RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-05_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 15.77 23.0813 0.853377
2 to 25 15.37 24.3789 0.890501
3 to 26 15.75 13.2687 0.281977
4 to 27 15.71 14.4162 0.362546
5 to 28 15.73 21.2425 0.784370
6 to 29 15.77 8.4337 0.043626
7 to 30 15.69 13.8893 0.325080
8 to 31 15.97 14.7379 0.385646
9 to 32 15.92 19.3025 0.688553
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.927623
Tough bday spacings test for dh-ranFile-2018-07-05_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 7 32 58 105 105 79 56 31 16 6 5
(O-E)^2/E 0.5 0.6 3.2 0.5 0.5 0.0 0.3 0.1 0.1 0.1 0.2
Birthday Spacings: Sum(O-E)^2/E= 6.077, p= 0.191
RESULTS OF GCD FOR dh-ranFile-2018-07-05_15:31
Euclid's algorithm:
p-value, steps to gcd: 0.125239
p-value, dist. of gcd's: 0.886068
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-05_15:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.273 0.909 0.094 0.668 0.446 0.180 0.512 0.361
Bits 8 to 15---> 0.523 0.718 0.868 0.844 0.886 0.481 0.899 0.619
Bits 16 to 23---> 0.880 0.854 0.374 0.749 0.282 0.128 0.022 0.524
Bits 24 to 31---> 0.110 0.404 0.659 0.572 0.455 0.657 0.671 0.071
KS test for the above 32 p values: 0.219
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-05_15:31,
p-values for 5 runs: 0.8181, 0.8202, 0.2675, 0.4788, 0.3178
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-05_15:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 179 211.4 4.971 4.971
r= 29 5011 5134.0 2.947 7.918
r= 30 23291 23103.0 1.529 9.447
r= 31 11519 11551.5 0.092 9.539
chi-square = 9.539 with df = 3; p-value = 0.977
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-05_15:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 225 211.4 0.873 0.873
r= 30 5122 5134.0 0.028 0.901
r= 31 23014 23103.0 0.343 1.244
r= 32 11639 11551.5 0.662 1.906
chi-square = 1.906 with df = 3; p-value = 0.408
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-05_15:31
b-rank test for bits 1 to 8, p=0.42933
b-rank test for bits 2 to 9, p=0.31923
b-rank test for bits 3 to 10, p=0.06752
b-rank test for bits 4 to 11, p=0.62786
b-rank test for bits 5 to 12, p=0.47954
b-rank test for bits 6 to 13, p=0.66368
b-rank test for bits 7 to 14, p=0.35289
b-rank test for bits 8 to 15, p=0.02276
b-rank test for bits 9 to 16, p=0.27743
b-rank test for bits 10 to 17, p=0.22832
b-rank test for bits 11 to 18, p=0.72566
b-rank test for bits 12 to 19, p=0.22772
b-rank test for bits 13 to 20, p=0.30999
b-rank test for bits 14 to 21, p=0.29328
b-rank test for bits 15 to 22, p=0.87799
b-rank test for bits 16 to 23, p=0.86634
b-rank test for bits 17 to 24, p=0.16878
b-rank test for bits 18 to 25, p=0.51190
b-rank test for bits 19 to 26, p=0.07246
b-rank test for bits 20 to 27, p=0.28694
b-rank test for bits 21 to 28, p=0.78610
b-rank test for bits 22 to 29, p=0.79910
b-rank test for bits 23 to 30, p=0.17051
b-rank test for bits 24 to 31, p=0.33946
b-rank test for bits 25 to 32, p=0.36811
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 = 0.155065
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-05_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 141920 0.02 0.509945
2 142535 1.46 0.928108
3 142291 0.89 0.813737
4 141940 0.07 0.528563
5 141454 -1.06 0.143697
6 141248 -1.55 0.061153
7 141834 -0.18 0.430145
8 141947 0.09 0.535067
9 142455 1.27 0.898833
10 142493 1.36 0.913671
11 141430 -1.12 0.131372
12 142618 1.66 0.951116
13 142003 0.22 0.586619
14 141819 -0.21 0.416424
15 141883 -0.06 0.475473
16 142311 0.94 0.826001
17 141968 0.14 0.554516
18 141901 -0.02 0.492236
19 141319 -1.38 0.083905
20 141918 0.02 0.508081
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-05_15:31
Bits used No. missing words z-score p-value
23 to 32 141859 -0.1736 0.431109
22 to 31 142236 1.1264 0.870012
21 to 30 141735 -0.6011 0.273874
20 to 29 141710 -0.6873 0.245933
19 to 28 141232 -2.3356 0.009756
18 to 27 141558 -1.2115 0.112855
17 to 26 142097 0.6471 0.741229
16 to 25 141589 -1.1046 0.134669
15 to 24 141255 -2.2563 0.012026
14 to 23 141891 -0.0632 0.474801
13 to 22 142033 0.4264 0.665109
12 to 21 141660 -0.8598 0.194961
11 to 20 141593 -1.0908 0.137682
10 to 19 141972 0.2161 0.585547
9 to 18 142028 0.4092 0.658806
8 to 17 141428 -1.6598 0.048482
7 to 16 141711 -0.6839 0.247020
6 to 15 141923 0.0471 0.518798
5 to 14 141360 -1.8942 0.029096
4 to 13 142039 0.4471 0.672612
3 to 12 142361 1.5575 0.940322
2 to 11 141951 0.1437 0.557127
1 to 10 141860 -0.1701 0.432464
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-05_15:31
Bits used No. missing words z-score p-value
28 to 32 142646 2.4972 0.993741
27 to 31 142069 0.5413 0.705834
26 to 30 141916 0.0226 0.509019
25 to 29 142481 1.9379 0.973680
24 to 28 142400 1.6633 0.951873
23 to 27 141960 0.1718 0.568188
22 to 26 142032 0.4158 0.661233
21 to 25 141892 -0.0587 0.476577
20 to 24 142222 1.0599 0.855405
19 to 23 141652 -0.8723 0.191521
18 to 22 141810 -0.3367 0.368167
17 to 21 141319 -2.0011 0.022690
16 to 20 142243 1.1311 0.870990
15 to 19 141799 -0.3740 0.354202
14 to 18 141839 -0.2384 0.405783
13 to 17 141727 -0.6181 0.268265
12 to 16 142096 0.6328 0.736561
11 to 15 141782 -0.4316 0.333006
10 to 14 142056 0.4972 0.690471
9 to 13 142183 0.9277 0.823217
8 to 12 142116 0.7006 0.758216
7 to 11 142535 2.1209 0.983036
6 to 10 141828 -0.2757 0.391391
5 to 9 142083 0.5887 0.721973
4 to 8 142124 0.7277 0.766600
3 to 7 142021 0.3785 0.647486
2 to 6 142046 0.4633 0.678421
1 to 5 142039 0.4396 0.669872
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-05_15:31
Bits used No. missing words z-score p-value
31 to 32 142328 1.2350 0.891588
30 to 31 141250 -1.9449 0.025892
29 to 30 142159 0.7365 0.769284
28 to 29 141662 -0.7296 0.232821
27 to 28 142249 1.0020 0.841823
26 to 27 141542 -1.0836 0.139278
25 to 26 142315 1.1967 0.884282
24 to 25 142208 0.8810 0.810850
23 to 24 141518 -1.1544 0.124175
22 to 23 141752 -0.4641 0.321288
21 to 22 142055 0.4297 0.666295
20 to 21 142071 0.4769 0.683284
19 to 20 141847 -0.1839 0.427060
18 to 19 141726 -0.5408 0.294324
17 to 18 141700 -0.6175 0.268455
16 to 17 141476 -1.2783 0.100579
15 to 16 142075 0.4887 0.687474
14 to 15 141807 -0.3019 0.381380
13 to 14 141888 -0.0629 0.474915
12 to 13 142264 1.0462 0.852271
11 to 12 141784 -0.3697 0.355801
10 to 11 142153 0.7188 0.763865
9 to 10 141260 -1.9154 0.027719
8 to 9 141835 -0.2193 0.413223
7 to 8 141812 -0.2871 0.387014
6 to 7 141865 -0.1308 0.447980
5 to 6 141798 -0.3284 0.371302
4 to 5 141833 -0.2252 0.410927
3 to 4 141629 -0.8269 0.204138
2 to 3 142549 1.8869 0.970415
1 to 2 142069 0.4710 0.681181
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-05_15:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2630.09 1.840 0.967094
Test results for specific bytes for dh-ranFile-2018-07-05_15:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2542.19 0.597 0.724630
2 to 9 2508.25 0.117 0.546428
3 to 10 2418.96 -1.146 0.125869
4 to 11 2477.41 -0.320 0.374666
5 to 12 2427.04 -1.032 0.151084
6 to 13 2459.02 -0.580 0.281112
7 to 14 2485.28 -0.208 0.417532
8 to 15 2509.67 0.137 0.554400
9 to 16 2448.93 -0.722 0.235086
10 to 17 2504.72 0.067 0.526620
11 to 18 2484.77 -0.215 0.414708
12 to 19 2461.72 -0.541 0.294105
13 to 20 2491.49 -0.120 0.452105
14 to 21 2435.41 -0.913 0.180517
15 to 22 2341.36 -2.243 0.012434
16 to 23 2469.61 -0.430 0.333692
17 to 24 2562.96 0.890 0.813385
18 to 25 2460.80 -0.554 0.289644
19 to 26 2656.42 2.212 0.986519
20 to 27 2425.89 -1.048 0.147289
21 to 28 2547.51 0.672 0.749172
22 to 29 2405.61 -1.335 0.090965
23 to 30 2404.01 -1.358 0.087303
24 to 31 2573.77 1.043 0.851582
25 to 32 2596.18 1.360 0.913118
CDPARK for dh-ranFile-2018-07-05_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
3571 2.1918 0.985802
3517 -0.2740 0.392053
3525 0.0913 0.536383
3539 0.7306 0.767486
3534 0.5023 0.692266
3529 0.2740 0.607947
3534 0.5023 0.692266
3495 -1.2785 0.100530
3532 0.4110 0.659449
3572 2.2374 0.987371
Square side=100, avg. no. parked=3534.80 sample std.=21.80
p-value of the KSTEST for those 10 p-values: 0.117759
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-05_15:31
0.1643,0.6618,0.3830,0.1746,0.4653,0.5059,0.2088,0.7878,0.6941,0.5349,
The KS test for those 10 p-values: 0.591726
The 3DSPHERES test for dh-ranFile-2018-07-05_15:31
sample no r^3 equiv. uni.
1 14.780 0.388996
2 5.226 0.159884
3 9.451 0.270240
4 26.899 0.592053
5 48.185 0.799344
6 2.826 0.089892
7 20.486 0.494835
8 10.066 0.285045
9 36.396 0.702754
10 83.904 0.938994
11 3.682 0.115501
12 36.247 0.701277
13 51.032 0.817511
14 28.604 0.614595
15 70.660 0.905139
16 2.692 0.085826
17 45.611 0.781365
18 52.307 0.825104
19 11.136 0.310087
20 23.760 0.547069
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.941023
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-05_15:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 0.9 -0.8 -0.3 0.4 0.1
-0.2 0.6 -0.7 -1.1 1.5 -1.3
0.0 0.9 -0.3 0.9 -0.3 -0.4
-0.4 -1.1 0.1 1.1 1.4 -1.5
0.5 -0.9 -0.8 1.8 1.4 0.7
-0.9 -0.3 -0.8 0.7 -2.3 -0.3
-0.5 -0.1 -1.6 -0.1 0.9 0.0
0.8
Chi-square with 42 degrees of freedom:35.499335
z-score=-0.709281, p-value=0.249590
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-05_15:31
Test no p-value
1 0.033745
2 0.166615
3 0.726434
4 0.091509
5 0.001870
6 0.549785
7 0.911167
8 0.388862
9 0.935444
10 0.099618
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.112169
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-05_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 66586 0.10 66393 1.12
3 25000.00 25106 0.45 25154 0.95
4 6666.67 6630 0.20 6797 2.55
5 1388.89 1400 0.09 1399 0.07
6 238.10 229 0.35 235 0.04
7 34.72 42 1.53 19 7.12
8 4.96 6 0.22 2 1.77
p=0.18237 p=0.96579
Number of rngs required: 688662, p-value: 0.617
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-05_15:31
No. of wins: Observed Expected
98702 98585.9
z-score= 0.519, pvalue=0.69828
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66241 66666.7 2.718 2.718
2 37708 37654.3 0.077 2.794
3 26906 26954.7 0.088 2.883
4 19367 19313.5 0.148 3.031
5 14058 13851.4 3.081 6.112
6 10002 9943.5 0.344 6.456
7 7278 7145.0 2.475 8.930
8 5075 5139.1 0.799 9.729
9 3682 3699.9 0.086 9.815
10 2687 2666.3 0.161 9.976
11 1944 1923.3 0.222 10.198
12 1387 1388.7 0.002 10.200
13 947 1003.7 3.205 13.405
14 766 726.1 2.188 15.593
15 539 525.8 0.330 15.923
16 397 381.2 0.659 16.582
17 311 276.5 4.294 20.876
18 190 200.8 0.584 21.460
19 144 146.0 0.027 21.487
20 99 106.2 0.490 21.977
21 272 287.1 0.796 22.773
Chisq= 22.77 for 20 degrees of freedom, p= 0.69991
SUMMARY of craptest
p-value for no. of wins: 0.698277
p-value for throws/game: 0.699908
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-05_15:31
No. of wins: Observed Expected
97780 98585.9
z-score=-3.604, pvalue=0.00016
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66345 66666.7 1.552 1.552
2 37845 37654.3 0.966 2.518
3 27141 26954.7 1.287 3.805
4 19247 19313.5 0.229 4.034
5 14024 13851.4 2.150 6.184
6 9770 9943.5 3.029 9.213
7 7196 7145.0 0.364 9.576
8 5170 5139.1 0.186 9.762
9 3748 3699.9 0.626 10.389
10 2595 2666.3 1.907 12.295
11 1967 1923.3 0.992 13.287
12 1345 1388.7 1.378 14.664
13 1004 1003.7 0.000 14.664
14 708 726.1 0.453 15.118
15 523 525.8 0.015 15.133
16 340 381.2 4.443 19.576
17 273 276.5 0.045 19.621
18 214 200.8 0.864 20.485
19 149 146.0 0.062 20.547
20 109 106.2 0.073 20.620
21 287 287.1 0.000 20.620
Chisq= 20.62 for 20 degrees of freedom, p= 0.58021
SUMMARY of craptest
p-value for no. of wins: 0.000157
p-value for throws/game: 0.580209
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0002,0.0019,0.0098,0.0120,0.0124,0.0223,0.0227,0.0228,0.0259,0.0277,
0.0291,0.0337,0.0436,0.0485,0.0612,0.0675,0.0710,0.0725,0.0839,0.0858,
0.0873,0.0899,0.0910,0.0915,0.0939,0.0996,0.1005,0.1006,0.1104,0.1122,
0.1129,0.1155,0.1178,0.1242,0.1252,0.1259,0.1276,0.1314,0.1347,0.1377,
0.1393,0.1437,0.1473,0.1511,0.1551,0.1599,0.1643,0.1666,0.1688,0.1705,
0.1746,0.1799,0.1805,0.1824,0.1913,0.1915,0.1950,0.2041,0.2088,0.2190,
0.2277,0.2283,0.2328,0.2351,0.2459,0.2470,0.2496,0.2675,0.2683,0.2685,
0.2702,0.2731,0.2739,0.2774,0.2811,0.2820,0.2823,0.2850,0.2869,0.2896,
0.2933,0.2941,0.2943,0.3100,0.3101,0.3178,0.3192,0.3213,0.3251,0.3330,
0.3337,0.3395,0.3529,0.3542,0.3558,0.3612,0.3625,0.3681,0.3682,0.3713,
0.3743,0.3747,0.3814,0.3830,0.3856,0.3870,0.3889,0.3890,0.3914,0.3921,
0.4038,0.4058,0.4079,0.4109,0.4132,0.4147,0.4164,0.4175,0.4271,0.4293,
0.4301,0.4311,0.4325,0.4462,0.4480,0.4521,0.4549,0.4653,0.4748,0.4749,
0.4755,0.4766,0.4788,0.4795,0.4808,0.4922,0.4948,0.5059,0.5081,0.5090,
0.5099,0.5119,0.5123,0.5188,0.5227,0.5245,0.5266,0.5286,0.5349,0.5351,
0.5364,0.5464,0.5471,0.5498,0.5544,0.5545,0.5571,0.5682,0.5718,0.5802,
0.5855,0.5866,0.5917,0.5921,0.6079,0.6146,0.6172,0.6189,0.6279,0.6475,
0.6568,0.6588,0.6590,0.6594,0.6612,0.6618,0.6637,0.6651,0.6663,0.6682,
0.6699,0.6706,0.6726,0.6784,0.6812,0.6833,0.6875,0.6886,0.6905,0.6923,
0.6923,0.6941,0.6983,0.6999,0.7013,0.7028,0.7058,0.7183,0.7220,0.7246,
0.7257,0.7264,0.7366,0.7412,0.7492,0.7492,0.7582,0.7639,0.7666,0.7675,
0.7693,0.7814,0.7844,0.7861,0.7878,0.7991,0.7993,0.8108,0.8134,0.8137,
0.8175,0.8181,0.8202,0.8232,0.8251,0.8260,0.8418,0.8436,0.8516,0.8523,
0.8534,0.8544,0.8554,0.8663,0.8678,0.8700,0.8710,0.8780,0.8801,0.8843,
0.8861,0.8861,0.8905,0.8916,0.8988,0.8991,0.9051,0.9091,0.9112,0.9131,
0.9137,0.9276,0.9281,0.9354,0.9390,0.9403,0.9410,0.9511,0.9519,0.9658,
0.9671,0.9704,0.9737,0.9771,0.9830,0.9858,0.9865,0.9874,0.9937,
Overall p-value after applying KStest on 269 p-values = 0.984315
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.