RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-07_19:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.72 14.3654 0.358908
2 to 25 16.09 8.4892 0.045062
3 to 26 15.63 36.1691 0.995646
4 to 27 15.83 7.5245 0.024313
5 to 28 15.91 9.7777 0.087326
6 to 29 15.74 16.0678 0.480966
7 to 30 15.65 22.9681 0.849708
8 to 31 15.92 17.2734 0.564004
9 to 32 15.81 18.1918 0.623159
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.432729
Tough bday spacings test for dh-ranFile-2018-07-07_19:31: 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 6 33 64 97 102 87 53 30 11 13 4
(O-E)^2/E 1.1 0.4 1.2 0.0 0.2 1.0 0.0 0.0 1.0 6.2 0.0
Birthday Spacings: Sum(O-E)^2/E= 11.012, p= 0.643
RESULTS OF GCD FOR dh-ranFile-2018-07-07_19:31
Euclid's algorithm:
p-value, steps to gcd: 0.972469
p-value, dist. of gcd's: 0.873403
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-07_19:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.741 0.833 0.630 0.162 0.147 0.519 0.418 0.598
Bits 8 to 15---> 0.238 0.469 0.140 0.124 0.848 0.676 0.303 0.598
Bits 16 to 23---> 0.156 0.087 0.301 0.465 0.853 0.119 0.117 0.425
Bits 24 to 31---> 0.796 0.072 0.600 0.276 0.641 0.211 0.941 0.179
KS test for the above 32 p values: 0.816
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-07_19:31,
p-values for 5 runs: 0.6958, 0.9707, 0.2325, 0.5807, 0.3022
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-07_19:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 211 211.4 0.001 0.001
r= 29 5029 5134.0 2.148 2.149
r= 30 23244 23103.0 0.860 3.009
r= 31 11516 11551.5 0.109 3.118
chi-square = 3.118 with df = 3; p-value = 0.626
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-07_19:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 220 211.4 0.348 0.348
r= 30 5036 5134.0 1.871 2.219
r= 31 23218 23103.0 0.572 2.791
r= 32 11526 11551.5 0.056 2.848
chi-square = 2.848 with df = 3; p-value = 0.584
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-07_19:31
b-rank test for bits 1 to 8, p=0.93724
b-rank test for bits 2 to 9, p=0.01094
b-rank test for bits 3 to 10, p=0.32056
b-rank test for bits 4 to 11, p=0.96852
b-rank test for bits 5 to 12, p=0.81833
b-rank test for bits 6 to 13, p=0.91205
b-rank test for bits 7 to 14, p=0.04614
b-rank test for bits 8 to 15, p=0.39406
b-rank test for bits 9 to 16, p=0.89388
b-rank test for bits 10 to 17, p=0.87835
b-rank test for bits 11 to 18, p=0.74719
b-rank test for bits 12 to 19, p=0.54765
b-rank test for bits 13 to 20, p=0.73990
b-rank test for bits 14 to 21, p=0.84453
b-rank test for bits 15 to 22, p=0.14678
b-rank test for bits 16 to 23, p=0.67217
b-rank test for bits 17 to 24, p=0.68452
b-rank test for bits 18 to 25, p=0.62034
b-rank test for bits 19 to 26, p=0.63687
b-rank test for bits 20 to 27, p=0.75509
b-rank test for bits 21 to 28, p=0.22967
b-rank test for bits 22 to 29, p=0.03581
b-rank test for bits 23 to 30, p=0.24058
b-rank test for bits 24 to 31, p=0.34464
b-rank test for bits 25 to 32, p=0.27895
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 = 0.529335
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-07_19:31
(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 141972 0.15 0.558207
2 141543 -0.86 0.196023
3 142816 2.12 0.982929
4 141854 -0.13 0.448570
5 141314 -1.39 0.082119
6 142333 0.99 0.838884
7 142040 0.31 0.619933
8 142871 2.25 0.987677
9 141485 -0.99 0.160739
10 141787 -0.29 0.387509
11 141409 -1.17 0.121203
12 142205 0.69 0.755160
13 141929 0.05 0.518328
14 141205 -1.65 0.049920
15 141759 -0.35 0.362705
16 141666 -0.57 0.284838
17 142223 0.73 0.768182
18 141333 -1.35 0.089060
19 141546 -0.85 0.197968
20 142785 2.05 0.979620
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-07_19:31
Bits used No. missing words z-score p-value
23 to 32 141734 -0.6046 0.272727
22 to 31 141882 -0.0942 0.462459
21 to 30 142248 1.1678 0.878562
20 to 29 142157 0.8540 0.803457
19 to 28 142159 0.8609 0.805362
18 to 27 141381 -1.8218 0.034241
17 to 26 142096 0.6437 0.740112
16 to 25 142247 1.1644 0.877865
15 to 24 141897 -0.0425 0.483043
14 to 23 141967 0.1989 0.578815
13 to 22 142251 1.1782 0.880636
12 to 21 142060 0.5196 0.698312
11 to 20 142313 1.3920 0.918034
10 to 19 142093 0.6333 0.736746
9 to 18 141845 -0.2218 0.412224
8 to 17 141574 -1.1563 0.123777
7 to 16 142066 0.5402 0.705485
6 to 15 141517 -1.3529 0.088050
5 to 14 141855 -0.1873 0.425695
4 to 13 142478 1.9609 0.975056
3 to 12 141723 -0.6425 0.260269
2 to 11 141835 -0.2563 0.398856
1 to 10 141807 -0.3529 0.362096
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-07_19:31
Bits used No. missing words z-score p-value
28 to 32 141971 0.2091 0.582796
27 to 31 142214 1.0328 0.849147
26 to 30 142297 1.3141 0.905600
25 to 29 142263 1.1989 0.884713
24 to 28 142206 1.0057 0.842711
23 to 27 142130 0.7480 0.772780
22 to 26 141798 -0.3774 0.352942
21 to 25 142128 0.7413 0.770730
20 to 24 141811 -0.3333 0.369446
19 to 23 142196 0.9718 0.834416
18 to 22 141831 -0.2655 0.395302
17 to 21 141958 0.1650 0.565521
16 to 20 142262 1.1955 0.884053
15 to 19 142064 0.5243 0.699967
14 to 18 141849 -0.2045 0.418978
13 to 17 142191 0.9548 0.830164
12 to 16 142261 1.1921 0.883389
11 to 15 142230 1.0870 0.861485
10 to 14 141645 -0.8960 0.185117
9 to 13 141881 -0.0960 0.461747
8 to 12 141510 -1.3537 0.087922
7 to 11 141800 -0.3706 0.355464
6 to 10 142140 0.7819 0.782873
5 to 9 141948 0.1311 0.552146
4 to 8 141366 -1.8418 0.032752
3 to 7 142044 0.4565 0.675988
2 to 6 141788 -0.4113 0.340431
1 to 5 141740 -0.5740 0.282984
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-07_19:31
Bits used No. missing words z-score p-value
31 to 32 141366 -1.6027 0.054496
30 to 31 141556 -1.0423 0.148643
29 to 30 141740 -0.4995 0.308714
28 to 29 142141 0.6834 0.752821
27 to 28 141790 -0.3520 0.362417
26 to 27 141836 -0.2163 0.414372
25 to 26 142087 0.5241 0.699896
24 to 25 141332 -1.7030 0.044280
23 to 24 141747 -0.4788 0.316023
22 to 23 141798 -0.3284 0.371302
21 to 22 141620 -0.8535 0.196696
20 to 21 142236 0.9636 0.832384
19 to 20 142071 0.4769 0.683284
18 to 19 141939 0.0875 0.534872
17 to 18 141676 -0.6883 0.245635
16 to 17 141816 -0.2753 0.391539
15 to 16 142233 0.9548 0.830155
14 to 15 141194 -2.1101 0.017424
13 to 14 141095 -2.4022 0.008149
12 to 13 141730 -0.5290 0.298404
11 to 12 141966 0.1672 0.566381
10 to 11 141964 0.1613 0.564059
9 to 10 141984 0.2203 0.587168
8 to 9 142805 2.6421 0.995880
7 to 8 141777 -0.3904 0.348137
6 to 7 142201 0.8604 0.805211
5 to 6 142856 2.7925 0.997385
4 to 5 141789 -0.3550 0.361311
3 to 4 141981 0.2114 0.583719
2 to 3 142359 1.3265 0.907656
1 to 2 141957 0.1406 0.555915
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-07_19:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2496.26 -0.053 0.478920
Test results for specific bytes for dh-ranFile-2018-07-07_19:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2512.43 0.176 0.569745
2 to 9 2609.60 1.550 0.939430
3 to 10 2463.11 -0.522 0.300957
4 to 11 2675.06 2.476 0.993353
5 to 12 2565.37 0.924 0.822376
6 to 13 2472.49 -0.389 0.348644
7 to 14 2619.00 1.683 0.953797
8 to 15 2509.03 0.128 0.550802
9 to 16 2438.42 -0.871 0.191900
10 to 17 2575.88 1.073 0.858383
11 to 18 2583.09 1.175 0.880014
12 to 19 2570.65 0.999 0.841139
13 to 20 2472.77 -0.385 0.350081
14 to 21 2323.23 -2.500 0.006211
15 to 22 2329.75 -2.408 0.008028
16 to 23 2501.91 0.027 0.510792
17 to 24 2470.62 -0.415 0.338907
18 to 25 2531.50 0.445 0.671994
19 to 26 2445.57 -0.770 0.220733
20 to 27 2428.98 -1.004 0.157601
21 to 28 2576.05 1.076 0.858937
22 to 29 2482.42 -0.249 0.401838
23 to 30 2479.84 -0.285 0.387759
24 to 31 2468.59 -0.444 0.328466
25 to 32 2446.60 -0.755 0.225053
CDPARK for dh-ranFile-2018-07-07_19:31: 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
3507 -0.7306 0.232514
3554 1.4155 0.921543
3525 0.0913 0.536383
3571 2.1918 0.985802
3509 -0.6393 0.261324
3495 -1.2785 0.100530
3535 0.5479 0.708135
3484 -1.7808 0.037471
3530 0.3196 0.625377
3530 0.3196 0.625377
Square side=100, avg. no. parked=3524.00 sample std.=25.02
p-value of the KSTEST for those 10 p-values: 0.920758
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-07_19:31
0.0323,0.4674,0.0193,0.1185,0.1141,0.0845,0.3691,0.6611,0.5357,0.7115,
The KS test for those 10 p-values: 0.039908
The 3DSPHERES test for dh-ranFile-2018-07-07_19:31
sample no r^3 equiv. uni.
1 33.073 0.667942
2 15.277 0.399044
3 13.749 0.367635
4 23.916 0.549408
5 37.917 0.717449
6 42.175 0.754836
7 58.752 0.858914
8 4.549 0.140688
9 2.043 0.065818
10 2.934 0.093169
11 27.358 0.598250
12 60.771 0.868098
13 44.733 0.774877
14 2.526 0.080758
15 5.424 0.165398
16 1.269 0.041431
17 21.698 0.514833
18 55.082 0.840559
19 0.263 0.008715
20 96.346 0.959706
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.532051
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-07_19:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 2.2 -0.1 -0.5 -0.2 0.3
-1.8 0.4 0.1 -0.9 0.1 -0.2
-1.1 -0.2 -1.4 -0.0 0.7 1.4
0.7 0.2 0.3 0.2 1.4 0.4
-1.3 -0.8 0.3 0.4 -0.3 -0.4
-0.2 0.3 -1.6 -1.6 -0.9 1.1
-0.7 -2.0 0.5 0.4 -1.3 0.0
0.8
Chi-square with 42 degrees of freedom:37.042525
z-score=-0.540905, p-value=0.311988
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-07_19:31
Test no p-value
1 0.003913
2 0.034519
3 0.714297
4 0.362753
5 0.080290
6 0.282042
7 0.400073
8 0.005727
9 0.799069
10 0.038090
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.002738
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-07_19:31:
(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 66658 0.00 66584 0.10
3 25000.00 24940 0.14 24955 0.08
4 6666.67 6725 0.51 6798 2.59
5 1388.89 1420 0.70 1389 0.00
6 238.10 225 0.72 226 0.61
7 34.72 29 0.94 40 0.80
8 4.96 2 1.77 7 0.84
p=0.42785 p=0.45965
Number of rngs required: 688299, p-value: 0.452
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-07_19:31
No. of wins: Observed Expected
98390 98585.9
z-score=-0.876, pvalue=0.19052
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66180 66666.7 3.553 3.553
2 37773 37654.3 0.374 3.927
3 26831 26954.7 0.568 4.495
4 19315 19313.5 0.000 4.495
5 13906 13851.4 0.215 4.710
6 10014 9943.5 0.499 5.209
7 7290 7145.0 2.942 8.151
8 5307 5139.1 5.487 13.638
9 3688 3699.9 0.038 13.676
10 2721 2666.3 1.122 14.798
11 1919 1923.3 0.010 14.808
12 1399 1388.7 0.076 14.884
13 1003 1003.7 0.001 14.884
14 724 726.1 0.006 14.891
15 548 525.8 0.934 15.825
16 359 381.2 1.287 17.112
17 276 276.5 0.001 17.113
18 205 200.8 0.087 17.200
19 127 146.0 2.469 19.669
20 102 106.2 0.167 19.836
21 313 287.1 2.334 22.170
Chisq= 22.17 for 20 degrees of freedom, p= 0.66863
SUMMARY of craptest
p-value for no. of wins: 0.190517
p-value for throws/game: 0.668633
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-07_19:31
No. of wins: Observed Expected
98413 98585.9
z-score=-0.773, pvalue=0.21972
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66793 66666.7 0.239 0.239
2 37687 37654.3 0.028 0.268
3 26965 26954.7 0.004 0.272
4 19302 19313.5 0.007 0.278
5 13765 13851.4 0.539 0.818
6 9960 9943.5 0.027 0.845
7 7120 7145.0 0.088 0.933
8 5208 5139.1 0.924 1.857
9 3600 3699.9 2.696 4.553
10 2645 2666.3 0.170 4.723
11 1921 1923.3 0.003 4.725
12 1392 1388.7 0.008 4.733
13 1018 1003.7 0.203 4.936
14 743 726.1 0.391 5.328
15 518 525.8 0.117 5.445
16 354 381.2 1.934 7.379
17 297 276.5 1.514 8.892
18 186 200.8 1.095 9.988
19 126 146.0 2.736 12.723
20 105 106.2 0.014 12.737
21 295 287.1 0.217 12.954
Chisq= 12.95 for 20 degrees of freedom, p= 0.12064
SUMMARY of craptest
p-value for no. of wins: 0.219724
p-value for throws/game: 0.120644
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0027,0.0039,0.0057,0.0062,0.0080,0.0081,0.0087,0.0109,0.0174,0.0193,
0.0243,0.0323,0.0328,0.0342,0.0345,0.0358,0.0375,0.0381,0.0399,0.0414,
0.0443,0.0451,0.0461,0.0499,0.0545,0.0658,0.0723,0.0803,0.0808,0.0821,
0.0845,0.0873,0.0873,0.0879,0.0880,0.0891,0.0932,0.1005,0.1141,0.1168,
0.1185,0.1186,0.1206,0.1212,0.1238,0.1244,0.1403,0.1407,0.1468,0.1470,
0.1486,0.1564,0.1576,0.1607,0.1622,0.1654,0.1795,0.1851,0.1905,0.1919,
0.1960,0.1967,0.1980,0.2111,0.2197,0.2207,0.2251,0.2297,0.2325,0.2325,
0.2385,0.2406,0.2456,0.2603,0.2613,0.2727,0.2762,0.2790,0.2820,0.2830,
0.2848,0.2984,0.3010,0.3012,0.3022,0.3031,0.3087,0.3120,0.3160,0.3206,
0.3285,0.3389,0.3404,0.3446,0.3481,0.3486,0.3501,0.3529,0.3555,0.3589,
0.3613,0.3621,0.3624,0.3627,0.3628,0.3676,0.3691,0.3694,0.3713,0.3875,
0.3878,0.3915,0.3941,0.3953,0.3989,0.3990,0.4001,0.4018,0.4122,0.4144,
0.4181,0.4190,0.4246,0.4257,0.4279,0.4327,0.4486,0.4524,0.4597,0.4617,
0.4625,0.4651,0.4674,0.4687,0.4789,0.4810,0.4830,0.5108,0.5148,0.5183,
0.5191,0.5293,0.5321,0.5349,0.5357,0.5364,0.5476,0.5494,0.5508,0.5521,
0.5559,0.5582,0.5640,0.5641,0.5655,0.5664,0.5697,0.5788,0.5807,0.5828,
0.5837,0.5843,0.5872,0.5980,0.5982,0.5985,0.5997,0.6199,0.6203,0.6232,
0.6254,0.6254,0.6262,0.6303,0.6369,0.6410,0.6434,0.6611,0.6679,0.6686,
0.6720,0.6722,0.6757,0.6760,0.6833,0.6845,0.6958,0.6983,0.6999,0.7000,
0.7055,0.7081,0.7115,0.7143,0.7174,0.7367,0.7399,0.7401,0.7406,0.7472,
0.7528,0.7548,0.7551,0.7552,0.7682,0.7707,0.7728,0.7749,0.7829,0.7955,
0.7991,0.8035,0.8052,0.8054,0.8158,0.8183,0.8224,0.8302,0.8302,0.8324,
0.8331,0.8344,0.8389,0.8406,0.8411,0.8427,0.8445,0.8480,0.8491,0.8497,
0.8525,0.8584,0.8589,0.8589,0.8615,0.8681,0.8734,0.8779,0.8784,0.8786,
0.8800,0.8806,0.8834,0.8841,0.8847,0.8939,0.9056,0.9077,0.9121,0.9180,
0.9208,0.9215,0.9372,0.9394,0.9406,0.9538,0.9597,0.9685,0.9707,0.9725,
0.9751,0.9796,0.9829,0.9858,0.9877,0.9934,0.9956,0.9959,0.9974,
Overall p-value after applying KStest on 269 p-values = 0.368140
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.