RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-08_14:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.76 16.4681 0.509073
2 to 25 15.88 11.8667 0.191858
3 to 26 15.82 9.9729 0.095258
4 to 27 15.89 18.7236 0.655374
5 to 28 16.02 27.6056 0.950237
6 to 29 15.70 16.0520 0.479851
7 to 30 15.69 13.1171 0.271689
8 to 31 15.47 25.3315 0.912467
9 to 32 15.79 21.0597 0.776368
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.979384
Tough bday spacings test for dh-ranFile-2018-07-08_14:31: 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 6 37 86 96 87 67 59 32 13 10 7
(O-E)^2/E 1.1 0.0 2.2 0.0 1.2 1.6 0.9 0.2 0.2 1.7 2.1
Birthday Spacings: Sum(O-E)^2/E= 11.263, p= 0.663
RESULTS OF GCD FOR dh-ranFile-2018-07-08_14:31
Euclid's algorithm:
p-value, steps to gcd: 0.222268
p-value, dist. of gcd's: 0.447011
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-08_14:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.751 0.782 0.761 0.879 0.693 0.827 0.367 0.270
Bits 8 to 15---> 0.426 0.835 0.081 0.874 0.508 0.563 0.792 0.221
Bits 16 to 23---> 0.464 0.442 0.806 0.851 0.927 0.912 0.627 0.807
Bits 24 to 31---> 0.937 0.443 0.795 0.916 0.769 0.919 0.040 0.942
KS test for the above 32 p values: 0.999
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-08_14:31,
p-values for 5 runs: 0.8140, 0.1569, 0.7878, 0.3890, 0.9884
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-08_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 225 211.4 0.873 0.873
r= 29 4953 5134.0 6.382 7.254
r= 30 23189 23103.0 0.320 7.574
r= 31 11633 11551.5 0.575 8.149
chi-square = 8.149 with df = 3; p-value = 0.957
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-08_14:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 229 211.4 1.462 1.462
r= 30 5078 5134.0 0.611 2.073
r= 31 23189 23103.0 0.320 2.393
r= 32 11504 11551.5 0.196 2.589
chi-square = 2.589 with df = 3; p-value = 0.540
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-08_14:31
b-rank test for bits 1 to 8, p=0.52533
b-rank test for bits 2 to 9, p=0.46620
b-rank test for bits 3 to 10, p=0.69117
b-rank test for bits 4 to 11, p=0.00506
b-rank test for bits 5 to 12, p=0.68323
b-rank test for bits 6 to 13, p=0.30883
b-rank test for bits 7 to 14, p=0.07521
b-rank test for bits 8 to 15, p=0.01243
b-rank test for bits 9 to 16, p=0.60649
b-rank test for bits 10 to 17, p=0.69337
b-rank test for bits 11 to 18, p=0.51944
b-rank test for bits 12 to 19, p=0.32342
b-rank test for bits 13 to 20, p=0.92018
b-rank test for bits 14 to 21, p=0.03516
b-rank test for bits 15 to 22, p=0.09381
b-rank test for bits 16 to 23, p=0.40880
b-rank test for bits 17 to 24, p=0.22455
b-rank test for bits 18 to 25, p=0.55615
b-rank test for bits 19 to 26, p=0.91432
b-rank test for bits 20 to 27, p=0.25437
b-rank test for bits 21 to 28, p=0.41991
b-rank test for bits 22 to 29, p=0.46328
b-rank test for bits 23 to 30, p=0.98536
b-rank test for bits 24 to 31, p=0.42396
b-rank test for bits 25 to 32, p=0.80328
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 = 0.555520
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-08_14:31
(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 142100 0.45 0.672017
2 141408 -1.17 0.120733
3 141532 -0.88 0.188993
4 141647 -0.61 0.269964
5 141692 -0.51 0.305804
6 142374 1.09 0.861189
7 141692 -0.51 0.305804
8 141175 -1.72 0.043106
9 141626 -0.66 0.253990
10 141730 -0.42 0.337610
11 142445 1.25 0.894636
12 142096 0.44 0.668634
13 141546 -0.85 0.197968
14 142317 0.95 0.829578
15 141930 0.05 0.519259
16 141841 -0.16 0.436579
17 142153 0.57 0.715431
18 141802 -0.25 0.400996
19 141940 0.07 0.528563
20 141806 -0.24 0.404613
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-08_14:31
Bits used No. missing words z-score p-value
23 to 32 141734 -0.6046 0.272727
22 to 31 141614 -1.0184 0.154249
21 to 30 141788 -0.4184 0.337835
20 to 29 141847 -0.2149 0.414911
19 to 28 142106 0.6782 0.751169
18 to 27 141656 -0.8736 0.191181
17 to 26 142013 0.3575 0.639635
16 to 25 141993 0.2885 0.613525
15 to 24 141992 0.2851 0.612204
14 to 23 141839 -0.2425 0.404190
13 to 22 142668 2.6161 0.995553
12 to 21 141846 -0.2184 0.413567
11 to 20 141712 -0.6804 0.248110
10 to 19 142191 0.9713 0.834295
9 to 18 141800 -0.3770 0.353087
8 to 17 141699 -0.7253 0.234141
7 to 16 141273 -2.1942 0.014109
6 to 15 141620 -0.9977 0.159215
5 to 14 142067 0.5437 0.706673
4 to 13 142572 2.2851 0.988846
3 to 12 142095 0.6402 0.738992
2 to 11 141819 -0.3115 0.377717
1 to 10 141997 0.3023 0.618792
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-08_14:31
Bits used No. missing words z-score p-value
28 to 32 141529 -1.2893 0.098655
27 to 31 141735 -0.5909 0.277277
26 to 30 141227 -2.3130 0.010362
25 to 29 142028 0.4023 0.656258
24 to 28 141945 0.1209 0.548121
23 to 27 141226 -2.3164 0.010269
22 to 26 142557 2.1955 0.985936
21 to 25 142079 0.5752 0.717406
20 to 24 142039 0.4396 0.669872
19 to 23 142312 1.3650 0.913871
18 to 22 141685 -0.7604 0.223496
17 to 21 141463 -1.5130 0.065142
16 to 20 141716 -0.6554 0.256119
15 to 19 142160 0.8497 0.802262
14 to 18 142060 0.5107 0.695236
13 to 17 141912 0.0091 0.503611
12 to 16 142044 0.4565 0.675988
11 to 15 142282 1.2633 0.896757
10 to 14 142462 1.8735 0.969497
9 to 13 141638 -0.9198 0.178848
8 to 12 141870 -0.1333 0.446969
7 to 11 142136 0.7684 0.778867
6 to 10 142335 1.4429 0.925483
5 to 9 141527 -1.2960 0.097482
4 to 8 141957 0.1616 0.564187
3 to 7 141871 -0.1299 0.448310
2 to 6 141968 0.1989 0.578822
1 to 5 142265 1.2057 0.886026
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-08_14:31
Bits used No. missing words z-score p-value
31 to 32 142034 0.3678 0.643473
30 to 31 141679 -0.6794 0.248430
29 to 30 141584 -0.9597 0.168609
28 to 29 142099 0.5595 0.712089
27 to 28 142038 0.3796 0.647863
26 to 27 142211 0.8899 0.813235
25 to 26 142444 1.5772 0.942625
24 to 25 141121 -2.3255 0.010024
23 to 24 142114 0.6037 0.726994
22 to 23 141902 -0.0216 0.491375
21 to 22 141953 0.1288 0.551250
20 to 21 141986 0.2262 0.589464
19 to 20 141860 -0.1455 0.442152
18 to 19 142427 1.5271 0.936626
17 to 18 141598 -0.9184 0.179211
16 to 17 141346 -1.6617 0.048282
15 to 16 141854 -0.1632 0.435174
14 to 15 142073 0.4828 0.685382
13 to 14 142116 0.6096 0.728952
12 to 13 142146 0.6981 0.757456
11 to 12 142249 1.0020 0.841823
10 to 11 142024 0.3383 0.632416
9 to 10 141791 -0.3491 0.363524
8 to 9 142036 0.3737 0.645671
7 to 8 142059 0.4415 0.670576
6 to 7 141650 -0.7650 0.222140
5 to 6 142121 0.6244 0.733816
4 to 5 142270 1.0639 0.856318
3 to 4 142185 0.8132 0.791944
2 to 3 141467 -1.3048 0.095979
1 to 2 141918 0.0256 0.510202
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-08_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2532.01 0.453 0.674595
Test results for specific bytes for dh-ranFile-2018-07-08_14:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2510.46 0.148 0.558809
2 to 9 2507.80 0.110 0.543927
3 to 10 2561.97 0.876 0.809608
4 to 11 2442.17 -0.818 0.206714
5 to 12 2438.31 -0.872 0.191487
6 to 13 2562.24 0.880 0.810618
7 to 14 2472.83 -0.384 0.350380
8 to 15 2538.26 0.541 0.705780
9 to 16 2471.18 -0.408 0.341769
10 to 17 2440.21 -0.846 0.198886
11 to 18 2453.84 -0.653 0.256964
12 to 19 2669.25 2.394 0.991656
13 to 20 2586.43 1.222 0.889194
14 to 21 2529.44 0.416 0.661399
15 to 22 2411.80 -1.247 0.106141
16 to 23 2473.83 -0.370 0.355676
17 to 24 2468.30 -0.448 0.326942
18 to 25 2640.58 1.988 0.976596
19 to 26 2341.31 -2.244 0.012409
20 to 27 2514.68 0.208 0.582218
21 to 28 2418.90 -1.147 0.125716
22 to 29 2497.23 -0.039 0.484365
23 to 30 2545.90 0.649 0.741871
24 to 31 2417.08 -1.173 0.120461
25 to 32 2388.25 -1.580 0.057014
CDPARK for dh-ranFile-2018-07-08_14:31: 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
3519 -0.1826 0.427537
3506 -0.7763 0.218799
3547 1.0959 0.863437
3515 -0.3653 0.357445
3510 -0.5936 0.276387
3487 -1.6438 0.050105
3529 0.2740 0.607947
3512 -0.5023 0.307734
3512 -0.5023 0.307734
3492 -1.4155 0.078457
Square side=100, avg. no. parked=3512.90 sample std.=16.21
p-value of the KSTEST for those 10 p-values: 0.144520
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-08_14:31
0.6456,0.3265,0.3977,0.4468,0.0217,0.8700,0.1146,0.2350,0.9249,0.7182,
The KS test for those 10 p-values: 0.992352
The 3DSPHERES test for dh-ranFile-2018-07-08_14:31
sample no r^3 equiv. uni.
1 7.371 0.217853
2 12.969 0.350993
3 0.320 0.010604
4 12.694 0.345018
5 19.350 0.475329
6 71.720 0.908432
7 13.336 0.358882
8 18.865 0.466788
9 77.545 0.924592
10 4.610 0.142450
11 15.609 0.405661
12 3.855 0.120583
13 88.894 0.948343
14 14.477 0.382813
15 26.955 0.592814
16 20.347 0.492479
17 1.885 0.060900
18 29.559 0.626677
19 5.707 0.173226
20 4.634 0.143120
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.208062
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-08_14:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 0.1 -0.1 -2.3 0.1 -0.4
1.0 0.5 0.3 1.2 -0.1 -0.0
-1.6 -1.4 -0.2 1.4 -1.1 0.5
-1.2 0.1 0.8 -1.3 1.6 1.1
0.6 -0.8 0.6 0.1 0.0 -0.6
-0.2 0.9 1.0 0.9 0.2 0.4
0.0 -2.6 0.1 1.5 -0.6 -1.0
-0.1
Chi-square with 42 degrees of freedom:38.635573
z-score=-0.367089, p-value=0.380541
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-08_14:31
Test no p-value
1 0.744862
2 0.107656
3 0.070456
4 0.011516
5 0.058007
6 0.325587
7 0.290619
8 0.667995
9 0.342997
10 0.362815
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.034978
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-08_14:31:
(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 66588 0.09 66522 0.31
3 25000.00 25133 0.71 25069 0.19
4 6666.67 6682 0.04 6696 0.13
5 1388.89 1336 2.01 1417 0.57
6 238.10 230 0.28 252 0.81
7 34.72 26 2.19 38 0.31
8 4.96 4 0.19 5 0.00
p=0.51864 p=0.11244
Number of rngs required: 689259, p-value: 0.839
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-08_14:31
No. of wins: Observed Expected
98827 98585.9
z-score= 1.079, pvalue=0.85960
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66967 66666.7 1.353 1.353
2 37516 37654.3 0.508 1.861
3 26803 26954.7 0.854 2.715
4 19619 19313.5 4.834 7.549
5 13743 13851.4 0.849 8.397
6 9560 9943.5 14.794 23.192
7 7104 7145.0 0.236 23.427
8 5245 5139.1 2.183 25.610
9 3646 3699.9 0.784 26.395
10 2704 2666.3 0.533 26.928
11 1926 1923.3 0.004 26.932
12 1421 1388.7 0.749 27.681
13 1034 1003.7 0.914 28.595
14 717 726.1 0.115 28.710
15 558 525.8 1.967 30.677
16 381 381.2 0.000 30.677
17 298 276.5 1.665 32.343
18 219 200.8 1.644 33.987
19 154 146.0 0.440 34.427
20 111 106.2 0.216 34.642
21 274 287.1 0.599 35.241
Chisq= 35.24 for 20 degrees of freedom, p= 0.98114
SUMMARY of craptest
p-value for no. of wins: 0.859600
p-value for throws/game: 0.981143
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-08_14:31
No. of wins: Observed Expected
98299 98585.9
z-score=-1.283, pvalue=0.09975
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66520 66666.7 0.323 0.323
2 37698 37654.3 0.051 0.373
3 26993 26954.7 0.054 0.428
4 19376 19313.5 0.203 0.630
5 13889 13851.4 0.102 0.732
6 9947 9943.5 0.001 0.733
7 7097 7145.0 0.323 1.056
8 5136 5139.1 0.002 1.058
9 3650 3699.9 0.672 1.730
10 2622 2666.3 0.736 2.466
11 1924 1923.3 0.000 2.466
12 1420 1388.7 0.704 3.170
13 1015 1003.7 0.127 3.297
14 714 726.1 0.203 3.500
15 560 525.8 2.220 5.719
16 407 381.2 1.753 7.472
17 284 276.5 0.201 7.674
18 203 200.8 0.023 7.697
19 165 146.0 2.477 10.174
20 115 106.2 0.727 10.901
21 265 287.1 1.703 12.604
Chisq= 12.60 for 20 degrees of freedom, p= 0.10628
SUMMARY of craptest
p-value for no. of wins: 0.099746
p-value for throws/game: 0.106277
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0051,0.0100,0.0103,0.0104,0.0106,0.0115,0.0124,0.0124,0.0141,0.0217,
0.0350,0.0352,0.0398,0.0431,0.0483,0.0501,0.0570,0.0580,0.0609,0.0651,
0.0705,0.0752,0.0785,0.0810,0.0938,0.0953,0.0960,0.0975,0.0987,0.0997,
0.1061,0.1063,0.1077,0.1124,0.1146,0.1205,0.1206,0.1207,0.1257,0.1425,
0.1431,0.1445,0.1542,0.1569,0.1592,0.1686,0.1732,0.1788,0.1792,0.1890,
0.1912,0.1915,0.1919,0.1980,0.1989,0.2067,0.2081,0.2179,0.2188,0.2205,
0.2221,0.2223,0.2235,0.2246,0.2341,0.2350,0.2481,0.2484,0.2540,0.2544,
0.2561,0.2570,0.2696,0.2700,0.2717,0.2727,0.2764,0.2773,0.2906,0.3058,
0.3058,0.3077,0.3077,0.3088,0.3234,0.3256,0.3265,0.3269,0.3376,0.3378,
0.3418,0.3430,0.3450,0.3504,0.3510,0.3531,0.3557,0.3574,0.3589,0.3628,
0.3635,0.3669,0.3777,0.3805,0.3828,0.3890,0.3977,0.4010,0.4042,0.4046,
0.4057,0.4088,0.4136,0.4149,0.4199,0.4240,0.4257,0.4275,0.4352,0.4366,
0.4422,0.4423,0.4433,0.4468,0.4470,0.4470,0.4483,0.4633,0.4641,0.4662,
0.4668,0.4753,0.4799,0.4844,0.4914,0.4925,0.5036,0.5082,0.5091,0.5102,
0.5186,0.5193,0.5194,0.5253,0.5286,0.5405,0.5439,0.5481,0.5513,0.5555,
0.5562,0.5588,0.5633,0.5642,0.5788,0.5822,0.5895,0.5928,0.6065,0.6079,
0.6122,0.6135,0.6188,0.6267,0.6272,0.6324,0.6396,0.6435,0.6456,0.6457,
0.6479,0.6554,0.6563,0.6614,0.6626,0.6680,0.6686,0.6699,0.6706,0.6720,
0.6746,0.6760,0.6832,0.6854,0.6912,0.6933,0.6934,0.6952,0.7058,0.7067,
0.7121,0.7154,0.7174,0.7182,0.7270,0.7290,0.7338,0.7390,0.7419,0.7449,
0.7506,0.7512,0.7575,0.7610,0.7689,0.7764,0.7789,0.7818,0.7878,0.7919,
0.7921,0.7947,0.8023,0.8033,0.8056,0.8065,0.8096,0.8106,0.8132,0.8140,
0.8272,0.8296,0.8343,0.8349,0.8393,0.8418,0.8510,0.8563,0.8596,0.8612,
0.8634,0.8700,0.8744,0.8791,0.8860,0.8892,0.8946,0.8968,0.9084,0.9118,
0.9125,0.9139,0.9143,0.9157,0.9193,0.9202,0.9246,0.9249,0.9255,0.9269,
0.9366,0.9374,0.9419,0.9426,0.9483,0.9502,0.9570,0.9695,0.9766,0.9794,
0.9811,0.9854,0.9859,0.9884,0.9888,0.9917,0.9924,0.9956,0.9988,
Overall p-value after applying KStest on 269 p-values = 0.968745
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.