RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-22_12:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.69 22.4299 0.831255
2 to 25 15.87 22.5658 0.836073
3 to 26 15.84 15.0063 0.404974
4 to 27 15.86 21.3903 0.790683
5 to 28 15.97 11.2515 0.156805
6 to 29 15.88 15.9287 0.471107
7 to 30 15.56 22.8884 0.847081
8 to 31 15.70 15.8346 0.464413
9 to 32 15.62 20.9429 0.771147
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.231194
Tough bday spacings test for dh-ranFile-2018-06-22_12:31: 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 36 78 87 91 76 58 32 15 10 6
(O-E)^2/E 0.4 0.0 0.3 1.2 0.5 0.1 0.7 0.2 0.0 1.7 0.9
Birthday Spacings: Sum(O-E)^2/E= 5.860, p= 0.173
RESULTS OF GCD FOR dh-ranFile-2018-06-22_12:31
Euclid's algorithm:
p-value, steps to gcd: 0.800136
p-value, dist. of gcd's: 0.955708
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-22_12:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.748 0.239 0.535 0.155 0.648 0.236 0.995 0.865
Bits 8 to 15---> 0.215 0.869 0.484 0.757 0.394 0.746 0.062 0.401
Bits 16 to 23---> 0.345 0.550 0.935 0.142 0.559 0.963 0.974 0.355
Bits 24 to 31---> 0.528 0.981 0.772 0.272 0.545 0.124 0.090 0.180
KS test for the above 32 p values: 0.307
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-22_12:31,
p-values for 5 runs: 0.0230, 0.3882, 0.7886, 0.1776, 0.9240
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-22_12:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 214 211.4 0.032 0.032
r= 29 5167 5134.0 0.212 0.244
r= 30 23028 23103.0 0.244 0.487
r= 31 11591 11551.5 0.135 0.622
chi-square = 0.622 with df = 3; p-value = 0.109
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-22_12:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 227 211.4 1.148 1.148
r= 30 5123 5134.0 0.024 1.172
r= 31 22975 23103.0 0.710 1.882
r= 32 11675 11551.5 1.320 3.202
chi-square = 3.202 with df = 3; p-value = 0.638
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-22_12:31
b-rank test for bits 1 to 8, p=0.70425
b-rank test for bits 2 to 9, p=0.54424
b-rank test for bits 3 to 10, p=0.68365
b-rank test for bits 4 to 11, p=0.25267
b-rank test for bits 5 to 12, p=0.22393
b-rank test for bits 6 to 13, p=0.52624
b-rank test for bits 7 to 14, p=0.63469
b-rank test for bits 8 to 15, p=0.26472
b-rank test for bits 9 to 16, p=0.78536
b-rank test for bits 10 to 17, p=0.47167
b-rank test for bits 11 to 18, p=0.68314
b-rank test for bits 12 to 19, p=0.77300
b-rank test for bits 13 to 20, p=0.99377
b-rank test for bits 14 to 21, p=0.91273
b-rank test for bits 15 to 22, p=0.14803
b-rank test for bits 16 to 23, p=0.13983
b-rank test for bits 17 to 24, p=0.02147
b-rank test for bits 18 to 25, p=0.42464
b-rank test for bits 19 to 26, p=0.91137
b-rank test for bits 20 to 27, p=0.89410
b-rank test for bits 21 to 28, p=0.51456
b-rank test for bits 22 to 29, p=0.56874
b-rank test for bits 23 to 30, p=0.44073
b-rank test for bits 24 to 31, p=0.60625
b-rank test for bits 25 to 32, p=0.00368
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 = 0.825140
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-22_12:31
(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 141461 -1.05 0.147435
2 141928 0.04 0.517397
3 141122 -1.84 0.032917
4 141873 -0.08 0.466177
5 141478 -1.01 0.156780
6 142195 0.67 0.747759
7 141986 0.18 0.571084
8 142245 0.78 0.783561
9 141345 -1.32 0.093663
10 142346 1.02 0.846197
11 141901 -0.02 0.492236
12 141913 0.01 0.503421
13 142011 0.24 0.593884
14 142258 0.81 0.792364
15 142765 2.00 0.977208
16 141628 -0.66 0.255490
17 141962 0.12 0.548971
18 141729 -0.42 0.336756
19 141992 0.19 0.576581
20 142619 1.66 0.951352
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-22_12:31
Bits used No. missing words z-score p-value
23 to 32 141820 -0.3080 0.379028
22 to 31 141510 -1.3770 0.084256
21 to 30 141550 -1.2391 0.107660
20 to 29 141497 -1.4218 0.077538
19 to 28 142137 0.7851 0.783793
18 to 27 142029 0.4127 0.660070
17 to 26 142017 0.3713 0.644784
16 to 25 142110 0.6920 0.755521
15 to 24 142156 0.8506 0.802500
14 to 23 141852 -0.1977 0.421644
13 to 22 142033 0.4264 0.665109
12 to 21 142351 1.5230 0.936121
11 to 20 141611 -1.0287 0.151805
10 to 19 141631 -0.9598 0.168588
9 to 18 141967 0.1989 0.578815
8 to 17 141516 -1.3563 0.087500
7 to 16 141290 -2.1356 0.016355
6 to 15 141960 0.1747 0.569352
5 to 14 141953 0.1506 0.559849
4 to 13 141547 -1.2494 0.105757
3 to 12 141938 0.0989 0.539376
2 to 11 141976 0.2299 0.590914
1 to 10 141806 -0.3563 0.360804
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-22_12:31
Bits used No. missing words z-score p-value
28 to 32 141884 -0.0859 0.465787
27 to 31 141574 -1.1367 0.127829
26 to 30 141975 0.2226 0.588081
25 to 29 142131 0.7514 0.773801
24 to 28 141945 0.1209 0.548121
23 to 27 141816 -0.3164 0.375860
22 to 26 142109 0.6768 0.750749
21 to 25 142199 0.9819 0.836933
20 to 24 141991 0.2768 0.609051
19 to 23 141932 0.0768 0.530628
18 to 22 142393 1.6396 0.949452
17 to 21 141707 -0.6859 0.246399
16 to 20 142592 2.3141 0.989670
15 to 19 141419 -1.6621 0.048243
14 to 18 142407 1.6870 0.954200
13 to 17 142411 1.7006 0.955489
12 to 16 141267 -2.1774 0.014726
11 to 15 142003 0.3175 0.624578
10 to 14 142294 1.3040 0.903877
9 to 13 141824 -0.2893 0.386193
8 to 12 141551 -1.2147 0.112244
7 to 11 141650 -0.8791 0.189678
6 to 10 141759 -0.5096 0.305168
5 to 9 142008 0.3345 0.630989
4 to 8 141703 -0.6994 0.242144
3 to 7 142230 1.0870 0.861485
2 to 6 142062 0.5175 0.697605
1 to 5 142171 0.8870 0.812465
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-22_12:31
Bits used No. missing words z-score p-value
31 to 32 142209 0.8840 0.811647
30 to 31 141860 -0.1455 0.442152
29 to 30 142275 1.0787 0.859633
28 to 29 141889 -0.0600 0.476090
27 to 28 141795 -0.3373 0.367962
26 to 27 141558 -1.0364 0.150014
25 to 26 141544 -1.0777 0.140591
24 to 25 142189 0.8250 0.795310
23 to 24 141910 0.0020 0.500789
22 to 23 141934 0.0728 0.529007
21 to 22 141572 -0.9951 0.159850
20 to 21 142685 2.2881 0.988935
19 to 20 141911 0.0049 0.501965
18 to 19 141945 0.1052 0.541900
17 to 18 141576 -0.9833 0.162736
16 to 17 141301 -1.7945 0.036368
15 to 16 142191 0.8309 0.796981
14 to 15 142159 0.7365 0.769284
13 to 14 141691 -0.6440 0.259774
12 to 13 142030 0.3560 0.639064
11 to 12 142788 2.5919 0.995228
10 to 11 142392 1.4238 0.922749
9 to 10 141787 -0.3609 0.359104
8 to 9 141568 -1.0069 0.156998
7 to 8 141664 -0.7237 0.234629
6 to 7 141885 -0.0718 0.471393
5 to 6 141958 0.1436 0.557080
4 to 5 141292 -1.8210 0.034301
3 to 4 141675 -0.6912 0.244708
2 to 3 141661 -0.7325 0.231921
1 to 2 141982 0.2144 0.584869
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-22_12:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2438.77 -0.866 0.193270
Test results for specific bytes for dh-ranFile-2018-06-22_12:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2450.83 -0.695 0.243419
2 to 9 2395.95 -1.471 0.070589
3 to 10 2399.61 -1.420 0.077843
4 to 11 2494.33 -0.080 0.468039
5 to 12 2472.97 -0.382 0.351112
6 to 13 2483.02 -0.240 0.405127
7 to 14 2477.56 -0.317 0.375478
8 to 15 2317.86 -2.576 0.005000
9 to 16 2484.53 -0.219 0.413417
10 to 17 2582.29 1.164 0.877743
11 to 18 2351.06 -2.106 0.017585
12 to 19 2573.91 1.045 0.852053
13 to 20 2563.00 0.891 0.813506
14 to 21 2455.24 -0.633 0.263388
15 to 22 2460.39 -0.560 0.287688
16 to 23 2455.70 -0.627 0.265473
17 to 24 2405.31 -1.339 0.090274
18 to 25 2631.16 1.855 0.968192
19 to 26 2537.59 0.532 0.702482
20 to 27 2566.83 0.945 0.827710
21 to 28 2515.78 0.223 0.588282
22 to 29 2406.68 -1.320 0.093456
23 to 30 2524.36 0.345 0.634770
24 to 31 2570.60 0.998 0.840961
25 to 32 2465.81 -0.484 0.314338
CDPARK for dh-ranFile-2018-06-22_12:31: 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
3530 0.3196 0.625377
3479 -2.0091 0.022262
3536 0.5936 0.723613
3509 -0.6393 0.261324
3506 -0.7763 0.218799
3546 1.0502 0.853193
3499 -1.0959 0.136563
3525 0.0913 0.536383
3531 0.3653 0.642555
3537 0.6393 0.738676
Square side=100, avg. no. parked=3519.80 sample std.=19.76
p-value of the KSTEST for those 10 p-values: 0.873969
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-22_12:31
0.6417,0.0512,0.6666,0.6613,0.3631,0.5026,0.8003,0.8910,0.3694,0.5568,
The KS test for those 10 p-values: 0.613980
The 3DSPHERES test for dh-ranFile-2018-06-22_12:31
sample no r^3 equiv. uni.
1 53.119 0.829777
2 26.975 0.593098
3 14.684 0.387046
4 15.511 0.403716
5 101.206 0.965732
6 59.826 0.863879
7 57.607 0.853428
8 15.373 0.400966
9 17.200 0.436359
10 48.885 0.803975
11 30.027 0.632457
12 6.525 0.195472
13 71.310 0.907171
14 76.726 0.922503
15 49.859 0.810232
16 15.270 0.398905
17 7.460 0.220148
18 0.738 0.024299
19 33.613 0.673860
20 4.472 0.138477
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.410143
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-22_12:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 0.9 -0.1 0.0 -0.3 1.1
0.4 0.6 -0.7 1.0 1.1 0.4
0.5 1.9 0.1 -1.7 0.1 -0.2
-1.3 -1.1 1.2 1.1 -1.5 0.4
-0.4 1.1 -1.4 -0.1 1.4 -1.3
-2.2 -1.1 -0.7 0.3 1.5 -0.8
-0.5 0.5 2.1 -0.7 -0.6 0.0
-0.1
Chi-square with 42 degrees of freedom:43.800521
z-score=0.196453, p-value=0.604988
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-22_12:31
Test no p-value
1 0.000279
2 0.402543
3 0.875222
4 0.167324
5 0.553942
6 0.067141
7 0.518013
8 0.573844
9 0.258042
10 0.627957
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.283285
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-22_12:31:
(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 66762 0.14 66543 0.23
3 25000.00 25019 0.01 25006 0.00
4 6666.67 6599 0.69 6747 0.97
5 1388.89 1354 0.88 1418 0.61
6 238.10 233 0.11 255 1.20
7 34.72 29 0.94 27 1.72
8 4.96 3 0.77 3 0.77
p=0.26136 p=0.51857
Number of rngs required: 689125, p-value: 0.798
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-22_12:31
No. of wins: Observed Expected
98635 98585.9
z-score= 0.220, pvalue=0.58698
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66995 66666.7 1.617 1.617
2 37427 37654.3 1.372 2.989
3 27131 26954.7 1.153 4.142
4 19149 19313.5 1.400 5.543
5 13827 13851.4 0.043 5.586
6 9883 9943.5 0.369 5.954
7 7166 7145.0 0.062 6.016
8 5151 5139.1 0.028 6.043
9 3669 3699.9 0.257 6.301
10 2612 2666.3 1.106 7.407
11 1952 1923.3 0.427 7.834
12 1403 1388.7 0.146 7.980
13 1026 1003.7 0.495 8.475
14 734 726.1 0.085 8.560
15 502 525.8 1.080 9.641
16 382 381.2 0.002 9.643
17 263 276.5 0.663 10.306
18 187 200.8 0.952 11.258
19 143 146.0 0.061 11.319
20 108 106.2 0.030 11.349
21 290 287.1 0.029 11.378
Chisq= 11.38 for 20 degrees of freedom, p= 0.06417
SUMMARY of craptest
p-value for no. of wins: 0.586982
p-value for throws/game: 0.064175
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-22_12:31
No. of wins: Observed Expected
98606 98585.9
z-score= 0.090, pvalue=0.53589
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66750 66666.7 0.104 0.104
2 37377 37654.3 2.042 2.147
3 26880 26954.7 0.207 2.354
4 19359 19313.5 0.107 2.461
5 14094 13851.4 4.248 6.709
6 9726 9943.5 4.759 11.469
7 7403 7145.0 9.314 20.783
8 5021 5139.1 2.713 23.496
9 3747 3699.9 0.600 24.096
10 2707 2666.3 0.621 24.718
11 1891 1923.3 0.543 25.261
12 1407 1388.7 0.240 25.501
13 991 1003.7 0.161 25.662
14 711 726.1 0.316 25.978
15 554 525.8 1.508 27.486
16 395 381.2 0.503 27.990
17 275 276.5 0.009 27.998
18 183 200.8 1.583 29.581
19 138 146.0 0.437 30.018
20 116 106.2 0.901 30.919
21 275 287.1 0.511 31.430
Chisq= 31.43 for 20 degrees of freedom, p= 0.95024
SUMMARY of craptest
p-value for no. of wins: 0.535890
p-value for throws/game: 0.950242
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0003,0.0037,0.0050,0.0147,0.0164,0.0176,0.0215,0.0223,0.0230,0.0243,
0.0329,0.0343,0.0364,0.0482,0.0512,0.0622,0.0642,0.0671,0.0706,0.0775,
0.0778,0.0843,0.0875,0.0896,0.0903,0.0935,0.0937,0.1058,0.1077,0.1087,
0.1122,0.1242,0.1278,0.1366,0.1385,0.1398,0.1406,0.1420,0.1474,0.1480,
0.1500,0.1518,0.1547,0.1568,0.1568,0.1570,0.1599,0.1627,0.1673,0.1686,
0.1731,0.1776,0.1798,0.1897,0.1933,0.1955,0.2153,0.2188,0.2201,0.2239,
0.2312,0.2319,0.2346,0.2359,0.2394,0.2421,0.2434,0.2447,0.2464,0.2527,
0.2555,0.2580,0.2598,0.2613,0.2614,0.2634,0.2647,0.2655,0.2720,0.2833,
0.2877,0.3052,0.3073,0.3143,0.3368,0.3449,0.3511,0.3550,0.3591,0.3608,
0.3631,0.3680,0.3694,0.3755,0.3759,0.3790,0.3862,0.3870,0.3882,0.3944,
0.3989,0.4010,0.4010,0.4025,0.4037,0.4050,0.4051,0.4101,0.4134,0.4216,
0.4246,0.4364,0.4407,0.4422,0.4644,0.4658,0.4662,0.4680,0.4711,0.4714,
0.4717,0.4761,0.4841,0.4922,0.5008,0.5020,0.5026,0.5034,0.5146,0.5174,
0.5180,0.5186,0.5262,0.5277,0.5290,0.5306,0.5345,0.5359,0.5364,0.5394,
0.5419,0.5442,0.5452,0.5481,0.5490,0.5500,0.5539,0.5568,0.5571,0.5592,
0.5598,0.5687,0.5694,0.5711,0.5738,0.5766,0.5788,0.5849,0.5870,0.5881,
0.5883,0.5909,0.5931,0.5939,0.6050,0.6062,0.6091,0.6140,0.6246,0.6254,
0.6280,0.6310,0.6325,0.6347,0.6348,0.6384,0.6391,0.6417,0.6426,0.6448,
0.6481,0.6601,0.6613,0.6651,0.6666,0.6739,0.6831,0.6837,0.6976,0.7025,
0.7042,0.7236,0.7387,0.7461,0.7478,0.7483,0.7507,0.7555,0.7574,0.7693,
0.7711,0.7716,0.7730,0.7738,0.7836,0.7838,0.7854,0.7886,0.7907,0.7924,
0.7953,0.7970,0.7981,0.8001,0.8003,0.8025,0.8040,0.8102,0.8116,0.8125,
0.8135,0.8251,0.8277,0.8298,0.8313,0.8361,0.8369,0.8410,0.8462,0.8471,
0.8521,0.8532,0.8534,0.8596,0.8615,0.8639,0.8646,0.8686,0.8740,0.8752,
0.8777,0.8910,0.8941,0.9039,0.9072,0.9114,0.9127,0.9225,0.9227,0.9240,
0.9349,0.9361,0.9495,0.9502,0.9514,0.9542,0.9555,0.9557,0.9626,0.9657,
0.9682,0.9737,0.9772,0.9813,0.9889,0.9897,0.9938,0.9952,0.9952,
Overall p-value after applying KStest on 269 p-values = 0.908926
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.