RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-28_06:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.89 19.7559 0.713095
2 to 25 15.72 16.2463 0.493554
3 to 26 15.69 16.0458 0.479407
4 to 27 15.41 27.6057 0.950239
5 to 28 15.54 31.0953 0.980554
6 to 29 15.86 19.5268 0.700854
7 to 30 15.47 35.3306 0.994372
8 to 31 15.78 10.7699 0.131726
9 to 32 15.54 30.5145 0.977135
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.008727
Tough bday spacings test for dh-ranFile-2018-06-28_06:31: 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 35 85 99 83 90 51 27 11 6 3
(O-E)^2/E 0.1 0.1 1.9 0.0 2.2 1.8 0.0 0.3 1.0 0.1 0.3
Birthday Spacings: Sum(O-E)^2/E= 7.685, p= 0.340
RESULTS OF GCD FOR dh-ranFile-2018-06-28_06:31
Euclid's algorithm:
p-value, steps to gcd: 0.630497
p-value, dist. of gcd's: 0.098676
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-28_06:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.116 0.517 0.674 0.918 0.345 0.682 0.661 0.191
Bits 8 to 15---> 0.440 0.493 0.628 0.022 0.172 0.992 0.144 0.010
Bits 16 to 23---> 0.018 0.303 0.442 0.855 0.507 0.582 0.569 0.979
Bits 24 to 31---> 0.217 0.183 0.214 0.415 0.292 0.137 0.757 0.129
KS test for the above 32 p values: 0.791
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-28_06:31,
p-values for 5 runs: 0.1786, 0.8082, 0.3842, 0.2054, 0.0157
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-28_06:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 200 211.4 0.617 0.617
r= 29 5222 5134.0 1.508 2.125
r= 30 23031 23103.0 0.225 2.349
r= 31 11547 11551.5 0.002 2.351
chi-square = 2.351 with df = 3; p-value = 0.497
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-28_06:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 210 211.4 0.010 0.010
r= 30 5251 5134.0 2.666 2.675
r= 31 23074 23103.0 0.037 2.712
r= 32 11465 11551.5 0.648 3.360
chi-square = 3.360 with df = 3; p-value = 0.661
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-28_06:31
b-rank test for bits 1 to 8, p=0.45400
b-rank test for bits 2 to 9, p=0.54557
b-rank test for bits 3 to 10, p=0.63534
b-rank test for bits 4 to 11, p=0.09189
b-rank test for bits 5 to 12, p=0.44326
b-rank test for bits 6 to 13, p=0.60526
b-rank test for bits 7 to 14, p=0.24836
b-rank test for bits 8 to 15, p=0.78027
b-rank test for bits 9 to 16, p=0.29573
b-rank test for bits 10 to 17, p=0.90062
b-rank test for bits 11 to 18, p=0.12931
b-rank test for bits 12 to 19, p=0.86492
b-rank test for bits 13 to 20, p=0.97693
b-rank test for bits 14 to 21, p=0.90867
b-rank test for bits 15 to 22, p=0.13112
b-rank test for bits 16 to 23, p=0.19838
b-rank test for bits 17 to 24, p=0.25071
b-rank test for bits 18 to 25, p=0.54976
b-rank test for bits 19 to 26, p=0.07459
b-rank test for bits 20 to 27, p=0.82651
b-rank test for bits 21 to 28, p=0.70789
b-rank test for bits 22 to 29, p=0.34156
b-rank test for bits 23 to 30, p=0.80090
b-rank test for bits 24 to 31, p=0.01346
b-rank test for bits 25 to 32, p=0.75990
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 = 0.997095
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-28_06:31
(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 141546 -0.85 0.197968
2 142774 2.02 0.978322
3 142001 0.21 0.584798
4 142252 0.80 0.788327
5 142477 1.33 0.907635
6 142405 1.16 0.876590
7 142369 1.07 0.858588
8 142113 0.48 0.682915
9 142162 0.59 0.722522
10 142322 0.96 0.832523
11 141765 -0.34 0.367976
12 141596 -0.73 0.232060
13 141601 -0.72 0.235640
14 141980 0.17 0.565574
15 142208 0.70 0.757357
16 142950 2.43 0.992481
17 142146 0.55 0.709857
18 141844 -0.15 0.439341
19 142053 0.34 0.631443
20 142515 1.42 0.921483
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-28_06:31
Bits used No. missing words z-score p-value
23 to 32 141811 -0.3391 0.367279
22 to 31 141501 -1.4080 0.079560
21 to 30 142061 0.5230 0.699513
20 to 29 141541 -1.2701 0.102024
19 to 28 142312 1.3885 0.917510
18 to 27 141720 -0.6529 0.256923
17 to 26 141816 -0.3218 0.373792
16 to 25 141403 -1.7460 0.040408
15 to 24 142386 1.6437 0.949880
14 to 23 141472 -1.5080 0.065773
13 to 22 142343 1.4954 0.932597
12 to 21 141811 -0.3391 0.367279
11 to 20 142173 0.9092 0.818380
10 to 19 142088 0.6161 0.731087
9 to 18 141929 0.0678 0.527039
8 to 17 141827 -0.2839 0.388245
7 to 16 142011 0.3506 0.637051
6 to 15 141359 -1.8977 0.028868
5 to 14 141441 -1.6149 0.053163
4 to 13 142114 0.7058 0.759831
3 to 12 142309 1.3782 0.915925
2 to 11 141967 0.1989 0.578815
1 to 10 142086 0.6092 0.728806
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-28_06:31
Bits used No. missing words z-score p-value
28 to 32 141893 -0.0554 0.477928
27 to 31 142219 1.0497 0.853079
26 to 30 141995 0.2904 0.614248
25 to 29 142325 1.4091 0.920590
24 to 28 141999 0.3040 0.619423
23 to 27 142494 1.9819 0.976257
22 to 26 141905 -0.0147 0.494145
21 to 25 141912 0.0091 0.503611
20 to 24 141777 -0.4486 0.326869
19 to 23 141970 0.2057 0.581472
18 to 22 142008 0.3345 0.630989
17 to 21 141578 -1.1232 0.130686
16 to 20 141658 -0.8520 0.197116
15 to 19 142248 1.1480 0.874523
14 to 18 141308 -2.0384 0.020755
13 to 17 141720 -0.6418 0.260503
12 to 16 141593 -1.0723 0.141792
11 to 15 141799 -0.3740 0.354202
10 to 14 141702 -0.7028 0.241086
9 to 13 142015 0.3582 0.639905
8 to 12 141947 0.1277 0.550805
7 to 11 141624 -0.9672 0.166717
6 to 10 141481 -1.4520 0.073256
5 to 9 142232 1.0938 0.862978
4 to 8 141644 -0.8994 0.184214
3 to 7 142404 1.6768 0.953214
2 to 6 141774 -0.4587 0.323208
1 to 5 142150 0.8158 0.792702
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-28_06:31
Bits used No. missing words z-score p-value
31 to 32 142580 1.9784 0.976057
30 to 31 141490 -1.2370 0.108051
29 to 30 142092 0.5388 0.705005
28 to 29 142055 0.4297 0.666295
27 to 28 142403 1.4563 0.927339
26 to 27 141067 -2.4847 0.006482
25 to 26 141952 0.1259 0.550083
24 to 25 141831 -0.2311 0.408633
23 to 24 142016 0.3147 0.623490
22 to 23 141999 0.2645 0.604308
21 to 22 141871 -0.1131 0.454988
20 to 21 142151 0.7129 0.762043
19 to 20 141851 -0.1721 0.431693
18 to 19 141325 -1.7237 0.042382
17 to 18 142178 0.7925 0.785976
16 to 17 142250 1.0049 0.842534
15 to 16 141972 0.1849 0.573333
14 to 15 141660 -0.7355 0.231022
13 to 14 141978 0.2026 0.580263
12 to 13 141827 -0.2429 0.404056
11 to 12 141732 -0.5231 0.300453
10 to 11 141326 -1.7207 0.042649
9 to 10 141566 -1.0128 0.155584
8 to 9 141752 -0.4641 0.321288
7 to 8 142077 0.4946 0.689559
6 to 7 141951 0.1229 0.548915
5 to 6 141728 -0.5349 0.296361
4 to 5 141915 0.0167 0.506672
3 to 4 141994 0.2498 0.598615
2 to 3 141964 0.1613 0.564059
1 to 2 141430 -1.4140 0.078688
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-28_06:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2521.41 0.303 0.618968
Test results for specific bytes for dh-ranFile-2018-06-28_06:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2531.78 0.449 0.673434
2 to 9 2654.34 2.183 0.985473
3 to 10 2470.12 -0.423 0.336311
4 to 11 2483.68 -0.231 0.408742
5 to 12 2616.36 1.646 0.950082
6 to 13 2441.83 -0.823 0.205343
7 to 14 2544.68 0.632 0.736246
8 to 15 2564.06 0.906 0.817510
9 to 16 2435.31 -0.915 0.180117
10 to 17 2478.22 -0.308 0.379055
11 to 18 2503.90 0.055 0.522012
12 to 19 2510.49 0.148 0.558942
13 to 20 2521.89 0.310 0.621579
14 to 21 2516.19 0.229 0.590560
15 to 22 2410.93 -1.260 0.103903
16 to 23 2579.53 1.125 0.869648
17 to 24 2511.50 0.163 0.564595
18 to 25 2421.40 -1.112 0.133159
19 to 26 2524.98 0.353 0.638077
20 to 27 2543.05 0.609 0.728668
21 to 28 2561.51 0.870 0.807832
22 to 29 2598.87 1.398 0.918970
23 to 30 2506.67 0.094 0.537591
24 to 31 2400.93 -1.401 0.080592
25 to 32 2472.54 -0.388 0.348870
CDPARK for dh-ranFile-2018-06-28_06:31: 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
3526 0.1370 0.554479
3508 -0.6849 0.246694
3548 1.1416 0.873180
3520 -0.1370 0.445521
3554 1.4155 0.921543
3542 0.8676 0.807188
3551 1.2785 0.899470
3522 -0.0457 0.481790
3535 0.5479 0.708135
3495 -1.2785 0.100530
Square side=100, avg. no. parked=3530.10 sample std.=18.44
p-value of the KSTEST for those 10 p-values: 0.452406
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-28_06:31
0.2128,0.2661,0.5821,0.1922,0.0287,0.7204,0.0307,0.2023,0.9284,0.3339,
The KS test for those 10 p-values: 0.124895
The 3DSPHERES test for dh-ranFile-2018-06-28_06:31
sample no r^3 equiv. uni.
1 5.827 0.176521
2 5.319 0.162474
3 6.483 0.194346
4 25.209 0.568414
5 17.537 0.442653
6 74.259 0.915862
7 29.365 0.624252
8 38.351 0.721511
9 25.511 0.572742
10 7.771 0.228211
11 18.044 0.451996
12 66.647 0.891563
13 86.924 0.944838
14 27.194 0.596047
15 66.274 0.890205
16 21.420 0.510324
17 20.498 0.495037
18 79.667 0.929740
19 65.708 0.888111
20 45.923 0.783631
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.161800
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-28_06:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -0.3 2.0 2.7 0.5 1.6
-0.1 -1.4 0.1 0.3 0.2 0.1
-0.6 -1.5 2.2 -0.2 0.7 -0.4
-0.4 -0.9 -0.2 -0.3 0.7 1.1
-1.0 2.4 -1.3 -0.0 -0.2 -0.8
-0.1 -0.1 -0.5 -1.0 -1.0 0.1
-1.2 -0.7 0.9 1.5 0.1 -1.0
-1.1
Chi-square with 42 degrees of freedom:45.876406
z-score=0.422951, p-value=0.685408
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-28_06:31
Test no p-value
1 0.085937
2 0.759112
3 0.002063
4 0.860611
5 0.008918
6 0.021485
7 0.028699
8 0.201837
9 0.070467
10 0.887055
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.000606
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-28_06:31:
(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 66777 0.18 66401 1.06
3 25000.00 25082 0.27 25153 0.94
4 6666.67 6478 5.34 6787 2.17
5 1388.89 1372 0.21 1405 0.19
6 238.10 254 1.06 212 2.86
7 34.72 32 0.21 38 0.31
8 4.96 4 0.19 3 0.77
p=0.71942 p=0.78294
Number of rngs required: 687550, p-value: 0.162
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-28_06:31
No. of wins: Observed Expected
98516 98585.9
z-score=-0.312, pvalue=0.37735
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66621 66666.7 0.031 0.031
2 37628 37654.3 0.018 0.050
3 26897 26954.7 0.124 0.173
4 19307 19313.5 0.002 0.175
5 13843 13851.4 0.005 0.181
6 10030 9943.5 0.752 0.932
7 7368 7145.0 6.958 7.891
8 5273 5139.1 3.490 11.381
9 3661 3699.9 0.408 11.789
10 2619 2666.3 0.839 12.628
11 1840 1923.3 3.610 16.238
12 1364 1388.7 0.441 16.679
13 994 1003.7 0.094 16.773
14 673 726.1 3.889 20.662
15 505 525.8 0.826 21.488
16 354 381.2 1.934 23.422
17 297 276.5 1.514 24.936
18 209 200.8 0.332 25.268
19 147 146.0 0.007 25.275
20 96 106.2 0.982 26.258
21 274 287.1 0.599 26.857
Chisq= 26.86 for 20 degrees of freedom, p= 0.86065
SUMMARY of craptest
p-value for no. of wins: 0.377350
p-value for throws/game: 0.860651
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-28_06:31
No. of wins: Observed Expected
98758 98585.9
z-score= 0.770, pvalue=0.77933
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66451 66666.7 0.698 0.698
2 37750 37654.3 0.243 0.941
3 27084 26954.7 0.620 1.561
4 19178 19313.5 0.950 2.511
5 13957 13851.4 0.805 3.316
6 9958 9943.5 0.021 3.337
7 7164 7145.0 0.050 3.387
8 5100 5139.1 0.297 3.684
9 3647 3699.9 0.755 4.439
10 2682 2666.3 0.092 4.532
11 1949 1923.3 0.343 4.875
12 1430 1388.7 1.226 6.100
13 966 1003.7 1.417 7.518
14 724 726.1 0.006 7.524
15 513 525.8 0.313 7.837
16 408 381.2 1.891 9.729
17 296 276.5 1.369 11.098
18 221 200.8 2.026 13.124
19 160 146.0 1.346 14.469
20 83 106.2 5.074 19.543
21 279 287.1 0.229 19.773
Chisq= 19.77 for 20 degrees of freedom, p= 0.52778
SUMMARY of craptest
p-value for no. of wins: 0.779325
p-value for throws/game: 0.527778
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0006,0.0021,0.0065,0.0087,0.0089,0.0097,0.0135,0.0157,0.0179,0.0208,
0.0215,0.0224,0.0287,0.0287,0.0289,0.0307,0.0404,0.0424,0.0426,0.0532,
0.0658,0.0705,0.0733,0.0746,0.0787,0.0796,0.0806,0.0859,0.0919,0.0987,
0.1005,0.1020,0.1039,0.1081,0.1161,0.1249,0.1288,0.1293,0.1307,0.1311,
0.1317,0.1332,0.1366,0.1418,0.1438,0.1556,0.1615,0.1618,0.1625,0.1667,
0.1725,0.1765,0.1786,0.1801,0.1827,0.1842,0.1908,0.1922,0.1943,0.1971,
0.1980,0.1984,0.2018,0.2023,0.2053,0.2054,0.2128,0.2137,0.2168,0.2282,
0.2310,0.2321,0.2356,0.2411,0.2467,0.2484,0.2507,0.2569,0.2605,0.2661,
0.2920,0.2957,0.2964,0.3005,0.3029,0.3213,0.3232,0.3269,0.3339,0.3363,
0.3404,0.3416,0.3453,0.3489,0.3542,0.3673,0.3673,0.3680,0.3738,0.3773,
0.3791,0.3842,0.3882,0.4041,0.4086,0.4087,0.4147,0.4317,0.4393,0.4399,
0.4424,0.4427,0.4433,0.4455,0.4520,0.4524,0.4540,0.4550,0.4779,0.4794,
0.4818,0.4935,0.4936,0.4941,0.4950,0.4972,0.5036,0.5066,0.5067,0.5103,
0.5172,0.5220,0.5270,0.5278,0.5376,0.5456,0.5489,0.5498,0.5501,0.5508,
0.5545,0.5589,0.5641,0.5646,0.5656,0.5684,0.5686,0.5727,0.5733,0.5788,
0.5803,0.5815,0.5820,0.5821,0.5848,0.5906,0.5960,0.5986,0.6043,0.6053,
0.6142,0.6190,0.6194,0.6216,0.6235,0.6243,0.6281,0.6305,0.6310,0.6314,
0.6353,0.6371,0.6381,0.6399,0.6606,0.6606,0.6663,0.6734,0.6741,0.6824,
0.6829,0.6854,0.6896,0.6995,0.7009,0.7050,0.7079,0.7081,0.7099,0.7131,
0.7194,0.7204,0.7215,0.7225,0.7287,0.7288,0.7311,0.7362,0.7572,0.7574,
0.7591,0.7598,0.7599,0.7620,0.7793,0.7803,0.7829,0.7836,0.7860,0.7883,
0.7912,0.7927,0.8009,0.8072,0.8078,0.8082,0.8175,0.8184,0.8265,0.8325,
0.8425,0.8531,0.8549,0.8586,0.8606,0.8607,0.8630,0.8649,0.8696,0.8732,
0.8745,0.8766,0.8871,0.8881,0.8902,0.8916,0.8995,0.9006,0.9076,0.9087,
0.9159,0.9159,0.9175,0.9178,0.9190,0.9206,0.9215,0.9215,0.9273,0.9284,
0.9297,0.9326,0.9448,0.9499,0.9501,0.9502,0.9532,0.9761,0.9763,0.9769,
0.9771,0.9783,0.9790,0.9806,0.9855,0.9918,0.9925,0.9944,0.9971,
Overall p-value after applying KStest on 269 p-values = 0.503561
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.