RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-05_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 15.83 25.0691 0.906825
2 to 25 15.74 14.8381 0.392862
3 to 26 15.92 5.8765 0.006022
4 to 27 15.73 24.5510 0.894779
5 to 28 15.54 19.1801 0.681704
6 to 29 15.73 13.3062 0.284540
7 to 30 15.84 21.2884 0.786343
8 to 31 15.82 26.7828 0.938669
9 to 32 16.00 18.6510 0.651074
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.254717
Tough bday spacings test for dh-ranFile-2018-07-05_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 36 76 96 92 88 36 35 13 11 5
(O-E)^2/E 0.9 0.0 0.1 0.0 0.3 1.2 5.0 0.9 0.2 2.9 0.2
Birthday Spacings: Sum(O-E)^2/E= 11.849, p= 0.705
RESULTS OF GCD FOR dh-ranFile-2018-07-05_16:31
Euclid's algorithm:
p-value, steps to gcd: 0.929600
p-value, dist. of gcd's: 0.890342
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-05_16:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.717 0.096 0.658 0.006 0.655 0.552 0.489 0.593
Bits 8 to 15---> 0.105 0.437 0.375 0.577 0.936 0.975 0.998 0.762
Bits 16 to 23---> 0.743 0.768 0.064 0.162 0.481 0.218 0.785 0.234
Bits 24 to 31---> 0.097 0.346 0.430 0.743 0.419 0.390 0.487 0.752
KS test for the above 32 p values: 0.147
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-05_16:31,
p-values for 5 runs: 0.2451, 0.8906, 0.6115, 0.7221, 0.3715
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-05_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 191 211.4 1.972 1.972
r= 29 5062 5134.0 1.010 2.982
r= 30 23029 23103.0 0.237 3.219
r= 31 11718 11551.5 2.399 5.618
chi-square = 5.618 with df = 3; p-value = 0.868
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-05_16:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 208 211.4 0.055 0.055
r= 30 5223 5134.0 1.542 1.598
r= 31 23116 23103.0 0.007 1.605
r= 32 11453 11551.5 0.840 2.445
chi-square = 2.445 with df = 3; p-value = 0.515
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-05_16:31
b-rank test for bits 1 to 8, p=0.24295
b-rank test for bits 2 to 9, p=0.54689
b-rank test for bits 3 to 10, p=0.64987
b-rank test for bits 4 to 11, p=0.81630
b-rank test for bits 5 to 12, p=0.68134
b-rank test for bits 6 to 13, p=0.93703
b-rank test for bits 7 to 14, p=0.66544
b-rank test for bits 8 to 15, p=0.07056
b-rank test for bits 9 to 16, p=0.94340
b-rank test for bits 10 to 17, p=0.53625
b-rank test for bits 11 to 18, p=0.79598
b-rank test for bits 12 to 19, p=0.81384
b-rank test for bits 13 to 20, p=0.44073
b-rank test for bits 14 to 21, p=0.99344
b-rank test for bits 15 to 22, p=0.10587
b-rank test for bits 16 to 23, p=0.57976
b-rank test for bits 17 to 24, p=0.33308
b-rank test for bits 18 to 25, p=0.20855
b-rank test for bits 19 to 26, p=0.31056
b-rank test for bits 20 to 27, p=0.70239
b-rank test for bits 21 to 28, p=0.76579
b-rank test for bits 22 to 29, p=0.44234
b-rank test for bits 23 to 30, p=0.73390
b-rank test for bits 24 to 31, p=0.89380
b-rank test for bits 25 to 32, p=0.88521
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 = 0.130007
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-05_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 142807 2.10 0.982019
2 141304 -1.41 0.078634
3 142454 1.27 0.898419
4 141949 0.09 0.536924
5 141800 -0.26 0.399190
6 142257 0.81 0.791694
7 142450 1.26 0.896750
8 141624 -0.67 0.252495
9 142360 1.05 0.853822
10 141350 -1.31 0.095633
11 141234 -1.58 0.057297
12 142250 0.80 0.786972
13 141990 0.19 0.574750
14 142315 0.95 0.828391
15 142010 0.24 0.592977
16 142608 1.63 0.948703
17 142102 0.45 0.673704
18 141967 0.13 0.553593
19 141867 -0.10 0.460608
20 142415 1.18 0.881292
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-05_16:31
Bits used No. missing words z-score p-value
23 to 32 141840 -0.2391 0.405526
22 to 31 141675 -0.8080 0.209535
21 to 30 142138 0.7885 0.784803
20 to 29 142212 1.0437 0.851686
19 to 28 142361 1.5575 0.940322
18 to 27 141975 0.2264 0.589574
17 to 26 142240 1.1402 0.872907
16 to 25 141938 0.0989 0.539376
15 to 24 142127 0.7506 0.773549
14 to 23 141816 -0.3218 0.373792
13 to 22 141641 -0.9253 0.177411
12 to 21 141595 -1.0839 0.139205
11 to 20 141482 -1.4736 0.070301
10 to 19 142259 1.2058 0.886045
9 to 18 142366 1.5747 0.942340
8 to 17 142209 1.0333 0.849279
7 to 16 141594 -1.0873 0.138442
6 to 15 141937 0.0954 0.538007
5 to 14 141906 -0.0115 0.495419
4 to 13 142627 2.4747 0.993333
3 to 12 141980 0.2437 0.596264
2 to 11 142326 1.4368 0.924612
1 to 10 141650 -0.8942 0.185596
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-05_16:31
Bits used No. missing words z-score p-value
28 to 32 142055 0.4938 0.689275
27 to 31 142316 1.3785 0.915982
26 to 30 142233 1.0972 0.863720
25 to 29 142067 0.5345 0.703493
24 to 28 141952 0.1446 0.557504
23 to 27 141982 0.2463 0.597290
22 to 26 141945 0.1209 0.548121
21 to 25 141911 0.0057 0.502258
20 to 24 142399 1.6599 0.951533
19 to 23 141943 0.1141 0.545435
18 to 22 141877 -0.1096 0.456366
17 to 21 142018 0.3684 0.643702
16 to 20 142259 1.1853 0.882055
15 to 19 141938 0.0972 0.538711
14 to 18 141716 -0.6554 0.256119
13 to 17 142280 1.2565 0.895534
12 to 16 141754 -0.5265 0.299256
11 to 15 141840 -0.2350 0.407098
10 to 14 142609 2.3718 0.991148
9 to 13 141926 0.0565 0.522532
8 to 12 141667 -0.8215 0.205693
7 to 11 142215 1.0362 0.849938
6 to 10 141917 0.0260 0.510371
5 to 9 141783 -0.4282 0.334239
4 to 8 142156 0.8362 0.798470
3 to 7 141937 0.0938 0.537365
2 to 6 142062 0.5175 0.697605
1 to 5 142245 1.1379 0.872411
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-05_16:31
Bits used No. missing words z-score p-value
31 to 32 141416 -1.4553 0.072800
30 to 31 141957 0.1406 0.555915
29 to 30 141469 -1.2989 0.096988
28 to 29 142212 0.8928 0.814026
27 to 28 141918 0.0256 0.510202
26 to 27 142660 2.2144 0.986598
25 to 26 142306 1.1701 0.879023
24 to 25 142275 1.0787 0.859633
23 to 24 141441 -1.3815 0.083562
22 to 23 142040 0.3855 0.650051
21 to 22 141947 0.1111 0.544240
20 to 21 141972 0.1849 0.573333
19 to 20 140826 -3.1957 0.000698
18 to 19 142305 1.1672 0.878429
17 to 18 141780 -0.3815 0.351415
16 to 17 142295 1.1377 0.872371
15 to 16 141246 -1.9567 0.025190
14 to 15 142160 0.7394 0.770180
13 to 14 142137 0.6716 0.749079
12 to 13 141695 -0.6322 0.263614
11 to 12 142177 0.7896 0.785116
10 to 11 142021 0.3294 0.629077
9 to 10 141966 0.1672 0.566381
8 to 9 142097 0.5536 0.710073
7 to 8 141927 0.0521 0.520785
6 to 7 142204 0.8692 0.807640
5 to 6 141985 0.2232 0.588316
4 to 5 142253 1.0138 0.844655
3 to 4 142593 2.0167 0.978138
2 to 3 141739 -0.5024 0.307676
1 to 2 142186 0.8161 0.792789
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-05_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2428.35 -1.013 0.155451
Test results for specific bytes for dh-ranFile-2018-07-05_16:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2471.76 -0.399 0.344806
2 to 9 2408.10 -1.300 0.096868
3 to 10 2477.58 -0.317 0.375581
4 to 11 2440.59 -0.840 0.200417
5 to 12 2457.07 -0.607 0.271881
6 to 13 2456.60 -0.614 0.269706
7 to 14 2456.91 -0.609 0.271144
8 to 15 2597.12 1.373 0.915191
9 to 16 2443.99 -0.792 0.214143
10 to 17 2577.09 1.090 0.862197
11 to 18 2443.33 -0.801 0.211451
12 to 19 2558.11 0.822 0.794409
13 to 20 2462.18 -0.535 0.296361
14 to 21 2453.16 -0.662 0.253837
15 to 22 2416.86 -1.176 0.119842
16 to 23 2527.71 0.392 0.652426
17 to 24 2522.41 0.317 0.624375
18 to 25 2480.22 -0.280 0.389860
19 to 26 2499.59 -0.006 0.497701
20 to 27 2369.99 -1.839 0.032988
21 to 28 2503.02 0.043 0.517025
22 to 29 2628.59 1.819 0.965511
23 to 30 2516.81 0.238 0.593957
24 to 31 2595.28 1.348 0.911092
25 to 32 2607.19 1.516 0.935221
CDPARK for dh-ranFile-2018-07-05_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
3509 -0.6393 0.261324
3517 -0.2740 0.392053
3538 0.6849 0.753306
3553 1.3699 0.914635
3492 -1.4155 0.078457
3520 -0.1370 0.445521
3521 -0.0913 0.463617
3503 -0.9132 0.180558
3510 -0.5936 0.276387
3529 0.2740 0.607947
Square side=100, avg. no. parked=3519.20 sample std.=16.71
p-value of the KSTEST for those 10 p-values: 0.761888
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-05_16:31
0.7960,0.7505,0.1740,0.1963,0.3129,0.7051,0.3964,0.1949,0.5126,0.6884,
The KS test for those 10 p-values: 0.702978
The 3DSPHERES test for dh-ranFile-2018-07-05_16:31
sample no r^3 equiv. uni.
1 15.441 0.402312
2 78.243 0.926325
3 43.977 0.769130
4 12.889 0.349257
5 1.940 0.062621
6 46.325 0.786510
7 12.564 0.342163
8 25.133 0.567323
9 17.243 0.437156
10 122.677 0.983248
11 3.827 0.119757
12 36.302 0.701820
13 44.672 0.774420
14 4.020 0.125415
15 38.425 0.722196
16 38.729 0.724994
17 16.678 0.426458
18 5.130 0.157189
19 50.699 0.815476
20 6.413 0.192460
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.920193
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-05_16:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 0.5 -0.1 0.2 -0.6 0.5
0.3 -2.5 2.8 0.2 -0.0 -0.3
2.2 -0.7 -0.9 0.9 -0.6 -0.3
0.9 -0.0 -0.2 0.3 -1.1 0.1
1.4 -0.4 -0.1 -1.2 -2.1 0.4
0.2 -0.7 -0.6 -1.2 1.0 0.6
0.3 -0.4 0.5 -0.1 -1.3 1.0
-0.1
Chi-square with 42 degrees of freedom:42.296256
z-score=0.032324, p-value=0.541823
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-05_16:31
Test no p-value
1 0.057549
2 0.498714
3 0.518612
4 0.674702
5 0.002897
6 0.011002
7 0.300576
8 0.967247
9 0.654266
10 0.104405
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.090836
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-05_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 66821 0.36 66801 0.27
3 25000.00 24932 0.18 24934 0.17
4 6666.67 6642 0.09 6626 0.25
5 1388.89 1359 0.64 1360 0.60
6 238.10 202 5.47 231 0.21
7 34.72 39 0.53 39 0.53
8 4.96 4 0.19 8 1.86
p=0.71979 p=0.30928
Number of rngs required: 689033, p-value: 0.767
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-05_16:31
No. of wins: Observed Expected
98848 98585.9
z-score= 1.172, pvalue=0.87949
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66831 66666.7 0.405 0.405
2 37551 37654.3 0.284 0.689
3 26814 26954.7 0.735 1.423
4 19289 19313.5 0.031 1.454
5 13883 13851.4 0.072 1.526
6 9999 9943.5 0.309 1.836
7 7314 7145.0 3.996 5.832
8 5119 5139.1 0.078 5.910
9 3629 3699.9 1.357 7.267
10 2574 2666.3 3.195 10.462
11 1940 1923.3 0.144 10.607
12 1350 1388.7 1.081 11.688
13 1060 1003.7 3.156 14.844
14 729 726.1 0.011 14.855
15 504 525.8 0.907 15.762
16 394 381.2 0.433 16.195
17 285 276.5 0.259 16.454
18 218 200.8 1.468 17.922
19 127 146.0 2.469 20.391
20 100 106.2 0.364 20.754
21 290 287.1 0.029 20.783
Chisq= 20.78 for 20 degrees of freedom, p= 0.59002
SUMMARY of craptest
p-value for no. of wins: 0.879492
p-value for throws/game: 0.590023
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-05_16:31
No. of wins: Observed Expected
98583 98585.9
z-score=-0.013, pvalue=0.49490
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66692 66666.7 0.010 0.010
2 37623 37654.3 0.026 0.036
3 26971 26954.7 0.010 0.045
4 19323 19313.5 0.005 0.050
5 13782 13851.4 0.348 0.398
6 9993 9943.5 0.246 0.644
7 7011 7145.0 2.514 3.158
8 5196 5139.1 0.631 3.789
9 3742 3699.9 0.480 4.269
10 2651 2666.3 0.088 4.356
11 1939 1923.3 0.128 4.484
12 1358 1388.7 0.680 5.165
13 1033 1003.7 0.854 6.019
14 690 726.1 1.799 7.818
15 545 525.8 0.698 8.516
16 370 381.2 0.326 8.842
17 295 276.5 1.232 10.075
18 192 200.8 0.388 10.463
19 169 146.0 3.629 14.092
20 97 106.2 0.800 14.891
21 328 287.1 5.822 20.713
Chisq= 20.71 for 20 degrees of freedom, p= 0.58582
SUMMARY of craptest
p-value for no. of wins: 0.494900
p-value for throws/game: 0.585824
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0007,0.0029,0.0058,0.0060,0.0110,0.0252,0.0330,0.0573,0.0575,0.0626,
0.0641,0.0703,0.0706,0.0728,0.0785,0.0786,0.0836,0.0908,0.0956,0.0960,
0.0969,0.0970,0.0970,0.1044,0.1051,0.1059,0.1198,0.1198,0.1254,0.1300,
0.1384,0.1392,0.1469,0.1555,0.1572,0.1621,0.1740,0.1774,0.1806,0.1856,
0.1925,0.1949,0.1963,0.2004,0.2057,0.2086,0.2095,0.2115,0.2141,0.2180,
0.2342,0.2430,0.2451,0.2525,0.2538,0.2547,0.2561,0.2613,0.2636,0.2697,
0.2711,0.2719,0.2764,0.2845,0.2964,0.2993,0.3006,0.3077,0.3093,0.3106,
0.3129,0.3331,0.3342,0.3422,0.3448,0.3457,0.3493,0.3514,0.3715,0.3738,
0.3753,0.3756,0.3899,0.3900,0.3921,0.3929,0.3964,0.3992,0.4023,0.4055,
0.4071,0.4187,0.4265,0.4304,0.4372,0.4372,0.4407,0.4423,0.4455,0.4564,
0.4606,0.4636,0.4811,0.4875,0.4892,0.4949,0.4954,0.4977,0.4987,0.5023,
0.5102,0.5104,0.5126,0.5147,0.5170,0.5186,0.5208,0.5225,0.5363,0.5369,
0.5374,0.5380,0.5387,0.5394,0.5418,0.5442,0.5454,0.5469,0.5481,0.5525,
0.5536,0.5559,0.5575,0.5664,0.5673,0.5733,0.5748,0.5775,0.5798,0.5858,
0.5883,0.5896,0.5900,0.5927,0.5930,0.5940,0.5963,0.5973,0.6079,0.6115,
0.6244,0.6291,0.6437,0.6499,0.6501,0.6511,0.6524,0.6543,0.6551,0.6585,
0.6654,0.6737,0.6747,0.6813,0.6817,0.6884,0.6893,0.6976,0.7018,0.7024,
0.7030,0.7035,0.7047,0.7051,0.7101,0.7170,0.7198,0.7221,0.7222,0.7250,
0.7339,0.7426,0.7434,0.7491,0.7505,0.7518,0.7533,0.7619,0.7620,0.7658,
0.7665,0.7680,0.7691,0.7702,0.7735,0.7744,0.7848,0.7850,0.7851,0.7863,
0.7865,0.7870,0.7917,0.7928,0.7944,0.7960,0.7960,0.7985,0.8076,0.8138,
0.8140,0.8155,0.8163,0.8284,0.8447,0.8493,0.8499,0.8517,0.8538,0.8596,
0.8622,0.8637,0.8683,0.8724,0.8724,0.8729,0.8784,0.8790,0.8795,0.8813,
0.8821,0.8852,0.8860,0.8903,0.8906,0.8938,0.8948,0.8955,0.8967,0.8984,
0.9068,0.9111,0.9146,0.9152,0.9160,0.9202,0.9246,0.9263,0.9296,0.9352,
0.9363,0.9370,0.9387,0.9403,0.9423,0.9434,0.9487,0.9515,0.9655,0.9672,
0.9752,0.9781,0.9820,0.9832,0.9866,0.9911,0.9933,0.9934,0.9977,
Overall p-value after applying KStest on 269 p-values = 0.008764
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.