RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-12_00:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.59 26.7922 0.938813
2 to 25 15.65 15.0182 0.405828
3 to 26 15.83 20.0937 0.730533
4 to 27 15.59 15.9981 0.476031
5 to 28 15.68 18.1826 0.622587
6 to 29 15.39 18.3759 0.634497
7 to 30 15.92 22.0135 0.815801
8 to 31 15.65 17.5031 0.579183
9 to 32 15.71 21.8542 0.809609
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.098113
Tough bday spacings test for dh-ranFile-2018-07-12_00:31: 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 39 72 95 91 79 57 29 17 8 3
(O-E)^2/E 0.1 0.2 0.0 0.1 0.5 0.0 0.5 0.0 0.3 0.3 0.3
Birthday Spacings: Sum(O-E)^2/E= 2.144, p= 0.005
RESULTS OF GCD FOR dh-ranFile-2018-07-12_00:31
Euclid's algorithm:
p-value, steps to gcd: 0.233458
p-value, dist. of gcd's: 0.534050
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-12_00:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.326 0.126 0.753 0.302 0.394 0.914 0.016 0.671
Bits 8 to 15---> 0.054 0.834 0.709 0.241 0.129 0.238 0.573 0.921
Bits 16 to 23---> 0.801 0.285 0.537 0.685 0.423 0.032 0.159 0.306
Bits 24 to 31---> 0.778 0.918 0.776 0.798 0.395 0.003 0.259 0.367
KS test for the above 32 p values: 0.435
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-12_00:31,
p-values for 5 runs: 0.0682, 0.4772, 0.6543, 0.7387, 0.6418
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-12_00:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 204 211.4 0.260 0.260
r= 29 5055 5134.0 1.216 1.476
r= 30 23156 23103.0 0.121 1.598
r= 31 11585 11551.5 0.097 1.695
chi-square = 1.695 with df = 3; p-value = 0.362
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-12_00:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 212 211.4 0.002 0.002
r= 30 5042 5134.0 1.649 1.651
r= 31 23249 23103.0 0.922 2.573
r= 32 11497 11551.5 0.257 2.830
chi-square = 2.830 with df = 3; p-value = 0.581
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-12_00:31
b-rank test for bits 1 to 8, p=0.67988
b-rank test for bits 2 to 9, p=0.81949
b-rank test for bits 3 to 10, p=0.93339
b-rank test for bits 4 to 11, p=0.72632
b-rank test for bits 5 to 12, p=0.24132
b-rank test for bits 6 to 13, p=0.73534
b-rank test for bits 7 to 14, p=0.59930
b-rank test for bits 8 to 15, p=0.52060
b-rank test for bits 9 to 16, p=0.45512
b-rank test for bits 10 to 17, p=0.54150
b-rank test for bits 11 to 18, p=0.03290
b-rank test for bits 12 to 19, p=0.85718
b-rank test for bits 13 to 20, p=0.87050
b-rank test for bits 14 to 21, p=0.82131
b-rank test for bits 15 to 22, p=0.32674
b-rank test for bits 16 to 23, p=0.85155
b-rank test for bits 17 to 24, p=0.99500
b-rank test for bits 18 to 25, p=0.85740
b-rank test for bits 19 to 26, p=0.93542
b-rank test for bits 20 to 27, p=0.72813
b-rank test for bits 21 to 28, p=0.80263
b-rank test for bits 22 to 29, p=0.86051
b-rank test for bits 23 to 30, p=0.11596
b-rank test for bits 24 to 31, p=0.37164
b-rank test for bits 25 to 32, p=0.61460
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 = 0.010925
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-12_00:31
(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 142762 1.99 0.976827
2 142398 1.14 0.873222
3 142205 0.69 0.755160
4 142284 0.88 0.809321
5 141188 -1.69 0.045960
6 142064 0.36 0.641092
7 141255 -1.53 0.063156
8 141900 -0.02 0.491304
9 141453 -1.07 0.143169
10 141073 -1.95 0.025348
11 142166 0.60 0.725646
12 141647 -0.61 0.269964
13 142106 0.46 0.677066
14 141930 0.05 0.519259
15 141855 -0.13 0.449494
16 141840 -0.16 0.435658
17 141754 -0.36 0.358332
18 142279 0.86 0.806128
19 141436 -1.11 0.134382
20 142240 0.77 0.780119
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-12_00:31
Bits used No. missing words z-score p-value
23 to 32 141548 -1.2460 0.106389
22 to 31 141814 -0.3287 0.371182
21 to 30 141943 0.1161 0.546215
20 to 29 141916 0.0230 0.509175
19 to 28 142350 1.5196 0.935688
18 to 27 142006 0.3333 0.630563
17 to 26 142142 0.8023 0.788813
16 to 25 141953 0.1506 0.559849
15 to 24 141628 -0.9701 0.165998
14 to 23 141899 -0.0356 0.485792
13 to 22 142417 1.7506 0.959991
12 to 21 142055 0.5023 0.692275
11 to 20 142265 1.2264 0.889985
10 to 19 142401 1.6954 0.955002
9 to 18 141846 -0.2184 0.413567
8 to 17 141482 -1.4736 0.070301
7 to 16 142217 1.0609 0.855639
6 to 15 141741 -0.5804 0.280806
5 to 14 142218 1.0644 0.856422
4 to 13 141973 0.2196 0.586890
3 to 12 141789 -0.4149 0.339096
2 to 11 141950 0.1402 0.555765
1 to 10 141747 -0.5598 0.287822
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-12_00:31
Bits used No. missing words z-score p-value
28 to 32 142728 2.7752 0.997241
27 to 31 141833 -0.2587 0.397916
26 to 30 142026 0.3955 0.653760
25 to 29 141996 0.2938 0.615543
24 to 28 142038 0.4362 0.668643
23 to 27 141922 0.0429 0.517129
22 to 26 141690 -0.7435 0.228592
21 to 25 142421 1.7345 0.958583
20 to 24 141575 -1.1333 0.128540
19 to 23 141809 -0.3401 0.366890
18 to 22 141764 -0.4926 0.311132
17 to 21 141761 -0.5028 0.307548
16 to 20 142544 2.1514 0.984279
15 to 19 141854 -0.1876 0.425611
14 to 18 141606 -1.0282 0.151919
13 to 17 141551 -1.2147 0.112244
12 to 16 141905 -0.0147 0.494145
11 to 15 141906 -0.0113 0.495497
10 to 14 141904 -0.0181 0.492792
9 to 13 141568 -1.1571 0.123626
8 to 12 141669 -0.8147 0.207628
7 to 11 141615 -0.9977 0.159205
6 to 10 142181 0.9209 0.821453
5 to 9 141962 0.1785 0.570852
4 to 8 141490 -1.4215 0.077592
3 to 7 141471 -1.4859 0.068658
2 to 6 141441 -1.5876 0.056193
1 to 5 141788 -0.4113 0.340431
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-12_00:31
Bits used No. missing words z-score p-value
31 to 32 141656 -0.7473 0.227445
30 to 31 141894 -0.0452 0.481966
29 to 30 141547 -1.0688 0.142575
28 to 29 141523 -1.1396 0.127223
27 to 28 142098 0.5565 0.711082
26 to 27 141821 -0.2606 0.397216
25 to 26 142051 0.4179 0.661992
24 to 25 142047 0.4061 0.657668
23 to 24 141990 0.2380 0.594046
22 to 23 141580 -0.9715 0.165656
21 to 22 141817 -0.2724 0.392673
20 to 21 141403 -1.4936 0.067640
19 to 20 142156 0.7276 0.766583
18 to 19 141297 -1.8063 0.035437
17 to 18 142031 0.3589 0.640168
16 to 17 141879 -0.0895 0.464355
15 to 16 142408 1.4710 0.929355
14 to 15 141422 -1.4376 0.075281
13 to 14 141569 -1.0039 0.157708
12 to 13 142270 1.0639 0.856318
11 to 12 141869 -0.1190 0.452651
10 to 11 141660 -0.7355 0.231022
9 to 10 142087 0.5241 0.699896
8 to 9 141526 -1.1308 0.129077
7 to 8 141776 -0.3933 0.347048
6 to 7 141778 -0.3874 0.349229
5 to 6 141820 -0.2635 0.396079
4 to 5 141854 -0.1632 0.435174
3 to 4 142309 1.1790 0.880794
2 to 3 141772 -0.4051 0.342701
1 to 2 142443 1.5742 0.942285
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-12_00:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2480.99 -0.269 0.394006
Test results for specific bytes for dh-ranFile-2018-07-12_00:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2383.41 -1.649 0.049588
2 to 9 2438.42 -0.871 0.191914
3 to 10 2349.61 -2.127 0.016719
4 to 11 2478.69 -0.301 0.381564
5 to 12 2630.56 1.846 0.967586
6 to 13 2521.64 0.306 0.620234
7 to 14 2487.37 -0.179 0.429100
8 to 15 2373.63 -1.787 0.036957
9 to 16 2421.70 -1.107 0.134063
10 to 17 2417.00 -1.174 0.120236
11 to 18 2529.78 0.421 0.663154
12 to 19 2428.79 -1.007 0.156965
13 to 20 2477.11 -0.324 0.373098
14 to 21 2350.99 -2.107 0.017543
15 to 22 2497.66 -0.033 0.486797
16 to 23 2524.23 0.343 0.634079
17 to 24 2439.64 -0.854 0.196649
18 to 25 2506.61 0.093 0.537233
19 to 26 2530.32 0.429 0.665972
20 to 27 2512.60 0.178 0.570701
21 to 28 2582.16 1.162 0.877373
22 to 29 2436.15 -0.903 0.183282
23 to 30 2554.58 0.772 0.779917
24 to 31 2575.94 1.074 0.858588
25 to 32 2466.43 -0.475 0.317507
CDPARK for dh-ranFile-2018-07-12_00:31: 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
3494 -1.3242 0.092718
3515 -0.3653 0.357445
3528 0.2283 0.590298
3488 -1.5982 0.055002
3526 0.1370 0.554479
3496 -1.2329 0.108811
3450 -3.3333 0.000429
3550 1.2329 0.891189
3514 -0.4110 0.340551
Square side=100, avg. no. parked=3508.00 sample std.=26.07
p-value of the KSTEST for those 10 p-values: 0.078444
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-12_00:31
0.7912,0.9414,0.9313,0.7975,0.2976,0.4211,0.0216,0.2283,0.1780,0.1854,
The KS test for those 10 p-values: 0.665517
The 3DSPHERES test for dh-ranFile-2018-07-12_00:31
sample no r^3 equiv. uni.
1 20.723 0.498810
2 51.873 0.822555
3 51.450 0.820037
4 1.209 0.039494
5 16.919 0.431055
6 73.536 0.913809
7 11.073 0.308640
8 32.271 0.658937
9 0.833 0.027375
10 19.683 0.481123
11 2.184 0.070201
12 61.329 0.870528
13 22.189 0.522715
14 18.242 0.455590
15 74.564 0.916712
16 11.428 0.316769
17 38.609 0.723894
18 15.108 0.395659
19 44.680 0.774481
20 1.146 0.037465
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.724381
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-12_00:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 0.1 0.6 1.4 0.8 0.1
0.9 -1.4 -1.2 1.6 -0.2 -1.9
-0.5 -0.9 0.9 -0.8 -0.3 1.0
1.0 0.1 -0.1 0.1 0.8 -1.7
-0.2 1.3 0.1 -0.7 0.1 0.9
1.4 1.2 0.6 -1.2 0.2 -1.2
0.0 -0.4 2.1 -1.3 0.9 0.0
-0.1
Chi-square with 42 degrees of freedom:38.988810
z-score=-0.328548, p-value=0.396089
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-12_00:31
Test no p-value
1 0.902883
2 0.164427
3 0.348528
4 0.011899
5 0.430142
6 0.253996
7 0.070760
8 0.347481
9 0.140848
10 0.788754
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.133802
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-12_00:31:
(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 67004 1.71 66442 0.76
3 25000.00 24725 3.02 25285 3.25
4 6666.67 6598 0.71 6641 0.10
5 1388.89 1399 0.07 1339 1.79
6 238.10 225 0.72 252 0.81
7 34.72 43 1.97 36 0.05
8 4.96 5 0.00 4 0.19
p=0.77674 p=0.67377
Number of rngs required: 688087, p-value: 0.358
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-12_00:31
No. of wins: Observed Expected
98881 98585.9
z-score= 1.320, pvalue=0.90659
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66549 66666.7 0.208 0.208
2 37775 37654.3 0.387 0.594
3 26885 26954.7 0.180 0.775
4 19225 19313.5 0.405 1.180
5 13958 13851.4 0.820 2.000
6 10112 9943.5 2.854 4.854
7 7132 7145.0 0.024 4.878
8 5037 5139.1 2.027 6.905
9 3709 3699.9 0.023 6.928
10 2630 2666.3 0.494 7.422
11 1927 1923.3 0.007 7.429
12 1415 1388.7 0.497 7.925
13 981 1003.7 0.514 8.439
14 747 726.1 0.599 9.039
15 527 525.8 0.003 9.041
16 382 381.2 0.002 9.043
17 280 276.5 0.043 9.086
18 198 200.8 0.040 9.126
19 139 146.0 0.334 9.460
20 104 106.2 0.046 9.507
21 288 287.1 0.003 9.509
Chisq= 9.51 for 20 degrees of freedom, p= 0.02378
SUMMARY of craptest
p-value for no. of wins: 0.906590
p-value for throws/game: 0.023778
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-12_00:31
No. of wins: Observed Expected
98267 98585.9
z-score=-1.426, pvalue=0.07692
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67007 66666.7 1.737 1.737
2 37676 37654.3 0.012 1.750
3 27023 26954.7 0.173 1.923
4 19185 19313.5 0.854 2.777
5 13787 13851.4 0.300 3.077
6 9722 9943.5 4.936 8.013
7 7056 7145.0 1.109 9.122
8 5270 5139.1 3.336 12.458
9 3648 3699.9 0.727 13.185
10 2672 2666.3 0.012 13.197
11 1937 1923.3 0.097 13.294
12 1378 1388.7 0.083 13.377
13 1002 1003.7 0.003 13.380
14 697 726.1 1.169 14.550
15 532 525.8 0.072 14.622
16 417 381.2 3.372 17.994
17 282 276.5 0.108 18.101
18 190 200.8 0.584 18.686
19 139 146.0 0.334 19.020
20 100 106.2 0.364 19.383
21 280 287.1 0.176 19.560
Chisq= 19.56 for 20 degrees of freedom, p= 0.51424
SUMMARY of craptest
p-value for no. of wins: 0.076917
p-value for throws/game: 0.514237
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0004,0.0035,0.0049,0.0109,0.0119,0.0159,0.0167,0.0175,0.0216,0.0238,
0.0253,0.0274,0.0317,0.0329,0.0354,0.0370,0.0375,0.0395,0.0460,0.0496,
0.0537,0.0550,0.0562,0.0632,0.0676,0.0682,0.0687,0.0702,0.0703,0.0708,
0.0753,0.0769,0.0776,0.0784,0.0927,0.0981,0.1064,0.1088,0.1122,0.1160,
0.1202,0.1236,0.1256,0.1272,0.1285,0.1291,0.1294,0.1338,0.1341,0.1344,
0.1408,0.1426,0.1432,0.1519,0.1570,0.1577,0.1587,0.1592,0.1644,0.1657,
0.1660,0.1780,0.1833,0.1854,0.1919,0.1966,0.2076,0.2274,0.2283,0.2286,
0.2310,0.2335,0.2381,0.2409,0.2413,0.2540,0.2589,0.2700,0.2808,0.2845,
0.2878,0.2976,0.3024,0.3061,0.3075,0.3086,0.3111,0.3168,0.3175,0.3261,
0.3267,0.3391,0.3404,0.3406,0.3427,0.3470,0.3475,0.3485,0.3492,0.3574,
0.3580,0.3583,0.3619,0.3666,0.3669,0.3712,0.3716,0.3731,0.3816,0.3927,
0.3938,0.3940,0.3947,0.3957,0.3961,0.3961,0.3972,0.3979,0.4058,0.4136,
0.4211,0.4226,0.4256,0.4275,0.4291,0.4301,0.4311,0.4352,0.4355,0.4357,
0.4495,0.4527,0.4551,0.4556,0.4644,0.4760,0.4772,0.4811,0.4820,0.4858,
0.4868,0.4913,0.4928,0.4941,0.4955,0.4988,0.5092,0.5142,0.5171,0.5193,
0.5206,0.5227,0.5340,0.5372,0.5374,0.5415,0.5462,0.5545,0.5558,0.5598,
0.5707,0.5709,0.5730,0.5792,0.5814,0.5869,0.5903,0.5940,0.5993,0.6146,
0.6155,0.6202,0.6226,0.6306,0.6341,0.6345,0.6402,0.6411,0.6418,0.6538,
0.6543,0.6577,0.6589,0.6620,0.6632,0.6655,0.6660,0.6686,0.6709,0.6738,
0.6771,0.6799,0.6853,0.6923,0.6999,0.7089,0.7111,0.7239,0.7244,0.7256,
0.7263,0.7281,0.7305,0.7353,0.7387,0.7530,0.7552,0.7666,0.7745,0.7759,
0.7767,0.7778,0.7799,0.7801,0.7888,0.7888,0.7912,0.7975,0.7981,0.8012,
0.8026,0.8061,0.8093,0.8096,0.8158,0.8195,0.8200,0.8213,0.8215,0.8226,
0.8342,0.8516,0.8556,0.8563,0.8564,0.8572,0.8574,0.8586,0.8605,0.8705,
0.8705,0.8732,0.8774,0.8808,0.8900,0.8912,0.9029,0.9066,0.9138,0.9145,
0.9167,0.9182,0.9212,0.9294,0.9313,0.9334,0.9354,0.9357,0.9388,0.9414,
0.9423,0.9550,0.9586,0.9600,0.9676,0.9768,0.9843,0.9950,0.9972,
Overall p-value after applying KStest on 269 p-values = 0.184059
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.