RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-26_21:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.82 16.3176 0.498558
2 to 25 15.85 22.4934 0.833520
3 to 26 15.60 28.1626 0.956926
4 to 27 15.65 18.8472 0.662630
5 to 28 15.69 23.3545 0.861937
6 to 29 15.49 23.6644 0.871156
7 to 30 15.68 11.9753 0.198368
8 to 31 15.73 32.5281 0.987072
9 to 32 15.50 26.6265 0.936222
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.006550
Tough bday spacings test for dh-ranFile-2018-06-26_21:31: 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 13 38 76 91 103 73 52 23 20 7 4
(O-E)^2/E 1.6 0.1 0.1 0.5 0.3 0.3 0.0 1.5 1.8 0.0 0.0
Birthday Spacings: Sum(O-E)^2/E= 6.172, p= 0.199
RESULTS OF GCD FOR dh-ranFile-2018-06-26_21:31
Euclid's algorithm:
p-value, steps to gcd: 0.549615
p-value, dist. of gcd's: 0.342864
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-26_21:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.250 0.717 0.946 0.751 0.810 0.560 0.886 0.696
Bits 8 to 15---> 0.468 0.713 0.585 0.836 0.869 0.901 0.694 0.234
Bits 16 to 23---> 0.945 0.822 0.996 0.263 0.254 0.880 0.583 0.457
Bits 24 to 31---> 0.266 0.234 0.491 0.098 0.850 0.800 0.725 0.678
KS test for the above 32 p values: 0.988
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-26_21:31,
p-values for 5 runs: 0.2377, 0.7073, 0.1621, 0.1990, 0.8688
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-26_21:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 195 211.4 1.275 1.275
r= 29 5121 5134.0 0.033 1.308
r= 30 22970 23103.0 0.766 2.074
r= 31 11714 11551.5 2.285 4.359
chi-square = 4.359 with df = 3; p-value = 0.775
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-26_21:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 197 211.4 0.983 0.983
r= 30 5232 5134.0 1.870 2.854
r= 31 23204 23103.0 0.441 3.295
r= 32 11367 11551.5 2.948 6.242
chi-square = 6.242 with df = 3; p-value = 0.900
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-26_21:31
b-rank test for bits 1 to 8, p=0.72335
b-rank test for bits 2 to 9, p=0.98934
b-rank test for bits 3 to 10, p=0.22783
b-rank test for bits 4 to 11, p=0.35894
b-rank test for bits 5 to 12, p=0.21287
b-rank test for bits 6 to 13, p=0.01346
b-rank test for bits 7 to 14, p=0.20403
b-rank test for bits 8 to 15, p=0.01217
b-rank test for bits 9 to 16, p=0.39786
b-rank test for bits 10 to 17, p=0.10412
b-rank test for bits 11 to 18, p=0.82658
b-rank test for bits 12 to 19, p=0.92386
b-rank test for bits 13 to 20, p=0.26292
b-rank test for bits 14 to 21, p=0.57801
b-rank test for bits 15 to 22, p=0.81775
b-rank test for bits 16 to 23, p=0.96787
b-rank test for bits 17 to 24, p=0.73942
b-rank test for bits 18 to 25, p=0.93383
b-rank test for bits 19 to 26, p=0.76597
b-rank test for bits 20 to 27, p=0.93677
b-rank test for bits 21 to 28, p=0.82571
b-rank test for bits 22 to 29, p=0.99959
b-rank test for bits 23 to 30, p=0.81341
b-rank test for bits 24 to 31, p=0.04665
b-rank test for bits 25 to 32, p=0.21655
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 = 0.077753
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-26_21:31
(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 141293 -1.44 0.074930
2 142573 1.55 0.939505
3 141268 -1.50 0.067010
4 142176 0.62 0.733378
5 142124 0.50 0.692013
6 142171 0.61 0.729526
7 141649 -0.61 0.271512
8 142392 1.13 0.870284
9 142291 0.89 0.813737
10 142202 0.68 0.752952
11 142606 1.63 0.948209
12 141516 -0.92 0.179049
13 142105 0.46 0.676227
14 142224 0.74 0.768894
15 141992 0.19 0.576581
16 141554 -0.83 0.203210
17 142614 1.65 0.950162
18 142353 1.04 0.850042
19 142305 0.92 0.822377
20 141999 0.21 0.582975
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-26_21:31
Bits used No. missing words z-score p-value
23 to 32 141428 -1.6598 0.048482
22 to 31 141877 -0.1115 0.455617
21 to 30 141378 -1.8322 0.033463
20 to 29 141812 -0.3356 0.368579
19 to 28 140993 -3.1598 0.000789
18 to 27 141842 -0.2322 0.408202
17 to 26 141347 -1.9391 0.026246
16 to 25 142081 0.5920 0.723063
15 to 24 141466 -1.5287 0.063166
14 to 23 142179 0.9299 0.823788
13 to 22 142048 0.4782 0.683736
12 to 21 142124 0.7402 0.770423
11 to 20 142029 0.4127 0.660070
10 to 19 141625 -0.9804 0.163432
9 to 18 142270 1.2437 0.893193
8 to 17 142307 1.3713 0.914856
7 to 16 141700 -0.7218 0.235200
6 to 15 142098 0.6506 0.742343
5 to 14 141578 -1.1425 0.126620
4 to 13 141554 -1.2253 0.110236
3 to 12 142363 1.5644 0.941136
2 to 11 141497 -1.4218 0.077538
1 to 10 141986 0.2644 0.604256
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-26_21:31
Bits used No. missing words z-score p-value
28 to 32 141926 0.0565 0.522532
27 to 31 141867 -0.1435 0.442951
26 to 30 141421 -1.6554 0.048926
25 to 29 141934 0.0836 0.533324
24 to 28 141963 0.1819 0.572182
23 to 27 141715 -0.6587 0.255030
22 to 26 142064 0.5243 0.699967
21 to 25 141656 -0.8587 0.195240
20 to 24 141660 -0.8452 0.199003
19 to 23 141853 -0.1909 0.424283
18 to 22 142089 0.6091 0.728755
17 to 21 141675 -0.7943 0.213499
16 to 20 142206 1.0057 0.842711
15 to 19 141632 -0.9401 0.173583
14 to 18 141733 -0.5977 0.275010
13 to 17 141766 -0.4859 0.313532
12 to 16 141578 -1.1232 0.130686
11 to 15 141508 -1.3604 0.086845
10 to 14 142394 1.6429 0.949803
9 to 13 142191 0.9548 0.830164
8 to 12 142115 0.6972 0.757157
7 to 11 142016 0.3616 0.641172
6 to 10 141794 -0.3909 0.347917
5 to 9 142403 1.6735 0.952881
4 to 8 141820 -0.3028 0.381016
3 to 7 141971 0.2091 0.582796
2 to 6 141644 -0.8994 0.184214
1 to 5 142052 0.4836 0.685675
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-26_21:31
Bits used No. missing words z-score p-value
31 to 32 142067 0.4651 0.679071
30 to 31 142091 0.5359 0.703986
29 to 30 141944 0.1023 0.540729
28 to 29 140922 -2.9125 0.001793
27 to 28 142140 0.6804 0.751888
26 to 27 141888 -0.0629 0.474915
25 to 26 141792 -0.3461 0.364632
24 to 25 142094 0.5447 0.707037
23 to 24 142185 0.8132 0.791944
22 to 23 141805 -0.3078 0.379133
21 to 22 142696 2.3206 0.989845
20 to 21 141967 0.1701 0.567541
19 to 20 141873 -0.1072 0.457328
18 to 19 142140 0.6804 0.751888
17 to 18 141830 -0.2340 0.407488
16 to 17 141783 -0.3727 0.354703
15 to 16 141867 -0.1249 0.450314
14 to 15 141954 0.1318 0.552417
13 to 14 141982 0.2144 0.584869
12 to 13 141939 0.0875 0.534872
11 to 12 141539 -1.0924 0.137325
10 to 11 141584 -0.9597 0.168609
9 to 10 141871 -0.1131 0.454988
8 to 9 141819 -0.2665 0.394942
7 to 8 141955 0.1347 0.553583
6 to 7 142043 0.3943 0.653323
5 to 6 141863 -0.1367 0.445647
4 to 5 142254 1.0167 0.845358
3 to 4 141611 -0.8800 0.189422
2 to 3 141934 0.0728 0.529007
1 to 2 142092 0.5388 0.705005
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-26_21:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2558.79 0.831 0.797143
Test results for specific bytes for dh-ranFile-2018-06-26_21:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2486.61 -0.189 0.424893
2 to 9 2512.94 0.183 0.572576
3 to 10 2649.40 2.113 0.982695
4 to 11 2536.18 0.512 0.695554
5 to 12 2604.63 1.480 0.930524
6 to 13 2512.83 0.181 0.571970
7 to 14 2366.58 -1.887 0.029593
8 to 15 2389.85 -1.558 0.059648
9 to 16 2441.68 -0.825 0.204740
10 to 17 2624.98 1.767 0.961421
11 to 18 2520.86 0.295 0.615988
12 to 19 2490.33 -0.137 0.445600
13 to 20 2503.00 0.042 0.516897
14 to 21 2693.09 2.731 0.996840
15 to 22 2517.83 0.252 0.599540
16 to 23 2627.20 1.799 0.963978
17 to 24 2684.98 2.616 0.995551
18 to 25 2556.01 0.792 0.785856
19 to 26 2547.81 0.676 0.750511
20 to 27 2467.93 -0.454 0.325088
21 to 28 2526.32 0.372 0.645133
22 to 29 2417.84 -1.162 0.122626
23 to 30 2500.11 0.002 0.500617
24 to 31 2456.66 -0.613 0.269977
25 to 32 2353.66 -2.070 0.019244
CDPARK for dh-ranFile-2018-06-26_21:31: 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
3525 0.0913 0.536383
3526 0.1370 0.554479
3510 -0.5936 0.276387
3529 0.2740 0.607947
3493 -1.3699 0.085365
3548 1.1416 0.873180
3493 -1.3699 0.085365
3511 -0.5479 0.291865
3499 -1.0959 0.136563
3533 0.4566 0.676028
Square side=100, avg. no. parked=3516.70 sample std.=17.51
p-value of the KSTEST for those 10 p-values: 0.540540
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-26_21:31
0.6131,0.0310,0.0846,0.0160,0.4026,0.5354,0.3380,0.0527,0.0543,0.7359,
The KS test for those 10 p-values: 0.011101
The 3DSPHERES test for dh-ranFile-2018-06-26_21:31
sample no r^3 equiv. uni.
1 64.764 0.884536
2 23.740 0.546766
3 17.122 0.434891
4 60.777 0.868125
5 9.674 0.275641
6 9.995 0.283345
7 177.550 0.997310
8 57.432 0.852568
9 76.537 0.922015
10 23.998 0.550647
11 118.648 0.980840
12 77.314 0.924009
13 7.704 0.226465
14 36.517 0.703957
15 60.465 0.866747
16 18.372 0.457957
17 48.795 0.803381
18 8.165 0.238281
19 8.853 0.255541
20 43.555 0.765859
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.028297
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-26_21:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 1.3 -0.4 0.0 -0.8 2.4
-2.0 0.5 0.6 0.2 0.8 -0.6
1.3 0.1 -0.2 0.7 -0.9 -0.8
-1.3 1.1 -0.7 0.0 0.2 0.2
-0.1 0.4 1.0 1.5 -2.6 -0.6
0.2 -0.3 0.9 -0.5 -0.5 -0.5
0.3 0.5 0.5 0.4 -1.3 0.0
-1.1
Chi-square with 42 degrees of freedom:37.592184
z-score=-0.480932, p-value=0.335275
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-26_21:31
Test no p-value
1 0.008651
2 0.495314
3 0.397527
4 0.065838
5 0.223637
6 0.808794
7 0.719988
8 0.947662
9 0.595659
10 0.633050
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.933996
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-26_21:31:
(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 66516 0.34 66672 0.00
3 25000.00 25344 4.73 25126 0.64
4 6666.67 6526 2.97 6578 1.18
5 1388.89 1349 1.15 1363 0.48
6 238.10 231 0.21 218 1.70
7 34.72 30 0.64 34 0.01
8 4.96 3 0.77 8 1.86
p=0.90575 p=0.56228
Number of rngs required: 687927, p-value: 0.292
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-26_21:31
No. of wins: Observed Expected
98758 98585.9
z-score= 0.770, pvalue=0.77933
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66769 66666.7 0.157 0.157
2 37743 37654.3 0.209 0.366
3 26879 26954.7 0.213 0.579
4 19288 19313.5 0.034 0.612
5 13974 13851.4 1.085 1.697
6 9991 9943.5 0.226 1.924
7 7318 7145.0 4.188 6.111
8 5023 5139.1 2.622 8.733
9 3634 3699.9 1.173 9.905
10 2546 2666.3 5.428 15.333
11 1905 1923.3 0.175 15.507
12 1272 1388.7 9.813 25.321
13 978 1003.7 0.659 25.980
14 703 726.1 0.737 26.717
15 548 525.8 0.934 27.651
16 404 381.2 1.370 29.021
17 282 276.5 0.108 29.129
18 218 200.8 1.468 30.597
19 131 146.0 1.538 32.135
20 113 106.2 0.433 32.568
21 281 287.1 0.130 32.699
Chisq= 32.70 for 20 degrees of freedom, p= 0.96360
SUMMARY of craptest
p-value for no. of wins: 0.779325
p-value for throws/game: 0.963600
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-26_21:31
No. of wins: Observed Expected
98795 98585.9
z-score= 0.935, pvalue=0.82521
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66627 66666.7 0.024 0.024
2 37841 37654.3 0.925 0.949
3 26755 26954.7 1.480 2.429
4 19384 19313.5 0.258 2.687
5 13730 13851.4 1.064 3.751
6 9925 9943.5 0.035 3.786
7 7350 7145.0 5.880 9.666
8 5159 5139.1 0.077 9.743
9 3584 3699.9 3.628 13.372
10 2702 2666.3 0.478 13.850
11 1994 1923.3 2.597 16.446
12 1401 1388.7 0.108 16.555
13 989 1003.7 0.216 16.770
14 719 726.1 0.070 16.841
15 511 525.8 0.419 17.259
16 354 381.2 1.934 19.193
17 271 276.5 0.111 19.304
18 179 200.8 2.373 21.677
19 151 146.0 0.172 21.849
20 118 106.2 1.308 23.157
21 256 287.1 3.372 26.529
Chisq= 26.53 for 20 degrees of freedom, p= 0.85095
SUMMARY of craptest
p-value for no. of wins: 0.825210
p-value for throws/game: 0.850947
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0008,0.0018,0.0066,0.0087,0.0111,0.0122,0.0135,0.0160,0.0192,0.0262,
0.0283,0.0296,0.0310,0.0335,0.0467,0.0485,0.0489,0.0527,0.0543,0.0596,
0.0632,0.0658,0.0670,0.0749,0.0775,0.0778,0.0846,0.0854,0.0854,0.0868,
0.0977,0.1041,0.1102,0.1226,0.1266,0.1307,0.1366,0.1373,0.1621,0.1634,
0.1686,0.1736,0.1790,0.1842,0.1894,0.1952,0.1984,0.1990,0.1990,0.1994,
0.2032,0.2040,0.2047,0.2129,0.2135,0.2166,0.2236,0.2265,0.2278,0.2340,
0.2345,0.2352,0.2377,0.2383,0.2495,0.2539,0.2550,0.2555,0.2629,0.2634,
0.2658,0.2700,0.2715,0.2750,0.2756,0.2764,0.2833,0.2916,0.2919,0.3135,
0.3251,0.3353,0.3380,0.3429,0.3479,0.3547,0.3589,0.3646,0.3686,0.3791,
0.3810,0.3949,0.3975,0.3979,0.4026,0.4075,0.4082,0.4243,0.4249,0.4349,
0.4430,0.4456,0.4456,0.4503,0.4550,0.4556,0.4572,0.4573,0.4580,0.4683,
0.4749,0.4910,0.4953,0.4986,0.5006,0.5169,0.5225,0.5290,0.5333,0.5349,
0.5354,0.5364,0.5405,0.5407,0.5468,0.5496,0.5506,0.5524,0.5536,0.5545,
0.5604,0.5623,0.5675,0.5720,0.5722,0.5726,0.5766,0.5780,0.5828,0.5830,
0.5832,0.5849,0.5854,0.5957,0.5995,0.6043,0.6079,0.6131,0.6160,0.6330,
0.6412,0.6451,0.6533,0.6601,0.6626,0.6760,0.6762,0.6776,0.6791,0.6837,
0.6857,0.6920,0.6937,0.6956,0.6965,0.7000,0.7040,0.7040,0.7050,0.7070,
0.7073,0.7126,0.7174,0.7200,0.7231,0.7233,0.7255,0.7288,0.7295,0.7334,
0.7359,0.7394,0.7423,0.7505,0.7513,0.7519,0.7519,0.7530,0.7572,0.7659,
0.7660,0.7689,0.7704,0.7748,0.7793,0.7859,0.7919,0.7971,0.8002,0.8034,
0.8088,0.8096,0.8134,0.8137,0.8178,0.8223,0.8224,0.8238,0.8252,0.8257,
0.8266,0.8302,0.8335,0.8357,0.8427,0.8454,0.8500,0.8503,0.8509,0.8526,
0.8619,0.8667,0.8681,0.8686,0.8688,0.8703,0.8712,0.8732,0.8799,0.8845,
0.8863,0.8932,0.8996,0.9010,0.9057,0.9149,0.9220,0.9239,0.9240,0.9305,
0.9338,0.9340,0.9362,0.9368,0.9395,0.9411,0.9447,0.9462,0.9477,0.9482,
0.9498,0.9502,0.9529,0.9569,0.9614,0.9636,0.9640,0.9679,0.9808,0.9827,
0.9871,0.9880,0.9893,0.9898,0.9956,0.9961,0.9968,0.9973,0.9996,
Overall p-value after applying KStest on 269 p-values = 0.013129
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.