RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-11_09:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.70 16.8252 0.533734
2 to 25 16.04 19.7191 0.711152
3 to 26 15.58 25.5176 0.916292
4 to 27 15.83 28.5817 0.961417
5 to 28 15.89 24.0640 0.882293
6 to 29 15.95 4.9336 0.002048
7 to 30 16.02 22.1265 0.820098
8 to 31 15.93 22.1250 0.820041
9 to 32 15.76 11.1877 0.153358
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.081394
Tough bday spacings test for dh-ranFile-2018-07-11_09:31: 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 36 61 107 119 79 49 20 13 4 5
(O-E)^2/E 0.5 0.0 2.1 0.9 4.7 0.0 0.2 3.2 0.2 1.0 0.2
Birthday Spacings: Sum(O-E)^2/E= 12.999, p= 0.776
RESULTS OF GCD FOR dh-ranFile-2018-07-11_09:31
Euclid's algorithm:
p-value, steps to gcd: 0.364707
p-value, dist. of gcd's: 0.789738
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-11_09:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.351 0.376 0.070 0.664 0.359 0.726 0.817 0.405
Bits 8 to 15---> 0.834 0.349 0.133 0.630 0.313 0.355 0.468 0.380
Bits 16 to 23---> 0.151 0.096 0.362 0.057 0.991 0.056 0.357 0.925
Bits 24 to 31---> 0.579 0.217 0.237 0.963 0.749 0.043 0.211 0.313
KS test for the above 32 p values: 0.848
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-11_09:31,
p-values for 5 runs: 0.0100, 0.1442, 0.4230, 0.4929, 0.3668
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-11_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 238 211.4 3.342 3.342
r= 29 5317 5134.0 6.522 9.864
r= 30 23023 23103.0 0.277 10.142
r= 31 11422 11551.5 1.452 11.594
chi-square = 11.594 with df = 3; p-value = 0.991
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-11_09:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 232 211.4 2.004 2.004
r= 30 4977 5134.0 4.802 6.805
r= 31 23073 23103.0 0.039 6.845
r= 32 11718 11551.5 2.399 9.244
chi-square = 9.244 with df = 3; p-value = 0.974
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-11_09:31
b-rank test for bits 1 to 8, p=0.42883
b-rank test for bits 2 to 9, p=0.47470
b-rank test for bits 3 to 10, p=0.78744
b-rank test for bits 4 to 11, p=0.20996
b-rank test for bits 5 to 12, p=0.55852
b-rank test for bits 6 to 13, p=0.35210
b-rank test for bits 7 to 14, p=0.79744
b-rank test for bits 8 to 15, p=0.52760
b-rank test for bits 9 to 16, p=0.01556
b-rank test for bits 10 to 17, p=0.34440
b-rank test for bits 11 to 18, p=0.32733
b-rank test for bits 12 to 19, p=0.74661
b-rank test for bits 13 to 20, p=0.33641
b-rank test for bits 14 to 21, p=0.79174
b-rank test for bits 15 to 22, p=0.16508
b-rank test for bits 16 to 23, p=0.89435
b-rank test for bits 17 to 24, p=0.86233
b-rank test for bits 18 to 25, p=0.83198
b-rank test for bits 19 to 26, p=0.62496
b-rank test for bits 20 to 27, p=0.06558
b-rank test for bits 21 to 28, p=0.67278
b-rank test for bits 22 to 29, p=0.61862
b-rank test for bits 23 to 30, p=0.52872
b-rank test for bits 24 to 31, p=0.21197
b-rank test for bits 25 to 32, p=0.37317
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 = 0.782084
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-11_09:31
(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 142036 0.30 0.616369
2 142221 0.73 0.766755
3 141921 0.03 0.510876
4 142352 1.03 0.849496
5 141719 -0.44 0.328270
6 141422 -1.14 0.127431
7 142828 2.15 0.984080
8 142251 0.80 0.787650
9 141973 0.15 0.559129
10 141340 -1.33 0.091725
11 141592 -0.74 0.229218
12 142206 0.69 0.755894
13 141974 0.15 0.560051
14 142197 0.67 0.749248
15 141521 -0.91 0.182121
16 142038 0.30 0.618152
17 141666 -0.57 0.284838
18 141706 -0.48 0.317369
19 141810 -0.23 0.408238
20 142092 0.43 0.665237
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-11_09:31
Bits used No. missing words z-score p-value
23 to 32 141714 -0.6736 0.250298
22 to 31 142048 0.4782 0.683736
21 to 30 141725 -0.6356 0.262512
20 to 29 141836 -0.2529 0.400187
19 to 28 141370 -1.8598 0.031460
18 to 27 141738 -0.5908 0.277330
17 to 26 141573 -1.1598 0.123074
16 to 25 142168 0.8920 0.813794
15 to 24 142225 1.0885 0.861817
14 to 23 141671 -0.8218 0.205588
13 to 22 142080 0.5885 0.721907
12 to 21 142144 0.8092 0.790802
11 to 20 142120 0.7264 0.766218
10 to 19 141669 -0.8287 0.203630
9 to 18 142082 0.5954 0.724217
8 to 17 142289 1.3092 0.904768
7 to 16 141870 -0.1356 0.446061
6 to 15 141965 0.1920 0.576115
5 to 14 141778 -0.4529 0.325324
4 to 13 142078 0.5816 0.719589
3 to 12 141870 -0.1356 0.446061
2 to 11 142319 1.4127 0.921121
1 to 10 141625 -0.9804 0.163432
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-11_09:31
Bits used No. missing words z-score p-value
28 to 32 141908 -0.0045 0.498201
27 to 31 141806 -0.3503 0.363068
26 to 30 141974 0.2192 0.586761
25 to 29 141774 -0.4587 0.323208
24 to 28 141646 -0.8926 0.186024
23 to 27 142066 0.5311 0.702320
22 to 26 141716 -0.6554 0.256119
21 to 25 141982 0.2463 0.597290
20 to 24 141874 -0.1198 0.452336
19 to 23 141730 -0.6079 0.271628
18 to 22 142645 2.4938 0.993681
17 to 21 141720 -0.6418 0.260503
16 to 20 141863 -0.1571 0.437602
15 to 19 142827 3.1107 0.999067
14 to 18 141865 -0.1503 0.440275
13 to 17 141628 -0.9537 0.170128
12 to 16 141799 -0.3740 0.354202
11 to 15 141321 -1.9943 0.023058
10 to 14 141958 0.1650 0.565521
9 to 13 141908 -0.0045 0.498201
8 to 12 142000 0.3074 0.620714
7 to 11 141727 -0.6181 0.268265
6 to 10 142008 0.3345 0.630989
5 to 9 141760 -0.5062 0.306357
4 to 8 141681 -0.7740 0.219465
3 to 7 141928 0.0633 0.525232
2 to 6 141718 -0.6486 0.258306
1 to 5 141896 -0.0452 0.481979
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-11_09:31
Bits used No. missing words z-score p-value
31 to 32 141818 -0.2694 0.393807
30 to 31 142503 1.7512 0.960048
29 to 30 142638 2.1495 0.984201
28 to 29 142135 0.6657 0.747196
27 to 28 142034 0.3678 0.643473
26 to 27 142391 1.4209 0.922321
25 to 26 142468 1.6480 0.950323
24 to 25 142658 2.2085 0.986394
23 to 24 141923 0.0403 0.516083
22 to 23 141659 -0.7384 0.230125
21 to 22 141896 -0.0393 0.484317
20 to 21 142071 0.4769 0.683284
19 to 20 141975 0.1937 0.576801
18 to 19 142262 1.0403 0.850905
17 to 18 141736 -0.5113 0.304571
16 to 17 142169 0.7660 0.778158
15 to 16 141721 -0.5555 0.289261
14 to 15 142015 0.3117 0.622370
13 to 14 141694 -0.6352 0.262652
12 to 13 141968 0.1731 0.568701
11 to 12 141959 0.1465 0.558244
10 to 11 142756 2.4976 0.993747
9 to 10 141907 -0.0069 0.497258
8 to 9 142054 0.4268 0.665221
7 to 8 141366 -1.6027 0.054496
6 to 7 141687 -0.6558 0.255963
5 to 6 142224 0.9282 0.823356
4 to 5 142136 0.6686 0.748138
3 to 4 141804 -0.3107 0.378011
2 to 3 141809 -0.2960 0.383631
1 to 2 141906 -0.0098 0.496081
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-11_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2566.64 0.942 0.827001
Test results for specific bytes for dh-ranFile-2018-07-11_09:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2506.03 0.085 0.533960
2 to 9 2490.80 -0.130 0.448263
3 to 10 2665.01 2.334 0.990190
4 to 11 2462.70 -0.528 0.298916
5 to 12 2519.37 0.274 0.607948
6 to 13 2435.47 -0.913 0.180738
7 to 14 2624.60 1.762 0.960976
8 to 15 2516.60 0.235 0.592817
9 to 16 2473.62 -0.373 0.354525
10 to 17 2527.40 0.388 0.650830
11 to 18 2527.77 0.393 0.652721
12 to 19 2479.76 -0.286 0.387325
13 to 20 2443.78 -0.795 0.213301
14 to 21 2499.28 -0.010 0.495956
15 to 22 2421.42 -1.111 0.133218
16 to 23 2461.50 -0.544 0.293075
17 to 24 2391.08 -1.540 0.061744
18 to 25 2482.85 -0.243 0.404156
19 to 26 2388.94 -1.571 0.058136
20 to 27 2368.93 -1.854 0.031899
21 to 28 2434.53 -0.926 0.177268
22 to 29 2558.53 0.828 0.796092
23 to 30 2505.36 0.076 0.530211
24 to 31 2490.24 -0.138 0.445087
25 to 32 2487.75 -0.173 0.431209
CDPARK for dh-ranFile-2018-07-11_09:31: 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
3527 0.1826 0.572463
3509 -0.6393 0.261324
3509 -0.6393 0.261324
3516 -0.3196 0.374623
3534 0.5023 0.692266
3465 -2.6484 0.004044
3505 -0.8219 0.205562
3478 -2.0548 0.019949
3508 -0.6849 0.246694
3521 -0.0913 0.463617
Square side=100, avg. no. parked=3507.20 sample std.=20.06
p-value of the KSTEST for those 10 p-values: 0.042347
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-11_09:31
0.1529,0.2932,0.1656,0.2302,0.9374,0.7518,0.2296,0.9309,0.2952,0.9681,
The KS test for those 10 p-values: 0.297432
The 3DSPHERES test for dh-ranFile-2018-07-11_09:31
sample no r^3 equiv. uni.
1 70.551 0.904794
2 6.871 0.204704
3 32.714 0.663937
4 34.246 0.680676
5 93.405 0.955554
6 0.429 0.014187
7 9.880 0.280591
8 26.627 0.588348
9 5.328 0.162718
10 22.444 0.526757
11 41.336 0.747888
12 11.518 0.318827
13 25.784 0.576611
14 6.936 0.206428
15 15.417 0.401851
16 9.769 0.277928
17 7.008 0.208309
18 81.647 0.934227
19 28.889 0.618247
20 116.924 0.979707
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.888186
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-11_09:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
-0.1 -0.3 0.3 -0.3 1.4 -1.5
0.8 -0.5 -0.0 0.8 0.3 -0.2
-0.7 -0.7 -0.7 0.8 -0.4 -1.0
0.5 -1.1 -1.0 -0.0 1.3 1.1
1.1 0.8 0.4 1.2 0.1 0.1
0.3 -0.7 -0.7 0.1 0.8 0.1
-0.9 -1.0 2.5 1.5 -1.3 1.0
-0.1
Chi-square with 42 degrees of freedom:33.370447
z-score=-0.941561, p-value=0.173368
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-11_09:31
Test no p-value
1 0.327098
2 0.107952
3 0.049805
4 0.456581
5 0.043143
6 0.017022
7 0.002786
8 0.347187
9 0.360335
10 0.578657
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.001789
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-11_09:31:
(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 66709 0.03 66745 0.09
3 25000.00 25019 0.01 24938 0.15
4 6666.67 6669 0.00 6662 0.00
5 1388.89 1346 1.32 1393 0.01
6 238.10 209 3.56 229 0.35
7 34.72 38 0.31 28 1.30
8 4.96 9 3.29 4 0.19
p=0.79774 p=0.08925
Number of rngs required: 687381, p-value: 0.118
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-11_09:31
No. of wins: Observed Expected
98411 98585.9
z-score=-0.782, pvalue=0.21709
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66381 66666.7 1.224 1.224
2 37630 37654.3 0.016 1.240
3 27034 26954.7 0.233 1.473
4 19198 19313.5 0.690 2.163
5 13979 13851.4 1.175 3.338
6 10081 9943.5 1.900 5.238
7 7292 7145.0 3.023 8.262
8 5079 5139.1 0.702 8.964
9 3688 3699.9 0.038 9.002
10 2654 2666.3 0.057 9.059
11 1941 1923.3 0.162 9.221
12 1396 1388.7 0.038 9.259
13 1016 1003.7 0.150 9.409
14 699 726.1 1.014 10.424
15 548 525.8 0.934 11.358
16 373 381.2 0.174 11.532
17 289 276.5 0.561 12.094
18 202 200.8 0.007 12.101
19 129 146.0 1.976 14.077
20 101 106.2 0.256 14.333
21 290 287.1 0.029 14.362
Chisq= 14.36 for 20 degrees of freedom, p= 0.18830
SUMMARY of craptest
p-value for no. of wins: 0.217087
p-value for throws/game: 0.188305
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-11_09:31
No. of wins: Observed Expected
98623 98585.9
z-score= 0.166, pvalue=0.56597
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 67005 66666.7 1.717 1.717
2 37709 37654.3 0.079 1.796
3 26716 26954.7 2.114 3.911
4 19260 19313.5 0.148 4.059
5 13758 13851.4 0.630 4.689
6 9966 9943.5 0.051 4.740
7 7199 7145.0 0.408 5.147
8 5114 5139.1 0.122 5.270
9 3614 3699.9 1.993 7.262
10 2693 2666.3 0.267 7.530
11 1866 1923.3 1.709 9.239
12 1422 1388.7 0.797 10.035
13 1048 1003.7 1.954 11.989
14 761 726.1 1.673 13.663
15 506 525.8 0.748 14.411
16 372 381.2 0.220 14.630
17 276 276.5 0.001 14.632
18 192 200.8 0.388 15.020
19 144 146.0 0.027 15.047
20 103 106.2 0.097 15.144
21 276 287.1 0.430 15.574
Chisq= 15.57 for 20 degrees of freedom, p= 0.25734
SUMMARY of craptest
p-value for no. of wins: 0.565968
p-value for throws/game: 0.257342
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0018,0.0020,0.0028,0.0040,0.0100,0.0142,0.0156,0.0170,0.0199,0.0231,
0.0315,0.0319,0.0423,0.0431,0.0431,0.0498,0.0545,0.0556,0.0571,0.0581,
0.0617,0.0656,0.0696,0.0814,0.0893,0.0917,0.0963,0.1080,0.1175,0.1231,
0.1274,0.1325,0.1332,0.1442,0.1509,0.1529,0.1534,0.1627,0.1634,0.1651,
0.1656,0.1701,0.1734,0.1773,0.1807,0.1821,0.1860,0.1883,0.2036,0.2047,
0.2056,0.2056,0.2064,0.2083,0.2100,0.2111,0.2120,0.2133,0.2171,0.2172,
0.2195,0.2292,0.2296,0.2301,0.2302,0.2373,0.2467,0.2503,0.2560,0.2561,
0.2573,0.2583,0.2605,0.2613,0.2613,0.2625,0.2627,0.2683,0.2716,0.2773,
0.2779,0.2806,0.2848,0.2893,0.2931,0.2932,0.2952,0.2974,0.2989,0.3046,
0.3064,0.3130,0.3131,0.3174,0.3188,0.3232,0.3253,0.3271,0.3273,0.3283,
0.3364,0.3444,0.3472,0.3492,0.3510,0.3521,0.3542,0.3545,0.3547,0.3570,
0.3588,0.3603,0.3615,0.3631,0.3647,0.3668,0.3732,0.3746,0.3756,0.3780,
0.3797,0.3836,0.3873,0.3938,0.4002,0.4019,0.4042,0.4047,0.4082,0.4230,
0.4288,0.4312,0.4376,0.4403,0.4451,0.4461,0.4461,0.4483,0.4523,0.4566,
0.4636,0.4680,0.4747,0.4820,0.4843,0.4929,0.4960,0.4961,0.4973,0.4982,
0.4982,0.5109,0.5161,0.5252,0.5268,0.5276,0.5287,0.5302,0.5337,0.5340,
0.5582,0.5585,0.5591,0.5601,0.5655,0.5660,0.5687,0.5725,0.5761,0.5766,
0.5768,0.5786,0.5787,0.5868,0.5883,0.5928,0.5973,0.6079,0.6164,0.6182,
0.6182,0.6186,0.6207,0.6224,0.6250,0.6305,0.6310,0.6435,0.6508,0.6527,
0.6639,0.6644,0.6652,0.6652,0.6728,0.6807,0.6833,0.6837,0.6923,0.7023,
0.7112,0.7196,0.7219,0.7242,0.7264,0.7466,0.7472,0.7479,0.7481,0.7492,
0.7495,0.7518,0.7559,0.7662,0.7668,0.7763,0.7782,0.7821,0.7874,0.7877,
0.7897,0.7908,0.7917,0.7961,0.7974,0.7977,0.8138,0.8172,0.8200,0.8201,
0.8234,0.8270,0.8320,0.8337,0.8482,0.8495,0.8509,0.8618,0.8623,0.8823,
0.8882,0.8943,0.9048,0.9048,0.9163,0.9211,0.9223,0.9247,0.9309,0.9342,
0.9374,0.9503,0.9556,0.9600,0.9610,0.9614,0.9631,0.9681,0.9738,0.9797,
0.9841,0.9842,0.9864,0.9902,0.9911,0.9911,0.9937,0.9937,0.9991,
Overall p-value after applying KStest on 269 p-values = 0.117663
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.