RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-26_17:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.88 7.4751 0.023478
2 to 25 15.52 24.0437 0.881746
3 to 26 15.95 16.9775 0.544107
4 to 27 15.59 20.5747 0.754107
5 to 28 15.67 19.3070 0.688802
6 to 29 15.86 18.3485 0.632819
7 to 30 15.62 16.8173 0.533194
8 to 31 15.58 20.5844 0.754567
9 to 32 15.73 27.3281 0.946572
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.174411
Tough bday spacings test for dh-ranFile-2018-06-26_17:31: 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 8 40 77 94 93 62 63 40 14 4 5
(O-E)^2/E 0.1 0.3 0.2 0.1 0.2 3.3 2.3 3.5 0.1 1.0 0.2
Birthday Spacings: Sum(O-E)^2/E= 11.444, p= 0.676
RESULTS OF GCD FOR dh-ranFile-2018-06-26_17:31
Euclid's algorithm:
p-value, steps to gcd: 0.658187
p-value, dist. of gcd's: 0.328427
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-26_17:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.209 0.686 0.640 0.216 0.363 0.489 0.348 0.292
Bits 8 to 15---> 0.290 0.191 0.476 0.846 0.837 0.986 0.679 0.933
Bits 16 to 23---> 0.869 0.952 0.555 0.603 0.214 0.197 0.714 0.950
Bits 24 to 31---> 0.348 0.534 0.909 0.308 0.978 0.811 0.791 0.546
KS test for the above 32 p values: 0.888
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-26_17:31,
p-values for 5 runs: 0.2154, 0.6271, 0.5832, 0.5141, 0.2000
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-26_17:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 190 211.4 2.170 2.170
r= 29 5219 5134.0 1.407 3.577
r= 30 23255 23103.0 0.999 4.576
r= 31 11336 11551.5 4.021 8.597
chi-square = 8.597 with df = 3; p-value = 0.965
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-26_17:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 209 211.4 0.028 0.028
r= 30 5198 5134.0 0.798 0.825
r= 31 23237 23103.0 0.777 1.602
r= 32 11356 11551.5 3.309 4.911
chi-square = 4.911 with df = 3; p-value = 0.822
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-26_17:31
b-rank test for bits 1 to 8, p=0.78204
b-rank test for bits 2 to 9, p=0.55437
b-rank test for bits 3 to 10, p=0.88674
b-rank test for bits 4 to 11, p=0.84270
b-rank test for bits 5 to 12, p=0.72955
b-rank test for bits 6 to 13, p=0.99654
b-rank test for bits 7 to 14, p=0.82527
b-rank test for bits 8 to 15, p=0.39631
b-rank test for bits 9 to 16, p=0.54086
b-rank test for bits 10 to 17, p=0.84476
b-rank test for bits 11 to 18, p=0.21287
b-rank test for bits 12 to 19, p=0.52551
b-rank test for bits 13 to 20, p=0.19219
b-rank test for bits 14 to 21, p=0.09965
b-rank test for bits 15 to 22, p=0.79630
b-rank test for bits 16 to 23, p=0.51456
b-rank test for bits 17 to 24, p=0.61935
b-rank test for bits 18 to 25, p=0.76728
b-rank test for bits 19 to 26, p=0.25245
b-rank test for bits 20 to 27, p=0.94387
b-rank test for bits 21 to 28, p=0.92382
b-rank test for bits 22 to 29, p=0.61685
b-rank test for bits 23 to 30, p=0.30418
b-rank test for bits 24 to 31, p=0.08642
b-rank test for bits 25 to 32, p=0.73670
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 = 0.136403
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-26_17:31
(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 142004 0.22 0.587528
2 140938 -2.27 0.011620
3 141536 -0.87 0.191532
4 141407 -1.17 0.120264
5 141473 -1.02 0.153992
6 141783 -0.30 0.383935
7 141302 -1.42 0.077950
8 141658 -0.59 0.278528
9 141895 -0.03 0.486645
10 142310 0.94 0.825401
11 142226 0.74 0.770315
12 142368 1.07 0.858063
13 141740 -0.40 0.346189
14 142104 0.45 0.675387
15 141362 -1.28 0.100482
16 141502 -0.95 0.170623
17 141843 -0.15 0.438420
18 141907 -0.01 0.497828
19 141879 -0.07 0.471753
20 141685 -0.52 0.300092
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-26_17:31
Bits used No. missing words z-score p-value
23 to 32 142001 0.3161 0.624038
22 to 31 142280 1.2782 0.899406
21 to 30 141482 -1.4736 0.070301
20 to 29 141922 0.0437 0.517424
19 to 28 142057 0.5092 0.694696
18 to 27 142087 0.6127 0.729948
17 to 26 142309 1.3782 0.915925
16 to 25 141956 0.1609 0.563926
15 to 24 141918 0.0299 0.511925
14 to 23 141672 -0.8184 0.206570
13 to 22 141795 -0.3942 0.346701
12 to 21 142062 0.5264 0.700712
11 to 20 141725 -0.6356 0.262512
10 to 19 141837 -0.2494 0.401520
9 to 18 142556 2.2299 0.987123
8 to 17 141487 -1.4563 0.072653
7 to 16 142002 0.3196 0.625346
6 to 15 141294 -2.1218 0.016926
5 to 14 141682 -0.7839 0.216550
4 to 13 141795 -0.3942 0.346701
3 to 12 141674 -0.8115 0.208544
2 to 11 142001 0.3161 0.624038
1 to 10 142333 1.4609 0.927983
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-26_17:31
Bits used No. missing words z-score p-value
28 to 32 142524 2.0836 0.981403
27 to 31 142216 1.0396 0.850728
26 to 30 142024 0.3887 0.651255
25 to 29 141494 -1.4079 0.079581
24 to 28 142158 0.8429 0.800372
23 to 27 142016 0.3616 0.641172
22 to 26 142043 0.4531 0.674768
21 to 25 141891 -0.0621 0.475227
20 to 24 141648 -0.8859 0.187845
19 to 23 141953 0.1480 0.558842
18 to 22 141811 -0.3333 0.369446
17 to 21 142431 1.7684 0.961501
16 to 20 141956 0.1582 0.562852
15 to 19 141681 -0.7740 0.219465
14 to 18 142026 0.3955 0.653760
13 to 17 141728 -0.6147 0.269384
12 to 16 141613 -1.0045 0.157567
11 to 15 141930 0.0701 0.527930
10 to 14 142060 0.5107 0.695236
9 to 13 142058 0.5040 0.692857
8 to 12 141397 -1.7367 0.041219
7 to 11 141629 -0.9503 0.170987
6 to 10 141707 -0.6859 0.246399
5 to 9 141686 -0.7571 0.224510
4 to 8 142147 0.8057 0.789781
3 to 7 142470 1.9006 0.971321
2 to 6 142060 0.5107 0.695236
1 to 5 141681 -0.7740 0.219465
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-26_17:31
Bits used No. missing words z-score p-value
31 to 32 142300 1.1524 0.875426
30 to 31 141890 -0.0570 0.477264
29 to 30 142368 1.3530 0.911974
28 to 29 142034 0.3678 0.643473
27 to 28 141694 -0.6352 0.262652
26 to 27 142042 0.3914 0.652233
25 to 26 141922 0.0374 0.514907
24 to 25 142461 1.6273 0.948168
23 to 24 141371 -1.5880 0.056144
22 to 23 142077 0.4946 0.689559
21 to 22 142133 0.6598 0.745307
20 to 21 141956 0.1377 0.554749
19 to 20 141726 -0.5408 0.294324
18 to 19 141957 0.1406 0.555915
17 to 18 142012 0.3029 0.619002
16 to 17 141615 -0.8682 0.192634
15 to 16 141696 -0.6293 0.264579
14 to 15 142336 1.2586 0.895915
13 to 14 142148 0.7040 0.759297
12 to 13 142272 1.0698 0.857651
11 to 12 141848 -0.1809 0.428217
10 to 11 141626 -0.8358 0.201639
9 to 10 141942 0.0964 0.538387
8 to 9 141678 -0.6824 0.247496
7 to 8 141507 -1.1868 0.117650
6 to 7 142133 0.6598 0.745307
5 to 6 142707 2.3530 0.990689
4 to 5 141771 -0.4081 0.341617
3 to 4 142062 0.4504 0.673772
2 to 3 141380 -1.5614 0.059209
1 to 2 141514 -1.1662 0.121774
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-26_17:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2524.00 0.339 0.632827
Test results for specific bytes for dh-ranFile-2018-06-26_17:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2381.43 -1.677 0.046781
2 to 9 2580.89 1.144 0.873684
3 to 10 2560.30 0.853 0.803102
4 to 11 2487.41 -0.178 0.429315
5 to 12 2567.87 0.960 0.831425
6 to 13 2683.73 2.598 0.995315
7 to 14 2476.08 -0.338 0.367579
8 to 15 2409.53 -1.279 0.100361
9 to 16 2625.81 1.779 0.962397
10 to 17 2376.69 -1.744 0.040593
11 to 18 2518.43 0.261 0.602818
12 to 19 2404.30 -1.353 0.087963
13 to 20 2510.89 0.154 0.561211
14 to 21 2474.33 -0.363 0.358266
15 to 22 2534.67 0.490 0.688054
16 to 23 2424.51 -1.068 0.142854
17 to 24 2393.25 -1.510 0.065555
18 to 25 2458.21 -0.591 0.277242
19 to 26 2559.70 0.844 0.800759
20 to 27 2463.86 -0.511 0.304626
21 to 28 2483.07 -0.239 0.405367
22 to 29 2546.02 0.651 0.742424
23 to 30 2513.47 0.191 0.575549
24 to 31 2580.92 1.144 0.873775
25 to 32 2522.30 0.315 0.623749
CDPARK for dh-ranFile-2018-06-26_17:31: 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
3553 1.3699 0.914635
3490 -1.5068 0.065925
3526 0.1370 0.554479
3551 1.2785 0.899470
3532 0.4110 0.659449
3525 0.0913 0.536383
3538 0.6849 0.753306
3521 -0.0913 0.463617
3507 -0.7306 0.232514
3548 1.1416 0.873180
Square side=100, avg. no. parked=3529.10 sample std.=18.99
p-value of the KSTEST for those 10 p-values: 0.511110
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-26_17:31
0.3780,0.1726,0.1938,0.9032,0.1252,0.9655,0.9850,0.4841,0.4372,0.7371,
The KS test for those 10 p-values: 0.563873
The 3DSPHERES test for dh-ranFile-2018-06-26_17:31
sample no r^3 equiv. uni.
1 88.006 0.946791
2 56.233 0.846560
3 73.113 0.912585
4 16.857 0.429880
5 12.337 0.337177
6 43.488 0.765334
7 48.709 0.802816
8 53.906 0.834184
9 7.733 0.227218
10 89.484 0.949349
11 38.061 0.718807
12 45.326 0.779281
13 24.702 0.561063
14 54.048 0.834965
15 19.580 0.479339
16 15.880 0.411009
17 20.949 0.502571
18 3.141 0.099416
19 6.905 0.205596
20 78.871 0.927851
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.065849
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-26_17:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.8 1.3 0.1 0.2 -0.8 -0.8
1.8 -0.5 -1.4 -0.5 -0.5 0.6
0.1 1.1 -0.1 1.8 0.0 -1.3
-0.7 -0.9 -0.4 -0.5 2.7 0.2
-0.3 -0.8 -0.6 0.5 0.2 -0.5
0.0 -0.1 -0.0 0.5 -0.1 -0.1
-0.5 -0.7 0.5 -0.7 0.1 1.0
-1.1
Chi-square with 42 degrees of freedom:30.587841
z-score=-1.245169, p-value=0.095865
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-26_17:31
Test no p-value
1 0.324794
2 0.719752
3 0.483132
4 0.334175
5 0.978104
6 0.141943
7 0.802742
8 0.043189
9 0.321629
10 0.881447
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.966711
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-26_17:31:
(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 66694 0.01 66564 0.16
3 25000.00 25114 0.52 25160 1.02
4 6666.67 6592 0.84 6615 0.40
5 1388.89 1319 3.52 1391 0.00
6 238.10 234 0.07 230 0.28
7 34.72 38 0.31 33 0.09
8 4.96 8 1.86 6 0.22
p=0.69081 p=0.09602
Number of rngs required: 687459, p-value: 0.137
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-26_17:31
No. of wins: Observed Expected
98342 98585.9
z-score=-1.091, pvalue=0.13771
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66443 66666.7 0.750 0.750
2 37581 37654.3 0.143 0.893
3 26889 26954.7 0.160 1.053
4 19517 19313.5 2.145 3.198
5 14118 13851.4 5.131 8.329
6 10028 9943.5 0.717 9.046
7 7191 7145.0 0.296 9.342
8 5150 5139.1 0.023 9.365
9 3510 3699.9 9.743 19.109
10 2671 2666.3 0.008 19.117
11 1863 1923.3 1.892 21.009
12 1465 1388.7 4.188 25.197
13 916 1003.7 7.665 32.862
14 728 726.1 0.005 32.867
15 505 525.8 0.826 33.693
16 397 381.2 0.659 34.352
17 267 276.5 0.329 34.681
18 198 200.8 0.040 34.721
19 170 146.0 3.951 38.672
20 108 106.2 0.030 38.702
21 285 287.1 0.016 38.717
Chisq= 38.72 for 20 degrees of freedom, p= 0.99277
SUMMARY of craptest
p-value for no. of wins: 0.137707
p-value for throws/game: 0.992772
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-26_17:31
No. of wins: Observed Expected
98389 98585.9
z-score=-0.880, pvalue=0.18930
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66778 66666.7 0.186 0.186
2 37773 37654.3 0.374 0.560
3 26876 26954.7 0.230 0.790
4 19486 19313.5 1.541 2.331
5 13754 13851.4 0.685 3.017
6 9920 9943.5 0.056 3.072
7 7206 7145.0 0.520 3.593
8 4938 5139.1 7.867 11.460
9 3767 3699.9 1.218 12.678
10 2626 2666.3 0.609 13.287
11 1860 1923.3 2.085 15.372
12 1406 1388.7 0.215 15.587
13 1014 1003.7 0.105 15.692
14 740 726.1 0.265 15.957
15 498 525.8 1.474 17.430
16 370 381.2 0.326 17.756
17 275 276.5 0.009 17.765
18 183 200.8 1.583 19.348
19 137 146.0 0.553 19.901
20 117 106.2 1.095 20.996
21 276 287.1 0.430 21.426
Chisq= 21.43 for 20 degrees of freedom, p= 0.62756
SUMMARY of craptest
p-value for no. of wins: 0.189303
p-value for throws/game: 0.627555
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0116,0.0169,0.0235,0.0406,0.0412,0.0432,0.0468,0.0561,0.0592,0.0656,
0.0658,0.0659,0.0703,0.0727,0.0780,0.0796,0.0864,0.0880,0.0959,0.0960,
0.0994,0.0996,0.1004,0.1005,0.1177,0.1203,0.1218,0.1252,0.1364,0.1367,
0.1377,0.1419,0.1429,0.1540,0.1576,0.1706,0.1710,0.1726,0.1744,0.1878,
0.1893,0.1908,0.1915,0.1922,0.1926,0.1938,0.1974,0.2000,0.2016,0.2056,
0.2066,0.2085,0.2089,0.2129,0.2143,0.2154,0.2163,0.2166,0.2195,0.2195,
0.2245,0.2272,0.2325,0.2464,0.2475,0.2524,0.2625,0.2627,0.2646,0.2694,
0.2772,0.2785,0.2902,0.2915,0.2943,0.3001,0.3042,0.3046,0.3081,0.3216,
0.3248,0.3284,0.3342,0.3372,0.3416,0.3462,0.3467,0.3467,0.3480,0.3485,
0.3583,0.3635,0.3676,0.3694,0.3780,0.3839,0.3963,0.4015,0.4054,0.4110,
0.4282,0.4293,0.4299,0.4372,0.4384,0.4636,0.4718,0.4752,0.4756,0.4773,
0.4793,0.4831,0.4841,0.4866,0.4887,0.4978,0.5026,0.5111,0.5119,0.5141,
0.5146,0.5149,0.5174,0.5255,0.5279,0.5332,0.5338,0.5364,0.5384,0.5409,
0.5441,0.5456,0.5544,0.5545,0.5547,0.5549,0.5559,0.5588,0.5611,0.5612,
0.5629,0.5639,0.5639,0.5755,0.5832,0.5875,0.6028,0.6034,0.6169,0.6190,
0.6193,0.6237,0.6240,0.6240,0.6253,0.6271,0.6276,0.6328,0.6328,0.6398,
0.6412,0.6435,0.6513,0.6522,0.6538,0.6582,0.6594,0.6738,0.6748,0.6754,
0.6760,0.6791,0.6857,0.6881,0.6888,0.6896,0.6908,0.6929,0.6947,0.6952,
0.6952,0.7007,0.7142,0.7188,0.7198,0.7296,0.7299,0.7367,0.7371,0.7424,
0.7453,0.7453,0.7533,0.7541,0.7546,0.7593,0.7653,0.7673,0.7703,0.7793,
0.7820,0.7898,0.7910,0.7963,0.8004,0.8008,0.8027,0.8028,0.8031,0.8114,
0.8216,0.8253,0.8254,0.8314,0.8342,0.8350,0.8368,0.8427,0.8448,0.8461,
0.8466,0.8507,0.8577,0.8581,0.8686,0.8732,0.8737,0.8738,0.8754,0.8814,
0.8817,0.8867,0.8881,0.8959,0.8994,0.8995,0.9032,0.9089,0.9120,0.9126,
0.9146,0.9159,0.9238,0.9279,0.9280,0.9333,0.9439,0.9466,0.9468,0.9482,
0.9493,0.9497,0.9522,0.9615,0.9624,0.9648,0.9655,0.9667,0.9713,0.9779,
0.9781,0.9814,0.9850,0.9856,0.9871,0.9907,0.9928,0.9953,0.9965,
Overall p-value after applying KStest on 269 p-values = 0.080067
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.