RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-22_03:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.44 24.2403 0.886948
2 to 25 16.04 25.0839 0.907152
3 to 26 15.73 22.9748 0.849926
4 to 27 15.90 16.2561 0.494240
5 to 28 15.65 15.0947 0.411337
6 to 29 15.59 30.4913 0.976988
7 to 30 15.57 24.3077 0.888686
8 to 31 15.61 18.0498 0.614295
9 to 32 15.83 21.4683 0.793959
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.009360
Tough bday spacings test for dh-ranFile-2018-06-22_03:31: 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 10 40 64 96 114 67 51 26 19 8 5
(O-E)^2/E 0.1 0.3 1.2 0.0 2.7 1.6 0.0 0.5 1.1 0.3 0.2
Birthday Spacings: Sum(O-E)^2/E= 8.045, p= 0.376
RESULTS OF GCD FOR dh-ranFile-2018-06-22_03:31
Euclid's algorithm:
p-value, steps to gcd: 0.926149
p-value, dist. of gcd's: 0.732981
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-22_03:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.057 0.896 0.041 0.700 0.233 0.656 0.494 0.550
Bits 8 to 15---> 0.451 0.600 0.472 0.375 0.393 0.899 0.009 0.980
Bits 16 to 23---> 0.289 0.772 0.215 0.239 0.863 0.089 0.969 0.707
Bits 24 to 31---> 0.204 0.146 0.166 0.547 0.766 0.060 0.080 0.481
KS test for the above 32 p values: 0.439
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-22_03:31,
p-values for 5 runs: 0.1769, 0.2853, 0.3220, 0.4642, 0.6689
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-22_03:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 220 211.4 0.348 0.348
r= 29 5118 5134.0 0.050 0.398
r= 30 22981 23103.0 0.645 1.043
r= 31 11681 11551.5 1.451 2.494
chi-square = 2.494 with df = 3; p-value = 0.524
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-22_03:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 210 211.4 0.010 0.010
r= 30 5116 5134.0 0.063 0.073
r= 31 23146 23103.0 0.080 0.153
r= 32 11528 11551.5 0.048 0.200
chi-square = 0.200 with df = 3; p-value = 0.022
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-22_03:31
b-rank test for bits 1 to 8, p=0.54489
b-rank test for bits 2 to 9, p=0.76784
b-rank test for bits 3 to 10, p=0.91902
b-rank test for bits 4 to 11, p=0.13055
b-rank test for bits 5 to 12, p=0.21298
b-rank test for bits 6 to 13, p=0.33591
b-rank test for bits 7 to 14, p=0.08040
b-rank test for bits 8 to 15, p=0.28216
b-rank test for bits 9 to 16, p=0.22462
b-rank test for bits 10 to 17, p=0.08389
b-rank test for bits 11 to 18, p=0.48138
b-rank test for bits 12 to 19, p=0.54663
b-rank test for bits 13 to 20, p=0.05061
b-rank test for bits 14 to 21, p=0.25412
b-rank test for bits 15 to 22, p=0.86116
b-rank test for bits 16 to 23, p=0.89283
b-rank test for bits 17 to 24, p=0.33504
b-rank test for bits 18 to 25, p=0.61775
b-rank test for bits 19 to 26, p=0.05452
b-rank test for bits 20 to 27, p=0.89166
b-rank test for bits 21 to 28, p=0.85801
b-rank test for bits 22 to 29, p=0.67542
b-rank test for bits 23 to 30, p=0.30390
b-rank test for bits 24 to 31, p=0.17807
b-rank test for bits 25 to 32, p=0.61644
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 = 0.553797
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-22_03:31
(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 141580 -0.77 0.220809
2 142266 0.83 0.797674
3 142176 0.62 0.733378
4 141862 -0.11 0.455973
5 141258 -1.52 0.064030
6 142237 0.77 0.778038
7 142539 1.47 0.929380
8 142169 0.61 0.727977
9 141531 -0.88 0.188362
10 141698 -0.49 0.310737
11 141631 -0.65 0.257748
12 141774 -0.32 0.375929
13 141736 -0.40 0.342747
14 142181 0.63 0.737202
15 141947 0.09 0.535067
16 141718 -0.45 0.327426
17 141879 -0.07 0.471753
18 141690 -0.51 0.304167
19 142175 0.62 0.732610
20 141056 -1.99 0.023089
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-22_03:31
Bits used No. missing words z-score p-value
23 to 32 141611 -1.0287 0.151805
22 to 31 142108 0.6851 0.753350
21 to 30 142127 0.7506 0.773549
20 to 29 142388 1.6506 0.950588
19 to 28 142440 1.8299 0.966367
18 to 27 142286 1.2989 0.903004
17 to 26 142235 1.1230 0.869281
16 to 25 141876 -0.1149 0.454250
15 to 24 141677 -0.8011 0.211526
14 to 23 141949 0.1368 0.554403
13 to 22 142119 0.7230 0.765160
12 to 21 142006 0.3333 0.630563
11 to 20 141893 -0.0563 0.477547
10 to 19 142044 0.4644 0.678812
9 to 18 141937 0.0954 0.538007
8 to 17 141915 0.0196 0.507800
7 to 16 142149 0.8264 0.795725
6 to 15 142136 0.7816 0.782781
5 to 14 142000 0.3127 0.622729
4 to 13 141778 -0.4529 0.325324
3 to 12 141626 -0.9770 0.164285
2 to 11 141766 -0.4942 0.310568
1 to 10 141847 -0.2149 0.414911
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-22_03:31
Bits used No. missing words z-score p-value
28 to 32 141809 -0.3401 0.366890
27 to 31 142445 1.8158 0.965302
26 to 30 141680 -0.7774 0.218464
25 to 29 141683 -0.7672 0.221475
24 to 28 142147 0.8057 0.789781
23 to 27 141978 0.2328 0.592034
22 to 26 142047 0.4667 0.679635
21 to 25 141467 -1.4994 0.066882
20 to 24 141613 -1.0045 0.157567
19 to 23 142078 0.5718 0.716259
18 to 22 142569 2.2362 0.987330
17 to 21 142331 1.4294 0.923554
16 to 20 142151 0.8192 0.793670
15 to 19 142325 1.4091 0.920590
14 to 18 141841 -0.2316 0.408414
13 to 17 141880 -0.0994 0.460401
12 to 16 142081 0.5819 0.719694
11 to 15 141765 -0.4893 0.312331
10 to 14 141901 -0.0282 0.488737
9 to 13 141600 -1.0486 0.147187
8 to 12 142197 0.9752 0.835258
7 to 11 141447 -1.5672 0.058532
6 to 10 141982 0.2463 0.597290
5 to 9 141207 -2.3808 0.008638
4 to 8 141907 -0.0079 0.496849
3 to 7 141429 -1.6282 0.051737
2 to 6 142400 1.6633 0.951873
1 to 5 142031 0.4124 0.659992
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-22_03:31
Bits used No. missing words z-score p-value
31 to 32 142117 0.6126 0.729928
30 to 31 142173 0.7778 0.781653
29 to 30 142307 1.1731 0.879616
28 to 29 141451 -1.3520 0.088187
27 to 28 141967 0.1701 0.567541
26 to 27 141740 -0.4995 0.308714
25 to 26 142105 0.5772 0.718097
24 to 25 141711 -0.5850 0.279259
23 to 24 141322 -1.7325 0.041589
22 to 23 141703 -0.6086 0.271381
21 to 22 141696 -0.6293 0.264579
20 to 21 141545 -1.0747 0.141250
19 to 20 141778 -0.3874 0.349229
18 to 19 142065 0.4592 0.676956
17 to 18 141893 -0.0482 0.480790
16 to 17 142062 0.4504 0.673772
15 to 16 142445 1.5801 0.942963
14 to 15 141646 -0.7768 0.218643
13 to 14 142409 1.4740 0.929753
12 to 13 141815 -0.2783 0.390407
11 to 12 141916 0.0197 0.507849
10 to 11 142162 0.7453 0.771967
9 to 10 142059 0.4415 0.670576
8 to 9 142128 0.6450 0.740551
7 to 8 141753 -0.4612 0.322345
6 to 7 142452 1.6008 0.945289
5 to 6 141562 -1.0246 0.152783
4 to 5 141706 -0.5998 0.274322
3 to 4 141709 -0.5909 0.277279
2 to 3 141616 -0.8653 0.193443
1 to 2 141872 -0.1101 0.456158
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-22_03:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2557.17 0.808 0.790595
Test results for specific bytes for dh-ranFile-2018-06-22_03:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2478.60 -0.303 0.381061
2 to 9 2528.00 0.396 0.653943
3 to 10 2601.34 1.433 0.924090
4 to 11 2320.94 -2.532 0.005665
5 to 12 2509.12 0.129 0.551317
6 to 13 2472.69 -0.386 0.349670
7 to 14 2505.68 0.080 0.532007
8 to 15 2447.13 -0.748 0.227313
9 to 16 2409.34 -1.282 0.099901
10 to 17 2565.86 0.931 0.824182
11 to 18 2520.41 0.289 0.613553
12 to 19 2472.59 -0.388 0.349126
13 to 20 2471.53 -0.403 0.343629
14 to 21 2406.43 -1.323 0.092877
15 to 22 2526.75 0.378 0.647401
16 to 23 2469.80 -0.427 0.334671
17 to 24 2480.79 -0.272 0.392962
18 to 25 2413.82 -1.219 0.111463
19 to 26 2483.29 -0.236 0.406619
20 to 27 2482.14 -0.253 0.400311
21 to 28 2430.34 -0.985 0.162294
22 to 29 2484.40 -0.221 0.412692
23 to 30 2497.81 -0.031 0.487624
24 to 31 2426.57 -1.038 0.149523
25 to 32 2486.29 -0.194 0.423116
CDPARK for dh-ranFile-2018-06-22_03:31: 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
3527 0.1826 0.572463
3514 -0.4110 0.340551
3514 -0.4110 0.340551
3533 0.4566 0.676028
3522 -0.0457 0.481790
3532 0.4110 0.659449
3503 -0.9132 0.180558
3512 -0.5023 0.307734
3545 1.0046 0.842447
3523 0.0000 0.500000
Square side=100, avg. no. parked=3522.50 sample std.=11.67
p-value of the KSTEST for those 10 p-values: 0.517899
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-22_03:31
0.4719,0.8675,0.3804,0.2307,0.6097,0.7014,0.1517,0.3263,0.9906,0.5252,
The KS test for those 10 p-values: 0.881961
The 3DSPHERES test for dh-ranFile-2018-06-22_03:31
sample no r^3 equiv. uni.
1 6.315 0.189826
2 85.630 0.942405
3 67.525 0.894689
4 94.794 0.957566
5 10.926 0.305240
6 61.997 0.873380
7 48.396 0.800750
8 31.123 0.645636
9 42.443 0.757019
10 8.163 0.238211
11 12.295 0.336232
12 15.761 0.408671
13 5.937 0.179543
14 77.759 0.925127
15 34.430 0.682623
16 21.958 0.519029
17 5.790 0.175512
18 0.664 0.021891
19 4.893 0.150506
20 9.644 0.274925
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.763521
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-22_03:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 0.1 0.8 -0.5 1.9 2.2
-0.9 -0.1 0.4 -0.8 -1.0 -0.4
0.1 1.9 -0.4 1.5 0.1 -0.9
-0.5 -1.4 -0.1 0.0 -0.7 0.7
-2.1 1.6 0.3 1.0 1.1 -0.3
0.1 2.5 -0.3 -0.3 -1.0 2.0
-0.2 0.5 1.7 -0.7 -1.3 -1.0
0.8
Chi-square with 42 degrees of freedom:50.364116
z-score=0.912600, p-value=0.823788
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-22_03:31
Test no p-value
1 0.684643
2 0.068293
3 0.072280
4 0.386704
5 0.063994
6 0.017157
7 0.940859
8 0.920678
9 0.489256
10 0.596051
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.233236
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-22_03:31:
(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 66608 0.05 66826 0.38
3 25000.00 25071 0.20 24732 2.87
4 6666.67 6673 0.01 6754 1.14
5 1388.89 1385 0.01 1409 0.29
6 238.10 220 1.38 243 0.10
7 34.72 40 0.80 30 0.64
8 4.96 2 1.77 5 0.00
p=0.35237 p=0.51028
Number of rngs required: 687760, p-value: 0.229
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-22_03:31
No. of wins: Observed Expected
98397 98585.9
z-score=-0.845, pvalue=0.19914
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66562 66666.7 0.164 0.164
2 37675 37654.3 0.011 0.176
3 27127 26954.7 1.101 1.277
4 19358 19313.5 0.103 1.379
5 13758 13851.4 0.630 2.009
6 9927 9943.5 0.028 2.037
7 7201 7145.0 0.439 2.475
8 5095 5139.1 0.378 2.853
9 3649 3699.9 0.699 3.553
10 2698 2666.3 0.377 3.930
11 1947 1923.3 0.291 4.221
12 1336 1388.7 2.003 6.224
13 1009 1003.7 0.028 6.252
14 702 726.1 0.803 7.054
15 550 525.8 1.110 8.165
16 366 381.2 0.602 8.767
17 269 276.5 0.206 8.972
18 211 200.8 0.515 9.487
19 147 146.0 0.007 9.495
20 104 106.2 0.046 9.541
21 309 287.1 1.668 11.209
Chisq= 11.21 for 20 degrees of freedom, p= 0.05938
SUMMARY of craptest
p-value for no. of wins: 0.199143
p-value for throws/game: 0.059381
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-22_03:31
No. of wins: Observed Expected
98116 98585.9
z-score=-2.101, pvalue=0.01780
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66364 66666.7 1.374 1.374
2 37424 37654.3 1.409 2.783
3 27316 26954.7 4.842 7.625
4 19344 19313.5 0.048 7.673
5 13787 13851.4 0.300 7.973
6 10002 9943.5 0.344 8.316
7 7194 7145.0 0.336 8.652
8 5127 5139.1 0.028 8.680
9 3747 3699.9 0.600 9.281
10 2632 2666.3 0.441 9.722
11 1933 1923.3 0.049 9.771
12 1375 1388.7 0.136 9.907
13 1048 1003.7 1.954 11.861
14 736 726.1 0.134 11.994
15 546 525.8 0.773 12.768
16 369 381.2 0.387 13.155
17 268 276.5 0.264 13.419
18 238 200.8 6.880 20.298
19 164 146.0 2.223 22.522
20 104 106.2 0.046 22.568
21 282 287.1 0.091 22.659
Chisq= 22.66 for 20 degrees of freedom, p= 0.69415
SUMMARY of craptest
p-value for no. of wins: 0.017799
p-value for throws/game: 0.694146
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0057,0.0086,0.0086,0.0094,0.0172,0.0178,0.0219,0.0225,0.0231,0.0414,
0.0416,0.0506,0.0517,0.0545,0.0567,0.0585,0.0594,0.0604,0.0640,0.0640,
0.0669,0.0683,0.0723,0.0797,0.0804,0.0839,0.0882,0.0891,0.0929,0.0999,
0.1115,0.1306,0.1413,0.1458,0.1472,0.1495,0.1505,0.1517,0.1518,0.1528,
0.1576,0.1623,0.1643,0.1656,0.1755,0.1769,0.1781,0.1795,0.1806,0.1884,
0.1898,0.1934,0.1991,0.2037,0.2115,0.2130,0.2145,0.2185,0.2186,0.2208,
0.2215,0.2246,0.2273,0.2288,0.2307,0.2332,0.2334,0.2382,0.2387,0.2541,
0.2577,0.2646,0.2714,0.2743,0.2749,0.2773,0.2793,0.2822,0.2853,0.2890,
0.3039,0.3042,0.3052,0.3077,0.3087,0.3106,0.3107,0.3123,0.3220,0.3223,
0.3253,0.3263,0.3274,0.3347,0.3350,0.3359,0.3362,0.3406,0.3406,0.3427,
0.3436,0.3491,0.3492,0.3497,0.3524,0.3669,0.3750,0.3756,0.3759,0.3804,
0.3811,0.3867,0.3904,0.3929,0.3930,0.4003,0.4066,0.4084,0.4087,0.4113,
0.4127,0.4149,0.4231,0.4392,0.4510,0.4542,0.4560,0.4562,0.4604,0.4642,
0.4718,0.4719,0.4723,0.4775,0.4808,0.4808,0.4814,0.4818,0.4876,0.4887,
0.4893,0.4936,0.4942,0.4968,0.5000,0.5078,0.5078,0.5103,0.5179,0.5190,
0.5237,0.5252,0.5320,0.5351,0.5380,0.5449,0.5466,0.5468,0.5503,0.5513,
0.5538,0.5544,0.5675,0.5725,0.5920,0.5961,0.5973,0.6001,0.6097,0.6136,
0.6143,0.6164,0.6177,0.6227,0.6306,0.6456,0.6474,0.6539,0.6556,0.6594,
0.6600,0.6689,0.6706,0.6738,0.6754,0.6760,0.6770,0.6788,0.6796,0.6826,
0.6846,0.6941,0.7002,0.7014,0.7069,0.7163,0.7181,0.7197,0.7280,0.7299,
0.7326,0.7330,0.7334,0.7372,0.7406,0.7533,0.7570,0.7635,0.7652,0.7657,
0.7678,0.7717,0.7720,0.7735,0.7780,0.7817,0.7828,0.7898,0.7906,0.7937,
0.7940,0.7957,0.7977,0.8007,0.8238,0.8242,0.8353,0.8424,0.8499,0.8580,
0.8612,0.8633,0.8675,0.8693,0.8734,0.8796,0.8820,0.8869,0.8887,0.8917,
0.8928,0.8947,0.8964,0.8991,0.9030,0.9072,0.9190,0.9206,0.9207,0.9236,
0.9241,0.9251,0.9261,0.9294,0.9298,0.9409,0.9424,0.9430,0.9453,0.9506,
0.9519,0.9576,0.9653,0.9664,0.9693,0.9770,0.9802,0.9873,0.9906,
Overall p-value after applying KStest on 269 p-values = 0.726411
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.