RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-06-24_15:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 16.06 20.6574 0.758008
2 to 25 15.62 38.0291 0.997565
3 to 26 15.73 12.6273 0.239243
4 to 27 15.85 14.1521 0.343690
5 to 28 15.99 17.2882 0.564986
6 to 29 15.83 33.2822 0.989622
7 to 30 15.87 10.4542 0.116506
8 to 31 15.68 13.0019 0.263940
9 to 32 15.90 20.0750 0.729587
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.291000
Tough bday spacings test for dh-ranFile-2018-06-24_15:31: 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 42 78 95 96 69 42 30 20 9 8
(O-E)^2/E 0.4 0.8 0.3 0.1 0.0 1.1 2.0 0.0 1.8 0.9 3.8
Birthday Spacings: Sum(O-E)^2/E= 11.019, p= 0.644
RESULTS OF GCD FOR dh-ranFile-2018-06-24_15:31
Euclid's algorithm:
p-value, steps to gcd: 0.432628
p-value, dist. of gcd's: 0.791532
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-06-24_15:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.746 0.062 0.962 0.001 0.162 0.249 0.585 0.332
Bits 8 to 15---> 0.488 0.612 0.714 0.829 0.469 0.379 0.902 0.340
Bits 16 to 23---> 0.906 0.596 0.256 0.107 0.126 0.932 0.841 0.766
Bits 24 to 31---> 0.871 0.989 0.105 0.494 0.337 0.134 0.921 0.612
KS test for the above 32 p values: 0.245
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-06-24_15:31,
p-values for 5 runs: 0.2431, 0.0121, 0.4310, 0.7015, 0.6958
Rank test for binary matrices (31x31) for dh-ranFile-2018-06-24_15:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 208 211.4 0.055 0.055
r= 29 5211 5134.0 1.155 1.210
r= 30 23047 23103.0 0.136 1.346
r= 31 11534 11551.5 0.027 1.372
chi-square = 1.372 with df = 3; p-value = 0.288
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-06-24_15:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 200 211.4 0.617 0.617
r= 30 5099 5134.0 0.239 0.855
r= 31 23249 23103.0 0.922 1.777
r= 32 11452 11551.5 0.857 2.635
chi-square = 2.635 with df = 3; p-value = 0.549
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-06-24_15:31
b-rank test for bits 1 to 8, p=0.29101
b-rank test for bits 2 to 9, p=0.31922
b-rank test for bits 3 to 10, p=0.80978
b-rank test for bits 4 to 11, p=0.78807
b-rank test for bits 5 to 12, p=0.71785
b-rank test for bits 6 to 13, p=0.93820
b-rank test for bits 7 to 14, p=0.64032
b-rank test for bits 8 to 15, p=0.08708
b-rank test for bits 9 to 16, p=0.71302
b-rank test for bits 10 to 17, p=0.82771
b-rank test for bits 11 to 18, p=0.14009
b-rank test for bits 12 to 19, p=0.63352
b-rank test for bits 13 to 20, p=0.41199
b-rank test for bits 14 to 21, p=0.59185
b-rank test for bits 15 to 22, p=0.96095
b-rank test for bits 16 to 23, p=0.21284
b-rank test for bits 17 to 24, p=0.59365
b-rank test for bits 18 to 25, p=0.55547
b-rank test for bits 19 to 26, p=0.85684
b-rank test for bits 20 to 27, p=0.93618
b-rank test for bits 21 to 28, p=0.21700
b-rank test for bits 22 to 29, p=0.10828
b-rank test for bits 23 to 30, p=0.77574
b-rank test for bits 24 to 31, p=0.64363
b-rank test for bits 25 to 32, p=0.45152
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 = 0.392067
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-06-24_15:31
(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 142003 0.22 0.586619
2 141514 -0.92 0.177830
3 141974 0.15 0.560051
4 141722 -0.44 0.330807
5 141950 0.10 0.537852
6 142268 0.84 0.798989
7 142920 2.36 0.990896
8 141880 -0.07 0.472683
9 141611 -0.70 0.242891
10 142044 0.31 0.623486
11 141820 -0.21 0.417335
12 141788 -0.28 0.388404
13 141907 -0.01 0.497828
14 141390 -1.21 0.112491
15 141505 -0.94 0.172407
16 142251 0.80 0.787650
17 141382 -1.23 0.108960
18 141608 -0.70 0.240703
19 141839 -0.16 0.434739
20 141651 -0.60 0.273063
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-06-24_15:31
Bits used No. missing words z-score p-value
23 to 32 142142 0.8023 0.788813
22 to 31 142216 1.0575 0.854854
21 to 30 141858 -0.1770 0.429754
20 to 29 141408 -1.7287 0.041929
19 to 28 142197 0.9920 0.839393
18 to 27 142365 1.5713 0.941941
17 to 26 142364 1.5678 0.941539
16 to 25 141486 -1.4598 0.072178
15 to 24 141515 -1.3598 0.086953
14 to 23 141802 -0.3701 0.355653
13 to 22 141779 -0.4494 0.326567
12 to 21 141331 -1.9942 0.023063
11 to 20 141913 0.0127 0.505049
10 to 19 141939 0.1023 0.540745
9 to 18 141947 0.1299 0.551676
8 to 17 141861 -0.1667 0.433821
7 to 16 141831 -0.2701 0.393540
6 to 15 141718 -0.6598 0.254704
5 to 14 142067 0.5437 0.706673
4 to 13 141900 -0.0322 0.487167
3 to 12 141576 -1.1494 0.125193
2 to 11 142134 0.7747 0.780749
1 to 10 141699 -0.7253 0.234141
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-06-24_15:31
Bits used No. missing words z-score p-value
28 to 32 142112 0.6870 0.753964
27 to 31 141474 -1.4757 0.070013
26 to 30 142266 1.2091 0.886678
25 to 29 141764 -0.4926 0.311132
24 to 28 141488 -1.4282 0.076612
23 to 27 142311 1.3616 0.913337
22 to 26 142120 0.7141 0.762428
21 to 25 141892 -0.0587 0.476577
20 to 24 142152 0.8226 0.794635
19 to 23 141796 -0.3842 0.350426
18 to 22 141813 -0.3265 0.372007
17 to 21 141167 -2.5164 0.005928
16 to 20 142078 0.5718 0.716259
15 to 19 141253 -2.2248 0.013046
14 to 18 141690 -0.7435 0.228592
13 to 17 141663 -0.8350 0.201854
12 to 16 142451 1.8362 0.966834
11 to 15 142149 0.8124 0.791731
10 to 14 142107 0.6701 0.748593
9 to 13 141596 -1.0621 0.144087
8 to 12 141454 -1.5435 0.061356
7 to 11 142276 1.2429 0.893057
6 to 10 141730 -0.6079 0.271628
5 to 9 141797 -0.3808 0.351683
4 to 8 141851 -0.1977 0.421629
3 to 7 141928 0.0633 0.525232
2 to 6 142282 1.2633 0.896757
1 to 5 141741 -0.5706 0.284132
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-06-24_15:31
Bits used No. missing words z-score p-value
31 to 32 142637 2.1465 0.984084
30 to 31 141022 -2.6175 0.004429
29 to 30 142034 0.3678 0.643473
28 to 29 141732 -0.5231 0.300453
27 to 28 142192 0.8338 0.797813
26 to 27 142414 1.4887 0.931717
25 to 26 141947 0.1111 0.544240
24 to 25 141974 0.1908 0.575646
23 to 24 141771 -0.4081 0.341617
22 to 23 141656 -0.7473 0.227445
21 to 22 141689 -0.6499 0.257865
20 to 21 142380 1.3884 0.917493
19 to 20 141916 0.0197 0.507849
18 to 19 141663 -0.7266 0.233724
17 to 18 142234 0.9577 0.830900
16 to 17 142317 1.2026 0.885428
15 to 16 141533 -1.1101 0.133474
14 to 15 141658 -0.7414 0.229230
13 to 14 141429 -1.4169 0.078256
12 to 13 141596 -0.9243 0.177671
11 to 12 141989 0.2350 0.592901
10 to 11 142395 1.4327 0.924022
9 to 10 141721 -0.5555 0.289261
8 to 9 142282 1.0993 0.864186
7 to 8 141677 -0.6853 0.246565
6 to 7 141835 -0.2193 0.413223
5 to 6 141725 -0.5437 0.293308
4 to 5 141892 -0.0511 0.479615
3 to 4 141617 -0.8623 0.194253
2 to 3 141754 -0.4582 0.323404
1 to 2 142006 0.2852 0.612240
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-06-24_15:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2523.92 0.338 0.632442
Test results for specific bytes for dh-ranFile-2018-06-24_15:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2469.53 -0.431 0.333268
2 to 9 2620.38 1.702 0.955664
3 to 10 2537.18 0.526 0.700497
4 to 11 2522.05 0.312 0.622409
5 to 12 2496.69 -0.047 0.481343
6 to 13 2438.94 -0.864 0.193909
7 to 14 2443.88 -0.794 0.213679
8 to 15 2643.32 2.027 0.978662
9 to 16 2562.99 0.891 0.813481
10 to 17 2409.94 -1.274 0.101385
11 to 18 2493.65 -0.090 0.464214
12 to 19 2502.95 0.042 0.516613
13 to 20 2403.12 -1.370 0.085338
14 to 21 2498.71 -0.018 0.492706
15 to 22 2542.70 0.604 0.727047
16 to 23 2458.48 -0.587 0.278545
17 to 24 2412.45 -1.238 0.107822
18 to 25 2420.98 -1.118 0.131876
19 to 26 2388.84 -1.572 0.057972
20 to 27 2455.45 -0.630 0.264342
21 to 28 2498.64 -0.019 0.492336
22 to 29 2625.18 1.770 0.961662
23 to 30 2593.08 1.316 0.905980
24 to 31 2565.41 0.925 0.822544
25 to 32 2550.81 0.719 0.763780
CDPARK for dh-ranFile-2018-06-24_15:31: 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
3482 -1.8721 0.030593
3542 0.8676 0.807188
3524 0.0457 0.518210
3507 -0.7306 0.232514
3505 -0.8219 0.205562
3540 0.7763 0.781201
3500 -1.0502 0.146807
3474 -2.2374 0.012629
3529 0.2740 0.607947
Square side=100, avg. no. parked=3515.60 sample std.=24.96
p-value of the KSTEST for those 10 p-values: 0.443047
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-06-24_15:31
0.9559,0.4152,0.9366,0.5882,0.5300,0.7148,0.4447,0.1036,0.4627,0.0595,
The KS test for those 10 p-values: 0.873628
The 3DSPHERES test for dh-ranFile-2018-06-24_15:31
sample no r^3 equiv. uni.
1 15.890 0.411195
2 24.563 0.559018
3 17.889 0.449150
4 37.456 0.713076
5 43.029 0.761722
6 1.817 0.058773
7 10.345 0.291661
8 66.117 0.889626
9 141.838 0.991155
10 26.002 0.579673
11 8.357 0.243131
12 39.613 0.732977
13 1.493 0.048548
14 95.710 0.958842
15 116.666 0.979531
16 5.353 0.163432
17 41.673 0.750697
18 8.323 0.242282
19 10.501 0.295325
20 24.653 0.560340
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.777699
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-06-24_15:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-1.5 -1.6 0.3 -0.7 -0.9 -0.2
0.1 0.0 0.8 0.5 1.0 0.1
-0.0 -0.5 -0.0 -0.8 -1.1 -0.1
0.5 1.2 1.1 0.0 0.6 -1.8
-1.3 -1.0 0.1 0.9 0.5 -1.0
0.9 0.6 -0.3 1.3 0.1 1.7
1.7 -0.1 -0.4 -0.1 0.1 -1.0
-0.1
Chi-square with 42 degrees of freedom:30.782349
z-score=-1.223946, p-value=0.100400
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-06-24_15:31
Test no p-value
1 0.562025
2 0.427378
3 0.618341
4 0.321471
5 0.006805
6 0.430592
7 0.029844
8 0.983763
9 0.034036
10 0.157442
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.083383
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-06-24_15:31:
(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 66419 0.92 66882 0.70
3 25000.00 25157 0.99 24965 0.05
4 6666.67 6750 1.04 6514 3.50
5 1388.89 1403 0.14 1382 0.03
6 238.10 227 0.52 218 1.70
7 34.72 35 0.00 30 0.64
8 4.96 8 1.86 8 1.86
p=0.51534 p=0.79473
Number of rngs required: 690050, p-value: 0.974
RESULTS OF CRAPS TEST for dh-ranFile-2018-06-24_15:31
No. of wins: Observed Expected
98722 98585.9
z-score= 0.609, pvalue=0.72871
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66608 66666.7 0.052 0.052
2 37734 37654.3 0.169 0.220
3 26598 26954.7 4.721 4.941
4 19581 19313.5 3.706 8.647
5 13969 13851.4 0.998 9.646
6 10038 9943.5 0.897 10.543
7 7058 7145.0 1.060 11.603
8 5151 5139.1 0.028 11.630
9 3714 3699.9 0.054 11.684
10 2707 2666.3 0.621 12.306
11 1912 1923.3 0.067 12.373
12 1326 1388.7 2.834 15.207
13 952 1003.7 2.665 17.872
14 741 726.1 0.304 18.176
15 531 525.8 0.051 18.226
16 391 381.2 0.255 18.481
17 260 276.5 0.989 19.470
18 197 200.8 0.073 19.543
19 145 146.0 0.007 19.550
20 102 106.2 0.167 19.717
21 285 287.1 0.016 19.733
Chisq= 19.73 for 20 degrees of freedom, p= 0.52524
SUMMARY of craptest
p-value for no. of wins: 0.728706
p-value for throws/game: 0.525237
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-06-24_15:31
No. of wins: Observed Expected
98627 98585.9
z-score= 0.184, pvalue=0.57300
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67055 66666.7 2.262 2.262
2 37816 37654.3 0.694 2.956
3 26971 26954.7 0.010 2.966
4 18989 19313.5 5.451 8.417
5 13883 13851.4 0.072 8.489
6 9848 9943.5 0.918 9.407
7 7111 7145.0 0.162 9.569
8 5133 5139.1 0.007 9.576
9 3645 3699.9 0.814 10.390
10 2605 2666.3 1.409 11.799
11 1890 1923.3 0.578 12.377
12 1412 1388.7 0.390 12.766
13 976 1003.7 0.765 13.531
14 702 726.1 0.803 14.334
15 522 525.8 0.028 14.362
16 373 381.2 0.174 14.536
17 272 276.5 0.075 14.611
18 219 200.8 1.644 16.255
19 168 146.0 3.320 19.575
20 106 106.2 0.000 19.575
21 304 287.1 0.993 20.568
Chisq= 20.57 for 20 degrees of freedom, p= 0.57708
SUMMARY of craptest
p-value for no. of wins: 0.572997
p-value for throws/game: 0.577083
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0008,0.0044,0.0059,0.0068,0.0121,0.0126,0.0130,0.0231,0.0298,0.0306,
0.0340,0.0419,0.0485,0.0580,0.0588,0.0595,0.0614,0.0618,0.0700,0.0722,
0.0766,0.0783,0.0834,0.0853,0.0870,0.0871,0.1004,0.1014,0.1036,0.1054,
0.1067,0.1078,0.1083,0.1090,0.1125,0.1165,0.1252,0.1261,0.1319,0.1335,
0.1335,0.1401,0.1441,0.1468,0.1574,0.1624,0.1634,0.1724,0.1777,0.1778,
0.1939,0.1943,0.2019,0.2056,0.2128,0.2137,0.2170,0.2274,0.2286,0.2292,
0.2325,0.2337,0.2341,0.2392,0.2407,0.2423,0.2429,0.2431,0.2431,0.2452,
0.2466,0.2494,0.2547,0.2557,0.2579,0.2639,0.2643,0.2716,0.2731,0.2785,
0.2841,0.2880,0.2893,0.2910,0.2910,0.2917,0.2933,0.2953,0.3005,0.3111,
0.3192,0.3215,0.3234,0.3266,0.3308,0.3316,0.3333,0.3375,0.3399,0.3416,
0.3437,0.3504,0.3517,0.3557,0.3720,0.3786,0.3884,0.3921,0.3935,0.4112,
0.4120,0.4132,0.4152,0.4173,0.4216,0.4274,0.4298,0.4306,0.4310,0.4326,
0.4338,0.4347,0.4430,0.4447,0.4492,0.4515,0.4627,0.4642,0.4686,0.4727,
0.4766,0.4796,0.4813,0.4872,0.4884,0.4923,0.4927,0.4942,0.4978,0.5050,
0.5078,0.5153,0.5166,0.5182,0.5252,0.5252,0.5300,0.5379,0.5407,0.5442,
0.5486,0.5517,0.5555,0.5590,0.5601,0.5603,0.5620,0.5650,0.5730,0.5756,
0.5771,0.5797,0.5848,0.5866,0.5882,0.5918,0.5929,0.5937,0.5960,0.6079,
0.6117,0.6119,0.6122,0.6183,0.6224,0.6235,0.6324,0.6335,0.6403,0.6435,
0.6436,0.6440,0.6958,0.7005,0.7015,0.7067,0.7130,0.7131,0.7142,0.7148,
0.7163,0.7179,0.7270,0.7287,0.7296,0.7330,0.7457,0.7486,0.7507,0.7540,
0.7580,0.7617,0.7624,0.7638,0.7657,0.7757,0.7777,0.7807,0.7812,0.7877,
0.7881,0.7888,0.7915,0.7917,0.7946,0.7947,0.7978,0.7990,0.8072,0.8098,
0.8135,0.8225,0.8277,0.8286,0.8309,0.8394,0.8412,0.8549,0.8568,0.8642,
0.8713,0.8736,0.8854,0.8867,0.8896,0.8931,0.8968,0.9019,0.9060,0.9060,
0.9133,0.9146,0.9175,0.9209,0.9240,0.9317,0.9318,0.9362,0.9366,0.9382,
0.9415,0.9419,0.9557,0.9559,0.9588,0.9609,0.9617,0.9625,0.9668,0.9739,
0.9787,0.9795,0.9838,0.9841,0.9885,0.9896,0.9909,0.9912,0.9976,
Overall p-value after applying KStest on 269 p-values = 0.880485
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.