RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-05-26_04:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.80 23.3567 0.862006
2 to 25 15.82 16.3082 0.497898
3 to 26 15.88 24.8387 0.901622
4 to 27 15.72 25.5536 0.917013
5 to 28 15.95 10.1588 0.103181
6 to 29 15.80 14.0815 0.338678
7 to 30 15.66 20.4008 0.745754
8 to 31 16.14 9.4913 0.076421
9 to 32 16.33 21.3141 0.787446
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.468418
Tough bday spacings test for dh-ranFile-2018-05-26_04:31: 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 8 34 74 108 101 66 48 36 17 6 2
(O-E)^2/E 0.1 0.2 0.0 1.1 0.1 1.9 0.3 1.3 0.3 0.1 1.0
Birthday Spacings: Sum(O-E)^2/E= 6.467, p= 0.225
RESULTS OF GCD FOR dh-ranFile-2018-05-26_04:31
Euclid's algorithm:
p-value, steps to gcd: 0.295321
p-value, dist. of gcd's: 0.178440
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-05-26_04:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.685 0.873 0.100 0.819 0.811 0.948 0.226 0.552
Bits 8 to 15---> 0.860 0.547 0.818 0.479 0.090 0.916 0.965 0.049
Bits 16 to 23---> 0.607 0.491 0.544 0.458 0.132 0.988 0.734 0.153
Bits 24 to 31---> 0.317 0.706 0.201 0.813 0.603 0.174 0.898 0.181
KS test for the above 32 p values: 0.594
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-05-26_04:31,
p-values for 5 runs: 0.5257, 0.6853, 0.1625, 0.7056, 0.6056
Rank test for binary matrices (31x31) for dh-ranFile-2018-05-26_04:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 220 211.4 0.348 0.348
r= 29 5160 5134.0 0.132 0.480
r= 30 23122 23103.0 0.016 0.495
r= 31 11498 11551.5 0.248 0.743
chi-square = 0.743 with df = 3; p-value = 0.137
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-05-26_04:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 213 211.4 0.012 0.012
r= 30 5226 5134.0 1.648 1.660
r= 31 23151 23103.0 0.100 1.760
r= 32 11410 11551.5 1.734 3.493
chi-square = 3.493 with df = 3; p-value = 0.678
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-05-26_04:31
b-rank test for bits 1 to 8, p=0.29018
b-rank test for bits 2 to 9, p=0.73045
b-rank test for bits 3 to 10, p=0.28764
b-rank test for bits 4 to 11, p=0.14125
b-rank test for bits 5 to 12, p=0.06791
b-rank test for bits 6 to 13, p=0.07267
b-rank test for bits 7 to 14, p=0.53990
b-rank test for bits 8 to 15, p=0.33451
b-rank test for bits 9 to 16, p=0.71464
b-rank test for bits 10 to 17, p=0.59738
b-rank test for bits 11 to 18, p=0.61749
b-rank test for bits 12 to 19, p=0.37057
b-rank test for bits 13 to 20, p=0.07972
b-rank test for bits 14 to 21, p=0.45101
b-rank test for bits 15 to 22, p=0.47754
b-rank test for bits 16 to 23, p=0.74949
b-rank test for bits 17 to 24, p=0.89931
b-rank test for bits 18 to 25, p=0.65899
b-rank test for bits 19 to 26, p=0.87172
b-rank test for bits 20 to 27, p=0.57228
b-rank test for bits 21 to 28, p=0.87271
b-rank test for bits 22 to 29, p=0.42839
b-rank test for bits 23 to 30, p=0.52794
b-rank test for bits 24 to 31, p=0.34394
b-rank test for bits 25 to 32, p=0.50626
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 = 0.620738
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-05-26_04:31
(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 142045 0.32 0.624373
2 142619 1.66 0.951352
3 141790 -0.28 0.390196
4 141206 -1.64 0.050161
5 141843 -0.15 0.438420
6 142194 0.67 0.747012
7 142300 0.91 0.819321
8 141635 -0.64 0.260775
9 141710 -0.47 0.320706
10 142848 2.19 0.985852
11 142911 2.34 0.990367
12 142248 0.79 0.785611
13 141944 0.08 0.532281
14 142035 0.29 0.615476
15 141775 -0.31 0.376816
16 141776 -0.31 0.377703
17 141669 -0.56 0.287222
18 141373 -1.25 0.105083
19 141548 -0.84 0.199271
20 141437 -1.10 0.134889
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-05-26_04:31
Bits used No. missing words z-score p-value
23 to 32 141928 0.0644 0.525666
22 to 31 142156 0.8506 0.802500
21 to 30 141698 -0.7287 0.233085
20 to 29 141976 0.2299 0.590914
19 to 28 142030 0.4161 0.661333
18 to 27 141903 -0.0218 0.491293
17 to 26 141616 -1.0115 0.155893
16 to 25 141910 0.0023 0.500922
15 to 24 142068 0.5471 0.707858
14 to 23 141619 -1.0011 0.158380
13 to 22 141799 -0.3804 0.351806
12 to 21 141884 -0.0873 0.465199
11 to 20 142046 0.4713 0.681278
10 to 19 142036 0.4368 0.668869
9 to 18 141694 -0.7425 0.228887
8 to 17 141728 -0.6253 0.265895
7 to 16 142006 0.3333 0.630563
6 to 15 141664 -0.8460 0.198786
5 to 14 141407 -1.7322 0.041621
4 to 13 141688 -0.7632 0.222670
3 to 12 141964 0.1885 0.574764
2 to 11 141350 -1.9287 0.026883
1 to 10 141596 -1.0804 0.139971
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-05-26_04:31
Bits used No. missing words z-score p-value
28 to 32 142074 0.5582 0.711647
27 to 31 142046 0.4633 0.678421
26 to 30 142347 1.4836 0.931046
25 to 29 141774 -0.4587 0.323208
24 to 28 142135 0.7650 0.777859
23 to 27 142016 0.3616 0.641172
22 to 26 141983 0.2497 0.598602
21 to 25 141866 -0.1469 0.441613
20 to 24 141831 -0.2655 0.395302
19 to 23 142061 0.5141 0.696421
18 to 22 142259 1.1853 0.882055
17 to 21 141888 -0.0723 0.471180
16 to 20 142114 0.6938 0.756095
15 to 19 141739 -0.5774 0.281838
14 to 18 141712 -0.6689 0.251775
13 to 17 141997 0.2972 0.616838
12 to 16 141872 -0.1265 0.449651
11 to 15 141635 -0.9299 0.176203
10 to 14 141843 -0.2248 0.411049
9 to 13 141837 -0.2452 0.403156
8 to 12 141663 -0.8350 0.201854
7 to 11 142220 1.0531 0.853857
6 to 10 142307 1.3480 0.911176
5 to 9 141885 -0.0825 0.467135
4 to 8 142429 1.7616 0.960931
3 to 7 141501 -1.3842 0.083153
2 to 6 141972 0.2124 0.584118
1 to 5 141713 -0.6655 0.252857
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-05-26_04:31
Bits used No. missing words z-score p-value
31 to 32 141749 -0.4729 0.318125
30 to 31 141676 -0.6883 0.245635
29 to 30 142283 1.1023 0.864828
28 to 29 141487 -1.2458 0.106417
27 to 28 141766 -0.4228 0.336220
26 to 27 141860 -0.1455 0.442152
25 to 26 141726 -0.5408 0.294324
24 to 25 141482 -1.2606 0.103734
23 to 24 141662 -0.7296 0.232821
22 to 23 141458 -1.3314 0.091536
21 to 22 142470 1.6539 0.950925
20 to 21 142050 0.4150 0.660913
19 to 20 141656 -0.7473 0.227445
18 to 19 142273 1.0728 0.858314
17 to 18 142030 0.3560 0.639064
16 to 17 141874 -0.1042 0.458498
15 to 16 141730 -0.5290 0.298404
14 to 15 141627 -0.8328 0.202470
13 to 14 141026 -2.6057 0.004584
12 to 13 142085 0.5182 0.697841
11 to 12 141779 -0.3845 0.350321
10 to 11 142008 0.2911 0.614498
9 to 10 141396 -1.5142 0.064982
8 to 9 141098 -2.3933 0.008349
7 to 8 142109 0.5890 0.722068
6 to 7 141477 -1.2753 0.101100
5 to 6 141314 -1.7561 0.039533
4 to 5 141717 -0.5673 0.285240
3 to 4 141711 -0.5850 0.279259
2 to 3 141707 -0.5968 0.275306
1 to 2 141875 -0.1013 0.459669
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-05-26_04:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2563.73 0.901 0.816266
Test results for specific bytes for dh-ranFile-2018-05-26_04:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2353.54 -2.071 0.019170
2 to 9 2382.20 -1.666 0.047867
3 to 10 2507.02 0.099 0.539529
4 to 11 2524.52 0.347 0.635636
5 to 12 2518.20 0.257 0.601559
6 to 13 2486.16 -0.196 0.422423
7 to 14 2481.81 -0.257 0.398478
8 to 15 2498.19 -0.026 0.489767
9 to 16 2568.48 0.968 0.833601
10 to 17 2601.23 1.432 0.923879
11 to 18 2495.42 -0.065 0.474186
12 to 19 2534.27 0.485 0.686026
13 to 20 2455.85 -0.624 0.266205
14 to 21 2629.94 1.838 0.966938
15 to 22 2617.91 1.667 0.952291
16 to 23 2524.94 0.353 0.637850
17 to 24 2528.42 0.402 0.656153
18 to 25 2463.18 -0.521 0.301289
19 to 26 2644.57 2.045 0.979549
20 to 27 2545.37 0.642 0.739447
21 to 28 2411.90 -1.246 0.106393
22 to 29 2426.91 -1.034 0.150663
23 to 30 2528.11 0.398 0.654516
24 to 31 2473.92 -0.369 0.356146
25 to 32 2617.89 1.667 0.952266
CDPARK for dh-ranFile-2018-05-26_04:31: 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
3533 0.4566 0.676028
3525 0.0913 0.536383
3524 0.0457 0.518210
3528 0.2283 0.590298
3490 -1.5068 0.065925
3526 0.1370 0.554479
3518 -0.2283 0.409702
3497 -1.1872 0.117571
3523 0.0000 0.500000
3516 -0.3196 0.374623
Square side=100, avg. no. parked=3518.00 sample std.=13.15
p-value of the KSTEST for those 10 p-values: 0.273226
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-05-26_04:31
0.1196,0.0801,0.7041,0.0275,0.8822,0.4750,0.5844,0.5284,0.0830,0.8534,
The KS test for those 10 p-values: 0.452590
The 3DSPHERES test for dh-ranFile-2018-05-26_04:31
sample no r^3 equiv. uni.
1 34.894 0.687491
2 31.347 0.648268
3 26.312 0.583999
4 1.146 0.037466
5 71.012 0.906245
6 62.178 0.874142
7 61.718 0.872198
8 22.464 0.527066
9 55.561 0.843080
10 31.352 0.648332
11 5.761 0.174716
12 9.621 0.274351
13 47.776 0.796589
14 12.360 0.337676
15 6.574 0.196777
16 4.864 0.149680
17 21.068 0.504534
18 43.162 0.762770
19 17.515 0.442252
20 50.659 0.815227
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.594630
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-05-26_04:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -0.7 -0.1 -0.5 0.2 -0.5
1.9 0.6 1.2 0.9 -1.6 1.1
-1.2 2.2 0.4 0.3 -1.8 0.5
0.4 -1.5 0.4 1.2 -0.6 -0.5
0.3 -1.5 -0.3 -0.8 -1.9 -0.4
1.0 0.2 0.8 0.8 -1.3 -0.7
-0.2 1.8 1.7 -0.1 0.1 0.0
-0.1
Chi-square with 42 degrees of freedom:43.054314
z-score=0.115035, p-value=0.574074
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-05-26_04:31
Test no p-value
1 0.094949
2 0.236517
3 0.671952
4 0.723592
5 0.517967
6 0.858173
7 0.021061
8 0.004622
9 0.378003
10 0.004122
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.028978
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-05-26_04:31:
(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 66598 0.07 66585 0.10
3 25000.00 24976 0.02 25088 0.31
4 6666.67 6777 1.83 6637 0.13
5 1388.89 1387 0.00 1384 0.02
6 238.10 227 0.52 263 2.61
7 34.72 28 1.30 35 0.00
8 4.96 6 0.22 7 0.84
p=0.31764 p=0.32406
Number of rngs required: 689932, p-value: 0.964
RESULTS OF CRAPS TEST for dh-ranFile-2018-05-26_04:31
No. of wins: Observed Expected
98494 98585.9
z-score=-0.411, pvalue=0.34059
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66504 66666.7 0.397 0.397
2 37863 37654.3 1.156 1.553
3 27089 26954.7 0.669 2.222
4 19402 19313.5 0.406 2.628
5 13824 13851.4 0.054 2.682
6 9797 9943.5 2.160 4.842
7 7099 7145.0 0.296 5.139
8 5114 5139.1 0.122 5.261
9 3659 3699.9 0.451 5.712
10 2675 2666.3 0.028 5.741
11 1898 1923.3 0.334 6.074
12 1422 1388.7 0.797 6.871
13 1006 1003.7 0.005 6.876
14 759 726.1 1.487 8.363
15 483 525.8 3.490 11.852
16 385 381.2 0.039 11.891
17 275 276.5 0.009 11.900
18 199 200.8 0.017 11.917
19 153 146.0 0.337 12.254
20 95 106.2 1.184 13.438
21 299 287.1 0.492 13.930
Chisq= 13.93 for 20 degrees of freedom, p= 0.16597
SUMMARY of craptest
p-value for no. of wins: 0.340593
p-value for throws/game: 0.165970
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-05-26_04:31
No. of wins: Observed Expected
98803 98585.9
z-score= 0.971, pvalue=0.83427
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66469 66666.7 0.586 0.586
2 37728 37654.3 0.144 0.730
3 26996 26954.7 0.063 0.793
4 19381 19313.5 0.236 1.030
5 13739 13851.4 0.912 1.942
6 9816 9943.5 1.636 3.578
7 7254 7145.0 1.662 5.240
8 5194 5139.1 0.587 5.827
9 3750 3699.9 0.679 6.506
10 2630 2666.3 0.494 7.001
11 2058 1923.3 9.430 16.430
12 1409 1388.7 0.296 16.726
13 1003 1003.7 0.001 16.726
14 716 726.1 0.142 16.868
15 523 525.8 0.015 16.883
16 335 381.2 5.588 22.471
17 272 276.5 0.075 22.546
18 179 200.8 2.373 24.919
19 143 146.0 0.061 24.980
20 93 106.2 1.644 26.624
21 312 287.1 2.157 28.781
Chisq= 28.78 for 20 degrees of freedom, p= 0.90784
SUMMARY of craptest
p-value for no. of wins: 0.834271
p-value for throws/game: 0.907836
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0041,0.0046,0.0046,0.0083,0.0192,0.0211,0.0269,0.0275,0.0290,0.0375,
0.0395,0.0416,0.0479,0.0491,0.0502,0.0650,0.0659,0.0679,0.0727,0.0764,
0.0797,0.0801,0.0830,0.0832,0.0896,0.0915,0.0949,0.0996,0.1011,0.1032,
0.1037,0.1051,0.1064,0.1064,0.1176,0.1196,0.1319,0.1349,0.1371,0.1400,
0.1412,0.1497,0.1507,0.1528,0.1559,0.1584,0.1625,0.1660,0.1740,0.1747,
0.1762,0.1784,0.1811,0.1968,0.1988,0.1993,0.2006,0.2019,0.2025,0.2227,
0.2253,0.2259,0.2274,0.2289,0.2328,0.2331,0.2365,0.2456,0.2518,0.2529,
0.2608,0.2659,0.2662,0.2732,0.2744,0.2753,0.2793,0.2818,0.2852,0.2872,
0.2876,0.2902,0.2943,0.2953,0.2984,0.3013,0.3175,0.3176,0.3181,0.3207,
0.3232,0.3241,0.3345,0.3362,0.3377,0.3387,0.3406,0.3439,0.3503,0.3518,
0.3561,0.3706,0.3746,0.3768,0.3777,0.3780,0.3902,0.3953,0.3985,0.4032,
0.4097,0.4110,0.4224,0.4284,0.4384,0.4416,0.4422,0.4423,0.4497,0.4510,
0.4526,0.4582,0.4585,0.4597,0.4652,0.4671,0.4684,0.4712,0.4742,0.4750,
0.4775,0.4790,0.4898,0.4913,0.4915,0.4979,0.5000,0.5009,0.5045,0.5063,
0.5180,0.5182,0.5257,0.5257,0.5271,0.5279,0.5284,0.5323,0.5364,0.5395,
0.5399,0.5436,0.5472,0.5520,0.5545,0.5723,0.5741,0.5748,0.5840,0.5841,
0.5844,0.5903,0.5909,0.5941,0.5946,0.5974,0.5986,0.6016,0.6026,0.6056,
0.6065,0.6145,0.6155,0.6168,0.6175,0.6207,0.6244,0.6306,0.6356,0.6378,
0.6391,0.6412,0.6483,0.6483,0.6545,0.6562,0.6590,0.6609,0.6613,0.6689,
0.6720,0.6760,0.6784,0.6784,0.6813,0.6852,0.6853,0.6860,0.6875,0.6964,
0.6978,0.7041,0.7056,0.7065,0.7079,0.7116,0.7146,0.7221,0.7236,0.7305,
0.7344,0.7394,0.7458,0.7470,0.7495,0.7561,0.7628,0.7779,0.7856,0.7874,
0.7966,0.8025,0.8114,0.8132,0.8152,0.8163,0.8184,0.8187,0.8193,0.8336,
0.8343,0.8431,0.8534,0.8539,0.8582,0.8583,0.8601,0.8620,0.8648,0.8717,
0.8722,0.8727,0.8727,0.8741,0.8821,0.8822,0.8983,0.8993,0.9016,0.9062,
0.9078,0.9112,0.9163,0.9170,0.9239,0.9310,0.9483,0.9509,0.9514,0.9523,
0.9523,0.9609,0.9638,0.9647,0.9669,0.9795,0.9859,0.9883,0.9904,
Overall p-value after applying KStest on 269 p-values = 0.536749
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.