9026,0.9036,0.9103,
0.9184,0.9310,0.9528,0.9567,0.9572,0.9611,0.9612,0.9626,0.9632,0.9640,
0.9646,0.9661,0.9664,0.9696,0.9727,0.9846,0.9913,0.9920,0.9961,
Overall p-value after applying KStest on 269 p-values = 0.575742
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.