RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-29_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 15.79 14.7324 0.385247
2 to 25 15.74 14.5311 0.370783
3 to 26 15.79 33.7870 0.991056
4 to 27 15.66 11.4896 0.169991
5 to 28 15.66 16.6745 0.523379
6 to 29 15.80 12.4745 0.229407
7 to 30 15.61 26.7709 0.938485
8 to 31 15.86 13.1431 0.273445
9 to 32 16.00 11.8724 0.192197
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.373050
Tough bday spacings test for dh-ranFile-2018-06-29_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 16 35 59 91 106 76 58 28 19 8 4
(O-E)^2/E 5.1 0.1 2.8 0.5 0.7 0.1 0.7 0.1 1.1 0.3 0.0
Birthday Spacings: Sum(O-E)^2/E= 11.388, p= 0.672
RESULTS OF GCD FOR dh-ranFile-2018-06-29_04:31
Euclid's algorithm:
p-value, steps to gcd: 0.264718
p-value, dist. of gcd's: 0.913659
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-29_04:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.711 0.679 0.468 0.214 0.670 0.238 0.928 0.916
Bits 8 to 15---> 0.646 0.711 0.157 0.819 0.847 0.191 0.792 0.832
Bits 16 to 23---> 0.543 0.061 0.993 0.038 0.552 0.130 0.431 0.321
Bits 24 to 31---> 0.379 0.812 0.547 0.215 0.950 0.803 0.344 0.773
KS test for the above 32 p values: 0.469
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-29_04:31,
p-values for 5 runs: 0.1204, 0.5805, 0.8594, 0.2426, 0.2738
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-29_04:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 215 211.4 0.061 0.061
r= 29 5064 5134.0 0.955 1.015
r= 30 23220 23103.0 0.592 1.607
r= 31 11501 11551.5 0.221 1.828
chi-square = 1.828 with df = 3; p-value = 0.391
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-29_04:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 230 211.4 1.633 1.633
r= 30 5053 5134.0 1.278 2.911
r= 31 23123 23103.0 0.017 2.929
r= 32 11594 11551.5 0.156 3.085
chi-square = 3.085 with df = 3; p-value = 0.621
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-29_04:31
b-rank test for bits 1 to 8, p=0.31345
b-rank test for bits 2 to 9, p=0.25413
b-rank test for bits 3 to 10, p=0.96931
b-rank test for bits 4 to 11, p=0.56086
b-rank test for bits 5 to 12, p=0.56062
b-rank test for bits 6 to 13, p=0.97190
b-rank test for bits 7 to 14, p=0.86064
b-rank test for bits 8 to 15, p=0.75482
b-rank test for bits 9 to 16, p=0.29980
b-rank test for bits 10 to 17, p=0.96399
b-rank test for bits 11 to 18, p=0.52954
b-rank test for bits 12 to 19, p=0.15064
b-rank test for bits 13 to 20, p=0.16048
b-rank test for bits 14 to 21, p=0.55477
b-rank test for bits 15 to 22, p=0.92653
b-rank test for bits 16 to 23, p=0.42157
b-rank test for bits 17 to 24, p=0.47872
b-rank test for bits 18 to 25, p=0.15346
b-rank test for bits 19 to 26, p=0.59279
b-rank test for bits 20 to 27, p=0.89537
b-rank test for bits 21 to 28, p=0.45195
b-rank test for bits 22 to 29, p=0.09125
b-rank test for bits 23 to 30, p=0.26917
b-rank test for bits 24 to 31, p=0.36490
b-rank test for bits 25 to 32, p=0.22584
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 = 0.625943
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-29_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 142300 0.91 0.819321
2 141573 -0.79 0.215987
3 142360 1.05 0.853822
4 142098 0.44 0.670328
5 141766 -0.33 0.368857
6 142426 1.21 0.886317
7 141984 0.17 0.569249
8 141879 -0.07 0.471753
9 141674 -0.55 0.291216
10 142382 1.10 0.865284
11 141229 -1.59 0.055967
12 141766 -0.33 0.368857
13 141881 -0.07 0.473613
14 140995 -2.14 0.016328
15 141487 -0.99 0.161882
16 141484 -0.99 0.160169
17 142378 1.10 0.863247
18 141929 0.05 0.518328
19 141680 -0.54 0.296042
20 141575 -0.78 0.217359
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-29_04:31
Bits used No. missing words z-score p-value
23 to 32 141531 -1.3046 0.096017
22 to 31 142086 0.6092 0.728806
21 to 30 141843 -0.2287 0.409542
20 to 29 141727 -0.6287 0.264765
19 to 28 141253 -2.2632 0.011811
18 to 27 142319 1.4127 0.921121
17 to 26 141618 -1.0046 0.157548
16 to 25 141767 -0.4908 0.311786
15 to 24 142375 1.6058 0.945837
14 to 23 142392 1.6644 0.951982
13 to 22 141887 -0.0770 0.469312
12 to 21 142119 0.7230 0.765160
11 to 20 141694 -0.7425 0.228887
10 to 19 142330 1.4506 0.926552
9 to 18 141902 -0.0253 0.489918
8 to 17 141612 -1.0253 0.152617
7 to 16 141797 -0.3873 0.349251
6 to 15 141633 -0.9529 0.170330
5 to 14 141640 -0.9287 0.176516
4 to 13 141831 -0.2701 0.393540
3 to 12 141640 -0.9287 0.176516
2 to 11 142078 0.5816 0.719589
1 to 10 141698 -0.7287 0.233085
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-29_04:31
Bits used No. missing words z-score p-value
28 to 32 142360 1.5277 0.936706
27 to 31 141834 -0.2554 0.399224
26 to 30 142124 0.7277 0.766600
25 to 29 141753 -0.5299 0.298080
24 to 28 142112 0.6870 0.753964
23 to 27 141889 -0.0689 0.472529
22 to 26 141701 -0.7062 0.240031
21 to 25 141199 -2.4079 0.008022
20 to 24 142249 1.1514 0.875221
19 to 23 141911 0.0057 0.502258
18 to 22 141868 -0.1401 0.444290
17 to 21 141528 -1.2926 0.098067
16 to 20 142453 1.8429 0.967332
15 to 19 141517 -1.3299 0.091770
14 to 18 142110 0.6802 0.751823
13 to 17 141751 -0.5367 0.295733
12 to 16 141426 -1.6384 0.050668
11 to 15 142168 0.8768 0.809715
10 to 14 142133 0.7582 0.775835
9 to 13 141874 -0.1198 0.452336
8 to 12 142029 0.4057 0.657504
7 to 11 141772 -0.4655 0.320778
6 to 10 141562 -1.1774 0.119520
5 to 9 142061 0.5141 0.696421
4 to 8 141791 -0.4011 0.344166
3 to 7 141611 -1.0113 0.155939
2 to 6 142167 0.8735 0.808793
1 to 5 142332 1.4328 0.924040
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-29_04:31
Bits used No. missing words z-score p-value
31 to 32 141719 -0.5614 0.287247
30 to 31 141701 -0.6145 0.269428
29 to 30 142291 1.1259 0.869890
28 to 29 141441 -1.3815 0.083562
27 to 28 141543 -1.0806 0.139933
26 to 27 141537 -1.0983 0.136033
25 to 26 142395 1.4327 0.924022
24 to 25 141899 -0.0305 0.487845
23 to 24 141785 -0.3668 0.356901
22 to 23 141984 0.2203 0.587168
21 to 22 141743 -0.4906 0.311837
20 to 21 141488 -1.2429 0.106959
19 to 20 142552 1.8958 0.971006
18 to 19 141982 0.2144 0.584869
17 to 18 142072 0.4799 0.684334
16 to 17 141790 -0.3520 0.362417
15 to 16 142058 0.4386 0.669508
14 to 15 142047 0.4061 0.657668
13 to 14 141856 -0.1573 0.437498
12 to 13 142019 0.3235 0.626846
11 to 12 142385 1.4032 0.919715
10 to 11 142606 2.0551 0.980064
9 to 10 141748 -0.4759 0.317073
8 to 9 141552 -1.0541 0.145925
7 to 8 141815 -0.2783 0.390407
6 to 7 141924 0.0433 0.517259
5 to 6 141327 -1.7178 0.042918
4 to 5 141262 -1.9095 0.028097
3 to 4 141825 -0.2488 0.401773
2 to 3 142305 1.1672 0.878429
1 to 2 141981 0.2114 0.583719
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-29_04:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2550.81 0.719 0.763813
Test results for specific bytes for dh-ranFile-2018-06-29_04:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2436.31 -0.901 0.183861
2 to 9 2546.99 0.665 0.746840
3 to 10 2540.81 0.577 0.718096
4 to 11 2540.16 0.568 0.714954
5 to 12 2537.11 0.525 0.700131
6 to 13 2401.60 -1.392 0.082017
7 to 14 2519.09 0.270 0.606418
8 to 15 2515.53 0.220 0.586901
9 to 16 2598.76 1.397 0.918744
10 to 17 2470.10 -0.423 0.336227
11 to 18 2530.51 0.431 0.666924
12 to 19 2438.69 -0.867 0.192943
13 to 20 2406.12 -1.328 0.092138
14 to 21 2550.88 0.720 0.764088
15 to 22 2571.10 1.006 0.842687
16 to 23 2575.81 1.072 0.858162
17 to 24 2499.90 -0.001 0.499463
18 to 25 2461.42 -0.546 0.292679
19 to 26 2563.70 0.901 0.816185
20 to 27 2403.16 -1.370 0.085418
21 to 28 2512.11 0.171 0.567992
22 to 29 2439.28 -0.859 0.195255
23 to 30 2364.65 -1.914 0.027805
24 to 31 2453.30 -0.660 0.254507
25 to 32 2509.50 0.134 0.553450
CDPARK for dh-ranFile-2018-06-29_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
3534 0.5023 0.692266
3516 -0.3196 0.374623
3510 -0.5936 0.276387
3540 0.7763 0.781201
3528 0.2283 0.590298
3537 0.6393 0.738676
3532 0.4110 0.659449
3514 -0.4110 0.340551
3515 -0.3653 0.357445
3501 -1.0046 0.157553
Square side=100, avg. no. parked=3522.70 sample std.=12.48
p-value of the KSTEST for those 10 p-values: 0.591049
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-29_04:31
0.6312,0.3525,0.4562,0.4297,0.8872,0.3928,0.2834,0.4601,0.6150,0.4669,
The KS test for those 10 p-values: 0.233239
The 3DSPHERES test for dh-ranFile-2018-06-29_04:31
sample no r^3 equiv. uni.
1 24.324 0.555497
2 12.607 0.343114
3 21.251 0.507548
4 74.078 0.915352
5 30.271 0.635430
6 8.803 0.254299
7 17.738 0.446379
8 17.747 0.446535
9 28.623 0.614837
10 38.091 0.719083
11 17.431 0.440672
12 5.355 0.163478
13 24.155 0.552983
14 25.834 0.577324
15 49.076 0.805217
16 31.530 0.650414
17 71.959 0.909157
18 9.387 0.268672
19 17.746 0.446514
20 276.665 0.999901
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.179754
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-29_04:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 -1.2 -0.1 -2.3 -0.2 -1.1
1.5 0.2 -0.5 -1.3 -1.0 0.4
-0.8 -0.4 -0.2 -0.4 1.2 -0.5
0.3 0.5 -0.1 1.3 1.0 0.2
-0.3 -2.3 1.2 1.2 -0.0 -0.7
-2.0 0.9 1.1 -0.1 -0.2 -0.5
0.7 2.1 -0.4 1.5 -0.6 1.0
0.8
Chi-square with 42 degrees of freedom:45.284747
z-score=0.358395, p-value=0.663421
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-29_04:31
Test no p-value
1 0.885739
2 0.252160
3 0.772029
4 0.859347
5 0.270768
6 0.967222
7 0.571358
8 0.156764
9 0.798018
10 0.176555
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.523376
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-29_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 66413 0.97 66740 0.08
3 25000.00 25185 1.37 24917 0.28
4 6666.67 6763 1.39 6713 0.32
5 1388.89 1346 1.32 1362 0.52
6 238.10 247 0.33 238 0.00
7 34.72 35 0.00 24 3.31
8 4.96 10 5.12 5 0.00
p=0.89515 p=0.39186
Number of rngs required: 688180, p-value: 0.399
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-29_04:31
No. of wins: Observed Expected
98398 98585.9
z-score=-0.840, pvalue=0.20039
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66526 66666.7 0.297 0.297
2 37708 37654.3 0.077 0.373
3 27158 26954.7 1.533 1.906
4 19181 19313.5 0.908 2.815
5 14004 13851.4 1.681 4.495
6 9804 9943.5 1.958 6.454
7 7145 7145.0 0.000 6.454
8 5155 5139.1 0.049 6.503
9 3679 3699.9 0.118 6.621
10 2685 2666.3 0.131 6.752
11 1950 1923.3 0.370 7.122
12 1399 1388.7 0.076 7.198
13 994 1003.7 0.094 7.292
14 709 726.1 0.405 7.696
15 530 525.8 0.033 7.729
16 364 381.2 0.772 8.501
17 271 276.5 0.111 8.612
18 193 200.8 0.305 8.917
19 133 146.0 1.155 10.072
20 107 106.2 0.006 10.078
21 305 287.1 1.114 11.192
Chisq= 11.19 for 20 degrees of freedom, p= 0.05891
SUMMARY of craptest
p-value for no. of wins: 0.200394
p-value for throws/game: 0.058911
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-29_04:31
No. of wins: Observed Expected
98616 98585.9
z-score= 0.135, pvalue=0.55362
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66464 66666.7 0.616 0.616
2 37625 37654.3 0.023 0.639
3 27066 26954.7 0.459 1.098
4 19250 19313.5 0.209 1.307
5 13878 13851.4 0.051 1.358
6 10017 9943.5 0.543 1.900
7 7078 7145.0 0.629 2.529
8 5202 5139.1 0.771 3.300
9 3747 3699.9 0.600 3.900
10 2732 2666.3 1.619 5.519
11 1917 1923.3 0.021 5.540
12 1400 1388.7 0.091 5.631
13 1021 1003.7 0.298 5.929
14 728 726.1 0.005 5.934
15 545 525.8 0.698 6.632
16 356 381.2 1.660 8.292
17 272 276.5 0.075 8.366
18 169 200.8 5.045 13.411
19 151 146.0 0.172 13.583
20 100 106.2 0.364 13.947
21 282 287.1 0.091 14.038
Chisq= 14.04 for 20 degrees of freedom, p= 0.17145
SUMMARY of craptest
p-value for no. of wins: 0.553619
p-value for throws/game: 0.171447
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0080,0.0118,0.0163,0.0278,0.0281,0.0384,0.0429,0.0507,0.0560,0.0589,
0.0613,0.0820,0.0836,0.0854,0.0912,0.0918,0.0921,0.0960,0.0981,0.1070,
0.1195,0.1204,0.1298,0.1360,0.1399,0.1459,0.1506,0.1526,0.1535,0.1559,
0.1568,0.1572,0.1575,0.1576,0.1602,0.1605,0.1619,0.1635,0.1700,0.1703,
0.1714,0.1765,0.1765,0.1766,0.1798,0.1839,0.1909,0.1922,0.1929,0.1953,
0.2004,0.2136,0.2153,0.2160,0.2174,0.2258,0.2289,0.2294,0.2331,0.2332,
0.2383,0.2400,0.2426,0.2522,0.2541,0.2543,0.2545,0.2647,0.2648,0.2687,
0.2692,0.2694,0.2708,0.2734,0.2738,0.2764,0.2834,0.2872,0.2912,0.2927,
0.2957,0.2960,0.2981,0.2998,0.3118,0.3118,0.3135,0.3171,0.3206,0.3208,
0.3362,0.3406,0.3431,0.3440,0.3442,0.3493,0.3525,0.3569,0.3574,0.3624,
0.3649,0.3689,0.3689,0.3708,0.3731,0.3746,0.3792,0.3852,0.3904,0.3912,
0.3919,0.3928,0.3935,0.3987,0.3992,0.4018,0.4095,0.4216,0.4297,0.4310,
0.4375,0.4407,0.4443,0.4464,0.4465,0.4465,0.4520,0.4523,0.4562,0.4601,
0.4669,0.4678,0.4692,0.4693,0.4718,0.4725,0.4736,0.4787,0.4878,0.4899,
0.4995,0.5023,0.5075,0.5173,0.5183,0.5234,0.5234,0.5295,0.5431,0.5470,
0.5520,0.5530,0.5534,0.5536,0.5548,0.5555,0.5606,0.5609,0.5680,0.5692,
0.5714,0.5773,0.5805,0.5837,0.5849,0.5869,0.5872,0.5903,0.5910,0.5928,
0.6064,0.6148,0.6150,0.6213,0.6259,0.6268,0.6312,0.6354,0.6458,0.6504,
0.6575,0.6577,0.6594,0.6634,0.6669,0.6695,0.6703,0.6705,0.6719,0.6791,
0.6843,0.6923,0.6964,0.7001,0.7110,0.7113,0.7150,0.7181,0.7191,0.7196,
0.7288,0.7387,0.7468,0.7518,0.7540,0.7548,0.7638,0.7641,0.7652,0.7666,
0.7720,0.7733,0.7758,0.7812,0.7915,0.7980,0.8030,0.8052,0.8088,0.8097,
0.8116,0.8162,0.8193,0.8194,0.8322,0.8427,0.8471,0.8538,0.8582,0.8593,
0.8594,0.8606,0.8632,0.8653,0.8699,0.8752,0.8784,0.8857,0.8863,0.8872,
0.8951,0.8954,0.9092,0.9137,0.9154,0.9162,0.9187,0.9197,0.9211,0.9240,
0.9240,0.9265,0.9266,0.9281,0.9367,0.9385,0.9458,0.9503,0.9520,0.9640,
0.9672,0.9673,0.9693,0.9710,0.9719,0.9801,0.9911,0.9932,0.9999,
Overall p-value after applying KStest on 269 p-values = 0.452954
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.