RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-04_03:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.78 14.3513 0.357902
2 to 25 15.59 14.5266 0.370464
3 to 26 15.82 18.1900 0.623048
4 to 27 15.63 15.9775 0.474569
5 to 28 15.94 10.9320 0.139923
6 to 29 15.91 12.4112 0.225375
7 to 30 15.69 14.9693 0.402304
8 to 31 15.70 20.2929 0.740476
9 to 32 15.81 9.6209 0.081248
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.301094
Tough bday spacings test for dh-ranFile-2018-07-04_03:31: 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 41 74 103 89 72 58 28 14 8 2
(O-E)^2/E 0.4 0.5 0.0 0.3 0.8 0.5 0.7 0.1 0.1 0.3 1.0
Birthday Spacings: Sum(O-E)^2/E= 4.610, p= 0.084
RESULTS OF GCD FOR dh-ranFile-2018-07-04_03:31
Euclid's algorithm:
p-value, steps to gcd: 0.666583
p-value, dist. of gcd's: 0.002628
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-04_03:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.739 0.852 0.689 0.527 0.669 0.763 0.843 0.001
Bits 8 to 15---> 0.242 0.404 0.865 0.638 0.758 0.222 0.930 0.322
Bits 16 to 23---> 0.391 0.335 0.925 0.780 0.753 0.131 0.413 0.056
Bits 24 to 31---> 0.991 0.092 0.148 0.088 0.040 0.307 0.829 0.713
KS test for the above 32 p values: 0.289
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-04_03:31,
p-values for 5 runs: 0.6445, 0.9288, 0.9939, 0.3070, 0.9684
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-04_03:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 198 211.4 0.852 0.852
r= 29 5238 5134.0 2.106 2.958
r= 30 23111 23103.0 0.003 2.961
r= 31 11453 11551.5 0.840 3.801
chi-square = 3.801 with df = 3; p-value = 0.716
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-04_03:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 229 211.4 1.462 1.462
r= 30 5168 5134.0 0.225 1.687
r= 31 23092 23103.0 0.005 1.692
r= 32 11511 11551.5 0.142 1.835
chi-square = 1.835 with df = 3; p-value = 0.393
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-04_03:31
b-rank test for bits 1 to 8, p=0.05074
b-rank test for bits 2 to 9, p=0.71414
b-rank test for bits 3 to 10, p=0.88133
b-rank test for bits 4 to 11, p=0.99565
b-rank test for bits 5 to 12, p=0.68103
b-rank test for bits 6 to 13, p=0.52099
b-rank test for bits 7 to 14, p=0.64958
b-rank test for bits 8 to 15, p=0.38463
b-rank test for bits 9 to 16, p=0.98768
b-rank test for bits 10 to 17, p=0.12728
b-rank test for bits 11 to 18, p=0.78296
b-rank test for bits 12 to 19, p=0.08663
b-rank test for bits 13 to 20, p=0.32785
b-rank test for bits 14 to 21, p=0.92192
b-rank test for bits 15 to 22, p=0.75260
b-rank test for bits 16 to 23, p=0.05557
b-rank test for bits 17 to 24, p=0.22978
b-rank test for bits 18 to 25, p=0.96110
b-rank test for bits 19 to 26, p=0.41567
b-rank test for bits 20 to 27, p=0.12251
b-rank test for bits 21 to 28, p=0.86079
b-rank test for bits 22 to 29, p=0.34593
b-rank test for bits 23 to 30, p=0.41933
b-rank test for bits 24 to 31, p=0.66479
b-rank test for bits 25 to 32, p=0.15470
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 = 0.653101
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-04_03:31
(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 141612 -0.69 0.243623
2 142174 0.62 0.731840
3 141576 -0.78 0.218046
4 141622 -0.67 0.251005
5 141628 -0.66 0.255490
6 141393 -1.21 0.113836
7 141949 0.09 0.536924
8 141667 -0.57 0.285632
9 141577 -0.78 0.218735
10 142140 0.54 0.705039
11 142111 0.47 0.681248
12 142416 1.18 0.881756
13 142273 0.85 0.802253
14 142453 1.27 0.898003
15 142307 0.93 0.823591
16 141447 -1.08 0.140024
17 142026 0.27 0.607417
18 142351 1.03 0.848950
19 141177 -1.71 0.043536
20 141984 0.17 0.569249
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-04_03:31
Bits used No. missing words z-score p-value
23 to 32 141829 -0.2770 0.390890
22 to 31 141863 -0.1598 0.436536
21 to 30 141436 -1.6322 0.051322
20 to 29 142118 0.7196 0.764100
19 to 28 141930 0.0713 0.528411
18 to 27 142131 0.7644 0.777679
17 to 26 142259 1.2058 0.886045
16 to 25 141943 0.1161 0.546215
15 to 24 142072 0.5609 0.712578
14 to 23 142067 0.5437 0.706673
13 to 22 141751 -0.5460 0.292545
12 to 21 141546 -1.2529 0.105128
11 to 20 141568 -1.1770 0.119598
10 to 19 141947 0.1299 0.551676
9 to 18 141867 -0.1460 0.441974
8 to 17 142215 1.0540 0.854066
7 to 16 141799 -0.3804 0.351806
6 to 15 141751 -0.5460 0.292545
5 to 14 141593 -1.0908 0.137682
4 to 13 141999 0.3092 0.621418
3 to 12 141921 0.0402 0.516050
2 to 11 141701 -0.7184 0.236262
1 to 10 141733 -0.6080 0.271582
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-04_03:31
Bits used No. missing words z-score p-value
28 to 32 141853 -0.1909 0.424283
27 to 31 142412 1.7040 0.955806
26 to 30 142144 0.7955 0.786836
25 to 29 141493 -1.4113 0.079080
24 to 28 141700 -0.7096 0.238978
23 to 27 141535 -1.2689 0.102236
22 to 26 141673 -0.8011 0.211532
21 to 25 141883 -0.0893 0.464440
20 to 24 141817 -0.3130 0.377147
19 to 23 142122 0.7209 0.764519
18 to 22 141671 -0.8079 0.209575
17 to 21 141900 -0.0316 0.487385
16 to 20 141618 -0.9876 0.161684
15 to 19 141580 -1.1164 0.132131
14 to 18 141442 -1.5842 0.056578
13 to 17 142034 0.4226 0.663710
12 to 16 141828 -0.2757 0.391391
11 to 15 141829 -0.2723 0.392694
10 to 14 141984 0.2531 0.599912
9 to 13 141768 -0.4791 0.315939
8 to 12 142193 0.9616 0.831873
7 to 11 141511 -1.3503 0.088465
6 to 10 141931 0.0735 0.529279
5 to 9 142033 0.4192 0.662473
4 to 8 142219 1.0497 0.853079
3 to 7 142037 0.4328 0.667413
2 to 6 141585 -1.0994 0.135792
1 to 5 141448 -1.5638 0.058929
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-04_03:31
Bits used No. missing words z-score p-value
31 to 32 141631 -0.8210 0.205814
30 to 31 142026 0.3442 0.634637
29 to 30 142028 0.3501 0.636853
28 to 29 141821 -0.2606 0.397216
27 to 28 141787 -0.3609 0.359104
26 to 27 141817 -0.2724 0.392673
25 to 26 142554 1.9017 0.971394
24 to 25 141515 -1.1632 0.122371
23 to 24 141777 -0.3904 0.348137
22 to 23 141983 0.2173 0.586019
21 to 22 142369 1.3560 0.912444
20 to 21 141612 -0.8771 0.190222
19 to 20 142009 0.2940 0.615626
18 to 19 141715 -0.5732 0.283240
17 to 18 142493 1.7217 0.957442
16 to 17 142616 2.0846 0.981446
15 to 16 142194 0.8397 0.799471
14 to 15 142543 1.8692 0.969205
13 to 14 142307 1.1731 0.879616
12 to 13 141667 -0.7148 0.237355
11 to 12 142284 1.1052 0.865468
10 to 11 142144 0.6922 0.755607
9 to 10 142138 0.6745 0.750017
8 to 9 142135 0.6657 0.747196
7 to 8 142119 0.6185 0.731876
6 to 7 142783 2.5772 0.995020
5 to 6 141960 0.1495 0.559408
4 to 5 141878 -0.0924 0.463183
3 to 4 141897 -0.0364 0.485493
2 to 3 142049 0.4120 0.659832
1 to 2 141676 -0.6883 0.245635
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-04_03:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2556.76 0.803 0.788937
Test results for specific bytes for dh-ranFile-2018-07-04_03:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2518.10 0.256 0.600992
2 to 9 2407.85 -1.303 0.096243
3 to 10 2479.33 -0.292 0.385046
4 to 11 2573.67 1.042 0.851254
5 to 12 2537.76 0.534 0.703336
6 to 13 2335.26 -2.330 0.009911
7 to 14 2604.51 1.478 0.930288
8 to 15 2409.13 -1.285 0.099372
9 to 16 2594.07 1.330 0.908302
10 to 17 2552.57 0.743 0.771380
11 to 18 2454.05 -0.650 0.257923
12 to 19 2503.40 0.048 0.519177
13 to 20 2598.69 1.396 0.918593
14 to 21 2403.81 -1.360 0.086863
15 to 22 2536.72 0.519 0.698208
16 to 23 2501.82 0.026 0.510279
17 to 24 2640.06 1.981 0.976194
18 to 25 2502.91 0.041 0.516405
19 to 26 2462.00 -0.537 0.295484
20 to 27 2486.66 -0.189 0.425199
21 to 28 2409.40 -1.281 0.100037
22 to 29 2414.43 -1.210 0.113103
23 to 30 2597.48 1.379 0.915997
24 to 31 2574.39 1.052 0.853604
25 to 32 2548.87 0.691 0.755269
CDPARK for dh-ranFile-2018-07-04_03:31: 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
3548 1.1416 0.873180
3532 0.4110 0.659449
3488 -1.5982 0.055002
3490 -1.5068 0.065925
3507 -0.7306 0.232514
3532 0.4110 0.659449
3529 0.2740 0.607947
3541 0.8219 0.794438
3549 1.1872 0.882429
3488 -1.5982 0.055002
Square side=100, avg. no. parked=3520.40 sample std.=23.56
p-value of the KSTEST for those 10 p-values: 0.460145
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-04_03:31
0.8418,0.7560,0.8137,0.3771,0.5967,0.6388,0.8344,0.9298,0.3216,0.6870,
The KS test for those 10 p-values: 0.066124
The 3DSPHERES test for dh-ranFile-2018-07-04_03:31
sample no r^3 equiv. uni.
1 60.226 0.865679
2 11.548 0.319510
3 12.116 0.332277
4 10.546 0.296397
5 28.225 0.609698
6 2.953 0.093730
7 53.051 0.829386
8 23.651 0.545410
9 21.203 0.506761
10 49.974 0.810959
11 18.094 0.452902
12 12.833 0.348041
13 9.547 0.272577
14 6.095 0.183864
15 2.733 0.087071
16 3.242 0.102440
17 11.017 0.307363
18 0.370 0.012270
19 21.230 0.507200
20 8.155 0.238014
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.111628
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-04_03:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 0.9 -1.6 1.5 -0.6 0.3
-0.0 0.4 -1.4 1.1 -1.6 0.6
1.4 0.6 0.8 -0.9 -0.1 -1.4
1.3 0.3 -0.4 1.1 -0.7 -0.0
-0.2 -1.7 -0.1 -0.9 0.3 0.0
1.7 -1.5 -0.6 -0.5 0.9 2.0
1.9 -2.3 0.5 -0.1 -0.6 -1.0
-1.1
Chi-square with 42 degrees of freedom:47.813794
z-score=0.634337, p-value=0.751509
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-04_03:31
Test no p-value
1 0.059345
2 0.950157
3 0.745331
4 0.554227
5 0.017076
6 0.013697
7 0.036418
8 0.334138
9 0.342729
10 0.091756
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.013961
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-04_03:31:
(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 66550 0.20 66893 0.77
3 25000.00 25230 2.12 24738 2.75
4 6666.67 6604 0.59 6696 0.13
5 1388.89 1336 2.01 1388 0.00
6 238.10 238 0.00 242 0.06
7 34.72 36 0.05 33 0.09
8 4.96 5 0.00 9 3.29
p=0.45246 p=0.68682
Number of rngs required: 687859, p-value: 0.265
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-04_03:31
No. of wins: Observed Expected
98673 98585.9
z-score= 0.390, pvalue=0.65164
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66654 66666.7 0.002 0.002
2 37542 37654.3 0.335 0.337
3 26911 26954.7 0.071 0.408
4 19380 19313.5 0.229 0.638
5 13981 13851.4 1.212 1.850
6 9875 9943.5 0.472 2.322
7 7133 7145.0 0.020 2.343
8 5284 5139.1 4.087 6.430
9 3707 3699.9 0.014 6.443
10 2679 2666.3 0.061 6.504
11 1809 1923.3 6.796 13.300
12 1423 1388.7 0.845 14.145
13 992 1003.7 0.137 14.282
14 711 726.1 0.316 14.598
15 521 525.8 0.044 14.642
16 382 381.2 0.002 14.644
17 279 276.5 0.022 14.666
18 214 200.8 0.864 15.530
19 134 146.0 0.984 16.513
20 105 106.2 0.014 16.527
21 284 287.1 0.034 16.561
Chisq= 16.56 for 20 degrees of freedom, p= 0.31874
SUMMARY of craptest
p-value for no. of wins: 0.651638
p-value for throws/game: 0.318742
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-04_03:31
No. of wins: Observed Expected
98659 98585.9
z-score= 0.327, pvalue=0.62822
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66723 66666.7 0.048 0.048
2 37280 37654.3 3.721 3.769
3 27094 26954.7 0.720 4.488
4 19300 19313.5 0.009 4.498
5 13699 13851.4 1.677 6.175
6 10210 9943.5 7.140 13.315
7 7162 7145.0 0.040 13.355
8 5168 5139.1 0.163 13.518
9 3663 3699.9 0.367 13.886
10 2655 2666.3 0.048 13.933
11 1927 1923.3 0.007 13.940
12 1422 1388.7 0.797 14.737
13 1019 1003.7 0.233 14.970
14 717 726.1 0.115 15.085
15 538 525.8 0.281 15.366
16 380 381.2 0.003 15.370
17 285 276.5 0.259 15.629
18 196 200.8 0.116 15.745
19 149 146.0 0.062 15.807
20 96 106.2 0.982 16.789
21 317 287.1 3.111 19.900
Chisq= 19.90 for 20 degrees of freedom, p= 0.53582
SUMMARY of craptest
p-value for no. of wins: 0.628216
p-value for throws/game: 0.535820
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0014,0.0026,0.0099,0.0123,0.0137,0.0140,0.0171,0.0364,0.0403,0.0435,
0.0507,0.0513,0.0550,0.0550,0.0556,0.0562,0.0566,0.0589,0.0593,0.0659,
0.0661,0.0791,0.0812,0.0843,0.0866,0.0869,0.0871,0.0881,0.0885,0.0918,
0.0921,0.0937,0.0962,0.0994,0.1000,0.1022,0.1024,0.1051,0.1116,0.1131,
0.1138,0.1196,0.1224,0.1225,0.1273,0.1307,0.1321,0.1358,0.1377,0.1399,
0.1400,0.1483,0.1547,0.1617,0.1839,0.1902,0.2058,0.2096,0.2115,0.2180,
0.2187,0.2215,0.2254,0.2298,0.2325,0.2363,0.2374,0.2380,0.2390,0.2423,
0.2436,0.2456,0.2510,0.2555,0.2579,0.2651,0.2716,0.2726,0.2832,0.2856,
0.2888,0.2925,0.2925,0.2955,0.2964,0.3011,0.3069,0.3070,0.3074,0.3159,
0.3187,0.3195,0.3216,0.3218,0.3278,0.3323,0.3341,0.3351,0.3427,0.3459,
0.3480,0.3481,0.3518,0.3579,0.3591,0.3705,0.3771,0.3771,0.3846,0.3850,
0.3909,0.3911,0.3914,0.3926,0.3927,0.3927,0.3972,0.4023,0.4038,0.4134,
0.4157,0.4193,0.4243,0.4252,0.4365,0.4420,0.4525,0.4529,0.4601,0.4632,
0.4644,0.4746,0.4855,0.4874,0.5068,0.5072,0.5103,0.5160,0.5164,0.5192,
0.5210,0.5272,0.5284,0.5293,0.5358,0.5369,0.5454,0.5462,0.5517,0.5542,
0.5594,0.5692,0.5860,0.5967,0.5999,0.6010,0.6074,0.6079,0.6097,0.6156,
0.6214,0.6230,0.6282,0.6346,0.6369,0.6378,0.6388,0.6445,0.6496,0.6516,
0.6531,0.6594,0.6594,0.6598,0.6625,0.6637,0.6648,0.6666,0.6674,0.6693,
0.6810,0.6812,0.6868,0.6870,0.6893,0.6982,0.7033,0.7050,0.7067,0.7126,
0.7133,0.7141,0.7162,0.7318,0.7319,0.7392,0.7405,0.7453,0.7472,0.7500,
0.7515,0.7526,0.7526,0.7553,0.7556,0.7560,0.7584,0.7634,0.7641,0.7645,
0.7714,0.7777,0.7800,0.7830,0.7868,0.7889,0.7944,0.7995,0.8023,0.8110,
0.8137,0.8236,0.8286,0.8294,0.8319,0.8344,0.8418,0.8426,0.8489,0.8513,
0.8515,0.8531,0.8536,0.8541,0.8608,0.8647,0.8655,0.8657,0.8732,0.8796,
0.8813,0.8818,0.8824,0.8860,0.8980,0.9083,0.9124,0.9160,0.9186,0.9219,
0.9249,0.9288,0.9298,0.9303,0.9303,0.9502,0.9558,0.9574,0.9611,0.9684,
0.9692,0.9714,0.9762,0.9814,0.9877,0.9906,0.9939,0.9950,0.9957,
Overall p-value after applying KStest on 269 p-values = 0.673501
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.