RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-24_05:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.58 12.9147 0.258120
2 to 25 16.01 18.4186 0.637095
3 to 26 16.01 15.6740 0.452948
4 to 27 15.96 27.9737 0.954753
5 to 28 15.89 6.7943 0.013940
6 to 29 15.79 15.7705 0.459844
7 to 30 15.81 11.5914 0.175775
8 to 31 15.51 14.0253 0.334690
9 to 32 15.75 15.1687 0.416669
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.501115
Tough bday spacings test for dh-ranFile-2018-06-24_05:31: 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 9 39 69 108 91 80 44 29 18 8 5
(O-E)^2/E 0.0 0.2 0.2 1.1 0.5 0.0 1.3 0.0 0.7 0.3 0.2
Birthday Spacings: Sum(O-E)^2/E= 4.429, p= 0.074
RESULTS OF GCD FOR dh-ranFile-2018-06-24_05:31
Euclid's algorithm:
p-value, steps to gcd: 0.921552
p-value, dist. of gcd's: 0.229464
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-24_05:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.613 0.916 0.771 0.957 0.668 0.215 0.266 0.710
Bits 8 to 15---> 0.668 0.822 0.071 0.995 0.264 0.485 0.844 0.373
Bits 16 to 23---> 0.872 0.517 0.413 0.609 0.551 0.850 0.140 0.388
Bits 24 to 31---> 0.073 0.657 0.704 0.699 0.533 0.977 0.002 0.066
KS test for the above 32 p values: 0.524
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-24_05:31,
p-values for 5 runs: 0.2466, 0.7959, 0.2175, 0.3167, 0.4927
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-24_05:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 227 211.4 1.148 1.148
r= 29 5154 5134.0 0.078 1.226
r= 30 23212 23103.0 0.514 1.740
r= 31 11407 11551.5 1.808 3.548
chi-square = 3.548 with df = 3; p-value = 0.685
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-24_05:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 229 211.4 1.462 1.462
r= 30 5101 5134.0 0.212 1.674
r= 31 23227 23103.0 0.665 2.339
r= 32 11443 11551.5 1.020 3.359
chi-square = 3.359 with df = 3; p-value = 0.660
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-24_05:31
b-rank test for bits 1 to 8, p=0.71509
b-rank test for bits 2 to 9, p=0.46335
b-rank test for bits 3 to 10, p=0.79237
b-rank test for bits 4 to 11, p=0.02124
b-rank test for bits 5 to 12, p=0.05326
b-rank test for bits 6 to 13, p=0.78692
b-rank test for bits 7 to 14, p=0.14437
b-rank test for bits 8 to 15, p=0.45627
b-rank test for bits 9 to 16, p=0.15421
b-rank test for bits 10 to 17, p=0.56740
b-rank test for bits 11 to 18, p=0.68606
b-rank test for bits 12 to 19, p=0.29959
b-rank test for bits 13 to 20, p=0.01425
b-rank test for bits 14 to 21, p=0.46520
b-rank test for bits 15 to 22, p=0.56686
b-rank test for bits 16 to 23, p=0.96809
b-rank test for bits 17 to 24, p=0.91881
b-rank test for bits 18 to 25, p=0.50920
b-rank test for bits 19 to 26, p=0.99609
b-rank test for bits 20 to 27, p=0.99951
b-rank test for bits 21 to 28, p=0.98633
b-rank test for bits 22 to 29, p=0.64216
b-rank test for bits 23 to 30, p=0.20597
b-rank test for bits 24 to 31, p=0.10958
b-rank test for bits 25 to 32, p=0.37998
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 = 0.299082
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-24_05:31
(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 141022 -2.07 0.019077
2 141449 -1.08 0.141067
3 141832 -0.18 0.428310
4 142311 0.94 0.826001
5 141542 -0.86 0.195378
6 142355 1.04 0.851128
7 141143 -1.79 0.036688
8 141668 -0.56 0.286426
9 142503 1.39 0.917291
10 141682 -0.53 0.297659
11 141397 -1.20 0.115647
12 142024 0.27 0.605620
13 141759 -0.35 0.362705
14 141580 -0.77 0.220809
15 141606 -0.71 0.239251
16 141377 -1.24 0.106794
17 141759 -0.35 0.362705
18 140889 -2.38 0.008564
19 142392 1.13 0.870284
20 141463 -1.04 0.148514
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-24_05:31
Bits used No. missing words z-score p-value
23 to 32 141188 -2.4873 0.006435
22 to 31 141369 -1.8632 0.031217
21 to 30 142285 1.2954 0.902411
20 to 29 142035 0.4333 0.667618
19 to 28 141730 -0.6184 0.268163
18 to 27 141929 0.0678 0.527039
17 to 26 142037 0.4402 0.670119
16 to 25 141987 0.2678 0.605584
15 to 24 141671 -0.8218 0.205588
14 to 23 141959 0.1713 0.567997
13 to 22 141433 -1.6425 0.050241
12 to 21 141849 -0.2080 0.417601
11 to 20 142397 1.6816 0.953679
10 to 19 142265 1.2264 0.889985
9 to 18 141687 -0.7667 0.221643
8 to 17 142057 0.5092 0.694696
7 to 16 142000 0.3127 0.622729
6 to 15 142334 1.4644 0.928455
5 to 14 142429 1.7920 0.963431
4 to 13 141850 -0.2046 0.418948
3 to 12 142008 0.3402 0.633163
2 to 11 142092 0.6299 0.735619
1 to 10 142319 1.4127 0.921121
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-24_05:31
Bits used No. missing words z-score p-value
28 to 32 141904 -0.0181 0.492792
27 to 31 142046 0.4633 0.678421
26 to 30 142197 0.9752 0.835258
25 to 29 141650 -0.8791 0.189678
24 to 28 141766 -0.4859 0.313532
23 to 27 141814 -0.3232 0.373290
22 to 26 142282 1.2633 0.896757
21 to 25 141568 -1.1571 0.123626
20 to 24 141905 -0.0147 0.494145
19 to 23 141879 -0.1028 0.459056
18 to 22 141971 0.2091 0.582796
17 to 21 142210 1.0192 0.845951
16 to 20 142237 1.1107 0.866661
15 to 19 141650 -0.8791 0.189678
14 to 18 142138 0.7752 0.780875
13 to 17 142042 0.4497 0.673547
12 to 16 142269 1.2192 0.888620
11 to 15 141881 -0.0960 0.461747
10 to 14 141614 -1.0011 0.158385
9 to 13 141532 -1.2791 0.100434
8 to 12 141981 0.2429 0.595978
7 to 11 141863 -0.1571 0.437602
6 to 10 142019 0.3718 0.644965
5 to 9 142063 0.5209 0.698787
4 to 8 142288 1.2836 0.900364
3 to 7 141694 -0.7299 0.232716
2 to 6 142298 1.3175 0.906169
1 to 5 141595 -1.0655 0.143319
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-24_05:31
Bits used No. missing words z-score p-value
31 to 32 142481 1.6863 0.954135
30 to 31 142301 1.1554 0.876030
29 to 30 142330 1.2409 0.892681
28 to 29 141785 -0.3668 0.356901
27 to 28 142728 2.4150 0.992131
26 to 27 141687 -0.6558 0.255963
25 to 26 141030 -2.5939 0.004745
24 to 25 141900 -0.0275 0.489022
23 to 24 141817 -0.2724 0.392673
22 to 23 142156 0.7276 0.766583
21 to 22 142005 0.2822 0.611110
20 to 21 141808 -0.2989 0.382505
19 to 20 142171 0.7719 0.779910
18 to 19 141934 0.0728 0.529007
17 to 18 141442 -1.3786 0.084016
16 to 17 141569 -1.0039 0.157708
15 to 16 142051 0.4179 0.661992
14 to 15 141607 -0.8918 0.186242
13 to 14 142100 0.5624 0.713095
12 to 13 141769 -0.4140 0.339454
11 to 12 142208 0.8810 0.810850
10 to 11 141612 -0.8771 0.190222
9 to 10 142332 1.2468 0.893767
8 to 9 141573 -0.9921 0.160569
7 to 8 141612 -0.8771 0.190222
6 to 7 141791 -0.3491 0.363524
5 to 6 142031 0.3589 0.640168
4 to 5 142008 0.2911 0.614498
3 to 4 141429 -1.4169 0.078256
2 to 3 141407 -1.4818 0.069197
1 to 2 141856 -0.1573 0.437498
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-24_05:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2366.55 -1.887 0.029560
Test results for specific bytes for dh-ranFile-2018-06-24_05:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2571.63 1.013 0.844466
2 to 9 2403.90 -1.359 0.087057
3 to 10 2517.37 0.246 0.597045
4 to 11 2525.25 0.357 0.639474
5 to 12 2535.87 0.507 0.694011
6 to 13 2486.32 -0.194 0.423270
7 to 14 2483.27 -0.237 0.406473
8 to 15 2525.38 0.359 0.640161
9 to 16 2571.38 1.009 0.843618
10 to 17 2454.00 -0.651 0.257671
11 to 18 2381.20 -1.680 0.046471
12 to 19 2516.01 0.226 0.589557
13 to 20 2472.93 -0.383 0.350911
14 to 21 2391.16 -1.539 0.061873
15 to 22 2602.02 1.443 0.925467
16 to 23 2527.52 0.389 0.651436
17 to 24 2526.46 0.374 0.645869
18 to 25 2468.40 -0.447 0.327474
19 to 26 2545.52 0.644 0.740148
20 to 27 2476.99 -0.325 0.372422
21 to 28 2592.94 1.314 0.905648
22 to 29 2493.79 -0.088 0.464987
23 to 30 2574.22 1.050 0.853056
24 to 31 2472.18 -0.393 0.346991
25 to 32 2486.90 -0.185 0.426508
CDPARK for dh-ranFile-2018-06-24_05:31: 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
3546 1.0502 0.853193
3548 1.1416 0.873180
3543 0.9132 0.819442
3496 -1.2329 0.108811
3478 -2.0548 0.019949
3502 -0.9589 0.168804
3533 0.4566 0.676028
3517 -0.2740 0.392053
3568 2.0548 0.980051
3528 0.2283 0.590298
Square side=100, avg. no. parked=3525.90 sample std.=26.17
p-value of the KSTEST for those 10 p-values: 0.652073
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-24_05:31
0.1884,0.8498,0.9714,0.5774,0.1807,0.4150,0.0167,0.1726,0.9971,0.9805,
The KS test for those 10 p-values: 0.117150
The 3DSPHERES test for dh-ranFile-2018-06-24_05:31
sample no r^3 equiv. uni.
1 3.460 0.108943
2 11.889 0.327187
3 123.162 0.983517
4 6.078 0.183386
5 91.212 0.952185
6 0.134 0.004465
7 4.130 0.128600
8 52.632 0.826991
9 50.194 0.812341
10 14.507 0.383422
11 18.507 0.460392
12 1.552 0.050409
13 28.128 0.608428
14 109.632 0.974123
15 71.429 0.907539
16 23.891 0.549034
17 31.267 0.647338
18 15.304 0.399592
19 52.961 0.828878
20 38.096 0.719126
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.561135
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-24_05:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 -0.7 0.6 1.8 -1.0 0.0
-1.9 -2.6 1.4 -0.6 0.6 -1.5
-0.9 -0.7 1.3 1.4 0.2 -0.6
1.4 0.4 0.4 -1.1 -0.1 0.3
-1.4 0.7 0.0 0.4 0.2 -0.6
-0.8 -0.6 -0.2 0.8 0.6 0.2
2.1 -1.7 -0.8 0.4 1.6 0.0
-1.1
Chi-square with 42 degrees of freedom:46.291401
z-score=0.468230, p-value=0.700345
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-24_05:31
Test no p-value
1 0.135890
2 0.553184
3 0.155128
4 0.628259
5 0.843274
6 0.882905
7 0.151076
8 0.592100
9 0.362973
10 0.483666
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.889322
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-24_05:31:
(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 66516 0.34 66756 0.12
3 25000.00 25109 0.48 24952 0.09
4 6666.67 6714 0.34 6640 0.11
5 1388.89 1375 0.14 1393 0.01
6 238.10 243 0.10 221 1.23
7 34.72 38 0.31 32 0.21
8 4.96 4 0.19 5 0.00
p=0.07024 p=0.06054
Number of rngs required: 688050, p-value: 0.342
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-24_05:31
No. of wins: Observed Expected
98578 98585.9
z-score=-0.035, pvalue=0.48598
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66335 66666.7 1.650 1.650
2 37933 37654.3 2.062 3.713
3 26891 26954.7 0.151 3.863
4 19421 19313.5 0.599 4.462
5 13732 13851.4 1.030 5.492
6 9898 9943.5 0.209 5.700
7 7120 7145.0 0.088 5.788
8 5167 5139.1 0.152 5.940
9 3761 3699.9 1.010 6.950
10 2747 2666.3 2.443 9.392
11 1927 1923.3 0.007 9.399
12 1395 1388.7 0.028 9.428
13 974 1003.7 0.880 10.307
14 713 726.1 0.238 10.545
15 548 525.8 0.934 11.479
16 390 381.2 0.205 11.685
17 297 276.5 1.514 13.199
18 203 200.8 0.023 13.222
19 142 146.0 0.109 13.331
20 110 106.2 0.135 13.466
21 296 287.1 0.275 13.741
Chisq= 13.74 for 20 degrees of freedom, p= 0.15661
SUMMARY of craptest
p-value for no. of wins: 0.485981
p-value for throws/game: 0.156608
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-24_05:31
No. of wins: Observed Expected
98845 98585.9
z-score= 1.159, pvalue=0.87678
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66506 66666.7 0.387 0.387
2 37699 37654.3 0.053 0.440
3 27037 26954.7 0.251 0.691
4 19341 19313.5 0.039 0.731
5 14101 13851.4 4.497 5.228
6 9748 9943.5 3.845 9.073
7 7170 7145.0 0.087 9.160
8 5079 5139.1 0.702 9.863
9 3715 3699.9 0.062 9.924
10 2645 2666.3 0.170 10.095
11 1913 1923.3 0.055 10.150
12 1399 1388.7 0.076 10.226
13 990 1003.7 0.187 10.413
14 737 726.1 0.162 10.576
15 556 525.8 1.730 12.306
16 348 381.2 2.883 15.189
17 267 276.5 0.329 15.518
18 205 200.8 0.087 15.605
19 162 146.0 1.757 17.362
20 106 106.2 0.000 17.362
21 276 287.1 0.430 17.793
Chisq= 17.79 for 20 degrees of freedom, p= 0.39893
SUMMARY of craptest
p-value for no. of wins: 0.876778
p-value for throws/game: 0.398930
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0018,0.0045,0.0047,0.0064,0.0086,0.0139,0.0142,0.0167,0.0191,0.0199,
0.0212,0.0296,0.0312,0.0367,0.0465,0.0502,0.0504,0.0533,0.0605,0.0619,
0.0658,0.0692,0.0702,0.0712,0.0726,0.0741,0.0783,0.0840,0.0871,0.1004,
0.1068,0.1088,0.1089,0.1096,0.1156,0.1171,0.1236,0.1286,0.1359,0.1398,
0.1411,0.1433,0.1444,0.1485,0.1511,0.1542,0.1551,0.1566,0.1577,0.1584,
0.1606,0.1688,0.1726,0.1758,0.1807,0.1834,0.1862,0.1884,0.1897,0.1897,
0.1902,0.1902,0.1954,0.2056,0.2060,0.2146,0.2175,0.2208,0.2216,0.2295,
0.2327,0.2393,0.2466,0.2560,0.2577,0.2581,0.2640,0.2660,0.2682,0.2864,
0.2977,0.2991,0.2996,0.3135,0.3167,0.3272,0.3275,0.3347,0.3395,0.3422,
0.3470,0.3509,0.3569,0.3627,0.3627,0.3630,0.3635,0.3724,0.3729,0.3733,
0.3800,0.3825,0.3834,0.3882,0.3921,0.3927,0.3989,0.3996,0.4065,0.4133,
0.4150,0.4167,0.4176,0.4189,0.4233,0.4265,0.4283,0.4375,0.4376,0.4529,
0.4563,0.4591,0.4598,0.4604,0.4617,0.4633,0.4650,0.4652,0.4837,0.4853,
0.4860,0.4890,0.4927,0.4928,0.4941,0.5011,0.5092,0.5168,0.5235,0.5270,
0.5290,0.5330,0.5490,0.5508,0.5532,0.5611,0.5669,0.5674,0.5680,0.5774,
0.5828,0.5896,0.5903,0.5921,0.5960,0.5970,0.6056,0.6056,0.6084,0.6086,
0.6111,0.6132,0.6145,0.6227,0.6283,0.6332,0.6371,0.6395,0.6402,0.6402,
0.6422,0.6450,0.6459,0.6473,0.6514,0.6521,0.6571,0.6605,0.6620,0.6676,
0.6680,0.6680,0.6701,0.6735,0.6760,0.6784,0.6854,0.6861,0.6940,0.6947,
0.6987,0.6988,0.7003,0.7045,0.7098,0.7131,0.7151,0.7191,0.7356,0.7401,
0.7666,0.7712,0.7799,0.7809,0.7869,0.7924,0.7959,0.8108,0.8123,0.8194,
0.8215,0.8260,0.8270,0.8289,0.8353,0.8433,0.8436,0.8439,0.8445,0.8460,
0.8498,0.8501,0.8511,0.8531,0.8532,0.8667,0.8703,0.8716,0.8732,0.8760,
0.8768,0.8829,0.8886,0.8893,0.8900,0.8927,0.8938,0.8968,0.9004,0.9024,
0.9056,0.9062,0.9075,0.9162,0.9173,0.9188,0.9211,0.9216,0.9255,0.9285,
0.9522,0.9537,0.9541,0.9548,0.9571,0.9634,0.9681,0.9714,0.9741,0.9766,
0.9801,0.9805,0.9835,0.9863,0.9921,0.9950,0.9961,0.9971,0.9995,
Overall p-value after applying KStest on 269 p-values = 0.571675
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.