RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-02_12:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.82 18.5878 0.647304
2 to 25 15.60 23.7806 0.874479
3 to 26 15.59 17.1565 0.556190
4 to 27 15.76 15.9789 0.474668
5 to 28 15.93 14.2954 0.353905
6 to 29 15.78 20.7768 0.763565
7 to 30 15.81 12.5828 0.236361
8 to 31 15.81 18.6445 0.650688
9 to 32 15.82 22.2956 0.826385
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.394096
Tough bday spacings test for dh-ranFile-2018-07-02_12:31: 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 11 36 64 105 113 80 38 23 18 7 5
(O-E)^2/E 0.4 0.0 1.2 0.5 2.4 0.0 3.8 1.5 0.7 0.0 0.2
Birthday Spacings: Sum(O-E)^2/E= 10.789, p= 0.626
RESULTS OF GCD FOR dh-ranFile-2018-07-02_12:31
Euclid's algorithm:
p-value, steps to gcd: 0.276581
p-value, dist. of gcd's: 0.954359
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-02_12:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.578 0.838 0.786 0.897 0.255 0.570 0.684 0.865
Bits 8 to 15---> 0.960 0.250 0.161 0.389 0.532 0.564 0.041 0.640
Bits 16 to 23---> 0.612 0.674 0.214 0.165 0.823 0.652 0.168 0.566
Bits 24 to 31---> 0.447 0.898 0.338 0.253 0.033 0.063 0.620 0.906
KS test for the above 32 p values: 0.088
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-02_12:31,
p-values for 5 runs: 0.5373, 0.4288, 0.4600, 0.9653, 0.3654
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-02_12:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 204 211.4 0.260 0.260
r= 29 4930 5134.0 8.107 8.367
r= 30 23221 23103.0 0.602 8.969
r= 31 11645 11551.5 0.756 9.726
chi-square = 9.726 with df = 3; p-value = 0.979
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-02_12:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 219 211.4 0.272 0.272
r= 30 5166 5134.0 0.199 0.471
r= 31 22856 23103.0 2.642 3.113
r= 32 11759 11551.5 3.726 6.839
chi-square = 6.839 with df = 3; p-value = 0.923
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-02_12:31
b-rank test for bits 1 to 8, p=0.02014
b-rank test for bits 2 to 9, p=0.22625
b-rank test for bits 3 to 10, p=0.77534
b-rank test for bits 4 to 11, p=0.69627
b-rank test for bits 5 to 12, p=0.73137
b-rank test for bits 6 to 13, p=0.22024
b-rank test for bits 7 to 14, p=0.32761
b-rank test for bits 8 to 15, p=0.62807
b-rank test for bits 9 to 16, p=0.95004
b-rank test for bits 10 to 17, p=0.24252
b-rank test for bits 11 to 18, p=0.23785
b-rank test for bits 12 to 19, p=0.17969
b-rank test for bits 13 to 20, p=0.73861
b-rank test for bits 14 to 21, p=0.48327
b-rank test for bits 15 to 22, p=0.22065
b-rank test for bits 16 to 23, p=0.98900
b-rank test for bits 17 to 24, p=0.95812
b-rank test for bits 18 to 25, p=0.62741
b-rank test for bits 19 to 26, p=0.67110
b-rank test for bits 20 to 27, p=0.00664
b-rank test for bits 21 to 28, p=0.27886
b-rank test for bits 22 to 29, p=0.68915
b-rank test for bits 23 to 30, p=0.79311
b-rank test for bits 24 to 31, p=0.11834
b-rank test for bits 25 to 32, p=0.61496
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 = 0.735463
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-02_12:31
(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 141861 -0.11 0.455047
2 142322 0.96 0.832523
3 141845 -0.15 0.440263
4 141142 -1.79 0.036500
5 141893 -0.04 0.484782
6 142513 1.41 0.920796
7 142426 1.21 0.886317
8 141013 -2.09 0.018120
9 141482 -1.00 0.159034
10 142065 0.36 0.641965
11 142044 0.31 0.623486
12 142095 0.43 0.667786
13 142169 0.61 0.727977
14 141612 -0.69 0.243623
15 141813 -0.23 0.410962
16 141945 0.08 0.533210
17 141417 -1.15 0.125009
18 141925 0.04 0.514603
19 141924 0.03 0.513671
20 141945 0.08 0.533210
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-02_12:31
Bits used No. missing words z-score p-value
23 to 32 141954 0.1540 0.561209
22 to 31 142017 0.3713 0.644784
21 to 30 142014 0.3609 0.640925
20 to 29 141832 -0.2667 0.394867
19 to 28 142231 1.1092 0.866330
18 to 27 141858 -0.1770 0.429754
17 to 26 141501 -1.4080 0.079560
16 to 25 142033 0.4264 0.665109
15 to 24 141793 -0.4011 0.344159
14 to 23 142038 0.4437 0.671367
13 to 22 141393 -1.7804 0.037501
12 to 21 142376 1.6092 0.946214
11 to 20 141950 0.1402 0.555765
10 to 19 142158 0.8575 0.804411
9 to 18 142158 0.8575 0.804411
8 to 17 141599 -1.0701 0.142286
7 to 16 142298 1.3402 0.909917
6 to 15 141451 -1.5804 0.057002
5 to 14 141686 -0.7701 0.220619
4 to 13 142262 1.2161 0.888027
3 to 12 141490 -1.4460 0.074093
2 to 11 142168 0.8920 0.813794
1 to 10 141896 -0.0460 0.481669
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-02_12:31
Bits used No. missing words z-score p-value
28 to 32 141915 0.0192 0.507667
27 to 31 142161 0.8531 0.803203
26 to 30 141905 -0.0147 0.494145
25 to 29 141937 0.0938 0.537365
24 to 28 142380 1.5955 0.944699
23 to 27 141932 0.0768 0.530628
22 to 26 142248 1.1480 0.874523
21 to 25 142184 0.9311 0.824095
20 to 24 142191 0.9548 0.830164
19 to 23 141899 -0.0350 0.486033
18 to 22 141996 0.2938 0.615543
17 to 21 142090 0.6124 0.729877
16 to 20 141653 -0.8689 0.192447
15 to 19 141627 -0.9571 0.169271
14 to 18 141568 -1.1571 0.123626
13 to 17 142750 2.8497 0.997812
12 to 16 142216 1.0396 0.850728
11 to 15 141704 -0.6960 0.243204
10 to 14 141503 -1.3774 0.084196
9 to 13 141762 -0.4994 0.308741
8 to 12 141885 -0.0825 0.467135
7 to 11 141979 0.2362 0.593349
6 to 10 141987 0.2633 0.603836
5 to 9 141947 0.1277 0.550805
4 to 8 141753 -0.5299 0.298080
3 to 7 142632 2.4497 0.992852
2 to 6 141775 -0.4554 0.324427
1 to 5 141548 -1.2248 0.110316
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-02_12:31
Bits used No. missing words z-score p-value
31 to 32 141770 -0.4110 0.340535
30 to 31 141969 0.1760 0.569860
29 to 30 141371 -1.5880 0.056144
28 to 29 142236 0.9636 0.832384
27 to 28 141843 -0.1957 0.422437
26 to 27 141753 -0.4612 0.322345
25 to 26 141890 -0.0570 0.477264
24 to 25 142046 0.4032 0.656583
23 to 24 142398 1.4415 0.925279
22 to 23 142188 0.8220 0.794472
21 to 22 141492 -1.2311 0.109150
20 to 21 141956 0.1377 0.554749
19 to 20 142039 0.3825 0.648958
18 to 19 142184 0.8102 0.791098
17 to 18 142638 2.1495 0.984201
16 to 17 141352 -1.6440 0.050084
15 to 16 141860 -0.1455 0.442152
14 to 15 142644 2.1672 0.984889
13 to 14 141915 0.0167 0.506672
12 to 13 141116 -2.3402 0.009637
11 to 12 142266 1.0521 0.853629
10 to 11 142190 0.8279 0.796146
9 to 10 142341 1.2734 0.898555
8 to 9 142165 0.7542 0.774632
7 to 8 141620 -0.8535 0.196696
6 to 7 142064 0.4563 0.675896
5 to 6 141708 -0.5939 0.276292
4 to 5 141857 -0.1544 0.438661
3 to 4 141702 -0.6116 0.270404
2 to 3 142389 1.4150 0.921459
1 to 2 141931 0.0639 0.525484
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-02_12:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2359.42 -1.988 0.023403
Test results for specific bytes for dh-ranFile-2018-07-02_12:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2583.23 1.177 0.880408
2 to 9 2532.89 0.465 0.679086
3 to 10 2502.96 0.042 0.516721
4 to 11 2461.79 -0.540 0.294470
5 to 12 2648.92 2.106 0.982400
6 to 13 2504.60 0.065 0.525910
7 to 14 2404.62 -1.349 0.088682
8 to 15 2415.50 -1.195 0.116034
9 to 16 2496.05 -0.056 0.477699
10 to 17 2601.14 1.430 0.923688
11 to 18 2329.67 -2.409 0.008002
12 to 19 2553.35 0.755 0.774733
13 to 20 2508.56 0.121 0.548185
14 to 21 2496.34 -0.052 0.479337
15 to 22 2537.28 0.527 0.700976
16 to 23 2529.27 0.414 0.660529
17 to 24 2414.71 -1.206 0.113873
18 to 25 2511.00 0.156 0.561817
19 to 26 2553.11 0.751 0.773681
20 to 27 2560.98 0.862 0.805767
21 to 28 2495.87 -0.058 0.476699
22 to 29 2569.89 0.988 0.838516
23 to 30 2501.00 0.014 0.505631
24 to 31 2544.07 0.623 0.733452
25 to 32 2479.98 -0.283 0.388533
CDPARK for dh-ranFile-2018-07-02_12:31: 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
3499 -1.0959 0.136563
3519 -0.1826 0.427537
3528 0.2283 0.590298
3503 -0.9132 0.180558
3553 1.3699 0.914635
3503 -0.9132 0.180558
3515 -0.3653 0.357445
3530 0.3196 0.625377
3496 -1.2329 0.108811
3526 0.1370 0.554479
Square side=100, avg. no. parked=3517.20 sample std.=16.83
p-value of the KSTEST for those 10 p-values: 0.462593
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-02_12:31
0.8430,0.6047,0.5583,0.9199,0.2389,0.5295,0.1807,0.4814,0.9647,0.0578,
The KS test for those 10 p-values: 0.933056
The 3DSPHERES test for dh-ranFile-2018-07-02_12:31
sample no r^3 equiv. uni.
1 37.493 0.713431
2 5.627 0.171030
3 14.654 0.386443
4 16.017 0.413680
5 0.816 0.026843
6 18.009 0.451347
7 2.820 0.089711
8 10.277 0.290048
9 60.611 0.867393
10 68.099 0.896683
11 55.276 0.841582
12 3.949 0.123351
13 11.464 0.317592
14 34.337 0.681636
15 12.140 0.332794
16 9.000 0.259191
17 10.515 0.295675
18 16.498 0.423017
19 68.223 0.897111
20 9.323 0.267108
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.408748
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-02_12:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
0.6 0.1 1.1 -1.3 0.8 -0.2
-0.0 -1.1 -0.1 -0.0 0.0 0.7
-1.1 0.6 0.4 -0.6 0.2 -1.1
0.4 0.8 0.2 1.3 -0.9 -0.5
-0.6 -0.1 2.8 0.1 -2.3 -1.8
0.5 0.0 0.0 1.3 -0.2 1.5
1.7 -2.0 0.9 -0.1 -0.6 0.0
-1.1
Chi-square with 42 degrees of freedom:42.590626
z-score=0.064443, p-value=0.554437
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-02_12:31
Test no p-value
1 0.129258
2 0.792828
3 0.073745
4 0.501145
5 0.012335
6 0.389539
7 0.001997
8 0.663130
9 0.801383
10 0.265179
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.091281
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-02_12:31:
(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 66560 0.17 66798 0.26
3 25000.00 25065 0.17 24886 0.52
4 6666.67 6636 0.14 6653 0.03
5 1388.89 1444 2.19 1408 0.26
6 238.10 241 0.04 219 1.53
7 34.72 48 5.08 30 0.64
8 4.96 5 0.00 5 0.00
p=0.74554 p=0.22220
Number of rngs required: 688390, p-value: 0.494
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-02_12:31
No. of wins: Observed Expected
98503 98585.9
z-score=-0.371, pvalue=0.35547
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66575 66666.7 0.126 0.126
2 37575 37654.3 0.167 0.293
3 26748 26954.7 1.586 1.879
4 19426 19313.5 0.656 2.534
5 13728 13851.4 1.100 3.634
6 10074 9943.5 1.712 5.346
7 7268 7145.0 2.117 7.462
8 5316 5139.1 6.091 13.554
9 3708 3699.9 0.018 13.571
10 2725 2666.3 1.292 14.864
11 1865 1923.3 1.769 16.633
12 1404 1388.7 0.168 16.800
13 994 1003.7 0.094 16.894
14 686 726.1 2.219 19.113
15 501 525.8 1.173 20.286
16 382 381.2 0.002 20.288
17 291 276.5 0.756 21.045
18 203 200.8 0.023 21.068
19 131 146.0 1.538 22.606
20 117 106.2 1.095 23.701
21 283 287.1 0.059 23.760
Chisq= 23.76 for 20 degrees of freedom, p= 0.74697
SUMMARY of craptest
p-value for no. of wins: 0.355471
p-value for throws/game: 0.746968
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-02_12:31
No. of wins: Observed Expected
98211 98585.9
z-score=-1.677, pvalue=0.04681
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66594 66666.7 0.079 0.079
2 37887 37654.3 1.438 1.517
3 26811 26954.7 0.766 2.283
4 19213 19313.5 0.523 2.806
5 13904 13851.4 0.200 3.006
6 10092 9943.5 2.216 5.222
7 7143 7145.0 0.001 5.223
8 5170 5139.1 0.186 5.409
9 3671 3699.9 0.225 5.634
10 2593 2666.3 2.015 7.649
11 1843 1923.3 3.355 11.004
12 1396 1388.7 0.038 11.042
13 973 1003.7 0.940 11.982
14 692 726.1 1.605 13.587
15 544 525.8 0.627 14.214
16 386 381.2 0.062 14.276
17 320 276.5 6.830 21.106
18 212 200.8 0.621 21.728
19 153 146.0 0.337 22.065
20 95 106.2 1.184 23.249
21 308 287.1 1.519 24.768
Chisq= 24.77 for 20 degrees of freedom, p= 0.78956
SUMMARY of craptest
p-value for no. of wins: 0.046812
p-value for throws/game: 0.789561
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0020,0.0066,0.0080,0.0096,0.0123,0.0181,0.0201,0.0234,0.0268,0.0330,
0.0365,0.0375,0.0406,0.0468,0.0501,0.0561,0.0570,0.0578,0.0629,0.0737,
0.0741,0.0796,0.0842,0.0882,0.0887,0.0897,0.0913,0.1088,0.1091,0.1103,
0.1139,0.1160,0.1183,0.1234,0.1236,0.1250,0.1293,0.1366,0.1423,0.1590,
0.1612,0.1648,0.1679,0.1693,0.1710,0.1797,0.1806,0.1806,0.1807,0.1924,
0.1967,0.2140,0.2202,0.2206,0.2207,0.2222,0.2262,0.2364,0.2378,0.2389,
0.2425,0.2432,0.2436,0.2498,0.2530,0.2551,0.2592,0.2652,0.2671,0.2704,
0.2763,0.2766,0.2789,0.2900,0.2945,0.2957,0.2981,0.3087,0.3176,0.3223,
0.3244,0.3276,0.3328,0.3379,0.3405,0.3442,0.3539,0.3555,0.3574,0.3654,
0.3864,0.3885,0.3890,0.3895,0.3941,0.3949,0.4087,0.4110,0.4137,0.4224,
0.4230,0.4275,0.4288,0.4298,0.4387,0.4403,0.4422,0.4467,0.4513,0.4550,
0.4600,0.4626,0.4671,0.4747,0.4767,0.4773,0.4777,0.4793,0.4814,0.4817,
0.4833,0.4848,0.4860,0.4940,0.4941,0.5011,0.5056,0.5067,0.5077,0.5137,
0.5146,0.5167,0.5255,0.5259,0.5295,0.5306,0.5317,0.5332,0.5332,0.5373,
0.5374,0.5482,0.5508,0.5544,0.5545,0.5547,0.5558,0.5562,0.5583,0.5612,
0.5618,0.5638,0.5656,0.5699,0.5702,0.5779,0.5903,0.5933,0.6038,0.6047,
0.6119,0.6150,0.6155,0.6198,0.6235,0.6254,0.6258,0.6274,0.6281,0.6397,
0.6409,0.6420,0.6448,0.6473,0.6490,0.6507,0.6520,0.6566,0.6605,0.6631,
0.6651,0.6678,0.6711,0.6714,0.6735,0.6759,0.6791,0.6816,0.6841,0.6892,
0.6963,0.7010,0.7134,0.7280,0.7299,0.7314,0.7335,0.7355,0.7386,0.7455,
0.7470,0.7636,0.7737,0.7746,0.7747,0.7753,0.7856,0.7896,0.7911,0.7928,
0.7931,0.7945,0.7961,0.8014,0.8032,0.8044,0.8044,0.8058,0.8138,0.8226,
0.8241,0.8264,0.8302,0.8324,0.8325,0.8377,0.8385,0.8416,0.8430,0.8507,
0.8536,0.8652,0.8663,0.8674,0.8745,0.8745,0.8804,0.8863,0.8880,0.8967,
0.8971,0.8972,0.8978,0.8986,0.9057,0.9099,0.9146,0.9199,0.9208,0.9215,
0.9228,0.9237,0.9253,0.9331,0.9447,0.9462,0.9500,0.9544,0.9581,0.9596,
0.9647,0.9653,0.9790,0.9824,0.9842,0.9849,0.9890,0.9929,0.9978,
Overall p-value after applying KStest on 269 p-values = 0.735248
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.