RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-10_22:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.77 12.3642 0.222401
2 to 25 15.58 20.3830 0.744892
3 to 26 15.86 12.0327 0.201845
4 to 27 15.76 21.9434 0.813094
5 to 28 15.68 14.1272 0.341925
6 to 29 15.87 34.9209 0.993628
7 to 30 15.71 14.4661 0.366122
8 to 31 15.96 19.1319 0.678984
9 to 32 15.90 19.3614 0.691812
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.634229
Tough bday spacings test for dh-ranFile-2018-07-10_22:31: 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 39 68 112 100 72 50 29 9 8 2
(O-E)^2/E 0.4 0.2 0.4 2.1 0.1 0.5 0.1 0.0 2.3 0.3 1.0
Birthday Spacings: Sum(O-E)^2/E= 7.309, p= 0.304
RESULTS OF GCD FOR dh-ranFile-2018-07-10_22:31
Euclid's algorithm:
p-value, steps to gcd: 0.043714
p-value, dist. of gcd's: 0.310502
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-10_22:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.437 0.929 0.273 0.703 0.480 0.895 0.176 0.645
Bits 8 to 15---> 0.219 0.297 0.091 0.054 0.468 0.263 0.796 0.345
Bits 16 to 23---> 0.355 0.076 0.992 0.565 0.868 0.143 0.941 0.702
Bits 24 to 31---> 0.412 0.337 0.674 0.218 0.934 0.709 0.835 0.963
KS test for the above 32 p values: 0.185
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-10_22:31,
p-values for 5 runs: 0.6344, 0.8188, 0.4978, 0.0071, 0.9948
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-10_22:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 206 211.4 0.139 0.139
r= 29 5231 5134.0 1.832 1.971
r= 30 22995 23103.0 0.505 2.476
r= 31 11568 11551.5 0.024 2.500
chi-square = 2.500 with df = 3; p-value = 0.525
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-10_22:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 208 211.4 0.055 0.055
r= 30 5180 5134.0 0.412 0.467
r= 31 23144 23103.0 0.073 0.540
r= 32 11468 11551.5 0.604 1.144
chi-square = 1.144 with df = 3; p-value = 0.233
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-10_22:31
b-rank test for bits 1 to 8, p=0.50330
b-rank test for bits 2 to 9, p=0.82431
b-rank test for bits 3 to 10, p=0.77240
b-rank test for bits 4 to 11, p=0.08806
b-rank test for bits 5 to 12, p=0.41582
b-rank test for bits 6 to 13, p=0.70746
b-rank test for bits 7 to 14, p=0.63223
b-rank test for bits 8 to 15, p=0.07939
b-rank test for bits 9 to 16, p=0.88825
b-rank test for bits 10 to 17, p=0.26193
b-rank test for bits 11 to 18, p=0.27899
b-rank test for bits 12 to 19, p=0.75611
b-rank test for bits 13 to 20, p=0.93444
b-rank test for bits 14 to 21, p=0.05275
b-rank test for bits 15 to 22, p=0.33724
b-rank test for bits 16 to 23, p=0.93931
b-rank test for bits 17 to 24, p=0.24776
b-rank test for bits 18 to 25, p=0.54245
b-rank test for bits 19 to 26, p=0.60339
b-rank test for bits 20 to 27, p=0.12508
b-rank test for bits 21 to 28, p=0.77354
b-rank test for bits 22 to 29, p=0.88808
b-rank test for bits 23 to 30, p=0.15155
b-rank test for bits 24 to 31, p=0.29095
b-rank test for bits 25 to 32, p=0.89470
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 = 0.883235
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-10_22:31
(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 141798 -0.26 0.397387
2 142285 0.88 0.809956
3 141599 -0.73 0.234205
4 141659 -0.58 0.279313
5 141849 -0.14 0.443952
6 141733 -0.41 0.340175
7 142060 0.35 0.637593
8 141997 0.20 0.581150
9 142454 1.27 0.898419
10 141066 -1.97 0.024396
11 141420 -1.14 0.126458
12 141446 -1.08 0.139505
13 141730 -0.42 0.337610
14 141895 -0.03 0.486645
15 141952 0.10 0.539707
16 142042 0.31 0.621711
17 141930 0.05 0.519259
18 142289 0.89 0.812482
19 142455 1.27 0.898833
20 141962 0.12 0.548971
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-10_22:31
Bits used No. missing words z-score p-value
23 to 32 141423 -1.6770 0.046771
22 to 31 141613 -1.0218 0.153431
21 to 30 141400 -1.7563 0.039518
20 to 29 141858 -0.1770 0.429754
19 to 28 141863 -0.1598 0.436536
18 to 27 141401 -1.7529 0.039813
17 to 26 142074 0.5678 0.714924
16 to 25 141835 -0.2563 0.398856
15 to 24 141822 -0.3011 0.381655
14 to 23 141883 -0.0908 0.463829
13 to 22 141945 0.1230 0.548947
12 to 21 142260 1.2092 0.886708
11 to 20 141708 -0.6942 0.243765
10 to 19 141955 0.1575 0.562568
9 to 18 141865 -0.1529 0.439254
8 to 17 141383 -1.8149 0.034767
7 to 16 141379 -1.8287 0.033720
6 to 15 141761 -0.5115 0.304507
5 to 14 142085 0.6058 0.727663
4 to 13 142179 0.9299 0.823788
3 to 12 141854 -0.1908 0.424344
2 to 11 141676 -0.8046 0.210529
1 to 10 141689 -0.7598 0.223699
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-10_22:31
Bits used No. missing words z-score p-value
28 to 32 141981 0.2429 0.595978
27 to 31 142687 2.6362 0.995808
26 to 30 141532 -1.2791 0.100434
25 to 29 141910 0.0023 0.500906
24 to 28 142372 1.5684 0.941603
23 to 27 141911 0.0057 0.502258
22 to 26 141878 -0.1062 0.457711
21 to 25 141748 -0.5469 0.292230
20 to 24 142021 0.3785 0.647486
19 to 23 141673 -0.8011 0.211532
18 to 22 141661 -0.8418 0.199951
17 to 21 141752 -0.5333 0.296905
16 to 20 142237 1.1107 0.866661
15 to 19 142178 0.9107 0.818785
14 to 18 141350 -1.8960 0.028978
13 to 17 142097 0.6362 0.737667
12 to 16 141681 -0.7740 0.219465
11 to 15 141894 -0.0520 0.479278
10 to 14 141756 -0.5198 0.301615
9 to 13 141910 0.0023 0.500906
8 to 12 142038 0.4362 0.668643
7 to 11 142113 0.6904 0.755031
6 to 10 142163 0.8599 0.805077
5 to 9 141513 -1.3435 0.089556
4 to 8 141808 -0.3435 0.365614
3 to 7 141390 -1.7604 0.039167
2 to 6 141832 -0.2621 0.396609
1 to 5 141592 -1.0757 0.141032
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-10_22:31
Bits used No. missing words z-score p-value
31 to 32 141688 -0.6529 0.256913
30 to 31 141779 -0.3845 0.350321
29 to 30 141428 -1.4199 0.077825
28 to 29 142271 1.0669 0.856985
27 to 28 142049 0.4120 0.659832
26 to 27 141701 -0.6145 0.269428
25 to 26 141600 -0.9125 0.180759
24 to 25 141870 -0.1160 0.453819
23 to 24 142168 0.7630 0.777280
22 to 23 141508 -1.1839 0.118233
21 to 22 141421 -1.4405 0.074863
20 to 21 141747 -0.4788 0.316023
19 to 20 142464 1.6362 0.949101
18 to 19 142166 0.7571 0.775517
17 to 18 142314 1.1937 0.883706
16 to 17 141986 0.2262 0.589464
15 to 16 141500 -1.2075 0.113627
14 to 15 142070 0.4740 0.682233
13 to 14 141613 -0.8741 0.191024
12 to 13 142161 0.7424 0.771074
11 to 12 141622 -0.8476 0.198336
10 to 11 141966 0.1672 0.566381
9 to 10 141862 -0.1396 0.444482
8 to 9 142355 1.3147 0.905688
7 to 8 141485 -1.2517 0.105338
6 to 7 141784 -0.3697 0.355801
5 to 6 141753 -0.4612 0.322345
4 to 5 141258 -1.9213 0.027345
3 to 4 142121 0.6244 0.733816
2 to 3 142104 0.5742 0.717100
1 to 2 141868 -0.1219 0.451482
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-10_22:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2577.59 1.097 0.863729
Test results for specific bytes for dh-ranFile-2018-07-10_22:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2491.21 -0.124 0.450523
2 to 9 2406.82 -1.318 0.093796
3 to 10 2749.33 3.526 0.999789
4 to 11 2491.34 -0.122 0.451269
5 to 12 2624.76 1.764 0.961164
6 to 13 2701.24 2.846 0.997786
7 to 14 2583.63 1.183 0.881546
8 to 15 2529.11 0.412 0.659710
9 to 16 2587.10 1.232 0.890992
10 to 17 2587.61 1.239 0.892338
11 to 18 2586.29 1.220 0.888830
12 to 19 2501.56 0.022 0.508801
13 to 20 2575.43 1.067 0.856968
14 to 21 2574.95 1.060 0.855426
15 to 22 2540.95 0.579 0.718754
16 to 23 2301.25 -2.811 0.002472
17 to 24 2490.76 -0.131 0.448023
18 to 25 2357.52 -2.015 0.021954
19 to 26 2536.99 0.523 0.699567
20 to 27 2529.71 0.420 0.662840
21 to 28 2623.80 1.751 0.960014
22 to 29 2541.20 0.583 0.719917
23 to 30 2455.08 -0.635 0.262627
24 to 31 2510.54 0.149 0.559223
25 to 32 2365.88 -1.897 0.028927
CDPARK for dh-ranFile-2018-07-10_22:31: 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
3486 -1.6895 0.045562
3497 -1.1872 0.117571
3517 -0.2740 0.392053
3527 0.1826 0.572463
3522 -0.0457 0.481790
3521 -0.0913 0.463617
3542 0.8676 0.807188
3535 0.5479 0.708135
3533 0.4566 0.676028
3502 -0.9589 0.168804
Square side=100, avg. no. parked=3518.20 sample std.=17.08
p-value of the KSTEST for those 10 p-values: 0.754935
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-10_22:31
0.4443,0.3821,0.0418,0.9306,0.3519,0.3834,0.5982,0.4017,0.5413,0.7332,
The KS test for those 10 p-values: 0.596018
The 3DSPHERES test for dh-ranFile-2018-07-10_22:31
sample no r^3 equiv. uni.
1 50.668 0.815286
2 39.451 0.731533
3 16.328 0.419725
4 1.582 0.051371
5 90.377 0.950835
6 3.190 0.100877
7 72.240 0.910006
8 58.585 0.858130
9 0.255 0.008480
10 67.978 0.896265
11 3.838 0.120096
12 9.347 0.267694
13 5.415 0.165155
14 12.780 0.346884
15 50.937 0.816930
16 53.015 0.829187
17 13.797 0.368650
18 54.116 0.835342
19 69.223 0.900485
20 18.537 0.460927
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.276946
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-10_22:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 -0.3 -1.6 -0.7 2.4 1.6
-1.0 -0.7 -0.1 1.2 0.2 1.3
0.7 0.1 -0.8 -1.5 1.0 -1.2
0.9 0.7 1.0 -0.2 -1.2 -0.8
0.7 -1.8 -0.2 0.4 0.7 0.1
-1.3 -0.1 -0.7 -0.8 0.2 0.2
0.3 -0.4 -0.8 -0.1 -1.3 0.0
-1.1
Chi-square with 42 degrees of freedom:37.346233
z-score=-0.507768, p-value=0.324798
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-10_22:31
Test no p-value
1 0.035336
2 0.354348
3 0.126425
4 0.106933
5 0.660285
6 0.421197
7 0.032322
8 0.012976
9 0.709959
10 0.196279
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.008629
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-10_22:31:
(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 66753 0.11 66869 0.61
3 25000.00 24888 0.50 25069 0.19
4 6666.67 6646 0.06 6438 7.84
5 1388.89 1441 1.96 1344 1.45
6 238.10 238 0.00 238 0.00
7 34.72 27 1.72 37 0.15
8 4.96 6 0.22 4 0.19
p=0.39964 p=0.89249
Number of rngs required: 687430, p-value: 0.129
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-10_22:31
No. of wins: Observed Expected
98839 98585.9
z-score= 1.132, pvalue=0.87122
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67063 66666.7 2.356 2.356
2 37791 37654.3 0.496 2.852
3 27089 26954.7 0.669 3.521
4 18955 19313.5 6.653 10.174
5 13619 13851.4 3.900 14.074
6 9998 9943.5 0.298 14.372
7 7046 7145.0 1.372 15.745
8 5049 5139.1 1.579 17.324
9 3675 3699.9 0.167 17.491
10 2703 2666.3 0.505 17.996
11 2004 1923.3 3.384 21.379
12 1402 1388.7 0.127 21.506
13 995 1003.7 0.076 21.582
14 720 726.1 0.052 21.634
15 530 525.8 0.033 21.667
16 360 381.2 1.174 22.840
17 259 276.5 1.112 23.953
18 220 200.8 1.830 25.783
19 162 146.0 1.757 27.540
20 95 106.2 1.184 28.724
21 265 287.1 1.703 30.427
Chisq= 30.43 for 20 degrees of freedom, p= 0.93678
SUMMARY of craptest
p-value for no. of wins: 0.871224
p-value for throws/game: 0.936778
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-10_22:31
No. of wins: Observed Expected
98837 98585.9
z-score= 1.123, pvalue=0.86933
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66704 66666.7 0.021 0.021
2 37684 37654.3 0.023 0.044
3 26852 26954.7 0.392 0.436
4 19244 19313.5 0.250 0.686
5 13847 13851.4 0.001 0.687
6 9953 9943.5 0.009 0.696
7 7065 7145.0 0.896 1.592
8 5241 5139.1 2.022 3.614
9 3705 3699.9 0.007 3.621
10 2630 2666.3 0.494 4.115
11 2016 1923.3 4.465 8.580
12 1402 1388.7 0.127 8.707
13 1008 1003.7 0.018 8.725
14 713 726.1 0.238 8.963
15 510 525.8 0.477 9.440
16 396 381.2 0.579 10.019
17 282 276.5 0.108 10.126
18 232 200.8 4.838 14.964
19 143 146.0 0.061 15.025
20 106 106.2 0.000 15.026
21 267 287.1 1.409 16.435
Chisq= 16.43 for 20 degrees of freedom, p= 0.31068
SUMMARY of craptest
p-value for no. of wins: 0.869335
p-value for throws/game: 0.310682
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0025,0.0071,0.0085,0.0086,0.0130,0.0220,0.0244,0.0273,0.0289,0.0290,
0.0323,0.0337,0.0348,0.0353,0.0392,0.0395,0.0398,0.0418,0.0437,0.0456,
0.0468,0.0514,0.0527,0.0538,0.0749,0.0764,0.0778,0.0794,0.0881,0.0896,
0.0911,0.0938,0.1004,0.1009,0.1053,0.1069,0.1136,0.1176,0.1182,0.1201,
0.1251,0.1264,0.1265,0.1293,0.1395,0.1410,0.1434,0.1516,0.1534,0.1652,
0.1688,0.1761,0.1808,0.1853,0.1910,0.1963,0.1983,0.2000,0.2018,0.2105,
0.2115,0.2179,0.2193,0.2195,0.2224,0.2237,0.2335,0.2342,0.2438,0.2478,
0.2569,0.2619,0.2626,0.2630,0.2677,0.2694,0.2730,0.2769,0.2790,0.2793,
0.2910,0.2922,0.2969,0.2974,0.3016,0.3040,0.3045,0.3105,0.3107,0.3160,
0.3223,0.3248,0.3372,0.3375,0.3376,0.3402,0.3419,0.3447,0.3469,0.3503,
0.3519,0.3543,0.3552,0.3558,0.3656,0.3661,0.3686,0.3817,0.3821,0.3834,
0.3921,0.3966,0.3974,0.3989,0.3996,0.4017,0.4116,0.4158,0.4197,0.4212,
0.4243,0.4298,0.4365,0.4369,0.4393,0.4440,0.4443,0.4445,0.4480,0.4505,
0.4513,0.4515,0.4538,0.4577,0.4609,0.4636,0.4638,0.4679,0.4793,0.4796,
0.4818,0.4866,0.4978,0.5009,0.5009,0.5023,0.5033,0.5088,0.5193,0.5247,
0.5397,0.5413,0.5425,0.5489,0.5490,0.5592,0.5626,0.5654,0.5664,0.5725,
0.5812,0.5895,0.5960,0.5960,0.5982,0.6034,0.6217,0.6322,0.6342,0.6344,
0.6376,0.6450,0.6475,0.6597,0.6598,0.6603,0.6628,0.6686,0.6742,0.6760,
0.6790,0.6822,0.6918,0.6996,0.7020,0.7028,0.7075,0.7081,0.7090,0.7100,
0.7149,0.7171,0.7188,0.7199,0.7277,0.7315,0.7332,0.7338,0.7377,0.7449,
0.7549,0.7550,0.7561,0.7711,0.7724,0.7735,0.7755,0.7773,0.7960,0.8051,
0.8072,0.8100,0.8125,0.8131,0.8153,0.8169,0.8188,0.8188,0.8238,0.8243,
0.8292,0.8353,0.8355,0.8554,0.8570,0.8570,0.8581,0.8637,0.8667,0.8679,
0.8693,0.8712,0.8815,0.8832,0.8837,0.8867,0.8881,0.8882,0.8888,0.8910,
0.8923,0.8925,0.8947,0.8953,0.8963,0.8984,0.8988,0.9005,0.9057,0.9100,
0.9292,0.9306,0.9344,0.9345,0.9368,0.9393,0.9410,0.9416,0.9491,0.9508,
0.9600,0.9612,0.9627,0.9919,0.9936,0.9948,0.9958,0.9978,0.9998,
Overall p-value after applying KStest on 269 p-values = 0.536021
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.