RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-22_10:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 16.08 20.3037 0.741011
2 to 25 15.77 9.2255 0.067079
3 to 26 15.71 51.3195 0.999974
4 to 27 16.00 14.1056 0.340384
5 to 28 16.37 22.2586 0.825021
6 to 29 16.07 10.7409 0.130288
7 to 30 16.18 15.9224 0.470658
8 to 31 15.76 31.5515 0.982902
9 to 32 15.88 7.5240 0.024305
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.123750
Tough bday spacings test for dh-ranFile-2018-06-22_10:31: 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 36 69 115 85 87 47 32 11 9 3
(O-E)^2/E 1.1 0.0 0.2 3.1 1.6 1.0 0.5 0.2 1.0 0.9 0.3
Birthday Spacings: Sum(O-E)^2/E= 9.886, p= 0.549
RESULTS OF GCD FOR dh-ranFile-2018-06-22_10:31
Euclid's algorithm:
p-value, steps to gcd: 0.708537
p-value, dist. of gcd's: 0.898803
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-22_10:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.426 0.507 0.147 0.113 0.558 0.827 0.334 0.661
Bits 8 to 15---> 0.175 0.385 0.070 0.752 0.471 0.882 0.865 0.650
Bits 16 to 23---> 0.093 0.781 0.016 0.824 0.043 0.614 0.493 0.602
Bits 24 to 31---> 0.997 0.690 0.311 0.323 0.658 0.904 0.512 0.576
KS test for the above 32 p values: 0.080
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-22_10:31,
p-values for 5 runs: 0.9610, 0.5622, 0.4819, 0.2394, 0.7477
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-22_10:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 222 211.4 0.530 0.530
r= 29 5184 5134.0 0.487 1.016
r= 30 22999 23103.0 0.469 1.485
r= 31 11595 11551.5 0.164 1.649
chi-square = 1.649 with df = 3; p-value = 0.352
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-22_10:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 192 211.4 1.783 1.783
r= 30 5139 5134.0 0.005 1.788
r= 31 23059 23103.0 0.084 1.872
r= 32 11610 11551.5 0.296 2.168
chi-square = 2.168 with df = 3; p-value = 0.462
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-22_10:31
b-rank test for bits 1 to 8, p=0.08103
b-rank test for bits 2 to 9, p=0.46609
b-rank test for bits 3 to 10, p=0.43172
b-rank test for bits 4 to 11, p=0.89965
b-rank test for bits 5 to 12, p=0.56366
b-rank test for bits 6 to 13, p=0.20001
b-rank test for bits 7 to 14, p=0.04247
b-rank test for bits 8 to 15, p=0.22253
b-rank test for bits 9 to 16, p=0.09810
b-rank test for bits 10 to 17, p=0.25840
b-rank test for bits 11 to 18, p=0.13419
b-rank test for bits 12 to 19, p=0.98490
b-rank test for bits 13 to 20, p=0.96902
b-rank test for bits 14 to 21, p=0.54086
b-rank test for bits 15 to 22, p=0.08411
b-rank test for bits 16 to 23, p=0.61493
b-rank test for bits 17 to 24, p=0.23508
b-rank test for bits 18 to 25, p=0.28799
b-rank test for bits 19 to 26, p=0.95023
b-rank test for bits 20 to 27, p=0.82186
b-rank test for bits 21 to 28, p=0.02430
b-rank test for bits 22 to 29, p=0.23167
b-rank test for bits 23 to 30, p=0.21310
b-rank test for bits 24 to 31, p=0.92325
b-rank test for bits 25 to 32, p=0.49662
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 = 0.165685
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-22_10:31
(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 142365 1.06 0.856483
2 142538 1.47 0.929064
3 142163 0.59 0.723305
4 141708 -0.47 0.319036
5 140696 -2.83 0.002292
6 142525 1.44 0.924851
7 142367 1.07 0.857538
8 141879 -0.07 0.471753
9 142370 1.08 0.859111
10 142105 0.46 0.676227
11 141706 -0.48 0.317369
12 141723 -0.44 0.331654
13 141692 -0.51 0.305804
14 141873 -0.08 0.466177
15 142253 0.80 0.789003
16 141576 -0.78 0.218046
17 141181 -1.70 0.044405
18 142556 1.51 0.934594
19 142469 1.31 0.904502
20 142293 0.90 0.814987
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-22_10:31
Bits used No. missing words z-score p-value
23 to 32 142040 0.4506 0.673856
22 to 31 142291 1.3161 0.905930
21 to 30 141656 -0.8736 0.191181
20 to 29 141756 -0.5287 0.298498
19 to 28 142101 0.6609 0.745672
18 to 27 142231 1.1092 0.866330
17 to 26 142304 1.3609 0.913232
16 to 25 141664 -0.8460 0.198786
15 to 24 141961 0.1782 0.570706
14 to 23 142176 0.9196 0.821097
13 to 22 142007 0.3368 0.631864
12 to 21 141754 -0.5356 0.296110
11 to 20 141405 -1.7391 0.041011
10 to 19 141861 -0.1667 0.433821
9 to 18 141847 -0.2149 0.414911
8 to 17 141726 -0.6322 0.263637
7 to 16 142032 0.4230 0.663852
6 to 15 142300 1.3471 0.911032
5 to 14 141727 -0.6287 0.264765
4 to 13 141683 -0.7804 0.217564
3 to 12 142251 1.1782 0.880636
2 to 11 142054 0.4989 0.691062
1 to 10 141536 -1.2873 0.098987
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-22_10:31
Bits used No. missing words z-score p-value
28 to 32 142090 0.6124 0.729877
27 to 31 141581 -1.1130 0.132858
26 to 30 142173 0.8938 0.814285
25 to 29 141809 -0.3401 0.366890
24 to 28 141931 0.0735 0.529279
23 to 27 142279 1.2531 0.894919
22 to 26 142013 0.3514 0.637365
21 to 25 141357 -1.8723 0.030582
20 to 24 142363 1.5379 0.937959
19 to 23 141918 0.0294 0.511723
18 to 22 141540 -1.2520 0.105291
17 to 21 141637 -0.9232 0.177964
16 to 20 142111 0.6836 0.752895
15 to 19 141502 -1.3808 0.083673
14 to 18 141923 0.0463 0.518480
13 to 17 142171 0.8870 0.812465
12 to 16 142270 1.2226 0.889262
11 to 15 141987 0.2633 0.603836
10 to 14 142044 0.4565 0.675988
9 to 13 141464 -1.5096 0.065574
8 to 12 141811 -0.3333 0.369446
7 to 11 141963 0.1819 0.572182
6 to 10 142385 1.6124 0.946567
5 to 9 142089 0.6091 0.728755
4 to 8 141866 -0.1469 0.441613
3 to 7 142077 0.5684 0.715109
2 to 6 142195 0.9684 0.833571
1 to 5 142291 1.2938 0.902132
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-22_10:31
Bits used No. missing words z-score p-value
31 to 32 142545 1.8751 0.969613
30 to 31 140935 -2.8741 0.002026
29 to 30 141418 -1.4494 0.073620
28 to 29 141782 -0.3756 0.353605
27 to 28 141769 -0.4140 0.339454
26 to 27 141427 -1.4228 0.077397
25 to 26 141686 -0.6588 0.255015
24 to 25 142244 0.9872 0.838234
23 to 24 141855 -0.1603 0.436336
22 to 23 141348 -1.6558 0.048877
21 to 22 141716 -0.5703 0.284239
20 to 21 142141 0.6834 0.752821
19 to 20 141324 -1.7266 0.042116
18 to 19 142061 0.4474 0.672708
17 to 18 141622 -0.8476 0.198336
16 to 17 142070 0.4740 0.682233
15 to 16 142048 0.4091 0.658751
14 to 15 141739 -0.5024 0.307676
13 to 14 141922 0.0374 0.514907
12 to 13 142007 0.2881 0.613370
11 to 12 142101 0.5654 0.714099
10 to 11 142193 0.8368 0.798643
9 to 10 141574 -0.9892 0.161289
8 to 9 141921 0.0344 0.513731
7 to 8 141584 -0.9597 0.168609
6 to 7 141768 -0.4169 0.338375
5 to 6 142064 0.4563 0.675896
4 to 5 141724 -0.5467 0.292294
3 to 4 141824 -0.2517 0.400632
2 to 3 141820 -0.2635 0.396079
1 to 2 142335 1.2557 0.895381
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-22_10:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2545.11 0.638 0.738241
Test results for specific bytes for dh-ranFile-2018-06-22_10:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2447.38 -0.744 0.228393
2 to 9 2453.83 -0.653 0.256914
3 to 10 2424.76 -1.064 0.143664
4 to 11 2475.28 -0.350 0.363298
5 to 12 2517.96 0.254 0.600246
6 to 13 2474.34 -0.363 0.358345
7 to 14 2644.65 2.046 0.979606
8 to 15 2592.84 1.313 0.905410
9 to 16 2553.65 0.759 0.776000
10 to 17 2463.66 -0.514 0.303644
11 to 18 2403.09 -1.371 0.085255
12 to 19 2365.34 -1.904 0.028433
13 to 20 2436.18 -0.903 0.183371
14 to 21 2562.42 0.883 0.811315
15 to 22 2545.69 0.646 0.740923
16 to 23 2504.91 0.069 0.527660
17 to 24 2479.08 -0.296 0.383696
18 to 25 2588.91 1.257 0.895695
19 to 26 2332.95 -2.362 0.009078
20 to 27 2442.92 -0.807 0.209779
21 to 28 2506.04 0.085 0.534052
22 to 29 2493.99 -0.085 0.466142
23 to 30 2587.09 1.232 0.890957
24 to 31 2475.01 -0.353 0.361865
25 to 32 2495.55 -0.063 0.474886
CDPARK for dh-ranFile-2018-06-22_10:31: 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
3534 0.5023 0.692266
3530 0.3196 0.625377
3486 -1.6895 0.045562
3526 0.1370 0.554479
3563 1.8265 0.966111
3515 -0.3653 0.357445
3525 0.0913 0.536383
3473 -2.2831 0.011212
3536 0.5936 0.723613
Square side=100, avg. no. parked=3521.40 sample std.=24.22
p-value of the KSTEST for those 10 p-values: 0.589415
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-22_10:31
0.4143,0.3182,0.8827,0.3775,0.1414,0.2637,0.5987,0.6029,0.9396,0.8825,
The KS test for those 10 p-values: 0.813718
The 3DSPHERES test for dh-ranFile-2018-06-22_10:31
sample no r^3 equiv. uni.
1 0.097 0.003240
2 5.656 0.171833
3 50.518 0.814358
4 0.998 0.032703
5 5.128 0.157130
6 18.238 0.455525
7 7.963 0.233124
8 1.496 0.048645
9 17.137 0.435175
10 11.197 0.311493
11 17.118 0.434805
12 19.015 0.469453
13 87.155 0.945260
14 32.916 0.666200
15 9.090 0.261401
16 5.524 0.168168
17 65.171 0.886094
18 30.102 0.633365
19 74.359 0.916142
20 21.770 0.515992
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.412360
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-22_10:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 0.5 -0.8 -0.1 -0.5 2.7
-0.5 0.4 -0.7 -0.6 0.3 -0.2
-1.8 0.3 0.5 0.5 -0.5 0.4
-0.6 1.0 -0.6 0.5 -0.3 0.7
-0.5 0.8 -1.6 0.1 1.6 -1.1
1.0 -0.7 0.8 0.4 -1.3 2.6
-0.2 -0.1 -1.6 0.4 1.6 0.0
-1.1
Chi-square with 42 degrees of freedom:41.330447
z-score=-0.073054, p-value=0.499789
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-22_10:31
Test no p-value
1 0.011242
2 0.235576
3 0.781822
4 0.449699
5 0.835166
6 0.526156
7 0.788367
8 0.000017
9 0.302999
10 0.427020
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.160578
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-22_10:31:
(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 66547 0.21 66486 0.49
3 25000.00 25055 0.12 25083 0.28
4 6666.67 6747 0.97 6732 0.64
5 1388.89 1385 0.01 1405 0.19
6 238.10 227 0.52 250 0.60
7 34.72 33 0.09 36 0.05
8 4.96 5 0.00 7 0.84
p=0.07285 p=0.20046
Number of rngs required: 688119, p-value: 0.372
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-22_10:31
No. of wins: Observed Expected
98959 98585.9
z-score= 1.669, pvalue=0.95243
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67035 66666.7 2.035 2.035
2 37446 37654.3 1.153 3.188
3 26907 26954.7 0.085 3.272
4 19191 19313.5 0.777 4.049
5 13865 13851.4 0.013 4.062
6 9920 9943.5 0.056 4.118
7 7085 7145.0 0.504 4.622
8 5155 5139.1 0.049 4.671
9 3716 3699.9 0.070 4.742
10 2616 2666.3 0.949 5.690
11 1916 1923.3 0.028 5.718
12 1450 1388.7 2.702 8.421
13 1018 1003.7 0.203 8.624
14 751 726.1 0.851 9.475
15 542 525.8 0.497 9.972
16 382 381.2 0.002 9.974
17 304 276.5 2.727 12.701
18 179 200.8 2.373 15.074
19 145 146.0 0.007 15.080
20 110 106.2 0.135 15.215
21 267 287.1 1.409 16.624
Chisq= 16.62 for 20 degrees of freedom, p= 0.32277
SUMMARY of craptest
p-value for no. of wins: 0.952432
p-value for throws/game: 0.322772
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-22_10:31
No. of wins: Observed Expected
98717 98585.9
z-score= 0.587, pvalue=0.72124
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66740 66666.7 0.081 0.081
2 37509 37654.3 0.561 0.642
3 26853 26954.7 0.384 1.025
4 19397 19313.5 0.361 1.387
5 14049 13851.4 2.818 4.205
6 9914 9943.5 0.088 4.293
7 7057 7145.0 1.084 5.377
8 5056 5139.1 1.343 6.720
9 3752 3699.9 0.735 7.455
10 2646 2666.3 0.155 7.609
11 1970 1923.3 1.133 8.742
12 1418 1388.7 0.616 9.358
13 988 1003.7 0.246 9.604
14 684 726.1 2.446 12.050
15 572 525.8 4.053 16.103
16 393 381.2 0.368 16.471
17 270 276.5 0.155 16.626
18 207 200.8 0.190 16.815
19 145 146.0 0.007 16.822
20 98 106.2 0.635 17.457
21 282 287.1 0.091 17.549
Chisq= 17.55 for 20 degrees of freedom, p= 0.38288
SUMMARY of craptest
p-value for no. of wins: 0.721244
p-value for throws/game: 0.382878
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0000,0.0020,0.0023,0.0032,0.0091,0.0112,0.0112,0.0164,0.0243,0.0243,
0.0284,0.0306,0.0327,0.0410,0.0421,0.0425,0.0433,0.0444,0.0456,0.0486,
0.0489,0.0656,0.0671,0.0702,0.0728,0.0736,0.0774,0.0802,0.0810,0.0837,
0.0841,0.0853,0.0932,0.0981,0.0990,0.1053,0.1128,0.1237,0.1303,0.1329,
0.1342,0.1414,0.1437,0.1469,0.1571,0.1606,0.1613,0.1657,0.1682,0.1686,
0.1718,0.1748,0.1780,0.1834,0.1912,0.1983,0.1988,0.2000,0.2005,0.2098,
0.2131,0.2176,0.2180,0.2225,0.2284,0.2317,0.2331,0.2351,0.2356,0.2394,
0.2550,0.2569,0.2584,0.2614,0.2636,0.2637,0.2648,0.2842,0.2880,0.2923,
0.2961,0.2985,0.3030,0.3036,0.3058,0.3077,0.3113,0.3115,0.3174,0.3182,
0.3190,0.3228,0.3231,0.3317,0.3338,0.3384,0.3395,0.3404,0.3516,0.3536,
0.3574,0.3583,0.3619,0.3633,0.3669,0.3694,0.3719,0.3775,0.3829,0.3837,
0.3852,0.3961,0.4006,0.4124,0.4143,0.4149,0.4255,0.4270,0.4317,0.4338,
0.4348,0.4352,0.4363,0.4416,0.4497,0.4555,0.4618,0.4661,0.4661,0.4662,
0.4695,0.4707,0.4707,0.4718,0.4749,0.4819,0.4931,0.4966,0.4998,0.5070,
0.5117,0.5121,0.5137,0.5149,0.5160,0.5185,0.5262,0.5277,0.5293,0.5341,
0.5364,0.5409,0.5495,0.5545,0.5545,0.5583,0.5622,0.5637,0.5707,0.5722,
0.5758,0.5894,0.5987,0.6002,0.6016,0.6029,0.6038,0.6134,0.6136,0.6149,
0.6254,0.6319,0.6334,0.6374,0.6499,0.6579,0.6588,0.6605,0.6639,0.6662,
0.6727,0.6739,0.6759,0.6760,0.6762,0.6822,0.6904,0.6911,0.6923,0.7085,
0.7141,0.7151,0.7212,0.7233,0.7236,0.7288,0.7299,0.7382,0.7409,0.7410,
0.7457,0.7477,0.7518,0.7528,0.7529,0.7760,0.7808,0.7818,0.7884,0.7890,
0.7986,0.8113,0.8125,0.8137,0.8143,0.8144,0.8150,0.8211,0.8219,0.8238,
0.8250,0.8271,0.8336,0.8352,0.8382,0.8565,0.8575,0.8591,0.8649,0.8663,
0.8806,0.8819,0.8825,0.8827,0.8861,0.8893,0.8910,0.8949,0.8954,0.8957,
0.8988,0.8997,0.9021,0.9037,0.9045,0.9054,0.9059,0.9110,0.9132,0.9161,
0.9232,0.9249,0.9291,0.9346,0.9380,0.9396,0.9453,0.9466,0.9502,0.9524,
0.9610,0.9661,0.9690,0.9696,0.9796,0.9829,0.9849,0.9971,1.0000,
Overall p-value after applying KStest on 269 p-values = 0.712663
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.