RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-18_16:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.91 23.0329 0.851819
2 to 25 16.01 18.4922 0.641553
3 to 26 15.87 11.3855 0.164164
4 to 27 15.91 11.6083 0.176748
5 to 28 15.89 11.7229 0.183381
6 to 29 15.84 13.6028 0.305006
7 to 30 15.93 17.7147 0.592949
8 to 31 15.78 12.5228 0.232503
9 to 32 15.48 25.6566 0.919053
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.669817
Tough bday spacings test for dh-ranFile-2018-06-18_16:31: 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 12 40 73 94 88 80 47 35 18 10 3
(O-E)^2/E 0.9 0.3 0.0 0.1 1.0 0.0 0.5 0.9 0.7 1.7 0.3
Birthday Spacings: Sum(O-E)^2/E= 6.416, p= 0.221
RESULTS OF GCD FOR dh-ranFile-2018-06-18_16:31
Euclid's algorithm:
p-value, steps to gcd: 0.653371
p-value, dist. of gcd's: 0.818600
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-18_16:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.052 0.247 0.795 0.585 0.378 0.370 0.781 0.768
Bits 8 to 15---> 0.690 0.450 0.597 0.495 0.303 0.289 0.193 0.742
Bits 16 to 23---> 0.742 0.268 0.366 0.993 0.038 0.468 0.797 0.610
Bits 24 to 31---> 0.684 0.728 0.416 0.070 0.962 0.781 0.707 0.253
KS test for the above 32 p values: 0.376
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-18_16:31,
p-values for 5 runs: 0.7530, 0.6765, 0.0335, 0.7684, 0.8192
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-18_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 164 211.4 10.635 10.635
r= 29 5091 5134.0 0.360 10.995
r= 30 23182 23103.0 0.270 11.265
r= 31 11563 11551.5 0.011 11.277
chi-square = 11.277 with df = 3; p-value = 0.990
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-18_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 190 211.4 2.170 2.170
r= 30 5110 5134.0 0.112 2.282
r= 31 23227 23103.0 0.665 2.947
r= 32 11473 11551.5 0.534 3.481
chi-square = 3.481 with df = 3; p-value = 0.677
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-18_16:31
b-rank test for bits 1 to 8, p=0.65699
b-rank test for bits 2 to 9, p=0.39848
b-rank test for bits 3 to 10, p=0.22636
b-rank test for bits 4 to 11, p=0.27140
b-rank test for bits 5 to 12, p=0.26212
b-rank test for bits 6 to 13, p=0.23958
b-rank test for bits 7 to 14, p=0.38608
b-rank test for bits 8 to 15, p=0.33673
b-rank test for bits 9 to 16, p=0.00831
b-rank test for bits 10 to 17, p=0.54041
b-rank test for bits 11 to 18, p=0.52012
b-rank test for bits 12 to 19, p=0.79798
b-rank test for bits 13 to 20, p=0.48710
b-rank test for bits 14 to 21, p=0.83042
b-rank test for bits 15 to 22, p=0.85934
b-rank test for bits 16 to 23, p=0.85097
b-rank test for bits 17 to 24, p=0.48325
b-rank test for bits 18 to 25, p=0.80964
b-rank test for bits 19 to 26, p=0.83006
b-rank test for bits 20 to 27, p=0.15370
b-rank test for bits 21 to 28, p=0.14952
b-rank test for bits 22 to 29, p=0.83151
b-rank test for bits 23 to 30, p=0.87147
b-rank test for bits 24 to 31, p=0.51623
b-rank test for bits 25 to 32, p=0.70197
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 = 0.612138
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-18_16:31
(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 142137 0.53 0.702616
2 141966 0.13 0.552669
3 141626 -0.66 0.253990
4 142199 0.68 0.750733
5 142361 1.06 0.854357
6 141751 -0.37 0.355717
7 141766 -0.33 0.368857
8 141491 -0.98 0.164184
9 141989 0.19 0.573834
10 141902 -0.02 0.493168
11 141652 -0.60 0.273841
12 142855 2.21 0.986430
13 141695 -0.50 0.308266
14 142455 1.27 0.898833
15 141961 0.12 0.548045
16 141602 -0.72 0.236360
17 141373 -1.25 0.105083
18 141955 0.11 0.542489
19 141836 -0.17 0.431981
20 141881 -0.07 0.473613
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-18_16:31
Bits used No. missing words z-score p-value
23 to 32 141891 -0.0632 0.474801
22 to 31 142005 0.3299 0.629261
21 to 30 141629 -0.9667 0.166858
20 to 29 141559 -1.2080 0.113517
19 to 28 142014 0.3609 0.640925
18 to 27 141770 -0.4804 0.315454
17 to 26 141921 0.0402 0.516050
16 to 25 142030 0.4161 0.661333
15 to 24 141655 -0.8770 0.190243
14 to 23 141960 0.1747 0.569352
13 to 22 141899 -0.0356 0.485792
12 to 21 141611 -1.0287 0.151805
11 to 20 141632 -0.9563 0.169458
10 to 19 142084 0.6023 0.726516
9 to 18 141528 -1.3149 0.094267
8 to 17 141932 0.0782 0.531155
7 to 16 142030 0.4161 0.661333
6 to 15 141752 -0.5425 0.293731
5 to 14 141731 -0.6149 0.269300
4 to 13 142214 1.0506 0.853276
3 to 12 141204 -2.4322 0.007504
2 to 11 142339 1.4816 0.930779
1 to 10 141651 -0.8908 0.186520
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-18_16:31
Bits used No. missing words z-score p-value
28 to 32 142117 0.7040 0.759273
27 to 31 141745 -0.5571 0.288746
26 to 30 141510 -1.3537 0.087922
25 to 29 141583 -1.1062 0.134319
24 to 28 142106 0.6667 0.747511
23 to 27 141989 0.2701 0.606446
22 to 26 142293 1.3006 0.903298
21 to 25 141943 0.1141 0.545435
20 to 24 142141 0.7853 0.783868
19 to 23 141901 -0.0282 0.488737
18 to 22 141606 -1.0282 0.151919
17 to 21 141806 -0.3503 0.363068
16 to 20 141655 -0.8621 0.194306
15 to 19 142075 0.5616 0.712803
14 to 18 141947 0.1277 0.550805
13 to 17 141903 -0.0215 0.491440
12 to 16 141980 0.2396 0.594664
11 to 15 141907 -0.0079 0.496849
10 to 14 142172 0.8904 0.813376
9 to 13 141782 -0.4316 0.333006
8 to 12 141783 -0.4282 0.334239
7 to 11 142019 0.3718 0.644965
6 to 10 141655 -0.8621 0.194306
5 to 9 141819 -0.3062 0.379725
4 to 8 141686 -0.7571 0.224510
3 to 7 141464 -1.5096 0.065574
2 to 6 142504 2.0158 0.978091
1 to 5 142002 0.3141 0.623291
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-18_16:31
Bits used No. missing words z-score p-value
31 to 32 141309 -1.7709 0.038290
30 to 31 142135 0.6657 0.747196
29 to 30 142063 0.4533 0.674835
28 to 29 140996 -2.6942 0.003528
27 to 28 141211 -2.0600 0.019701
26 to 27 141605 -0.8977 0.184665
25 to 26 141676 -0.6883 0.245635
24 to 25 142085 0.5182 0.697841
23 to 24 142104 0.5742 0.717100
22 to 23 141651 -0.7620 0.223019
21 to 22 142079 0.5005 0.691639
20 to 21 142079 0.5005 0.691639
19 to 20 141975 0.1937 0.576801
18 to 19 142335 1.2557 0.895381
17 to 18 142012 0.3029 0.619002
16 to 17 142631 2.1288 0.983365
15 to 16 141968 0.1731 0.568701
14 to 15 141809 -0.2960 0.383631
13 to 14 141583 -0.9626 0.167868
12 to 13 142086 0.5212 0.698869
11 to 12 141879 -0.0895 0.464355
10 to 11 142432 1.5418 0.938439
9 to 10 141540 -1.0895 0.137974
8 to 9 141837 -0.2134 0.415522
7 to 8 142082 0.5094 0.694747
6 to 7 141708 -0.5939 0.276292
5 to 6 142370 1.3589 0.912912
4 to 5 141916 0.0197 0.507849
3 to 4 142062 0.4504 0.673772
2 to 3 141798 -0.3284 0.371302
1 to 2 142172 0.7748 0.780782
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-18_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2440.51 -0.841 0.200089
Test results for specific bytes for dh-ranFile-2018-06-18_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2366.86 -1.883 0.029862
2 to 9 2490.49 -0.134 0.446517
3 to 10 2592.12 1.303 0.903680
4 to 11 2560.07 0.850 0.802201
5 to 12 2468.99 -0.438 0.330520
6 to 13 2389.69 -1.560 0.059383
7 to 14 2374.14 -1.780 0.037549
8 to 15 2422.14 -1.101 0.135415
9 to 16 2437.62 -0.882 0.188833
10 to 17 2580.13 1.133 0.871436
11 to 18 2483.85 -0.228 0.409654
12 to 19 2443.08 -0.805 0.210405
13 to 20 2509.09 0.129 0.551132
14 to 21 2477.50 -0.318 0.375185
15 to 22 2609.26 1.545 0.938840
16 to 23 2546.53 0.658 0.744762
17 to 24 2519.11 0.270 0.606494
18 to 25 2500.24 0.003 0.501327
19 to 26 2623.10 1.741 0.959147
20 to 27 2577.16 1.091 0.862407
21 to 28 2470.62 -0.416 0.338881
22 to 29 2462.36 -0.532 0.297280
23 to 30 2417.40 -1.168 0.121370
24 to 31 2582.72 1.170 0.878970
25 to 32 2466.06 -0.480 0.315616
CDPARK for dh-ranFile-2018-06-18_16:31: 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
3500 -1.0502 0.146807
3535 0.5479 0.708135
3513 -0.4566 0.323972
3500 -1.0502 0.146807
3497 -1.1872 0.117571
3521 -0.0913 0.463617
3535 0.5479 0.708135
3534 0.5023 0.692266
3528 0.2283 0.590298
3510 -0.5936 0.276387
Square side=100, avg. no. parked=3517.30 sample std.=14.55
p-value of the KSTEST for those 10 p-values: 0.444578
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-18_16:31
0.3838,0.5884,0.4717,0.9921,0.3433,0.3884,0.8256,0.5207,0.5687,0.9331,
The KS test for those 10 p-values: 0.247310
The 3DSPHERES test for dh-ranFile-2018-06-18_16:31
sample no r^3 equiv. uni.
1 63.576 0.879873
2 25.352 0.570469
3 14.110 0.375200
4 13.391 0.360045
5 6.773 0.202089
6 19.757 0.482400
7 25.584 0.573785
8 22.227 0.523313
9 11.614 0.321011
10 39.533 0.732269
11 34.971 0.688295
12 10.301 0.290633
13 148.782 0.992983
14 162.304 0.995529
15 86.555 0.944154
16 17.580 0.443443
17 29.605 0.627242
18 16.392 0.420963
19 49.297 0.806643
20 28.755 0.616535
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.125313
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-18_16:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 -0.7 -1.1 0.9 1.1 1.0
-0.7 -0.0 -0.1 -0.7 1.0 0.2
-0.5 0.2 0.2 -0.0 0.2 1.9
0.6 -0.5 0.1 -1.6 0.3 -2.9
0.4 0.5 -1.5 -0.1 0.8 1.1
0.2 -0.4 -0.2 0.4 -0.8 -0.1
0.5 0.8 -1.2 -0.1 0.1 -1.0
1.8
Chi-square with 42 degrees of freedom:36.187055
z-score=-0.634244, p-value=0.276782
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-18_16:31
Test no p-value
1 0.184384
2 0.503335
3 0.276041
4 0.253835
5 0.147347
6 0.040612
7 0.262328
8 0.936936
9 0.726413
10 0.265808
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.149665
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-18_16:31:
(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 66705 0.02 66677 0.00
3 25000.00 24860 0.78 24985 0.01
4 6666.67 6750 1.04 6689 0.07
5 1388.89 1388 0.00 1387 0.00
6 238.10 256 1.35 227 0.52
7 34.72 38 0.31 33 0.09
8 4.96 2 1.77 1 3.16
p=0.49044 p=0.30328
Number of rngs required: 688231, p-value: 0.422
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-18_16:31
No. of wins: Observed Expected
98840 98585.9
z-score= 1.137, pvalue=0.87216
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67329 66666.7 6.580 6.580
2 37177 37654.3 6.051 12.631
3 26958 26954.7 0.000 12.631
4 19104 19313.5 2.272 14.903
5 13943 13851.4 0.605 15.509
6 10007 9943.5 0.405 15.914
7 7093 7145.0 0.379 16.292
8 5108 5139.1 0.188 16.480
9 3634 3699.9 1.173 17.653
10 2669 2666.3 0.003 17.655
11 1885 1923.3 0.764 18.419
12 1388 1388.7 0.000 18.420
13 1015 1003.7 0.127 18.547
14 747 726.1 0.599 19.146
15 534 525.8 0.127 19.273
16 374 381.2 0.134 19.407
17 277 276.5 0.001 19.407
18 206 200.8 0.133 19.541
19 157 146.0 0.831 20.372
20 120 106.2 1.789 22.161
21 275 287.1 0.511 22.672
Chisq= 22.67 for 20 degrees of freedom, p= 0.69481
SUMMARY of craptest
p-value for no. of wins: 0.872162
p-value for throws/game: 0.694811
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-18_16:31
No. of wins: Observed Expected
98441 98585.9
z-score=-0.648, pvalue=0.25853
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66823 66666.7 0.367 0.367
2 37552 37654.3 0.278 0.645
3 26823 26954.7 0.644 1.288
4 19190 19313.5 0.789 2.078
5 13900 13851.4 0.170 2.248
6 10106 9943.5 2.654 4.902
7 7142 7145.0 0.001 4.904
8 5090 5139.1 0.469 5.372
9 3676 3699.9 0.154 5.526
10 2673 2666.3 0.017 5.543
11 1910 1923.3 0.092 5.635
12 1359 1388.7 0.637 6.272
13 1011 1003.7 0.053 6.325
14 782 726.1 4.297 10.622
15 557 525.8 1.847 12.469
16 398 381.2 0.745 13.214
17 266 276.5 0.402 13.616
18 198 200.8 0.040 13.656
19 148 146.0 0.028 13.683
20 107 106.2 0.006 13.689
21 289 287.1 0.012 13.702
Chisq= 13.70 for 20 degrees of freedom, p= 0.15470
SUMMARY of craptest
p-value for no. of wins: 0.258527
p-value for throws/game: 0.154699
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0035,0.0075,0.0083,0.0197,0.0299,0.0335,0.0375,0.0380,0.0383,0.0406,
0.0519,0.0594,0.0656,0.0699,0.0879,0.0943,0.1051,0.1135,0.1176,0.1214,
0.1253,0.1343,0.1354,0.1380,0.1468,0.1468,0.1473,0.1495,0.1497,0.1518,
0.1519,0.1537,0.1547,0.1642,0.1642,0.1669,0.1679,0.1695,0.1767,0.1834,
0.1844,0.1847,0.1865,0.1888,0.1902,0.1929,0.1943,0.1943,0.2001,0.2021,
0.2104,0.2208,0.2230,0.2245,0.2264,0.2325,0.2364,0.2396,0.2456,0.2473,
0.2475,0.2525,0.2538,0.2540,0.2585,0.2621,0.2623,0.2658,0.2675,0.2693,
0.2714,0.2738,0.2760,0.2763,0.2764,0.2768,0.2887,0.2890,0.2906,0.2937,
0.2973,0.3027,0.3033,0.3050,0.3083,0.3155,0.3156,0.3210,0.3240,0.3305,
0.3330,0.3342,0.3367,0.3389,0.3433,0.3557,0.3600,0.3631,0.3662,0.3689,
0.3704,0.3713,0.3752,0.3752,0.3760,0.3778,0.3797,0.3836,0.3838,0.3861,
0.3884,0.3985,0.4097,0.4155,0.4159,0.4210,0.4216,0.4320,0.4434,0.4446,
0.4465,0.4497,0.4636,0.4644,0.4680,0.4717,0.4736,0.4748,0.4824,0.4833,
0.4858,0.4871,0.4887,0.4904,0.4914,0.4932,0.4951,0.4968,0.5013,0.5033,
0.5078,0.5160,0.5162,0.5201,0.5207,0.5233,0.5312,0.5404,0.5425,0.5454,
0.5480,0.5508,0.5511,0.5527,0.5687,0.5687,0.5694,0.5705,0.5738,0.5738,
0.5768,0.5851,0.5884,0.5903,0.5929,0.5947,0.5972,0.6064,0.6065,0.6103,
0.6121,0.6165,0.6190,0.6233,0.6272,0.6293,0.6409,0.6416,0.6450,0.6534,
0.6570,0.6613,0.6613,0.6698,0.6738,0.6748,0.6765,0.6768,0.6837,0.6883,
0.6901,0.6916,0.6916,0.6923,0.6947,0.6948,0.6978,0.6989,0.7020,0.7026,
0.7068,0.7081,0.7081,0.7128,0.7171,0.7264,0.7265,0.7283,0.7323,0.7416,
0.7419,0.7448,0.7472,0.7475,0.7507,0.7530,0.7593,0.7682,0.7684,0.7808,
0.7813,0.7813,0.7839,0.7948,0.7971,0.7980,0.8022,0.8066,0.8096,0.8134,
0.8186,0.8192,0.8256,0.8301,0.8304,0.8315,0.8510,0.8518,0.8533,0.8544,
0.8593,0.8624,0.8714,0.8715,0.8722,0.8790,0.8799,0.8954,0.8988,0.9033,
0.9037,0.9129,0.9191,0.9308,0.9331,0.9369,0.9384,0.9388,0.9442,0.9591,
0.9620,0.9781,0.9834,0.9864,0.9897,0.9921,0.9930,0.9935,0.9955,
Overall p-value after applying KStest on 269 p-values = 0.228141
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.